Comparison of Single Shot Methods for R2* Estimation

COMPARISON OF SINGLE SHOT METHODS FOR R2* ESTIMATION

HRISHIKESH DESHPANDE

DONALD TWIEG, CHAIR NARASIMHA AKELLA GEORG DEUTSCH

A THESIS

Submitted to the graduate faculty of The University of Alabama at Birmingham,

in partial fulfillment of the requirements for the degree of

Master of Science in Biomedical Engineering

BIRMINGHAM, ALABAMA

2009 COMPARISON OF SINGLE SHOT METHODS FOR R2* ESTIMATION

HRISHIKESH DESHPANDE

BIOMEDICAL ENGINEERING

ABSTRACT

In functional MRI (fMRI), typically a series of images are acquired in rapid suc- cession in control and stimulation cycles to detect functional changes in regions of the brain. These changes are signified by changes in tissue R2*, caused by the Blood Oxy- genation Level Dependent (BOLD) mechanism. In most fMRI experiments R2* changes are not directly measured, but are inferred from signal changes from a series of R2*- weighted echo-planar imaging (EPI) images.

A potentially more accurate method of measuring changes in R2* is the multiple- gradient echo EPI method (MEPI), which acquires separate EPI images at several echo times following a single excitation (1). A recently introduced technique for R2* measurement, single-shot parameter assessment by retrieval from signal encoding (SS-

PARSE) maps R2*, frequency and local magnetization M0 by modeling the local signal and solving an inverse problem.

Because it explicitly models local phase evolution during the signal, it is inherent- ly free of off-resonance geometric distortion. The sensitivity and accuracy of the activation maps generated from fMRI block design experiment depend critically on the ability to measure the small changes in R2* representing differences between control and stimulation states. The changes in R2* between the control and stimulation states need to be

i consistent to get meaningful activation maps. To compare the temporal variability of R2* estimates for MEPI and SS-PARSE, studies of repeatability were performed using phantoms with a range of R2* values typically found in human brain tissue.

After analyses, the performance of SS-PARSE was found to be consistently supe- rior to MEPI in all the experiments. Within the SS-PARSE technique itself, the sequence with lower variation in R2* estimation was deemed to be the most advantageous in fMRI experiments.

ii DEDICATION

To the field of diagnostic imaging and to the researchers who have shaped it into

what it is today.

iii ACKNOWLEDGMENTS

I would like to express my sincere thanks to Dr. Donald Twieg, whose guidance made this research possible. His advice and encouragement propelled this work to its completion. I would also like to thank Debbie and Jerry for their helping me out with the equipment setup for the experiments. I am also grateful to my colleague, Rajiv, who taught me the use of Varian interface and helped me with many of my experiments. I also thank my colleague Ningzhi for her help with thesis documentation. I would also like to thank Yun Jiang who helped in the initial experimental design. I would like to thank my committee members, Dr. Twieg, Dr. Akella and Dr. Deutsch for their valuable time and effort.

I would especially like to thank Mark Bolding who helped in the design of pulse sequences and setting up the system to work for our experiments. His assistance made most of this work possible. The help we got from Dr. Stan Reeves and his team at

Auburn University was quite invaluable. I am quite grateful to them for keeping the multi-core machine up and running throughout the duration of the project.

Also, I thank my sister, Himani, and people in the department of Material Science and Engineering for their willingness to provide equipment needed for phantom design. I

iv would also extend my thank to some of my friends in Birmingham, especially Michelle,

Chris and Jon, who made my stay in Birmingham a pleasant and memorable experience and through whom I learned how much this city has to offer. And finally I would like to thank my parents for giving me the encouragement and the freedom to pursue my ambi- tions and being supportive all along.

v TABLE OF CONTENTS

ABSTRACT ii LIST OF FIGURES ix LIST OF ABBREVIATIONSxi 1. INTRODUCTION 1 2. Background 3 2.1. Image acquisition using MRI 3 2.2. BOLD effect 5 2.2.1. Significance of R2* in fMRI...... 6 2.2.2. R2* measurements...... 7

* 2.3. Methods of R2 measurement 7 2.3.1. Gradient echo multiple shot (GEMS)...... 7 2.3.2. MEPI...... 9 2.3.3. SS-PARSE...... 10 2.4. Gradient tables and k-trajectory 12 2.5. Selection of maximum gradient amplitudes 13 2.6. Comparison between the single shot methods 15 3. methods 17 3.1. Gradient waveform generation for SS-PARSE 18 3.2. Phantoms 19 3.2.1. Calibration phantom...... 19 3.2.2. Fourtube phantom...... 20 3.3. Calibration 21 3.4. Phantom data acquisition 22 3.5. Data Analysis 23 3.6. Development of graphical user interface (GUI) 24 3.7. Parameter evaluation 27

vi 3.7.1. R2* calculation in GEMS...... 27 3.7.2. R2* calculation in MEPI...... 28 3.7.3. Analysis of SS-PARSE parameter maps...... 30 3.8. Comparison 31 3.8.1. Comparison of R2* estimates...... 31 3.8.2. Comparison between the TSDs of single shot methods...... 32 3.8.3. Comparing performance at off-resonance...... 33 4. Results and discussion 33 4.1. Comparing the accuracy of R2* estimation 33 4.2. Comparison of TSD 39 4.3. Performance under off-resonance 40 4.4. Discussion 42 5. Conclusions 46 6. REFERENCES 48

vii LIST OF FIGURES

Figure...... Page

Figure 1. Mechanism of BOLD effect...... 5

Figure 2. Pulse sequence diagram for gradient echo multiple shot (Adopted from Matt

Bernstein, Handbook of MRI Pulse Sequences, 2004, p. 580)...... 8

Figure 3. k,t-space plot of MEPI pulse sequence over four echoes (Donald Twieg,

Southeastern Magnetic Resonance Conference 2008)...... 10

Figure 4. 10ms section of a gradient waveform for 2.9 G/cm...... 18

Figure 5. Fourtube phantom...... 20

Figure 6. Calibrated k-trajectories for four different gradient amplitudes...... 21

Figure 7. Coverage of 3.8 G/cm gradient amplitude k-trajectory over time...... 22

Figure 8. GUI for SS-PARSE...... 26

Figure 9. GEMS images at 16 different TEs...... 27

Figure 10. MEPI images at four TEs...... 28

Figure 11. MEPI signal sampling at specific echo times...... 29

Figure 12. R2* estimated from SS-PARSE (Gmax=2.9 G/cm) over 50 repetitions...... 30

Figure 13. SS-PARSE parameter maps at different gradient amplitudes...... 34

Figure 14. R2* distribution of MEPI and SS-PARSE at Gmax=1.9 G/cm and the distribution of accuracy ratios...... 35

viii Figure 15. R2* distribution of MEPI and SS-PARSE at Gmax=2.29 G/cm and the distribution of accuracy ratios...... 35

Figure 21. TSD plots of SS-PARSE (at Gmax = 2.9G/cm) and MEPI (a) R2* GEMS vs. TSDSS-PARSE. (b) R2* GEMS vs. TSDMEPI (c) R2* GEMS vs. TSDSS-PARSE shown by blue dots and R2* GEMS vs. TSDMEPI shown by red dots. (d) TSDMEPI – TSDSS-PARSE vs.

R2* GEMS. 40

Figure 22. SS-PARSE parameter maps in presence of field inhomogeneities...... 41

Figure 23. MEPI images at 4 echo times in presence of field inhomogeneities...... 41

Figure 24. Reconstructed image from GEMS, SS-PARSE (Gmax=2.9 G/cm) and MEPI in presence of field inhomogeneities...... 42

ix LIST OF ABBREVIATIONS

BOLD Blood Oxygenation Level Dependent BW Bandwidth EPI Echo-Planar Imaging fMRI Functional Magnetic Resonance Imaging FOV Field of view GEMS Gradient Echo Multiple Shot GUI Graphical User Interface MEPI Multiple Gradient Echo-Echo Planar Imaging MRI Magnetic Resonance Imaging NMR Nuclear Magnetic Resonance PLCG Progressive Length Conjugate Gradient RF Radiofrequency ROI Region of interest SNR Signal to Noise Ratio Single-Shot Parameter Assessment by Retrieval from SS-PARSE Signal Encoding TE Echo Time TR Repetition Time TSD Temporal Standard Deviation

x 1. INTRODUCTION

Magnetic resonance imaging (MRI) was first employed for non invasive imaging of the human body in 1977 (1). Initially the focus of MRI was on scanning the anatomy.

Later, with the discovery of the blood oxygenation level dependent (BOLD) effect, MRI became a tool for observing the areas of the brain that are active while performing a specific task (2). This branch of MRI studying the functional changes brain came to be known as functional MRI (fMRI).

The BOLD effect is a function of tissue relaxation rate R2* (3). In order to correctly assess the brain activity in functional maps, it is sufficient to detect relative changes in R2*. For more quantitative functional mapping, an accurate and reliable method for measurement of R2* would be useful. A recently developed technique called the multiple gradient echo-echo planar imaging (MEPI) measures R2* from signal changes over several echoes following a single excitation pulse (4). However, since this technique computes each individual image neglecting phase changes during the signal, it is sensitive to off-resonance frequencies within the object, possibly leading to severe geometric distortion (5).

xi A new technique, single-shot parameter assessment by retrieval from signal encoding (SS-PARSE), solves an inverse problem to estimate R2* parameter values directly from the signal instead of detecting serial signal changes measuring it by fitting to the decay over the course of serial frames (6). It uses a reconstruction algorithm that employs a parametric signal model and estimates the encoded parameters using an iterative estimation process. The primary parameter of interest in our case is the tissue relaxation rate

In fMRI studies using a block design method, single shot images are acquired during control and stimulus periods. The activation maps are computed from a series of control and stimulus images (7). If these images are consistent we get accurate activation maps. If not, the accuracy of these maps can be quite questionable.

In our experiments we compare the temporal performance of R2* estimation for the MEPI and SS-PARSE techniques using gradient echo multiple shot (GEMS) technique as the gold standard. We also tested the behavior of the MEPI and SS-PARSE under off-resonance conditions to examine the robustness of these two single shot methods, and investigate the behavior of SS-PARSE technique at different gradient strengths in order to determine what would be the optimal range to use in fMRI experiments.

This thesis is divided into five chapters. After this introduction, chapter 2 gives a brief theoretical background about the techniques we use in our comparison study. In chapter 3 we discuss the experimental design setup and the data acquisition techniques.

Results and statistical analyses from our experiments are presented and discussed in

xii chapter 4. The results and ways to improve our results are discussed in this chapter.

Chapter 5 includes a summary and conclusions drawn from this work.

xiii 2. BACKGROUND

2.1. Image acquisition using MRI

MRI is an imaging modality which uses signal obtained through the nuclear magnetic resonance (NMR) phenomenon to construct images. In the field of medicine, we are mostly interested in looking at the NMR signal from water and fat, the major hydrogen containing components of the human body.

When placed in a magnetic field of strength B0, a proton with a net spin can ab- sorb a photon, of frequency υ. This frequency is a function of the gyromagnetic ratio (γ) and the external field and is known as the Larmor frequency (8).

υ = γ B0 (1)

If an external field such as a radiofrequency (RF) pulse at Larmor frequency is introduced into the system, it excites the spin systems causing them to precess around their axis and eventually return to their state of equilibrium. While returning to their state of equilibrium, these proton spins emit energy, which is detected as a signal during MR experiments (8).

xiv The net magnetization observed during the process can be considered to consist of two components, the longitudinal component Mz and the transverse component Mxy. The rate at which Mxy decays to zero is the spin-spin relaxation time and is described by the time constant T2 as:

t /T2 M xy (t)  M xy (0)e (2)

The rate at which Mz to returns to a steady state magnetization M0 is described by time constant T1 and can be described as:

t / T1 M z  M 0 (1 e ) (3)

The relaxation time constants for magnetization along the transverse and longitudinal component can be considered to be an exponential decay. The transverse magnetization is a combination of two factors one of which is the molecular interactions leading to the pure T2. Another factor that contributes to this decay is the variation in the field B0,

’ which is called impure T2 or T2 . The combined effect of pure and impure T2 is what re-

* sults in the decay of transverse component of magnetization, and is the time constant T2 .

The relationship between the time constants responsible for transverse magnetization is given as:

* ' 1/T2  1/T2 1/T2 (4)

During an experiment the signal obtained by the MRI system is in the spatial-frequency domain. The digitized data in the spatial-frequency domain is considered to be in the k-space. This data is encoded in the frequency domain and is best represented by a

xv Fourier transformed data matrix. Through the application of an inverse Fourier transform

(IFT) the signal in frequency domain can be reconstructed into an image Im in the spatial domain.

Im  S(k(t))e 2i(k (t)xk (t) y) dk 2 (x, y)  (5)

k(t)   G(t')dt' (6)

A set of linear gradients in x, y, and z planes are used to modify the local signal to indicate its location once the RF pulse has been applied. These linear gradients G determine the path of k(t) by what is termed as a k-trajectory.

These gradients can be used in a number of ways. They can be used to define a plane of acquisition. Rapid imaging in which all data are acquired following a single excitation pulse is called the single shot method (9). The other method is the multiple shot imaging method where several shots (rf pulses) are required in order to gather sufficient data for an image (9). Single shot techniques are much faster than multiple shot techniques.

xvi 2.2. BOLD effect

Figure 1. Mechanism of BOLD effect.

For several years, researchers have attempted to devise better methods to understand the workings of the human brain. The last few decades saw techniques such as elec- troencephalography (EEG), magnetoencephalography (MEG) and position emission to- mography (PET) gain momentum in their use in the study of brain function. However, most of these methods lacked either the spatial or temporal resolution that was required to understand brain function more accurately. With the discovery of BOLD effect, the use of fMRI in studying the functions of brain gained widespread popularity and acceptance.

The BOLD mechanism provides an explanation of how a change in stimulus gives rise to change in acquired signal (2). There are series of events that take place from the onset of stimulus until the final change in the NMR signal. A typical stimulus consists of some task that needs to be performed by the subject while in the scanner. Applying stimulus leads to increase in brain activity in order to accomplish that task. This increased brain activity is sustained by increased oxygen consumption and increase in blood flow to the region that is performing the given task. Increased blood flow results in the reduction of deoxyhemoglobin in that region, reducing the magnetic susceptibility of blood vessels

xvii and the surrounding tissues. Reduction in magnetic susceptibility leads to reduction in the

* relaxation rate R2 of the brain tissues (8).

* Thus the changes in relaxation rate R2 are associated with brain activity. In order to study the brain functions by means of BOLD fMRI, it is essential to obtain images that

* * have information pertaining to the R2 changes, i.e. the images need to R2 weighted.

2.2.1. Significance of R2* in fMRI

fMRI based neuroimaging techniques allow us to detect the brain areas which are involved in a task, a process or an emotion. A single shot technique is used to sequentially acquire brain images every few seconds over several minutes. fMRI cannot detect absolute activity of brain regions. It can only detect difference of brain activity between several conditions. During the fMRI image acquisitions, the patient or subjects are asked to alternately perform several tasks or a stimulus is provided to trigger several processes or emotions (7). Each of these conditions is repeated several times and can be separated by rest periods.

Since we are measuring the brain activity by computing signal changes, any signal change whose source is other than a brain task would lead to inaccuracy in the final

* activation maps. Since the signal changes are sensitive to R2 changes, it follows that any

* errors in R2 weighting would lead to errors in the activation maps. It is thus critical to

* have reliable means of R2 weighting and measurement.

xviii 2.2.2. R2* measurements

Accuracy of quantitative fMRI studies depends on the accuracy of R2* measurements. R2* can be measured using both the single shot and multiple shot techniques (11).

Even though the conventional multiple shot methods are used less frequently in fMRI studies, they can serve as a valuable tool by serving as a gold standard in measurement of some of the parameters of interest in fMRI.

* 2.3. Methods of R2 measurement

2.3.1. Gradient echo multiple shot (GEMS)

The GEMS sequence, as the name suggests, is a multiple shot imaging method. In this method each line in the k-space is scanned sequentially after excitation by a rf pulse.

This method relies on the formation of an echo by switching the linear gradients (8). The

GEMS technique allows us to take multiple acquisitions with a set of closely spaced echo

* times. The signal at different echo times is weighted with R2 relaxation parameter making it possible to estimate it as an unknown from the equation:

* R2 t S  S0e , (7) where S is the signal at individual echo time t. Gradient echo multiple shot images have a significantly better signal to noise ratio (SNR) than the single shot methods.

xix Figure 2. Pulse sequence diagram for gradient echo multiple shot (Adapted from Matt Bernstein, Handbook of MRI Pulse Sequences, 2004, p. 580)

2.3.2. MEPI

The encoding scheme employed in MEPI is similar to the one used in GEMS sequence. The main difference between the two is that GEMS is a multiple shot method, while MEPI is a single shot method.

In MEPI each line in the k-space is scanned rapidly following excitation by a single rf pulse. The sampling takes place over four echoes. These four echoes have similar

* characteristics as the echoes obtained with GEMS and R2 can be calculated by monoexponentially fitting the signal using equation 7.

* Measurement of M0, R2 and frequency f in a single shot poses a challenge for the conventional single shot MRI techniques since it requires traversing the entire k-space

xx within a single echo time TE to obtain a complete image (8). Measuring f requires very closely spaced TE values to accurately measure frequencies within reasonably wide bandwidth. On the other hand accurate measurement of net relaxation rate requires widely spaced TE values (12).

Figure 3. k,t-space plot of MEPI pulse sequence over four echoes (Donald Twieg, Southeastern Magnetic Resonance Conference 2008)

Since the MEPI sequence fails to keep track of changes in phase within each individual EPI scan, it is impossible to obtain reliable parameter maps in the presence of strong background gradients and off-resonance due to geometric distortions and intensity distortions.

xxi 2.3.3. SS-PARSE

The signal model used in GEMS and MEPI is a static model described as:

s(t)   M (x)e 2ik (t)x dx (8)

It assumes that no signal decay or phase evolution occurs during the acquisition time of the imaging data. This assumption gives rise to numerous image errors, like geometric distortion due to field inhomogeneities or off-resonance frequencies (8), N/2 ghosting and filtering effects due to differential R2* weighting of spatial frequency components (13).

SS-PARSE addresses these issues by using a continuous signal model which tracks the distribution M0 as it evolves across the k-space (6). This is accomplished by spatially encoding the signal as a function of linear gradient waveforms and parallel receiver coils, which gives relative amplitude for each location along with phase changes over time. The continuous signal model can be expressed as:

* s(t)  M (x)e[R2 (x)i2f (x)]t e2ik(t)xdx  0 (9)

* (R2 (x, y)i2f (x, y))nt 2ikn x Sd (n)   x  y M 0 (x, y)e e dx (10)

The discretized parametric model can be assumed to lie along the x, y grid (6).

Using this continuous model, it is possible to encode magnetization and relaxation rate, as well as frequency. By doing so, the model overcomes the limitations posed by background gradients and off-resonance. This makes the signal acquired and parameters estimated using SS-PARSE immune to geometric distortion or ghosting artifacts. xxii The discretized signal model forms an inverse problem in which we have to estimate the parameters from a spatio-temporally encoded signal. Each data sample is the sum of the deterministic signal and measurement noise which is usually assumed to have a zero-mean and is independently distributed.

The solution is a set of unique parameter values found iteratively to match the actual observed signal. In our case, we design a progressive length conjugate gradient

(PLCG) search which iteratively modifies the parameter values that need to be estimated

(6). The iteration is performed over incremental lengths of signal data with a goal of min- imizing the least square residual below a desired tolerance level (14). The algorithm iteratively modifies the unknown parameter values M0, R2* and f, in order to minimize the least-square residual to be below a desired tolerance level.

2.4. Gradient tables and k-trajectory

The k-trajectory required for acquiring SS-PARSE data is very different from the conventional Cartesian trajectories used in MEPI and GEMS. SS-PARSE makes use of a rosette trajectory which samples the center of k-space multiple times as it traverses the sampling space (6). Sampling the center of k-space multiple times gives us multiple samples along the time axis from which to estimate the frequency of the local signal.

The trajectories result from continually varying gradients that are orthogonal to each other (15). We have to know the system parameters and make some assumptions before we can proceed with the development of gradient waveforms. The k-trajectory for

xxiii -1 -1 SS-PARSE was computed within a k-space radius of kf=2.82 cm . A 2.82 cm k-disc with this radius has the same area as a square 5 cm-1 x 5 cm-1 Cartesian grid, with spatial resolution comparable to 64x64 single-shot MEPI for a 12.8 cm field of view (FOV).

These gradient waveforms were generated using:

Using these, we get the complex gradient waveform values,

  k (((   )(cos(   ).n  )  (i.sin(   ).n  ))  ... r 1 2 1 2 2 1 2 2   (12) ((1  2 )(cos(1  2 ).n  )  (i.sin(1  2 ).n  ))) G (1: n)  2 2 s 2

These gradient tables require further resampling in order to conform to the specific dynamic range of the digital to analog converter of the system.

Since actual k-sampling locations depart from nominal values in system-specific fashion, the effective k, t locations of the signal samples were determined experimentally by the method of Zhang et al. (16). We call this the calibration process. Along with the values of kx and ky at each time, calibration also determines the phase, Φ(t), a time-varying spatially constant field offset attributable largely to eddy currents (16). xxiv 2.5. Selection of maximum gradient amplitudes

One of the parameters that is used in the development of gradient waveforms is the maximum gradient amplitude. The choice of gradient amplitude affects a number of parameters, especially the sampling density. Using lower gradient strength yields fewer sample data points. It also results in the k-trajectory crossing the origin less frequently.

The effect of number of data points is also visible in solving the inverse problem used to generate the parameter maps. A higher number of data points makes it feasible for the PLCG algorithm to search for solutions on longer data lengths. This enables the algorithm to converge more accurately on the x, y spatial grid. One would come to a logical conclusion that using larger gradient strength waveforms for data acquisition would result in parameter maps that are more accurate than the ones obtained by using lower gradient strength waveforms. However, using higher gradient strengths can only improve the results to a certain point after which the performance begins to deteriorate.

The bandwidth (BW) of a system is a measure of the range between the highest and lowest frequency of the signal that could be acquired. For analog signals, BW is the frequency range in which the signal's Fourier transform is nonzero (17). The receiver BW is the range of frequencies accepted by the receiver to sample the acquisition data. It depends upon the strength of gradients that are being used and the sampling rate of the system.

BW  SamplingRate (13)

xxv Since Nsamples is directly proportional to gradient strength, we can see that higher gradient strengths result in wider receiver BW. Signal is proportional to the number of samples acquired during the fixed time of acquisition, i.e., signal is proportional to bandwidth, while the standard deviation of the noise is proportional to the square root of the bandwidth. Thus the SNR of the system is proportional to the square root of the bandwidth:

SNR  BW (14)

From equations 9, 13 and 14 we can see that if the gradient amplitude is at its maximum throughout the signal readout, the SNR of the system is proportional to the square root of the gradient strength being used.

SNR  Gmax (15)

We are now faced with a choice between better parameter estimation by selecting larger gradient strengths which will give us longer data lengths, and having to deal with noise as a result of higher gradient amplitudes. The analytical solution of an optimal range is difficult to obtain since it would require finding solution to a large non-linear problem. This problem can be addressed empirically by evaluating the performance over a range of gradient amplitudes in order to determine the range over which we can have good spatial resolution and parameter estimation as well as have a good ability to handle noise.

xxvi 2.6. Comparison between the single shot methods

Activation maps in fMRI studies rely upon accuracy and stability of R2*. In order to be proven useful, a single shot method must be capable of producing consistent and accurate R2* maps.

In SS-PARSE we need to investigate the accuracy and consistency over a wide range of gradient strength in order to determine which one would give the best trade-off between SNR and data length.

The performance of the single shot methods, MEPI and SS-PARSE, is done by using GEMS as the gold standard. GEMS is a multiple shot method. This allows us to use a small acquisition BW thus giving us high SNR. The ability to obtain images with high

SNR with closely stacked TE values in GEMS, justifies its use as the gold standard.

Taking GEMS as a reference, we investigate the temporal standard deviation

TSD) of R2* in MEPI and SS-PARSE over a set of acquisitions. We also look at the accuracy of these R2* maps by comparing them with GEMS. In order to be useful for fMRI studies, these methods must demonstrate their usability over the range of typical R2* values found in human brain tissues. Thus we need to examine the performance of these two methods over a range of R2* values that can be typically found in human brain.

Achieving best possible shims is not possible in every human fMRI experiment because of time constraints, and even then, the best possible shimming job typically leaves significant field inhomogeneities within the imaged region, simply because of the complex patterns of susceptibility gradients within the tissues. This means that there is

xxvii bound to be some level of frequency off-resonance in every fMRI study. Sometimes the off-resonance can be large enough to cause serious deterioration in acquired data. This makes it necessary to determine how the chosen single shot methods fare under severe of- f-resonance conditions.

xxviii 3. METHODS

The comparison study was performed on phantoms using MEPI and SS-PARSE, using GEMS as the gold standard. Gradient waveforms were generated to obtain rosette trajectories which were then used for SS-PARSE trajectory calibration and data acquisition. Experimental phantoms were constructed to give R2* ranges that would be comparable to those found in brain tissue. Data was collected using GEMS, MEPI and SS-

PARSE sequences on a Varian 4.7 T vertical bore scanner. Data analysis was performed remotely on a cluster that utilized 16 AMD64-K8 processors with 64 GB of RAM (@Xi

Computer Corp.). SS-PARSE reconstruction made use of the PLCG algorithm to estimate the parameter maps. Temporal standard deviation of the relaxation rates, R2*, of SS-

PARSE and MEPI were compared on basis of converged pixels. The accuracy of R2* estimation on a pixel by pixel basis and over a region of interest was also performed. Be- havior of the single shot methods was observed under severe off-resonance condition to test their robustness. SS-PARSE was analyzed over a wide range of gradient amplitudes to find an optimal operating range that yielded the best trade-off between SNR and parameter estimation.

xxix 3.1. Gradient waveform generation for SS-PARSE

The k-trajectories for SS-PARSE (see equation 12) were computed within a k-s- pace radius of kf=2.82 cm. A k-disc with a 2.82 cm radius has the same area as a square 5 cm-1 x 5 cm-1 Cartesian grid, with spatial resolution closely comparable to 64x64 single-shot EPI for the same 12.8 cm FOV. Using kf=2.82 cm, FOV=12.8 cm, and resolution of 64x64, gradient waveforms were generated using equation 12.

Figure 4. 10 ms section of a gradient waveform for 2.9 G/cm

The gradient strength used in the case of MEPI is 2.29 G/cm. We investigated the k-trajectories for SS-PARSE with gradient amplitudes that were lower as well as higher than the MEPI gradient amplitude. To do so, we generated gradient tables for seven different amplitudes; 1.9 G/cm, 2.29 G/cm, 2.5 G/cm, 2.9 G/cm, 3.2 G/cm, 3.5 G/cm and

3.8 G/cm. These gradient tables were scaled to ±32767 to correspond to the dynamic xxx range of the digital to analog converter amplifier of the Varian 4.7 T system. The gradient waveforms must start and end at zero amplitude, making it necessary to add a ramp-up section at the beginning of the gradient waveform which starts at zero and smoothly transitions to starting values of the two orthogonal readout gradients. Similarly we need to add a ramp-down section at the end of the gradient waveform which smoothly transitions from the end of the waveform to zero.

The gradient waveforms are designed for an acquisition period of 69 ms, which includes 65 ms of the actual gradient waveform with 2 ms each of ramp-up and ramp- down intervals.

3.2. Phantoms

3.2.1. Calibration phantom

The phantom used for calibration experiments is a plastic sphere with an internal volume of 25 cc. Selecting a phantom of appropriate dimensions is crucial for calibration.

The phantom should be large enough to give a good, noise free signal, while at the same time it should be small enough to avoid excessive through-slice dephasing of the signal.

The calibration phantom is filled with water. Every precaution was taken to en- sure that there are no air bubbles trapped within the sphere. The presence of air bubbles leads to severe signal decay due to susceptibility induced intra-voxel dephasing (18). Cal- ibration over a phantom which has susceptibility related artifacts results in poor SNR in the calibration data. It also leads to incorrect computation of k-trajectory and local phase changes over time.

xxxi 3.2.2. Fourtube phantom

Figure 5. Fourtube phantom

Glass vials (5 cm long, 2.1 cm internal diameter) were filled with 1.5% agar gel and doped with copper sulphate (10 mg/100 ml to 60 mg/100 ml) and Sephadex G-25 beads to give R2* relaxation rates in between 15 sec-1 and 45 sec-1 (19). The glass vials were suspended in a glass jar filled with water so as to minimize the susceptibility artifacts. The jar has 4 vials suspended in it. The range of R2* relaxation rates is chosen based upon the R2* values in gray and white matter observed in the human brain at 4.7T

The lid on top of the jar has holes drilled in four quadrants. Each hole has the same diameter as the vials. This makes it possible to switch the vials with difference relaxation rates for different studies.

xxxii 3.3. Calibration

The behavior of gradient waveforms during acquisition is dependent upon the system parameters during the time of acquisition. If hardware settings remain the same, the gradient waveform continues to behave the same way on a particular system. Since actual k-sampling locations depart from nominal values in system-specific fashion, the effective k, t locations of the signal samples were determined experimentally by the method of

Zhang et al. (16). Along with the values of kx and ky at each time, this procedure also determines the phase, Φ(t), a time-varying spatially constant field offset attributable largely to eddy currents.

Figure 6. Calibrated k-trajectories for four different gradient amplitudes.

xxxiii All the gradient waveforms are calibrated to get the rosette trajectories and their corresponding time varying phase information. Figure 6 shows the difference in sampling density for at different gradient amplitudes when sampling over the same area.

Figure 7. Coverage of 3.8 G/cm gradient amplitude k-trajectory over time.

Once we have the calibrated k-trajectories and the phase information, we used these trajectories to acquire experimental data. These trajectories and phases can be assumed to be stable as long as no changes are made to the system hardware.

3.4. Phantom data acquisition

Experimental data was collected on a 4.7 T 60 cm-vertical-bore Varian primate

MRI system (Varian Inc., Palo Alto, CA) using a stripline resonator quadrature head coil

(Insight Neuroimaging, Worcester, MA).

xxxiv Several sets of phantom data are collected using three different pulse sequences.

The GEMS acquisitions consisted of a series of images 128x128 voxels, 12.8 cm FOV,

3mm thickness, repetition time (TR) 200 ms, and 16 echo times (TE): 5, 8, 10, 12, 15, 20,

25, 30, 35, 40, 45, 50, 55, 60, 65, 70 ms. MEPI acquisitions were acquired at 4 different

TE; 22.3 ms, 66.8 ms, 96.4 ms and 124.2 ms, following a single RF pulse. They had 50 repetitions of 64x64 voxel images, 12.8 cm FOV, 3mm slice thickness, and TR of 5 sec.

SS-PARSE acquisitions consisted of 50 repetitions, 12.8 cm FOV, 3 mm slice thickness,

TR of 5 sec, and pulse sequences with maximum gradient amplitude of 1.9 G/cm,

2.29G/cm, 2.5 G/cm, 2.9 G/cm, 3.2 G/cm, 3.5 G/cm and 3.8 G/cm.

3.5. Data Analysis

Data analysis was performed in Matlab (Version 7.5, The Mathworks Inc., Natick,

MA). SS-PARSE parameter maps were estimated using the PLCG algorithm. Some of the parameters that had to be specified were:

1. Start (startx) and end (endx) points of the trajectory: These points are chosen by

observing the k-trajectory and noting the positions of the first and last echoes.

2. Swoop length (N1): The number of samples between two consecutive echoes is

the swoop length of that particular trajectory.

3. Data lengths (NLIST): Data lengths are integral multiples of swoops that are pro-

gressively incremented while running the PLCG. The data lengths have to be set

empirically for data sets at different gradient amplitudes.

xxxv 4. Tolerances (FLIST): Each data length has to be associated with a tolerance level.

The tolerance levels set a limit on the minimum accuracy of estimation required

for a particular length of data before the length is incremented. The choice of

these parameters is subject to the gradient amplitude being currently used. Toler-

ance values have to be set empirically.

5. Initial frequency estimate (offr): PLCG is capable of estimating frequencies over

a wide range. However in practical settings there can be a huge frequency drifts

across the slice arising due to number of reasons. For this reason it is necessary to

specify an initial frequency which might help in convergence at more points in the

x, y grid. Even this initial frequency estimate has to be determined empirically.

6. Scaling (ffac): In order to obtain correctly determine the values of M0, R2* and f,

it is sometimes necessary to scale the FID signal by a factor. For a given object

size in a FOV, the scaling factor usually remains the same.

3.6. Development of graphical user interface (GUI)

There are several parameters that need to be specified for each data set. In many cases the set of parameters required for running the PLCG are unique for that set. Storing the variables for PLCG as well as the resulting parameter maps can lead to numerous book keeping errors if not handled correctly.

Under such circumstances, it is much more convenient to automate the process of passing the PLCG parameters to the programs through an intuitive interface. If the process of passing the PLCG parameters, file handling and display of parameter maps is xxxvi implemented on a single interface, it makes the entire process far more efficient than if done manually.

With this in mind, a GUI was developed which reads in parameters such as N1, startx, endx, offr, etc. that are required to run the PLCG algorithm. It also reads in the data sets, and provides an option of saving the parameters in case we need to reproduce the results. Estimated parameter maps are displayed in real time while the PLCG is running. If the maps show no sign of converging, we can repeat the process all over again without having to make changes in the actual programs. Thus we can see that the GUI serves as a beneficial tool in this project.

xxxvii Figure 8. GUI for SS-PARSE

xxxviii 3.7. Parameter evaluation

3.7.1. R2* calculation in GEMS

Figure 9. GEMS images at 16 different TEs.

xxxix GEMS images are obtained at 16 different TEs. Figure 9 shows the GEMS images obtained from a fourtube phantom at echo times between 5ms and 70ms. The R2* values that need to be computed lie in the region within the glass vials. In order to compute the

R2* values, we select the ROI as shown in by the green circles in Figure 9. The signal within this ROI is monoexponentially fitted using Equation 2, with TEs used as t. By applying a non-linear fit to the signal intensities corresponding to their TEs, we obtain the

R2* maps over those FOVs.

This gives us a pixel-by-pixel map of R2*. By averaging over all the pixels within the ROI, we get average R2* over the entire region. These R2* values are used as the gold standard in comparison of single shot methods.

3.7.2. R2* calculation in MEPI

Figure 10. MEPI images at four TEs.

Using the single shot MEPI sequence to obtain R2* weighted images provides much less flexibility than in GEMS. In MEPI, we don’t have fine control over TEs like we had for GEMS. Images can only be acquired at discrete times, which are odd multiples of the first TE (see Figure 11). In order to obtain four echoes in MEPI, we have to

xl acquire the signal over a period of 150 ms. If the system is properly shimmed and if the

R2* values aren’t too high, we can get reasonably good data until the fourth echo. How- ever if the system is poorly shimmed or if the phantom has large R2* values, the signal acquired at last TE decays to amplitudes that are comparable to the amplitude of system noise. Typical SNR values observed at the four echoes for R2* of 42 sec-1 were 39 dB,

32 dB, 28 dB and 25 dB under good shimming conditions.

Figure 11. MEPI signal sampling at specific echo times.

The method for computing R2* in MEPI is the same as the one that has been described for GEMS. The difference here is that the R2* is computed for each of the repetitions over the series of 50 repetitions. We proceed to find the average R2* over the ROI over the entire series as well as the pixel-by-pixel map of R2* averaged over the time series, but not over the ROI. Finally we find the TSD of R2* on a pixel-by-pixel basis over the ROI.

xli 3.7.3. Analysis of SS-PARSE parameter maps

Figure 12. R2* estimated from SS-PARSE (Gmax=2.9 G/cm) over 50 repetitions

Parameter estimation in SS-PARSE is accomplished using the PLCG algorithm.

The parameters estimated from the SS-PARSE experimental data are M0, R2* and f. Just like MEPI, the estimation process has to be carried out over all the 50 repetitions. Once we have the parameter maps, we need to compute separate out the R2* values over the

ROI over 50 repetitions. This process was carried out for data sets from all seven gradient amplitudes.

xlii 3.8. Comparison

3.8.1. Comparison of R2* estimates

Once we have the pixel-by-pixel and averaged R2* maps over the ROI, we compare the accuracy of R2* obtained from MEPI and SS-PARSE using the R2* values from

GEMS as the reference. By arranging the R2* estimates in ascending order of GEMS

R2* estimates, we are able to compare the relative differences between the two single shot methods as well as their accuracy in absolute terms.

Images are reconstructed from the experimental data sets. All the images are scaled to 64x64 pixel resolution in order to facilitate an one on one comparison. We selected a ROI with a 5 pixel radius that lay completely within the area covered by the tubes. This gave us 80 pixels for each ROI. Pixel-by-pixel R2* calculations are performed for SS-PARSE, GEMS and MEPI. From the 18 studies we had a total of 72 different values for R2*. Among these we selected 20 ROIs which had R2* values in the range of 15 sec-1 to 45 sec-1.

The performance of SS-PARSE at different gradient strengths was compared with

MEPI using F-test for each pixel contained within the ROIs. This statistical method can help us in determining if the distributions in SS-PARSE and MEPI have equal variances

(20). The null hypothesis for the F-test was that there was no difference in the variances of R2* distributions obtained using the two methods at a 95% confidence interval.

xliii The rejection of null hypothesis at a given pixel indicates that SS-PARSE estima- tions at that pixel location are better compared to that obtained using MEPI. This test was repeated for all the gradient strengths used in the study.

Next, in order to compare the accuracy of the two single shot methods, we compared R2* values for each pixel from MEPI and SS-PARSE with that in GEMS. To test for accuracy we used the ratio:

* * | R2 MEPI  R2GEMS | * * (16) | R2 SSPARSE  R2GEMS |

This ratio was computed for each pixel in the selected ROIs. A ratio of more than

1 implies that estimation of R2* by SS-PARSE at that pixel was more accurate compared to the estimation of R2* done using MEPI. The percentage of pixels for which this ratio was more than one was calculated for the each of the gradient amplitudes used in SS-

PARSE acquisitions.

3.8.2. Comparison between the TSDs of single shot methods

The TSDs computed from the R2* maps in SS-PARSE and MEPI are used for comparing the temporal behavior of these two methods. We compare the temporal performance of SS-PARSE and MEPI on a pixel-by-pixel basis, using the pixel values of

GEMS R2* as a reference. The TSDs from the two single shot methods are compared on an ascending R2* scale from GEMS.

To compare the temporal performance, we computed the temporal standard deviation of estimated R2* values from MEPI and SS-PARSE at the chosen gradient ampli-

xliv tude. This was done by computing the standard deviation of each pixel within the ROIs along the time axis, i.e. standard deviation of pixels within the ROI was computed over

50 acquisitions in the time series. Standard deviation is a measure of variability of the data set [ref]. The standard deviation of R2* indicates how much the relaxation rates vary over time. Since it’s a phantom experiment, we would ideally expect to see R2* remain constant across all acquisitions. However this isn’t the case and we do observe some variation in R2* over the course of acquisitions. A higher value of TSD would indicate more variations in R2* and a lower TSD would indicate higher stability.

To compare the two methods, we subtract the TSD of SS-PARSE from TSD of

MEPI and plot it against the GEMS R2* value at that pixel (see Figure 21).

3.8.3. Comparing performance at off-resonance

One set of data was acquired under severe off-resonance by intentionally deshimming the shim coils. This caused the field B0 to be inhomogeneous over the entire imaging volume. The parameter estimation of data sets acquired with SS-PARSE was performed for all the gradient amplitudes. The purpose of this exercise was to see if there is any geometric distortion caused due to field inhomogeneities.

The data acquired under severe off-resonance conditions is observed for its ability to reconstruct M0 maps. Parameter analysis for these maps is not possible owing to the severe geometric distortion that’s prevalent in the Cartesian methods under off-resonance.

xlv 4. RESULTS AND DISCUSSION

4.1. Comparing the accuracy of R2* estimation

From a total of 1600 pixels, the number of pixels at which the null hypothesis was rejected was 241, 307, 468, 547, 485, 338 and 214 for gradient strengths of 1.9 G/cm,

2.29 G/cm, 2.5 G/cm, 2.9 G/cm, 3.2 G/cm, 3.5 G/cm and 3.8 G/cm respectively.

The rejection of null hypothesis was observed to be the highest in the SS-PARSE acquisition when the acquisitions were done at 2.9 G/cm.

In the comparison of error ratios, the percentage of pixels with a ratio greater than

1 were 61.3%, 64.2%, 66.4%, 67.6%, 65.6% and 61.2% for gradient amplitude strengths of 1.9 G/cm, 2.29 G/cm, 2.5 G/cm, 2.9 G/cm, 3.2 G/cm, 3.5 G/cm and 3.8 G/cm respectively. Based on these percentages we determined that R2* estimation using SS-PARSE was most accurate in comparison to MEPI when the gradient strength used during acquisition was 2.9 G/cm.

From the test for variances and test for accuracy compared to the gold standard, we determined that the R2* estimation by SS-PARSE acquired with a gradient amplitude of 2.9 G/cm had a much better performance as compared to MEPI than the rest of the gradient strengths used.

xlvi Figure 13. SS-PARSE parameter maps at different gradient amplitudes.

Figure 14. R2* distribution of MEPI and SS-PARSE at Gmax=1.9 G/cm and the distribution of accuracy ratios.

xlvii Figure 15. R2* distribution of MEPI and SS-PARSE at Gmax=2.29 G/cm and the distribution of accuracy ratios.

xlviii Figure 17. R2* distribution of MEPI and SS-PARSE at Gmax=2.9 G/cm and the distribution of accuracy ratios.

xlix Figure 19. R2* distribution of MEPI and SS-PARSE at Gmax=3.5 G/cm and the distribution of accuracy ratios.

l From Figures 14-20, it can be seen that estimation accuracy increases as we go from 1.9 G/cm to 2.9 G/cm. It may be due to denser sampling which takes place at higher gradient amplitudes, leading to more accurate parameter estimates. With increasing gradient amplitudes, we also increase the system noise; however the higher number of sampled points at higher gradient amplitudes may offset the effect due to noise.

As gradient amplitude increases beyond 2.9 G/cm, noise begins to overshadow the improvements brought about by increased number of sampled data points. From that point onwards, the performance of SS-PARSE begins to deteriorate. At 3.8 G/cm the accuracy of R2* estimates from SS-PARSE are only marginally better than those calculated from MEPI acquisitions.

The parameter estimates from data sets that are acquired using gradient waveforms at 2.9 G/cm are more accurate than those acquired with the other gradient amplitudes.

4.2. Comparison of TSD

For the pixels where the difference is positive, SS-PARSE performed better than

MEPI, whereas at pixels with negative value of MEPI performed better. From Figure

21(d) we notice that the difference between TSDs is greater than zero for majority of the pixels at low R2* values. The percentage of pixels with a difference greater than zero was

79.3%, 82.9%, 83.4%, 85.2%, 86.1%, 87.4%, 88.3%, 89.4%, 90.8%, 91.5%, 92.7%,

93.1%, 93.5%, 94.2%, 94.8%, 95.6%, 96.0%, 96.3%, 96.9% and 97.3% for average

li GEMS R2* values ranging between 15 sec-1 to 45 sec-1. We notice that the performance of SS-PARSE compared to MEPI improves with increasing values of R2* over the range that we observed.

lii Figure 21. TSD plots of SS-PARSE (at Gmax = 2.9G/cm) and MEPI (a) R2* GEMS vs. TSDSS-PARSE. (b) R2* GEMS vs. TSDMEPI (c) R2* GEMS vs. TSDSS-PARSE shown by blue dots and R2* GEMS vs. TSDMEPI shown by red dots. (d) TSDMEPI – TSDSS-PARSE vs. R2* GEMS.

4.3. Performance under off-resonance

The data set acquired under severe off-resonance by intentionally deshimming the shim coils showed a rapid decay in the signal as compared to the sets that were obtained using well shimmed coils. The images from GEMS acquisition did not show geometric distortion but instead, showed significant amount of ghosting even at lower echo times.

liii Figure 22. SS-PARSE parameter maps in presence of field inhomogeneities.

Parameter maps were computed with some adjustments in variables used in the

PLCG algorithm. We noticed that there was no geometric distortion in the parameter maps for any of the gradient amplitudes used for acquisition (see Figure 22).

On the other hand, we notice a significant amount of distortion in the MEPI echo series (see Figure 23). This is because standard Fourier reconstruction for the MEPI sequence does not keep track of frequency changes over the k-space. Off-resonance and the resulting field inhomogeneities lead to geometric distortion and significant reduction in signal at higher echo times. It becomes impossible to compute the relaxation rate in presence of geometric distortion and loss of signal strength at the third and fourth echo times.

Figure 23. MEPI images at 4 echo times in presence of field inhomogeneities.

liv Figure 24. Reconstructed image from GEMS, SS-PARSE (Gmax=2.9 G/cm) and MEPI in presence of field inhomogeneities.

In order to demonstrate the performance under off-resonance conditions, we compared the images from GEMS, SS-PARSE and the first echo of MEPI. By drawing a ROI over one of the tubes on images reconstructed from all three modalities, we notice that there is an one to one correspondence between the GEMS and SS-PARSE images. The

ROI in the image from the first echo time in MEPI fails to match the ROI in GEMS. This shows that it is almost impossible to use MEPI in the presence of field inhomogeneities, but SS-PARSE can still be used to obtain the parameter maps.

4.4. Discussion

R2* is an important parameter to consider when we are conducting experiments that make use of the BOLD effect, thus making it an important parameter in fMRI studies. Accuracy and temporal reliability of R2* play a big role in fMRI experiments.

Through carefully designed experiments, we conducted comparison studies of two single- shot pulse sequences to evaluate their feasibility in fMRI studies. One of these methods,

lv MEPI computes the R2* values using signal changes at different echo times. The other method, SS-PARSE estimates the parameters by solving an inverse problem.

Parameter estimation in SS-PARSE is done using the PLCG algorithm. PLCG requires the selection of an optimum set of parameters in order to minimize the least squared residuals and generate M0, R2* and frequency maps. These parameters have to be determined empirically for each set of experiments that we conduct. However once we arrive at these parameters, PLCG can estimate the parameter maps for the entire time series.

Comparing the experimental results of MEPI and SS-PARSE provides us a lot of information. It is noticed that accuracy and TSD of MEPI is quite good at lower values of

R2* and its results are comparable to those obtained with SS-PARSE. As R2* increases we begin to see a gradual decline in the performance of MEPI. This can be attributed to declining signal strength from the third and fourth echoes in regions with high R2* values. Such conditions make the calculation of R2* somewhat unreliable when R2* is higher. But high R2* values are unavoidable in fMRI studies. Consequences of using MEPI to generate activation maps in brain regions with high R2* can result in erroneous maps.

Data acquisition for SS-PARSE involves acquiring data over a range of gradient strengths. Lower gradient amplitudes have fewer samples and lower noise levels. This results in parameter maps with a lower spatial resolution with some smoothing observed along the boundaries with different R2* values. This would make it somewhat difficult to distinguish between the brain regions. The accuracy of parameter estimation is also lower at lower gradient amplitudes because of fewer samples.

lvi With an increase in gradient amplitudes there is an improvement in the spatial resolution and parameter accuracies. However this improvement in resolution and accuracy with increasing gradient amplitudes continues only up to a certain point. At higher gradient amplitudes the acquisition BW also becomes higher, causing more noise to be added into the system. Due to higher number of acquired samples, SS-PARSE is able to handle this increased noise and give an improvement in R2* maps until the gradient amplitude reaches 2.9 G/cm. Beyond 2.9 G/cm noise begins to put a limitation on the level of accuracy and reliability we can expect from SS-PARSE.

From the parameter maps generated using the experimental data we noticed that as we progressed from gradient amplitude of 2.5G/cm to 3.2G/cm, there was a performance peak at 2.9 G/cm. While the performance of SS-PARSE in comparison to MEPI was best at 2.9 G/cm it is not the best achievable performance that one would observe on a 4.7 T MRI system. In practice, we expect the optimal performance at a gradient amplitude that is somewhere between 2.5 G/cm and 3.2 G/cm.

Among the parameters that are encoded into the signal, one is local frequency. By keeping track of local frequencies, SS-PARSE can create reliable parameter maps even when the scanner is poorly shimmed during a particular study. This ability is absent in the conventional fMRI sequences which make use of the Fourier transform alone for signal encoding and reconstruction. Thus, when we have a poorly shimmed system, the data acquired using Cartesian methods becomes quite unusable. However under the same conditions, SS-PARSE would yield results that are completely usable in the generation of activation maps. However there is a theoretical limit to which SS-PARSE can track changes

lvii in frequency, and it is the sampling frequency observed at k=0 in a rosette trajectory which is typically a few kilohertz. In practical setup, this limit can be much lower because of poor conditioning of the inverse problem.

PLCG is an iterative algorithm which can takes somewhere between 3 to 4 minutes to converge for moderate lengths of data (10000 to 15000 sample points). However convergence times are subject to the choice of stopping tolerances used in the algorithm.

Using very tight tolerances would require tens of minutes for the algorithm to converge with a very little improvement in the accuracy of the maps. However convergence times for tight stopping tolerances can be lowered by using faster processors and by paralleliz- ing the PLCG algorithm.

SS-PARSE is quite dependent on the stability of the scanning hardware. It is necessary to determine the behavior of the k-trajectory and the local phase information over time in the actual system. This is done by the process of calibration. Once we obtain this information, we continue to get repeatable performance using the calibrated parameters in the PLCG algorithm as long as the hardware settings remain unchanged. If there is a change in gradient hardware settings, such as change in the RF amplifiers, the gradient amplifiers or analog-to-digital converter cards or digital-to-analog converter cards, the old calibration information can no longer yield reliable results. Any change in gradient hardware settings necessitates recalibration to determine the path of k-trajectory and the phase information.

lviii 5. CONCLUSIONS

Two single shot methods, MEPI and SS-PARSE were tested for R2* estimation accuracy and temporal reliability, using a multiple shot method, GEMS, as the gold standard. Gradient waveforms at seven gradient amplitudes were developed to test the performance of SS-PARSE. Data acquisition was done using a fourtube phantom containing aqueous mixtures with R2* ranges typically observed in brain tissues at 4.7T.

M0, R2* and frequency maps were estimated using the PLCG algorithm. The comparison of accuracy of R2* estimation in SS-PARSE and MEPI was conducted using

R2* from GEMS as the gold standard. The R2* accuracy in MEPI was comparable with

SS-PARSE at lower values of R2*, however at higher values of R2*, SS-PARSE was significantly more accurate than MEPI. Accuracy of R2* estimation in SS-PARSE was tested using seven different gradient amplitudes ranging between 1.9 G/cm to 3.8 G/cm. As gradient amplitudes went higher the performance of parameter estimates improved until it reached 2.9 G/cm. As the gradient strength increases beyond 2.9 G/cm the performance gradually deteriorates.

SS-PARSE is capable of estimating R2* more reliably than MEPI over a number of repetitions. When used in fMRI studies, SS-PARSE would estimate the R2* values

lix more accurately and reliably during the control and stimulus cycles, thus giving activation maps that are more accurate than those obtained using MEPI.

fMRI studies performed with poor shimming can introduce geometric distortions in MEPI acquisitions. This can render the study completely useless. However, since SS-

PARSE keeps track of change in local frequencies over time, it is capable of estimating parameter maps even in the presence of severe off-resonance frequencies.

SS-PARSE makes use of PLCG algorithm for parameter estimation. Convergence of PLCG algorithm requires the adjustment of several variables that are determined heuristically. Over time, as more knowledge is gained about the estimation process, it may be possible to set these variables in a deterministic manner. Doing so would enable its integration into the system software enabling its use in clinical systems.

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