Magnetic Resonance Imaging of Diffusion and Perfusion: Techniques and Applications to Cerebral Ischaemia
David Lee Thomas
Department of Medical Physics and Bioengineering University College London
Submitted for the Degree of Doctor of Philosophy University of London
January 1999 ProQuest Number: U644089
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ProQuest LLC 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106-1346 Abstract
Stroke and other cerebrovascular diseases are among the most common causes of death and disease in the Western world. Over recent years, magnetic resonance imaging (MRI) has been shown to be a sensitive indicator of tissue damage caused by cerebral ischaemia. Several techniques have been developed using MRI methods which enable different aspects of tissue status to be monitored. The aim of the work presented in this thesis was to develop these techniques and apply them to the study of experimental cerebral ischaemia in animal models of stroke.
The non-invasive method of perfusion imaging known as FAIR was implemented. The method was developed to enable accurate quantitation of perfusion with good time efficiency by incorporation of a global pre-saturation pulse into the sequence. Transit time effects were minimised by the use of high definition adiabatic RF pulses. Use of the sequence to follow a perfusion time course in a gerbil model of transient global ischaemia is demonstrated. New techniques were developed for T 2 * mapping, using an interleaved echo planar imaging (EPI) approach, and diffusion-weighted imaging (DWI), using a version of magnetisation prepared TurboFLASH. The use of both the T 2 * and DWI sequences is demonstrated on phantoms and in vivo. Finally, MRI was used in the investigation of cerebral pathophysiology following middle cerebral artery occlusion in the rat at 8.5T. Continuous arterial spin labelling was used to monitor levels of perfusion, and ADC, Ti and T2 were also measured for a period of several hours after occlusion. Immediate changes in all parameters were observed, and physiological mechanisms for these changes and the potential for their diagnostic use are discussed. ______Contents______
1 INTRODUCTION...... 1
1.1 H ist o r ic a l B a c k g r o u n d ...... 3
1.2 T h e sis A im s ...... 7
2 NMR THEORY AND IMAGING TECHNIQUES...... 9
2.1 P r in c ip l e s o f N u c l e a r M a g n e t ic R e s o n a n c e - T h e Q u a n t u m A p p r o a c h 9
2.1.1 Quantum mechanics and the nuclear magnetic moment ...... 9 2.1.2 Nuclear energy levels in a static magnetic field ...... 11 2.1.3 Transitions between nuclear energy levels ...... 13 2.1.4 The population distribution of the nuclear energy states ...... 14
2 .2 P r in c ipl e s o f N u c l e a r M a g n e t ic R e s o n a n c e - T h e C l a s s ic a l A p p r o a c h ... 15 2.2.1 Nuclear magnetism and the net magnetisation vector...... 15 2.2.2 Spin excitation: the rotating frame of reference and the oscillating Bj field 15 2.2.3 Relaxation ...... 17 2.2.4 The Free Induction Decay and Signal Detection ...... 18 2.2.5 The Hahn spin echo ...... 19 2.2.6 The Inversion Recovery sequence ...... 19
2.2.7 Adiabatic RF pulses ...... 22
2.3 Im a g e F o r m a t io n u s in g N u c l e a r M a g n e t ic R e s o n a n c e T e c h n iq u e s ...... 23
2 .3.1 Slice selection ...... 24 2.3.2 Frequency encoding ...... 24 2.3.3 Phase encoding ...... 26
2.3.4 The concept ofk-space ...... 2 7 2.3.5 Fast Low Angle Shot (FLASH) imaging ...... 28
2.3.6 Echo Planar Imaging (EPI) ...... 2 9
2 .4 Im a g e W e ig h t in g in M a g n e t ic Re s o n a n c e Im a g in g ...... 31 2.4.1 Image weighting using NMR parameters ...... 31 2.4.2 Image weighting using biological parameters ...... 33
111 3 INTRODUCTION TO PERFUSION AND DIFFUSION...... 35
3.1 T h e c o n c e p t o f p e r f u s io n ...... 35
3 .2 M e t h o d s o f m e a s u r in g c e r e b r a l p e r f u s io n ...... 35 3.2.1 Group I methods ...... 37 3.2.2 Group II methods ...... 38
3 .3 M a t h e m a t ic s o f in e r t g a s c l e a r a n c e m e t h o d s ...... 43 3.3.1 Fick principle ...... 43 3.3.2 Kety-Schmidt method ...... 43
3 .4 M e a s u r in g p e r f u sio n u s in g NMR...... 4 4 3.4.1 Perfusion MR Imaging with Exogenous Contrast Agents ...... 45 3.4.2 Assessment of Tissue Perfusion using an Endogenous Susceptibility Contrast Agent - BOLD imaging ...... 49 3.4.3 Introduction to Non-invasive Perfusion MR Imaging using Spin Labelling of Arterial Water ...... 50 3.4.4 Continuous Arterial Spin Labelling techniques ...... 57 3.4.5 Pulsed Arterial Spin Labelling techniques ...... 57
3 .5 D if f u sio n in b io l o g ic a l s y s t e m s ...... 62 3.5.1 Molecular Diffusion ...... 62 3.5.2 Random walk and Einstein’s equation ...... 63 3.5.3 Boundaries and restriction ...... 63
3 .6 E ffe c t s o f d if f u s io n o n t h e sp in e c h o MR s i g n a l ...... 64 3.6.1 Motion, gradient and MR signal ...... 64 3.6.2 Spin echo and constant gradient ...... 66 3.6.3 Pulsed gradients and Stejskal-Tanner sequence ...... 67 3.6.4 Diffusion imaging ...... 67
3.7 D if f u sio n MRI a n d c e r e b r a l is c h a e m ia ...... 7 0 3.7.1 Potential mechanism for DWI changes ...... 70
3.7.2 Diffusion-weighted imaging and the therapeutic window ...... 77
4 NON-INVASIVE QUANTITATION OF CEREBRAL PERFUSION USING FAIR MRI...... 72
4.1 Introduction ...... 7 2
4 .2 D emonstrating th e b a s ic f l o w sensitivity o f FAIR...... 73
IV 4 .3 P e r f u s io n quantitation u s in g t h e s t a n d a r d F A IR T i m o d e l ...... 7 7
4.4 Increasing the time EFFICIENCY of FAIR perfusion m easurem ents ...... 82 4.4.1 Using a global pre-saturation pulse with FAIR ...... 85 4.4.2 Optimisation of reduced TR FAIR sequence parameters ...... 88 4.4.3 Measuring Tia and perfusion using reduced TR FAIR ...... 89
4 .5 T r a n s it t im e a n d slic e pr o file e f f e c t s ...... 101 4.5.1 Implementation of improved RF pulses ...... 107 4.5.2 In vivo measurements of transit time and CBF: comparison of standard and improved RF pulse combinations ...... 113
4 .6 U s in g F A IR to fo l l o w a p e r f u sio n tim e c o u r s e ...... 120 4.6.1 Introduction ...... 120 4.6.2 Methods ...... 121 4.6.3 Results...... 123 4.6.4 Discussion ...... 127
4 .7 D is c u s s io n a n d C o n c l u s io n s ...... 129
4 .8 A p p e n d ix ...... 131 I Integrated form of the Bloch equation ...... 131 II Transit time effects ...... 131 III Short TR FAIR : (no pre-saturation) ...... 131 IV Short TR FAIR (with pre-saturation) ...... 133 V Short TR FAIR (with pre-saturation and coil inflow effects ) ...... 134
5 RAPID T2* m a p p in g USING INTERLEAVED ECHO PLANAR IMAGING ...... 137
5.1 Introduction ...... 137
5 .2 M e t h o d s ...... 141
5.3 R e s u l t s ...... 149
5 .4 D is c u s s io n ...... 157
5 .5 C o n c l u s io n s ...... 161
6 A QUANTITATIVE METHOD FOR FAST DIFFUSION IMAGING USING MAGNETISATION PREPARED TURBOFLASH...... 162
6.1 Introduction ...... 162 6 .2 T h e o r y ...... 165 6.2.1 Elimination of eddy current effects using phase cycling ...... 165 6.2.2 Effect of reduced inter-experiment delay time on ADC measurements 167
6.3 M a t e r ia l s a n d M e t h o d s ...... 169 6.3.1 NMR hardware ...... 169 6.3.2 Pulse sequence ...... 170 6.3.3 Phantom experiments ...... 172 6.3.4 In vivo experiments ...... 174
6 .4 Re s u l t s a n d D is c u s s io n ...... 174 6.4.1 Theoretical Results ...... 174 6.4.2 Phantom studies ...... 176 6.4.3 In vivo studies ...... 182
6.5 C o n c l u s io n s ...... 186
6 .6 A p p e n d ix ...... 188
7 MEASUREMENT OF PERFUSION USING CONTINUOUS ARTERIAL SPIN LABELLING IN A RAT MODEL OF STROKE...... 192
7.1 Implementation o f c o n t in u o u s A S L ...... 192 7.1.1 Use of TurboFLASH imaging ...... 192 7.1.2 Spin labelling RF pulse ...... 194 7.1.3 Measurement of Tj and a for perfusion quantification ...... 199 7.1.4 Use of CASE with a post-labelling delay ...... 204
7 .2 A STUDY OF THE EARLY CHANGES IN PERFUSION, DIFFUSION, T] AND T 2 OF BRAIN
WATER FOLLOWING MIDDLE CEREBRAL ARTERY OCCLUSION IN THE RAT AT 8 .5 T ...... 2 0 9 7.2.1 Introduction ...... 209 7.2.2 Methods...... 211 7.2.3 Results...... 217 7.2.4 Discussion ...... 226
8 GENERAL DISCUSSION AND CONCLUSIONS ...... 233
8.1 Is IT POSSIBLE TO MEASURE ISCHAEMIC BLOOD FLOW USING ARTERIAL SPIN
LABELLING METHODS?...... 233
VI 8 .2 W h a t physiological p r o c e s s e s d o c h a n g e s in m a g n e t ic r e s o n a n c e im a g e s
REFLECT?...... 2 4 2 8.2.1 Mechanism for tissue water ADC change during ischaemia ...... 242
8.2.2 The importance of measuring T 2* ...... 245
8.2.3 Utilising the information provided by changes in Tj and T 2 during the hyperacute phase of stroke ...... 247
8.3 F u t u r e WORK...... 2 5 0
8 .4 T h e s is SUMMARY ...... 2 5 2
REFERENCES...... 257
V ll List of Figures
Figure 1.1 The different scales of biological and physical matter ...... 2 Figure 2.1 Nuclear energy levels in a magnetic field Bq for a spin Vi nucleus...... 12 Figure 2.2 Using a 180° refocusing pulse to create a spin echo ...... 20 Figure 2.3 The inversion recovery sequence ...... 21 Figure 2.4 Standard spin echo 2D-FT imaging sequence ...... 25 Figure 2.5 Example of an echo planar imaging sequence ...... 30 Figure 3.1 Schematic diagram of tissue perfusion ...... 36 Figure 3.2 Diffusion behaviour of molecules in free and restricted media ...... 65 Figure 3.3 2D-FT spin echo diffusion-weighted imaging sequence ...... 69 Figure 4.1 Pulse sequence diagram for the FAIR experiment ...... 74 Figure 4.2 Difference between the ssIR and nsIR images of a flowing water phantom.. 74 Figure 4.3 ssIR - nsIR subtraction image of the gerbil brain ...... 76 Figure 4.4 Inversion recovery images of the gerbil brain at various different inversion times...... 79 Figure 4.5 Calculation of CBF in the gerbil brain by biexponential fitting ...... 81 Figure 4.6 Comparison between approximate and exact reduced TR FAIR equations.... 84 Figure 4.7 Comparison of reduced TR FAIR signal with and without pre-saturation 87 Figure 4.8 FAIR difference signal per unit time ...... 90 Figure 4.9 Measurement of the longitudinal relaxation time of blood in vivo ...... 92 Figure 4.10 The state of blood magnetisation in reduced TR FA IR ...... 96 Figure 4.11 Determination of the coil inflow time using reduced TR FAIR ...... 98 Figure 4.12 Slice thickness requirements for zero static subtraction in FAIR ...... 102 Figure 4.13 Comparison of adiabatic inversion pulses ...... 106 Figure 4.14 Comparison of slice profiles generated using various RF pulses ...... 109 Figure 4.15 FAIR signal intensity difference of a static phantom as a function of inversion slice thickness ...... I ll Figure 4.16 CBF and transit time values using various RF pulse combinations 116 Figure 4.17 Post-reperfusion single subtraction FAIR perfusion values in the gerbil brain ...... 119 Figure 4.18 Representative CBF maps obtained in two gerbil occlusion-reperfusion studies...... 125
Vlll Figure 4.19 Perfusion time courses from ROI in the gerbil brain before and after 4 minutes of forebrain ischaemia ...... 126 Figure 5.1 An example of a standard interleaved EPI acquisition...... 140 Figure 5.2 Schematic diagram of interleaved EPI pulse sequence ...... 142
Figure 5.3 k-space representation of the T 2 * lEPI sequence ...... 145
Figure 5.4 T 2 * related modulation transfer function of the interleaved EPI sequence with echo time shifting ...... 147 Figure 5.5 Phantom images acquired using 4 different imaging methods ...... 150 Figure 5.6 Phantom images acquired at later echo times ...... 152 Figure 5.7 Example of a single exponential fit of to signal intensity at multiple echo times in a ROI in the cortex of the rat brain ...... 154
Figure 5.8 Time course of T 2 * changes from a region of grey matter in the rat brain during a series of anoxic events ...... 156 Figure 5.9 Simulated PSF of imaging techniques ...... 159 Figure 6-1 Diffusion weighted TurboFLASH sequence ...... 171 Figure 6-2 Variation of TurboFLASH image signal intensity with the phase of the third DEFT pulse ...... 177 Figure 6-3 Diffusion weighted images of an agar phantom at three different b values . 179 Figure 6-4 ADC measurements acquired using spin echo DWI and TurboFLASH DWI 180 Figure 6-5 Signal to noise per unit time of the coefficient Y(n) as a function of TD/Ti 183 Figure 6-6 ADC maps of the rat brain calculated from diffusion weighted spin echo images and the TurboFLASH sequence ...... 184 Figure 6-7 Pixel scatter plots comparing ADC values from spin echo and TurboFLASH images of a rat brain ...... 185 Figure 7-1 Schematic diagram of the CASL perfusion sequence ...... 195 Figure 7-2 Variation of echo amplitude in the FLASH image echo train ...... 195 Figure 7-3 Spoiled centre-out TurboFLASH ...... 196 Figure 7-4 Coronal scout image of the rat brain showing the position of the control and inversion planes ...... 198 Figure 7-5 Reduction of signal intensity from the rat brain as the off-resonance RF pulse power increases ...... 202 Figure 7-6 Variation of inversion efficiency in the carotid artery of a rat as a function of inversion RF pulse power ...... 202
IX Figure 7-7 An example of the images used to create a perfusion map ...... 203 Figure 7-8 Comparison of the longitudinal relaxation times of rat brain tissue water in the presence and absence of off-resonance RF irradiation ...... 206 Figure 7-9 Variation of measured CBF values with length of post-labelling delay in a control rat ...... 208 Figure 7-10 Typical maps obtained from a rat following MCAO ...... 216 Figure 7-11 CBF time courses of MCAO rat brain ...... 218 Figure 7-12 Trace ADC time courses from MCAO rat brain ...... 221
Figure 7-13 T2 time courses from MCAO rat brain ...... 222 Figure 7-14 Ti time courses from MCAO rat brain ...... 225 List of Tables
Table 4-1 Comparison of measured flow values using long TR and reduced TR FAIR (ROI in cerebral cortex). Mean ± SD are given where appropriate ...... 93 Table 5-1 T2* values (mean ± standard error, in ms) for the four MnCli solutions using three different techniques ...... 153 Table 6-1 Values for the coefficients in Equations (6.2), (6.7), and (6.10), expressed as a fraction of A(n) ...... 175 Table 6-2 Paired t-test results comparing TurboFLASH diffusion-weighted sequence with spin echo sequence on an agar phantom ...... 181 Table 6-3 Definitions of terms used in derivations and calculations ...... 191
XI Acknowledgements
The work described in this thesis was carried out under the supervision of Professor Roger Ordidge. I would like to take the opportunity here to thank him for his unfailing enthusiasm and excellent advice and help throughout the past three years. I would also like to thank my second supervisor. Professor David Gadian, who provided me with the opportunity to work in his laboratory at the Institute of Child Health (ICH), and who has been a constant source of encouragement and motivation.
This work would not have been possible without the following people: my fellow Ph.D. students, Gaby Pell, Mark Lythgoe, and Fernando Calamante, with whom I worked closely on most of the experiments described here; Neil Harris, Albert Busza, Martin King, Janel Le Belle, John Houseman and Steve Williams from the RCS Unit of Biophysics at the ICH, whom I have had the opportunity to work with and learn a great deal from. I thank David Guilfoyle and Graham Naylor from Surrey Medical Imaging Systems (SMIS) at Guildford for their assistance in pulse sequence development and image processing; Alistair Howseman, for setting up echo planar imaging on the 2.35T magnet at ICH and helping me to understand its intricacies; Bob Turner, Alan Connelly, David Porter and Matthew Clemence for useful comments and discussions; and Sally Dowsett for all her help.
I would like express my sincere appreciation to my parents and family, whose support has been invaluable throughout my education. Finally, a special thank you goes to Uma Kulkarni for her encouragement and understanding, and to the rest of the Kulkarni family for their respect and faith in me.
XII Introduction
1 Introduction
Since the discovery of X-rays over a hundred years ago, there has been a great deal of interest in developing methods that allow one to look inside the living body non- invasively. Over recent years, nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) have come to play an increasingly important role in this area, especially in the study and diagnosis of disease. The extent to which medical imaging, and in particular MRI, has become an accepted part of twentieth century culture is demonstrated by its use in clinical evaluations and surgical planning, and also in various other contexts. For example, a decade after NMR machines were introduced into the clinic, their images were accepted as evidence in court. MRI pictures provided dramatic corroboration of the notorious beating of Rodney King by four policemen in Los Angeles on March 3, 1991. The images produced by magnetised hydrogen protons in King's bruised head convinced the jury in a civil trial to award him $3.8 million in compensatory damages. King's lawyers were successful in convincing the court that an NMR image was a scientifically accepted procedure which showed the (otherwise invisible) damage that had been inflicted that night. Another recently developed application of MRI is its use in cognitive neuroscience to look inside the human brain and to map the functional activation corresponding to a given external stimulus. This has become a very active area of research, and is the best scientific effort yet made to bridge the gap between the concepts of the brain and the mind.
NMR is based on a fundamental physical phenomenon which exists at the subatomic level
(see figure 1.1). This chapter puts NMR and MRI into a historical context, from the discovery of the basic phenomenon to its most recent applications. The chapter concludes Introduction
10-5m
Proteins
Nucleic acids
W ater Carbon dioxide lO'^m
+ many other molecules...
Magnetic moment \x nucleus T 1 electron
(f)
Figure 1.1 The different scales of biological and physical matter; (a) the human body, (b) human tissue, (c) the cell body, (d) a water molecule, (e) a hydrogen atom, (f) a hydrogen nucleus (proton) Introduction
by explaining how the work included in this thesis fits into this context, and precisely what the aims of this project are.
1.1 Historical Background
The concept of nuclear magnetic resonance stems from ideas that were first proposed in
1924 by the Austrian physicist Wolfgang Pauli (Pauli, 1924). His suggestion, based on a consideration of the electron, was that atomic particles possess the property of angular momentum associated with their motion, and that this explained the fine structure of their emission spectra in the presence of a magnetic field. As quantum mechanics developed, this idea was refined so that it predicted discrete quantum states of magnetic moment. In order to test this theory. Stem and Gerlach passed a highly collimated beam of silver atoms in vacuo through a strong gradient of magnetic field, and observed a splitting of the beam which, while certainly quantum in nature, did not agree precisely with the theoretical predictions (Gerlach and Stern, 1924). Specifically, they had expected to see an odd number of different levels (since the orbital angular momentum quantum number could only take integral values), but the observed result was an even number. The answer to this problem was provided by Uhlenbeck and Goudsmit in 1925, who realised that a great simplification of the description of atomic spectra could be obtained if it was assumed that electrons had an intrinsic angular momentum with a quantum number I = Vi.
Thus, from empirical motivations, the concept of particle spin^ was bom. In the theory
' Although ‘spin’ is an evocative name, and the idea of a physically spinning charged particle giving rise to the observed magnetic moment is an attractive one, one should bear in mind that half-integral angular momentum is an entirely quantum mechanical concept with no classical counterpart. Introduction
later developed by Paul Dirac (in which quantum mechanics is derived taking into
account the effects of special relativity), the existence of particles with half-integral
quantum numbers for angular momentum appeared naturally, and so particle spin was
given a sound theoretical basis.
The first Nobel Prize for research in the field of NMR was awarded to the American
physicist I. I. Rabi in 1944 for his method of measuring the nuclear magnetic moment.
Eight years later NMR research earned the Nobel prize in physics again when Edward
Purcell at Harvard and Felix Bloch at Stanford shared the award for their independent but
almost simultaneous announcements that they had measured the NMR signal in bulk matter (Purcell et al, 1946; Bloch et al, 1946). Since the magnetic levels of the nucleus
are separated by a fixed energy (the Zeeman energy), it is possible to excite transitions between levels by applying photons of the appropriate frequency. By sweeping the frequency and measuring absorption, Purcell and Bloch showed that accurate measurements of this energy could be made. The next key discovery, which led to the
single most important application of NMR to date, was that nuclei in chemically distinct sites resonate at slightly different frequencies. This phenomenon of ‘chemical shift’ was reported by several groups at around the same time (Knight, 1949; Dickinson, 1950;
Proctor and Yu, 1950), and led to proton NMR becoming a virtually indispensable tool in the organic chemistry laboratory. NMR opened up a new window on a molecular level which was soon exploited by researchers in physics, chemistry and biology. Biology in particular benefited, as it became possible to investigate the chemical processes directly within living tissues. The slow continuous wave absorption methods were soon
superseded by combining radio frequency (RF) pulse techniques with Fourier analysis. Introduction
The use of RF pulses for interrogating the nuclear signal was first demonstrated by Hahn in 1950 with his discovery of spin echoes (Hahn, 1950).
NMR imaging developments, based largely on the detection of ^H signal from water, began in the early 1970s. They were preceded by the introduction of the first commercially produced X-ray head scanner by Hounsfield at EMI in 1972, which demonstrated the radiological benefit of such imaging systems. Damadian had reported that certain malignant tumours of rats differed from normal tissues in their NMR relaxation properties, and suggested that ^H NMR might therefore have diagnostic value.
In 1973, Lauterbur at the State University of New York at Stonybrook published the first
NMR image of a heterogeneous object (Lauterbur, 1973), produced in a similar way to
Hounsfield’s scanner using a projection-reconstruction technique. At about the same time,
Mansfield and Grannell were working on NMR ‘diffraction’ studies at Nottingham
University. Both groups had realised that, since the resonant frequency of a nuclear spin is proportional to the strength of the applied magnetic field, a magnetic field gradient would give rise to a range of resonant frequencies which reflected the spatial distribution of the contributing spins. In the following years many NMR imaging techniques were proposed, but with the help of the increasing power of computers and the development of the Fast Fourier Transform, Fourier Transform techniques soon became the method of choice. Image quality has continually improved over the years, partly through engineering and technological developments, and partly through increasing skills and experience in the manipulation of field gradients and RF pulse sequences. Reduced scan times and larger image matrix size have gone hand in hand with the development of the necessary computing power to process the information. Introduction
Over recent years, in vivo imaging has become one of the principal aims of MRI. The medical benefits of a non-invasive, diagnostic tool capable of probing the interior of the body and of revealing such a wealth of information are enormous. However, in vivo imaging imposes major demands on the hardware and techniques used. One of the most difficult initial problems to overcome was building a magnet of the necessary strength with a sufficiently large bore size and homogeneity to obtain an NMR signal. Permanent magnets were soon replaced by resistive and then superconducting magnets. The latter, while being more expensive to produce and run because of stringent cryogenic requirements, produce the most stable fields with strengths from 0.1 up to 25 Tesla currently in use. The imaging techniques used at present are generally based on two types of sequence. 2DFT (Two Dimensional Fourier Transform), or more accurately spin-warp imaging, developed by Edelstein from an initial demonstration by Ernst, is one of the most prevalent imaging sequences available on commercial scanners. Whilst producing images of extremely high quality, it requires long scanning times and subject motion can lead to degradation of the image. The second sequence, proposed in 1977 by Mansfield
(Mansfield, 1977) and called Echo Planar Imaging (EPI), has become increasingly popular over recent years because it offers the ability to acquire an image in as little as tens of milliseconds. This technique, however, requires specialised gradient hardware, which has limited its general availability, and suffers from poorer signal to noise ratio than the 2DFT method. Issues such as image distortion and ghosting are also more problematic with EPI.
One of the main advantages of MRI over other imaging modalities is its ability to reveal more than just nuclear spin density, and as such it has the potential to become a truly universal medical tool. Images can be weighted according to the magnetic relaxation Introduction
properties of the nuclei (e.g. Tp and T 2 -weighting), and also according to various physiological parameters. Diffusion-weighted images have been shown to highlight regions affected by an ischaemic event (Moseley et al, 1990), and methods are currently being developed to generate quantitative images of blood flow and perfusion. These methods include the tracking of an exogenous paramagnetic tracer (usually gadolinium or dysprosium based contrast agents), or using the blood water itself as an endogenous tracer. The details of these techniques will be discussed at length in the following chapters. Another approach to image contrast uses the transient local dependence of relaxation rate on physiological state, and it is one of these methods (Ti^-weighted imaging) which is most widely used in functional MRI to monitor regional brain activation. It seems likely that over the coming years the widespread implementation and refinement of techniques presently being developed, and the innovation of new and better sequences, will mean that NMR and MRI will continue to offer a high quality, radiation- free, non-invasive opportunity to examine the interior of the living body.
1.2 Thesis Aims
The main aims of the work undertaken for this thesis were;
• to develop non-invasive MRI techniques to measure physical and biological
parameters with a high level of accuracy and good time resolution
• to apply these techniques to the study of experimental ischaemia in animal models of
stroke
Based on these goals, I have developed and modified MR sequences which are sensitive to cerebral blood flow (perfusion MRI), cerebral blood oxygenation levels (T 2 * MRI) and cerebral oedema (diffusion MRI). MRI has already proven to be a highly effective tool in
7 Introduction
the evaluation of both clinical stroke and experimental cerebral ischaemia. Provided the data acquisition is sufficiently rapid, the application of several different MR methods in combination can provide valuable multi-parametric information on the dynamic processes occurring during ischaemia. Therefore, the focus of the work presented here is the development of fast, quantitative MRI sequences that are sensitive to changing physiological conditions. NMR Theory and Imaging Techniques
2 NMR Theory and Imaging Techniques______
The aim of this chapter is to present the theory of nuclear magnetic resonance, and to demonstrate how it can be manipulated to provide useful information. It begins with a quantum mechanical treatment, which is then taken to its classical limit by assuming a system which contains a very large number of nuclei acting independently, thus appearing continuous on the macroscopic level. The basic properties of the NMR signal are then described by using the concept of the bulk magnetisation vector, and the many uses to which this signal can be put are detailed. Techniques for producing images based on the acquisition of the NMR signal are described, and it is shown how these images can be weighted in various ways, by both NMR-based and/or physiological parameters.
2.1 Principles of Nuclear Magnetic Resonance - The
Quantum Approach
2.1.1 Quantum mechanics and the nuclear magnetic moment
Atomic nuclei are characterised by states which are inherently quantum mechanical in their behaviour. This means that their spin state may be described in terms of a set of discrete possibilities, determined by the nuclear spin quantum number I. The proton has a spin quantum number I = Vi, and the neutron has I = -Vi. In a nucleus made up of these two constituents, the spin angular momenta combine with the rotational motion of the whole nucleus to give a total I which is either integer or 16-integer. Nuclei can be characterised by their net value of I: NMR Theory and Imaging Techniques
1. Nuclei with an even mass number and an odd charge number have an integral value of
I, e.g. deuterium-2, nitrogen-14
2. Nuclei with an even mass number and an even charge number have zero spin, e.g.
carbon-12, oxygen-16
3. Nuclei with an odd mass number have half integral spin, e.g. hydrogen-1, carbon-13,
phosphorus-31
The magnitude, p, of the nuclear angular momentum is related to the spin number by:
p = h^I(I + 1) (2.1)
Angular momentum is a vector and therefore requires specification of both its magnitude and its direction. Quantum theory demands that the directional component of angular momentum can only have discrete values with respect to any given direction, and these directions are defined by the introduction of another quantum number m. The component
Pz of angular momentum along the (arbitrarily defined) z-direction is:
p^ = mfi (2.2) where m may have any of the 21 + 1 values 1,1 - 1, ..., -I. For a nucleus with spin V2 (such as hydrogen- 1), m can be +V2 or -Vi, and therefore pz = . The existence of such angular momentum, in combination with the internal charge distributions associated with the nucleons, leads to the generation of a magnetic moment, \iz, where:
\^z=lPz~ (2.3)
Y is the gyromagnetic ratio, which depends on the exact structure of the nucleus and, therefore, varies for different nuclei. For the hydrogen-1 nucleus, it has a value of 2.675 x
10^ radians/second/T esla.
10 NMR Theory and Imaging Techniques
2.1.2 Nuclear energy levels in a static magnetic field
Nuclear energy is independent of angular momentum in the absence of an external magnetic field i.e. the energy levels of nuelei with different angular momenta are degenerate. If a static magnetic field^ Bq is applied along the z-axis, a nucleus will acquire energy E as a result of the interaction between the field Bo and the nuclear moment, given by:
E = -p. Bg = (2.4) or equivalently (from equation (2.3)):
E = -yhmBo (2.5)
Since m ean have any of the values 1,1 - 1 , the nuclear energy levels are split into 21
+ 1 states by the applieation of the magnetic field. For a nueleus of spin 1 = Vi, there are two possible energy states, corresponding to m = +V2 and m = -V2, and the difference between these two energy levels is (see figure 2.1):
AE = yhBg (2.6)
The lower energy nuelei have magnetie moment pointing in the direetion of the magnetic field and are said to be the parallel state, whilst the remainder are said to be anti-parallel.
Since the magnitude of the angular momentum, p, and its eomponent in the direction of the applied magnetic field, Pz, are both known (which is possible beeause the operators
and 7^ commute), the angle between the angular momentum vector and the applied field is also known. There is, however, no way of determining the components of angular
' A magnetic field can be described in terms of its flux density B q which determines the force exerted on other magnets. Henceforth, for simplicity, I will refer to B q as the magnetic field rather than the magnetic flux density. The unit of Bo is the Tesla (T).
11 NMR Theory and Imaging Techniques
m= - V i Iêo
Figure 2.1 Nuclear energy levels in a magnetic field for a spin V i nucleus. Arrows represent nuclear spins at each energy level; transitions between energy levels are induced by supplying photons with an energy AE
12 NMR Theory and Imaging Techniques
momentum in the x and y directions (/^, îy and ^ do not commute). Therefore the magnetic dipole might be oriented anywhere around the surface of one of two cones, depending on whether the nucleus is in a parallel or anti-parallel state.
2.1.3 Transitions between nuclear energy levels
In order to obtain an NMR signal, it is necessary to induce transitions between the different energy states. A nucleus can transfer between energy levels when a quantum of energy exactly equal to the energy difference is supplied or removed from the system.
This energy must be in the form of an oscillating magnetic field in the jry-plane, and the field should oscillate with a frequency Vq that satisfies the fundamental relationship:
AE = /zVo (2.7)
Using equation (2.6), this means that
Vo=jBJ2k (2.8) or equivalently, since to is equal to 2 tw,
CÛQ = y^o (2.9)
Equation (2.9) is the principal equation of nuclear magnetic resonance describing the resonance condition for magnetic nuclei, and the resonant frequency at which transitions occur is called the Larmor frequency. Since y differs for each nuclear isotope, different nuclei resonate at widely different frequencies in a given field Bo At conventional values of Bq the frequencies occur in a convenient radio frequency band, and the oscillating field
B] is commonly referred to as the radio frequency (RE) field.
13 NMR Theory and Imaging Techniques
2.1.4 The population distribution of the nuclear energy states
The populations of nuclei in each of the energy states are determined by the Boltzmann distribution. The larger the separation of energies and the lower the thermal energy, the larger is the proportion of spins in the lower state. At a thermal equilibrium characteristic of the temperature T, the relative numbers and n of nuclei in the spin +16 and -Vi states respectively are given by
— = exp (-^E|kT) n* f'V / / (2.10) = exp {--fiBjkT) where k is the Boltzmann constant. For protons in a magnetic field of 5 T the magnitude of AE is 10'^ electron volts (eV), whereas at 20°C the thermal energy kT is about 2.5x10'^ eV. Therefore the ratio n^ln is very close to unity, and the populations differ by less than one part in 10"^. The similarity of the energy states means that net signal emission is only seen from a very small proportion of the nuclei, and thus the inherent sensitivity of the technique is quite low. It is worth noting that an increase in the magnetic field Bq increases the difference between adjacent states (equation (2.6)) and hence their population difference (equation (2.10)). This considerably enhances the net absorption of energy. As a result, a high magnetic field is generally desirable to improve the signal to noise ratio.
14 NMR Theory and Imaging Techniques
2.2 Principles of Nuclear Magnetic Resonance - The
Classical Approach
2.2.1 Nuclear magnetism and the net magnetisation vector
If we consider an atom with a magnetic moment to be analogous to a tiny spinning bar magnet, we would expect it to precess about a magnetic field with a characteristic frequency coo which is identical to that derived in the previous section (see equation (2.9)) and is directly proportional to the strength of the interaction between the two magnetic fields. In an NMR experiment, we study a sample containing a very large number of magnetic nuclei. The sum of their magnetisation vectors is called the net magnetisation vector. At equilibrium, there is no preferred orientation in the plane perpendicular to
(the xy-plane), and so the net component of magnetic moment in the xy-plane is zero.
However, there is a net magnetisation along the z-axis due to the unequal populations in the two energy states. In order to interrogate this net magnetisation, it is necessary to add energy to the system so that the state of equilibrium is upset, and a proportion of the magnetisation is tilted into the xy-plane. The next section explains how this can be achieved.
2.2.2 Spin excitation: the rotating frame of reference and the oscillating
Bi field
To understand the concepts of spin excitation more easily, it is convenient to deal with vectors in a frame of reference which is rotating about the z-axis at the Larmor frequency.
In such a rotating frame of reference, slower processes such as spin relaxation will become the dominant time dependant effects. The equation of motion for the net
15 NMR Theory and Imaging Techniques
magnetisation transforms as:
f m ' = yMx B + — (2 . 11) dt / rot I y ) where Ü is the angular velocity at which the frame is rotating. Hence in the rotating frame, M follows the same equation of motion as in the stationary frame but with an effective field Beff equal to the bracketed term on the right-hand side of equation (2.11). If the frame rotates at the frequency Q = -')Bo = 0%, the Larmor frequency, then Beff = 0, and the precession is stationary in that frame.
The rotating frame is especially useful for expressing the effects of a second field, Bi, in the transverse direction, also rotating at the frequency coq. This field will appear static in the rotating frame. In the same way that the application of Bo causes the nuclei to precess about its direction with angular frequency y B q, so the application of Bi in the rotating frame causes the nuclear magnetisation to precess about Bi with angular frequency y Bi
This is because the Bi is the only apparent field experienced in the rotating frame. If the field Bi is applied for a time tp, the nuclei will rotate through an angle 0 given by the product of angular frequency with time,
0 = yBitp (2.12)
The nuclei will rotate through an angle of 90° (corresponding to 0 = nl2 radians) if tp is such that
YB,tp=7c/2 (2.13)
A pulse of Bi field that has this duration is known as a 90° pulse, and its effect is to tilt the net magnetisation away from the z-axis into the xy-plane of the rotating frame.
Following a 90° pulse, the system returns to equilibrium via processes known as spin relaxation.
16 NMR Theory and Imaging Techniques
2.2.3 Relaxation
The behaviour of the net magnetisation is best understood by considering two components separately; the longitudinal component in the direction of Bo (Mz), and the transverse component in the perpendicular plane (M%y). After a disturbance, Mz and M%y return to their equilibrium values through spin-lattice (or longitudinal) and spin-spin (or transverse) relaxation respectively.
Spin-lattice relaxation is characterised by a time constant Ti known as the spin-lattice, or longitudinal, relaxation time. This describes the return of the magnetisation Mz to its equilibrium value Mo according to the Bloch equation:
dM , Mn - M (2.14) dt T,
The processes that are responsible for longitudinal relaxation are fluctuating magnetic fields that have a component in the xy-plane that oscillates at the resonant frequency.
These fluctuations will induce transitions between the spin states of the nuclei, and if they are associated with the lattice (lattice is used in this context to mean the molecular framework in which the nuclei reside), there will be an exchange of energy until the nuclear spins are in thermal equilibrium with the lattice. The fluctuating magnetic fields are created by the random tumbling of neighbouring molecules, and the resulting time- dependant effect of their magnetic dipoles.
Spin-spin relaxation causes the return of M%y to its equilibrium value, and is characterised by a time constant T 2 known as the spin-spin, or transverse, relaxation time. Since the equilibrium value of Mxy is zero, the Bloch equation for spin-spin relaxation is
17 NMR Theory and Imaging Techniques
T2 relaxation involves interaction between neighbouring spins without exchange of energy to the lattice. The value of T 2 is limited by Ti and is also determined by the spread of frequencies at which the spins are resonating. This depends on local Bq field inhomogeneities caused by neighbouring spins (not necessarily rotating at the Larmor frequency), and means that for any biological sample, T 2 will be considerably shorter than
Ti. In addition to these signal decay processes, the presence of bulk magnetic field inhomogeneities may also act to dephase spins around the precessionary orbit. This results in dephasing in the xy-plane and is called T 2 ' relaxation. The combined effect of T 2 and T2 ' relaxation is called T 2 * relaxation, defined by:
+ (2.16)
T2 relaxation is irreversible. However, dephasing caused by T 2 ' can be reversed by using a
180° refocusing pulse to produce a spin echo, as discussed in section 2.2.5.
2.2.4 The Free Induction Decay and Signal Detection
Following a 90y° RF pulse, the coherent rotation of the transverse magnetisation Mxy behaves according to:
M^ = [MoC(95(cûot)] My = [MQ.sm(cOot)] x (2.17) where Mx and My are the components of magnetisation along the x- and y-axes respectively, and the exponential term describes the T 2 * decay of the signal. The voltage induced in a conducting wire placed near the sample (the receiver) oscillates at a frequency cOo and is called the free induction decay (FID) signal. The receiver is usually a
18 NMR Theory and Imaging Techniques
coil which is designed to be as sensitive as possible to the FID, and can either be the same coil as that used to generate the Bi excitation pulse or a separate device used only to receive signal.
2.2.5 The Hahn spin echo
As shown by equation (2.17), following a 90° pulse the transverse magnetisation generated decays at a rate determined by T 2 *. A 180° refocusing RF pulse can partially reverse this evolution to form a spin echo (see figure 2.2). If a 180° pulse is applied at a time T after the 90° pulse, the individual components of magnetisation remain in the xy- plane but their phase is inverted so that those precessing at a faster rate now lag behind the slower ones. After another time t the faster components will have caught up, resulting in phase coherence and thus producing a signal which is known as the spin echo (Hahn,
1950). The formation of an echo in this way counteracts only the dephasing caused by static field inhomogeneity, and at the time of the echo the nuclei are still partly dephased because of the random effects of T 2 relaxation and molecular Brownian motion. The extent of this dephasing (or T 2 ~weighting) depends on the value of x which is used. This parameter is one of many which can be manipulated in MRI to generate different image contrast (see section 2.4).
2.2.6 The Inversion Recovery sequence
Figure 2.3 shows a sequence which is commonly used to weight the NMR signal according to the longitudinal relaxation time (Ti) of the sample under study. A 180° pulse is first applied to tip the magnetisation anti-parallel to the z-axis, or to ‘invert’ the magnetisation. The spins then relax back toward equilibrium at a rate determined by T%.
19 NMR Theory and Imaging Techniques
90° 180 ° (a) Spin echo FID
< TE/2 TE/2 ►
(b) Time TE/2
-►
J (i) X
(V) Time TE/2 (iv)
Figure 2.2 Using a 180° refocusing pulse to create a spin echo (a) RF pulse sequence and observed signal (b) the process by which the spin echo is formed
2 0 NMR Theory and Imaging Techniques
180 90
TI TD n
180T
TI TD
Figure 2.3 The inversion recovery sequence, (a) the RF pulse sequence and observed signal (b) behaviour of the magnetisation. The magnetisation is initially inverted by a 180° pulse, and undergoes an amount of T^ relaxation determined by the choice of TI. It is then tipped into the xy- plane using a 90° pulse and the resulting FID is sampled
21 NMR Theory and Imaging Techniques
As this relaxation is occurring, a 90° pulse is applied to rotate any longitudinal magnetisation M% into the xy-plane so that it gives a FID signal. The amplitude of the signal depends on the size of Mz at the time of the 90° pulse, and so Ti dependence is introduced by appropriate choice of timing in the sequence. If a series of measurements is taken at varying inversion times (TI) then an inversion recovery curve may be built up, and a measurement of Ti can be made.
2.2.7 Adiabatic RF pulses
Adiabatic RF pulses are a special type of RF pulse which can be used for spin manipulation and have the advantage of being relatively insensitive to inhomogeneities in the applied Bi field. For a standard RF pulse, variation of the amplitude of Bi across the region of excitation leads to differences in the flip angle experienced by spins in different areas. This can potentially confuse interpretation of the resulting images. If an adiabatic pulse is used, small variations in B% amplitude do not affect the flip angle produced.
The design of adiabatic pulses is based on the following theorem. Suppose there is a magnetic field Bo of fixed magnitude whose magnitude may be varied (no other magnetic field present). Let the magnetisation M be parallel to Bo at time t=0. If the direction of Bo is changed with an angular velocity O), and if ')Bo » O), then the theorem states that M will turn with Bo, always remaining aligned along Bo as it rotates. This theorem can be proved quite simply (e.g, see (Abragam, 1961)). The fact that the magnetisation follows the direction of the magnetic field when the field changes direction sufficiently slowly is the reason that these pulses are known as adiabatic.
22 NMR Theory and Imaging Techniques
By utilising this principle, one can turn to the case of a rotating magnetic field Bi of frequency co, perpendicular to a static field Bo If one starts far below resonance, the magnetisation is nearly parallel to the effective field in the rotating frame since
= >'+[(û>/r)-BoP (2.18 )
As one approaches resonance, both magnitude and direction of the effective field change, but if resonance is approached sufficiently slowly, M will remain parallel to Beff in the rotating frame according to the above theorem. Thus, exactly at resonance, the magnetisation will lie along B i, making a 90° angle with Bq. If co is swept through resonance to a value far above, the magnetisation ends up pointing in the negative z- direction. This technique of inverting M is very useful experimentally, since it is insensitive to calibration errors of the Bi amplitude, and is known as adiabatic inversion or adiabatic fast passage. Examples of adiabatic inversion pulses are the hyperbolic secant and frequency-offset corrected inversion (FOCI) pulses used for spin inversion in Flow- sensitive Alternating Inversion Recovery (FAIR) perfusion experiments, as described in chapters 3 and 4, and the principle is used to bring about velocity-induced adiabatic inversion in continuous arterial spin labelling perfusion techniques (see chapters 3 and 7).
2.3 Image Formation using Nuclear Magnetic Resonance
Techniques
The aim of magnetic resonance imaging (MRI) is to produce representations of objects containing NMR sensitive nuclei with good spatial accuracy. This is done nowadays almost exclusively by the use of Fourier analysis techniques, in which spins are spatially encoded by manipulating their resonant frequency using magnetic field gradients. For a
23 NMR Theory and Imaging Techniques
Standard two dimensional Fourier Transform (2D FT) image pulse sequence (see figure
2.4), the main features for consideration are:
1) the use of a frequency selective pulse (a ‘shaped’ 90° pulse) to excite a single slice
from the three dimensional region
2) the use of phase-encoding gradients, Gy, to provide information along one direction
(the y-direction) within the slice
3) the use of the read gradient, G%, to provide information along the x-direction within the
slice
I will briefly describe each of these procedures to show how they can, with the aid of a two-dimensional Fourier transformation, be used to generate a cross-sectional image.
2.3.1 Slice selection
Protons in the slice of interest can be selectively excited by the combination of a frequency-selective RF pulse and a magnetic field gradient applied perpendicular to the imaging plane. The bandwidth of the RF pulse and the amplitude of the slice-selection gradient determine the thickness of the slice. In order to excite the material within the slice evenly the RF pulse must be of a certain shape. The shape is that of a sine function
[(sin cot)/ cot] which is the Fourier transform of a square pulse. Also, because the slice is of finite thickness, the slice selection gradient, as well as enabling the slice to be selected, causes nuclei through the slice to be dephased. A negative gradient after the RF pulse compensates for this by rephasing the nuclei.
2.3.2 Frequency encoding
Following a slice selective 90° pulse, nuclei precess about Bq at the Larmor frequency cOq .
24 NMR Theory and Imaging Techniques
•4 TE ►
RF
Slice select
Phase encoding
n Frequency encoding
n TR
Figure 2.4 A standard spin echo 2D-FT imaging sequence. Magnetic field gradients applied along the three perpendicular directions x, y and z allow spatial encoding of the signal. The sequence is repeated for incrementally changing magnitudes of the phase encoding gradient; an image can be created by 2D Fourier transformation of the resulting echo set.
25 NMR Theory and Imaging Techniques
Ignoring field inhomogeneity effects, all spins resonate at the same frequency. A magnetic field gradient applied along the x-direction causes neighbouring spins within the gradient to precess at different frequencies. Frequency encoding involves acquisition of an echo in the presence of a linear field gradient. Frequency analysis of the echo by
Fourier transformation produces a profile of the sample.
2.3.3 Phase encoding
To obtain a second axis of spatial information, spins are subjected to a third magnetic field gradient Gy perpendicular to both the slice select and frequency encoding gradients.
This causes the nuclei to precess at different rates according to their position along the y- axis, and if the gradient is applied for a period of time At the nuclei at a point y will have accumulated a phase shift A(|) equal to
A(l) = '}GyyAt (2.19)
It can be seen that the gradient Gy causes the nuclei to acquire a phase shift that is proportional to their y-co-ordinate. If the size of the gradient is increased in a stepwise manner, the signal will be modulated with a frequency that is determined by the y-co- ordinate of the nuclei generating the signal. Fourier analysis of how the signal varies from one scan to another provides the means of disentangling the frequency modulations and hence yielding the y-distribution of the nuclei that give rise to the signals. This provides the second dimension for the image, and the combination of phase and frequency encoding enables the reconstruction of a two dimensional image.
26 NMR Theory and Imaging Techniques
2.3.4 The concept of k-space
It is useful at this point to introduce a graphical representation of imaging techniques, based on the received signal being a Fourier transform, which helps to visualise the effects of applied gradients. It can be shown that, neglecting relaxation and other attenuating effects, the received signal from a sample S(t) is related to the spatial density function, p(r). If the Fourier transform is defined as
p(k) = |p (r> '’‘Vr (2.20) then the received signal S(t) may be written as
.S(0 = p(k(f» (2.21) where k(t) is a vector in Fourier space, of k-space, which depends upon the field gradient
G(t) according to the expression
\L(t) = y\'G {t')dt' (2.22)
The temporal variation in G(t) is related to a vector in k-space which represents the signal at time t. Hence the 2D-FT imaging experiment described above consists of modulating the gradients to create a trajectory in k-space allowing sufficient samples of S(t) to be taken to allow the original spin density to be recovered via a two dimensional Fourier transform. The size of the field of view and the resolution of an image can be conveniently described in terms of the k-space characteristics of the acquisition. For a
2D-FT image, the field of view (FOV) is determined by:
M ,=y-G ,A / = - ^ (2.23a)
M ,=r-AG,.f,=^ (2.23b)
27 NMR Theory and Imaging Techniques
where At is the dwell time between sample points collected in the presence of the read gradient G%, ty is the duration of the phase encode gradient and AGy is the gradient increment between one line of k-space and the next. The image resolution (X) is:
(2.24) ^x,y where represents the outermost point of k-space acquired in the respective directions.
In the 2D-FT experiment, one line of k-space in the read direction is acquired per excitation of the spin system, and k-space is stepped through in the orthogonal direction by incrementally increasing the phase encode gradient for successive acquisitions. This means that the scan time for a spin warp image tends to be on the order of a few minutes, and is the reason why this type of image acquisition is rather prone to motion artefacts. In an effort to reduce the motion sensitivity of MRI, techniques have been proposed which reduce the length of the imaging period. I will describe the most important of these in the next two sections.
2.3.5 Fast Low Angle Shot (FLASH) imaging
The Fast Low Angle Shot (FLASH) sequence is an example of a 2D-FT gradient echo sequence, in which a 180° refocusing pulse is not used and the sampled data comes from the FID of a single excitation pulse. The read gradients immediately follow the excitation pulse, thus reducing the echo time of the sequence. The scan time can also be reduced by making the time between successive excitations much less than the Ti of the sample (the value typically used in spin echo imaging). This leads to loss in the signal to noise ratio
28 NMR Theory and Imaging Techniques
(SNR) of the resulting image, but for a given repetition time, the SNR can be optimised by adjusting the flip angle of the excitation pulse according to the Ernst equation:
cos a = exp(-TR / ) (2.25) where a is the pulse flip angle and TR is the sequence repetition time. FLASH imaging therefore offers the possibility of a greatly reduced scan time at the cost of a degradation of image quality. The minimisation of repetition time is taken to its physical limit in
TurboFLASH imaging, which is discussed further in Chapter 6.
2.3.6 Echo Planar Imaging (EPI)
After the completion of a line in k-space in the 2D-FT sequence there remains a substantial amount of transverse magnetisation since typical sample times are much less than Ti, although the spins are dephased because of the previous application of the read gradient. This signal is a potential source of information and by reversing the polarity of the read gradient, a recalled echo is formed which may then be sampled. An imaging approach offered by Mansfield in 1977 (Mansfield, 1977) exploited this by repeatedly reversing the read gradient polarity. Thus if the experiment could be compressed into the duration of one FID, the entire k-space data set could be obtained from one RF excitation leading to sub-second imaging times. This approach is known as echo planar imaging
(EPI), and the exact pulse sequence is shown in Figure 2.5a. K-space is stepped through in the phase encode direction by the application of short gradient blips between the read gradient reversals, producing the square k-space scanning pattern shown in Figure 2.5b.
The large negative blip on the phase encode axis serves to move the initial sample point so that the whole of k-space can be scanned in one experiment from bottom to top. An
EPI image takes on the order of 50ms to acquire, depending on the resolution and
29 NMR Theory and Imaging Techniques
(a) 90
RF
U J II II .11 II II Gy U
(b)
Figure 2.5 Example of an echo planar imaging sequence, (a) A single RF pulse excites the magnetisation, and suitable modulation of the read and phase encoding gradients (in this case, blipped phase encode gradient and trapezoidal read gradient) enables coverage of the whole of k-space (b)
30 NMR Theory and Imaging Techniques
sampling rate, and it is this rapidity of acquisition that is the principle advantage of EPI, allowing motion (e.g. of the heart) to be effectively frozen. The price for such rapid acquisition is a lower SNR than that of conventional 2D-FT techniques and an inherent T% contrast (see next section). In addition, EPI is more technically demanding since, in order to compress the experiment into one FID, the sampling must be faster with correspondingly higher gradients which have to be switched more rapidly. Such large gradient amplitudes bring the problem of time dependent eddy currents induced in the body of the magnet, which can lead to image distortion. In fact, EPI is particularly sensitive to any type of magnetic field inhomogeneity or off-resonance effects, which cause misregistration and distortion of the images produced. Indeed, this is viewed by many as the major drawback of the technique. Nevertheless, in most experiments where high time resolution measurements are the main priority, EPI is now the technique of choice on systems with the required gradient capabilities.
2.4 Image Weighting in Magnetic Resonance imaging
A major benefit of MRI is that the images can be tailored to show contrast in various different ways, each of which represents unique and valuable information. I will now describe how the image acquisition can be controlled to weight the images according to the relevant parameters, which I have divided into two categories: NMR and biological.
2.4.1 Image weighting using NMR parameters
Traditionally, NMR sequences and images have been weighted according to parameters such as:
31 NMR Theory and Imaging Techniques
Spin density: using a sequence with a short echo time and a long time between excitations to allow for full relaxation results in an image which predominantly represents the density distribution of the NMR sensitive nuclei.
Ti-weighting: to produce an image in which contrast relates directly to the Ti variation within the sample, two main approaches are used. A pre-inversion pulse can be applied and the magnetisation sampled at a point during the ensuing recovery (the IR sequence, see section 2.2.6). However, an IR image takes a relatively long time to acquire, since full relaxation is required between inversion pulses. The alternative is to acquire a 2D-FT or EPI image with a short repetition time i.e. a repetition time = Ti of the sample. If a range of Ti values is present in the sample, which will be the case if T% contrast is desired, then a repetition time within the range should be chosen. The extent to which spins have relaxed between excitations will depend on their Ti, and thus the amount of signal produced will also be Ti-dependant. Regions of the sample with a short Ti will appear bright since they almost fully relax between excitations; conversely, regions with long Ti will appear dark in the T%-weighted image.
T2‘Weighting: as described in section 2.2.5, the use of a 180° pulse to form a spin echo produces a signal whose amplitude is related to the echo time and the T 2 of the sample.
If a long echo time is used, signal from regions of the sample with a short T 2 will have almost completely decayed, whereas regions with a long T 2 will still have a significant amount of signal remaining. Therefore, short T 2 regions appear dark, long T 2 regions appear bright, and T 2 contrast is generated. This technique can be applied to both EPI and 2D-FT imaging. Indeed EPI will inevitably have a certain degree of T 2 -weighting due to limitations on its minimum echo time. In order to avoid any T 1 contamination, these sequences are usually run with long repetition times to allow for full longitudinal relaxation of all spins between excitations.
32 NMR Theory and Imaging Techniques
Magnetisation transfer: macromolecular protons (such as those attached to proteins)
have resonance linewidths which are too broad to detect directly in conventional MRI.
However, if these signals are selectively saturated using irradiation which is several
kHz off-resonance with respect to the free water signal, a perturbation of the steady-
state magnetisation of the free water protons is observed. This is caused by
magnetisation transfer and cross-relaxation between the two coupled spin systems.
Magnetisation transfer contrast (MTC) can be used to look at the rate of exchange of
magnetisation between the free and bound states, and at the relative populations of the
two states. Magnetisation transfer affects the longitudinal relaxation time constant T%,
which is shortened in the presence of off-resonance irradiation. This is important when
an off-resonance pulse is used for a different purpose, e.g. spin tagging in perfusion
MRI, and will be discussed further in the relevant chapter.
2.4.2 Image weighting using biological parameters
More recently, techniques have been developed to directly image biological parameters.
This thesis deals with a number of these methods, including:
• T2*-yveighting: as mentioned above, images can be sensitised to the effect of magnetic
field inhomogeneity by using gradient echo sequences. Local magnetic field
inhomogenities can be induced by the presence of so-called contrast agents, which are
paramagnetic and so generate field gradients in their immediate vicinity. These cause
extra spin dephasing, leading to a dropout in signal. Contrast agents can either be
exogenous such as the gadolinium based Gd-DTPA which is used as a marker for
cerebral blood volume, or endogenous such as deoxyhaemoglobin, which is used to
generate contrast in functional neuroimaging and experimental studies of cerebral
33 NMR Theory and Imaging Techniques
ischaemia. In fact, more specific information can be obtained by creating maps of T 2 * and a rapid method for doing this is introduced in Chapter 5.
Diffusion-weighting: the NMR signal can be specifically sensitised to molecular diffusion by using an approach first proposed by Stejskal and Tanner in the 1960s.
This technique has been shown to be extremely important in the study and evaluation of stroke, where the diffusion of cellular water changes with the onset of cytotoxic oedema. The details of this technique are described fully in Chapter 3, and Chapter 6 introduces a new technique to measure the apparent diffusion coefficient in a time efficient manner at high field.
Perfusion-weighting: the use of exogenous contrast agents which act as a blood marker can be extended to measure blood flow as well as blood volume. If a short bolus of the contrast agent is injected intravenously, and its first passage through the brain is tracked by means of transient changes of signal intensity observed in a series of rapid images obtained at intervals of approximately one second, then flow can be estimated. Alternatively, blood water itself can be used as an endogenous tracer. The blood magnetisation can be ‘labelled’ in the arteries by either a saturation or inversion pulse, and these labelled spins alter the magnetisation of the tissue into which they flow. There are a number of different versions of these ‘spin tagging’ techniques, and this thesis deals extensively with both the continuous and pulsed labelling approaches.
The exact details of these sequences are left to the appropriate chapters.
34 Introduction to Perfusion and Diffusion
3 Introduction to Perfusion and Diffusion______
3.1 The concept of perfusion
The measurement of tissue perfusion is of critical importance to our understanding and assessment of many of the major human diseases, since cerebral vascular disorders are among the most common causes of death and disease in the Western world. Perfusion is defined as the volume of blood delivered to the capillary beds of a block of tissue in a given period of time, and its units are therefore ml/lOOg/minute. It is important to distinguish between perfusion and bulk flow: perfusion is flow at the capillary level, where exchange of nutrients between the blood and tissue occurs, whereas bulk flow corresponds to flow through major vessels such as veins and arteries, where no exchange takes place (see figure 3.1). Perfusing blood delivers substances such as oxygen and glucose to the tissue, which are necessary for cellular metabolism, and carries away the waste products. The survival of the brain is dependent on a continuous and adequate supply of oxygen and nutrients, and failure of the cerebral circulation results in the death of nerve cells within 5 minutes. For these reasons, the ability to measure perfusion accurately and with good spatial precision would offer the chance to assess which regions of an organ are at risk following a stroke or thrombosis. Various attempts have been made to develop techniques that achieve this goal.
3.2 Methods of measuring cerebrai perfusion
I will deal here with techniques that are designed to specifically measure cerebral perfusion. The techniques can be split into two main groups: those which are influenced
35 Introduction to Perfusion and Diffusion
Inflowing Outflowing arterial blood venous blood
exchange
Tissue and capillary network
Figure 3.1 Schematic diagram of tissue perfusion
36 Introduction to Perfusion and Diffusion
by cerebrovascular anatomy (i.e. connections between blood vessels which supply the brain and the surrounding tissue, or intra-extracranial anastomoses) and those which are not.
3.2.1 Group I methods
These methods are influenced by cerebrovascular anatomy.
Kety-Schmidt method: The first successful measurements of cerebral blood flow in man were performed by Kety and Schmidt in the 1940s. The method depends on labelling the brain with an inert diffusible indicator; in the original method, low concentrations of nitrous oxide were inhaled by the subject. The rate of uptake (or clearance) of the indicator by the brain is determined from a time plot of the arterial and cerebral venous concentrations of the indicator. At the end of the inhalation period, the arterial blood, cerebral venous blood and the brain tissue are in equilibrium for the nitrous oxide and the final cerebral venous concentration is assumed to be that of the brain tissue. The main difficulty of the method is that cerebral venous blood must be sampled from a vein draining blood from the brain alone and not be contaminated by blood from extracerebral sources. This is possible by sampling from the internal jugular bulb in man but is extremely difficult in experimental animals.
^^^Xenon clearance: This is basically an adaptation of the Kety-Schmidt technique. An inert diffusible tracer, ^^^Xe, is injected into the internal carotid artery or inhaled. The indicator diffuses very rapidly and equilibrates between the blood and brain tissue. When the injection is stopped, fresh arterial blood (containing no xenon, as this is almost completely cleared in one passage through the lungs) will wash out the isotope present in
37 Introduction to Perfusion and Diffusion
the brain tissue. The faster the washout, the faster the flow, and vice versa. The rate of clearance of the gamma emissions of the isotope are monitored by means of a scintillation crystal(s) mounted over the intact skull. These are collimated with lead to narrow the focus of the counting of radioactivity. The scintillation crystal is connected to a rate meter
(to give a continuous record of radioactivity) and a chart recorder. The major problem with this method is to ensure that only brain tissue is labelled with ^^^Xe. If extracranial tissues are labelled and are ‘seen’ by the counter, the readings obtained will not represent flow solely through the brain tissue. This is particularly important when looking at substances such as serotonin which can have dramatically different effects on brain as opposed to blood flow through extracerebral tissues.
Arterial flowmeters: The use of flowmeters (usually electromagnetic) on the arteries supplying the brain is severely limited in the experimental animal by the presence of intra-extracranial arterial anastomoses. Surgical preparations can help to alleviate these problems, but it is generally accepted that the use of arterial flowmeters is not a reliable technique for experimental work involving the brain.
3.2.2 Group II methods
These methods are not influenced by species cerebrovascular anatomy. Most are only possible in anaesthetised experimental animals, but the more recent techniques such as
SPECT and PET can be applied to the human brain.
Isolated cerebral vessels: The vasoconstricting or vasodilatory effects of various substances or physiological stimuli can be tested in sections of cerebral artery perfused in an organ bath. This method can be useful for detecting the presence of various
38 Introduction to Perfusion and Diffusion
neuroreceptors or for the testing of drugs. Unfortunately the effects of a substance on a cerebral artery in vitro is no guarantee that it will affect cerebral blood flow in the same way in vivo. The major cerebral blood vessels (such as the middle cerebral artery) which are usually used in these preparations do not have the same innervation nor necessarily the same physiological responses as the resistance arterioles within the brain substance.
Isolated vessel preparations can be useful tools for the pharmacologist but unqualified predictions about cerebral blood flow should not be made from their responses.
Pial vessel responses: Observations of the diameter of the arteries and arterioles running over the surface of the brain is a useful technique. The surface of the brain is surgically exposed and the vessel under study viewed through an image splitter and video camera attached to a microscope. Measurement of a vessel pial diameter does not give a direct measure of cerebral blood flow. Pial vessels can constrict in response to induced hypertension and dilate in response to lowering the arterial blood pressure with no change in blood flow. However, in the presence of a stable blood pressure, pial vessel constriction or dilation indicates, but does not prove, a decrease or increase in cerebral blood flow.
Krypton clearance: The rate of clearance of ^^Kr injected into the carotid artery can be measured by a Geiger-Miiller tube mounted over the exposed brain cortex. As only the beta emissions are detected, the measurement reflects flow through the superficial 1 mm of cortex over which the detector is mounted. Flow in mMOOg'^-min'^ is calculated from the initial slope of the clearance curve following a prolonged injection.
39 Introduction to Perfusion and Diffusion
Heat clearance: The rate of clearance of heat from a warmed thermocouple can be used to measure flow. The probe must either be mounted over the exposed cortex or inserted into the brain tissue. The method gives qualitative results only but can be used to give an index of rapid changes in flow as continuous measurements are possible.
Hydrogen clearance: The rate of clearance of can be measured from multiple platinum electrodes inserted into the brain tissue. The H 2 is administered by inhalation for a period long enough to ensure brain tissue saturation. When the H 2 is stopped, the rate of clearance (calculated from a plot of H 2 concentration against time) is used to calculate flow. The advantage of this method is that localised and serial measurements are possible.
The main disadvantage is the possibility of tissue damage around the probes.
Transcranial Doppler ultrasonography: Blood flow velocity can be calculated by measuring the flow-induced Doppler shift of ultrasonic waves when they are reflected by red blood cells. This technique measures blood flux rather than perfusion per se, and can also be used to measure red blood cell concentration. However, attenuation of the ultrasound signal by bone means that its use is limited to experimental animals and neonates.
Microspheres: Radioactive carbonised microspheres (commonly 15 pm in diameter) are injected into the left side of the heart. On reaching the brain they are trapped in capillaries. The number trapped in the capillaries, and therefore the radioactivity present in the brain, is flow-dependent. Various isotopes with different gamma emission characteristics (e.g. ^^^Gd, ^^Co, ^^Cr and ^^^Sn) can be used, and up to four different injections of microspheres with different labels can be used without significantly
4 0 Introduction to Perfusion and Diffusion
altering blood flow by plugging of the capillaries. When the animal is finally killed, the brain is removed and the radioactivity at different energy peaks is counted in a liquid scintillation analyser. Flow in macroscopically discrete areas can therefore be measured on four different occasions in the same animal.
Autoradiography: A diffusible indicator (usually [^"^CJiodoantipyrine) is injected intravenously. On reaching the brain the indicator is distributed through the brain in a flow-dependent fashion. The animal is killed, the brain immediately removed, frozen and cut into thin sections. These are developed on X-ray film. The resulting images are placed in a densitometer which measures the degree of darkening of the X-ray film. This optical density is related to the radioactivity of the brain which is in turn dependent on the blood flow. Flow can be calculated in numerous areas of the brain (typically 1 mm^ in size) from serial sections and thus calculated in many different brain nuclei and areas of the cortex. The chief disadvantage of the method is that, since brain removal is required, flow can be measured only once in each animal, although in a multiplicity of different areas.
Single Photon Emission Computerised Tomography (SPECT): This technique combines cerebral scintigraphy and tomography. The gamma camera, invented by Anger in 1961, consists of a sodium iodide crystal which converts the gamma rays emitted by a patient
(after the intravenous injection of a gamma emitting radionuclide) into photons, which are then converted to an electrical signal. A commonly used radionuclide is technetium-99m, a nearly pure gamma emitter, and safe for patient administration. The fact that a two or three-dimensional object can be reconstructed from the set of all its projections has been known for many years. Kuhl and Edwards (Kuhl and Edwards, 1963) first used this principle to obtain a cross-sectional image of the brain by rotating scintillation detectors
41 Introduction to Perfusion and Diffusion
around the head. Essentially the same technique is still used in SPECT, except that a rotating gamma camera is used instead of a rectilinear scanner. A SPECT scanner is relatively cheap and easy to set up, but the technique suffers from low spatial resolution and is only semi-quantitative.
Positron Emission Tomography (PET): A positron is a positively charged particle with the same mass as an electron. When emitted from a radionuclide (administered intravenously or as an inhaled gas), it travels at most a few millimetres within the tissue, losing most of its kinetic energy. It then interacts with an electron, and the resulting annihilation produces two gamma rays, each with an energy of 511 keV (where 1 eV =
1.6 X 10'^^ Joules), which are emitted simultaneously and travel at almost 180° to each other. This energy can be detected externally and used to define the location of the positron emitter by coincidence counting with symmetrically opposite pairs of detectors.
Cerebral blood flow is measured using radio-labelled oxygen (^^O) which is inhaled as
C^^Oi and is rapidly transferred to the water pool in the pulmonary capillaries. The resulting radioactivity is thus due to circulating H 2 ^ ^ 0 that is constantly generated in the lungs. After approximately 10 minutes of inhalation, the concentration reaches an equilibrium, in which continuous delivery of to the tissue is balanced by its rate of washout into the venous circulation and the radioactive decay of the (half life = 2.1 minutes). Blood flow is then proportional to the concentration of the tracer in the tissue.
Advantages of this method are its reasonably good spatial resolution and the ability to measure cerebral blood volume, oxygen extraction fraction and the cerebral metabolic rate for oxygen at the same time as blood flow.
4 2 Introduction to Perfusion and Diffusion
3.3 Mathematics of inert gas ciearance methods
3.3.1 Fick principle
The methods described above all derive from the original Fick principle which states that the quantity of substance Q taken up by an organ in time t is the arteriovenous difference in the concentration of the substance (Ca - Cv) multiplied by the blood flow (F) through the organ. This can be written as:
2 = F(Ca -C v ) (3.1) or,
f = e/(CA-Cv) (3.2)
3.3.2 Kety-Schmidt method
Kety and Schmidt applied equation (3.2) to measure cerebral blood flow. The denominator is modified to the integral of the arteriovenous differences over the time period in which measurements are made i.e.
Jo(CA-Cv)dt (3.3)
The numerator of the equation, Q, which is the total amount of indicator taken up by the brain in a time t, could not be detected directly in the original method. However, the quantity of the substance taken up by the brain is the same as its concentration in the brain (Cb) multiplied by the weight of the brain (W), i e.
Q = C ^ W (3.4)
When the indicator has been inhaled for long enough (i.e. time r = 10 minutes) the brain and blood are in equilibrium and Ca = Cb = Cvt where Cvt is the concentration in the venous blood at time t. (One also has to take into account the ratio of solubilities of the substance between brain tissue and blood. This is termed the partition coefficient (À). In
43 Introduction to Perfusion and Diffusion
the case of the original Kety-Schmidt method, the X value for nitrous oxide was unity; for the sake of simplicity it is ignored here). Equation (3.4) can now be rewritten:
(2== Cv, IWf (3.5)
Substituting equations (3.3) and (3.5) into equation (3.2):
The denominator of the equation is a finite number which can be calculated from the area between the curves of arterial and venous concentrations. Cy, can also be measured as the final cerebral venous concentration of the indicator at time t, but the weight of the brain
(W) is unknown. Therefore equation (3.6) is rewritten as:
C y , (3.7) j‘K-C,)dt
A value can thus be calculated for the quantity F/W, which is the flow per unit weight of tissue. By applying the appropriate constants and correction factors, cerebral blood flow is usually expressed in millilitres of blood per 100 grams of tissue per minute (ml lOOg'
^ min'^).
3.4 Measuring perfusion using NMR
Over recent years, methods for measuring perfusion using NMR techniques have been proposed. These techniques have been made practically feasible by the development of ultrafast technology, which greatly increases the efficiency of MRI in data collection and allows images to be acquired on the time scale required for the measurement of rapid physiological changes. Several different methods have been suggested, most of which are based on one of two approaches: (i) the use of contrast agents (exogenous and
4 4 Introduction to Perfusion and Diffusion
endogenous), or (il) arterial spin labelling. Each approach has its inherent advantages and disadvantages, as described in the following sections.
3.4.1 Perfusion MR Imaging with Exogenous Contrast Agents
Dynamic susceptibility contrast imaging is well suited to studies of haemodynamic studies in the CNS. Gadolinium-DTPA (Gd-DTPA) enhanced, Ti-weighted contrast is useful when the blood-brain barrier (BBB) is grossly disrupted. When the BBB is intact, however, it has little impact on most brain regions since the intravascular space is small and Ti effects occur locally. Unlike Ti contrast, magnetic susceptibility (T 2 or T 2 *) contrast results from microscopic variations produced by the heterogeneous distribution of high magnetic susceptibility contrast agents within a tissue’s magnetic field. The concept of susceptibility contrast was introduced by Villringer et al (Villringer et al,
1988). Early studies (Villringer et al, 1988; Belliveau et al, 1987) reported that the injection of agents such as Gd(DTPA)^' or Dy(DTPA)^~ lead to a significant decrease in brain signal intensity on spin or gradient echo images. This magnetic susceptibility effect results from local field gradients induced by intravascular compartmentalisation of the contrast agent (Villringer et a l, 1988; Hardy and Henkelman, 1989). By using long echo times (80-100 ms), the magnetic susceptibility effect of a bolus of gadolinium contrast agent (0.1-0.2 mmol/kg) is quite large, producing signal losses upwards of 20% to 30%.
These effects are greater than those observed for the Ti enhancement when the blood- brain barrier is intact, due to the amplification effect of the microscopic field gradients outside the microvascular space. Within this space, these magnetic susceptibility effects relax the transverse magnetisation of surrounding tissue protons for a distance roughly equal to the radius of the blood vessel (Villringer et al, 1988). Magnetic susceptibility contrast phenomena can be coupled with rapid imaging to resolve the first pass tissue 45 Introduction to Perfusion and Diffusion
transit of intravenously administered contrast materials (Rosen et al, 1991; Rosen et al,
1990), thereby providing an index with which to measure cerebral blood flow and volume. To determine quantitative cerebral blood volume (CBV) or blood flow (CBF) measurements, however, it is necessary to convert regional changes in MR signal intensity with respect to time into contrast agent tissue concentration-time curves (Rosen et al, 1990; Belliveau et al, 1990). Empirical studies have shown that the degree of the signal drop rests on two factors: the concentration of an injected contrast agent within the blood and the fractional volume of intravascular space within the tissue (cerebral blood volume). After injection, the contrast agent’s concentration varies with time, while blood volume may vary region by region. Both contrast agent concentration and blood volume reflect approximately linear relationships to the change observed in the relaxation rate
AR% = A(1/T2). This can be measured easily by measuring the percent signal change from
baseline and using the relationship AR 2 = l/T 2 post - 1/T2pre (Villringer et al, 1988; Rosen et al, 1989). Within some limiting range, therefore, we can measure the contrast agent’s concentration in tissue as a function of time (the so-called ‘concentration-time’ curve) by mapping tissue signal loss dynamically over time (Belliveau et al, 1991). Because cerebral transit times are on the order of seconds (Axel, 1980) ultrafast imaging is needed to resolve the passage of an intravascular agent through the capillary bed. Echo planar imaging (EPI) based methods are well suited to the evaluation of the time course and the regional distribution of injected contrast agents.
Classical nuclear medicine principles have been found to be particularly useful for the analysis of dynamic NMR time course data sets. Tracer kinetic analysis of contrast concentration-time data can yield both flow and volume information (Axel, 1980). An early principle for the analysis of concentration-time data was outlined by Stewart and is
4 6 Introduction to Perfusion and Diffusion
known as the Central Volume theorem (Stewart, 1894). Derived simply from mass
conservation, the theorem states that tissue blood flow, F, can be determined by the following ratio:
F=V /M 7T (3.8) where F is in units of ml/min/mltissue, and V is the volume of distribution of the agent within the tissue (i.e. the tissue blood volume for an intravascular agent, measured in ml/mltissue)- The mean transit time (MTT) is the average time required for any given particle of contrast agent to pass through the tissue, following an idealised impulse function. Several reasons exist as to why this apparently simple equation may be difficult to solve in practice (Weisskoff et al, 1993). First, the agent’s volume of distribution may be biologically multi-compartmental, with its transfer occurring between different tissue volumes at different rates. To account for this, details of the agent’s passage through the tissue must be modelled, for which several basic approaches, depending upon the class of agents, have been proposed. For reasons discussed by Lassen (Lassen, 1984), measurement of the tissue concentration-time curve, rather than the venous output concentration-time curve, can only approximate the true MTT. Moreover, even for single compartment agents, such as purely intra-vascular markers, measurement of the true tissue transit time can be difficult. This is because the MTT is derived by the transit of an idealised bolus of zero time duration (delta function). The tissue concentration-time curve response to this bolus is called the tissue residue function. Since a delta function bolus cannot be achieved practically, the tissue residue function cannot be measured in vivo.
The actual measured tissue concentration-time curve, Tissue(t), is by superposition the convolution of the arterial input function Art{i) and residue function RF{\),
Tissue(t)= Art(t)*/?F(t) (3.9)
47 Introduction to Perfusion and Diffusion
In order to measure the residue function RF{i), and its associated MTT, we must deconvolve the measured tissue concentration-time curve with the observed arterial blood input function. Arf(t) can be measured directly with arterial blood sampling, as is conventionally done with PET imaging, or can theoretically be accomplished directly from MR images if sufficient temporal and spatial resolution is present. Tissue(t) can be determined regionally from imaging experiments. Accurate determination of MTT depends on the quality of both the Art(t) and Tissue(t) data. For freely diffusible markers, this is simplified by slower transit times through the tissue. Thus, the measurement of
MTT is less dependent on the arterial input curve and temporal resolution of the measurement. For purely intravascular markers, such as paramagnetic chelates in the brain, the true transit times are on the order of seconds. Thus a well-characterised bolus is needed to obtain accurate measurement of MTT.
In addition to measurement of MTT, determination of blood flow requires knowledge of the volume distribution of the agent. For intravascular agents, this volume distribution is the tissue blood volume, an important physiological parameter itself, especially during a cerebrovascular accident. Measurement of absolute blood volume, V, can be made by integrating the tissue concentration-time curve and normalising to the integrated arterial
(input) data. This has several important consequences. First, because the blood volume determination is reflected in the time integrated tissue and blood concentration data, measurement of blood volume alone has a somewhat diminished need for very high temporal resolution measurements. For the measurement of arterial blood data, this can mean that samples collected over time do not need to be fractionally measured and can simply be pooled for an average determination. Second, because the arterial input to an organ is ultimately derived from a common source, relative blood volume can be
48 Introduction to Perfusion and Diffusion
measured with no knowledge of the arterial concentration-time data. For these reasons, early attempts to quantify microcirculatory parameters from MRI data were focused on the somewhat simpler measurement of blood volume as the prerequisite to complete characterisation of tissue perfusion.
3.4.2 Assessment of Tissue Perfusion using an Endogenous
Susceptibility Contrast Agent - BOLD imaging
As seen above, if the magnetic susceptibility within a region of the brain varies rapidly (in space and/or time) near or within a given voxel, the spins inside experience a range of magnetic fields, and thus precess at varying frequencies. While they commence in phase with each other, after a time this phase coherence is lost. The MR signal arises as a vector sum of the spin magnetisation within a given voxel. The spread in phase angle thus results in some degree of cancellation of the net magnetisation, and hence a loss of signal. The attenuation depends on the spatial and temporal variation of the susceptibility, and the length of time during which the spins precess before data acquisition. This forms the basis of dynamic susceptibility contrast imaging (see above). Because deoxygenated haemoglobin is more paramagnetic than oxygenated blood and normal tissue, it can also act as an endogenous intravascular paramagnetic contrast agent. Variations in blood oxygenation can clearly be seen to affect the MR image intensity in gradient echo images with relatively long echo times, giving rise to the name blood oxygenation level dependent contrast (BOLD). This phenomenon is now widely used for MR functional neuroimaging, in which local increases of image intensity have been observed in association with specific brain activation tasks. However, a basic analysis of the biophysical and haemodynamic events relating to brain activation leads to the conclusion
4 9 Introduction to Perfusion and Diffusion
that many factors can affect the MR signal in such studies. The list includes blood volume, blood flow, arterial and venous haemoglobin saturation, oxygen extraction rate, blood velocity and haematocrit. This means that the use of BOLD imaging can not provide a method for quantitatively measuring tissue perfusion, but does provide important and unique complementary information when used in combination with techniques which do measure CBF directly (e.g. spin labelling methods, see next section).
3.4.3 Introduction to Non-invasive Perfusion MR Imaging using Spin
Labelling of Arterial Water
An MR image can be made sensitive to the effect of inflowing blood spins if those spins are in a different magnetic state to that of the static tissue. The family of techniques known as arterial spin labelling (ASL) techniques uses this idea by magnetically labelling blood flowing into the slice(s) of interest. Blood flowing into the imaging slice exchanges with tissue water, altering the tissue magnetisation. A perfusion-weighted image can be generated by the subtraction of an image in which inflowing spins have been labelled from an image in which spin labelling has not been performed. Quantitative perfusion maps can be calculated if other parameters (such as tissue Ti and the efficiency of spin labelling, see below) are also measured. Since exogenous contrast agents are not required for these techniques, the perfusion measurement is completely non-invasive. Under the general heading of arterial spin labelling, two distinct sub-groups exist: continuous ASL and pulsed ASL. Despite sharing a similar basis, the two approaches have different advantages and limitations that affect their ability to quantify perfusion. I will now consider each approach separately.
50 Introduction to Perfusion and Diffusion
3.4.4 Continuous Arterial Spin Labelling techniques
The first arterial spin labelling (ASL) technique, proposed by Detre et al in 1992 (Detre et al, 1992), is known as continuous ASL (CASL). In the initial implementation, blood water spins were repeatedly saturated as they flowed through a slice in the neck by the use of a train of RF pulses, applied over a period of several seconds. The labelled spins flow into the brain and, assuming water is a freely diffusible tracer, exchange completely with brain tissue water, thus reducing the overall tissue magnetisation. A steady state develops where the regional magnetisation in the brain is directly related to cerebral blood flow. Modifying the Bloch equation for longitudinal relaxation to include flow leads to the following equation for flow quantitation:
X (. Aff 1 / = 1 - (3.10) T^\app where /i s blood flow (perfusion) in ml/lOOg/min, A is the bloodibrain partition coefficient for water, is the steady state magnetisation per unit mass of brain tissue, Mb is the fully relaxed tissue magnetisation per unit mass, and Tjapp is the constant which describes the exponential decay to the steady state magnetisation and is defined by
^ = —+4 (3.11) r, A
By measuring Tiapp and the ratio of magnetisation with and without arterial spin saturation, a value for flow can be calculated. The values for cerebral perfusion in the rat brain reported by Detre et al (Detre et al, 1992) were in reasonable agreement with previously published values using other techniques. Soon after CASL was proposed,
Williams et al (Williams et al, 1992) improved the technique by using adiabatic fast passage to label the arterial water spins. Making use of the adiabatic theorem (see chapter
2), the magnetisation of a spin moving through a magnetic field gradient at velocity v will
51 Introduction to Perfusion and Diffusion
be inverted if a constant Bi field is applied perpendicular to the main field and the following condition is satisfied;
(3 .1 2 )
As the spins flow along the direction of the magnetic field, their frequency sweeps from far below resonance to far above (or vice versa, depending on the polarity of the gradient and the direction of flow). In this way, adiabatic inversion will be induced. If such an RF pulse is applied for several seconds to a plane in the neck of an animal, all inflowing arterial water spins will be inverted during this period, and a flow-related steady state will again be achieved. The advantage of labelling arterial spins by inversion is a two-fold increase in the difference between the labelled and unlabelled states, and flow is then given by:
A M r-M r Tu„ 2Mr where represents the magnetisation of tissue per unit mass without arterial spin inversion (the control image) and represents the magnetisation with arterial spin inversion. Greater sensitivity to flow is achieved using an inversion spin label, and blood flow values measured by Williams et al in the rat brain were again consistent with published values.
Two main problems soon became apparent for the use of continuous spin labelling as a method to measure tissue perfusion accurately. First, the time taken for spins to travel between the labelling plane and the imaging slice (henceforth referred to as the transit time) is non-zero, and therefore Ti relaxation will occur during this period. Different regions of the brain will have different transit times, depending on the distance from the labelling plane and cerebrovascular anatomy. For accurate quantitation, this effect must
52 Introduction to Perfusion and Diffusion
be taken into account. Second, the application of a long {i.e. several second) off- resonance RF pulse causes a decrease in the water signal due to magnetisation transfer effects. Although no direct saturation of observed water magnetisation in the imaging slice occurs due to the narrow linewidth of the free water peak, saturation of macromolecular spins does occur, resulting in attenuation of the free water signal via magnetisation transfer (MX). This reduces the perfusion related signal difference between the control and spin labelled images. Zhang et al. (Zhang et al, 1992) made an initial attempt to account for these two effects by incorporating MX effects into the Bloch equation analysis and measuring the time lag between the initiation of spin labelling and the first observable decrease in tissue magnetisation. The transit time effect was accounted for by modifying the degree of inversion, a, by an amount related to Xi relaxation:
1 ( M — M I a'=«-p(-A/rj (3.14)
Tib is the longitudinal relaxation time of brain tissue, Tia is the longitudinal relaxation time of arterial blood water and A is the transit time, a can be measured by imaging a slice in the neck just after the spin labelling has been performed and observing the difference in signal intensity in the main arteries when the inversion pulse is on and off
(Zhang et al, 1993). The method to account for transit time and MXC effects proposed by
Zhang et al (Zhang et al, 1992) was rather time consuming (their measurements were done on a single voxel using volume localised spectroscopy rather than imaging), making its routine implementation impractical. The transit time problem has also been noticed in experiments comparing CASL with the radioactive microsphere method of CBF quantification, where an underestimation of flow was observed with the spin tagging technique when the flow rates were low (Walsh et al, 1994).
53 Introduction to Perfusion and Diffusion
Magnetisation transfer complicates the extension of the above methods to multi-slice acquisition, since the control image must experience exactly equivalent MT effects as the spin labelled image. This means that the control ‘plane’ must be symmetrically opposite the inversion plane with respect to the imaging slice, which can only be true for a single imaging slice. The control image is acquired by changing the sign of the frequency offset of the tagging pulse (assuming symmetric MT effects) or by reversing the gradient polarity. In fact, it has been suggested (Pekar et al, 1996) that to properly account for MT effects (and possible eddy current effects caused by the labelling gradient) a four-step protocol for image acquisition should be used, in which both frequency and gradient polarity are alternated, although this still remains a point of debate (see, for example,
(Silva et ai, 1997)). Alternatively, a two-coil set-up can be used to avoid the saturation of macromolecular spins (Zhang et al, 1995). In this set-up, a small surface coil is placed on the neck of the subject, immediately adjacent to the artery supplying blood to the brain.
The physical range of the B] field produced by the surface coil is such that its effect is limited to a very localised region. Arterial water spins are inverted using the surface coil, but no MT effects are observed in the brain since the Bi field does not extend that far. A separate (actively decoupled) coil is used to apply the imaging pulses and receive signal.
Extension of this approach to multi-slice perfusion imaging is straightforward, since the control image does not need to contain any MT information (Silva et al, 1995). However, specialised hardware is needed for implementation of this method, and flow quantification is still restricted by the need to account for a large range of arterial transit times.
54 Introduction to Perfusion and Diffusion
Knowledge of the transit time for each pixel is necessary to produce quantitative perfusion maps using the techniques so far described. This has been attempted by Ye gr al (Ye et al, 1997b), where the difference between spin labelled and control images was measured as a function of the tagging period duration using single shot EPI techniques, but SNR was found to be insufficient to accurately estimate the transit time with high spatial resolution. An alternative approach has been taken by Alsop and Detre (Alsop and
Detre, 1996) in which a time delay is inserted into the sequence between the end of the tagging period and the image acquisition. Although this reduces the signal difference between the control and labelled images and complicates the quantification procedure, it can be shown (Alsop and Detre, 1996) that if this delay is greater than the arterial transit times across the image, then the resulting CBF maps will be almost completely insensitive to transit time variations. This technique has been shown to produce good quality perfusion images even in patients with cerebrovascular disease (and the concomitant large range of transit times throughout the brain) (Detre et al, 1998), though the length of the post-labelling delay, and thus the tolerance to very long transit times, is limited by Ti relaxation and SNR. Nevertheless, this approach appears to be the most robust and promising method presently available for the elimination of transit time effects.
Another possible source of systematic error in CASL techniques is the presence of intravascular signal in the subtraction (control minus labelled) images. All the theoretical models describing the relationship between flow and signal difference {e.g. equations
(3.10) to (3.14)) are based on the assumption that signal comes exclusively from tissue. If a significant amount of signal emanates from the vasculature, perfusion will be overestimated. The majority of spin labelling studies have been performed with flow-
55 Introduction to Perfusion and Diffusion
crushing gradients included in the imaging sequence, which are intended to completely eliminate signal from intravascular spins. Studies have shown that inclusion of a bipolar gradient pair with a b value (Le Bihan and Turner, 1992) of approximately 5 s/mm^ reduces the perfusion difference signal in human grey matter by almost 50% compared to with no crusher (Ye et al, 1997b). The behaviour of the difference signal as a function of b value can be used to estimate the relative amounts of spin-labelled signal in each compartment {i.e. intra- or extravascular), and this can be used to get an estimate of the extraction fraction for water (Silva et al, 1997). This is usually assumed to be equal to unity {le. that water is a freely diffusible tracer), but experiments by the same group using the arterial spin tagging technique with and without macromolecular saturation have shown this assumption to be slightly inaccurate at normal flow rates (where E ~ 0.9) and very inaccurate at high flow (E ~ 0.6 when / = 400ml/lOOg/min) in the rat brain
(Silva et al, 1997). The transit time insensitive sequence proposed by Alsop and Detre
(Alsop and Detre, 1996) mentioned above allows almost all of the labelled blood to either exchange with the tissue or ‘wash through’ the vasculature during the post-tagging delay, and therefore suffers less from the associated errors of arterial signal contributions. It is important to note that since transit time effects cause an underestimation of CBF and intravascular signal causes an overestimation, the two effects can tend to cancel out.
However, this will only be true under very specific circumstances, and both systematic errors need to be addressed. It seems that a combination of delayed acquisition and flow- crushing gradients is sufficient to account for both effects (Ye et al, 1997a).
Finally, the extension of CASL techniques to multi-slice perfusion imaging with standard hardware has recently become possible with another method devised by Alsop and Detre
(Alsop and Detre, 1998). Rather than acquiring the control image by changing the
56 Introduction to Perfusion and Diffusion
inversion RF frequency and/or gradient polarity, the amplitude of the RF labelling pulse is sinusoidally modulated at a certain frequency (p. Fourier transform of an RF waveform of base frequency tpo with sinusoidal amplitude modulation (p results in a pair of inversion planes at frequencies (po± 1998), Chapter 7 in this thesis) and functional activation ((Kerskens et al, 1996), (Ye et al, 1997), (Ye et al, 1998), (Lalith Talagala and Noll, 1998)) means that the future of these techniques looks extremely promising. 3.4.5 Pulsed Arterial Spin Labelling techniques As mentioned in the previous section, continuous ASL techniques suffer from two major problems: magnetisation transfer effects, caused by the application of a long off- resonance RF pulse prior to image acquisition, and the loss of the spin label by the blood water as it travels from the labelling plane to the imaging slice. In pulsed arterial spin labelling (PASL) approaches, the aim is to minimise these sources of error, and thus facilitate flow quantitation. This is achieved by using a short (typically -10ms) RF pulse to label spins, and minimising the distance between the labelling region and the imaging slice. 57 Introduction to Perfusion and Diffusion Measurements of changes in perfusion based on observed changes in tissue Ti were first performed by Kwong et al (Kwong et al, 1992). They demonstrated that if a slice selective inversion was used to invert spins within the imaging slice only, the Ti value obtained was dependent on flow in the way previously described by Detre et al in equation (3.11). The entry of fully relaxed blood spins into the imaging slice increased the apparent relaxation rate, with the increase being directly proportional to flow. Kwong et al used this relationship to calculate absolute changes in CBF associated with functional activation. However, measurements of resting values of perfusion were not possible using this method since the intrinsic tissue Ti was unknown. In order to identify the component of signal in the slice-selective inversion recovery (ssIR) image which is due purely to the inflow of blood spins during the inversion time, a second image is required which has relaxed with intrinsic tissue T%. At approximately the same time, Kwong et al (Kwong et al, 1995), Kim (Kim, 1995) and Schwarzbauer et al (Schwarzbauer et al, 1996) proposed the sequence which is now commonly referred to as Flow-sensitive Alternating Inversion Recovery, or FAIR. In this technique, two inversion recovery images are acquired. The first follows a slice selective inversion, and thus has a signal intensity determined by Tiapp (see equation 3.11); the second follows a global inversion, and so (assuming blood and tissue relax at the same rate) has no flow enhancement le. the image intensity is determined by intrinsic tissue Ti. Subtraction of the two images leaves a signal which is directly related to flow, as shown by Kim (Kim, 1995): AM =2M,-TI- ( / / A)exp(- TljT, ) (3,15) where AM is the difference signal between the ssIR and non-selective IR (nsIR) images. Mo is the equilibrium tissue magnetisation per unit mass of tissue, 77 is the time between spin inversion and image acquisition (inversion tim e),/is perfusion in ml/lOOg/min, X the bloodibrain partition coefficient for water and Ti is the intrinsic longitudinal relaxation 58 Introduction to Perfusion and Diffusion time for tissue. Equation (3.15) relies on several simplifying assumptions, such as tissue and blood Ti being equal and the efficiency of the inversion pulse being equal to one. Under certain circumstances these assumptions are not valid, and a more general analysis (Calamante et al, 1996), (Kwong et al, 1995) predicts a biexponential relationship between flow and TI: exp(-r//7;„^J-exp(-r//7;J' AM =2aoM o//A (3.16) where oto is the degree of inversion (equal to 0.5 for saturation, 1 for perfect inversion), Tia is the longitudinal relaxation time of blood water protons, and Tjapp is defined in equation (3.11). If Tja ~ Tj and Oo is unity, equation (3.16) reduces to equation (3.15). However, for brain tissue such as white matter where the Ti is approximately 50% of the blood water value, the error introduced by making the simplifying assumptions is large (Calamante et al, 1996). Quantitation of blood flow therefore requires a set of ssIR and nsIR images to be acquired at different inversion times, and the difference to be fitted to equation (3.16). An alternative pulsed spin tagging approach which was developed at approximately the same time as FAIR is known as EPISTAR (echo planar imaging and signal targeting with alternating radiofrequency) (Edelman et al, 1994). This technique is similar in theory to the continuous ASL methods. A slab of blood proximal to the imaging slice is labelled using a single RF pulse, allowed to flow into the imaging slice and then imaged at a time TI later. A control image is also acquired in which the label is applied distal to the imaging slab (Edelman et al, 1994) or with no slab selective gradient (a variant known as PICORE (Wong et al, 1997)). Subtraction of the images results in a flow-dependent image which obeys the same time dependence as the FAIR subtraction image le. 59 Introduction to Perfusion and Diffusion equation (3.16), assuming a negligible transit time for the tagged bolus to enter the imaging slice and fast exchange. An alternative kinetic model has been put forward by Buxton et al (Buxton et al, 1995) which takes into account a finite transit time and limited bolus width. These factors can be incorporated into the standard Ti model described above, leading to similar predictions for the behaviour of AM as a function of inversion time for the two models. FAIR and EPISTAR have been used to demonstrate the changes in cerebral blood flow associated with neuronal activation induced by motor and visual stimulation on human subjects. Combining FAIR and blood oxygenation level dependent (BOLD) contrast imaging, Kim and Ugurbil (Kim and Ugurbil, 1997) have attempted to calculate the changes in cerebral metabolic rate for oxygen based on various assumptions. Recently, cerebral blood flow values in the rat brain measured using FAIR have been compared with values obtained using autoradiographic methods and shown good correlation (Tsekos et al, 1998). The response to hypercapnia and middle cerebral artery (MCA) occlusion was also investigated. The pC02 index measured agreed well with previous measurements, and a large reduction in signal from the region corresponding to the MCA territory was observed, though no flow quantitation was attempted. Under ideal conditions, quantification of perfusion using PASL methods is reasonably straightforward. In practice, however, various complications become apparent. These problems will be discussed in detail in Chapter 4, where the work I have carried out to address the main difficulties is described. As with the continuous ASL approaches, accurate quantitation of PASL depends on several parameters, such as transit times, exchange fraction and macrovascular contamination. At present, both CASL and PASL 60 Introduction to Perfusion and Diffusion offer huge potential and the benefits and limitations of each are approximately equal. It will be interesting to see which method gains the upper hand over the next few years, and whether routine implementation of completely non-invasive MR perfusion imaging will become a clinical reality. 61 Introduction to Perfusion and Diffusion 3.5 Diffusion in bioiogicai systems Measuring molecular diffusion has brought several useful new approaches to tissue characterisation and functional studies, from the determination of cell geometry to the early clinical evaluation of cerebrovascular accidents (or strokes). This interest in diffusion results from the unique feature of this parameter: diffusion directly reflects molecular mobility. Molecular mobility also affects T] and T 2 relaxation times, but diffusion refers only to translational molecular motion, whereas Ti and T 2 reflect complex molecular interactions involving rotational motion and exchanges. Moreover, Ti and T2 are MR parameters affected by MR experimental conditions, such as the magnetic field strength. By contrast, diffusion is defined entirely outside the MR context and does not depend on the MR environment. However, MRI is the only in vivo technique available today to measure diffusion directly from molecular displacements. Thus diffusion has not been used previously in the clinical domain and represents a new parameter. Over recent years, it has been shown to be a parameter which holds a large amount of useful information. 3.5.1 Molecular Diffusion Molecular diffusion results from a random, microscopic, translational motion of molecules known as Brownian motion. Because of thermal agitation, molecules are constantly moving and colliding with each other. Diffusion was originally described in non-uniform systems, where a macroscopic flux of differing species of particles could be observed. Pick’s first law states that this flux density depends linearly on the concentration gradient of this particle species. The proportionality constant is known as the dijfusion coefficient (D). A typical experiment is to monitor the diffusion of a 62 Introduction to Perfusion and Diffusion substance between two compartments separated by a semi-permeable membrane. The diffusion coefficient can be determined, for instance, by measuring the concentration of the substance at different times, using either chemical or physical methods. The principle of Pick’s law is currently being applied, for example, in haemodialysis. 3.5.2 Random walk and Einstein’s equation For a particular molecule, the random molecular walk produces net displacements over time, which are randomly distributed if we consider large molecular populations. The probability that a molecule travels a distance r in a time interval t can be calculated. For a simple liquid, one finds a Gaussian distribution, the mean of which is zero because the probability to move in one direction is the same as that to move in the opposite direction. The variance of the distance travelled is proportional to the time interval t according to the so-called Einstein equation: (^r^^ = 2Dt (or 6 D r, for displacements in three dimensions) (3.17) The proportionality constant D, the diffusion coefficient, characterises the mobility of molecules within and relative to the diffusing medium. The D of water at 25°C is about 2.2 X 10'^ mm^/s. This means that, during 100ms, the standard deviation for water molecular displacements is 20|Ltm. In complex systems such as biological ones, the distribution of molecular displacements may deviate from the Gaussian model because of the presence of many obstacles. 3.5.3 Boundaries and restriction Restricted diffusion occurs when molecules are confined in a limited medium by borders. When the molecules reach these borders they are reflected back into the medium. 63 Introduction to Perfusion and Diffusion Therefore the diffusion distance is not found to increase indefinitely with the diffusion time, as seen with free diffusion: rather, this distance ‘saturates’ when all the molecules have reached the boundaries (see figure 3.2), By comparing this saturation diffusion value and the free diffusion coefficient, which can be measured using very short diffusion times so that molecules do not experience any restriction, it is theoretically possible to evaluate the dimensions of the restrictive boundaries. This is of great interest for tissue characterisation if the media in question are, for example, cells. In practice, the situation is complicated by the shape and permeability of the medium, and diffusion measurements can be used to estimate the permeability of cell membranes. The dependence of the measured diffusion coefficient on diffusion time means that equation (3.17) does not hold true, and the definition of the diffusion coefficient needs to modified. Le Bihan et al (Le Bihan et al, 1988) introduced the concept of the ‘apparent’ diffusion coefficient (ADC) to recognise the fact that in biological systems there is always some degree of restriction, and therefore some departure from the Gaussian model. When presenting diffusion measurements, it is important to state the diffusion time used to enable comparison with other reported values. 3.6 Effects of diffusion on ttie spin echo MR signai 3.6.1 Motion, gradient and MR signal As seen in chapter 2, a linear magnetic field gradient in the z direction causes the effective field B seen by nuclei at location z to be: B = B,+G^z (3.18) and the corresponding precession (Larmor) frequency is: 64 Introduction to Perfusion and Diffusion Free diffusion I 60 ÇJ(U § c _o "êZ Restricted diffusion û 20 m 100r '/ 2 900 r ‘/2 ^[diffusion time] (ms'^) Figure 3.2 Diffusion behaviour of molecules in free and restricted media. For free diffusion, the diffusion distance 65 Introduction to Perfusion and Diffusion (0 = '^ = ')BQ+yG^z (3.19) where y is the gyromagnetic ratio (see chapter 2). The phase accumulated by the transverse magnetisation of spins at any location r in the presence of any gradient G over a time interval t will then be ^ ^ ^ = ^0 + y j/G • r)df (3.20) where (])o is the phase accumulated by spins at location r = 0. Spins moving in the presence of a magnetic field gradient (or any field gradient inhomogeneity) have the phase of their transverse magnetisation shifted compared to that of static spins. This phase shift results from changes in the magnetic field, and the associated frequency, seen with spins that translate along the direction of the field gradient. In the situation where many molecules are moving with different velocities, the sum of the phase shifts results in destructive interference of the MR signal and an associated loss in signal amplitude. 3.6.2 Spin echo and constant gradient The effects of molecular diffusion have been studied since the early days of NMR (e.g. see (Hahn, 1950)). Because the probability distribution of diffusion displacements has a Gaussian shape, the attenuation of the spin echo has an exponential dependence: S = q Sexp(-6D) (3.21) D is the diffusion coefficient and b is a factor that depends on the magnetic field gradients. If a constant gradient G is applied during the echo delay TE of a spin echo sequence, one has b = y^G^TE^In (3.22) and the echo signal is 66 Introduction to Perfusion and Diffusion s = s, (N, T, )exp(- TE/T^ )exp(- fG ^T E ^D ln) (3.23) where N refers to spin density. Although b depends on the square of G and the cube of TE, diffusion effects can only be observed with strong gradients and/or quite long diffusion measurement times, since D is generally small in biological tissue. 3.6.3 Pulsed gradients and Stejskal-Tanner sequence A significant improvement in diffusion measurements using a single spin echo was introduced by Stejskal and Tanner (Stejskal and Tanner, 1965). By using very large but short gradient pulses placed on each side of the 180° pulse of the spin echo sequence, which are balanced and therefore have no effect on static spins, accurate measurements of low diffusion can be made. In the Stejskal-Tanner sequence the expression for b becomes: b = y^G^8\^-5|^) (3.24) where Ô is the duration of each gradient pulse and A is the time interval separating their onset (see figure 3.3). The Stejskal-Tanner sequence offers the following advantage: when 0 « A , the time during which the diffusion effect forms is exactly known and is controllable independently of TE. The diffusion measurement time in this sequence is A - 6/3 and can be made variable. This is particularly useful for restricted diffusion studies in which the diffusion time is a critical parameter. 3.6.4 Diffusion imaging The computation of diffusion images, i.e. maps where the diffusion coefficient is displayed for each pixel, is possible by using two or more MRI sequences that are differently sensitised (‘weighted’) to diffusion but otherwise identical (same T] and T 2 67 Introduction to Perfusion and Diffusion dependence). For a typical 2DFT spin echo imaging sequence that contains multiple but low-amplitude gradient pulses, the b factor of the imaging gradients remains low (typically less than Is/mm^) so that the diffusion effect is completely negligible (for D = 2.2 X 10'^ mm^/s the attenuation is less than 1%). To increase the sensitivity of the imaging sequence to diffusion, one must incorporate additional gradient pulses in the sequence (see figure 3.3). These gradients can be applied along any axis. The use of multiple gradient pulses in an imaging sequence necessitates recalculation of the expression for b, taking into account the effect of all the gradient pulses. A general expression is: ^ = Jo (3.25a) with k{t)=yjQG{t')dt' (3.25b) where G(t') is replaced by -G(t') for pulses occurring after the 180° pulse at TE/2. For instance, in the case of two images Si and Sq obtained with gradient factors bi and bo, the diffusion coefficient D can be determined in each pixel from the relative signal intensities So(x,y,z) and Si(x,y,z) by rearranging equation (3.21): D{x, y, z) = ln[A(x, y, z)]/{b^ - ) (3.26a) with A{x,y,z)= SQ{x,y,z)/S^{x,y,z) (3.26b) Diffusion coefficients can also be determined from more than two images obtained with different known b values by fitting the signal attenuation with equation (3.21). 68 Introduction to Perfusion and Diffusion Echo 180 ' RF Slice-select Read Phase encode Figure 3.3 2D-FT spin echo diffusion-weighted imaging sequence. Sensitisation to diffusion is obtained by inserting a pair of Stejskal-Tanner gradients, shown here along the read axis. By changing the amplitude (G) of these gradients, one can modulate the degree of diffusion-weighting of the echo. Diffusion maps are directly obtainable from the resulting set of images. 69 Introduction to Perfusion and Diffusion 3.7 Diffusion MRi and cerebrai ischaemia The introduction of diffusion-weighted (DW) MRI has had a major impact on the study and diagnosis of a number of cerebral dysfunctions, in particular cerebral ischaemia. Moseley et ai (Moseley et ai, 1990) were the first to demonstrate that ischaemic tissue resulting from large vessel occlusion in the cat brain could be highlighted by DW imaging (DWI). The ischaemic tissue appeared relatively hyperintense at the earliest measurement (45 minutes) following the induction of ischaemia, whilst conventional imaging techniques (Ti- and T%-weighted) failed to demonstrate any significant tissue damage up to 2-3 hours after occlusion. The precise mechanisms responsible for the changes seen with DWI during cerebral ischaemia and related pathologies remain uncertain, but despite this the capability of DWI to delineate ischaemic tissue in the acute stage has tremendous potential for monitoring therapy. 3.7.1 Potential mechanism for DWI changes It is established that the severity of cerebral ischaemia is critically dependent on the degree of perfusion deficit. As the CBF falls the brain compensates by increasing oxygen and glucose extraction. With a further reduction in flow these physiological compensatory mechanisms are insufficient to support neuronal electrical activity, as indicated by a suppression in neuronal activity, until a critical threshold of CBF is reached below which adeno-triphosphate (ATP) depletion results in a disruption of the actively maintained cellular ion homeostasis. Large amounts of intracellular potassium cross into the extracellular space, while sodium and osmotically obliged water move into the cell, resulting in cell swelling (a stage referred to as cytotoxic oedema). In a model of global ischaemia produced by occlusion of the common carotid arteries in the gerbil (see chapter 7 0 Introduction to Perfusion and Diffusion 4), Busza et al (Busza et al, 1992) were able to demonstrate that DW image signal enhancement only occurred when the cerebral blood flow fell below 15-20 ml/lOOg/min. This is similar to the flow threshold for the maintenance of tissue high energy metabolites. This and various other studies suggest that the DW imaging changes are a consequence of the redistribution of tissue water and closely associated with energy failure. 3.7.2 Diffusion-weighted imaging and the therapeutic window The notion of a therapeutic window arose from studies in which the size of the infarct which develops in transient ischaemia was compared with measurements made after permanent occlusion. It was shown that infarct size could be markedly reduced if the blood flow were restored after brief periods of focal ischaemia. This therapeutic window can be regarded as the time during which ischaemic tissue may be salvaged with appropriate physiological or pharmacological intervention. It is known that a reversal of the impending infarction can only be achieved within a limited period; in the case of focal ischaemia, for example, irreversible damage occurs within 2-4 hours of stroke onset. Conventional histopathological techniques for defining the extent of infarction are restricting not only by their invasive nature but also because long survival times are required (24-48 hours) for full morphological expression. Diffusion-weighted imaging provides a non-invasive and immediate alternative. 71 Non-invasive quantitation of cerebral perfusion using FAIR MRI 4 Non-invasive quantitation of cerebrai perfusion using FAIR MRI______ 4.1 Introduction The aims of this project were to use a FAIR based perfusion imaging technique to give reliable and accurate values of cerebral blood flow in the gerbil brain. The motivation for this was to be able to use FAIR imaging to monitor the time course of perfusion changes in animal models of cerebral ischaemia. In order to achieve this I have: • measured the relationship of the difference between non-selective inversion recovery (nsIR) and slice-selective inversion recovery (ssIR) images and inversion time (TI). This has been shown to improve the quantitation of flow compared to using a single TI time, since it is possible to account for the differences in tissue and blood Ti and transit time effects. • developed a method to increase the time efficiency of the FAIR technique by adding a global saturation pulse to the sequence which enables it to be run at a reduced repetition time without compromising the accuracy of the flow measurement. In addition, this method potentially offers a way of measuring blood water Ti directly in vivo, thereby completely removing any errors introduced by assuming a literature value. • used improved definition adiabatic RF pulses to minimise the transit time delay between spin inversion and the first exchange of labelled blood water with tissue in the slice of interest. I have used adiabatic Frequency Offset Corrected Inversion (FOCI) pulses (Ordidge et ai, 1997) to achieve this, both for the inversion tagging pulse and also as the 180° refocusing pulse in the EPI imaging section of the sequence. • applied the method to a gerbil model of transient forebrain ischaemia and reperfusion. 72 Non-invasive quantitation of cerebral perfusion using FAIR MRI 4.2 Demonstrating the basic fiow sensitivity of FAiR A pulse sequence diagram for the FAIR experiment is shown in figure 4.1. To verify the validity of subtracting a nsIR image from a ssIR image to obtain flow-related information, experiments were performed on a linear flow phantom. The phantom consisted of a long plastic tube which was filled with water and connected at one end to a syringe pump. As with all the experiments described in this chapter, images were acquired on a 2.35T horizontal bore magnet using a slotted-tube resonator RF transmitter coil. Spin echo echo planar imaging (SE-EPI) was used to acquire images in a single shot (TE=35ms, TR=20 seconds for full longitudinal relaxation). A section of the flow phantom was placed inside the RF coil adjacent to a tube containing static water which was used as a reference. The rate of flow of water through the flow phantom was varied between 0.0 and 3.2 mm/s. These linear flow rates were calculated by dividing the volumetric flow rates provided by the syringe pump by the cross sectional area of the flow phantom tube. An inversion time (TI) of 3 seconds was used, which was approximately equal to the measured Ti of static water. An adiabatic inversion pulse (t-shape FOCI from (Ordidge et ai, 1997)) was used to perform both the slice-selective and global inversions. The image slice thickness was 4mm and the slice-selective inversion slice thickness was chosen to be 10mm to ensure the imaging slice was completely contained within the inversion slice (see section 4.5 for further discussion of this point). The results of this experiment are shown in the graph in figure 4.2, and can be separated into three main sections. The first section ranges from flow rates of 0 to approximately 0.5 mm/s, where the subtraction for both the static and the flow phantom is zero. This insensitivity to slow flow can be explained in terms of the ratio of slice thicknesses used for the inversion and imaging slices. A gap of approximately 3mm exists between the edges of the image slice and the inversion slice (assuming perfect profiles), and therefore if a 3 second inversion time is used one would 73 Non-invasive quantitation of cerebral perfusion using FAIR MRI INVERSION 90° 180 ° RF slice interleaved ss/ns IR * read/phase EPI acquisition X4 pre-saturation for reduced TR FAIR Figure 4.1 Pulse sequence diagram for the FAIR experiment, t is the inter-experiment delay time; TI is the inversion time. Spoiler and crusher gradients are shown in grey 900 T 800 - 700 - 600 - 500 + Flow ing w ater 400 X Static w ater 300 200 100 - 100 0.5 3.5 Flow (mm per sec) Figure 4.2 Difference between the ssIR and nsIR images of a flowing and static water phantom for different flow rates of the flow phantom (x-axis values refer only to the flow phantom; the corresponding static water points represent measurements acquired at the same time) 74 Non-invasive quantitation of cerebral perfusion using FAIR MRI expect a minimum velocity of 1 mm/s to be required in order for a difference between the nsIR and ssIR images to be observed. Assuming laminar flow along the tube, for an average flow rate of 0.5 mm/s the fastest water will be flowing at approximately Imm/s, and thus begin to cause a difference between nsIR and ssIR signal intensity, as observed. The second section of the graph (flow rates 0.5 to 1.5 mm/s) is the linear rise of signal intensity difference with flow rate which one would expect. Finally, the third section of the graph (flow rates above 1.5 mm/s) shows that there a limit to the maximum flow rate that can be measured using this approach, as the signal intensity difference levels off. This can be explained by the fact that once uninverted water has fully ‘washed out’ all the inverted water in the ssIR imaging slice, further enhancement of ssIR signal intensity is not possible and therefore the difference between the ssIR and nsIR images will remain constant. Following the validation of flow sensitivity on a linear flow phantom, the FAIR sequence was tested in vivo on an adult male Mongolian gerbil. The gerbil was anaesthetised with a mixture of 1.5% halothane and 0.41/min of oxygen and allowed to breathe spontaneously. Images were acquired using the volume transmitter coil and a separate 3cm diameter surface coil as the receiver, decoupled as described in (Bendall et al, 1986; Styles, 1988). The imaging slice thickness was 4mm, the inversion slice thickness was 8mm (t-shape FOCI inversion pulse from (Ordidge et al, 1997)), the inversion time was 1300ms and the time between image acquisition and the next inversion was 7500ms to allow full longitudinal relaxation. SE-EPI was used for image acquisition, and 30 nsIR and ssIR image pairs were acquired in an interleaved manner and averaged to produce the images shown in figure 4.3. Figure 4.3a shows the nsIR image and can be used as an anatomical reference for the image shown in figure 4.3b which shows the ssIR - nsIR subtraction 75 Non-invasive quantitation of cerebral perfusion using FAIR MRI (a) (b) (c) Figure 4.3 The result of subtracting a nsIR image from a ssIR image of the gerbil brain, (a) the nsIR image (b) the ssIR - nsIR (FAIR) image of the alive gerbil (c) the same image when the gerbil is dead. The signal intensity in (b) is proportional to cerebral blood flow. 76 Non-invasive quantitation of cerebral perfusion using FAIR MRI image (N.B. the images in figure 4.3a and 4.3b have been grey scaled differently, since the difference signal is very much smaller than the base image signal). It is immediately apparent that the difference image contains signal in areas corresponding to brain tissue and blood vessels, and that image contrast is visible between different regions of the brain. On death (figure 4.3c), the difference signal disappears, indicating that the image shown in figure 4.2b is related directly to cerebral perfusion. However, the magnitude of the difference signal is also dependent on several other factors, such as tissue spin density and Ti. Quantification of cerebral blood flow requires a more sophisticated approach, which is described in the next section. 4.3 Perfusion quantitation using the standard FAiR T, modei Calamante et al. (Calamante et al, 1996) and Kwong et al (Kwong et a l, 1995) have shown that incorporation of a flow component into the Bloch equations leads to an expected difference of magnetisation between the nsIR and ssIR images equal to: / \ / \ / \ f - g-'/ ] ^ (4.1) 1 1 Tla T lapp where Oo is the degree of inversion of the adiabatic inversion pulse (cxo = 1 for a perfect inversion). Mo is the equilibrium magnetisation per unit mass of tissue, f is perfusion, X is the bloodibrain partition coefficient which is assumed in this thesis to have a constant value of 0.9ml/g (Herscovitch and Raichle, 1985), Tia is the longitudinal relaxation time of blood water, and Tiapp is defined as: 77 Non-invasive quantitation of cerebral perfusion using FAIR MRI T, X where T% is the intrinsic tissue longitudinal relaxation time. Equation (4.1) can be simplified under the assumptions that Ti « Tia and t.(f/l) « 1 to give the equation used by Kim (Kim, 1995) Since CBF is on the order of 0.01 ml/g/sec, X is 0.9ml/g, and the inversion time used will be ~1 sec, the latter assumption is valid. However, there is evidence that the T fs of blood and tissue can be sufficiently different to make the former assumption unjustified, especially in white matter brain tissue. For example, if we assume grey and white matter to have Ti values of 0.9s and 0.5s respectively and the Ti of blood to be 1.2s (typical values at 1.5T), the error in the calculated flow introduced by assuming equal Ti values are 20% and 100% for grey and white matter (Calamante et a l, 1996). Therefore, in this thesis I have based all calculations on the full model defined by equation (4.1), and obtained data at a range of inversion times to calculate values of flow. An example of a pair of nsIR and ssIR image data sets is shown in figure 4.4. In order to be able to fit experimental data to equation (4.1), images were collected over the range of TI values [200ms, 400ms, 700ms, 1000ms, 1300ms, 2000ms, 4000ms], as shown in the figure. The maximum difference between ssIR and nsIR images occurs when TI = Ti, which is approximately 1200-1300ms in grey matter in the gerbil brain at 2.35T (measured using a nsIR data set). The TI range stated should therefore cover both the rise and fall of the biexponential curve. Images were acquired with a spin echo single-shot blipped echo planar imaging (EPI) sequence using trapezoidal read gradients and an acquisition bandwidth of 200kHz. For these studies, 5 lobe sine RF pulses with 3kHz 78 ssIR images: nsIR images: TI (ms): Figure 4.4 Inversion recovery images of the gerbil brain at various different inversion times (TI) following slice-selective (ssIR) and global (nsIR) inversions. Non-invasive quantitation of cerebral perfusion using FAIR MRI bandwidth were used to produce slice selective 90° and 180° pulses. The imaging slice thickness was 2.3mm and a t-shape FOCI pulse was used to give an inversion slice of 6mm width. This inversion to imaging slice ratio was shown to give a good zero subtraction on dead animals and on static phantoms (see section 4.5). A bipolar crusher gradient with a b value (Le Bihan and Turner, 1992) of 5 s/mm^ was applied to crush signal from intravascular spins (see section 4.5). To give a reasonable signal to noise ratio (SNR) for the subtractions 20 acquisitions were averaged, which resulted in a total imaging time of just over 40 minutes. Fitting of the data was done via a two step process. First the ssIR data were taken and a 3-parameter fit was performed for Mq, Oq and Tjapp using the equation (Calamante et al, 1996): (4,4) The values for these parameters were then used in the biexponential equation (4.1) to fit for flow. Equation (4.1) also contains another variable: Tia, the blood water longitudinal relaxation time. It is therefore necessary to either measure, assume a value for, or fit for Tia. In this case, a constant value of 1500ms was assumed for Tia, based on extrapolation of data obtained at other field strengths (Schwarzbauer et a l, 1996; Tadamura et al, 1997). However, attempts were made to measure Tia directly in vivo and are described later in this chapter. The maps of Tiapp and CBF that result from applying this fitting procedure to the data shown in figure 4.4 are displayed in figure 4.5. Tiapp is reasonably constant because the gerbil brain consists mainly of grey matter with very little white matter, but contrast can be seen between the brain tissue and the ventricles in the centre of the brain, which have elevated Tiapp values. The CBF map shows contrast which is dependent on regional differences in cerebral perfusion. Also shown in figure 4.5 are examples of the 80 Non-invasive quantitation of cerebrai perfusion using FAIR MRI ■ Left cortex 1 00- ‘ Right cortex 75- o Left striatum Tiapp map Right striatum < 50- 25- 1 1 1 CBF map 0 1000 2000 3000 4000 5000 TI (ms) Left cortex Right cortex Left striatum Right striatum « 0 0.943 0.947 0.942 0.944 M o 2804 2649 2703 2922 F 177.6 158.6 115.1 121.0 Tlapp 1251 1278 1199 1172 T , a 1500 1500 1500 1500 Std. Error F 7.376 15.93 6.332 5.108 Goodness of Fit Degrees of Freedom 6 6 6 6 R2 0.9374 0.7924 0.9000 0.9235 Figure 4.5 Calculation of CBF in the gerbil brain by fitting the difference in tissue magnetisation following selective and non-selective inversions (AM) at various inversion times (TI) to equation (4.1). 81 Non-invasive quantitation of cerebral perfusion using FAIR MRI biexponential fits from four regions of interest in the gerbil brain. It can be seen that the data points correspond closely to the fit lines, confirming the validity of the quantification model. A point to note is that for all the data sets the last point {i.e. the subtraction of the image pair acquired at TI=4000ms) is below the fit line. A physical reason exists for this behaviour, and will be examined in section 4.4. Cortical flow is higher than that found in the striatal areas, and the values correlate well with those measured in the gerbil brain using other techniques (Kato et al, 1990; van Uitert and Levy, 1978). I therefore conclude that FAIR imaging at multiple TI points offers an accurate method for non- invasive in vivo determination of cerebral blood flow at normal levels. 4.4 Increasing the time efficiency of FAiR perfusion measurements All of the above analysis requires that sufficient time is left between IR experiments to allow full longitudinal relaxation of the spin system. However, if the intention is to use the sequence to follow a time course of changing perfusion, it would be advantageous to optimise the sequence to make it as time efficient as possible. A reduced repetition time version of the FAIR sequence has been used by Kim and Tsekos (Kim and Tsekos, 1997a), and based on a simple analysis leads to the equation: / f \ I A M = M q \ X j where TR is defined as the time between successive inversion pulses, i.e. the sum of the inversion time TI and the inter-experiment delay time x (assuming the image acquisition to be negligible). As with equation (4.3), this equation is derived making various simplifying assumptions. These include equality of tissue and blood Ti, a perfectly 82 Non-invasive quantitation of cerebral perfusion using FAIR MRI efficient inversion, and fully flow-enhanced relaxation during the inter-experiment delay. This latter assumption requires that all blood water entering the imaging slice following the acquisition of both the ssIR and nsIR images is in its fully relaxed equilibrium state. This is not true immediately after the nsIR image acquisition, at which point the blood water will still be relaxing from the inversion, and also may not be true following the ssIR image acquisition if the TR is sufficiently short. In fact, without making the simplifying assumptions described above, it can be shown (see Appendix) that the behaviour of AM is a complicated function of TR, Tja,T], TI, and /w hich reaches a steady state value after the application of a series of interleaved nsIR and ssIR acquisitions given by: y J 1_ LV T T la p p ■* la (4.6) X(TR) is given by the expression: = (4.7) n=0 and N is the total number of non-selective inversion pulses that have been applied prior to the acquisition of the nsIR and ssIR pair that are subtracted to give AM. X(TR) is a series which tends towards a constant value for typical experimental parameters when A > 4, and so practical implementation of reduced repetition time FAIR would require a set of 4 dummy scans to be acquired before data acquisition could begin. The difference between the expected behaviour of AM with inversion time for equations (4.5) and (4.6) is shown in figure 4.6. In this simulation, I have used the following typical values for physical constants and sequence parameters: flow =150 ml/lOOg/min, tissue Ti = 1.2 s, blood T% = 1.5 s, (Xo = 0.94, inter-experiment time x = 1.5 s. Also shown is the difference between the two curves. It is apparent that the error introduced by making the assumptions of Kim 83 Non-invasive quantitation of cerebral perfusion using FAIR MR! 0.025 — Approximate equation — Exact equation 0.02 (steady state) g 0.015 0.005 0 0 1 2 3 4 5 TI (s) 45 Difference (Exact-Approx)/Exact oo> c 2 10 - 0 1 2 3 4 5 Tl(s) Figure 4.6 Comparison between approximate (equation 4.5) and exact (equation 4.6) reduced TR FAIR (x= 1500ms) 8 4 Non-invasive quantitation of cerebral perfusion using FAIR MRI and Tsekos is dependent on the inversion time used, but will always result in an overestimation of the true flow value. It is therefore inappropriate to apply equation (4.5) to quantify flow when using reduced repetition time FAIR. However, flow quantitation based on equation (4.6) has two main drawbacks. First, it is necessary to use a set of dummy scans prior to data acquisition which reduces the time efficiency of the sequence (though for most time course studies would not present a major limitation for the technique). Second, the form of equation (4.6) is rather complicated and fitting experimental data to it in order to obtain a value for CBF would require many ssIR and nsIR image pairs at different TI points in order to achieve a good degree of accuracy. This would in turn increase the total acquisition time of the sequence, thus limiting its effective time efficiency. My aim was therefore to develop a modification of the FAIR sequence which could be run in such a way as to benefit from an improved signal to noise per unit time compared to the full relaxation approach and also to ensure that this method was simply and accurately quantifiable. 4.4.1 Using a global pre-saturation pulse with FAIR The main problem with merely reducing the repetition time of the standard FAIR experiment is that, as alluded to above, the tissue magnetisation in the imaging slice will be different when the non-selective and slice-selective inversion pulses are applied. This is due to the different apparent T] relaxation during the repetition time delay in the two experiments. The ns/sslR image difference will be dependent on the difference in initial states in addition to flow effects. A way to eliminate this problem is to apply a global saturation pulse immediately before the inter-experiment delay time that precedes both experiments. In this way, we ensure that relaxation during the T period is the same for both experiments and so any difference in magnetisation which arises in the ssIR and 85 Non-invasive quantitation of cerebral perfusion using FAIR MRI nsIR subtraction is purely flow-related. Calculation of the expected difference in magnetisation when a global pre-saturation pulse is included in the sequence gives (see Appendix): r Ig-rz/r,, _ j X T T lapp ^ la This result is very similar to the long repetition time equation (4.1). The only modification is the final term which relates to the relaxation of blood following the saturation. This is more convenient than equation (4.6) for several reasons. First, it is a relatively simple biexponential which is modulated by the constant blood relaxation term. Fitting experimental data to this curve should be far simpler than fitting to equation (4.6), especially if the value of Tia is known. Also, inspection of equation (4.8) shows that the variable t appears only in the last term, which describes a monoexponential recovery of the full AM signal with a time constant equal to Tia. Measurement of the variation of AM as a function of t should therefore enable calculation of the in vivo blood water longitudinal relaxation time via a one parameter fit, which can then be used in the biexponential part of equation (4.8) to fit for flow. Finally, flow can be calculated from this equation by either measuring the magnetisation difference at a number of TI points or, if the parameters Mo, oco and tissue Ti are known, by solving the equation for flow using data collected at a single TI point. The expected variation of AM with inversion time is shown in figure 4.7. For this simulation, the sequence parameters and physical constants were the same as those described above to generate the graphs in figure 4.6. Also shown for comparison is the AM curve for reduced TR FAIR when a global saturation pulse is not included in the 86 Non-invasive quantitation of cerebral perfusion using FAIR MRI 0.025 Short TR FAIR (steady state) 0.02 Short TR FAIR with sat pulse 0.015 B 0.01 0.005 0 0 1 2 3 4 5 TI (s) Figure 4.7 Comparison of the expected FAIR signal difference with and without a pre saturation pulse in reduced TR FAIR (i=l500ms) 8 7 Non-invasive quantitation of cerebral perfusion using FAIR MRI sequence (equation (4.6)). It can be seen that the maximum value of AM when a pre- saturation pulse is used is less than when the sequence is employed in the conventional way. This therefore represents a loss in SNR for the proposed sequence compared to the original. However, given the significant simplification of flow quantitation provided by the inclusion of the pre-saturation pulse, this sequence was considered the better of the two options and used in subsequent experiments with reduced TR FAIR. 4.4.2 Optimisation of reduced TR FAIR sequence parameters The aim of developing a reduced TR FAIR technique was to apply it to a situation where perfusion is changing rapidly, namely a gerbil model of transient forebrain ischaemia followed by reperfusion. Rather than measuring the full biexponential flow curve defined by equation (4.8) at each time point, the idea was to measure the values of oco and tissue Mo and Tj using a long repetition time acquisition during the pre-occlusion control period and consider these values to be constant for the duration of the subsequent experiment. Quantitative perfusion measurements can then be made during the acute phases of the occlusion-reperfusion experiment by obtaining a ss/nsIR image pair at a single TI value and solving equation (4.8) for/. In order to obtain the maximum available signal to noise per unit time for the single TI measurements, optimisation of the sequence parameters TI and T was performed. This involves maximising the function: AM{TI,t)x4n; AM(n.T)_ I t,„,„ AM{TI,r) t,o ,a , Vr/+T 7(r/+T) The VNa factor is necessary since it is the SNR of the AM signal which is important, and this is proportional to the square root of the number of averages (Na). ttotai represents the total acquisition time, which is equal to (TI + x) multiplied by the number of averages 88 Non-invasive quantitation of cerebral perfusion using FAIR MRI (assuming the echo time is negligible). The final term in equation (4.9) was numerically maximised by allowing TI and x to be free parameters, using the expression for AM(TI, x) given by equation (4.8). The Mathematica (Wolfram Inc.) software package was used to perform this maximisation. Values of 1.3s and 1.5s were assumed for tissue and blood T% respectively and flow was assumed to be 120 ml/lOOg/min. The form of equation (4.9) as a function of TI and x is shown in figure 4.8. The maximum point on the 2-D surface occurs at TI = 1165ms and x = 2740ms, and these therefore represent the optimum values for the parameters. 4.4.3 Measuring Tia and perfusion using reduced TR FAIR As discussed in section 4.4.1, the use of reduced TR FAIR with a global pre-saturation pulse should enable the determination of both Tia (by measuring the variation of AM with X at a given TI and fitting to a monoexponential recovery from AM = 0 to AM = AM(x = oo)) and CBF (using equation (4.8)). Experiments were performed to measure these two variables in the gerbil brain using a spin echo IR-EPI sequence at 2.35T as described above. To measure Tia an inversion time of 1300ms was used and the inter-experiment time X was varied between 100ms and 4000ms. Cerebral perfusion was measured with reduced TR FAIR with a saturation pulse using the optimised values of 1165ms and 2740ms for TI and x respectively. The aim for the sequence was to have a time resolution of 3 minutes, and so with these sequence parameters 23 averages were obtained for both ssIR and nsIR acquisitions. A train of four adiabatic half-passage hyperbolic secant pulses, each followed by a crusher gradient to spoil transverse magnetisation, were used to ensure good global saturation (this was seen to reduce the signal from a phantom by -99.5%). In order to quantify flow from the pair of images, the values of T/, Oo and Mq 89 Non-invasive quantitation of cerebral perfusion using FAIR MRI 0.008 am /Vtr 0.006 0.004 Figure 4.8 FAIR difference signal per unit time as a function of inversion time (TI) and inter-experiment delay time x 9 0 Non-invasive quantitation of cerebral perfusion using FAIR MRI were taken from the fits of a long repetition time acquisition. This means that the flow measurement from the pair of short repetition time images is not truly self-contained, but since the acquisition of a range of TI points with the short repetition time sequence was not feasible within a 3 minute time period due to SNR limitations, this was deemed the most satisfactory approach. The flow value calculated from the long TR, multi-TI experiment was used to verify the equivalence of the reduced TR FAIR measurements. A set of five reduced TR FAIR images was acquired successively to evaluate the repeatability of the measurements. The result of the Tia experiment from a region of interest in the gerbil cerebral cortex is shown in figure 4.9. It can be seen that the data fit reasonably well to a monoexponential recovery and the value of Tia obtained from the fit is approximately 900ms. This value was used to quantify flow for the reduced TR, single TI FAIR subtraction images according to equation (4.8). The results of this quantitation procedure are shown in the second column in table 4.1 ; the first column shows the flow value obtained using the long repetition time approach. Compared to the values obtained using the full biexponential fit, the reduced TR FAIR images appear to overestimate CBF. Therefore, there exists a discrepancy between the two versions of the sequence which must be explained before reduced TR FAIR can be trusted to produce reliable values for cerebral blood flow. A clue to the source of this discrepancy comes from the Tia experiment. When compared to the values of the Ti of blood reported in the literature {e.g. see (Bryant et a l, 1990; Schwarzbauer et al, 1996)), 900ms is very low for Tia at 2.35T. By extrapolation of the literature values, one would expect a value of approximately 1500ms. Therefore it appears that the blood is recovering from the global saturation pulse more rapidly than 91 Non-invasive quantitation of cerebral perfusion using FAIR MRI 75i 50- < Right cortex 25- Left cortex 0 1000 2000 3000 4000 5000 X (ms) Left cortex Right cortex Mo 58.26 64.36 T , a 910.2 869.8 Std. Error Mo 4.543 3.019 T . a 198.5 116.2 R2 0.9614 0.9849 Figure 4.9 Measurement of the longitudinal relaxation time of of blood in vivo by varying the inter-experiment time T and using a global pre-saturation pulse in the FAIR experiment 9 2 Non-invasive quantitation of cerebral perfusion using FAIR MRI Full repetition time, Flow calculated using Flow calculated using multi-TI equation (4.8) equation (4.1) biexponential fit X = 2740ms, Tia = 900ms X > inflow time, Tia=1.5s Measure 1 227.2 166.3 Measure 2 242.3 177.2 Measure 3 181.0 242.3 177.2 Measure 4 244.8 179.0 Measure 5 257.4 188.2 Mean 181.0 242.8 ±10.7 177.6 + 7.8 Table 4-1 Comparison of measured flow values using long TR and reduced TR FAIR (ROI in cerebral cortex). Mean ± SD is given where appropriate. can be accounted for by relaxation alone, resulting in a shortened apparent Tia- The cause for this enhanced recovery rate could be a factor previously noted by Kim (Kim, 1995; Kim et al, 1997b) which is related to the size of the RF transmitter coil used to provide the global saturation or inversion pulses. If the transmitter coil is sufficiently short, the possibility exists that, for long TR FAIR, water which was outside the coil at the time of application of the non-selective inversion pulse (and which was therefore not inverted by the pulse) will reach the imaging slice during the inversion time. Evidently, for longer inversion times the chance of this situation occurring increases. The analysis presented thus far has assumed all so-called global pulses to be truly global le. to affect all spins within the system. If spins from outside the RF coil enter the imaging slice during the latter parts of the TI period, the difference between the nsIR and ssIR images will be less than predicted by the current model. Evidence for this ‘inflow’ effect has already been noted in section 4.3, where the AM values for the longest TI value (4000ms) were 93 Non-invasive quantitation of cerebral perfusion using FAIR MRI observed to lie consistently below the biexponential fit line. After inflow occurs, the signal difference due to perfusion decays with Ti according to the following equation: / f A L-ATi. _ ] -(7 7 -A y AM =2M qŒq T r------— y x e TI>^ (4.10) 1 1 T\app T la where A is the inflow time, which is defined as the time taken for a spin to travel from just outside the active volume of the transmitter coil to the imaging slice. The behaviour of AM up to the time that inflow occurs is as previously described by equation (4.1). When reduced TR FAIR with a global pre-saturation pulse is implemented, the situation becomes more complex. Inflow can now potentially occur during the inter-experiment delay time t and/or the inversion time TI. The possible situations that need to be considered are: 1) X is sufficiently long for inflow to occur during the repetition time delay and a) TI is less than the inflow time b) TI is greater than the inflow time 2) X is less than the inflow time and a) TI is sufficiently less than the inflow time so that (TI+x) < A Le. all the water that reaches the imaging slice during the inversion time was saturated by the pre saturation pulse and then inverted b) TI is less than the inflow time but (Tl-bx) > A i.e. a proportion of the water which reaches the slice during the inversion time was inverted but not saturated by the pre-saturation pulse c) TI is greater than the inflow time Visualisation of the second set of cases is facilitated by thinking in terms of different 9 4 Non-invasive quantitation of cerebral perfusion using FAIR MRI ‘zones’ of inflowing blood spins, as illustrated in figure 4.10. Following the pre-saturation pulse, fresh blood moves into the coil but does not reach the imaging slice (since x < A). If a non-selective inversion pulse is then applied, three zones of blood water spins will evolve. The inner zone consists of water which was within the coil when both the saturation and inversion pulses were applied. The middle zone consists of water which has flowed in from outside the coil during x and is therefore fully inverted by the non- selective inversion. The outer zone consists of water which flows in from outside the coil during the inversion time TI i.e. fully relaxed blood. The combination of the values of the sequence parameters x and TI and the inflow time A determines which zones of spins will arrive at the slice before image acquisition and therefore which of the situations 2) a) - c) is applicable. Conversion of the resulting AM signal to quantitative flow values is dependent on the appropriate situation (see Appendix), and therefore in order to properly quantify flow, knowledge of the inflow time is necessary. The presence of coil inflow means that the dependence of AM on x is no longer the simple relationship defined by equation (4.8). The relationship now follows a piece-wise pattern, with different sections of the curve corresponding to the different situations described above. Although the data shown in figure 4.9 appears to follow a mono-exponential recovery, the behaviour is in fact more complex, leading to misleading values if the curve is used to fit for Tia using equation (4.8). In order to determine reasonable values for Tia and A based on short TR FAIR measurements, two approaches were taken. Another set of FAIR subtractions with different inter-experiment delays was acquired on the gerbil brain, but this time more points were taken to enable more accurate definition of the curve. An inversion time of 1300ms was used, and this was assumed to be less than the inflow time. A 2-parameter fit for x and A to equations (A4.8) and (A4.5) (see 95 Non-invasive quantitation of cerebral perfusion using FAIR MRI Inflowing blood Imaging slice ► M„“(l-exp(-T/T,J) ttttttI I I I I I I I I I I I I I I I I I ! V V V V V V y V Y Transmitter (A-x) coil Figure 4.10 The state of blood magnetisation at the end of the inter-experiment delay in a reduced TR FAIR experiment with coil inflow effects. For the case shown, x < A. The inflowing blood magnetisation at the beginning of the subsequent inversion time is shown by the solid arrows for a slice selective inversion and by the dashed arrows for a non-selective inversion. 9 6 Non-invasive quantitation of cerebral perfusion using FAIR MRI Appendix) on data from a ROI drawn in the cerebral cortex was performed, and the results of this fit are shown in figure 4.1 la. The mean values for t and A thereby obtained were approximately 1500ms and 1700ms respectively, which are intuitively feasible and consistent with previously published values. However, due to the complexity of the equations defining the behaviour of AM with x and A, the 95% confidence intervals of the fitted variables are large. In order to verify the reliability of these values, a second approach for estimation was employed. In this approach, a monoexponential recovery curve was fitted to the data as before (see figure 4.9). A value for the ‘apparent’ Tia (Tia*) was determined from this fit. Next, simulated data sets of AM(x) were generated from equations (A4.5) to (A4.9), using the measured values for Tiapp,/, Mo and (Xo, assuming a value for Tia of 1500ms, and using a range of values for A between 1000ms and 2500ms. For each value of A, the resulting simulated data set was fitted to a monoexponential recovery curve and a value for Tia* was calculated. The correct value for A was estimated by comparing the Tia* values obtained from the simulated and experimental data sets. The A which resulted in the same Tia* for both data sets was assumed to be the correct value. Figure 4.11b shows the result of the experimental fit and the closest simulated data fit. The value of A for this closest fit was 1800ms. This is similar to the value obtained by doing the full piece-wise fit to the experimental data. Therefore, it was decided that values of A = 1800ms and Tia = 1500ms would be used where necessary in the equations for flow quantification. Returning to the single TI, reduced TR FAIR measurements described at the beginning of this section, it can be seen that for the experimental parameters used (TI= 1165ms, x=2740ms), the situation at the time of image acquisition is that described above by 1 a) and therefore the applicable equation is (A4.5) (see Appendix). When this equation is 97 Non-invasive quantitation of cerebral perfusion using FAIR MRI A (ms) 1702 (a) Mo 1324 200n T 1 (ms) 1300 T,app (ms) 1260 T|a (ms) 1502 «0 0.94 < 100- Std. Error A 237.3 Mo 5339 T,a 1084 1000 2000 3000 4000 5000 6000 7000 T (ms) (b) 200 0 experimental data experimental data fit 150------— simulated data simulated data fit <1 100 0 1000 2000 3000 4000 5000 6000 7000 X (ms) Figure 4.11 Determination of the coil inflow time using reduced TR FAIR, (a) fitting AM piecewise to the equations shown in the appendix and (b) comparing the monoexponential fits of experimental and simulated data. The case shown is the closest match to the experimental data fit and corresponded to T,g = 1500ms and A 1800ms 98 Non-invasive quantitation of cerebral perfusion using FAIR MRI used to quantify flow, the results are as shown in the third column of table 4.1. It can be seen that these values correspond much more closely to the long TR, full biexponential fitting procedure. In fact, inspection of equation (A4.5) shows that with the above choice of experimental parameters (TI One further point to note is that, despite the fact that the recovery time is long enough for inflow to occur, it is still necessary to apply the global saturation pulse at the beginning of the recovery period. By doing this, one ensures that relaxation throughout the recovery period (i.e. before and after inflow occurs) is the same for both IR experiments. Only blood that enters the imaging slice during the inversion time will then contribute to the perfusion difference, making quantitation relatively simple. An alternative approach to the measurement of Tia is to withdraw a blood sample and perform the measurement ex vivo (see, for example, (Schwarzbauer et a l, 1996)). Although this may seem the simplest and most obvious approach, several practical factors need to be taken into account. First, the blood sample needs to kept very close to body temperature (~37°C) for the duration of the measurement. Second, the blood must be prevented from clotting by the addition of an anticoagulant such as heparin. The effect of the presence of heparin on Tia is not known. Third, when blood is taken ex vivo and placed in a specimen tube, the constituent molecules have a tendency to separate out due 99 Non-invasive quantitation of cerebral perfusion using FAIR MRI to gravity, thus making the measurement unreliable. Finally, it is difficult to control the oxygen saturation of the haemoglobin in the blood once it has been withdrawn. Although I did attempt to perform measurements of Tia vivo, the above mentioned factors resulted in the values being irreproducible and unreliable. A final method for the measurement of Tia which has been described elsewhere is to place the imaging slice in such a position that a major blood vessel is visible in the image. A non-selective IR sequence is then used, and Tia is fitted from a region of interest containing only signal from blood. This approach was not attempted here due the small size of gerbil arteries compared to the image resolution and the likelihood of blood-tissue partial volume effects. In summary, a new method for quantitative perfusion imaging using a modification of the FAIR technique with a reduced repetition time and a global pre-saturation pulse has been proposed. The accuracy of the technique has been verified by comparison with the less time efficient full relaxation multi-TI FAIR approach. The reduced TR technique also offers the potential to measure the in vivo longitudinal relaxation time of blood, which is necessary for flow quantification, in a relatively straightforward manner. However, practical limitations in the experiments presented here have complicated this measurement. It would be interesting to repeat the experiments described above using a full-body RF transmitter coil. This would eliminate the inflow of fresh blood during either the recovery or inversion times, and make the experimental situation the same as assumed in the original model which leads to equation (4.8). Unfortunately, such a coil was not available in our laboratory when these experiments were carried out. Nevertheless, a detailed analysis of the experimental situation allowed quantitative CBF maps to be acquired with a time resolution of three minutes, thus making the sequence applicable to 100 Non-invasive quantitation of cerebral perfusion using FAIR MRI the study of the dynamic changes in cerebral perfusion which occur during transient ischaemia followed by reperfusion (see Section 4.6). 4.5 Transit time and siice profiie effects I will now deal with another important issue which determines the accuracy of the perfusion measurement obtained using FAIR. In order for the signal in the FAIR subtraction image to be related directly to perfusion, it is important that the signal contribution from static tissue in both the nsIR and ssIR images is exactly the same. Since the inversion time for both is the identical, one would expect this always to be the case. There are, however, some practical considerations that need to be taken into account, the most important of which is the shape of the inversion slice profile compared to the imaging slice profile. In both the slice selective and global inversion experiments, an adiabatic RF pulse is used to produce efficient spin inversion. Adiabatic pulses are used in preference to standard 180° RF pulses because they are more efficient (i.e. oto is closer to 1) due to their reduced sensitivity to inhomogeneities in the Bi RF field. The most frequently used adiabatic inversion pulse is the hyperbolic secant (sech) pulse, which can be applied on its own to produce a global inversion, or in the presence of a gradient to produce a slice-selective inversion. The slice band of spins affected by a sech inversion pulse is well defined by the adiabatic condition, and so the inversion slice profile is quite sharp. However, spins at the edge of the inversion slice are on the limit between fulfilling and not fulfilling the adiabatic condition, resulting in a certain degree of slope at the edges of the slice (see figure 4.12). To ensure that all spins in the imaging slice are equally inverted in both the 101 Non-invasive quantitation of cerebral perfusion using FAIR MRI Selective IR Non-selective IR Inversion profiles: 0 — -M, Image slice profiles: Figure 4.12 Slice thickness requirements for zero static subtraction in FAIR 1 02 Non-invasive quantitation of cerebral perfusion using FAIR MRI slice selective and non-selective cases, it is therefore necessary to make the inversion slice slightly wider than the imaging slice, as shown in figure 4.12. If this is not done, signal from the edges of the slice will contaminate the slice selective image and cause a non-zero subtraction for static spins. Typical inversion slice thicknesses which have been used in FAIR have been approximately three times that of the imaging slice thickness (e.g. (Kim, 1995)). The need for the inversion slice to be significantly wider than the imaging slice can cause certain problems. The perfusion model described above assumes that the two slice thicknesses are identical, or equivalently that following the slice selective inversion, fully relaxed blood spins begin to flow into the imaging slice immediately. It is clear that if the imperfect inversion slice profile requires the inversion slice to be three times wider than the imaging slice, this assumption will not be valid. When a multi-slice approach is taken, where all the slices to be imaged must fit inside the inversion slab, the problem is exacerbated. The result is that a ‘transit time’ delay exists between the application of the inversion pulse and the initial inflow of fresh blood into the imaging slice, during which inverted or partially inverted blood enters the slice. Various attempts have been made to eliminate this problem. Wong et al (Wong et al, 1998) have introduced a set of sequences which make the perfusion measurement less sensitive to the transit time effect and potentially quantifiable from a single subtraction. In the most recent of these (QUIPSS II), the labelled blood is saturated at a time TIi after the inversion in both the selective and non-selective experiments, and therefore any subsequent blood flow does not contribute to a difference in magnetisation. The image is taken at a time TU after this saturation. In the ssIR case, a bolus of labelled blood of well-defined time width is created. As long as TU is longer than the longest transit time in the imaging slice, flow 103 Non-invasive quantitation of cerebral perfusion using FAIR MRI values calculated using this method should be transit time insensitive. However, the range and size of the transit times are never exactly known, particularly in regions of compromised flow, and so the timings of this sequence have to be derived empirically. Also, the inclusion of a delay before image acquisition causes the already small difference between ssIR and nsIR images to be further reduced. The sensitivity of the flow measurement is thus decreased. Another approach which can be used to account for the transit time effect is to incorporate it into the perfusion model. If one assumes that the effect consists of a period of time ôt following the slice selective inversion during which inverted blood enters the imaging slice, and after which fully relaxed blood enters (i.e. a wider but still perfectly square inversion profile), the flow equation becomes: AM = 0 t< 5t — 2M qCCq & (4.11) This again describes a biexponential curve, but one whose intercept is displaced from t=0 by Ôt and whose amplitude is attenuated by an amount related to Ôt. Experimental data can be fitted to this equation with ôt as a variable. The drawbacks of this approach are twofold. First, inclusion of another variable makes the numerical fitting procedure more difficult. Also, the basic assumption that the shape of the inversion slice profile is accurately represented by a square waveform is known not to be valid. The problem we face is entirely due to the fact that the hyperbolic secant pulse does not produce a sharp inversion profile, which is the reason the inversion slice needs to be widened. Therefore 104 Non-invasive quantitation of cerebral perfusion using FAIR MRI the above analysis can at best only offer limited, though still potentially useful, information. The third alternative for solving the transit time problem, and the approach I have adopted in the work presented here, is elimination of the problem by the use of improved RF pulses which have better slice definition. It has already been pointed out that the edges of the sech inversion pulse profile have a slope associated with them, and that the ideal pulse profile would consist of sharp, well-defined region of inversion. Ordidge et al (Ordidge et al, 1997) introduced a modification of the hyperbolic secant pulse (the Frequency Offset Corrected Inversion, or FOCI, pulse) which has the property of inverting a more sharply defined slice. The pulse is based on a sech waveform and works by increasing the slice selection gradient at the beginning and end of the pulse, which corresponds to the time when each edge of the slice is inverted. By doing this, one minimises the spatial region over which the sloping sides extend. The RF amplitude and frequency sweep also have to be scaled by the same multiplying factor as the slice select gradient, but since the gradient amplitude is the same as for the sech pulse at the centre, the RF power requirement remains unchanged. A comparison of the sech and a FOCI pulse waveforms (the t-shape from (Ordidge et al, 1997)) is shown in figure 4.13. Computer simulations and experimental data have demonstrated the improvement of the t-shape FOCI pulse slice definition over an equivalent sech pulse. Having improved the shape of the inversion pulse, it is necessary to examine the profile(s) of the imaging pulse(s). A standard sine pulse is generally used for spin excitation, and will be considered here. It is well known that the slice profile of a sine pulse is not the desired ‘top-hat’ function due to truncation. This results in side lobes of 105 Non-invasive quantitation of cerebral perfusion using FAIR MRI HS T-shape 8000 g 8000 5 6000 5 6000 — HS T-shape (i) ® 4000 ® 4000 i 2000 i 2000 oc 0.0 2.0 4.0 6.0 0.0 2.0 4.0 6.0 pulse tim e/m s pulse time /m s HS T-shape 50000 50000 30000 30000 10000 ë g- 10000 (ii) — HS T-shape ^ -loooox = ^ -10000 (o 0 2.0 4.0 6.0 4.0 6.0 -30000 -30000 -50000 -50000 pulse tim e/m s pulse time /m s HS T-shape 3000 3000 S 5 2000 g 2000 (iii) — MS 0> T-shape m '% 1000 4 € 1000 2 pulse tim e/m s pulse tim e/m s (a) sech (b) FOCI Figure 4.13 Comparison of the(a) hyperbolic secant and (b) t-shape FOCI RF inversion pulses. Row (i) shows the RF waveform amplitude modulation, row (ii) shows the frequency sweep during the pulse, and row (iii) shows the gradient waveform needed to produce a well-defined slice. 106 Non-invasive quantitation of cerebral perfusion using FAIR MRI excitation outside the slice of interest which are opposite in phase to the main excited slab. Since the edges of the imaging slice are as important in the FAIR experiment as the edges of the inversion slice, this may be expected to cause problems. A way to avoid this problem is to again use adiabatic RF pulses to achieve slice selection. If a non-selective 90° excitation pulse is applied, the slice of spins contributing to a spin echo can be selected using a pair of adiabatic sech pulses (Conolly et a l, 1991). A single sech pulse cannot be used as a refocusing pulse since spins at different positions through the slice are flipped at different times during the pulse, and so the amount of dephasing by the slice select gradient varies across the slice. The application of a second sech pulse undoes this phase incoherence across the slice and leads to the generation of a spin echo. The advantage of using a double sech (or indeed a double FOCI) refocusing pulse is that the slice profile of spins contributing to the spin echo is more like the ideal top-hat shape, and the side lobes associated with the sine pulse are eliminated. The hypothesis was that the combination of a FOCI inversion pulse followed by a non-selective 90° excitation and a slice-selective double FOCI refocusing pulse should provide the ideal combination for the FAIR experiment in terms of allowing the inversion and imaging slice thicknesses to be as similar as possible, thus minimising transit time effects. 4.5.1 Implementation of improved RF pulses The use of FOCI pulses to replace both the inversion and slice select imaging pulses in the FAIR experiment was investigated on a phantom. The main objective was to empirically determine the minimum inversion slice thickness that would give a zero subtraction on the static phantom for each RF pulse combination. The pulse combinations considered were: • sech inversion pulse followed by a slice selective 90° 5 lobe 3 kHz sine imaging pulse 107 Non-invasive quantitation of cerebral perfusion using FAIR MRI • t-shape FOCI inversion pulse followed by a slice selective 90° sine imaging pulse • sech inversion pulse followed by a slice selective 90°-180° sine imaging pulse combination • t-shape FOCI inversion pulse followed by a slice selective 90°-180° sine imaging pulse combination • t-shape FOCI inversion pulse followed by a non-selective 90° sine imaging pulse and a slice selective double t-shape FOCI refocusing pulse pair The parameters of the sech and FOCI pulses were: bandwidth = 1137Hz; p = 4.5; = 800s^; multiplying factor for FOCI = 5. The bandwidth was chosen based on the minimum slice thickness required (4mm) and the maximum gradient strength available on our system in the slice select direction (3.3 G/cm). The values for p and p were then optimised by numerical simulation of the Bloch equations (work carried out by a colleague, Gaby Pell, and detailed in his Ph.D. thesis). Experimental pulse profiles were obtained for all pulses. For the inversion pulses, a selective inversion pulse was followed by a spoiler to crush any residual transverse magnetisation and then a non-selective 90°- 180° was applied. The spin echo was collected under a read gradient which was applied in the same direction as the slice select gradient, and a slice profile was generated by Fourier transformation of the echo. Slice profiles of the imaging pulses were acquired in a similar manner, by removing the inversion pulse and making the required pulse slice-selective. The experimentally measured slice profiles of the imaging and inversion pulses are shown in figure 4.14. Figure 4.14a shows the profile of the 90° 3kHz sine pulse. A certain degree of sloping is evident at the edges of the main slice, and the truncation lobes are also readily observable. Figure 4.14b shows how the 90° and 180° pulses interact to form a slice profile which is considerably different to that from just a 90° pulse. The lobes are eliminated, but the width of the slice is narrower than desired. This is caused by the 108 Non-invasive quantitation of cerebral perfusion using FAIR MRI 4500 4500 4500 4000 4000 4000 3500 3500 3500 3000 3000 3000 - 2500 2500 2500 - 2000 - 2000 2000 1500 1500 1500 1000 1000 1000 500 500 500 4000 6000 -500 00004000 6000 80002000 10( 2000 4000 8000 10(POO -1000 J -500 -500 (a) (b) (c) 2500 2500 2000 2000 1500 1500 1000 1000 500 500 2000 600< 8000 10000 2000 1000 600( 8000 10000 -500 -500 -1000 -1000 -1500 -1500 -2000 -2000 - -2500 -2500 (d) (e) Figure 4.14 Comparison of slice profiles generated using (a) a 90° sine pulse, (b) a 90°- 180° sine pulse pair (both slice selective), (c) a non-selective 90° sine refocused with a double t-shape FOCI pulse pair, (d) a hyperbolic secant inversion pulse (e) a t-shape FOCI inversion pulse. Actual pulse profiles are shown in blue, and the corresponding ‘ideal’ pulse profiles are shown in pink for comparison 109 Non-invasive quantitation of cerebral perfusion using FAIR MRI sloping edges of the refocusing pulse which correspond to flip angles of less than 180° and thus produce less efficient spin refocusing. Figure 4.14c shows the slice profile of the double FOCI refocusing pulse (spin excitation caused by a non-selective 90° sine pulse), which has a much more sharply defined shape than either of the two preceding pulse combinations. Figure 4.14d and 4.14e compare the sech and t-shape FOCI inversion pulses respectively; as expected, the FOCI has the superior inversion pulse profile. In order to determine the minimum imaging:inversion slice thickness ratio, the imaging slice thickness was set at 4mm and the inversion slice was varied from 4mm to 12mm in steps of 0.25mm. A point was also taken with the inversion slice thickness of 50mm to ensure a good zero subtraction occurred at this extreme. Non-selective IR images were acquired interleaved with each selective IR image obtained. The Ti of the agar phantom was measured to be approximately 1000ms, and this value was used for TI. The inter experiment delay was 5 seconds. Image acquisition was performed using EPI with an echo time of 19ms for the gradient echo sequences, 35ms for the sine 90°-180° spin echo sequences and 66ms for the double FOCI spin echo sequence. These echo times are the minimum achievable for each sequence. The double FOCI sequence has a significantly longer echo time than the standard sequences due to the need for two adiabatic pulses to achieve spin refocusing. This has implications for the relative SNR obtained using each sequence which will be discussed in section 4.7. In these experiments, signal averaging from ten experiments was employed to increase signal to noise, and each experiment was repeated several times to confirm consistent results. The results of the experiment are shown in figure 4.15. Figure 4.15a shows the result for the sech and FOCI pulses when a 90° excitation pulse is used followed by a gradient echo EPI acquisition. An initial positive offset in the subtraction caused by overlap of the inversion and imaging slice 110 Non-invasive quantitation of cerebral perfusion using FAIR MRI (a) sech - 90 (GE-EPI) FOCI - 90 (GE-EPI) 9 7 5 3 1 ■1 40 50 -eo 3 Inv sith Inv sltti (b) sech-90 -180 (SE-EPI) FOCI-9 0 - 180 (SE-EPI) Inv dm FOCI - 90ns - FOCI pair (c) L Figure 4.15 Signal intensity difference of a static phantom as a function of inversion slice thickness for different RF pulse schemes (a) gradient echo (b) spin echo using sine pulses (c) spin echo using double FOCI pulse pair. Nominal image slice thickness was 4mm in all cases. Intensity differences are expressed as a percentage of the non-selective IR image intensity 11 Non-invasive quantitation of cerebral perfusion using FAIR MRI profiles becomes a significant negative undershoot of the signal. This is assumed to be due to the lobes of the 90° pulse generating negative signal (with respect to the main excited slab) from outside the inverted region in the ssIR acquisition, thus leading to less total signal in the ssIR image and a negative subtraction. The effect is more rapid for the FOCI pulse, reflecting the sharper pulse profile. When a 90°-180° imaging pulse combination is used (figure 4.15b), the negative undershoot disappears (because the lobes are removed by the 180° pulse) and only a positive offset is present which reflects the overlapping of the slice-selective inversion and imaging pulse profiles. As would be expected, the offset disappears more rapidly when the FOCI pulse is used because the actual inverted width is wider than for the sech. Figure 4.15c shows the result when a FOCI inversion pulse is used in combination with a double FOCI refocusing pulse. The initial overlap of slice profiles when the thicknesses are equal causes a positive subtraction which quickly reduces to zero as the inversion slice is widened. The first impression from figure 4.15 might be that the best pulse combination to use is the t-shape inversion with sine 90°-180° imaging pulses. However, it is important to consider the reduction in actual slice thickness which results when a slice-selective 90°-180° combination is used. A nominal slice thickness of 4mm corresponds to an actual slice of width -3mm, which means that as a fraction of the actual imaging slice thickness the double FOCI pulse is better. An inversion to imaging slice ratio of 7:4 can be reliably used in this case, which brings the practical experiment closer to the theoretical ideal, and should therefore reduce transit time related problems. 112 Non-invasive quantitation of cerebral perfusion using FAIR MRI 4.5.2 In vivo measurements of transit time and CBF: comparison of standard and improved RF pulse combinations In order to demonstrate the benefits of using improved RF pulses for the measurement of tissue perfusion, experiments were performed on the gerbil brain at 2.35T. Three of the sequences described above were compared: • sech inversion pulse with a sine 90°-180° SE-EPI image acquisition (‘standard’ sequence) • t-shape FOCI inversion pulse with a sine 90°-180° SE-EPI image acquisition • t-shape FOCI inversion pulse with a non-selective sine 90° pulse and a slice selective double t-shape FOCI refocusing pulse pair The image slice thickness was set at 4mm and the inversion slice thickness was chosen based on the results of the phantom experiment described in the previous section. The minimum inversion slice thickness which produced a zero subtraction on the static phantom was used for each case. From figure 4.15, this meant that for sequence 1 the inversion slice thickness was 9mm, for sequence 2 it was 5.5mm and for sequence 3 it was 7mm. The experiment was split into two main sections. During the first part of the experiment, six ss/nsIR data sets were acquired. These consisted of sequences 1-3 described above acquired both with and without bipolar crusher gradients between the 90° and 180° pulses of the EPI imaging sequence. The purpose of these crusher gradients is to eliminate the signal from intravascular water (since the pseudo-random incoherent motion of this compartment causes the signal to be rapidly attenuated when diffusion-weighting gradients are applied). Since the equations for flow quantification assume all signal to come only from the tissue, it is important to eliminate the intravascular signal (Ye et al., 113 Non-invasive quantitation of cerebral perfusion using FAIR MRI 1997). Calculation of flow based on biexponential data sets acquired with and without the crusher gradients should allow estimation of the error introduced by not eliminating the blood signal. The b value of the bipolar gradients was ~5s/mm^ in all three orthogonal directions. The inversion times used for the ss/nsIR data sets were 50ms, 200ms, 400ms, 600ms, 1000ms, 1300ms and 2000ms and the inter-experiment delay was 6 seconds to allow full relaxation. Single TI reduced TR FAIR images (TI= 1300ms, x=2500ms, pre saturation pulse included) were acquired between the six ss/nsIR acquisitions to verify that a constant level of flow was maintained throughout this period. The second section of the experiment began with a four minute period of forebrain ischaemia, induced by ligation of the common carotid arteries. It is known (see section 4.6) that a period of sustained hypoperfusion follows transient global ischaemia in the gerbil. During this period of hypoperfusion, it would be expected that the transit time caused by a physical gap between the edges of the inversion and image slice profiles would increase. It was my aim to demonstrate that this effect was less problematic when improved RF pulses (and the resulting closer match of inversion and image slices) were used in the FAIR sequence. If a significant transit time exists, and is not accounted for in the quantitation procedure, an underestimation of perfusion results. Therefore one would expect to measure higher values for CBF when using a pulse sequence in which transit time effects are minimised compared to a sequence in which a considerable transit time exists. To look for this effect, sequences 1 and 3 (see above) were run in an interleaved manner during the first hour of post-ischaemic recirculation. The acquisition parameters were the same for both sequences: single TI= 1200ms, x=2700ms with pre-saturation pulse, 30 averages, bipolar crusher b~5s/mm^. At approximately 2 hours post ischaemia, a multi-TI ss/nsIR data set was acquired (with the same parameters as described in the 114 Non-invasive quantitation of cerebral perfusion using FAIR MRI previous paragraph, with the bipolar crusher). A direct estimate of the tissue transit time can be obtained from this data and compared to the values measured before the occlusion. The values of perfusion obtained from the biexponential fit on the full ss/nsIR data sets are shown in figure 4.16a. Fits were performed on four regions of interest in the gerbil brain corresponding to the right and left cortex (ROI 1,2) and striatum (ROI 3,4). For the pre-occlusion data, two fits were performed on each data set. First, transit time effects were assumed to be negligible and the data was fitted according to the standard FAIR model (equation (4.1)). Second, the model which includes transit time was used i.e. data was fitted for/and Ô using equation (4.11). These two approaches were taken for the data acquired both with and without the bipolar crusher gradients. It can be seen from figure 4.16a that overall, the perfusion values measured using the three sequences appear to be different. The sequence using the sech inversion pulse measures the lowest values, and the sequence using a FOCI inversion with sine imaging pulses measures the highest. Single TI reduced TR FAIR images acquired between the biexponential data sets remained constant, indicating that CBF did not change during the control period. The inclusion of a bipolar crusher gradient causes the calculated value of perfusion to decrease for sequences 1 and 2, showing that blood water signal contaminates the AM signal if a bipolar crusher is not used. For sequence 3, this effect is not apparent. This can be explained by a property of the double FOCI refocusing pulse. In order for spins in the slice to be properly refocused by the two FOCI pulses, they must be in the same position in the slice-select direction when both pulses are applied. The dephasing-rephasing effect of the two slice-select gradients then cancels out and the spin echo forms a certain time later. If the spins move during the time between the application of the two FOCI pulses, cancellation of the two slice-select gradients will not occur, resulting in signal 115 Non-invasive quantitation of cerebral perfusion using FAIR MRI (a) 175- 150- 125- 3,100 I R O I 1 § E m R O I 2 mmRQs 75- ■ ■ R O I 4 50- 25- Sequence (b) 500- I R O I 1 m m R O I 2 H R O I 3 I w 250 (0 _ a SECH bp off SECH bp on FOCI bp off FOCI bp on F-PC bp off F-PC bp on SECH tiypo F-PC hypo Sequence Figure 4.16 CBF and transit time values using various RF pulse combinations for FAIR Sequences are denoted SECH (sech-sinc90-sincl80), FOCI (FOCI-sinc90-sincl80), and F- PC (FOCI-90ns-double FOCI 180). ROI drawn in cortex (1,2) and striatum (3,4). (a) flow values from biexponential fits for different sequences, bp on/off refers to whether a bipolar crusher gradient was used in the sequence; d yes/no refers to whether transit time was fitted for in CBF calculation, (b) the resulting values when transit time is fitted for in each of the sequences. All data from normal gerbil except those marked ‘hypo’ which come from period of hypoperfusion. 116 Non-invasive quantitation of cerebral perfusion using FAIR MRI attenuation. It seems that motion of tissue water due to diffusion is not large enough to make this effect noticeable (since the tissue signal appears as normal in the images), but flow of blood water through the vasculature is sufficiently fast to cause elimination of its signal in this sequence. The fourth set of data in the graph in figure 4.16a shows the perfusion values measured using the biexponential fit during the hypoperfusion phase. An obvious decrease in flow is apparent, with approximately equal values obtained using the sech and FOCI pulses. Since transit time effects were taken into account in the fitting procedure, one would expect this to be the case. Figure 4.16b shows the result of fitting for the transit time for each of the three sequences. For the first two sequences (sech and FOCI inversions with sine 90° and 180° pulses), the transit time is practically zero when the bipolar crusher is not included in the sequence. This means that at normal flow values the inflow of tagged blood is almost instantaneous irrespective of whether an improved pulse shape is used or not. The transit time is seen to increase to approximately 100ms when the bipolar gradient is introduced. Since the blood signal is crushed when the bipolar gradient is used, this time represents the time taken for inflowing blood to begin exchanging with the tissue water. For the third sequence, which uses a double FOCI refocusing pulse, the transit time is non-zero when the bipolar crusher is not used. This confirms the suggestion offered above that the fast moving blood does not contribute to the signal in these images. However, when the bipolar crusher is applied, the transit time increases to approximately the same value as measured with the other sequences {i.e. -100ms). Therefore it seems that a proportion of the blood signal is in fact refocused by the double FOCI pulses and a bipolar crusher is still needed for this sequence. This result also suggests that the transit time of ~ 100ms measured using a bipolar gradient with all sequences represents the physical limit for the minimum time 117 Non-invasive quantitation of cerebral perfusion using FAIR MRI necessary for spins outside the imaging slice to move to a position within the image slice where they can exchange with tissue water (the capillary exchange sites). This limit is probably determined by factors such as arterial blood velocity, image slice thickness and position in the brain, and will therefore be subject to considerable variation depending on the experimental situation. Also shown in figure 4.16b are the transit time values measured by the sech and FOCI sequences (1 and 3 above) during the hypoperfusion phase of the experiment. Although the fits from both sequences are very noisy due to the low levels of perfusion present at this point of the experiment, the transit time values from sequence 3 are approximately equivalent to their pre-occlusion values, whereas the transit times from the sech sequence are very different to their previous values. This would indicate that for sequence 3, the value for the transit time is still dominated by the fundamental limit described above, and not by the relative thicknesses of the inversion and imaging slices. For the standard sech sequence, this is not the case. Further demonstration of the improvement in accuracy of flow measurement using the optimised sequence is shown in figure 4.17. The graph in this figure shows the perfusion time course after initiation of recirculation following ischaemia (at time t = 0). The time course is characterised (see next section) by a transient period of hyperaemia followed by prolonged hypoperfusion. The time course here shows the transition between these two states. The perfusion values were calculated using equation (A4.5) and assuming the transit time to be negligible (0=0). Since a single TI approach was used to enable maximum time efficiency, values for Mo, oco and Tj were taken from the post-occlusion ssIR data set. It can be seen from the figure that values calculated from the sech sequence are lower than those based on the FOCI sequence. This is consistent with the expected underestimation of flow with a sequence in which transit time effects are present. Post 118 Non-invasive quantitation of cerebral perfusion using FAIR MR! 100-1 —^ sech ROI 1 sech ROI 2 75- I sech ROI 3 I —^ sech ROI 4 50- - FOCI ROI 1 u_ F O C I R Q 2 CD 25- O F O C I R G 3 -— FOCI R G 4 0 10 20 30 40 50 60 Time post reperfusion (min) Figure 4.17 Post-reperfusion single subtraction FAIR perfusion values in the gerbil brain using a sech-sinc90-sincl80 RF pulse scheme (sech) and a FOCI- ns90-double FOCI RF pulse scheme (FOCI). ROI in cortex (1,2) and striatum (3,4). 119 Non-invasive quantitation of cerebral perfusion using FAIR MRI mortem imaging on a different gerbil showed that the increased difference with the FOCI sequence was not a systematic error in the subtraction caused by the inversion slice being too narrow, confirming the phantom results shown in figure 4.15. Therefore, I conclude that the observed difference reflects a genuine improvement in sensitivity to cerebral blood flow caused by a reduction in the transit time effects evident in a standard FAIR experiment. The experiment described in this section was performed on a single animal, and statistical comparisons of the different sequences were therefore not possible. Unfortunately, time restrictions prevented further experiments, but it would be extremely useful to repeat the work done here to verify the benefit of using the improved RF pulse version of FAIR statistically. However, the data presented here strongly indicate the benefit of the proposed sequence. 4.6 Using FAIR to follow a perfusion time course 4.6.1 Introduction During a transient ischaemic attack (TLA) or cardiac arrest with subsequent resuscitation, the brain experiences a brief period of ischaemia followed by reperfusion. Ischaemia results in cell death if prolonged, but re-establishing the cerebral circulation at an early stage does not necessarily prevent the development of injury which began during the ischaemic period (Hossmann, 1985). It is likely that the extent and pattern of re circulation which occurs during the post-ischaemic period is critical in determining the outcome of the compromised tissue. With the increasing use of thrombolytic agents such as rtPA for the treatment of stroke, it is important to understand the nature of post- 120 Non-invasive quantitation of cerebral perfusion using FAIR MRI ischaemic reperfusion. Many techniques have been used for the study of this situation in animal models (e.g. autoradiography, xenon clearance, hydrogen clearance), all of which suffer from limitations in their applications to such studies. As described in chapter 3, autoradiography only allows one time point during the reperfusion phase per animal, hydrogen clearance involves the invasive placement of electrodes into the brain tissue, causing damage and affecting the CBF, and xenon clearance is limited in resolution and susceptible to partial volume effects. FAIR MRI perfusion imaging offers the opportunity to monitor the post-ischaemic reperfusion quantitatively and non-invasively with good temporal and spatial resolution. My aim was to use the time efficient reduced TR version of FAIR developed in section 4.4 to measure CBF in the gerbil brain during a transient period of global forebrain ischaemia and the subsequent reperfusion. 4.6.2 Methods Mongolian adult gerbils (n=8, 60-70g) were used in this study. The gerbil is a convenient model for investigating the effects of transient ischaemia since bilateral occlusion of the common carotid arteries can induce total forebrain ischaemia. The animals were anaesthetised with halothane and anaesthesia was subsequently maintained using a mixture of 1.5% halothane in 0.4 1/min of oxygen that was supplied via a nose cone. The animals were allowed to breathe spontaneously throughout the experiment. The common carotid arteries were surgically exposed. Nylon snares (Ethilon 2/0, Ethicon, Edinburgh, UK) were placed around both arteries and attached to individually controlled manual screw systems in order to allow remote bilateral occlusion with the animal in the magnet. Before the animal was placed inside the magnet bore, the mechanics of the occlusion procedure were verified. Body temperature was recorded with a rectal thermometer and maintained at between 37-38°C by blowing warm air into the magnet bore. Respiratory rate and ECG were also monitored. The experimental protocol commenced with a period 121 Non-invasive quantitation of cerebral perfusion using FAIR MRI of control imaging. Bilateral occlusion was then initiated by tightening the snares. This state was maintained for four minutes. The snares were then opened to begin the recirculation phase. Perfusion imaging was continued for at least three hours. Images of a single coronal slice in the gerbil brain were acquired at 2.35T using a volume transmitter coil and surface receive coil. Perfusion maps were obtained using the FAIR technique. The version of the FAIR technique used consisted of a t-shape FOCI inversion pulse to perform spin labelling and sine 90° and 180° pulses for image acquisition. The slice thicknesses used were 6mm and 2.3mm for the inversion and imaging slice respectively. A bipolar crusher gradient was included in the sequence between the imaging RF pulses to crush signal from intravascular water. Slice selective and non- selective acquisitions were interleaved. Perfusion measurements were performed using two approaches. During the first part of the experiment (the pre-occlusion control phase), the full relaxation multi-TI FAIR technique was used. The TI values used were 200, 400, 600, 1000, 1400, 1800, 2500 ms and the inter-experiment delay t was 6500ms.Averaging of 20 acquisitions at each TI resulted in a total imaging time of approximately 35 minutes for this phase of the experiment. For the high time resolution time course measurements of CBF, the reduced TR implementation of FAIR with a global pre-saturation pulse was employed. In initial experiments, values of TI= 1300ms and t= 1500ms were used; these were replaced in later experiments by the optimised parameter values TI= 1165ms and x=2740ms. For both sets of imaging parameters, the number of averages was adjusted to maintain the time resolution of the perfusion measurements at 3 minutes during the acute phase of the experiment. During the latter part of the experiment, the number of averages was increased in order to increase the SNR of the images, resulting in a 10 minutes time resolution. The control values of Mo, Ti and Oo obtained during the control phase were 122 Non-invasive quantitation of cerebral perfusion using FAIR MRI used to calculate perfusion directly from each subtraction image. Experiments which measured these 3 parameters during reperfusion showed that they remained constant over the time period studied here. Tia was assumed to be 1500ms and a coil inflow time A (see section 4.4) of 1800ms was used where necessary for flow quantification. 4.6.3 Results Cerebral blood flow was calculated on a pixel-by-pixel basis using the Interactive Data Language (IDL) software package (Floating Point Systems, Boulder, Colorado, USA). Four regions of interest were drawn on the resulting perfusion maps in the right and left cortex and the right and left striatum (see Figure 4.18). The control values of perfusion, Ti and Oo are shown in Table 4.2. The mean pre-occlusion blood flow measurements were 158+24 ml/lOOg/min in the cortex and 130 ml/lOOg/min in the striatum. Cortical and striatal control flows were statistically different (p=0.001, paired t-test). right hemisphere left hemisphere cortex striatum left cortex left striatum CBF (ml/lOOg/min) 155+27 132+26 161+25 129+26 T i (m s ) 1219±35 1207±27 1229±21 1226+14 oco 0.945+0.008 0.945±0.006 0.942+0.002 0.945±0.002 Table 4-2 Results of pre-occlusion inversion recovery experiments. Values are mean ± SD. CBF are obtained by solving the subtractions (selective - non-selective) for flow using equation (A4.5) or (A4.8) depending on the experimental parameters t and TI used. Ti is the longitudinal relaxation time and Oo is the degree of inversion. Data are averaged over all the animals studied (n=8). Examples of perfusion maps obtained at various points during the occlusion-reperfusion time course are shown in figure 4.18. Inspection of the time courses showed that the data 123 Non-invasive quantitation of cerebral perfusion using FAIR MRI could be split according to cerebral hemisphere into two separate groups distinguished by very different responses: • Group A hemispheres displayed almost immediate re-normalisation of blood flow levels following reperfusion (see left hemisphere of animal 1 in figure 4.18). This response occurred in one hemisphere of 4 of the animals in this study. The time courses of these hemispheres are shown in figure 4.19a. Linear regression on the data collected from one hour after reperfusion to the end of the experiment resulted in a line with gradient not significantly different from zero i.e. the level of perfusion was constant. This level was not significantly different to the pre-occlusion values. • Group B hemispheres displayed an early partial recovery of CBF followed by a delayed decline and subsequent slow recovery of perfusion (see both hemispheres of animal 2 in figure 4.18). The time courses of this type of hemisphere are shown in figure 4.19b. On initiation of recirculation the blood flow increases and, at approximately 5 minutes post-occlusion, reaches a maximal level. A period of hypoperfusion follows. In order to characterise the initial recovery and decline of CBF, an exponentially damped polynomial model was fitted to the first hour of the post-reperfusion data. The model was of the form: fit) = a + ipQ + j8/^)exp(-Ar) (4.12) where/represents flow, t is the time since the end of the occlusion, and a, po, Pi and X are random coefficients (Crowder and Tredger, 1981). This model was selected since it is economic in the number of coefficients and provides an adequate description of the zero-time and asymptotic behaviour [f(0)5^f(oo)]. The likelihood ratio test comparing a full, region-dependent coefficients model with the restricted common coefficients model was not significant (%^ = 0.3). Therefore, a common coefficients model (i.e. coefficients independent of region) was chosen to provide an adequate description of 124 Animal 1 Animal 2 ml lOOg"' min" pre-ischaemic occlusion +10 minutes +30 minutes +180 minutes K) LA ROI 1 ROI 2 ROI 3 ROI 4 Spin-echo pilot Figure 4.18 Representative CBF maps obtained in two gerbil occlusion-reperfusion studies. Times are denoted as minutes post-reperfusion. Pre-ischaemic, occlusion, +10 minute and +30 minute CBF maps were acquired in 3 minutes; the +180 minute maps were acquired in 10 minutes. A high-resolution spin-echo image of the imaging slice (1 mm slice thickness) is displayed for anatomical reference and to show the location of the ROI used for data analysis. Non-invasive quantitation of cerebral perfusion using FAIR MRI (a) occlusion reperfusion 200i y 150 - 100^ 8 -30 -20 -10 0 10 20 30 40 80 120 160 200 time [minutes] occlusion reperfusion (b) \ ,I I./ I I 200 - I I .1 I 'i I 150- —— flow data sets •.... model 100 - u. 50- CÛ Ü 0 - 1—'—I—'—1—‘I—I—'—r -30 -20 -10 0 10 20 30 40 50 60 time [minutes] Figure 4.19 Perfusion time courses from ROI in the gerbil brain before and after 4 minutes of forebrain ischaemia. Two responses are observed (a) immediate re-normalisation (Group A response) and (b) post-ischaemic hypoperfusion (Group B response). Also shown for Group B is the result of fitting the data to an exponentially damped polynomial model. Note that in Group B, there is considerable variation in the magnitude and the position of the maximal response. The maximum flow rate given by the fitted mean curve is not, therefore, equal to the mean of the independent maximal flow rates. 126 Non-invasive quantitation of cerebral perfusion using FAIR MRI the data. The common coefficients at the maximum likelihood solution of equation (4.12) were: a = 10.1±2, po= -102+13, pi = 2.81±0.4, X = 0.36+0.01. The mean time- dependent behaviour provided by the model is shown in figure 4.19b. The maximal level of the initial recovery on reperfusion was provided by the peak of the fitted model. A value of 85 ml/lOOg/min at 4.7 minutes post-reperfusion was obtained. This flow is 46% and 36% lower than the mean pre-occlusion levels in the cortex and striatum respectively. The flow subsequently dropped to an asymptotic level during this 60 minute period of 10 ml/lOOg/min. The rate of decline of the flow can be characterised by the time to reach a level that is 50% of the difference between this peak flow and the asymptotic flow level; this occurred 11.6 minutes post-reperfusion. At approximately 60 minutes post-reperfusion, the blood flow began to recover slowly. The mean slope of the recovery obtained by linear regression of data collected from Ihr post-reperfusion until the end of the experiment was significantly different from zero with values of 9.8+2.6 [ml/100g/min]/hour and 9.4±4.6 [ml/100g/min]/hour in the cortical and the striatal regions. By 3 hours post-reperfusion, the CBF had reached a level of 35+9 ml/lOOg/min and 37±14 ml/lOOg/min in the cortex and striatum respectively. 4.6.4 Discussion This investigation has demonstrated the use of high time resolution FAIR in the measurement of dynamically changing levels of cerebral perfusion. It has shown the ability to differentiate between the different responses which occur following a period of transient global ischaemia in the gerbil brain. The method offers the possibility of completely non-invasive longitudinal studies in single animals which other techniques do 127 Non-invasive quantitation of cerebral perfusion using FAIR MRI not permit. The serial measurements of blood flow have enabled the discrimination of two group responses to reperfusion, and the high time resolution of FAIR has allowed these two responses to be accurately mapped. The occurrence of a period of post-ischaemic hypoperfusion agrees with results reported in the literature (see, for example, (Hossmann et a l, 1973)). The degree of hypoperfusion measured in these experiments is rather severe compared to previously reported data. This is most likely due to underestimation of perfusion by the FAIR technique. As seen in section 4.5, the version of FAIR utilised in this study is susceptible to the effect of an increased transit time when flow is compromised. This effect can be alleviated using improved RF pulses (see section 4.5), and further experiments examining the pattern of post-ischaemic reperfusion would benefit from taking this approach. This approach was not used in the experiments described here because the development of the double FOCI pulse sequence was not complete when the experimental protocol was defined. The immediate and permanent recovery of perfusion that was observed unilaterally in a number of animals (Group A data) was unexpected. It has been noted that there is a variability in the number and the size of the small communicating blood vessels between the vertebro-basilar and the carotid circulation in the gerbil (Levy and Brierly, 1974). The degree of collateral circulation that originates from the unoccluded vertebral supply might therefore be the cause of the observed side-to-side asymmetry on reperfusion. A previous study has noted the side-to-side variations in the vasculature of the circle of Willis in gerbils (Tamura et al, 1981). At the conclusion of a number of the experiments (n=4), the animal was removed from the magnet and the snare set-up was examined. The pulsation of the arterial flow proximal and distal to the snares was checked for consistency. At the end of every study, a post-mortem examination was carried out in order to verify that the 128 Non-invasive quantitation of cerebral perfusion using FAIR MRI snares were fully open and that the external diameter of sections of the carotid arteries proximal and distal to the snares was constant. The mechanical screw system was also inspected and the operation of closing and opening the snares was validated. The internal and external diameters of the arteries were examined post-mortem for indications of wall thickening. No evidence of an unsuccessful occlusion or reperfusion was found. 4.7 Discussion and Conciusions This chapter has shown that FAIR imaging can be used to measure cerebral perfusion in a non-invasive manner with good spatial and temporal resolution. Two modifications have been proposed: the addition of a pre-saturation pulse before the inter-experiment delay time for reduced TR FAIR and the use of optimised RF pulses with sharper pulse profiles. Both modifications have been implemented and shown to improve the time resolution and sensitivity of the quantitative perfusion measurements made by FAIR. A drawback of both the changes proposed here is that they decrease the SNR available in the FAIR images compared to standard implementations of the sequence. For the reduced TR modification, inclusion of a global pre-saturation pulse reduces the expected difference signal, but simplifies the quantification procedure (as long as a suitable combination of inversion time and inter-experiment delay time are chosen). When the adiabatic RF pulses are used for spin refocusing, the echo time of the image is necessarily longer than when a standard sine pulse is used, thus reducing the SNR by Ti decay. However, a long echo time has the advantage of reducing the contribution of intravascular signal (see section 4.5) and the loss in SNR must be balanced against the greater reliability of the measurement. Better SNR does not improve a measurement that systematically underestimates perfusion as occurs with the standard FAIR sequence. Therefore I 129 Non-invasive quantitation of cerebral perfusion using FAIR MRI conclude that the modifications proposed in this chapter offer a genuine improvement to the FAIR approach to perfusion imaging, both in terms of sequence efficiency and measurement accuracy. An example of a perfusion time course study which utilises FAIR to monitor rapidly changing levels of cerebral perfusion has been presented. Based on the results presented here, FAIR imaging offers a viable and easy-to-implement option for CBF measurement during time course studies. This applies equally to functional neuroimaging experiments and studies of cerebrovascular disease in animal models. In combination with other MR based methods such as diffusion-weighted imaging, -weighted imaging and spectroscopy, it is possible to investigate the relationship between blood flow and various other physiological parameters in vivo in a completely non-invasive manner. 130 Non-invasive quantitation of cerebral perfusion using FAIR MRI 4.8 Appendix I Integrated form of the Bloch equation All calculations are based on the solution of the flow-modified Bloch equation (Detre et al, 1992) under the relevant initial conditions. Integration and rearrangement of this equation yields the following expression that relates magnetisation at time t = ti to the magnetisation at a later time t = t 2 tIT, M (?2 ) - M (r, ) e' = j \app dt (A4.1) II Transit time effects Incorporation of the effects of the transit time into the FAIR model, modifies AM(TI) so that AM(TI) = 0 for TI < Ô and the following expression for TI > Ô m (TI) = (TI) - (TI) = 2Moa„ (A4.2) Ï Î T T la lapp Therefore the transit time can be determined from the biexponential relationship from the intercept of the AM(TI) curve on the TI time axis. Ill Short TR FAIR : (no pre-saturation) Implementation of FAIR with a short repetition time introduces a modified set of initial conditions that are dependent upon the relaxation during the recovery time. The repeated application of non-selective inversion pulses results in a build-up of a steady state level for the degree of inversion of the inflowing blood magnetisation. This level is described 131 Non-invasive quantitation of cerebral perfusion using FAIR MRI by the factor X(TR) (see equation (4.7)). The expression for this factor is obtained by calculation of the magnetisation state that builds up after applying a series of global inversion pulses to a spin system that starts from a state of thermal equilibrium. Analysis of AM(TI) in this case necessitates splitting the analysis into components in order to calculate the magnetisation at the start and the end of the recovery period and at the start and the end of the subsequent inversion pulse. The initial conditions of the latter phase are defined by the final state of the former phase and vice versa. These conditions are as follows (with transit time effects neglected); Non-selective image (i) start of recovery time following selective image: M A M„,(r = 0) = 0 (it) start of inversion time (by definition ofX(TR)): M.(t) = ^ ( l - 2X(JR) ) A Selective image (i) start of recovery time following non-selective image: (0 = - ^ (l - 2X(TR) a„ ) A M „(t = 0) = 0 (ii) start of inversion time: M (0 = ^ (l - 2X (ÏÏ?) «0 ) A M„(r = 0) = (l-2ao)M„(r'=T) 132 Non-invasive quantitation of cerebral perfusion using FAIR MRI where Mss(t'=x) is the tissue magnetisation at the end of the previous recovery time. The resulting expression for AM(TI) is then derived by applying these conditions to solve Eq. [A4.1] and the resulting expression is given by equation (4.6). IV Short TR FAIR (with pre-saturation) The pre-saturation pulse eliminates the build up of the steady-state magnetisation or any complicating magnetisation difference that has evolved during the previous experiment. The selective and non-selective acquisitions can be considered in isolation and the flow- related signal in each experiment develops only during the inversion time and not during the recovery time. The initial conditions in this situation are as follows (with transit time effects neglected and assuming a perfectly efficient saturation): Non-selective and selective images (i) start of recovery time of proceeding image: M^(t = 0) = 0 M,„Jt = 0) = 0 (ii) start of inversion time: M ,(0 = [l + (d - 2 a ,) ( l ] (non-selective inversion) A (selective inversion) A - t /T, — e ^ n s /s s (^ — 0 ) — (1 2Œ q ) (A4.3) 1 1 T T la \app The expression for the difference in magnetisation, AM(TI), is given by equation (4.8) 133 Non-invasive quantitation of cerebral perfusion using FAIR MRI V Short TR FAIR (with pre-saturation and coil inflow effects ) Inflow of fresh arterial spins from outside the coil can occur during both the recovery time and the inversion time. The use of pre-saturation pulses is assumed in this situation as coil inflow effects would otherwise significantly complicate the quantification. A number of situations need to considered in the analysis of the effects of coil inflow on quantification. These regimes depend upon the choice of experimental parameters and the value of the inflow time (see figure 4.10). If the chosen recovery time is less than the coil inflow time (x < A), the coil volume fills with uninverted spins that will flow into the imaging slab during the subsequent inversion time at a time (A-x). The blood magnetisation during the TI time in such a case therefore fulfils the following conditions; Non-selective image W = ^ [l + (d - 2a„ )(l ] 0 < f < (A - T) A A = ^ t> ^ Selective image (f) = ^ [ l + ((1 - 2a„)(l )- ] 0 = 5 f>(A-T) Considering for example the non-selective image, while the inversion time is less than this secondary inflow time, (A - x), blood spins entering the imaging slice have been inverted during their recovery from the pre-saturation (see figure 4.10). Once this time has been reached, fresh spins that have entered the coil during the previous recovery time. 134 Non-invasive quantitation of cerebral perfusion using FAIR MRI arrive at the slice after having been inverted from their equilibrium state. Subsequent to the principal inflow time, A, fresh, uninverted, spins that have entered the coil during the inversion time reach the imaging slice. Expressions for AM(TI) in each of the regimes described in section 4.4.3 are shown here. Case la) T > A and TI < A (A4.5) Case lb) t > A and TI > A (A4.6) T T \app 1(1 Case 2a) t < A and TI < (A - x) (A4.7) 1 1 T T ^ \a p p \a Case 2b) x < A and (A - x) < TI < A M, / -MTupp) _ ^ - 5 (1/ 7-, A M ( T / ) = 7 ------(la,, (l-e~"'^‘“)) I 1 1 (A4.8) T T \iipp i« ^ 2^^g-(A-r)/r,„ ^^-(r/-A+r)/r,„ _ ^-(7-/-A+r)/r,„ 135 Non-invasive quantitation of cerebral perfusion using FAIR MRI Case 2c) T < A and TI > A (A4.9) T‘ Uipp ‘T \a 136 Rapid T2* Mapping Using Interleaved Echo Planar Imaging 5 Rapid T2* Mapping Using Interieaved Echo Pianar imaging 5.1 Introduction As described in chapter 3, the magnetic properties of deoxyhaemoglobin can be used to generate image contrast that reflects changes in tissue perfusion (as well as changes in other parameters such as cerebral blood volume etc.). Such contrast is evident when images are weighted by the effective transverse relaxation time T 2 *. This chapter describes a sequence which I designed and implemented to directly measure T 2 * with good time efficiency. It makes use of a technique known as interleaved echo planar imaging to produce maps of T 2 * with the same time resolution offered by conventional EPI techniques but with substantially better image quality {i.e. less image distortion). Application of this technique should allow more quantitative evaluation of the changes occurring during haemodynamic events. T2 * is an important parameter in many NMR studies of brain function and physiology, largely because changes in the oxygen saturation of cerebral blood give rise to local T 2 * variations (Thulbom et al., 1982; Ogawa et al, 1990). The most popular current method of functional magnetic resonance imaging (fMRI) is predicated on the use of T 2 *- weighted imaging to monitor regional changes in signal intensity associated with a particular task. Signal increases are detected as a consequence of a local reduction in the concentration of deoxyhaemoglobin caused by an over-compensatory increase in cerebral blood flow and blood volume in the vicinity of activated neural tissue (Ogawa et al, 1992). The microscopic magnetic field gradients which are established between 137 Rapid T2* Mapping Using Interleaved Echo Planar Imaging paramagnetic deoxyhaemoglobin and the surrounding diamagnetic environment cause signal dephasing to occur within voxels. These effects, in combination with macroscopic susceptibility and residual main field (shim) gradients, determine the value of T 2 * in a voxel. T 2 *-weighted imaging has also been used to monitor blood oxygenation changes in animal models during hypoxia (Turner et al, 1991; Prinster et al, 1997), ischaemia (Roussel et a l, 1995; De Crespigny et al, 1992; De Crespigny et al, 1993) and hypercapnia (Prinster et al, 1997). In another example of a T 2 * time course study, the effect of Levadopa therapy in hemiparkinsonian rhesus monkeys has been shown to change functional responsiveness within a few minutes of injection (Chen et al, 1997). It has also been shown in the cat brain that T 2 * has an approximately linear relationship with deoxyhaemoglobin concentration, as measured by spectrophotometry via a cranial window in the same experiment (Jezzard et a l, 1994). In the rat brain, T 2 * has also been shown to vary linearly with arterial oxygen saturation, over a range of 70% to 100% oxygenation (Prielmeier et a l, 1994). In fMRI, T 2 * values are not usually measured but image contrast is generated which can be used to identify functional change. Although T2 * contrast is sufficient to generate activation maps, the lack of quantitative values prevents estimation of the underlying blood oxygenation changes. T 2 * can be measured by acquiring a series of images at different echo times and fitting the signal to a relaxation curve. An fMRI study which adopted this approach reported increases in T 2 * of approximately 3% during a finger tapping protocol (Bandettini et a l, 1994). When cerebral blood oxygenation changes are measured using MRI, the haemodynamic autocorrelations have been estimated to be on the order of 6-10 seconds (Friston et al, 1994). This implies an upper limit to the temporal resolution necessary to measure changes in blood oxygenation and it suggests the measurement of T 2 * values on the time 138 Rapid T2* Mapping Using Interleaved Echo Planar Imaging scale of several seconds represents a worthwhile goal. The echo planar imaging (EPI) technique (Mansfield, 1977) enables such rapid measurements. Single shot EPI is frequently used when a short imaging time is the most critical factor in experimental design, overriding the lower spatial resolution, compromised signal-to-noise ratio (SNR) and the inherent geometric distortion of EPI. However, the values of T 2 * measured using single shot EPI at different echo times may be inaccurate due to the length of the data acquisition window relative to If a compromise between the imaging factors of speed, resolution, SNR and distortion is required then interleaved EPI (McKinnon, 1993; Ahn et al, 1986; Howseman, 1988) can be used. Interleaved EPI is a hybrid between true EPI and the conventional spin warp 2D-FT methods, in which multiple (Us) radio frequency excitations of the spin system are required. After each excitation, a certain number (n,) of lines of k-space are traversed and sampled. In the blipped gradient (phase encoding) direction a gap of k-space lines is left between adjacent echoes. The total number of points in the phase encode direction is N where N = ng x n%. The intermediate lines are acquired in successive excitations (see figure 5.1). A major advantage of using interleaving is that it can be performed using the gradient hardware associated with a typical clinical MRI scanner, which often precludes the use of EPI (Butts et a l, 1994). Here, a version of interleaved EPI is developed as a method which can be used for the rapid generation of T%* maps, typically within a few seconds. In this application, the principles of interleaving in k-space do not increase resolution or lessen the gradient requirements, but instead are used to introduce a temporal dimension into the data which consists of a series of images effectively acquired at different gradient echo times. This set of images can be used to calculate T%* maps of the sample while also benefiting from the reduced geometric distortion associated with interleaved EPI. 139 Rapid T2’ mapping using Interleaved Echo Planar Imaging \ I \f / I / / ' \ /; / / Acquisition 1 Acquisition 2 Acquisition 3 Acquisition 4 Figure 5.1 An example of a standard interleaved EPI acquisition. Each colour represents line of k-space acquired in a single shot; the data is then meshed together as shown to form one complete k-space set. 140 Rapid T2* Mapping Using Interleaved Echo Planar Imaging 5.2 Methods The principle behind this fast T 2 * imaging sequence is to use an echo train of duration similar to that used for single shot EPI, but to consider it split into short segments, each of which has a progressively longer effective gradient echo time, TE. Each segment consists of ni lines of k-space. The acquisition is repeated a number of times equal to the number of segments, ns, and each time different k-space lines are acquired. This allows the construction of ns data sets, each of which contains the complete k-space set and has a different TE, where TE is defined as the time at which the centre of k-space is acquired. Upon Fourier transformation of the data to create ns images, a map of T 2 * can be generated by fitting the image intensity decrease as a function of TE to an exponential decay curve. The exact form of the pulse sequence which has been implemented is shown in the schematic diagram of figure 5.2. The echo train is split into 8 segments, and consequently there are 8 separate acquisitions. The numbers in the segment boxes refer to the lines of k-space acquired; there are 8 echoes per segment and so the number of points in the phase encode direction is 64. The particular k-space strategy shown in figure 5.2 and its inherent advantages are explained in detail below. However it should be noted that in principle it does not matter which lines are placed in which segment, provided all the lines are collected for each TE time. In practice, the exact implementation of the sequence requires careful consideration of which k-space should be sampled during each acquisition. The aim is to traverse k-space efficiently (avoiding unnecessarily large blips in the phase encode direction, which increase the acquisition time, are limited by the available gradient strength, and could introduce eddy current problems) and to minimise the ghost artefacts which can be prevalent in multi-pass EPI experiments. This requires minimisation of the phase and amplitude errors which result from the concatenation of k- 141 Rapid T2* mapping using Interleaved Echo Planar Imaging W 1 8 0 ’ 1,9 , 64,56, 1,9, 64,56, 1,9, 64,56, 1,9, 64,56, ACQUISITION 1 ..,57 ..,57 ..,57 ..,57 90 ’ 180 (\ 2, 10, 63,55, 2, 10, 63,55, 2, 10, 63,55, 2, 10, 63,55, ACQUISITION 2 ..,58 ..,7 .,58 ..,7 ..,58 ..,7 ..,58 ..,7 I I M M A A G G E E 90 ’ 180 ’ 1 8 8,16, 57,49, ,16, 57,49, ,16, 57,49, ,16, 57,49, ACQUISITION 8 (M) ..,64 ,64 ..,1 ,64 ..,1 ,64 ..,1 Figure 5.2 Schematic diagram of T 2 * interleaved EPI pulse sequence. 8 separate excitations of the spin system are performed, separated by a TR. In each, a train of 64 gradient echoes is acquired which are segmented into 8 data sets corresponding to progressively later echo times. Each resultant data set contains all 64 lines of k-space as indicated by the numbers in the boxes. Fourier Transformation of each set yields an image with different weighting. The 180° pulse generates a spin echo in the centre of the 1st segment and therefore the 1st image of the series has zero T 2 * weighting. 142 Rapid T2* Mapping Using Interleaved Echo Planar Imaging space lines from different acquisitions and the time reversal of alternate echoes (Johnson and Hutchinson, 1985). Off resonance effects, due to chemical shift, shimming and susceptibility differences and instrumental instabilities are the major sources of these problems. In a simple form, the sequence could be designed so that in each acquisition the same lines of k-space were acquired 8 times. For example, in the first acquisition segment 1 would consist of lines 1, 9, 17, 25, 33, 41, 49, 57; segment 2 would contain lines 57, 49, 41, 33, 25, 17, 9, 1; and so on for segments 3-8. This means that k-space is traversed in opposite directions in alternate segments, which avoids the need for a large phase encoding blip that would be necessary to return to line 1 directly at the end of each segment. Covering k-space alternately in the positive and negative sense simply corresponds to the blips of the phase encoding gradient changing polarity every 8 echoes. In the second acquisition, lines 2, 10, 18, 26, 34, 42, 50, 58 for the odd segments, and the same lines in the opposite direction for the even segments, would be covered. For each acquisition, the even numbered segments traverse k-space in the opposite direction to the odd ones in both the phase encode and read directions and so during image processing, rearrangement of the k-space data is necessary in both dimensions. This simple version has certain limitations, however, because of the phase and amplitude discontinuities which occur in interleaved EPI. These effects can be reduced by the incorporation of echo time shifting (ETS) (Cho et al, 1987; Feinberg and Oshio, 1994) into the sequence. With ETS, the echo trains are started progressively later in each of the 8 acquisitions by a time equal to l/8th of the echo spacing. ETS is designed to reduce artefacts in the data by sampling the signals such that the T 2 * decay is smooth across k- 143 Rapid T2* Mapping Using Interleaved Echo Planar Imaging Space, rather than having the discontinuities introduced by the interleaving. For the sequence proposed here however there is the additional complication with using ETS because in the phase encode dimension, the direction of k-space traversal alternates between segments. If the even numbered segments corresponded to the same k-space lines as the odd segments, acquired in the opposite order (as in the simple version described above), then the ETS would take effect in the wrong direction in the even segments i.e. it would actually make the discontinuities worse rather than eliminating them. To overcome this problem, a modification can be made to the order of data acquisition so that, for each acquisition, the even segments do not contain the same lines as the odd segments (the implemented version shown in figure 5.2). The k-space trajectory which corresponds to the first of the 8 acquisitions is shown in figure 5.3. The red line refers to the lines acquired moving through k-space in the upwards direction, as in segments 1,3,5,7, and the green line shows the acquisition of the lines in segments 2,4,6,8 on the downwards trajectory. Between segments a small phase encoding blip is used to shift to the starting line of the next segment. The other seven acquisitions follow a similar pattern but for different k-space lines, as shown in figure 5.2. With this scheme, the first lines of k-space collected during the even segments from each of the 8 acquisitions are 64,63,62,...,57, and the second lines are 56,55,54,...,49. This linear progression of the lines as the segments are combined (as happens for the odd segments) is the criterion that needs to be met for the successful operation of ETS. This can be understood by considering the effects of interleaving and time reversal of data in the read direction on the data modulation transfer function. In figure 5.4 the form of the modulation transfer function due to T%* is shown, taking into account interleaving, ETS and data reversal. In figure 5.4a) the effect in odd numbered segments can be seen. A smooth decay is observed, except for the small effects in lines 9-16, 25-32, etc. where the reversal of the alternate echoes in the read direction 144 Rapid Tj* mapping using Interleaved Echo Planar Imaging START (EVEN SEGMENTS) 64 57 56 49 48 41 40 33 25 24 17 16 8 START (ODD SEGMENTS) Figure 5.3 k-space representation of the sequence described in the text (k^ is the read direction and k^ is phase encoding). The figure shows the lines traversed during the 1st of the set of 8 acquisitions. Starting at line 1 and incrementing through k-space in steps of 8 lines (red line), the final line in segment 1 is line 57. Segment 2 begins at line 64 and progresses down through k-space to line 8 (green line). Segments 3-8 follow the identical pattern. Note that between odd and even segments a phase encode gradient is applied to move the position from lines 57 to 64 and lines 8 toi. In the 7 later acquisitions the starting lines are 2,3,..8 and the increment in k-space remains at 8 lines. The numbering of the starting lines for the even segments is as shown in figure 5.1, to accommodate the concept of echo-time shifting. 145 Rapid T2* Mapping Using Interleaved Echo Planar Imaging causes small discontinuities. However, since the duration of each line is only on the order of 1ms, this effect can be ignored. In figure 5.4b) and 5.4c) the effect on the even numbered segments is considered. In figure 5.4b) the simple version of the experiment (lines acquired in the order 1,9,...,49,57,57,49,...,9,1 etc. during the first acquisition) is shown to introduce large discontinuities at the edges of the interleaved segments, whereas in figure 5.4c) the version which has been implemented is shown to have a smooth modulation transfer function. This function is the same as for the odd segments, except for a change in direction across k-space. However, due to the conjugate symmetry of k- space (and the centre of k-space having the same relative weighting in both cases) this should have little bearing on the final images. The sequence has been implemented on a 2.35T 30cm bore magnet system equipped with a SMIS (Guildford, UK) console and home built gradients with Gmax = 135mT/m. It generates 8 images of matrix size 128x64, created from the 8 interleaved EPI acquisitions. Each of the 8 acquisitions was of 72ms duration, separated by a repetition time delay (TR) of Is. An RF flip angle of 90° was used. Trapezoidal gradient waveforms were used with linear sampling on the plateaux; the echo spacing was 850|is and therefore the duration of a segment which contributes to a given image was 6.8ms. In terms of T 2 *-weighting, the first image has an effective gradient echo time of 0ms and spin echo time of 18ms because the centre of the first segment coincides with the spin echo generated by the slice selective 180° pulse. The following images have effective gradient echo times incremented by 6.8ms. Experiments to demonstrate the performance of this sequence were carried out on a 146 Rapid T2* mapping using Interleaved Echo Planar Imaging I 0 8 16 24 32 40 48 56 64 Phase encoding step 0 8 16 24 32 40 48 56 64 Phase encoding step Î 0 8 16 24 32 40 48 56 64 Phase encoding step Figure 5.4 T2* related modulation transfer function of the interleaved EPI sequence with echo time shifting. In (a) the smoothing effect on the odd segments as described in (15) is shown. For the even segments; if the simplest version of the k-space pattern (see text) is adopted then massive discontinuities are evident (b). If the modified k-space pattern is used, as shown in figure 1, then a smooth MTF results (c), although its direction is opposite to that in (a) for the odd segments. 147 Rapid T2* Mapping Using Interleaved Echo Planar Imaging phantom made up of 4 sample tubes containing different concentrations of manganese chloride (MnCl 2 ) solution (and therefore different T 2 and T2 * values) embedded in a gel filled vessel. A complete set of T 2 * images were acquired using the interleaved sequence in 8s. These were compared with the images acquired using conventional spin echo and FLASH methods, and also with single shot EPI. For single shot EPI and FLASH, 8 separate images were acquired at echo times approximately corresponding to those of the interleaved sequence. The phantom data were acquired using an RF saddle coil (70mm inner diameter) for transmission and reception. In order to demonstrate the use of this sequence with an in vivo application, experiments were performed in which T 2 * could be changed in a controlled way over time. It has been shown that following a one minute period of anoxia, the signal intensity from the grey matter of cat brain decreases by approximately 15% when imaged using T 2 *-weighted gradient echo EPI (Turner et al, 1991). The equivalent experiment was performed on the rat brain using the interleaved EPI sequence to monitor the time course of T 2 * changes during an anoxic challenge. A female Wistar rat (weight ~ 320g) was used in this investigation. Anaesthesia was induced with 3% halothane and maintained via a nose cone with a mixture of 0.8% halothane, 70% N 2 O and 30% O2 . The animal was allowed to breathe spontaneously throughout the experiment; respiratory rate and ECG were monitored and rectal temperature was maintained at 36.5±0.5°C using an air warming feedback system. A pulse oximeter (Nonin, USA) was used to measure the oxygen saturation fraction of the blood haemoglobin. Images were obtained at 2.35T using a volume coil (70mm inner diameter) to transmit RF and a surface coil (30mm inner diameter) placed adjacent to the rat head to receive. The spin echo time of the sequence was 18ms, and successive segments had effective gradient echo times of 0, 5.95, 13.6, 148 Rapid T%* Mapping Using Interleaved Echo Planar Imaging 19.55, 27.2, 33.15, 40.8 and 46.75 ms. The repetition time was 2s, which resulted in a measurement every 16s. The experiment consisted of three short epochs of anoxia (1-2 minutes), separated by ten minute periods of normal breathing. T%* was measured continuously to monitor the changes associated with the anoxic event and the immediately ensuing period. Anoxia was induced by replacing the oxygen content of the inspired gases with N2 . At the end of the experiment, the animal was sacrificed by changing the respiratory gases to 100% N 2 . T2 * measurements were also made during this period. 5.3 Results A comparison of the phantom data acquired with the different imaging techniques is shown in figure 5.5. In figure 5.5a) a high resolution (0.31 mm in-plane, slice thickness = 2.2 mm) spin echo image is shown, acquired at an echo time of 30 ms. In figure 5.5b) a gradient echo FLASH image acquired at an echo time of 26ms is shown. The FOV and resolution (0.625 mm in-plane, slice thickness = 2.2 mm) in this image was set to be the same as for the single shot GE EPI and interleaved SE EPI images of figures 5.5c) and 5.5d) respectively. The gradient echo time in the single shot EPI, defined as the time from the 90® RF pulse to the centre of k-space, is 19ms. The image in figure 5.5d) is the first of the set of 8 interleaved images generated by the rapid T 2 * sequence. This image corresponds to a spin echo time of 18ms and consequently is only T 2 -weighted and not T2 *'weighted. Both the improved resolution, by virtue of the narrower point spread function (see section 5.4), and the reduced geometric distortion in the phase encode direction can clearly be seen in the interleaved sequence compared to the single shot EPI image. It can also be seen that for both the high resolution SE sequence and the interleaved spin echo EPI image from the beginning of the T 2 * set, the intensity of the 149 Rapid Tj* mapping using Interleaved Echo Planar Imaging (a) (b) (c) (d ) Figure 5.5 Phantom images acquired using 4 different imaging methods of a vessel filled with 4 compartments with different T 2 * values, (a) 128x128 matrix spin echo image (0.31mm in-plane resolution, 2.2mm slice thickness), TE = 30ms. (b) 64x64 matrix GE FLASH image (0.63mm in-plane resolution, 2.2mm slice thickness), TE = 26ms. (c) 64x64 matrix GE EPI image (0.63mm in-plane resolution, 2.2mm slice thickness), TE = 19ms. (d) 64x64 matrix SE interleaved EPI image (0.63mm in-plane resolution, 2.2mm slice thickness), TE=18ms (1st segment of 8). Geometric distortion in the interleaved EPI image is minimal as is the level of ghost images. 150 Rapid T2* Mapping Using Interleaved Echo Planar Imaging background gel compartment is relatively uniform across the image when compared to the nonuniformity which can be seen in the FLASH and GE EPI images. This nonuniformity is due to spin dephasing which occurs across the width of the slice due to main field inhomogeneity (Frahm et al, 1988). In figure 5.6, images are shown at later gradient and spin echo times. The resolution and slice thicknesses are identical to those in the images in figures 5.5b) - 5.5d). The image in figure 5.6a) is acquired with FLASH at an echo time of 58 ms. In figure 5.6b) a single shot EPI image is shown at an echo time of 59 ms and in figure 5.6c) the last image from the set of weighted interleaved EPI images, which corresponds to a GE time of 47.6ms is shown. This image has been acquired at a time corresponding to 47.6+18 = 65.6ms on the T 2 decay curve. In figure 5.6d) an offset single shot spin echo EPI image is shown in which the centre of k-space corresponds to a time of 56ms after the 180° pulse and of 90ms on the T 2 decay curve. For all of the images, which have a considerable degree of T 2 * decay, the signal loss due to dephasing in the slice selection direction can be seen. However, as expected, the in plane geometric distortion remains minimal in the interleaved EPI image at this late echo time. Using the series of 8 T 2 *-weighted images acquired with single shot EPI, GE FLASH and the interleaved EPI method, T 2 * values were calculated using the single exponential decay defined by: S = S„expf-r£/r* I (5.1) and fitting signal intensity against echo time for So and T 2 * for each of the four compartments in the phantom. The T 2 * results and standard errors are displayed in table 5.1. 151 Rapid Tj* mapping using Interleaved Echo Planar Imaging (a) (b) (c) (d) Figure 5.6 Phantom images acquired at later echo times than those in figure 5.5. (a) FLASH, TE = 58ms. (b) Single shot EPI, TE = 59ms. (c) interleaved EPI image from segment 8, gradient echo time = 47.6ms, T 2 decay equivalent to 65.6 ms. (d) offset single shot SE EPI, centre of k-space 56ms after 180° pulse. In-plane geometric distortion in (c) remains equivalent to that in (a) and less than that in (b) and (d) at these late echo times. Signal loss due to through -slice dephasing at the longer echo times than those shown in figure 5.5 is apparent in all cases. 152 Rapid T2* Mapping Using Interleaved Echo Planar Imaging The values calculated from the interleaved EPI sequence are in good agreement with those calculated from the FLASH images acquired at 8 different echo times. Despite the long acquisition window associated with the technique, the single shot EPI T 2 * results are also in agreement with the values obtained using interleaved EPI. This is somewhat surprising because effectively each line in k-space will have been sampled at a different point on the T2 * curve and therefore the results may be expected to show some error. Evidently the same effect exists for all imaging techniques but is most severe for single shot EPI. The magnitude of the error will be dependent on the spatial frequency structure of the sample. For a fairly uniform sample, such as the phantom images shown here, the fraction of the signal close to the centre of k-space and therefore to the nominal echo time will be much higher than for a complex object which contains more high spatial frequency components. It may therefore be that T 2 * values of a complex structure such as the brain measured with single shot EPI would be rather less accurate than those shown here for the phantom data. 0.75 mM 0.50 mM 0.25 mM 0.10 mM FLASH 12.8 ±0.2 15.6 ±0.3 38.2 ±0.5 110±4 Interleaved EPI 12.4 ±1.4 18 ±1.0 35.8 ±1.0 110 ±5 GE-EPI 14.2 ±0.2 15.7 ± 1 33.4 ± 1.7 71 ± 6 Table 5-1 T2* values (mean ± standard error, in ms) for the four MnCL solutions using three different techniques All the data in the rat anoxia experiment fitted well to monoexponential decay curves, with correlation coefficients (R^) of 0.99 or greater. In figure 5.7 an example fit of the data to a single exponential is shown, which yields a value of T 2 * = 45.5 ±1.5 ms. The time course 153 Rapid T2* mapping using Interleaved Echo Planar Imaging 3000 '(/)I 2000 c g 1000 ■ 0 0 10 20 30 40 50 60 Echo Time (ms) Figure 5.7 Example of the fit of a single exponential to the signal level at multiple echo times in a region of interest defined in the cortex of the rat brain. This data was acquired with the interleaved EPI sequence (TR = 2 sec) during a control period of a time course experiment and yields a value for T 2 * = 45.5 ± 1.5 ms. 154 Rapid T2* Mapping Using Interleaved Echo Planar Imaging of T 2 * for a region of interest in the grey matter of rat brain during the anoxic challenge experiment is shown in figure 5.8. As expected (Turner et al, 1991), a sudden decrease in T2 * is observed following the onset of anoxia, which reflects the build-up of paramagnetic deoxyhaemoglobin in the cerebral vasculature. Initially, T 2 * has a value of approximately 45.5ms; it drops by -15% to a minimum of 39ms during the first period of anoxia. When the normal oxygen supply is restored, T 2 * rises to a value slightly above that of the control period, and this is thought to be due to wash-out of deoxyhaemoglobin by fresh, oxygenated blood which is flowing at an increased rate immediately post-anoxia. This theory is supported by the measurements made by the pulse oximeter, which showed the oxygen saturation fraction of the rat blood to be 88% following the first anoxic challenge, compared to 77% during the control period. T 2 * during the second anoxic period (also 1 minute) follows a very similar pattern, except that no post-anoxic overshoot is observed. This is a consequence of the elevated pre-anoxic T 2 * values compared to the control period. During the final anoxic challenge, which lasted 2 minutes, the minimum value is lower than for the previous anoxic periods (-38ms) and a post-anoxic overshoot is again observed. This reflects the greater severity of two minutes of anoxia. Measurements made by the pulse oximeter showed haemoglobin oxygen saturation to be 97% during this T 2 * overshoot. The final section of the time course in figure 5.8 shows the change of T 2 * on death. The base values reached are similar to the minimum values of the final anoxic challenge, indicating that two minutes of anoxia is sufficient to almost fully deoxygenate the blood. The data shown in figure 5.8 show that the T 2 * interleaved EPI sequence can be used to quantitatively follow the time course of stimulus evoked blood oxygenation changes with high temporal resolution, and could be used in other applications where this parameter is of interest. 155 Rapid T2* mapping using Interleaved Echo Planar Imaging ( a ) SO.On 47.5- 45.0- * 42.5- 40.0- 37.5- 35.0 - 1 h 0 24 6 8 18 20 26 34 36 38 40 42 44 46 48 50 Time (rrin) (b) TE (ms) 0 5.95 13.6 19.55 2T2 33.15 40.8 46.75 T / map Figure 5.8 (a) Time course of T 2 * changes from an area of grey matter in the rat brain during a series of anoxic events induced by switching breathing gases from oxygen to nitrogen. Time points labelled A indicate when anoxia was initiated; points labelled B show when normal breathing was resumed, and point X shows when the inspired gas mixture was permanently changed to 100% N 2 . The anoxic events are approximately ten minutes apart and during some of this period data is not acquired, as shown in the plot. In the initial baseline period T 2 * = 45.5ms, during anoxia T 2 * drops to a minimum value of 39ms. Immediately after anoxia, T 2 * returns to a level higher than baseline of 48ms. During the ten minute recovery period T 2 * decays slighly to 47ms but not to the initial value of 45.5ms. (b) An example of a set of 8 images from the rat brain acquired during the control period of the experiment, corresponding to different effective gradient echo times and used to generate a T2 * map. 156 Rapid T2* Mapping Using Interleaved Echo Planar Imaging 5.4 Discussion The interleaved EPI method presented here has been shown to yield a series of distortion free images which can be used to generate very accurate T 2 * values in a short time. The acquisition time for each measurement is n^ x TR where n^ is the number of segments. Depending on the image matrix size, the TR used and the number of points acquired on the T2 * decay curve, typical acquisition times without any averaging are on the order of a several seconds. Each of the ns acquisitions of an echo train is of duration approximately 50- 100ms, depending on field strength, matrix size etc. In multi-slice mode the sequence will therefore allow on the order of 5-20 slices to be acquired without loss of temporal resolution in the time series. The sequence has both the advantages and difficulties associated with other interleaved EPI techniques. The advantages include a reduction in the amount of geometric distortion in the phase encode direction and an improvement in the point spread function (PSF) (compared to single shot EPI). It is important to realise that there is an orientation dependence to the spatial resolution of EPI as manifested by a different PSF in the phase encode and readout directions. The Fourier transform of the modulation transfer function, determined by T 2 *, shows that the PSF in the read direction is similar to that in conventional spin echo imaging. It is dominated by sine function convolution due to the effect of finite sampling and is barely affected by field inhomogeneity or T 2 , whereas in the phase encode direction the effects of T 2 * can broaden the PSF beyond that determined by the sampling duration (Farzaneh et al, 1990). Here, the effect of the modulation transfer function, with and without ETS, on the PSF of interleaved EPI, has been compared to the PSF of single-shot EPI. By assuming that T 2 * is spatially invariant the 157 Rapid T2* Mapping Using Interleaved Echo Planar Imaging approach of Farzaneh et al (Farzaneh et al, 1990) has been followed, in which the PSF due to sampling is convolved with the FT of the decay function. The comparison has been limited to the phase encode direction only for the reason described above. In figure 5.9, the PSF of EPI and the 8 pass interleaved EPI sequence described here are shown. For both sequences a T 2 value of 50ms and field inhomogeneity corresponding to a T 2 ' of 50 ms (hence T2 * = 25ms) were chosen. The PSF are compared with the sine function due to sampling effects alone. The loss of resolution in EPI compared with the sine, which can be considered to be the ideal case of spin echo imaging, is clear, whereas for the interleaved sequence there is negligible broadening of the PSF, irrespective of whether ETS is used or not. The difference in the PSF of interleaved and single-shot EPI is rather significant in terms of misregistration of signal. The amplitude of the PSF at its centre, for single shot EPI, is approximately half of that for interleaved EPI and the amount of signal which is misassigned into adjacent voxels increases proportionately as a result. Outside of the central lobe, the integral of the PSF in the interleaved case is almost zero whereas for single-shot EPI the non-zero integral is concomitant with the loss in amplitude in the centre. Our analysis has been limited to the effect of the magnitude of the modulation transfer function and has not included the effect of phase errors. A previous analysis of PSF in interleaved EPI (Mugler and Brookeman, 1996) showed how sidebands due to phase discontinuities can predict multiple ghosts in interleaved EPI, which as described earlier, is the major difficulty associated with the technique (McKinnon, 1993; Feinberg and Oshio, 1994). These simulations of off resonance effects deliberately discarded the effect of sampling on the PSF to identify the sideband positions. If the off resonance component of the PSF were convolved with the sine function due to sampling, the resultant total PSF would describe the spatial resolution function in the presence of inhomogeneity and off resonance effects. All of the approaches to the MRI PSF described above assume a spatially invariant T 2 *. However, 158 Rapid T,* mapping using Interleaved Echo Planar Imaging 60 40 o ■o 3 a -20 Figure 5.9 Simulated PSF of imaging techniques. For the case of an idealised spin echo, in the absence of any T 2 * decay, the PSF is a pure sine function ( ------). Single-shot EPI with an acquisition window of 50ms and T 2 = T2 ’ = 50ms (------) has a much broader PSF 8 shot interleaved EPI with acquisition window of 6.25ms, T 2 = T2 ’ = 50ms, is also shown with ETS (------) and without ETS ( ). For both of the interleaved cases the PSF closely resembles the sine function. 159 Rapid T%* Mapping Using Interleaved Echo Planar Imaging it should be noted that this is clearly not the case and in fact, portions of the image which are significantly distorted by field inhomogeneity may be badly ghosted in interleaved EPI (Mugler and Brookeman, 1996) but will not necessarily have a poorer spatial resolution. Having reduced the source of ghost artefacts by using ETS, it is still necessary to determine the best method to minimise the Nyquist ghosts due to errors in gradient waveforms, timing of the data sampling comb and the reversal of alternate echoes. For the experiments performed here the ghosts are minimised by manually applying 0th and 1st order phase correction to the alternate echoes after 1 dimensional Fourier transformation. Slightly different phase correction values tend to be required for the images constructed from the odd and even segments because the alternate segments traverse the read direction in opposite directions and so errors in timing due to a D.C. read gradient (or shim) offset differ between them. For more routine operation, the use of phase reference scans and automated correction methods (Bruder et al, 1992) could be used. One further possible problem with the technique is that the alternate images in the time series have been acquired with a reversed direction of the phase encode gradient. This means that the geometric distortion in the odd and even images are reversed in direction and may possibly lead to errors in areas of gross field inhomogeneity. However, as previously discussed, the degree of geometric distortion in interleaved EPI is far less than for single shot EPI and therefore this should be a minor problem. The same point applies to the direction of the chemical shift offset for signal from fat but EPI is usually implemented with fat suppression and so this does not represent a major limitation. An alternative implementation of the technique using a large phase encode gradient between each image segment would avoid the complications associated with traversing the phase encode 160 Rapid T2* Mapping Using Interleaved Echo Planar Imaging dimension in different directions. However this implementation would increase each acquisition time by approximately l/8th and would not allow for uninterrupted data sampling throughout the entire echo train, which in itself can be a practical limitation on some MRI systems. Moreover it has been shown here that the additional k-space complexity does not represent a major obstacle to acquiring high quality images. 5 .5 Conclusions A new method to generate T 2 * maps in a few seconds has been described. This technique has been shown to yield superior image quality to that obtained with single-shot EPI. Furthermore, the T 2 * values calculated with this technique are in good agreement with those measured using FLASH imaging. It is anticipated that the method presented will be valuable for performing T 2 * mapping experiments when high temporal resolution is important. These are likely to include experiments in the animal and human brain which follow the time course of changes in blood oxygenation under a variety of experimental conditions. 161 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH 6 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH 6.1 Introduction Diffusion-weighted magnetic resonance imaging (Le Bihan et ai, 1988; Le Bihan and Turner, 1992) has been shown to provide important information which is not available from standard Ti- and T 2-weighted images. It has proved especially useful in the study of cell damage caused by cerebral ischaemia (Moseley et al, 1990; Mintorovich et ai, 1991; Pierpaoli et al, 1996), where changes in the apparent diffusion coefficient (ADC) of tissue water occur within minutes of the ischaemic insult, compared to the very much longer delay before the increase in T% (due to vasogenic oedema) is observed. As with all MRI techniques, it is desirable for the total imaging time of the diffusion- weighted imaging (DWI) sequence to be as short as possible, provided that ADC measurements can be made with the required accuracy. The reasons for this include reduced motion sensitivity (to which DWI is particularly susceptible), limited scan time in the clinical environment, and the need to keep up with evolving pathophysiology in animal model experiments. The implementation of single-shot echo planar imaging (EPI) with diffusion-weighting (Turner and Le Bihan, 1990) has been very effective in reducing the time taken to acquire a set of diffusion-weighted images. However, EPI techniques demand specialised hardware requirements which are not presently available at many sites, and also can not be implemented in high field systems without severe image distortion due to magnetic susceptibility effects. For these reasons, several groups have 162 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH explored the usefulness of TurboFLASH (Haase, 1990) and TurboSTEAM (Merboldt et al, 1992) imaging methods in conjunction with a magnetisation preparation scheme, and low flip angle spin echo sequences (Ordidge et al, 1994), to obtain ADC measurements. The fast spin echo approach (Ordidge et al, 1994) provides images with good temporal and spatial resolution and minimal distortion effects; however, the presence of higher order echoes generated from complex coherence pathways make ADC quantitation difficult. TurboSTEAM offers the advantage of the ability to use long diffusion times, and thus achieve substantial diffusion weighting without a large decrease in the available signal due to relaxation decay. However, quantitation is again difficult since the diffusion- weighting of the sequence (which can be expressed in terms of the “b value” (see (Le Bihan, 1991) and chapter 3)) is different for each line of k-space. In addition, SNR is compromised since there is intrinsically less signal available from a stimulated echo. Therefore, in this chapter I examine the use of TurboFLASH to obtain diffusion-weighted images. Diffusion-weighted TurboFLASH, first proposed by Deimling et al (Deimling et al, 1990) and Perman et al (Perman et al, 1990), consists of a driven equilibrium Fourier transform (DEFT) sequence (Becker et al, 1969) with a pair diffusion-sensitising gradients around the 180° refocusing RF pulse followed by a TurboFLASH imaging sequence. With standard TurboFLASH, the images produced using this sequence can be heavily contaminated by T] effects due to relaxation immediately before and during the imaging period, which typically lasts several hundred milliseconds (le. the same order of magnitude as TQ. This effect can be reduced by using centre-out phase encoded TurboFLASH (Lee and Price, 1994), and can be completely eliminated if a two-phase cycling scheme is used for the second 90° RF pulse of the DEFT preparation and the low 163 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH angle imaging pulses (Yamazaki et al, 1991). The improvement in the accuracy of ADC measurements using this method has been shown (Coremans et al, 1997). An alternative approach is to include a crusher gradient in the preparation whose effect is rephased during the readout period (Sinha and Sinha, 1996). This option, however, has the detrimental effect of lengthening the echo time and thus increasing the total imaging time. Another problem associated with TurboFLASH diffusion-weighted imaging is the effect of eddy currents generated by the diffusion sensitising gradients. These cause time varying magnetic field inhomogeneities across the sample, which act during the application of the diffusion gradients to cause phase shifts which prevent the return of magnetisation to the z axis by the second 90° pulse. This results in impairment of the magnetisation preparation process. It has been shown that this effect can be minimised by using a number of gradient dummy cycles prior to the magnetisation preparation period of the sequence (Kirsch, 1991) to set up a steady state eddy current environment. However, on imaging systems with unshielded gradients or significant eddy current problems, centre-out phase encoded TurboFLASH still suffers from the effects of magnetic field inhomogeneities when high gradient strengths, used to achieve the b values required for in vivo studies, are applied. These inhomogeneities cause spin dephasing, which is especially apparent at higher field strengths where the resonant frequency of precession is higher. In this study, I address two main issues. Firstly, an alternative method for overcoming the problems caused by eddy currents generated by the diffusion gradients is suggested. This method involves acquiring two images at each b value, with the 90° flip back DEFT pulse of the second image phase shifted by 7i/ 2 with respect to the first. Any phase shift of the spin echo created by the initial 90° and 180° pulses is therefore measured and can be taken into account. The true image intensity is calculated by squaring the intensities of 164 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH these two images, adding the squares, and taking the square root. Secondly, I look at the effect of reducing the delay time between acquisitions on the accuracy of the ADC measurement. Previous analyses have assumed full relaxation at the beginning of each magnetisation preparation; since the methods proposed here require two images for each b value, it is important to examine the situation where there is incomplete relaxation. This is also a consideration when signal averaging is being done, so that the optimum signal to noise ratio (SNR) per unit time can be achieved. 6.2 Theory 6.2.1 Elimination of eddy current effects using phase cycling The standard DEFT pulse sequence consists of a 90°-TE/2-180°-TB/2-90° pulse train, in which all the RF pulses have the same phase (x). The purpose of the DEFT sequence is to excite the equilibrium magnetisation, to modulate it in some way while it is in the transverse plane, and then to return this ‘prepared’ magnetisation to the longitudinal axis. The first 90° pulse causes spin excitation. The 180° pulse generates coherent magnetisation along the negative y axis at time TE, which then is returned to the z direction by the final 90° pulse. Typically the sequence is used to produce T%-weighting by merely allowing precession in the transverse plane for a given time TE; to produce diffusion-weighting, magnetic field gradients are added during this period. A modified DEFT pulse train which has better tolerance to Bi inhomogeneities has been suggested for use with diffusion-weighted TurboFLASH (Lee and Price, 1994), and is made up of a 90x°-180y°-90.x° sequence (see figure 6.1). This again results in the net magnetisation being aligned along the +z axis, assuming that the spin echo created by the 180° 165 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH refocusing pulse forms exactly along the +y axis. However, if diffusion gradients are inserted into the sequence, the eddy currents generated by the ramp up and down of the first diffusion gradient will affect the phase evolution before and after the 180° pulse (assuming the time constants of the eddy currents to be of the order of tens of milliseconds or greater); in contrast, the second diffusion gradient can only cause dephasing during the second half of the preparation period. A phase shift will therefore result, and the echo will not form along the y axis. This means that the second 90° pulse will only send a proportion of the total magnetisation back to the +z axis (McosO, where 0 is the angle between the vector M and the y axis). Since 0 depends on inhomogeneities which may vary across the imaging plane, the result is a non-uniform image whose intensity does not simply reflect diffusion attenuation. In order to obtain an image which is properly diffusion-weighted, it is also necessary to sample the MsinO component of the prepared magnetisation. This can be done by acquiring another image which is obtained following a 90x°-180y°-90.y° DEFT sequence. The ‘true’ image pixel intensity can thus be defined as ~ y ( ^ 9 o _ y f ( 6 - 1 ) where Igo-x represents the pixel intensity of the image taken after a (90x°-180y°-90_x°) preparation and Igo-y is the intensity of an image after a (90x°-180y°-90.y°) preparation. A resultant image can be generated by taking the two base images and performing this operation on a pixel-by-pixel basis; this new image will have the required diffusion- weighted contrast and can be used to fit for the ADC. 166 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH 6.2.2 Effect of reduced inter-experiment delay time on ADC measurements Following the analysis presented by Coremans et al (Coremans et al, 1997), the transverse magnetisation created by the nth low angle pulse of the TurboFLASH imaging sequence following magnetisation preparation can be written as: {n) = A(n)exp(- bD)+ B{n) (6.2) where A{n) = M qE^ exp(- r/T, )[£, cosa]”"^ sin a (6.3a) B{n) = M , (1 - exp(- T/r, ))x [(£, cosa)”-' + (l - E, )]x ^ sin a (6.3b) 1 -E , cosa and Mo represents the equilibrium magnetisation, a is the flip angle, Ei = exp(-TR/Ti), TR is the repetition time of the FLASH sequence, T% is the longitudinal relaxation time, E2 = exp(-TEp/T 2) with TEp as the preparation time, T 2 is the transverse relaxation time, t is the delay between the end of the preparation and the beginning of the FLASH imaging period, D is the diffusion coefficient and b is the gradient factor for the diffusion gradient pulses in the preparation period. The diffusion-independent B(n) term in equation (6.2) is eliminated in the two-phase cycling (or ‘subtraction’) scheme (Yamazaki et al, 1991) by changing the phases of the last 90° preparation pulse and of the slice-selective a RF pulse from [90x°-180y°-90.x°] - T - [ax]n to [90x°-180y°-90x°] - T -[oc.x]n, which causes the excited transverse magnetisation to be of the form MXn)= A{n)&\p{-bD)-B{n) (6.4) Addition of the two signals results in a value which is only dependent on A(n)exp(-bD). 167 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH At the end of the FLASH acquisition, the magnetisation is allowed to recover during the delay time TD. If this time is long compared to Ti (i.e. TD > 5TQ, then the magnetisation will be fully relaxed and the previous equations will again be valid. However, this makes the sequence time inefficient, and the following analysis considers the effect of reducing TD. Immediately after the last FLASH pulse (assuming 64 phase encoding steps), the longitudinal magnetisation will be = [A(64)exp(-^D)+5(64)]cota (6.5) where the cot a term represents the ratio of the longitudinal to the transverse magnetisation. If we allow the system to recover for a delay time, TD, M% will become M, (ro) = [A(64)exp(- bD)+ S(64)]cot a exp(- TD/r, exp(- TD/T, )) ( 6 .6 ) The next magnetisation preparation is carried out with this initial value of M% rather than Mz=Mo, and results in transverse magnetisation generated by the FLASH a pulses given by (see Appendix for full derivation): M ,(n)= X{n)QXip{-2bD)+Y{n)Qxp{-bD)+B{n) (6.7) where X («)= A(64)coscr • exp(- (TD + t )IT^)-{E^ c o s c c ) ”"’ (6 .8 ) Y{n)=A{n) 1 + exp(-TD/T,) (6.9) Mo and B(n) is as defined previously. Two main points are evident from equation (6.7). Firstly, one can see that the coefficient Y(n) which represents the required diffusion- weighted component of the signal is equal to A(n) (its previous value) multiplied by a factor related to exp(-TDZTi). As one would expect, this factor tends to unity as TD tends to infinity, causing Y(n) A(n). Secondly, a third term has appeared in equation (6.7) 168 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH which relates to the magnetisation which has been ‘diffusion prepared’ twice. The relative magnitude of this term depends on the particular experimental parameters used, but, as expected again, tends to zero as TD becomes large. A third image can be acquired a time TD after the second, and a similar analysis applies. The resulting signal intensities are given by (see Appendix) Mf («) =U («)exp(- 3bD)+ V (w)exp(- 2bD)+ 7(«)exp(- bD)+ B{n) (6 .10) where U{n)= ■X{n) (6.11) = (6. 12) and Y(n), B(n) and A(n) are as defined above. The coefficients of the higher order terms become increasingly less significant, since the amount of magnetisation which becomes diffusion-weighted three times before it relaxes is minimal. If ADC calculations are made assuming a monoexponential relationship between signal intensity and diffusion coefficient, the main source of error in the fit can be attributed to the exp(-2bD) term in the above equations. The size of this error depends on the experimental parameters used, and will be addressed in the Theoretical Results section. 6.3 Materials and Methods 6.3.1 NMR hardware All experiments were performed on an 8.5T Oxford Instruments magnet interfaced to an SMIS (Guildford, UK) console. The system has gradient coils with an internal diameter of 169 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH 54 mm and a maximum gradient strength of 160mT/m, with a switching time of 200|is. A birdcage coil tuned to 360MHz and with inner diameter 38mm was used to transmit and receive RF signal. 6.3.2 Pulse sequence The pulse sequence diagram is shown in figure 6 .1. The magnetisation preparation pulse train consisted of two hard 90° pulses of lOOjis duration, equally spaced around a central 200|is hard 180° pulse. The preparation time, TEp, was 60ms. The diffusion-weighting gradients were trapezoidal with ramp time 200|lis and plateau duration 24.1 ms. A delay of 10ms followed the third RF preparation pulse, during which spoiler gradients were applied to destroy any residual transverse magnetisation. The imaging period began with 3 FLASH dummy cycles, to minimise the ghosting caused by amplitude discontinuities which occur before the excited magnetisation reaches its steady state value, and then consisted of a centre-out phase encoded spoiled FLASH sequence with an incrementally increasing spoiler in the slice select and read directions. Spoilers were also applied along the phase encode direction which decreased and alternated sign with the phase encode gradient. The amplitude of the spoiler gradients was chosen experimentally to eliminate image artefacts. To keep the imaging time to a minimum, 64 phase encoding steps were used, with 128 data points acquired during each and a signal bandwidth of lOOkHz. The field of view (FOV) was 40mm x 40mm, and slice selective excitation was achieved using a sinc-shaped RF pulse (length 6 6 6 p.s, bandwidth 6 kHz) with a flip angle of approximately 14°. The echo time and repetition time of the FLASH sequence were 2ms and 5ms respectively, resulting in a total imaging time of 335ms. 170 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH hard hard hard sine 71/2. 71/2 . a . n times RF slice Followed by inter experiment delay TD phase read TE, TR Magnetisation preparation period Imaging period Figure 6.1 Diffusion weighted TurboFLASH sequence. A diffusion preparation period of length TEp consists of a 90°-180°-90° RF pulse scheme with diffusion gradients of duration ô and time separation A placed around the 180° pulse. Following the preparation period, spoiler gradients are applied during the delay time T to crush residual transverse magnetisation. The imaging sequence is gradient spoiled TurboFLASH with an echo time TE of 2ms and a repetition time TR of 5ms, which is centre-out phase encoded using 64 phase encoding steps. Rewinding of the phase encoding gradient is not necessary since the theory requires no transverse magnetisation to survive between successive low-angle excitations. The inter-experiment delay, TD, indicates the time allowed for relaxation after the FLASH sequence. 171 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH In order to remove Ti relaxation effects during the imaging period, the two-phase cycling subtraction method was used. Therefore, for each diffusion-weighted image it was necessary to make four acquisitions, since the two images needed to account for eddy current effects both needed two acquisitions to eliminate T% effects. 6.3.3 Phantom experiments Initial experiments were performed on a water phantom to demonstrate the effect of altering the phase of the third RF pulse of the DEFT preparation on the resulting TurboFLASH image signal intensity. The phases of the first and second pulses were kept constant (0° (4-x) and 90® (+y) respectively) and the phase of the third pulse was varied incrementally from 0° to 270°. Images were acquired using centre-out TurboFLASH as described above. Phantoms for diffusion studies were made using 150mM saline solution containing 1.5% by weight agar and doped with copper sulphate. Agar was used to reduce the convective flow within the phantom, and to bring the T 2 of the phantom down to a value closer to that of tissue (~ 70ms). Modification of the amount of CUSO 4 allowed control of the T% value of the phantom. For the phantom experiments, an imaging slice thickness of 4mm was used. Eight diffusion gradient strengths were used to give b values ranging from 100 s/mm^ to 800s/mm^, calculated from the Stejskal-Tanner formula (Stejskal and Tanner, 1965) including the effect of finite gradient ramp times, = [(A -5 /3 )5 ^ + e7 3 0 -e"5 /6 ] (6.13) where y is the gyromagnetic ratio for protons, G is the gradient strength, Ô is the gradient pulse duration, A is the time between beginning of the two pulses, and 8 is the gradient 172 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH ramp time. In our experiments, A was 32.4ms, ô was 24.3ms and e was 200|is. The contribution of the imaging gradients to the b value was ignored in the calculation, since their effect is very small compared to the main diffusion gradients. Experiments were firstly performed to verify the accuracy of the ADC measurements made by the new FLASH sequence described above, in which the two orthogonal components of the prepared magnetisation were sampled and combined to form the diffusion-weighted image. For these studies, the delay time between the end of each FLASH imaging period and the start of the following preparation period was 5 seconds so that the magnetisation could be assumed to fully relax during this time. A standard 2D FT diffusion-weighted spin echo sequence was used for comparison, and diffusion-weighting was applied separately along the slice, read and phase encode directions for both sequences. In order to obtain ADC values with sufficient precision, signal averaging was performed (Na = 24 for the FLASH experiments, Na = 2 for the SF). The measurements were performed on two phantoms with different Ti values (930ms and 1430ms, measured using IR-Snapshot FLASH) and repeated four times. The temperature of the phantom was measured continuously throughout the whole experiment, and variations were corrected for by assuming the relationship between ADC and temperature to be a 2.4% increase per °C (20). Measured ADCs were multiplied by this correction factor so that all values would be directly comparable. This technique was applied to all the experiments described in this chapter. Secondly, we looked at the effect of reducing the inter-experiment delay time, TD. A data set was acquired using the phantom with the longer T% (Ti = 1430ms and T% = 70 ms, measured using a 4 point multi-spin echo sequence) with each of the following delay 173 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH times: 5000 ms, 1500 ms, and 750ms. This was done to investigate how the measured ADC deviates from its true value as the delay time becomes less. 6.3.4 In vivo experiments To show that the proposed TurboFLASH sequence gave the correct diffusion contrast, experiments were carried out in vivo, interleaved with spin echo DW imaging for comparison. Male Wistar rats weighing 110-160g were used. Anaesthesia was induced with 3% halothane / 0 2 and continued via a nose cone at 1.25% halothane. Rectal temperature was recorded and maintained with an air cooling feedback system. Images at four different b values ( 1 0 0 , 600, 1 1 0 0 and 1600 s/mm^) were obtained with both sequences using similar diffusion times [ 6 (SE) = Ô(FLASH) = 24.3ms, A(SE) = 34.8ms, A(FLASH) = 32.4ms]. Other sequence parameters for the spin echo images were: FOV = 40x40 mm, TE = 65ms, TR = 1500ms, Na = 2, matrix size = 128x64, slice thickness = 2mm. Turbo FLASH parameters were the same, except TEp = 60ms, Na = 24 and TD = 5 seconds. 6.4 Results and Discussion 6.4.1 Theoretical Results As shown in the Theory section above, the transverse magnetisation which constitutes the FLASH signal can be split up into a number of terms, each of which represents magnetisation with a different diffusion preparation history (see equations (6.2), (6.7), 6.10)). The relative magnitude of these terms depends on the values of the coefficients A(n), B(n), X(n) etc., which in turn depend on the particular pulse sequence parameters 174 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH used. Inserting the pulse sequence parameters specified above in the Methods section into equations (6.3a), (6.3b), ( 6 .8 ) and (6.9), these coefficients can be calculated, and their values for the three values of TD used are shown in table 6 .1. Since it is the relative magnitudes which are important, all values are shown as a fraction of the first coefficient, A(n), and this fraction is called the coefficient ratio. Inter-experiment delay time, TD Coefficient Ratio TD = 5000ms TD = 1500ms TD = 750ms A(n) 1 B(n) 0.0162 + 2.65 X 10'^ x (0.967)'" X(n) 1.49 X 10'^ 0.0172 0.0290 Y(n) 0.972 0.682 0.462 U(n) 2.22 X 10'^ 2.96 X lO'"^ 8.44 X 10'^ V(n) 1.45 X 10'^ 0.0117 0.0134 Table 6-1 Values for the coefficients in Equations (6.2), (6.7), and (6.10), expressed as a fraction of A(n), calculated using the pulse sequence parameters which were used in the experimental studies Several points should be noted regarding the values shown in table 6.1. Firstly, the B(n) to A(n) ratio is a function of n, since the relative contributions of diffusion prepared and Ti relaxed magnetisation changes throughout the imaging period. However, the B(n) signal is eliminated using the phase cycling ‘subtraction’ method, and so is unimportant. All the other coefficient ratios are independent of n because they arise from diffusion prepared magnetisation. The Y(n) ratio represents the reduction in signal from diffusion-weighted spins caused by not allowing full relaxation. One can see that as TD is made shorter this ratio becomes smaller, because Ti recovery is less complete, and this will have direct implications regarding signal to noise ratio of the images. To examine the error in ADC measurement introduced by the extra exponential term in equation (6.7) (the e'^^^ term), it is necessary to compare the X(n) to Y(n) and V(n) to Y(n) ratios from table 6.1. When TD 175 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH = 5 s, X(n)/Y(n) is approximately 0.2%, which means that the extra term is insignificant and the ADC value should be accurate. As TD is reduced, the X(n) to Y(n) ratio becomes 2.5% (for TD = 1500ms) and 6.3% (for TD = 750 ms). For three or more averages it is the V(n) to Y(n) ratio which will be important, which is 0.1% (TD = 5s), 1.7% (TD = 1.5s) and 2.9% (TD = 0.75s). Depending on the required precision of ADC measurement this error may be significant. Furthermore, it is important to realise that the error term is also dependent on (exp(-bD))^, and so its effect will mainly occur on the less diffusion- weighted images, which could tend to skew measurements. 6.4.2 Phantom studies Figure 6.2 shows data from two regions of interest drawn on the water phantom used to investigate the dependence of the TurboFLASH signal intensity on the phase of the final pulse of the DEFT preparation sequence. It can be seen that the optimum phase value varies regionally (see also figure 6.3), and also differs considerably from the expected result of 180°. However, the form of the relationship between TurboFLASH signal intensity and DEFT flip-back pulse phase is as expected. This is a modulus sinusoidal relationship, corresponding to the DEFT pulse rotating in the transverse plane with respect to the excited magnetisation, with the two maxima of the curve having different amplitudes, corresponding to the different Ti relaxation effects on image intensity depending on whether the longitudinal magnetisation is aligned along the +z or -z axis prior to imaging. Three sets of images acquired using the TurboFLASH diffusion imaging technique at different b values are shown in figure 6.3. The first of each set was acquired using a 176 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH 3500 3000 - 2500 - X X X •c t cl 2000 X 0) 3 ♦ ♦ ♦ X i» X ir 1500 ♦ ♦ X< 500 -- V s : 50 100 150 200 250 300 Phase (degrees) Figure 6.2 Variation of TurboFLASH image signal intensity from two regions of interest in a water phantom as the phase of the third DEFT pulse is varied. The phase of the first and second DEFT pulses was kept constant at 0° (+x) and 90° (+y) respectively. 177 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH conventional 90x°-180y°-90_x° preparation sequence; the second was acquired using a 90x°-180y°-90.y° preparation sequence to sample the orthogonal component of transverse magnetisation. It can be seen that in each pair, both images contain a proportion of the prepared signal, and this proportion varies with position across the image. If only the first image of each pair is used to calculate the ADC, the result varies with position and so is unreliable. It is therefore necessary to use both images and apply the ‘root sum of squares’ technique described above to eliminate the eddy current effects and get an accurate measure of the ADC. The third image of each set in figure 6.3 shows the result of applying this technique to the two preceding images. It can be seen that the resulting image is homogeneous. To compare ADC values, regions of interest were drawn on the sets of diffusion-weighted images obtained using the TurboFLASH and spin echo sequences. Diffusion coefficients were calculated for these regions by performing a non linear monoexponential least squares fit on the mean pixel intensity. An example of a result of these calculations is shown in figure 6.4. Four ADC values of five regions are shown: the first value was that measured by the spin echo, and the second, third and fourth were those measured using the TurboFLASH sequence with an inter-experiment delay time of 5 s, 1.5 s, and 0.75 s respectively. One can see immediately that the values are very close, and in order to verify their equivalence statistically, t-tests were carried out. The data from each sequence consisted of measurements of x, y and z ADC values from 5 regions which had been repeated four times, resulting in a data set size of 60. A paired t-test was carried out to compare the spin echo data set with each of the TurboFLASH data sets. In order to verify the validity of the results, Kolmogorov- Smimov normality tests were performed on the three sets of paired differences, which showed all sets to be consistent with a Gaussian distribution. 178 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH n 2. T 2\l/2 DqO .. ^ ^ 90 .. ) b = 1 0 0 b=300 b=600 (a) (b) (c) Figure 6.3 Diffusion weighted images of an agar phantom at three different b values (in s/mm^) following (a) 90^-180^-90,^ and (b) 90^-180y-90_y magnetisation preparation schemes. The variation of intensity across the images reflects the differing effects of eddy currents at different points in space. Squaring, adding and square rooting pixel intensities yields a much more homogeneous image (c). The dark band at the top of the images is a susceptibility artifact due to the presence of an air bubble in the phantom, not an eddy current effect. 179 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH (a) 0 .0 0 3 - ]SE (/) CM I FLASH (TD=5s) Ë E 0.002- 3 FLASH (TD=1.5s) 0) ^ FLASH (TD=.75s) 3 (Q Q 0.0014 o < 0.000 roi rol2 roi 3 roi roi 5 (b) 0.003n 3SE (/) CM I FLASH (TD=5s) Ë E 0.002 3 FLASH (TD=1.5s) ^ FLASH (TD=.75s) 0 ) 3 (Q Q 0.001 n < 0.000 roi roi 2 roi 3 roi 4 roi 5 (c) 0.003-1 3 SE (A I FLASH (TD=5s) CM Ë E 0.002 3 FLASH (TD=1.5s) ^ FLASH (TD=.75s) 0 ) 3 § Q 0.0014 Û < 0.000 roi roi 2 roi 3 roi roi 5 Figure 6.4 ADC measurements from 5 regions of interest of an agar phantom, acquired using spin echo (SE) DWI and TurboFLASH DWI with various inter-experiment delay times (TD) and diffusion weighting along (a) x, (b) y, and (c) z. 180 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH The results of the t-tests are shown in table 6.2. They show that for the TurboFLASH sequence with the five second delay time, the mean measured ADC is not different from the spin echo value, despite the fact that the standard deviation of the differences was only about 0.2% of the ADC value. The 95% confidence interval of the differences between the values measured by the two sequences straddles zero, which shows that the sequences give equivalent ADC values. Inter-experiment delay time of TurboFLASH sequence TD = 5s TD= 1.5s TD = 0.75s p value p > 0.05 p > 0.05 p < 0.05 95% confidence interval of differences (lower limit, upper (-0.0016, 0.0133) (-0.0041,0.0110) (-0.0254, -0.0071) limit) in mm Vs x 1 0 '^ Table 6-2 Paired t-test results comparing TurboFLASH diffusion-weighted sequence with spin echo sequence on an agar phantom, p values are two-tailed; difference calculated by subtracting TurboFLASH ADC from spin echo ADC; p values greater than 0.05 indicate no difference between the two methods at this significance level; p values less than 0.05 indicate a difference between the two methods at this significance level. Table 6.2 also shows the results from the TurboFLASH experiments run with the shorter inter-experiment delay times. For an inter-experiment delay time of 1500ms (i.e. TD ~ Ti), the error in the ADC measurement is still not noticeable, but when the delay time is reduced further to 750 ms the difference between the two values becomes significant. The fact that the confidence interval is below zero means that the value obtained using the TurboFLASH method overestimates the ADC, which is consistent with the equations derived in the Theory section (see equation (6.7)). As a result of the error term (X(n)e'^^^) being dependent on b value, the intensities of the less diffusion-weighted images will be enhanced to a greater extent than the intensities of the heavily diffusion-weighted images, 181 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH thus producing a relationship between signal intensity and b value which has a higher apparent decay constant (i.e. higher ADC). The question arises as to whether this error imposes a limit on the signal to noise achievable using the TurboFLASH sequence. From equation (6.7), the important signal component is determined by the factor Y(n). If we intend to run the sequence for a given total time T, then we know that the signal to noise improvement will be proportional to V(T/TD), since SNR increases with the square root of the number of averages acquired. Therefore, maximising Y(n).V(l/TD) with respect to TD will yield the inter-experiment delay time which will result in the optimum SNR per unit time. This function is shown in figure 6.5, and one can see that the maximum occurs for a value of TD just greater than TD = Ti. For this value of the delay time, we have shown that the error in the measurement of the ADC is insignificant, and so it seems that the optimum experimental parameters can be used with no penalty regarding accuracy of measurement. 6.4.3 In vivo studies An example of the diffusion coefficient maps for each direction (ADC%, ADCy and ADCz) obtained from a rat brain using the spin echo and TurboFLASH sequences is shown in figure 6 .6 . Similar diffusion contrast, anisotropy effects and A D C values can be seen in the two sets of images, demonstrating their equivalence. Figure 6.7 shows a scatter plot of the pixel intensities of the maps from the two methods plotted against each other. The correlation between the data sets is very good, shown by the r values all being close to unity. The plots also show the lines of equivalence (a line with gradient of 1 and intercept at (0 ,0 )), and the data points in the three graphs are all scattered around these lines. 182 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH 0.8 0.75 - 0.7 - ^ 0.65 0.55 / 0.5 0.2 0.6 1 1.4 1 .8 2.2 TD/T1 Figure 6.5 Signal to noise per unit time of the coefficient Y(n) as a function of TD/T, (arbitrary units). Optimum delay time is slightly greater than TD = T,. 183 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH Spin echo ADC TurboFLASH raw images: TurboFLASH ADC maps: maps: (a) (b) b= 100 b= IIOO (c) i (d) b= 100 b= 1100 (e) (f) b= 100 b - 1100 Figure 6.6 ADC maps calculated from diffusion weighted spin echo images (left eolumn) and the TurboFLASH sequence (right column), with examples of diffusion weighted images obtained following the 90,-180y-90_, (I90.J and 90,-180y-90_y (l 9o_y) magnetisation preparation schemes at two b values (centre column). Diffusion weighting was applied along X (top row), y (middle) and z (bottom). Several anatomical features can be distinguished in both sets of images e.g. the external capsule white matter tracts (arrows in images (a) to (d)), the trigeminal nerves (arrows in (e) and (f)), and the cortical gray matter anisotropy shown by all the images, b values are in units of s/mm^. 184 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH (a) (b) r = 0.99 r = 0.99 U Q < < W W on on 0.6 0.6 0.4 0.4 0.2 0.2 0.2 0.4 0.6 0.8 1.0 1.2 0.2 0.4 0.6 0.8 1.0 1.2 FLASH ADC. FLASH ADC. (c) r = 0.99 0.6 0.4 0.2 0.2 0.4 0.6 0.8 1.0 1.2 FLASH ADC. Figure 6.7 Pixel scatterplots comparing ADC maps calculated from spin echo images (vertical axis) and TurboFLASH images (horizontal axis) of a rat brain. Diffusion weighting was applied along (a) x, (b) y and (c) z. ADC values are in units of 10'^ mm^/s. Correlation coefficient (r) values show good correlation between the techniques. The dashed line is the line of equivalence i.e. gradient = 1 , intercept both axes at ( 0 ,0 ), and is shown for reference. 185 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH 6.5 Conclusions I have presented a new method for fast quantitative diffusion imaging which is tolerant to eddy currents and can be used at high field. It has been shown that the delay between experiments can be reduced to a value which produces optimum SNR per unit time without compromising the accuracy of the measurement. The method for correcting DEFT spin echo phase shifts caused by eddy currents involves the acquisition of two images, which doubles the time required for a set of diffusion- weighted images compared to other FLASH sequences. This obviously limits the temporal resolution achievable using this technique, but it was found that in order to ensure accurate ADC measurements, this method of accounting for phase shifts was necessary. Using gradient dummy cycles prior to the magnetisation preparation period did not result in accurate ADC values. I have shown that the limit on the temporal resolution is made less severe by the result that it is not necessary to wait for full relaxation between experiments. The sequence can be run at a rate which optimises SNR, which is when the delay time between experiments is slightly greater than the Ti of the sample. If the delay time is reduced below this value, a systematic error is introduced which causes the ADC value to be too high. However, since the situation is non-optimal, this restriction is not important. The situation in vivo is complicated by the fact that a range of Ti values will be present in the subject. This could mean that if an inter-experiment time is chosen which is optimal for those spins which have the shorter T% values, the delay will not be sufficient to ensure accurate ADC values for spins which have longer Ti, and the measured ADC values 186 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH would effectively be weighted towards those of the water molecules with shorter Ti values. In order to avoid this problem, care should be taken to choose a delay time which is at least as long as the longest Ti in the region of interest. Another point which should be made concerns the quality of the FLASH images compared to their spin echo equivalents. Visual inspection of the FLASH images shows that they are slightly more blurred than the spin echo images. This is probably due to the low pass k space filter effect which results from using centre-out phase encoded TurboFLASH (see (Coremans et al, 1997)). This effect could be eliminated if excitation pulses with variable flip angles were used to ensure echoes of equal amplitude throughout the imaging period. Apart from this modification, the images obtained using the FLASH sequence are equally accurate and can be acquired far more quickly than the spin echo images. Finally, I have shown that the new technique can be applied in vivo to provide a fast and accurate assessment of ADC values in experimental animal studies. The sequence can be implemented in commercial scanners without active gradient shielding, since it is insensitive to eddy current effects, and the short acquisition time means that it should be useful in applications such as the detection of stroke lesions. 187 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH 6.6 Appendix Initially, we assume that the magnetisation of the system is in its equilibrium state. Taking the result given by Coremans et al (Coremans et al, 1997) as our starting point, we have the transverse magnetisation created by the nth low angle pulse of the TurboFLASH imaging sequence defined as: M, («) = A(«)exp(- bD)+ Bin) (A6 .1) where A(«) = MqEj Gxp(-T/7^X^i cosa)"~’ since (A 6 .2 ) B{n) = (1 - exp(- T/r, ))x ((£,cosa)"-' + (l - E, ))x' since 1-E; COS# (A6.3) The terms in this expression are defined at the end of the appendix. At the end of the TurboFLASH imaging period, the longitudinal magnetisation will be defined by: M ^ (64,+) = [A(64)exp(- Z?D)+ 5(64)]cotce (A6.4) where Mz(64,+) represents the value of the z magnetisation immediately after (+) the last (64th) low angle RF pulse. We are interested in what happens if we allow this magnetisation to relax for an inter-experiment delay time, TD, and then perform another diffusion preparation. Relaxation during the time TD will cause the longitudinal magnetisation to evolve to the state: (to) = [A(64)exp(- bD)+ fi(64)]cot a ■ exp(- TDjT, )+ (l - exp(- TDjT, )) (A6.5) We assume that TD is long enough to ensure all transverse magnetisation coherence will be lost due to T 2 decay. The value of M% given in equation (A6.5) will be the magnetisation which is available for diffusion-weighted preparation at time TD. 188 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH Following the preparation period, M% will be given by: M^ (l,-) = M^ {TD)E^ exp(- 6 D)exp(- r/Ji )+ Mq (l - exp(- r/T^ )) (A6 .6 ) where M z(l,-) represents the longitudinal magnetisation immediately before (-) the initial (1st) low angle RF pulse, the exp(-bD) term represents diffusion attenuation and the exp(- t/TD) terms represent relaxation during the time x between the preparation and imaging periods. Entering Mz(TD) explicitly into equation (A 6 .6 ), with some rearranging of terms we obtain: M ^ (l,-) = (A(64)cota • exp(- TD/T^ )exp(-x/T| ))xexp(- 2bD) + (fi(64)cotO' • exp(- TD/T^ )+ Mq(l - exp(- TD/T^ )))E2 exp(-x/Fj )exp(- bO) + Mq{1- exp(- r/r, )) (A6.7) The transverse magnetisation generated by the nth low angle pulse can be calculated from this using the following relationships (see (Coremans et ai, 1997) for derivation): = -X ê , c o s a L (A6.8) cosa MX») = M^(M,-)exp(-7E/Z^ )sin(% (A6.9) which gives M, (n) = X (n)exp(- 2bD)+Y{n)exp{- bD)+B{n) (A6 .10) where X {n) = A(64)cos a • exp(- TD/T^ )E^ exp(- x/T, X^i cos a ) ”"* (A 6 .11 ) Y(n) = (r(64)coscc • exp(- TD/Tj ) + sina(l - exp(- TD/T^ )))x E^ exp(-x/Zj X^i cosa)"~‘ = A(n)|l+ -^^co ta-l exp(-rD/r,) (A6.12) and B(n) is as defined before in equation [A3]. 189 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH At the end of the second TurboFLASH imaging period, the longitudinal magnetisation will again be in a different state, given by: M^(64,+)= [z(64)exp(- 2bD)+ y(64)exp(-6D)+ 5(64)]cota (A6.13) If this state is allowed to relax for the inter-experiment delay time TD and then undergoes the magnetisation preparation process, a similar analysis to that given above can be applied. The longitudinal magnetisation immediately before the preparation period will be: M , {TD)= [X(64)exp(- 2bD)+ y(64)exp(-èD)+B(64)]cota • exp(- TDjT, ) (A6.14) + M„(l-exp(-rD/T,)) Following the same steps which were used to go from equation (A 6 .6 ) to (A6.10), we can calculate the transverse magnetisation generated by the «th low angle pulse for this image, which turns out to be M, («) =U (w)exp(- 2>bD)+V(«)exp(- 2bD)+ y(«)exp(- bD)-\- B(n) (A6.15) where U{n)=X (64)cos a • exp(- TD/T^ exp(- t/T, X^i cos - « I W W,1« V{n)=Y(64)cos a • exp(- 7D/7] exp(- c o s a)""’ = X(n)|l+ ^5^cota-l exp(-ID/r,) (A6.17) M q Several important points have been demonstrated by this analysis. Firstly, the error term due purely to Ti relaxation immediately before and during the imaging sequence is always the same, irrespective of the inter-experiment delay. Secondly, the coefficient which determines the magnitude of the required diffusion-weighted signal (i.e. the signal which varies proportionally with exp(-bD)) is constant from the second experiment onwards (Y(n)). Finally, the error associated with measurement of the ADC using this sequence 190 A Quantitative Method for Fast Diffusion Imaging using Magnetisation Prepared TurboFLASH will be determined by the relative magnitudes of Y(n) and X(n) if two averages are taken, or Y(n) and V(n) if three or more averages are acquired. El Represents the term exp(-TR/Ti) E2 Represents the term exp(-TEp/T 2) a Flip angle in FLASH sequence X Delay between preparation and FLASH imaging periods Ti Longitudinal relaxation time T2 Transverse relaxation time b Diffusion-weighting b factor D Diffusion coefficient Mo Equilibrium magnetisation TR Repetition time of FLASH sequence TE Echo time of FLASH sequence TEp Time between the two 90° pulses of preparation period TD Inter-experiment delay time Table 6-3 Definitions of terms used in derivations and calculations 191 Measurement of Perfusion using CASL in a Rat Model of Stroke 7 Measurement of perfusion using continuous arteriai spin labeiiing in a rat model of stroke This chapter describes the implementation and application of continuous arterial spin labelling to measure changing levels of cerebral perfusion in the middle cerebral artery occlusion (MCAO) stroke model in the rat. In combination with various other parameters (Ti, T2 and tissue water diffusion), the pre- and post-occlusion time course was monitored over a period of several hours. The experiments were performed at high field (8.5T) in order to maximise the inherent SNR of the perfusion measurement, and to amplify changes in relaxation rate associated with ischaemia. I will firstly describe how the arterial spin labelling sequence was implemented, and then go on to show how it was integrated into the experimental protocol for the MCAO experiments. 7 .1 Implementation of continuous ASL The method of perfusion measurement using continuous arterial spin labelling has been described in chapter 3. In order to achieve good time resolution for the perfusion measurement, spin labelling was combined with TurboFLASH (Haase, 1990) imaging to produce a perfusion-weighted (or control) image in a single acquisition (see figure 7 . 1 ). The experimental details are described in the following sections. 7.1.1 Use of TurboFLASH imaging The use of TurboFLASH imaging with CASL techniques was suggested by Ewing et al. (Ewing et al, 1995). For the initial experiments, I used standard TurboFLASH imaging with experimental parameters: TE=2ms; TR=5ms; flip angle ~ 14°; image acquired 128 192 Measurement of Perfusion using CASL in a Rat Model of Stroke (read) x 64 (phase encode) and zero filled to 128x128 prior to Fourier transformation; FOV 40 X 40mm; slice thickness = 2mm. Therefore, the image acquisition lasted 320ms and immediately followed the labelling period. Perfusion measurements were made by subtracting a spin labelled image from a control image (see next section) and using the equation (see (Williams etal, 1992)): (M f- M f1 (7.1) 2 oM "' ^ where A/is the steady state value of the brain tissue water magnetisation when no spin labelling is performed (which is different to the equilibrium value Mo due to the effects of macromolecular saturation by the off-resonance RF pulse and the resulting magnetisation transfer effects), is the steady state value of the brain tissue magnetisation when spin labelling is performed {i.e. reduced by both magnetisation transfer and inverted inflowing blood), X is the bloodibrain partition coefficient, a is the efficiency of the flow- induced adiabatic arterial spin inversion and Ti is the observed longitudinal relaxation time of brain tissue water. An inaccuracy is introduced to the perfusion quantitation if TurboFLASH image acquisition is used and equation (7.1) is applied directly. This inaccuracy arises from the evolution of the TurboFLASH echo amplitude through the imaging period. The amount of longitudinal magnetisation available for excitation by the FLASH low angle RF pulses decreases as an increasing proportion of it is flipped into the transverse plane. The echo amplitude therefore decreases up to a certain point along the echo train. This decrease does not continue indefinitely due to the effect of Ti relaxation during the imaging period. A steady state will occur when the amount of longitudinal magnetisation excited by the TurboFLASH RF pulse is the same as the amount which relaxes between excitations. 193 Measurement of Perfusion using CASL in a Rat Model of Stroke This causes a problem for the arterial spin labelling perfusion measurement, since we are interested in the brain tissue magnetisation at the end of the labelling period. The bulk of the TurboFLASH image intensity will be determined by the central portions of k-space, which in the standard sequence occurs mid-way through the acquisition where the echo amplitudes are reduced. In order to account for this effect, two approaches were taken. Initially, a TurboFLASH echo train from the rat brain was acquired without phase encoding gradients, and the decay of the echo amplitude was examined. It was seen that the amplitudes of the 32"^ and 33^^ echoes were approximately 80% of the initial echo amplitude (see figure 7.2). Therefore, as an approximate correction factor, the perfusion- weighted and control images intensities were multiplied by (0.8)'\ However, this approach is only approximate because it does not account for the fact that the tissue in each pixel can have a different Ti value. A more satisfactory method, and one which was implemented in later experiments, was to use centre-out phase encoded TurboFLASH. In this approach, the central portions of k-space are acquired as the first echoes and the image intensity is dominated by the value of the longitudinal magnetisation at that point, as required. Spoiled centre-out TurboFLASH was used (see figure 7.3a). In this version of TurboFLASH, a spoiler gradient of varying amplitude was applied after every readout period to completely dephase all transverse magnetisation. This prevents the appearance of image artefacts which were caused by coherent magnetisation remaining in the transverse plane and contributing to several echoes (see figure 7.3b and 7.3c). Using spoiled centre-out TurboFLASH in the continuous ASL sequence allows one to use equation (7.1) directly to quantify perfusion. 7.1.2 Spin labelling RF pulse In order to perform the arterial spin labelling, it is necessary to use a long duration off- resonance RF pulse. The RF pulse must be applied in the presence of a magnetic field 194 Measurement of Perfusion using CASL in a Rat Model of Stroke 5 sec 5 sec < ► M------► RF FLASH spin FLASH labelled control image image slice \, / xN„ Figure 7.1 Schematic diagram of the CASL perfusion sequence. A continuous 9kHz off-resonance RF pulse is applied prior to both the spin labelled and control image; the location of the on-resonance plane is altered by reversing the polarity of the slice select gradient. The image pair acquisition is repeated times and the data averaged to achieve an improved signal to noise ratio 1.2 1 Q) ■o 0.8 Q. E m 0.6 o .c o 0 ) 0.4 0 > CO CD 0.2 oc 0 Echo 1 Echo 11 Echo 21 Echo 32 Figure 7.2 Variation of echo amplitude in the FLASH image echo train (phase encode gradient off). Due to the saturation effect of repeated RF excitation pulses, the echo amplitude decreases to approximately 80% of its initial value by half way through a 64 echo image acquisition 195 Measurement of Perfusion using CASL in a Rat Model of Stroke (a) a ~ 14° A RF é - Gei;slice M Gphase ^read u X Npe (b) Figure 7.3 Spoiled centre-out TurboFLASH. (a) pulse sequence diagram. A constant 14° flip angle excitation pulse was used; the phase encode gradient is alternated according to the scheme 0,+1,-1,+2,-2,...+31, -31,+32, and the spoiler gradients are alternated in a similar manner to ensure crushing of transverse magnetisation, (b) shows the effect of not including the spoiler gradients. Magnetisation from previous phase encoding steps interferes with subsequent echoes to produce an artefact through the centre of the image. When the spoilers are included this artefact disappears, as shown in (c) 1 9 6 Measurement of Perfusion using CASL in a Rat Model of Stroke gradient in the slice select direction so that the plane of inversion intersects the neck of the rat. It must also be of sufficient duration to ensure that the brain tissue water magnetisation has reached its flow-dependent steady state, and also sufficiently off- resonance to ensure that no direct saturation of free water magnetisation in the imaging slice occurs. For the experiments described here, the pulse duration was chosen to be 5 seconds and a frequency offset of 9000 Hz was used. The gradient applied during the labelling pulse was then determined based on an image of the rat taken in the coronal plane (see figure 7.4). The desired plane of inversion was located and the required gradient strength was calculated for the 9kHz off-resonance pulse. For the size of rats used in this study (130g - 150g), the labelling plane was usually approximately 14mm proximal to the imaging slice, which resulted in a gradient of -1.5 G/cm being applied. In order for the derivation of equation (7.1) to be valid, a condition relating to the power of the RF tagging pulse must be satisfied. It has been noted in chapter 3 that the effect of the tagging pulse on the brain water magnetisation is twofold: first, the direct effect of inverted inflowing arterial water and second, the indirect effect due to magnetisation transfer from saturated macromolecular and bound water spins. One of the assumptions that is made in the derivation of equation (7.1) is that the power of the RF labelling pulse is sufficient to cause complete saturation of the off-resonance spins (see (Williams et al, 1992)). To make sure that this condition was met in the experiments described here, 1 examined the behaviour of the ‘control’ image intensity {Le. the image acquired following the 5 second RF pulse with the gradient polarity reversed so as to place the plane of inversion distal to the imaging slice) as a function of the RF pulse power. The result of this investigation is shown in figure 7.5. It can be seen that as the power of the off- resonance RF pulse increases from zero, the intensity of the image initially decreases but 197 Measurement of Perfusion using CASL in a Rat Model of Stroke Control plane Imaging Inversion . plane in 11 owing arterial bhn il II Figure 7.4 Coronal scout image of the rat brain, showing the position of the imaging slice and approximate control and inversion planes. The offset for the inversion pulse was chosen for each animal by altering the slice select gradient until the plane of inversion was 2 mm proximal to the rear of the brain in this image; this corresponded on average to a 20mm offset from the imaging slice. The control plane was then chosen by default to be symmetrically opposite by reversing the polarity of the slice-select gradient 198 Measurement of Perfusion using CASL in a Rat Model of Stroke eventually approaches a constant level. This level corresponds to the situation where off- resonance spins are completely saturated, and so a pulse power of 70 (in the units used for pulse calibration on our scanner, and corresponding to a Bi field of magnitude ~ 150mG) was used for all subsequent spin labelling experiments. In addition to the condition of macromolecular saturation, it is also important that the RF pulse satisfies the adiabatic condition necessary to achieve arterial spin inversion (see section 3.4.4). The adiabatic condition is defined by: i/7;,i/r,«(i/B,X;-v«)e, (7.2) At 8.5T, the values for Ti and T 2 in the rat blood are approximately 2000ms and 100ms respectively, setting an upper value for the left hand side of equation (7.2) to be on the order of (0.1)'^ = 10 s '\ The Bi field generated by the RF pulse applied at the level determined above is 150mG; the magnitude of the gradient is 1.5 G/cm; and the blood velocity in the rat carotid arteries has been previously estimated to be approximately 1 0 cm/s (Petty, 1982). The central term of equation (7.2) is, therefore, (0.15)'^xl.5xl0 = 100 s '\ Taking y to be 2.675 x 10^ rad s'^ T '\ the right hand side of equation (7.2) is -600 s '\ Therefore, the combination of RF pulse power and gradient values used here are in the range required to meet the adiabatic condition for flow-induced inversion. 7.1.3 Measurement of Ti and a for perfusion quantifîcation It can be seen from equation (7.1) that in order to accurately quantify perfusion, knowledge of tissue T% and the arterial degree of inversion (a) is necessary. Rather than using assumed or calculated values for these parameters, they were measured directly in vivo using the methods described in the next two paragraphs. 199 Measurement of Perfusion using CASL in a Rat Model of Stroke Ti was measured using an inversion recovery Snapshot FLASH sequence (Haase, 1990). This sequence consists of a slice-selective inversion (performed using an adiabatic t- shape FOCI pulse (see (Ordidge et al, 1997) and chapter 4)) followed by a series of 20 Snapshot FLASH images. The experimental parameters were TE = 2.0ms, TR = 3.6ms and flip angle = 5°. The images follow standard inversion recovery type behaviour, but the relaxation rate is altered by the application of a 5° pulse every 3.6ms. This can be accounted for (Haase, 1990), and Ti can be calculated by fitting the images to the equation: M(77) = A -B e x p (-r //r ;) (7.3) where TI is the time of acquisition of the central line of k-space of the image, M(TI) is the tissue magnetisation (or pixel signal intensity) at time TI, and Ti* is related to Ti by the equation: r, =r,*[(B/A)-i] (7.4) The accuracy of the sequence was verified by comparing the values measured using the IR-Snapshot FLASH with a standard IR-SE sequence both on phantoms and on the rat brain. No difference was found between the two methods. A measurement of Ti was made in the MCAO experiments for each perfusion measurement, since it was anticipated that Ti would change post-occlusion and evolve during the ischaemic period. The results of these measurements will be described in the next section. The degree of arterial spin inversion (a) was measured using an approach previously described by Zhang et al (Zhang et al, 1993). In this approach, arterial spin labelling is performed as usual using a 9kHz off-resonance RF pulse, but the image slice is moved to a position closer to the inversion plane. By doing this, one can obtain an image which contains the carotid arteries slightly downstream from the plane of inversion, and by 2 0 0 Measurement of Perfusion using CASL in a Rat Model of Stroke comparing the signal intensity of the arterial blood water with and without arterial spin labelling one can estimate the efficiency of inversion of the labelling pulse. The imaging strategy is a flow-compensated gradient echo sequence with spin labelling performed prior to each phase encoding step. The value of a was measured for pulse powers ranging from Bi = OmG to 150mG (the power previously determined to be sufficient for macro molecular saturation in the imaging slice). The result of this experiment from a region of interest drawn on one of the carotid arteries of a control rat is shown in figure 7.6. It can be seen that the signal intensity change reaches a plateau level, and this level corresponds to a value for a of 0.71. This value was found to be typical and was used for all subsequent quantitation. An example of the images which combine to produce a perfusion map of the rat brain is shown in figure 7.7. Image 7.7a shows a TurboFLASH anatomical image of the slice of interest. The result of subtracting a spin labelled image from a control image for this slice is shown in figure 7.7b. This represents a perfusion-weighted image, though direct interpretation of the contrast is difficult due to its concomitant Ti-weighting. This can be removed by combining the T% map (figure 7.7c) with the perfusion subtraction image to produce a quantitative perfusion map, as shown in figure 7.7d. Perfusion values are calculated for each pixel by solving equation (7.1) using the values of Ti, from the control and spin labelled images and the Ti map, and using the previously determined value of 0.71 for a. Regions of interest drawn in the cortex of the rat brain yield perfusion values of -150 ml/lOOg/min. While this is roughly consistent with what has been reported previously, it has been noted that there are several inherent errors in the experimental technique, the magnitudes of which depend on factors such as arterial transit time and the presence of blood signal in the images (see chapter 3). For the MCAO 201 Measurement of Perfusion using CASL in a Rat Model of Stroke 3500 3000 1 “ 2500 Bc « 2000 O)c I 1500 E I 1000 500 0 10 20 30 40 50 60 70 80 RF pulse power (arbirary units) Figure 7.5 Reduction of signal intensity from a ROI in the rat brain as the off- resonance RF pulse power increases. The RF pulse was applied for 5 seconds at a frequency 9kHz off-resonance. No slice select gradient was applied. Saturation of macromolecules is achieved at a pulse power of 70, which corresponds to a B, field of approximately 150mG 0.7 0.6 .1 0.5 •2 I 1 0.4 0> 2 g 0.3 0.2 0 5 10 15 20 25 30 35 40 45 RF pulse power (arbitrary units) Figure 7.6 Variation of inversion efficiency based on signal intensity changes from a ROI in the carotid artery of a rat as a function of inversion RF pulse power. A maximum degree of inversion (a = 0.71) is achieved using a pulse power of approximately 2 0 or greater. Degree of inversion calculated using a = (M^p^q - Mrp)/2Mrp^o 2 0 2 Measurement of Perfusion using CASL in a Rat Model of Stroke (a) (b) (c) (d) '*4 ■ Figure 7.7 An example of the images which are used to create a perfusion map. (a) shows the control image of the perfusion image pair and (b) shows the result of subtracting the spin labelled image from this control image. A T, map (c) is then combined with these images according to equation (7.1 ) to produce a quantitative perfusion map (d). 203 Measurement of Perfusion using CASL in a Rat Model of Stroke experiments described in the next section, the basic version of continuous ASL (as described above) was used, since it has been empirically verified (Walsh et al, 1994). However, to examine the error in the flow quantitation caused by using this approach, a modification of the standard CASL proposed more recently (Alsop and Detre, 1996) was implemented. 7.1.4 Use of CASL with a post-labelling delay The modifications proposed by Alsop and Detre (Alsop and Detre, 1996) were: 1. To insert a delay between the end of the RF spin labelling pulse and the image acquisition. The purpose of this delay was to eliminate the dependence of the perfusion signal difference on the transit time of blood water from the plane of inversion to the point where it exchanges with tissue water. They showed that if the post-labelling delay is longer than the longest transit time present in the system, then the resulting perfusion quantification will be almost completely transit time insensitive. 2. To measure the Ti of the brain tissue water both in the absence and in the presence of the off-resonance RF labelling pulse. This is necessary because magnetisation transfer affects the Ti relaxation rate, and so in order to properly calculate the change in longitudinal magnetisation caused by perfusion, it is necessary to know how the presence of the RF pulse alters the relaxation rate. The longitudinal relaxation times were measured using previously described methods (Alsop and Detre, 1996). Briefly, Ti in the absence of off-resonance irradiation (Tin) was measured using a standard non-selective IR-Snapshot FLASH approach, and Ti in the presence of off-resonance radiation (Tis) was measured by examining the image signal intensity of a perfusion control image as the length of the RF pulse was varied. Tis is 20 4 Measurement of Perfusion using CASL in a Rat Model of Stroke related to the reduction in signal intensity with increasing pulse length x by the following equation: M(t)= (M„ -M „)exp(-T/7;J+M „ (7.5) and is calculated (along with Mo and Mss) via a 3 parameter fit to this equation. An example of experimentally measured values of Ti„ and Tis are shown in figure 7.8. It can be readily seen that they are significantly different, thus underlining the importance of knowledge of both values for accurate flow quantification. In order to determine the necessary length of the post-labelling delay (w), images were acquired at a range of delays and the resulting perfusion values were compared. Perfusion was calculated according to the equation derived in (Alsop and Detre, 1996): / = " ^ ^ C(r„. 7],, 7;.. (7.6) 2aM[ where ^ = 7’,„exp(-5/7’,J exp(min(5 - w,0)/r,„) - exp(- w/r,„ ) \ Tu yj + T,a [exp((min( 6 a - w,0)-&z)/T,^ ) - exp((min(5 - w, 0 ) - ô )/Tj^ )] where two transit times are defined: Ôa, which is the time taken for water to travel from the plane of inversion to the vasculature within the imaging slice, and Ô, which is the time taken for water to travel from the plane of inversion to the capillary exchange sites of the vasculature i.e. the point at which exchange between blood water and tissue water can occur. The values calculated using this approach were also compared to those obtained using the standard immediate acquisition method, and typical results are summarised in the graph in figure 7.9. The value which lies on the y-axis of the graph is that calculated using the standard method, and all CBF values at delays greater than 0ms were calculated using equation (7.6). Values for a, Ô, 6 a and Tia were assumed to be 0.95, 200ms, 400ms 205 Measurement of Perfusion using CASL in a Rat Model of Stroke (a) 5000n Left cortex Right cortex .è' 2500- Left striatum I Right striatum 1 (00 2000 3000 4000 5000 6000 2 .2> Tl(ms) -2500- (b) 4000- Left cortex Right cortex 30004 '(/) Left striatum I Right striatum ■E 2000 1 .5> 1000 - 1 1 1 1 1 1 1000 2000 3000 4000 5000 6000 7000 Duration of labelling pulse (ms) (c) Left cortex Right cortex Left striatum Right striatum Tin (ms) 1865.0 1868.0 1718.0 1680.0 Tis (ms) 522.8 548.2 511.7 516.7 Figure 7.8 Comparison of the longitudinal relaxation times of brain tissue water in the presence and absence of off-resonance RF irradiation. Data from 4 ROI drawn in the rat brain, (a) shows the inversion recovery curve used to measure T,; (b) shows the effect of a varying length of off-resonance RF pulse on subsequent image intensity, which is used to measure The measured values are summarised in the table (c). It can be seen that is substantially less than T, 206 Measurement of Perfusion using CASL in a Rat Model of Stroke and 2000ms respectively. It can be seen that even with a very short delay equation (7.6) gives lower flow values, which is due to the closer correlation of the perfusion model to the real situation i.e. accounting for a vascular component of signal, non-zero transit time etc. As the post-labelling delay is lengthened the calculated CBF values decrease, signifying elimination of the vascular signal from the perfusion subtraction and transit time independence of the measurement. Based on the graph in figure 7.9, a post labelling delay of 400ms or greater should be used on a normal rat in order to obtain accurate flow values. To acknowledge this fact, in the next section I will refer to the perfusion measurements as ‘apparent’ CBF since they were performed without a delay between spin labelling and image acquisition and therefore overestimate true perfusion. Nevertheless, the values are closely related to CBF and can be interpreted as such. It is also important to note that although a value of 400ms was found to be sufficient for the control rats used in these investigations, it would be expected that the transit times Ô and 8 a would increase for tissue in the MCA territory following occlusion of that artery. An increased post labelling delay would, therefore, be necessary after occlusion to accurately quantify flow in the affected region. However, as the delay increases, the expected signal difference decreases and the ability to measure low levels of perfusion is limited by the SNR available. For this reason, a compromise must be made between satisfying the requirement w > 8 and loss of precision due to a decrease in signal to noise. It remains to be seen whether continuous ASL can be used reliably to a good degree of accuracy in regions of severe hypoperfusion or ischaemia. 207 Measurement of Perfusion using CASL in a Rat Model of Stroke 300 2 5 0 I 200 D) Left cortex Right cortex Ç 150 Left striatum E Right striatum 50 0 1 0 0 200 300 40 0 500 600 700 Post-labelling delay (ms) Figure 7.9 Variation of measured CBF values with length of post-labelling delay in a control rat. With no delay, CBF is significantly overestimated due to transit time and intraluminal signal contamination effects. With a delay of approximately 400ms or greater, these effects are minimised and a reliable value of cerebral perfusion is obtained 208 Measurement of Perfusion using CASL in a Rat Model of Stroke 7.2 A study of the early changes in perfusion, diffusion, Ti and T2 of brain water following middle cerebral artery occlusion In the rat at 8.5T 7 .2.1 Introduction The cortex, basal ganglia and internal capsule supplied by the middle cerebral artery (MCA) and its small penetrating branches in humans are prone to infarction. Focal or lacunar infarcts of the MCA territory represent at least 25% of first time ischaemic strokes, although some studies have associated up to 80% of cerebral infarcts with ischaemic damage to the MCA territory (Warlow, 1993). The susceptibility of this area is partly because the small penetrating arteries to the brain are not supported by a good collateral circulation, and therefore occlusion of one of these arteries is likely to cause infarction. This suggests that animal models of focal ischaemia which involve occlusion of the MCA and/or vessels in the MCA territory would be extremely useful for advancing the understanding of human ischaemic stroke. A feature of focal ischaemia models is the creation of a region of tissue on the border of the severely ischaemic core region which is known as the penumbra. Tissue in this area experiences a reduction in blood flow, but is not compromised to the extent that immediate energy failure occurs. The penumbra is important because it represents tissue which is affected by the occlusion, and which may progress to infarction if a reduced level of perfusion persists for a prolonged period, but also is potentially salvageable if suitable intervention is performed to alleviate the state of hypoperfusion. In this respect, the penumbra represents the target of any therapeutic efforts, since it is generally recognised that the ischaemic core is irreversibly damaged before any kind of therapeutic action can be taken. The ability to unambiguously 2 0 9 Measurement of Perfusion using CASL in a Rat Model of Stroke distinguish between the core of the ischaemic lesion and the penumbra would be invaluable, and it is possible that measurement of a combination of NMR and physiological parameters will enable this to be done. As mentioned in previous chapters, diffusion-weighted imaging and measurements of the apparent diffusion coefficient (ADC) of brain tissue water now provide a means of investigating early events in cerebral ischaemia (Moseley et al, 1990). Measurements of T2 * provide an additional approach to the early assessment of damaged or compromised tissue due to their sensitivity to changes in the oxygenation state of haemoglobin (see chapter 5 and references therein). In contrast, Ti- and T 2 -weighted MRI investigations are generally regarded as being less useful in the early stages because of their poor sensitivity to ischaemic events during the first few hours after stroke. Later in the evolution of the disease process, increases in Ti and T 2 are seen which are thought to reflect the changes in total water content associated with vasogenic oedema; thus T 2 -weighted MRI in particular plays an important role in the radiological evaluation of stroke lesions. However, processes occur during the acute stages of ischaemia which could affect the relaxation times of brain tissue in a more subtle manner. At higher magnetic field strength, these effects are expected to be magnified. In particular, the dependence of T 2 on blood haemoglobin oxygenation level increases. This has been observed previously using spectroscopic methods of relaxation time measurement (Busza et al, 1994; van der Toom et al, 1994), and has been attributed to either diffusion of spins through the magnetic field gradients produced by the deoxyhaemoglobin molecules (Busza et al, 1994) or the rapid exchange of blood water between binding sites on plasma and erythrocytes (van Zijl et al, 1998). 210 Measurement of Perfusion using CASL in a Rat Model of Stroke The purpose of this study was twofold. First, the application of continuous ASL to study changes in perfusion during an ischaemic episode was investigated to see whether useful information could be obtained despite the presence of extended arterial transit times. Second, the changes in brain tissue relaxation times T% and T 2 during the acute period following MCA occlusion was studied. Diffusion imaging was also performed to enable identification of the region of cerebral ischaemia produced by the occlusion. 7.2.2 Methods Animal preparation: The animal model used in this study was the rat intraluminal MCA occlusion model. Ten male Wistar rats (130-150g) were prepared for MCA occlusion, which was subsequently carried out remotely with the animal inside the magnet. The surgical procedure was based on a modified Zea Longa approach (Zea Longa et al, 1989) adapted for a vertical magnet. Anaesthesia was induced with 3% halothane in oxygen and continued via a nose cone at 1.25% halothane for the duration of the surgery. Rectal temperature was recorded and maintained at 37.5 ± 0.5°C by blowing temperature- controlled air into the magnet bore. The remote occluding device was a blunted 0.24mm nylon thread occluder. To minimise motion artefacts during imaging, the skin was reflected from the dorsal aspect of the skull and connective subcutaneous tissue removed between the lambda and the bregma. A strip of clear plastic, securely fixed to the animal probe, was glued to the area of cleaned skull using an epoxy resin. No discernible image artefacts were produced from the epoxy glue. Once the animal was inside the magnet, the halothane concentration was reduced to 0.8% in a gas mixture of 70% N 2 O and 30% O2 . Experimental protocol: All experiments were carried out in an 8.5T vertical magnet operating at 360MHz. A 38mm birdcage coil was used for signal transmission and reception. The studies were performed on a single 2mm coronal slice, approximately 211 Measurement of Perfusion using CASL in a Rat Model of Stroke 7mm from the interaural line. The experimental protocol involved approximately 2 hours for positioning, shimming and the acquisition of control (pre-occlusion) data, followed by remote occlusion of the MCA, and subsequent continuous imaging for 4-6 hours. T%, T 2 , perfusion and diffusion measurements were made in an interleaved manner during both the pre- and post-occlusion periods. All images were acquired with 128 points in the read direction and 64 phase encoding steps; this matrix was then zero filled to 128 x 128 prior to Fourier transformation. Ti measurement: As described earlier in this chapter, Ti measurements were made using a slice-selective inversion recovery Snapshot FLASH technique. Twenty successive images were acquired during the inversion recovery period with the parameters TE = 2.0ms, TR = 3.6ms and Timage = 231ms; inter-FLASH delay = 2ms; flip angle = 5°. Signal averaging of twenty IR acquisitions was performed to increase SNR, with a 6 second delay between the end of image acquisition and subsequent inversion. The total time for a Ti measurement was approximately 3.5 minutes. T 2 measurement: A four echo multi-spin echo sequence was used to measure T%. The echo times were 35, 70, 105 and 140 ms. It is known that the extent of the changes in T 2 caused by changes in blood oxygenation (and indeed the baseline T 2 value) is dependent on the exact method used to measure T 2 . The effects are maximised if T 2 is measured using several single-echo spin echo experiments with different echo times. This is because the signal that contributes to each echo is refocused only once. If a multi-echo approach is used, the spin magnetisation is refocused every time a 180° pulse is applied, and the deoxyhaemoglobin-based reduction in T 2 is related to the inter-echo time ATE rather than the actual echo time TE (see (van Zijl et al, 1998)). However, the single-echo 2 1 2 Measurement of Perfusion using CASL in a Rat Model of Stroke approach increases the total acquisition time of the sequence by a factor equal to the number of echoes acquired. Therefore, in these experiments, a four point multi-echo sequence was used, and signal averaging was performed over 4 acquisitions to improve the SNR and increase the sensitivity to the smaller changes expected with this sequence. A repetition time of 1 second was used, resulting in a total imaging time for each T 2 image set of 4 minutes 16 seconds. Measurement of the trace of the diffusion tensor [Tr(D)]: In biological tissue, the so- called diffusion of water molecules may not be completely random; rather, there may be a preferred direction of translational motion. This is referred to as diffusion anisotropy, and can complicate the interpretation of diffusion-weighted images and ADC maps in which the weighting has been applied in a certain direction. In this situation, the diffusion coefficient can no longer be represented by a scalar constant but must be described by a second order tensor, the effective diffusion tensor D (Basser et al, 1994). Regional differences in tissue diffusion measured using single axis diffusion-weighting may reflect differences in fibre orientation rather than differences in true molecular mobility, and therefore contrast between ischaemic and normal tissue can be impaired (Lythgoe et al, 1997). An orientation-independent measurement of tissue water diffusion can be made if the trace of the diffusion tensor, Tr(D), is acquired. The trace is defined as the sum of the diagonal elements of the diffusion tensor, and can be written algebraically as Tr(D') = d ; + d ; +D'^=D„+ D„ +D^= Tr(D) (7.7) where D'xx is the ADC along a principal axis of the system, x', D' is the diffusion tensor in the principal axis system, D%x is the ADC along the x-axis in the laboratory frame and D is the diffusion tensor in the laboratory frame. D and D' are related by a rotation matrix (Basser et al, 1994). Equation (7.7) shows that the trace of any matrix is mathematically 213 Measurement of Perfusion using CASL in a Rat Model of Stroke invariant under rotations, and so can be measured without difficulty in the laboratory frame. A simple method of determining the trace of the diffusion tensor is to measure the diffusion coefficients in three orthogonal directions separately and average the result. However, this approach is not very time efficient and sequences have been proposed (Mori and van Zijl, 1995; Wong et al, 1995) in which isotropic diffusion-weighting is achieved in a single shot. This enables direct calculation of Tr(D) by monoexponential fitting of signal intensity decay with b value. In the experiments described here, the gradient arrangement proposed by Mori and van Zijl (pattern III in (Mori and van Zijl, 1995)) was used to obtain isotropic diffusion-weighting. The imaging gradients were arranged so as to minimise their effective diffusion-weighting and associated cross terms, both of which were assumed to be negligible in all subsequent calculations, ô and A were 5 and 5.4ms respectively; b values = 30, 800, 1700 s/mm^; TE/TR = 80/1000ms. Four acquisitions were averaged for each b value, giving a total imaging time of 1 2 . 8 minutes. Measurement of perfusion: As described in previous sections of this chapter, continuous arterial spin labelling was used in conjunction with TurboFLASH imaging to measure perfusion. A 5 second labelling pulse was used, with no delay between the labelling period and image acquisition and an inter-experiment time of 10ms. Twenty five averages for both the control and spin labelled images resulted in a total imaging time of 4 minutes 1 0 seconds for each perfusion image. Data processing and image analysis: Maps of T%, T 2 and Tr(D) were generated using routines written with IDL software (RSI, Boulder, Colorado) by non-linear curve fitting 21 4 Measurement of Perfusion using CASL in a Rat Model of Stroke on a pixel by pixel basis. Two-parameter single exponential fits were used with the T% and Tr(D) data, while a three-parameter fit to equation (7.3) was used with the T% data. The T% map was then combined with the spin labelled and control images to calculate perfusion using equation (7.1), assuming a brain-blood partition coefficient of 0.9 ml/g. A study of the time dependence of the various NMR parameters was performed by defining three regions of interest (ROIs) in each animal based on the combined information from the CBF and Tr(D) maps. One region was positioned in the contralateral normal hemisphere, while the other two were in the affected hemisphere: one in the core, and the other in a border area of moderate ischaemia (see figure 7.10). The ROI in the core of the lesion was chosen by identifying the area with the largest change in diffusion, as seen on the Tr(D) maps at a late stage (4-6 h post-occlusion). It always lay within the thalamic and hypothalamic region, but the exact location was different in each animal. The border region, located in the frontal parietal cortex between the areas supplied by the middle and anterior cerebral arteries was defined in 8 of the 1 0 animals as a region of moderately reduced blood flow with no change in Tr(D). In order to analyse the time evolution of the different parameters and to examine regional differences, separate multiple linear regression calculations were used to fit polynomials to the data obtained from each animal. This was done independently for the pre- and post-occlusion phases, and the regression coefficients, or parameters derived from them, were used as summary parameters in univariate analyses (Matthews et al, 1990). When a paired t test was used, the two animals that did not have a border region were excluded from the analysis. In order to document the absolute values of the various parameters, they are quoted as the mean ± SE over the total number of animals for each ROI (n = 10 for the core and contralateral regions, and n = 8 for the border region). It is important to note, however, 215 Measurement of Perfusion using CASL in a Rat Model of Stroke CBFapp Tr(D) (a) (b) (c) (d) T. (e) Regions 0 Unaffected r~] Moderately affected s 1 Severely affected Figure 7.10 Typical maps obtained from a rat following MCAO. (a) shows a perfusion map with reduced flow in the occluded side (acquired 4 hours post-occlusion), (b) shows a trace map (4 hours post-occlusion) with a region of reduced diffusion indicating the area of cytotoxic oedema, (c) shows a T 2 map (1 minute post-occlusion) with a region of reduced T2. (d) shows a T, map (5 minutes post-occlusion), with a region of increased Tj. The dark spot in the T, map is due to a DC artefact, (e) shows a schematic representation of the three main areas: “unaffected area”, where a relatively small and transient reduction in flow was detected; “moderately affected area”, with reduced CBF but normal Tr(D); and “severely affected area”, in which both the CBF and Tr(D) were significantly reduced. The ROIs represent typical regions used for the time-course analysis: core region (a), border region (b), and contralateral region (c). 216 Measurement of Perfusion using CASL in a Rat Model of Stroke that these standard errors were not used in any subsequent analysis of the within-subjects effects, which was performed using the paired t test and a selected summary parameter. 7.2.3 Results Figure 7.10 shows (a) perfusion, (b) Tr(D), (c) Ti and (d) T 2 maps from a representative animal, and demonstrates the regions of decreased CBF 4 hours post-occlusion), reduced diffusion (~ 4 hours post-occlusion), increased Ti (« 5 minutes post-occlusion) and decreased T% (~ 1 minute post-occlusion). Figure 7.10e shows a schematic diagram of the three main areas that were used for the subsequent analyses. Region (a) is a “severely affected area” in the core of the lesion, with reduced blood flow and diffusion; region (b) is a “moderately affected area”, with reduced cerebral blood flow (CBF) but no reduction in diffusion; and region (c) is an “unaffected area”, where a relatively small and transient reduction in flow was detected. In the following paragraphs, I will discuss in turn the time-course data for perfusion, diffusion, and the two relaxation times in these three selected regions of interest. Graphs (a) to (c) in figures 7.11 to 7.14 correspond to the time courses of the regions (a) to (c) as defined above. Perfusion (CBF): Figures 7.10a shows a typical perfusion map obtained 4 hours after occlusion, and figure 7.11 shows the time-course data for the three ROIs defined in 7.10e. The mean CBF before occlusion was 186 ± 11 ml/lOOg/min (range 144-244 ml/lOOg/min) in the core region (figure 7.11a). Similarly, the mean CBF was 146 ± 8 ml/lOOg/min (range 111-175 ml/lOOg/min) in the border region (figure 7.11b), and 205 ± 14 ml/lOOg/min (range 128-248 ml/lOOg/min) in the contralateral region (figure 7.11c). The high CBF values (compared to previously reported values using other techniques) were attributed, at least in part, to effects not accounted for in the quantification of 217 Measurement of Perfusion using CASL in a Rat Model of Stroke ( a ) '€0 - 20CÇ; ifp CBFapp (ml/lOOg/min) 'm, 40 1 -120 -90 -60 -30 -20 60 120 210 240 Time (minutes) (b) 240 -- 220 -- 200 - 180 -- CBF.PP (ml/lOOg/min) 10 O'-. 80 60 40 20 - 1 -90 -30 30 -60 -20 6090 120 ISO 180 210 240 Time (minutes) (c) CBFapp (ml/lOOg/min) 80 -- 60 -- 40 -- 20 -- 1 -120 -90 -60 30 60 90 120 150 180 210 240 ■40- Time (minutes) Figure 7.11 CBF time courses in (a) core, (b) border, and (c) contralateral regions of MCAO rat brain. Occlusion performed at time t = 0 minutes. The core experiences extreme an reduction in blood flow, the border zone a moderate reduction and the contralateral side a minimal reduction 218 Measurement of Perfusion using CASL in a Rat Model of Stroke perfusion, such as the contribution of vascular blood to the signal intensity (Alsop and Detre, 1996; Ye et al, 1997), and the effect of magnetisation transfer (Mclaughlin et al, 1997; Zhang et al, 1995). Both of these effects contribute to an overestimation of perfusion. The presence of a heterogeneous high vascular signal makes the measurement very dependent on the position of the ROI, and this could explain the large variability and the difference between regions prior to occlusion. In acknowledgement of the inherent errors of the technique, the values obtained in the present experiment with ASL are referred to as apparent cerebral blood flow (CBFapp). It can be seen from figure 7.1 la that following the initial drop induced by occlusion, the CBFapp in the core remained approximately constant. When CBFapp was less than =20 ml/lOOg/min, the measured perfusion was within the noise level. A decrease in CBFapp was also observed in the other two ROIs, with some of the rats showing a more variable flow in these two regions than in the core. Due to this variability, and the intrinsically low signal to noise ratio (SNR) in the measurement of perfusion using ASL, the difference ACBFapp between the mean pre-occluded measurement and the average of the first two post-occluded values was used as a summary variable to study the drop in CBFapp. A positive value of ACBFapp is used in the following paragraph to describe a reduction in perfusion. Although both ischaemic regions showed a highly significant reduction in CBFapp (p< 0 . 0 0 0 1 for both regions), ACBFapp was significantly larger (paired t test, p< 0 .0 0 0 1 ) in the core (mean value = 163±8 ml/lOOg/min) than in the border region (mean value = 83±6 ml/lOOg/min). The initial flow change in the contralateral side (mean ACBFapp = 39±11 ml/lOOg/min), although relatively small, was also statistically significant (p=0.01). 2 1 9 Measurement of Perfusion using CASL in a Rat Model of Stroke After this initial drop, the perfusion in the contralateral hemisphere gradually returned to pre-occluded values. Water diffusion: Figures 7.10b shows a typical trace map obtained 4 hours after occlusion, and figure 7.12 shows the time-courses of Tr(D). The normal pre-occluded Tr(D) values were 0.83±0.02, 0.81+0.01 and 0.83+0.01 x lO'^mm^/s, in the core, border, and contralateral regions, respectively. In the core region (figure 7.12a), Tr(D) was reduced by approximately 23% relative to pre-occlusion at the first time point (acquired 50 minutes post-occlusion). Following this initial rapid decline, it showed a gradual decrease for 2-3 hours after occlusion, towards an asymptotic value of 0.51+0.02 x 10"^ mm^/s. In contrast, in the border region (figure 7.12b) no reduction in Tr(D) was observed (p = 0.9). Furthermore, a paired t test showed that there was no significant difference (p = 0.1) between the asymptotic values in the border and contralateral regions, where Tr(D) remained unchanged throughout the experiment. The mean asymptotic values in these regions were: 0.80±0.01 xlO'^mm^/s in the border and 0.82±0.01 x 10'^ mm^/s in the contralateral region. Spin-spin relaxation time (T 2): Figure 7.10c shows a T 2 map obtained 1 minute after occlusion, and figure 7.13 shows the time-course data for the core (figure 7.13a), border (figure 7.13b) and contralateral (figure 7.13c) regions. The mean pre-occluded T 2 values were 42.5±0.9 ms in the core, 40.7±0.5 ms in the border region, and 41.8±0.7 ms in the contralateral region. A rapid decrease in T 2 from its pre-occluded value was seen in all rats in both the border and core regions at 1 minute post-occlusion. After this initial drop, the behaviour was different in each region. In the border region, T 2 returned to normal values (by 30-60 minutes after occlusion), thereafter increasing more slowly, while in the 2 2 0 Measurement of Perfusion using CASL in a Rat Model of Stroke ( a ) Trace ADC (X 10"^ mm^/s) 0.4 -120 -90 -60 -30 0 30 60 90 120 150 180 210 240 270 Time (minutes) Trace ADC (X 10'^ mm^/s) 0.6 120 -90 -60 -30 0 30 60 90 120 150 180 210 240 270 Time (minutes) Trace ADC 0.7 (x 10 ^ mm^/s) 0.6 120 -90 -60 -30 0 30 60 90 120 150 180 210 240 270 Time (minutes) Figure 7.12 Trace ADC time courses in (a) core, (b) border, and (c) contralateral regions of MCAO rat brain. Occlusion performed at time t = 0 minutes. A reduced ADC in the core signifies cytotoxic oedema, whereas the ADC remains unchanged in the border and contralateral regions 221 Measurement of Perfusion using CASL in a Rat Model of Stroke 2300 2150 2000 1550 1------1------M O e-4------1------1------1------1------1------1------1------1------120 -90 -60 -30 0 30 60 90 120 150 180 210 240 270 Time (minutes) 2150 2000 - T, (ms) 1550 i 1------1------# 0 2 - ^ ------1------1------1------1------1------1------1------1------i 120 -90 -60 -30 0 30 60 90 120 150 180 210 240 270 Time (minutes) (C) 2300 2150 2000 T, (ms) ------rTnT": ------4 3 0 0 -4400- -120 -90 -60 -30 0 30 60 90 120 150 180 210 240 270 Time (minutes) Figure 7.13 T, time courses in (a) core, (b) border, and (c) contralateral regions of MCAO rat brain. Occlusion performed at time t = 0 minutes. T, is elevated post- occlusion in the core and the border regions, and continues to rise over the next few hours in the core 222 Measurement of Perfusion using CASL in a Rat Model of Stroke core region the T 2 values rose linearly for the duration of the measurements. An analysis of the T 2 changes for measurements taken at times greater than 1 hour post-occlusion was performed using the slopes obtained from linear regression analysis of the individual time-course data. The statistical procedure outlined by Dobson (Dobson, 1990) for comparing a reduced model against a full model showed that a first order polynomial provided an adequate description of the data for times greater than 1 hour. Both the core and the border region exhibited a statistically significant slope (p < 0.0001 and 0.002, respectively), with a mean value of 1.77+0.24 ms/h in the core, and 0.39±0.07 ms/h in the border region. A paired t test showed that these slopes were significantly different (p = 0.003). In contrast, the slope in the contralateral region was not significantly different from zero (p = 0.7), with a mean value of 0.08+0.17 ms/h. The time resolution in this study was insufficient to provide a detailed description of the time dependence of the rapid initial drop in T 2. Therefore, the difference between the average of the pre-occluded values and the first post-occluded measurement (time ~ 1 minute post-occlusion) was used to characterise this initial decrease. Whether this is representative of the full extent of the T 2 change depends on the rate at which deoxygenation of the blood haemoglobin occurs, and is likely to be a conservative estimate of the true maximum T 2 change. Both the core (mean value = -2.19+0.29 ms) and the border region (-3.18+0.50 ms) yielded a statistically significant initial decrease (p < 0.0001 and 0.001, respectively), while the change in the contralateral region (0.1910.32 ms) was not significant (p = 0.6). Spin-lattice relaxation time (Ti): Figure 7.10d shows a typical T% map obtained 5 minutes after occlusion, and figure 7.14 shows the time-course data for the core (figure 223 Measurement of Perfusion using CASL in a Rat Model of Stroke 7.14a), border (figure 7.14b) and contralateral (figure 7.14c) regions. The mean pre- occluded Ti values were 1718±25 ms in the core, 1756±18 ms in the border region, and 1676±30 ms in the contralateral region. A rapid increase in Ti occurred in the two ischaemic regions within 5 minutes of occlusion {i.e. at the first post-occluded measurement). The time evolution after this early increase was different in the two regions, progressively increasing at a slow rate in the core, while remaining approximately constant in the border region. The initial change in Ti was too rapid, relative to the time resolution of this study, for its time dependence to be analysed. Consequently, the rapid and slow-response phases of the time-course data were examined separately. An analysis of the slow-response phase (at times greater than 25 minutes post-occlusion) was performed by fitting separate polynomials to the T% data obtained from each animal. The individual values predicted by the regression model at 45 and 240 minutes were then used to calculate the rate of change in Ti during this interval. The 45 and 240 minute time points were selected in preference to the 25 minute and final time point because the confidence interval of the estimates increases at the extremities of the time interval. The mean rate of change of Ti in the core was 46.1±5.5 ms/h, which is significantly different from zero (p < 0.0001) while the mean value in the border region was -2.3+1.6 ms/h, which does not achieve significance (p = 0.2). The value in the contralateral region was -5.6±1.9 ms/h, which is statistically significant compared with zero (p = 0.02). This decrease in Ti towards the pre-occluded values occurs simultaneously with the recovery in CBF in the contralateral ROI. An additional characterisation of the differing Ti behaviour in the three regions was obtained by examining the difference between the 45 minute value predicted by the 2 2 4 Measurement of Perfusion using CASL in a Rat Model of Stroke 52.5 50 - 47.5 1------1------1------92 :5 -4 ------1------1------1------1------1------1------1------1------150 -120 -90 -60 -30 0 30 60 90 120 150 180 210 240 270 Time (minutes) 52.5 - 50 - 47.5 45 - 37.5' 35 - -150 -120 -90 -60 -30 0 30 60 90 120 150 180 210 240 270 Time (minutes) 52.5 - 50 47.5 1------1------1------92 :5-4------1------1------1------1------1------1------1------1------150 -120 -90 -60 -30 0 30 60 90 120 150 180 210 240 270 Time (minutes) Figure 7.14 T 2 time courses in (a) core, (b) border, and (c) contralateral regions of MCAO rat brain. Occlusion performed at time t = 0 minutes. A rapid drop in T 2 is observed following occlusion in both the core and border regions, indicating increased levels of deoxyhaemoglobin. T 2 subsequently returns to normal in the border, and increases to values greater than the pre occlusion levels in the core, indicating increased tissue water content 225 Measurement of Perfusion using CASL in a Rat Model of Stroke regression model and the average pre-occluded Ti values. All three ROIs yielded differences that were significantly different from zero (mean values of 249±12 ms in the core, 126+10 ms in the border, and 68+7 ms in the contralateral region). The three pair wise tests on the differences were also highly significant (paired t tests: core vs. border region, p < 0.0001; core vs. contralateral region, p<0.0001; and border vs. contralateral region, p = 0.0005). Although it was not possible to analyse the time dependence of the rapid, initial Ti change, the difference between the average of the pre-occluded Ti values and the first post-occluded measurement (5 minutes post-occlusion) could be used as a summary variable. The values obtained for the core (mean value= 148+11 ms) and the border region (69±10 ms) were significantly different from the values obtained in the contralateral region (35±6 ms) (paired t test on the difference: p = 0.0001 and 0.01 respectively). The results demonstrate that high field MRI detects an immediate Ti response to an ischaemic insult. 7.2.4 Discussion The most important observation of this study were the early changes in the relaxation times Ti and T% following middle cerebral artery occlusion, both in the area destined to become the core of the lesion and in the border zone. These two zones have been defined based on changes in the diffusion and perfusion maps: the lesion core experiences a severely reduced level of perfusion and the concomitant reduction in water ADC associated with cytotoxic oedema, while the border zone suffers from a moderately reduced blood flow which is insufficient to induce cell depolarisation. 2 2 6 Measurement of Perfusion using CASL in a Rat Model of Stroke The decrease in T% was observed immediately following occlusion. Similar effects have been reported for T 2 measured using spectroscopic methods (van der Toom et al, 1994; Busza et al, 1994) and in T 2*-weighted images (Roussel et al, 1995). However, since the effect is several times smaller for T 2 than for T 2*, T 2 imaging has not been widely used in the study of ischaemia. At high field, where T 2* imaging becomes practically quite difficult due to the amplified effects of static field inhomogeneities which lead to signal dropout, T 2 imaging seems to be the natural choice. The most likely reason for the decrease in T2 is an increase of the amount of deoxyhaemoglobin in the ischaemic area. The exact mechanism of this effect still remains to be determined. It was originally proposed (Busza et al, 1994) that the diffusional motion of tissue water through the local field gradients which surround the deoxyhaemoglobin molecules during the echo time could lead to incomplete refocusing and, therefore, a drop in the observed T 2. More recently, van Zijl et al (van Zijl et al, 1998) have suggested a vascular mechanism for the reduction in T 2, with the intravascular water relaxation enhanced through fast exchange across the red blood cell membrane and the tissue relaxation enhanced by slow exchange with the blood pool. They were able to show good agreement between predictions from their model and experimental data acquired during varying degrees of hypoxic hypoxia in the cat brain. However, the assumptions made in predicting T 2 changes become invalid in the more severe case of cerebral ischaemia, and so extension of the model is to this situation remains to be demonstrated. Distinguishing between the two proposed mechanisms for T 2 change (diffusion or exchange) would be possible by examining the dependency of the effect on the inter-echo spacing of the multi-echo sequence. Intuitively, it seems most likely that a combination of the two effects is responsible for the observed changes. 2 27 Measurement of Perfusion using CASL in a Rat Model of Stroke It is worth noting that although the reduction of CBF in the border zone was less than in the core, there was no significant difference in the T% decrease in these two regions (paired t-test, p=0.09). Equivalent results have been observed using T 2*-weighted gradient echo imaging (Roussel et al, 1995). Interpretation of this result is complicated since the amount of deoxyhaemoglobin in a given voxel depends not only on blood flow but also on factors such as cerebral blood volume, the oxygen extraction fraction (OEF), and haematocrit levels. Furthermore, the effect of deoxyhaemoglobin on T 2 may depend on the diffusion properties of the water, which differs between the core and the border zone. The subsequent increase in T 2 in the core region may be related to modulation of the OEF, or compression of the capillaries caused by cytotoxic oedema. It may also reflect the development of vasogenic oedema during the later stages of the time course. In the border region, where cytotoxic and vasogenic oedema do not occur, T 2 rapidly returns to its pre-occlusion value. This would be expected if the OEF is adjusted via an autoregulatory process which returns the levels of blood deoxyhaemoglobin to their pre occlusion values. The increase in the longitudinal relaxation time T% began immediately following occlusion of the MCA. These effects have not been reported at lower field strengths, and occur prior to the onset of vasogenic oedema which is thought to be responsible for the elevated Ti values at later times (and which may contribute to the slow component of further Ti increase observed in the core region). In contrast to the T 2 decrease, the magnitude of the Ti increase in the core region was greater than that in the border region. This would suggest that the fundamental mechanisms driving the changes are different for the two relaxation times. This is not unexpected, since it is known that a changing level of 228 Measurement of Perfusion using CASL in a Rat Model of Stroke blood deoxyhaemoglobin has a negligible effect on the observed Ti (Tadamura et al, 1997). One possible explanation for the observed initial increase in Ti is its dependence on flow. Since a selective inversion pulse was used for the measurement of T% (so it could be used to quantify perfusion), there is a flow-related component of the observed T% value (Tiapp) defined by: ' = 1 4 (7.8) T, A where f is CBF and X is the blood:brain partition coefficient as defined previously. Using the CASL sequence introduced by Alsop and Detre (Alsop and Detre, 1996) which incorporates a post-labelling delay to eliminate transit time effects and intravascular signal, grey matter perfusion in normal rats was measured to be approximately lOOml/lOOg/min (see section 7.1.4). Taking an average pre-occlusion value of 1700ms for Tiapp, a drop in flow to zero would result in an increase in Tiapp of 50ms, or approximately 3%. This represents the most extreme change which could be possible due to a change in flow. However, a larger initial increase in Tiapp was observed in the core (-9%). Also, a gradual second phase increase in Tiapp was seen during the hours following occlusion, despite a constant level of perfusion. Therefore, although changes in flow are likely to account for a proportion of the T 1 increase observed in these experiments, this can not be the only effect responsible for the change. Several other possible causes for the Ti increase exist. One is the reduced level of tissue oxygen, which acts as a relaxation agent due to the paramagnetic properties of molecular oxygen. It has been shown previously (Tadamura et al, 1997) that Ti is modified by 229 Measurement of Perfusion using CASL in a Rat Model of Stroke alterations in the dissolved O 2 concentration. During ischaemia, the amount of oxygen in the brain tissue is reduced, which would be expected to lead to an increase in T% as observed. In the border region, where it has been hypothesised that the OEF is lower than normal (based on the return of T 2 to its pre-occlusion value) but not in the ischaemic range, one would expect the increase in Ti to be less than the core, which is consistent with observation. Another alternative for the Ti change is a change in water environment during ischaemia. Magnetisation transfer (MT) between the so-called free and bound water pools affects the observed longitudinal relaxation time (Wolff and Balaban, 1989). Changes in the relative proportion of water in each pool, and in the rate at which magnetisation exchanges between the two pools, alters the effective relaxation rate of the tissue water. This effect has been proposed previously as a possible explanation for the increase in Ti and T2 seen after 2 hours of ischaemia, before the development of vasogenic oedema. It is conceivable that the same effect could be responsible, at least in part, for the early changes of Ti observed at high field. Work recently done by Ewing et al (Ewing et al, 1996) has shown a decrease in the exchange rate of magnetisation from the bound to the free water pool (kf) as early as 45 minutes after MCAO. However, the same group has performed measurements which show that the extent of changes in Tisat following occlusion can not be accounted for only by a change in magnetisation transfer. This implies an underlying change in Ti, as observed in this study. The second phase gradual rise in T 1 that is seen in the core (but not in the border zone) is most likely due to a slow increase in tissue water content. This is consistent with the gradual second phase increase in T2, which is indicative of the same process. These experiments have demonstrated the feasibility of using non-invasive arterial spin labelling MRI techniques to measure cerebral perfusion in studies of focal ischaemia in 2 3 0 Measurement of Perfusion using CASL in a Rat Model of Stroke the rat. The measurement of perfusion using MRI offers many advantages, including non- invasiveness, the possibility of continuous monitoring, and direct spatial registration to other MR images. Although, in its implemented form, the sequence is known to suffer from problems related to the transit time of arterial blood from the neck of the rat to the imaging slice, this inherent source of error has not prevented the CBF maps produced using the technique from being very useful in defining regions of severe and moderate ischaemia. Quantification can be improved by inserting a post-labelling delay. However, the extremely low CBF in the occluded region introduces two significant problems. First, quantification of the resulting very small signal requires a large SNR in the two images used to obtain the perfusion difference. Second, there is a much longer and more heterogeneous distribution of transit times from the labelling plane to the occluded MCA territory, resulting in an underestimation of perfusion if an insufficiently long post labelling delay is used. Therefore, the absolute CBF values from the core of the ischaemic lesion are unlikely to be reliable and determination of, for example, a perfusion threshold for ADC change using this technique would be extremely difficult. However, the presence of extended transit times in areas of the brain that are underperfused has the potential to provide indirect identification of perfusion deficits, due to the presence of bright spots in the perfusion map corresponding to intraluminal signal. These areas should be easily recognisable since they will occur in regions of otherwise low perfusion signal, though whether quantification will possible based on analysis of such images has not yet been determined. In line with previous studies (see, for example, (van Bruggen et al, 1994; Hoehn-Berlage, 1995)), the measurements of the diffusion of water performed in this study have demonstrated a reduction of approximately 40% in the trace of the diffusion tensor in the 231 Measurement of Perfusion using CASL in a Rat Model of Stroke core of the ischaemic lesion 4 hours after occlusion. Moreover, combined analysis of CBF and Tr(D) maps has enabled the definition of a region of moderate ischaemia, where no reduction in diffusivity was detected over the 4-6 hour period during which measurements were performed. Presumably this indicates that the blood flow remained above the threshold required to maintain the cellular ion homeostasis. Further studies may reveal whether the area of reduced ADC expands to contain the border region at later times after MCA occlusion. It has been shown that progression of tissue to infarction depends not only on the severity but also the duration of ischaemia (Miyabe et al, 1996). In this respect, the border zone defined in these experiments could be related to the ischaemic penumbra. Le. tissue which is vulnerable to, but salvageable from, infarction. However, the exact relationship between ADC value and tissue status has not been established. Immediate ADC changes are known to be reversible and not a reliable indicator of final lesion volume (see (Baird and Warach, 1998)). At this stage, therefore, it is difficult to relate initial changes in the NMR parameters to eventual tissue outcome. The information provided by changes in perfusion, diffusion, Ti and T 2 reflects the state of the tissue at the time of measurement. Whether this information can be extrapolated to predict the fate of ischaemic tissue remains to be seen. 23 2 General discussion and conclusions 8 General discussion and conclusions______ The fundamental requirement of an experimental or clinical imaging system is the production of high quality images within the shortest possible time period. The preceding chapters of this thesis describe the work I have done to develop existing diffusion and perfusion MRI techniques to improve their accuracy and time efficiency. I have also applied the methods to investigations of focal and global cerebral ischaemia in order to demonstrate their ability to provide vital and unique information on tissue status and viability. In this chapter, I will discuss the benefits and problems that exist with each of the techniques in their current state, and how this affects the potential for their general use in the future. The chapter concludes with a summary of the results and conclusions from each of the experiments described in this thesis. 8.1 Is it possible to measure ischaemic blood flow using arterial spin label ling methods? One of the main disadvantages of arterial spin labelling is the inherently low signal to noise ratio of the perfusion-weighted subtraction image. For normal blood flow rates, the difference between the spin labelled and control images is only a few per cent. This means that in order to obtain a reliable value of CBF, a SNR of 100 or more is required in the base images. This does not represent a major problem, since signal averaging can be performed to achieve this goal. However, problems arise when the technique is required to measure low levels of perfusion. The first and most obvious of these is that as the blood flow decreases, the perfusion signal difference decreases. Therefore, in order to measure low flow with the same degree of accuracy as normal flow, higher SNR is 233 General discussion and conclusions required in the base images, which necessitates more signal averaging and the concomitant increase in total acquisition time. This applies to both continuous and pulsed ASL. A secondary consequence of a reduction in CBF is an increase in the transit time of spin labelled blood from the labelling region to the imaging slice. This is especially likely to be a problem for continuous ASL, where the physical distance between the two regions is necessarily larger. As a result, the degree of inversion of blood at the capillary exchange sites is reduced, since a greater amount of relaxation takes place in the vessels en route to the slice. This affects the quantitation procedure and, using conventional CASL, a perfusion map can not be created unless transit times are measured (or known) on a pixel- by-pixel basis. Although it is possible to estimate the spread of transit times across the image, the process is time consuming and prone to error due to the low SNR of the images involved. The method proposed by Alsop and Detre, described in chapter 7, attempts to alleviate this problem by introducing a delay between the end of the labelling period and the image acquisition. The criterion for accurate quantitation of perfusion is that the inserted delay is greater than the longest transit time present in the system. In this situation, the entire spin labelled ‘bolus’ will have entered the slice by the time of image acquisition and, as long as tissue and blood T% values are similar, an accurate perfusion map can be calculated. However, the maximum length of the post-labelling delay is limited by the tissue Ti since this determines the rate at which the perfusion difference signal decays. If there are transit times present which are significantly greater than the T% of tissue, it is not possible to achieve a completely transit time insensitive perfusion map. Coupled with the fact that regions of the brain which are hypoperfused only produce a small perfusion signal, the need to include a post-labelling decay (which reduces the 2 3 4 General discussion and conclusions signal difference still further) makes the accurate measurement of low levels of blood flow extremely difficult. In the work described in chapter 4 of this thesis, I have attempted to reduce the transit time related problems of ASL by using a modified version of the pulsed ASL sequence known as FAIR. The decision to use FAIR imaging rather than CASL was based on the fact that the physical distance between the distal edge of the labelling region can be placed closer to the imaging slice in FAIR compared to CASL, where it must be ensured that the plane of inversion intersects a major artery. In FAIR, the proximity of the edges of the imaging and inversion slices is limited only by the sharpness of the respective slice profiles. The slice-selective inversion should not overlap with the imaging slice, otherwise static tissue signal will contribute to the selective/non-selective IR subtraction and distort the perfusion measurement. In order to allow the closest possible match between slice thicknesses without overlap, I have used optimised adiabatic RF pulses in the FAIR sequence. This reduces the minimum achievable inversion:imaging slice thickness ratio to less than 2:1, and further optimisation using different variants of the adiabatic pulses could reduce this ratio further. However, it is extremely unlikely that it will be possible to use pulses with exactly the same width for inversion and imaging in FAIR, since there will always be a small amount of imperfection in pulse profile definition. Therefore, it seems that transit time effects and, more importantly for an experiment in which dynamic variations in levels of perfusion are to be observed, changes in transit time between measurements will continue to be a source of problems for CBF quantification. Further modifications are necessary to make the sequence insensitive to transit time effects. As shown in chapter 4, this can be achieved by acquiring FAIR images at a range of inversion times and fitting the resulting image 2 35 General discussion and conclusions intensities to a biexponential curve. However, this approach extends the total imaging time for a single perfusion measurement to an impractical length if the sequence is to be used to monitor a dynamic perfusion time course. Buxton et al (Buxton et al, 1998) have suggested the acquisition of a pair of FAIR images at two different inversion times, which is the minimum number necessary for estimation of both perfusion and transit time maps. Whether this approach is reliable and sufficiently immune to errors caused by the low SNR of the two FAIR images has yet to be demonstrated. Alternatively, the method proposed by Wong et al (Wong et al, 1998) known as QUIPSS II offers the potential to measure perfusion directly from a single FAIR-based subtraction. In a manner analogous to Alsop and Detre’s CASL technique, QUIPSS II removes the transit time dependence of the FAIR signal by allowing spin labelled blood to flow into the imaging slice for a certain period of time (TIi), and then waiting a delay time TU before image acquisition. If TI2 is longer than the longest transit time present, the resulting perfusion map will be transit time insensitive. However, we return to the problem that if a region of very low blood flow exists, it is likely that long transit times will also exist. Therefore, the use of extended delay times is necessary, making the quantification of low flow very difficult due to the very small remaining signal difference between spin labelled and control images. Based on consideration of the points discussed above, it seems that a combination of approaches is needed to enable the use of CASL techniques to perform quantitative perfusion imaging. Improved definition adiabatic RF pulses should be used to minimise transit times, by making the inversion and imaging slices as equivalent as possible. The FAIR technique is thereby optimised in its sensitivity to perfusion. However, it is not possible to completely eliminate transit time effects using this approach and, therefore, it 236 General discussion and conclusions will be necessary to use either QUIPSS II or multi-TI FAIR imaging to accurately quantify CBF. For QUIPSS H, the use of optimised RF pulses is beneficial since it reduces the maximum transit times of the system and so reduces the required length of the delay time TI2. The SNR of the perfusion subtraction is consequently improved, thus improving image quality or reducing total imaging time. For studies of ischaemia, knowledge of variations in transit time may provide supplementary information to direct CBF measurements, in which case the multi-TI method could be used. Using the kinetic model of cerebral perfusion (Buxton et al, 1998) it has been shown that two TI points are sufficient to create perfusion and transit time maps: a plot of difference signal against inversion time gives a line whose gradient is proportional to flow and whose intercept on the time axis is equal to the transit time. This method relies on the shorter TI time being at least as long as the transit time, and in situations where the value of the transit time is completely unknown, it may be more satisfactory to perform measurements at a range of TI points. However, with the use of improved definition RF pulses, the extent of the increase in transit time during ischaemia is minimised, and use of two FAIR subtractions for each perfusion measurement may be justifiable. The choice of parameters will depend on the exact requirements of any given experiment, but a compromise will always have to be made between accuracy of the measurement and temporal resolution of the sequence. Another factor which needs to be taken into account in quantification of the FAIR difference signal is the contribution of blood water signal. In the experiments described in chapter 4, a bipolar gradient between the 90° and 180° pulses of the imaging sequence was shown to reduce the perfusion signal and cause a lengthening of the measured transit time. This was interpreted as a reduction in the amount of spin labelled blood water signal present in the subtraction images, since the rapid motion of the intravascular water should 237 General discussion and conclusions cause its signal to decay rapidly in the presence of a field gradient. However, choice of the magnitude of the gradient strength (or ‘b’ value) is rather arbitrary, and was determined in my experiments by empirically determining the point at which a further increase in b value did not alter the calculated perfusion value. There remains some debate in the literature as to whether blood signal should contribute in any way to the perfusion signal. In the original Ti model for ASL it was assumed that all signal originated from tissue water, since cerebral blood volume is relatively small and crusher gradients were used around the 180° pulse. In further developments of this model, including the equations derived in this thesis describing the reduced repetition time FAIR sequences, this assumption was maintained. However, it has been recently suggested (Buxton et al, 1998) that blood water which is contained within a voxel in the imaging slice and is ultimately destined to perfuse that voxel, but which at the time of image acquisition is still in the intravascular space, should be contribute to the FAIR signal. This contrasts with blood which is merely passing through a voxel in an artery or arteriole and is travelling to a capillary bed outside the slice of interest; this blood should not be included in the perfusion signal. If the intravascular perfusing blood signal is not acquired, a quantity slightly different to absolute perfusion is measured. In fact, the measurement represents the water extraction fraction - flow product E(f)f (Zaharchuk et al, 1998). In the situation where the extraction fraction is approximately equal to unity (which is true under normal circumstances), this product is equivalent to CBF. However, at higher flow rates where the extraction fraction is known to deviate substantially from unity, a misleading result will be obtained if exclusively tissue water signal is acquired. In practice, the situation is somewhat difficult to assess since the source of signal is not easily identified. If a bipolar crusher gradient is applied, calculations may be performed to estimate the attenuation of randomly diffusing water signal, though how directly this 238 General discussion and conclusions relates to blood travelling through the arteriole-capillary-venule system is unclear. Complete elimination of signal from blood travelling through a voxel, while simultaneously leaving perfusing intravascular signal unaffected, is not possible with the use of bipolar gradients. For this reason, the use of a slice selective double adiabatic refocusing pulse pair, as described in chapter 4, is beneficial since the spins which contribute to the spin echo are only those which do not change position (in the slice select direction) significantly between the application of the two RF pulses. Flowing blood signal is automatically eliminated by the slice select gradients. The extent to which more slowly flowing capillary water is attenuated depends on factors such as the exact flow rate and vessel geometry. If blood water signal does contribute to the FAIR perfusion signal, a secondary complicating effect is introduced by the different Tj (or T 2*) values for blood water spins and tissue water spins. In the human brain, T 2 of intravascular water has been estimated to be a factor of approximately 3 greater than that of tissue water (240ms compared to 80 ms at 1.5T in (Buxton et ai, 1998)). This could pose a problem for methods which use EPI for image acquisition, since at any given echo time the signal will be weighted towards the intravascular compartment. For a multi-TI experiment, where spin labelled water progressively shifts from the intravascular to tissue compartments as the inversion time increases, this will introduce a systematic bias to the data. This problem has not yet been addressed in the literature, but could potentially affect the values of perfusion obtained using ASL quite substantially, depending on the intravascular lifetime of spin labelled water in voxels in the imaging slice. If TurboFLASH image acquisition is used, the problem is minimised due to the extremely short echo times used; however, T% relaxation during the imaging period and the saturation effects of repeated RF excitation pulses make the quantification of TurboFLASH ASL images subject to certain assumptions {e.g. that the image contrast is 239 General discussion and conclusions dominated by the central lines of k-space). Also, TurboFLASH is not amenable to rapid multi-slice imaging. It has recently been suggested that the problems of intravascular signal contamination and extended transit times in regions of reduced perfusion can, paradoxically, be used to assist in the identification of these areas. In CASL approaches which include a post-labelling delay, transit-time insensitivity should be achieved except in regions where the transit time is especially elevated. These regions, which are likely to correspond to areas of extremely low perfusion, will contain significant amounts of intravascular spin labelled water, and so in the ASL subtraction image will appear as bright foci of signal. Surrounding areas of moderately decreased CBF will appear dark, reflecting the desired contrast for the perfusion image. Therefore, it is possible to identify the most severely compromised tissue based on the observation of unusually bright spots in the perfusion map. Quantitative interpretation of the signal is difficult, since knowledge of exact transit times is required, but qualitative evaluation of perfusion deficits should be possible, which may be adequate for clinical applications of the technique. The main alternative approach currently used for measuring perfusion with MRI is the exogenous dynamic susceptibility contrast agent (DSCA) method. It is therefore important to evaluate the relative advantages and disadvantages associated with the two methods. For ASL, the important benefits and problems of the techniques have been discussed in detail. The experiments described in this thesis have made use of ASL in order to take advantage of its non-invasiveness, good temporal resolution and the possibility of absolute quantification. Contrast agent based approaches are currently employed in many laboratories because the contrast to noise ratio is greater than for ASL. 2 4 0 General discussion and conclusions The transient changes in signal intensity, which occur over a time period of less than one minute after injection of the bolus, are on the order of tens of per cent, compared to one or two per cent expected for ASL. Therefore, the sensitivity of the DSCA approach is greater, and the time required for a single measurement is less. However, there are several complicating factors which limit the use of DSCA in applications to quantitative tracking of cerebral perfusion in a dynamically changing system. First, the rate at which measurements can be performed is limited by the amount of contrast agent that can be safely injected into the subject within a given period of time. Issues such as toxicity and the dilution rate of the tracer determine how many and how often injections can be carried out. Secondly, the calculation of quantitative values of tissue perfusion from DSCA data is not straightforward. Knowledge of the arterial input function (AIF) of contrast agent is required for each voxel. Approximate measurement of the AIF is possible in vivo if an image is acquired which contains a major cerebral artery through which the contrast agent passes prior to transit through the tissue in the slice(s) of interest. This process must be performed concurrently with the acquisition of the perfusion images, thus reducing the definition of the concentration-time curves, and is problematic in small animals where identification of pixels containing signal coming exclusively from an artery can be difficult. In regions of heterogeneous blood flow, exact measurement of the AIF for every relevant voxel is practically impossible. If the AIF is measured (or estimated), combination of this information with the AR2-time relationships of the slices of interest enables calculation of cerebral blood volume (see, for example, (Ostergaard et al, 1996)). Extension of this procedure to the calculation of perfusion requires knowledge of a further parameter, namely the mean transit time (MTT). Again, evaluation of the MTT is not a simple matter (Weisskoff et al, 1993). Therefore, although DSCA data is useful in providing relative values of tissue perfusion and estimates of cerebral blood volume, 241 General discussion and conclusions obtaining quantitative CBF values is difficult with currently available techniques and theory. In conclusion, it has been shown that both continuous and pulsed ASL techniques hold considerable potential for quantitative assessment of tissue perfusion and, with certain modifications and refinements, should be applicable to both experimental animal studies of cerebral ischaemia and to the clinical evaluation of patients with cerebrovascular disease. 8.2 What physiological processes do changes in magnetic resonance images reflect? The work presented in this thesis has been concerned with the development and application of various MRI sequences to measure certain NMR and physiological parameters. In this section, I will give a brief outline of the current views on how the changes in these parameters are related to the underlying physiological events that drive them. 8.2.1 Mechanism for tissue water ADC change during ischaemia As described in chapter 3, and demonstrated in chapter 7, the ADC of tissue water decreases rapidly within minutes of an ischaemic insult. Although there is no debate that these hyperacute reductions of the ADC reflect early cytotoxic oedema, the relative contribution of several postulated biophysical mechanisms remains uncertain. Possible mechanisms which have been suggested include the redistribution of water between the intracellular and extracellular spaces (Moseley et al, 1990), decreased extracellular space 2 4 2 General discussion and conclusions (Hasegawa et al, 1996), increased restriction of intracellular diffusion (Neil et al, 1996), membrane depolarisation and reduced cell membrane permeability (Helpem et al, 1992), increased tortuosity of extracellular diffusion paths (Nicholson, 1993) and temperature effects. At present, it seems as though water redistribution and reduction of the extracellular space are the most likely causes for the observed changes in ADC. The extracellular space is known to decrease by up to 50% in cerebral ischaemia. Stimulation of anaerobic glycolysis leads to an intracellular accumulation of osmotically active products, and breakdown of the energy-dependent ion exchange pumps leads to equilibration of extracellular-intracellular ion gradients. There is a massive influx of sodium and water into the intracellular compartment and efflux of potassium into the extracellular compartment. In the absence of blood flow, the main source of water and electrolytes is that contained in the extracellular space, and the intracellular compartment swells at the expense of the extracellular space. Simultaneous ADC measurements and electrical impedance measurements of ischaemic tissue have shown that the ADC decrease is associated with a decrease in the extracellular space (Verheul et al, 1994). A reduction of ADC can be induced by ouabain administration which specifically inhibits Na^, K^-ATPase, and by the excitotoxins glutamate and N-methyl-D-aspartate (NMDA), both of which cause cell swelling (Beneviste et al, 1992). By assuming that the diffusion coefficients of the two compartments remains constant during ischaemia, with extracellular water being less restricted and therefore possessing a higher ADC, it has been shown that a shift of water from the extracellular space to the intracellular space is sufficient to explain the 40% decrease observed in acute ischaemic lesions. It is possible that the ADC of water in both the extracellular and intracellular compartments changes during ischaemia. As the extracellular volume reduces, the path 243 General discussion and conclusions followed by an average water molecule will become more obstructed and tortuous, and therefore one would expect the diffusivity of extracellular water to decrease. This effect has been demonstrated experimentally by van der Toom et al (van der Toom et al, 1998) by observing the change in diffusion characteristics of extracellularly infused tetramethyl ammonium following initiation of cerebral ischaemia. Recently, it has also been suggested that the ADC of intracellular water decreases during ischaemia. Based on the observation of the diffusion of 2-[^^F]luoro-2-deoxyglucose-6-phosphate (2FDG-6P), which is a purely intracellular or extracellular marker depending on how it is administered, Duong et al showed that under normal conditions, the two compartments are equivalent with respect to diffusion, and that following the induction of global ischaemia, the ADC of both compartments decreased by 35-40% (Duong et al, 1998). The change in extracellular ADC was attributed to increased tortuosity in this compartment; the change in intracellular ADC was proposed to be due to the loss of the cytoplasmic circulation which exists in normal cells to facilitate intracellular molecular transport. The feasibility of this hypothesis and how it relates to the observed changes in water ADC depends on the extent to which the diffusion of 2FDG-6P mimics that of water, which has yet to be fully determined. The molecular weight of 2FDG-6P is approximately a factor of ten greater than that of water; the in vivo ADC values are different by a factor of approximately 5 (-0.8x10 ^ mm^/s for water compared to -0.15x10’^ mm^/s for 2FDG-6P); and diffusion of 2FDG-6P is limited by its compartmental restriction, unlike water which can pass through the cell membranes. It is clear that direct extrapolation of the results presented by Duong et al to tissue water ADC would not be justified. Further investigation is necessary to identify the precise mechanisms which cause a reduction in water ADC during ischaemia. 2 4 4 General discussion and conclusions An important approach in the identification of the processes responsible for the ADC reduction is the correlation of temporal changes of the ADC with changes in other parameters. These can be NMR parameters such as Ti or T 2, levels of metabolites monitored using NMR spectroscopy such as lactate or phosphocreatine, or physiological parameters such as tissue perfusion or cerebral blood volume. In order to be able to correlate dynamically changing variables, it is vital to monitor them with good time resolution. For this reason, I have developed a robust method for measuring the ADC of tissue water with good time efficiency at high field. While not being as rapid as single shot echo planar imaging approaches, the magnetisation prepared TurboFLASH technique described in chapter 6 of this thesis offers the advantages of being applicable at high magnetic field and being relatively insensitive to eddy current effects. The ability to use the technique at high field is beneficial since DWI can then be combined more easily with NMR spectroscopic studies, and the effects of ischaemia on the NMR parameters Ti and T% of tissue water are greater. The method can be used to achieve better time resolution than conventional spin echo based approaches, or alternatively can be employed to increase the signal to noise ratio of the diffusion measurement for a given measurement duration. This will allow a more detailed and accurate comparison of the changes occurring during the hyperacute stages of cerebral ischaemia, which should in turn result in a better understanding of the common causes underlying these changes. 8.2.2 The importance of measuring T 2* Since it was first shown to detect changes in the level of blood oxygenation several years ago, T 2*-weighted BOLD MRI has been used extensively in cognitive neuroscience to associate increases in regional brain activity with the presentation of specific stimuli. Where available, gradient echo EPI has become the method of choice for functional 245 General discussion and conclusions imaging studies which use MRI. This is because of its extremely good temporal resolution and its sensitivity to the changes associated with functional activation. However, in order to study the physiological mechanisms which cause the BOLD effect, it is necessary to adopt a more quantitative approach. Changes in T 2*-weighted images can derive from several sources, which need to be separated if their relative contributions are to be assessed. The two main factors which can cause an increase in signal on a T 2*- weighted EPI image are a decrease in the local amount deoxyhaemoglobin in a voxel and an increase in the rate at which fresh {i.e. fully relaxed) inflowing blood enters the voxel. These two physiological effects are closely linked, and distinguishing between the two in order to determine the dominant effect using single shot gradient echo EPI is difficult unless a long repetition time is used between images. This is not desirable since it compromises the time efficiency of the experiment and potentially valuable information is lost. Also, baseline drifts in signal intensity during the experiment complicate the analysis of time course data, making it more difficult to unambiguously locate stimulus dependent changes. In experimental studies of cerebral ischaemia or hypoxia, where BOLD imaging can be used to determine areas of reduced blood flow and increased deoxyhaemoglobin concentration, factors such as temperature fluctuations which affect Ti also contribute to this baseline drift. When such factors are eliminated, it has been shown (in the neonatal piglet brain) that absolute values of T 2* correlate well with the regional concentration of deoxyhaemoglobin (Punwani et al, 1998). T 2* is evidently an extremely important parameter and knowledge of its value would certainly help to elucidate the physiology of cerebrovascular events. The multi-shot interleaved EPI technique proposed in chapter 5 overcomes the problems mentioned above by creating parameter maps of T 2*. In this way, direct monitoring of the 2 4 6 General discussion and conclusions parameter of interest is possible without interference from other confounding factors. A similar approach has recently been proposed by Speck and Hennig (Speck and Hennig, 1998) in which several differently Ti^-weighted images are formed following spin excitation. Their approach is rather more ambitious than the one described here, in that enough data is collected following a single excitation pulse to generate 8 entire images. Consequently, the spatial resolution of their images is relatively poor (64x32), limiting the use of the sequence in identifying focal areas of T 2* change. The method proposed in this thesis benefits from the advantages inherent in interleaved EPI techniques i.e. reduced image distortion in regions of large susceptibility gradients and a narrow point spread function compared to an equivalent single shot EPI acquisition. However, the time resolution of the sequence is not as good as that of the technique described by Speck and Hennig. If the time resolution of the sequence needed to be improved, one could envisage a compromise between the two approaches. In the form described in chapter 5, the lEPI sequence is an eight-shot approach; this could easily be reduced if more lines of k-space for each image are sampled per acquisition, with the corresponding reduction in image quality and spread in T 2*-weighting across k-space. The exact requirements of a given experiment will determine the extent of compromise necessary to produce accurate T 2* maps in a sufficiently short total acquisition time. 8.2.3 Utilising the information provided by changes in Ti and T 2 during the hyperacute phase of stroke In chapter 7 of this thesis, I have reported observations of early changes in the relaxation times of rat brain tissue following the induction of focal ischaemia, and discussed the possible mechanisms responsible for such changes. A consequential question relating to 2 47 General discussion and conclusions these observations naturally presents itself: could the information provided by measurement of these parameters, in conjunction with more traditional parameters, have clinical importance? Or, with the increasing use of more directly physiologically based MRI methods such as diffusion and perfusion imaging, is there any need to use relaxation times to generate image contrast in studies of ischaemia? In order to answer these questions, it is important to evaluate the specificity of the information provided by diffusion and perfusion MRI. Perfusion imaging produces maps which (ideally) show the extent to which blood flow, and therefore the supply of essential nutrients, is compromised during ischaemia. However, the relationship between blood flow level and tissue viability is known to be very complex, being dependent on several factors such as the duration of ischaemia and whether spontaneous reperfusion has occurred. Diffusion-weighted imaging reflects more directly the cell status in ischaemic tissue, since it is believed to highlight areas of cytotoxic oedema (see section 8.2.1). However, loss of cell ion homeostasis is not indicative of tissue which will inevitably progress to infarction, and the area of the brain which experiences an initial decrease in ADC comprises of both core and penumbral tissue (see (Hoehn-Berlage, 1995)). Differentiation between these two types of tissue is essential because penumbral tissue is potentially salvageable and thus the target of therapeutic intervention. Attempts have been made to distinguish the core from the penumbra in animal experiments based on the degree of ADC reduction, but the results indicate that there is no absolute threshold of ADC decrease that predicts if a lesion is reversible (Davis et al, 1994). Tissue which suffers an initial drop in ADC will progress to infarction if no intervention is performed; however, it is also known that initially unaffected tissue (showing no ADC changes) can become recruited as the lesion grows in the hours following occlusion, demonstrating the 248 General discussion and conclusions importance of the combined effect of duration and degree of hypoperfusion on tissue damage. It is apparent that much remains to be learnt about the mechanisms involved in the initial stages of cell necrosis, and how these relate to the changes observed using diffusion and perfusion MRI. Given this context, it would seem sensible to apply all the tools at one’s disposal to help in the investigation of the effect of cerebral ischaemia on brain tissue. From the NMR point of view, this includes observing acute changes in relaxation times. While it is known that increases in both Ti and 7% several hours after occlusion reflect the increase in total tissue water content associated with vasogenic oedema, immediate post-occlusion changes have not been examined in great detail. The work in this thesis has shown that effects due to changes in blood oxygenation levels on T 2 and due to changes in flow, tissue water content, tissue oxygenation and possibly other as yet unidentified sources on Ti are observable using high field (8.5T) MRI. Combination of this information with diffusion and perfusion data, and comparison of their respective time courses, will help identify common driving forces behind the observed changes. The results presented in chapter 7 show that these effects are present, but the time resolution of measurement of each parameter was insufficient to enable accurate characterisation of the rapid changes occurring. However, I believe that with further development, the results presented here are potentially relevant to human application. With the appearance of increasingly high field human MRI magnets (e.g. see (Robitaille et al, 1998)), it is important to take advantage of all the available information. It remains to be seen whether acute changes in Ti and T2 will be useful diagnostically or if their use will remain in the experimental regime. 2 4 9 General discussion and conclusions 8.3 Future work As alluded to in the previous sections of this chapter, much work remains to be done in many of the subject areas investigated in this thesis. Briefly, this includes: • more rigorous validation of the benefit of using optimised adiabatic RF pulses for slice definition in FAIR perfusion imaging, and application of the technique to monitor blood flow changes during haemodynamic perturbations. Arterial spin labelling methods offer the only approach currently available for measuring individual subject perfusion time courses quantitatively and with high temporal resolution, and therefore should be used increasingly in studies where changes in CBF are important. Advances in NMR hardware, such as higher field strength magnets and improved sensitivity RF coils, will help overcome the difficulties relating to SNR associated with ASL techniques. A direct comparison between the CBF values obtained using ASL and contrast agent based MRI methods would be useful to help evaluate the relative merits of each technique. • application of the techniques which I have developed to measure T 2 * and ADC with high time resolution and precision. T 2 * and ADC are extremely important parameters in the assessment of ischaemic or hypoperfused tissue, and work is currently being carried out to investigate the exact relationships between tissue status and T 2 * and ADC values. Also, many neuroscientific experiments are being performed using T 2 * and ADC changes to define regions of cerebral activation or damage, without regard to the exact biophysical mechanisms responsible for the changes. The techniques developed here should allow time course changes of the relevant parameters to be monitored with improved efficiency. Therefore, they should allow better definition of the response to a given stimulus or insult, thus facilitating analysis of the experimental data. From the clinical perspective, time is a decisive factor in stroke outcome. With 2 5 0 General discussion and conclusions the combination of fast ADC mapping and perfusion MRI, the entire lesion can be delineated and a diagnosis may be made within minutes. Rapid techniques improve the efficiency of MR as a diagnostic tool, and so are a clinical necessity, further investigation of the physiological processes occurring during cerebral ischaemia, with a view to being able to differentiate between core (unsalvageable) and penumbral (compromised but potentially salvageable) tissue. It is generally accepted that currently available MR methods (in common with any other approach) can not unequivocally discriminate reversible from irreversible damage in ischaemic tissue. One of the main advantages of MRI over other imaging techniques is the ability to measure numerous different and often independent parameters; the question remains whether this plethora of information can be put to good use in identifying tissue at risk and investigating the effects of therapeutic treatments. It should also be noted that recovery of tissue from cerebral injury is only of practical value when accompanied by neurological improvement. Current experimental studies on effects of therapy are mainly focused on reduction of ischaemic lesion size, but this may not be directly related to improved functional outcome. Proper validation, by the use of neurophysiological and neurobehavioural tests, should also be performed. 251 General discussion and conclusions 8.4 Thesis summary Chapter 1 begins with a general introduction to NMR and MRI. It gives a brief historical account of the development of the field, from the initial hypothesis of particle spin to the development of modem imaging techniques. The chapter ends with an overview of the aims of work that was carried out for this thesis. Chapter 2 introduces the theoretical basis of NMR. Using the principles of quantum mechanics, expressions are derived for the differences between nuclear spin energy levels in the presence of an externally applied magnetic field. By making certain assumptions, the situation is taken to the classical limit in order to simplify the analysis. The concept of the rotating frame of reference is introduced and spin excitation, detection and relaxation are described. Basic manipulation of the NMR signal is discussed, leading to an explanation of how spatial encoding can be performed, and thus how images can be created. The chapter ends with a brief review of the contrast mechanisms that are available in MRI. In Chapter 3, the discussion of MR contrast mechanisms is refined to address the two most relevant to the work described in this thesis: perfusion and diffusion. First, perfusion is defined, and a range of alternative techniques for its evaluation are described. The NMR techniques that have been developed to measure perfusion are then detailed, with particular attention being paid to the arterial spin labelling (ASL) approaches. The final part of the chapter looks at the importance of water diffusion in biological systems, and how changes in water diffusion can indicate changes in the physiological state of tissue. The method for sensitising the NMR signal to diffusion is described, and it is shown how 2 5 2 General discussion and conclusions data obtained from this approach can be used to calculate the apparent diffusion coefficient (ADC) of the system. The relevance of ADC measurements to ischaemia and stroke is described. Chapter 4 describes the work I have done to improve the pulsed ASL perfusion technique FAIR. This work is divided into two categories: RF pulse optimisation and improvement of the time efficiency of the sequence by the use of a global pre-saturation pulse. Both aspects are given a sound theoretical basis, and shown to be beneficial by practical implementation and experimental validation. The use of a pre-saturation pulse allows an improved SNR per unit time for the FAIR experiment, and also theoretically should allow estimation of the longitudinal relaxation time of blood water Tia, which is needed for the quantification of blood flow using this technique. However, due to limitations imposed by the physical length of the RF transmitter coil, measurement of Tia was not as straightforward as was initially hoped. With suitable modification of the theory to take account of these limitations, flow quantitation with the reduced repetition time sequence was shown to be equivalent to that of the standard experiment. RF pulse optimisation was achieved using purpose-designed adiabatic FOCI pulses, which have sharp slice edge definition. FOCI pulses were implemented to perform slice-selective inversion, and also as the slice-selective refocusing pulse of the imaging sequence. Phantom results showed significant improvements in the match-up between inversion and imaging slices, which is a fundamental goal of the FAIR technique. Finally, the modified version of the FAIR sequence was employed in a study of transient global ischaemia followed by reperfusion in the gerbil. It was demonstrated that ASL methods offer a quantitative method for following the dynamic changes in perfusion which occur during a cerebrovascular disturbance. 253 General discussion and conclusions In Chapter 5 I have introduced a pulse sequence which allows the rapid calculation of T2 * maps whilst minimising the extent to which image quality is compromised. The sequence is based on an interleaved EPI approach, and collects several data segments with different Ti^-weighting following each excitation pulse. The echoes from each of these segments are then combined with differently phase encoded echoes from subsequent excitations to form a data set with sufficient information to enable the generation of an image. A set of images is thus created whose effective acquisition window is relatively short compared to single-shot EPI and whose T 2 *-weighting is different from image to image. From this set of images T 2 * maps is calculated. The ability of this technique to accurately measure a range of T 2 * values in a non-uniform phantom is demonstrated, and the advantages over multi-echo time single-shot EPI are shown, which are the reduced image distortion and improved resolution due to a narrower point spread function. Use of the sequence to reflect changes in levels of cerebral blood oxygenation is demonstrated in the rat brain during transient periods of anoxia. Chapter 6 describes a sequence I have developed to enable rapid measurement of diffusion coefficients at high field. Although similar techniques have been proposed by several groups, practical implementation of magnetisation prepared TurboFLASH diffusion-weighted imaging on our 8.5T system required modification to enable quantitative values of the ADC to be obtained. This modification consisted of acquiring a pair of images with the same diffusion-weighting, but with the magnetisation preparation scheme modified so that orthogonal components of the diffusion-weighted spin echo are aligned along the longitudinal axis in the two cases. This eliminates the effect of eddy currents created by the diffusion gradients. As the diffusion-weighting of the sequence is altered, the amplitude of the diffusion gradients changes, and therefore the size and effect 2 5 4 General discussion and conclusions of the eddy currents change. This results in differing amounts of phase accumulation of magnetisation in the transverse plane, and if only a single component of this magnetisation is sampled, misleading results are obtained. Acquisition of both orthogonal components of the magnetisation allows unambiguous calculation of its magnitude, thus eliminating any errors due to phase. Also in this chapter I have looked at the effect of reducing the repetition time of the sequence in order to achieve greater time efficiency. I showed that the repetition time corresponding to maximum SNR per unit time can be used without significantly compromising the accuracy of the ADC measurement. In Chapter 7 I have described the implementation and application of continuous ASL in a rat model of focal ischaemia at 8.5T. The reasons for using centre-out phase encoded TurboFLASH for image acquisition are outlined. In addition to the perfusion-weighted ASL subtraction image, several other parameters are required for quantification of CBF. These are (i) the degree of spin labelling achieved by the off-resonance RF pulse, which was measured by observing the effect of the RF pulse on the signal intensity of blood in the carotid artery of the rat immediately distal to the plane of inversion, (ii) the Ti of brain tissue, which was measured using an inversion recovery TurboFLASH sequence, and (Hi) Ti of brain tissue in the presence of an off-resonance RF pulse (Tisat), if the more accurate method for perfusion quantification is to be performed, and this was measured using a previously described method in which the length of the RF pulse is varied. These methods were then applied to monitor the time course of cerebral perfusion, in addition to the time courses of ADC, Ti and T 2 , in the rat brain following permanent occlusion of the middle cerebral artery. Immediately after MCAO, it was possible to define three regions based on a combined analysis of the perfusion and diffusion maps: the core region, which suffered from reduced perfusion and displayed a reduced ADC value; the border region, in which 255 General discussion and conclusions a moderately reduced level of perfusion was observed but ADC remained unchanged; and unaffected tissue which was outside the MCA territory. Changes in both relaxation times were observed very soon after MCAO in both the core and border regions, and these are believed to reflect changes in the oxygenation state of the blood and tissue, before the effects of vasogenic oedema begin to dominate. These observations are not apparent at lower field strengths, demonstrating the advantage of performing investigations of the pathophysiological effects of ischaemia at high field. Finally, Chapter 8 has discussed the significance of the work described in the preceding chapters. Since ASL is a relatively new approach, the work described here is evaluated in the context of other recently proposed modifications to the technique. The problems which remain regarding flow quantitation using ASL methods are discussed, and the feasibility of using the technique to measure ischaemic flow is assessed. It is concluded that ASL holds considerable promise for the future in providing quantitative measurements of cerebral perfusion. The physiological significance of the various MR contrast mechanisms such as diffusion, T 2 * and inherent relaxation time is summarised. The potential and relative importance of each of these parameters in relation to stroke diagnosis and prognosis remains to be fully determined. 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