Measuring Perfusion with Magnetic Resonance Imaging Using Novel Data Acquisition and Reconstruction Strategies

MEASURING PERFUSION WITH MAGNETIC RESONANCE IMAGING USING NOVEL DATA ACQUISITION AND RECONSTRUCTION STRATEGIES

Katherine L. Wright

Submitted in partial fulfillment of the requirements

For the degree of Doctor of Philosophy

Dissertation Adviser: Dr. Vikas Gulani

Department of Biomedical Engineering

CASE WESTERN RESERVE UNIVERSITY

January 2015

CASE WESTERN RESERVE UNIVERSITY

SCHOOL OF GRADUATE STUDIES

We hereby approve the thesis/dissertation of

Katherine L. Wright

candidate for the degree of Doctor of Philosophy*.

Committee Chair

Vikas Gulani

Committee Member

Mark A. Griswold

Committee Member

David Wilson

Committee Member

Anant Madabhushi

Committee Member

Michael A. Martens

Date of Defense

October 3, 2014

*We also certify that written approval has been obtained

for any proprietary material contained therein.

Table of Contents

Table of Contents ...... 3 Dedication ...... 6 Acknowledgements ...... 7 List of Tables ...... 9 List of Figures ...... 10 List of Abbreviations ...... 12 Abstract ...... 15 Chapter 1. Introduction ...... 16 Section 1.1. Measuring Perfusion with MRI: Clinical Motivation ...... 17 Section 1.2. Overview of Thesis ...... 18 Chapter 2. MRI Background ...... 20 Chapter 3. Measuring Perfusion with MRI ...... 27 Section 3.1. Dynamic Contrast Enhanced MRI ...... 28 Section 3.1.1. DCE MRI Introduction ...... 28 Section 3.1.2. Data Acquisition ...... 30 Section 3.1.3. Perfusion Quantification ...... 32 Section 3.1.4. Advantages/Disadvantages of DCE MRI...... 36 Section 3.2. Arterial Spin Labeling ...... 37 Section 3.2.1. ASL Introduction ...... 37 Section 3.2.2. CASL/pCASL Methods ...... 39 Section 3.2.3. PASL Methods ...... 43 Section 3.2.4. Data Acquisition Strategies ...... 44 Section 3.2.5. Perfusion Quantification ...... 45 Section 3.2.6. Advantages/Disadvantages of ASL...... 48 Chapter 4. Highly Accelerated Data Acquisition and Reconstructions ...... 50 Section 4.1. Partial Fourier Acquisition and Reconstruction ...... 51 Section 4.2. Partial k-space Acquisitions and View-Sharing Reconstructions ...... 54 Section 4.3. Parallel Imaging ...... 60 Section 4.3.1. Parallel Imaging Introduction ...... 60

Section 4.3.2. Sensitivity Encoding (SENSE) ...... 61 Section 4.3.3. Generalized Autocalibrating Partially Parallel Acquisition (GRAPPA) ...... 64 Section 4.4. Non-Cartesian Trajectories ...... 68 Section 4.5. Non-Cartesian Parallel Imaging ...... 70 Section 4.5.1. Non-Cartesian Parallel Imaging Introduction ...... 70 Section 4.5.2. Conjugate Gradient SENSE (CG SENSE) ...... 72 Section 4.5.3. Non-Cartesian GRAPPA ...... 76 Chapter 5. Simultaneous MR Angiography Exam and Perfusion Measurement ...... 80 Section 5.1. MRAP Introduction ...... 80 Section 5.2. TWIST Data Acquisition and Reconstruction ...... 81 Section 5.2.1. Methods ...... 82 Section 5.2.2. Results ...... 83 Section 5.2.2. Discussion ...... 86 Section 5.3. Application for MRAP in Skeletal Muscle ...... 88 Section 5.3.1 Methods ...... 88 Section 5.3.2. Results ...... 93 Section 5.3.3. Discussion ...... 97 Chapter 6. Free-breathing, High Spatiotemporal Resolution Renal Perfusion Measurements .... 103 Section 6.1. Renal Perfusion Measurement Introduction ...... 103 Section 6.2. 3D Through-time Radial GRAPPA ...... 104 Section 6.2.1. Introduction ...... 104 Section 6.2.2. Theory ...... 106 Section 6.2.3. Methods ...... 108 Section 6.2.3. Results ...... 114 Section 6.2.4. Discussion ...... 122 Section 6.3. Free-breathing, High Spatiotemporal Resolution Renal Perfusion Imaging ...... 127 Section 6.3.1. Introduction ...... 127 Section 6.3.2. Methods ...... 127 Section 6.3.3. Results ...... 133 Section 6.3.4. Discussion ...... 141 Chapter 7. Magnetic Resonance Fingerprinting and Arterial Spin Labeling ...... 146 Section 7.1. MRF Introduction ...... 146

Section 7.2. MRF ASL...... 149 Section 7.2.1. Introduction ...... 149 Section 7.2.2. Theory ...... 151 Section 7.2.3. Methods ...... 154 Section 7.2.4. Results ...... 157 Section 7.2.5. Discussion ...... 162 Chapter 8. Conclusions ...... 165 Section 8.1. Summary ...... 165 Section 8.2. Future Directions ...... 166 Section 8.2.1. MRAP ...... 166 Section 8.2.2. Renal Perfusion and Filtration Quantification using 3D Through-time Radial GRAPPA ...... 167 Section 8.2.3. MRF ASL ...... 168 Section 8.3. Conclusions ...... 169 Bibliography ...... 171

To Joshua

Acknowledgements There are so many wonderful people that I have had the pleasure to work with throughout

my time at Case, and there are also countless people who have helped and supported me.

Because it seems impossible to thank all of these people individually, I want to begin by

saying how grateful I have been to be surrounded by such great people for the last six

years.

First and foremost, I feel so fortunate to have worked with Dr. Vikas Gulani as my

research advisor. He truly combines cutting-edge research and clinical innovation, and has been a great source of ideas and guidance. In addition to his scientific insight, he also has provided constant mentoring with a focus on career development, and has always encouraged me to be looking at what I want to do in the future. In addition to being a great research mentor, he is a wonderful person, who has been incredibly helpful and supportive throughout this entire process.

I would also like to thank Dr. Nicole Seiberlich and Dr. Mark Griswold for their mentoring and support. Dr. Seiberlich and I worked on several projects together, and she has been an incredible role model for me. She is a great teacher and mentor, and her advice and support has helped me survive the difficult parts of graduate school. Dr.

Griswold has also worked with me on many projects, and his insight on research is always inspirational. I am very grateful to have had him as a teacher and advisor.

I greatly appreciate the advice and feedback from my committee members: Dr. Vikas

Gulani, Dr. Mark Griswold, Dr. David Wilson, Dr. Anant Madabhushi, and Dr. Michael

Martens. Each committee meeting has provided insightful discussion and has been vital to my development and my research.

The MRI research group in the Case Center for Imaging Research has really wonderful facilities and resources, which enabled the work shown in this thesis. I want to thank the

CCIR faculty and staff (especially, Carol Rice, Barbara Richards, Cena Myers Hilliard).

Additionally, I want to thank all of the MRI staff and technologists at University

Hospitals including Katrina Howard, Maureen Kmetko, Annmarie Graven, Anne Barto, and Mark Clampitt for their endless patience and help performing all of the contrast exams.

Thank you to all of the past and present post-docs and graduate students in the MRI research group. The lab has been a wonderful place to work and learn over the past six years, and I have made so many lifelong friendships. There are far too many people to list here, but thank you so much for your help with research, advice, and moral support! You made it so enjoyable to come to lab every day!

I also want to thank all of my friends and family for being a great support system always.

I specifically want to thank my parents for all of their love and always supporting my education/career. Thank you to my entire family for all of your love! Thank you to

Alyssa, who helped me survive graduate school and is an amazing friend. Thank you to

Natalia, who was an amazing lab sister (and late night work buddy… and for all of those merienda breaks).

Finally, I want to say thank you to my best friend, biggest fan, and husband, Joshua.

Thank you for always being there to cheer me on in the happy moments and to cheer me up in the sad moments. Your love, support, and encouragement mean the world to me.

List of Tables

Table # Table Title Page # 5.1 Summary of results of radiologists' assessments of the MRA 93 MIPs. 5.2 Ktrans (min-1) and calculated perfusion (ml/100g/min) values for 95 resting and exercised muscles. 6.1 Parameters for in vivo experiments performed in Chapter 6. 113 6.2 Summary of renal perfusion and filtration parameters. 138

List of Figures

Figure # Figure Title Page # 2.1 Sampling MRI data in k-space. 24 2.2 GRE pulse sequence diagram and Cartesian k-space sampling. 26 3.1 Tracer pharmacokinetics in MRI. 27 3.2 Signal intensity changes during a DCE MRI experiment. 30 3.3 Pharmacokinetic modeling of a Gd-based tracer. 34 3.4 ASL pulse sequence diagrams. 39 3.5 ASL labeling techniques. 39 3.6 Pseudo-continuous ASL labeling pulse sequence diagram. 40 3.7 General kinetic model for ASL. 46 4.1 Diagram of a partial Fourier acquisition. 51 4.2 Comparison of reconstructed partial Fourier data. 54 4.3 k-space properties relevent to partial k-space acquisitions. 55 4.4 Data sampling in 3D Cartesian keyhole acquisitions. 56 4.5 TWIST data acquisition and reconstruction. 57 4.6 Images acquired using multiple receive coils. 61 4.7 SENSE image reconstruction. 63 4.8 GRAPPA reconstruction and GRAPPA weight calibration. 65 4.9 Non-Cartesian acquisitions with undersampling. 69 4.10 CS SENSE image reconstruction algorithm. 75 4.11 Non-Cartesian GRAPPA calibration strategies. 78 5.1 Reconstruction simulation results for TWIST with parallel 84 imaging and partial Fourier. 5.2 Imaging results for determining TWIST sampling scheme. 85 5.3 MIP MRA images in three different volunteers using MRAP. 94 5.4 Signal intensity curves during the MRAP experiment in relaxed 95 and exercised muscle. 5.5 Bland Altman plots describing the repeatability of the MRAP 96 exam. 5.6 Ktrans parameter map in a single volunteer in relaxed and 97 exercised muscle. 6.1 3D non-Cartesian GRAPPA weight calibration techniques. 107 6.2 Reconstruction simulation results for different 3D radial 115 GRAPPA weight calibration. 6.3 Imaging results for determining 3D radial GRAPPA weight 117 calibration. 6.4 Comparison of 3D through-time radial GRAPPA and CG 118 SENSE. 6.5 Renal trMRA reconstructed with TWIST and 3D through-time 120 radial GRAPPA.

6.6 Detailed comparison of renal MRA using TWIST and 3D 121 through-time radial GRAPPA. 6.7 Contrast-enhanced, breath-held renal trMRA with 3D through- 121 time radial GRAPPA. 6.8 3D through-time radial GRAPPA with different calibration 122 acquisition times. 6.9 Reconstruction of renal DCE MRI data with 3D through-time 134 radial GRAPPA. 6.10 Demonstration of reconstructed DCE MRI data with 3D 135 through-time radial GRAPPA. 6.11 Image registration of renal DCE MRI data. 136 6.12 Representative model fit of whole kidney ROI data using renal 139 pharmacokinetic model. 6.13 Quantitative perfusion and filtration maps of the renal cortex 140 using a half dose of Gd. 6.14 Quantitative perfusion and filtration maps of the renal cortex 141 using a quarter dose of Gd. 7.1 MRF relaxometry pulse sequence and parameter quantification. 147 7.2 MRF parameter maps. 148 7.3 Simplified pulse sequence diagram for MRF ASL. 151 7.4 Plots of an example labeling function, arterial input function, 154 and tissue signal generated with MRF ASL. 7.5 Diagram describing dictionary creation in MRF ASL. 154 7.6 Plots of label duration and post-label delay times for the MRF 155 ASL pulse sequence. 7.7 Plots of the labeling function, an example arterial input function, 158 and an example tissue signal generated with MRF ASL. 7.8 Plots of simulated MRF ASL signals. 158 7.9 Results of Monte Carlo simulations evaluating MRF ASL. 159 7.10 Pairwise subtracted images acquired using the MRF ASL 160 sequence. 7.11 Plots of data and the matched dictionary entry from ROIs in grey 161 and white matter. 7.12 Parameters maps of T1, perfusion, and transit time quantified 161 simultaneously with MRF ASL.

List of Abbreviations

Abbreviation Definition 2D Two Dimensional 3D Three Dimensional ACS Auto-Calibration Signal AIF Arterial Input Function AP Artifact Power ASL Arterial Spin Labeling BW Bandwidth CAIPIRINHA Controlled Aliasing in Parallel Imaging Results in Higher Acceleration CASL Continuous Arterial Spin Labeling CG SENSE Conjugate Gradient Sensitivity Encoding CPU Central Processing Unit CT Computed Tomography DCE Dynamic Contrast Enhanced DCF Density Compensation Function DSC Dynamic Susceptibility Contrast EES Extravascular, Extracellular Space EPI Echo Planar Imaging EPISTAR Echo Planar Imaging Signal Targeting with Alternating Radio Frequency FA Flip Angle FAIR Flow-sensitive Alternating Inversion Recovery FFT Fast Fourier Transform FISP Fast Imaging with Steady-state free Precession FLASH Fast Low-Angle Shot (more generally referred to as a Spoiled Gradient Echo) FMRIB Functional Magnetic Resonance Imaging of the Brain (Research Group at Oxford) FNIRT FMRIB's Nonlinear Image Registration Tool FoV Field-of-View Gd Gadolinium Gd-DTPA Gadopentetic acid GFR Glomerular Filtration Rate GPU Grapics Processing Unit GRAPPA Generalized Autocalibrating Partially Parallel Acquisitions GRASE Gradient echo and Spin Echo GRE Gradient Echo Hct Hematocrit HIPAA Health Insurance Portability and Accountability Act

Hz Hertz IRB Internal Review Board IV Intravenous m meter MHz Megahertz min minutes MIP Maximum Intensity Projection mL milliliter mm millimeter MR Magnetic Resonance MRA Magnetic Resonance Angiography MRAP Magnetic Resonance Angiography and Perfusion MRF Magnetic Resonance Fingerprinting MRI Magnetic Resonance Imaging ms milliseconds mT milliTesla MTT Mean Transit Time NMR Nuclear Magnetic Resonance NSF Nephrogenic Systemic Fibrosis NUFFT Non-uniform Fast Fourier Transform pA Percentage size of region A (TWIST) PAD Peripheral Arterial Disease PASL Pulsed Arterial Spin Labeling pB Percentage size of region B (TWIST) pCASL pseudo-Continuous Arterial Spin Labeling PET Positron Emission Tomography pF Partial Fourier Acceleration Factor PICORE Proximal Inversion with a Control for Off-Resonance Effects PLD Post-Labeling Delay POCS Projection onto Convex Sets PROPELLER Periodically Rotated Overlapping Parallel Lines with Enhanced Reconstruction PSF Point Spread Function PULSAR Pulsed Star Labeling of Arterial Regions QUIPPS Quantitative Imaging of Perfusion using a Single Subtraction R Reduction or Acceleration Factor (Parallel Imaging) RARE Rapid acquisition with relaxation enhancement RAS Renal Artery Stenosis RCC Renal Cell Carcinoma RF Radiofrequency RMSE Root Mean Squared Error

ROI Region of Interest s seconds SENSE Sensitivity Encoding SI Signal Intensity SNR Signal-to-Noise Ratio SPECT Single-photon Emission Computed Tomography T Tesla TE Echo Time TR Repetition Time trMRA time-resolved Magnetic Resonance Angiography TWIST Time-resolved Angiography with Interleaved Stochastic Trajectories

Measuring Perfusion with Magnetic Resonance Imaging Using Novel Data Acquisition and Reconstruction Strategies

KATHERINE L. WRIGHT

Abstract Tissue perfusion is an important metric that can provide valuable information for disease diagnosis, treatment planning, and treatment follow-up. MRI can quantify perfusion both with and without Gd-based contrast agents, and can provide spatially-localized perfusion maps. However, these techniques are rarely used in the clinical environment. The works in this thesis focused on providing novel data acquisition and/or reconstruction techniques to overcome limitations in DCE MRI and ASL in order to provide clinically- viable perfusion exams.

There are three main projects that will be described in this thesis. First, a simultaneous

3D magnetic resonance angiography and perfusion (MRAP) exam is proposed and is demonstrated in the distal lower extremities. Second, a 3D non-Cartesian parallel imaging method is described and used to achieve a low-dose, 3D, high spatiotemporal resolution renal DCE MRI exam that is acquired without breath-holding. Finally, a novel approach to ASL is proposed using the Magnetic Resonance Fingerprinting framework to simultaneously quantify perfusion, transit time, and tissue T1 in a single, efficient acquisition.

Chapter 1. Introduction Medical imaging is an invaluable set of technologies that provides important anatomical

and functional information during patient care. Many imaging modalities are used

clinically today including x-ray, fluoroscopy, CT, nuclear medicine (PET, SPECT),

ultrasound, and Magnetic Resonance Imaging (MRI). While each technology has its own

advantages and limitations, the work described in this thesis will focus on MRI. MRI has

many well-known advantages including a lack of ionizing radiation, excellent soft tissue

contrast, and the ability to use arbitrary scanning planes. However, MRI is still largely a

qualitative imaging modality, which can be a limitation in comparison to inherently

quantitative technologies such as CT and PET. The signal intensity in almost all MR

images is described in arbitrary units, and lesions are identified based on a hyper- or

hypo-intense appearance in images. In comparison, CT images provide quantitative

information on tissue density (measured in Hounsfield units), and PET images provide

quantitative information on radiotracer concentration.

While most clinical MR images are qualitative, MRI is sensitive to many physical and

physiological parameters that can each be quantified. For example, one such

physiological tissue property is perfusion. Perfusion is blood flow at the microvascular

level, and is defined as a volume of blood that reaches a volume of tissue in an amount of

time (measured in units of volume of blood per volume of tissue per time). Perfusion is

vital to tissue health and function because it allows for delivery of nutrient-rich blood to a tissue’s cells. In cases of ischemia, where perfusion is too low, the tissue begins to dysfunction and eventually has cell death. Hyperemia, where perfusion is too high, can lead to fluid accumulation in tissue. If an appropriate tracer is introduced to arterial blood, its flow into distal tissues can be quantitatively tracked with MRI, which allows

for the quantification of tissue perfusion. While it is clear that the measurement of this

physiological parameter can provide valuable functional information, quantitative MRI

perfusion techniques are still not commonly used, although they were first introduced 25

years ago. This is largely because these exams are difficult to perform in the clinical

environment. They typically require long exam times, have limited spatial coverage and

spatial resolution, are susceptible to patient motion, and are difficult for the user to

perform. The specific focus of this work will be to investigate new strategies for

measuring perfusion with MRI and provide novel and robust methods that will easily

translate to the clinical environment.

Section 1.1. Measuring Perfusion with MRI: Clinical Motivation Perfusion of tissue is a vital process that provides nutrient-rich blood to tissue. Abnormal

perfusion can be indicative of a change in tissue function or viability, and is therefore a

useful metric for following many diseases. In this thesis, perfusion will be explored in the

context of several clinical or physiological applications, each application providing an

MR protocol that could be improved with the development of appropriate technology.

The first application that will be explored is the measurement of skeletal muscle

perfusion in the distal lower extremities. This is directly applicable to Peripheral Arterial

Disease (PAD). Lower extremity PAD results from the development of occlusive atherosclerotic plaque in arteries that supply the lower limbs. The symptoms (leg weakness, claudication) result from a constellation of physiological changes secondary to reduced tissue perfusion. MRI perfusion methods could be used to evaluate the true physiological changes occurring in the muscle (1,2).

The second application that will be explored is in perfusion imaging of the kidneys. MRI can be used to measure renal perfusion and renal filtration, which are both impacted in several diseases (3–16). One of these is in the characterization of renal masses, including renal cell carcinoma (RCC), where perfusion can allow for classification of the mass

(3,6,8,9,11,15,17–19). A second area of interest in the kidneys is renal artery stenosis

(RAS) (4,5,7,9,13). In RAS, renal perfusion can be substantially reduced. Finally, renal perfusion and filtration analysis could be very important in transplant evaluation. These exams could examine donors prior to surgery and monitor recipients afterwards (6,9,10).

Finally, the third application considered here is the brain. There are several different diseases (for example, stroke) that affect perfusion levels in the brain. Identification of regions of poorly perfused brain after an acute ischemic stroke can help identify if a tissue is reversibly or irreversibly damaged, which is critical for treatment planning (20–

27). Another area of interest is in neuro-oncological applications, where perfusion is known to correlate to tumor grade and can be used to determine prognosis and for treatment planning (20,21,28–30). Perfusion quantification in tumors can also be important for monitoring treatment progress and success (21,30,31).

Section 1.2. Overview of Thesis Because of the clear clinical need for quantitative perfusion information, the work presented in this thesis focused on providing perfusion measurement techniques that could be easily added to current clinical protocols and would be robust and easy-to- execute in the clinical environment.

Before describing the novel MR perfusion methods, there is a brief review of MRI topics that will serve as background information for the developed MRI technologies. This

review will be presented in Chapters 2-4. Chapter 2 will describe basic MRI sequence information and signal encoding theory. Chapter 3 will provide background on perfusion

MRI for techniques that use exogenous contrast agents and techniques that use arterial water as an endogenous contrast agent.

The thesis will explore three different novel techniques for perfusion MRI in three different clinical applications. The first project is presented in Chapter 5, which will describe a method used to simultaneously acquire an MR Angiography exam and measure perfusion in skeletal muscle in the distal lower extremities. The second project is presented in Chapter 6, where a highly accelerated 3D non-Cartesian reconstruction is described and applied to measure perfusion in the kidneys. Finally, the third project is presented in Chapter 7, and a non-contrast perfusion technique is proposed using a new quantitative MR framework to measure perfusion in the brain.

Chapter 2. MRI Background The goal of this section is to describe basic MRI topics that are relevant to the works described in this thesis. There are several texts that provide an excellent background on

MRI, and are recommended for the interested reader (32–34). This chapter will begin with a brief introduction to Nuclear Magnetic Resonance (NMR) physics and signal generation, spatial localization to produce MR images, and a 2D MRI pulse sequence.

MRI is rooted in Nuclear Magnetic Resonance or NMR. For a sample to produce a signal when performing a NMR experiment, it must contain nuclei that have a non-zero intrinsic angular momentum (or spin). While many nuclei have this property and can therefore be examined with NMR, clinical MR predominately focuses on the proton in hydrogen atoms because of its prevalence in vivo. When exposed to an external magnetic field, these nuclear magnetic moments will align parallel or anti-parallel to the direction of the external field and precess about the magnetic field at a frequency proportional to the strength of the magnetic field (Bo):

= [2.1],

표 표 where ωo is the Larmor frequency and휔 γ is the훾퐵 gyromagnetic ratio divided by 2π. The gyromagnetic ratio is a physical constant (with units of frequency / magnetic field strength) that is specific to the nuclei of interest. Protons have a gyromagnetic ratio of

42.58 MHz/T. The ability to detect an NMR signal is due to the small excess of spins that align parallel to Bo in comparison to those that align anti-parallel. Although this excess is quite small (~3 in a million protons at 1T), the large overall number of protons in a volume of tissue results in a net magnetization that can be measured.

In order to detect this magnetization, a measurable signal must be created from it by tipping the magnetization away from alignment with Bo. This is achieved by applying a

short radiofrequency (RF) pulse at the Larmor frequency, which rotates the magnetization

vector away from the direction of Bo (known as the longitudinal axis). Once tipped, the magnetization precesses at the Larmor frequency and relaxes back to its equilibrium position along the longitudinal axis. The portion of the magnetization that is in the transverse plane induces a voltage in a receive coil and results in the NMR signal.

After an RF pulse, the magnetization vector experiences a relaxation effect that returns

the spins back to their equilibrium state. In order to characterize the strength of the MR

signal during an experiment, it is important to account for the relaxation effects. There

are two relaxation processes that occur after an RF pulse is applied. The first is related to

the interaction of the spins with local structures (referred to as the lattice), and is known

as the spin-lattice relaxation. The second relaxation effect is spin dephasing due to

microscopic magnetic field changes that are inherent to the sample’s structure, and is

known as spin-spin relaxation. The relaxation is characterized by two timing parameters

T1 and T2, respectively, and can be described by the following equations:

( ) = (1 ) [2.2a], −푡 �푇1 푀푧 푡 푀표 − 푒 ( ) = [2.2b], −푡 �푇2 ⫠ 표 where Mo is the equilibrium magnetization,푀 푡 푀 T푒1 is a characteristic constant describing the

recovery of longitudinal relaxation, and T2 is a characteristic constant describing

dephasing. T1 is defined as the time necessary to regain 63% of the equilibrium

magnetization value, and T2 is defined as the time necessary to lose 63% of the initial

transverse magnetization. As described in Equation 2.2, the magnetization level largely

depends on the time at which the signal is sampled (t) and how much relaxation occurs

during that time. If the object being imaged has different species with different Mo, T1,

and T2 values, the time of sampling can be strategically selected to achieve contrast

between these species.

These signal generation principles are similar in NMR and MRI. However, an MRI

experiment provides spatially localized NMR signals. Spatial localization in MRI is

performed by using spatially varying magnetic field gradients. This creates a spatially

varying magnetic field:

( ) = + [2.3],

표 푥 where Bo is the static magnetic field퐵 푥 strength,퐵 푥G퐺x is a constant gradient, and x is a spatial

location within the object being imaged. These magnetic field gradients are used to perform spatial encoding in two ways: frequency encoding and phase encoding.

In frequency encoding, the gradient is applied to make the precession frequency linearly related to the spatial location (combining Equations 2.1 and 2.3):

( ) = + [2.4].

표 푥 In phase encoding, the gradient is휔 applied푥 휔 for period훾푥퐺 of time (T), during which a phase is

linearly accumulated along the phase encoding direction (y):

( ) = [2.5].

푦 As can be seen from Equations 휑2.4푦 and 훾2.5,푦퐺 every푇 spatial location in this x-y plane will

correspond to a signal with a unique frequency and phase combination. These previous

equations are specific to the use of linear gradients, but the combination of arbitrary

gradient encoding can also be described. Here, a variable ‘k’ is used to describe the

spatial frequency domain, which is sampled by varying the gradient pulses over time:

( ) = ( ) [2.6], 푡 푘 푡 훾 ∫0 퐺 휏 푑휏

where G is a gradient pulse that is applied from time 0 to t. In MRI, the spatial frequency

domain containing all of the frequency and phase encoded signals is commonly referred

to as k-space.

The MRI signal that is sampled in k-space can be described by the following equation:

, = ( , ) ( ) [2.7], ∞ ∞ −푖2휋 푘푥푥+푘푦푦 푆�푘푥 푘푦� ∫−∞ ∫−∞ 휌 푥 푦 푒 푑푥 푑푦 where S(kx,ky) is the MR signal at a specific two-dimensional spatial frequency, ρ(x,y) is the proton density at a specific two-dimensional spatial location, x and y are variables in the spatial domain, and kx and ky are variables in k-space. In Equation 2.7, it can be seen that a two-dimensional inverse Fourier transform can be used to produce an image of the original object (ρ(x,y)).

In a Cartesian MRI experiment, a finite number of k-space points are measured on a rectangular grid as seen in Figure 2.1. This k-space sampling must meet the Nyquist sampling criteria to avoid aliasing in the resulting images. The Nyquist criterion is defined as the inverse relationship between the spacing between lines in k-space (Δk) and the image field-of-view (FoV):

1 [2.8].

The FoV is defined as the spatial� 훥푘extent∝ 퐹표푉 of the image. The FoV must be larger than the

object in order to avoid aliasing. So in a typical MRI experiment, the user defines the

FoV based on the anatomy of the object being imaged, and the Δk spacing can be

computed to meet Nyquist sampling criterion. Another important k-space sampling

parameter is the extent of k-space being sampled, which relates to image resolution:

1 1 = ( ) = (2 ) [2.9],

훥푥 � 푁 ∗ 훥푘 � ∗ 푘푚푎푥 23

where Δx is the image resolution, N is the number of k-space lines sampled, and kmax is

the maximum k-space line. As can be seen in Equation 2.9, image resolution is

determined by the outermost region of k-space, which contains high frequency information. The sampling and image parameters in Equations 2.8 and 2.9 are also described pictorially in Figure 2.1.

Figure 2.1. Description of Cartesian sampling parameters in k-space and the imaging domain.

The RF excitation pulses, gradient pulses, and acquisition of data in an MR imaging

experiment can be summarized in a pulse sequence diagram. Figure 2.2 shows a pulse

sequence diagram for a 2D gradient echo (GRE) sequence with a Cartesian sampling

scheme. In this GRE sequence, there is a single excitation RF pulse that tips the

magnetization into the transverse plane. This RF pulse has a flip angle (FA) of α,

indicating that the net magnetization will be tipped to this angle relative to the main

magnetic field.

In addition to the RF pulse, there are three types of gradient pulses: slice-selective (SS),

frequency encoding (FE), and phase encoding (PE). The slice-selective pulse is applied

during the RF pulse in order to provide frequency variation along the z-axis (Equation

2.4). If a 2D imaging slice with a thickness of Δz is desired, this will correspond to a

range of frequencies:

= ( ) [2.10]

훥푧 훥휔� 푆푆 where GSS is the slice selective gradient훾 퐺 magnitude and Δω is range of frequencies

corresponding to the slice thickness. The RF pulse will be centered at the Larmor

frequency and will have a bandwidth of Δω. Thus, only spins within the imaging slice

will be tipped into the transverse plane. Immediately following the slice-selective gradient pulse, an additional gradient (known as the slice selective rephrasing gradient) is applied on the slice-encoding axis in order to recover any dephasing that occurred during the slice-selective gradient.

The frequency and phase encoding gradient pulses are then applied to encode the signal to specific kx and ky locations as shown in Figure 2.2. Prior to these gradients, no

encoding has occurred in the x-y plane, and thus the experiment begins at the center of k-

space (kx = ky = 0). First, there is a dephasing gradient pulse played on the FE axis

simultaneously as the PE gradient is applied. These two gradients move to a specific

location along the ky axis at –kx,max. The frequency encoding gradient is then applied in order to move along an entire kx line. This GRE experiment produces an echo that is

temporally centered with the FE gradient, and will be measured with the receive coil and

sampled with an analog-to-digital converter (ADC). The timing of this experiment can be

adjusted to produce various image contrasts as described in Equation 2.2. The repetition

time (TR) can be varied to change the timing between RF pulses. The echo time (TE) can

be selected to change the timing between the RF pulse and the acquisition of the echo. As

25 can be seen in Figure 2.2, one k-space line is sampled in each TR of an experiment.

Therefore, the total duration of the experiment accounts for the TR and the number k- space lines being acquired:

= [2.11],

푎푐푞 푃퐸 퐴 where NPE is the number of phase푇 encoding푇푅 ∗ 푁lines∗ being푁 acquired and NA is the number of averages acquired (where the data is averaged together in order to improve SNR). In

Equation 2.11, the TR is typically fixed based on the desired contrast. Therefore, acquisition time and image resolution are inherently linked. Because high spatial resolution and large FoV are typically desired, and the experiment must be repeated multiple times to build up the data, MRI is inherently a relatively slow imaging modality.

Figure 2.2. (Left) Pulse sequence diagram of a basic GRE sequence. (Right) Diagram describing how the gradient pulses relate to traversing k-space.

Chapter 3. Measuring Perfusion with MRI In order to quantify perfusion with MRI, a tracer must be introduced to the arterial blood, and the change in MRI signal caused by the tracer must be quantified after it has flowed into the tissue of interest. This can be seen in Figure 3.1, where a tracer is introduced to the arterial blood, travels to the arterioles in the tissue of interest, and freely diffuses across the blood vessel wall into the extravascular, extracellular space (EES). Perfusion

MRI methods aim to quantify the rate at which this tracer moves into the EES of the tissue of interest. This rate is quantified as an aggregate flow rate averaged within a volume of interest, which yields a perfusion value in units of volume/time/volume-of- tissue (for example, ml/min/100ml-tissue).

Figure 3.1. This figure describes the broad concept of using tracer pharmacokinetics to measure perfusion with MRI. Here, the tracer could be exogenous or endogenous. It must be small enough to easily and rapidly move from the capillary vessel into the extravascular, extracellular space (EES).

There are two main classes of perfusion MRI methods: 1. Methods that use an intravenously injected gadolinium based contrast agent as an exogenous contrast agent,

and 2. Methods that manipulate local arterial magnetization as an endogenous contrast agent. There are two subtypes of contrast enhanced methods that are employed in MRI.

Section 3.1 will cover Dynamic Contrast Enhanced (DCE) MRI. Another contrast enhanced method for measuring perfusion is Dynamic Susceptibility Contrast (DSC)

MRI. Although DSC perfusion imaging is not explored within the work presented in this thesis, more details can be found in (30). The method which does not utilize injected gadolinium contrast is called Arterial Spin Labeling (ASL), and is discussed in Section

3.2.

Section 3.1. Dynamic Contrast Enhanced MRI

Section 3.1.1. DCE MRI Introduction The overall goal of DCE MRI is to administer a MR contrast agent, and dynamically track its kinetics as it moves through a tissue. The most commonly used contrast agents in

the clinic are Gadolinium based contrast agents, which are primarily composed of

Gadolinium (Gd) metal that is bound with chelates. Several Gd contrast agents have been

developed (35–38) with their own formulation, but a majority of contrast agents have

similar pharmacokinetic properties. Contrast agents are typically in solution form, which

are injected intravenously for many clinical exams. They are composed of small

molecules that can rapidly move from the intravascular space to the EES, but most do not

move into the intracellular space. The primary exception is in the brain, where the blood-

brain barrier prevents Gd from moving into the EES. There are certain types of contrast

agents that can be taken into the intracellular compartment or have a weak binding

property with albumin in the blood, and this must be considered if using these contrast

agents in DCE MRI.

Gadolinium based contrast agents have a paramagnetic property, which results in a change in local relaxation properties. Change in MR signal is related to the local effects on both T1 and T2 relaxation times:

1 = 1 + [ ] [3.1] , 1 �푇1 �푇1 표 푟 퐺푑 and

1 = 1 + [ ] [3.2], , 2 �푇2 �푇2 표 푟 퐺푑 where T1o and T2o are the relaxation times without contrast agent, T1 and T2 are the relaxation times with contrast agent, [Gd] is the concentration of Gadolinium, and r1 and r2 are the relaxivities of the contrast agent. The relaxivity values are constants that are specific to the formulation of the Gd contrast agent, and these have been measured in the literature (37). It is important to note that T1, T2, and relaxivity values are all dependent on field strength (32,37,39).

The change in relaxation parameters described in Equations 3.1 and 3.2 can have a dramatic impact on the MR Signal. For example, the change in T1 causes blood vessels and tissues to be hyperintense on T1-weighted images. This is shown in Figure 3.2. Here, images of the distal lower extremity are shown after contrast has been injected. Contrast agent concentration is higher in the large vessels at first, leading to a larger decrease in

T1, and a brighter signal. Once contrast agent diffuses into the capillary beds and EES, a change in signal can also be seen in the skeletal muscle. These dynamic changes in signal are measured using DCE MRI by acquiring a series of images in rapid succession.

Section 3.1.2 will describe how these data are acquired, and Section 3.1.3 will describe

29 how these signal changes can be used to quantify to perfusion and other physiological parameters of interest.

Figure 3.2. This figure describes the change in MRI Signal Intensity (SI) in a dynamic T1-weighted series of images. The signal increases as the concentration of Gd increases in a tissue. After an IV injection of Gd, there is initially a high concentration of Gd in the vasculature, which relates to a hyperintense signal shown in red on the line plot. The contrast agent will subsequently move into the microvascular and diffuse into the EES. Because the Gd has diffused across a larger volume, the overall change in signal will not be as high as in the artery, but an increase in signal will be seen as shown in blue on the line plot.

Section 3.1.2. Data Acquisition There are several considerations when determining a MRI pulse sequence protocol for a

DCE MRI application. The first consideration is that the sequence must be sensitive to the Gd-related change in signal. Because these contrast agents affect both T1 and T2 relaxation times, the sequence could be selected as either T1-weighted or T2-weighted to provide sensitivity to the changes in T1 or T2. However, DCE MRI sequences are usually selected to be T1-weighted sequences for several reasons (including but not limited to: fast acquisition times and increased SNR) (30). While spin echo sequences could be explored, most DCE MRI scans use T1-weighted gradient echo sequences because of their speed. The DCE MRI acquisitions in this thesis used a spoiled gradient echo

sequence referred to as FLASH (Fast Low Angle Shot) (40). The signal intensity in the

FLASH sequence can be described by the following equation (30,32):

( ) −푇 퐸 푅� −푇 ∗ = 푇1 � [3.3], sin 훼 ∗�1−푒 � 푇2 ( ) −푇 푅� 푇1 푆 푔 ∗ 휌 ∗ 1−cos 훼 ∗푒 ∗ 푒 where g is a constant that represents the receiver gain and other scaling factors, ρ is the

proton density, and α is the flip angle used in the sequence. It is important to note that

FLASH experiments use short TR and TE values, and an optimal flip angle (known as the

Ernst angle can be calculated for a specific T1 value. As seen in Equation 3.3, the signal

in a FLASH experiment is sensitive to the T1 value, making it suitable for DCE exam.

Another important DCE MRI sequence parameter is temporal resolution. DCE MRI

acquisitions should have a high enough temporal resolution to accurately track the

changes in signal in the tissue of interest and a supplying artery. The exact temporal

resolution requirements are dependent on the application of interest. For tissues with

relatively high perfusion (such as the kidneys), the temporal resolution requirements are

higher because the signal changes more rapidly. For tissue with relatively low perfusion

(such as resting skeletal muscle), the temporal resolution requirements can be slightly

more relaxed. The rate of change of signal in the arteries is also an important factor when

selecting the temporal resolution, and is more demanding than tissue enhancement rates.

Gd-based contrast agents are typically administered intravenously with a rapid bolus

injection, which is followed by an injection of saline to keep the bolus tight while

traveling through the cardiovascular system. When the bolus initially arrives in the

supplying artery (often referred to as the first pass), the change in signal is large and

occurs very rapidly, which requires a very high temporal resolution. To partially counter

31 this problem, many fast imaging approaches with rapid readouts (EPI readouts, turboFLASH) (30) or parallel imaging acceleration are utilized in perfusion imaging.

Despite this, in order to achieve high temporal resolutions, either (or both) spatial resolution or spatial coverage is typically sacrificed.

Section 3.1.3. Perfusion Quantification

Converting Signal Intensity to Concentration of Contrast Agent As described in the previous section, DCE MRI provides a series of T1-weighted images that are acquired in rapid succession after the injection of contrast agent. The first step in perfusion quantification is to link the change in signal intensity in these images to the changes in concentration of Gd. Once the concentration of Gd is known, a pharmacokinetic model can be used to describe how Gd travels through the tissue of interest. This modeling relates the change in concentration to important physiological parameters such as perfusion.

Equations 3.1 and 3.3 are primarily used to perform this conversion, but it also requires another piece of data. In addition to the DCE MRI data, the baseline T1 (T1 of tissue without contrast) must also be known. Either a separate series of scans can be used to estimate the baseline T1 prior to the DCE experiment or a literature value for T1 could be used.

First, Equation 3.3 can be written as a dynamic series of images where the T1 changes due to the arrival of contrast agent:

( ) ( ) −푇 푅� ( ) = 푇1 푡 [3.4]. sin 훼 ∗�1−푒 � ( ) ( ) −푇푅 �푇 푡 푆 푡 퐶 ∗ 1−cos 훼 ∗푒 1

Equation 3.4 also incorporated a new scaling factor C that combines the scaling/gain factor g and the proton density term. Because TE is selected to be as small as possible

(much smaller than T2), the T2 term is typically assumed to be negligible. All sequence parameters in Equation 3.4 are known (TR and α), but C must be estimated. Typically, several frames are acquired prior to contrast arrival, so these signal points (along with the baseline T1 value) can be used to solve for C. Now, all constants are known, and

Equation 3.4 and the acquired signal can be used to solve for the T1 at each time point acquired.

Using this dynamically changing T1 series and the baseline T1 value, Equation 3.1 can be used to solve for the concentration of Gd at each time point. This approach was used in all DCE MRI analyses done in this thesis. However, there are alternative approaches including those proposed in (30,41,42).

Pharmacokinetic Analysis Pharmacokinetic analysis of a drug provides information on how a drug will move through the body. In DCE MRI, a bolus of Gd contrast agent is injected intravenously, and the study of how it moves through the body can provide some valuable information on physiology. As mentioned above, most Gd contrast agents used in DCE MRI rapidly move from the vasculature into the EES (except in the brain) and do not penetrate cell membranes. These drugs are primarily eliminated via filtration by the kidneys (43).

This pharmacokinetics of Gd can be modeled in many tissues by a simplified two compartment model (one tissue compartment). As described in Figure 3.3, this model describes an input of Gd from the arterial vasculature, a transfer of Gd into the EES of a tissue of interest where it diffuses across the volume of the EES, and a transfer of Gd back into the venous vasculature for clearance. While this model may be very simplified,

it is one that is commonly used to describe the kinetics of Gd in many tissues in MRI

(44).

The two compartment model was described with standardized parameter definitions by

Tofts, et al. (44). For any pharmacokinetic model, it is important to define parameters

relating to tracer concentration, which include the volume of each compartment and the

transfer rates between each compartment. The volume of each individual compartment is

defined based on the volume that the tracer disperses in. For example, Gd does not enter

the cells, so the volume of tissue compartment neglects intracellular volume. Thus, the

volume of the tissue compartment is described by a fractional volume ve that is unitless,

and is defined as the volume of the EES per volume of tissue. For the arterial

compartment, the tracer only disperses within the plasma volume (Vp), which can be found by adjusting the blood volume (Vb) for the Hematocrit level (Hct).

Figure 3.3. The left hand figure shows a schematic of a blood vessel that contains a Gd-based tracer. This tracer is small enough to rapidly cross the vascular membrane into the EES, and it also can transfer back into the vasculature for clearance. In many tissues, this can be modeled by a two-compartment approach shown on the right. The arterial compartment has a known concentration of tracer (Cp), and the EES tissue compartment has a known concentration of tracer (Ct). Using DCE MRI, these concentrations can be

trans measured over times, and the rate of transfer between these compartments (noted here as K and kep from

(44)) can be estimated. These are linked to important physiological parameters including perfusion.

In the model described by Tofts, et al., Ktrans is defined as a transfer constant of Gd from

the plasma into the EES, which gives Ktrans units of min-1. It is assumed that the rate of

transfer across the vascular membrane is the same in both directions. Therefore, the rate

constant of Gd moving from EES back into the vascular compartment can be defined as

the ratio of Ktrans and the fractional dispersion volume:

= [3.5]. 푡푟푎푛푠 푒푝 퐾 푘 �푣푒 The final parameters that must be defined for the model are the concentrations of each

compartment. The previous section described how MRI can be used to dynamically monitor changes in concentration of a tracer, and these are described in volume concentrations with units of mM. Using the DCE MRI data, a region of tissue signal can be selected and converted to tissue concentration (Ct). Also, a region within an artery

proximal to our tissue of interest can be used and converted to arterial plasma

concentration (Cp). The arterial plasma concentration is sometimes referred to as the

arterial input function (AIF).

Using the terms described above, the change in concentration of Gd in a tissue can be

described using a simple differential equation:

= [3.6]. 푑퐶푡 푡푟푎푛푠 푑푡 푝 푒푝 푡 The differential equation in Equation퐾 3.6 퐶can− be푘 퐶solved, and the transfer and rate

constants can be estimated by performing a nonlinear fit between this model and the DCE

trans MRI concentration data. The estimated K and kep values are inherently linked to the

physiology of the tissue being examined. However, the exact interpretations of these

values is not always straight-forward. The rate at which the tracer can move out of the

vasculature is related to two terms: perfusion and permeability. If a tissue has high

permeability, the limiting factor is the flow of Gd into the tissue. In this case, Ktrans is

directly proportional to perfusion:

= (1 ) [3.7], 푡푟푎푛푠 where F is perfusion and ρ is tissue퐾 density.퐹휌 If− a 퐻푐푡tissue has restricted permeability, this

dominates how fast the Gd will transfer into the tissue. Thus, Ktrans is directly

proportional to permeability:

= 3.8], 푡푟푎푛푠 where P is the permeability of the capillary퐾 wall휌푃푆 and S is the surface area per unit mass of

tissue. In most tissues, the general tissue properties are known, allowing for selection

between Equations 3.7 and 3.8. The resulting Ktrans values from the DCE MRI experiment

can then provide quantitative information on perfusion or capillary leakage.

It is important to note that this simple two compartment model will not apply to all

tissues and physiologies. One example where this model is appropriate is in skeletal

muscle, which is explored in Chapter 5. However, DCE MRI is also applied to the kidneys in Chapter 6, which presents a more complicated pharmacokinetic analysis. In the kidneys, the model must account for the blood flow of Gd into the tissue, and it also must describe the filtration of Gd into the urine during excretion. In the kidneys, a three compartment (two tissue compartment) model is typically used, and the mathematical details are described in Chapter 6.

Section 3.1.4. Advantages/Disadvantages of DCE MRI DCE MRI is an established MR perfusion technique, and has been used clinically in applications such as oncology (30). The increase in signal (in a T1-weighted image)

36 related to delivery of the contrast agent improves the SNR of the exam, and the change in signal due to perfusion is easily quantified. Because of this high sensitivity of the exam,

DCE MRI can even be used to measure perfusion in tissues with low perfusion levels.

The exam is minimally invasive due to the intravenous injection of contrast agent, and the contrast agent has minimal associated risks in subjects without severe renal dysfunction. However, Gd-based contrast agents cannot be used in patients with severely impaired renal function because it may cause Nephrogenic Systemic Fibrosis (NSF)

(45,46).

One disadvantage of DCE MRI is that the exam cannot be repeated within 24 hours of the initial Gd injection. The pharmacokinetic modeling assumes that the initial concentration of Gd in tissue is zero. Therefore, if the exam fails for any reason after Gd is injected

(motion, incomplete Gd injection, etc.), the exam has to be repeated after the injected agent is allowed to be removed from the system.

Current DCE MRI methods do have some limitations. One main limitation is the need for a high temporal resolution, which typically results in high spatial resolution and low volumetric coverage. Another limitation is that generally only a single dose of Gd is given in each exam. Therefore, if Gd is needed for an MR Angiography (MRA) exam,

DCE MRI cannot be performed in the same exam.

Section 3.2. Arterial Spin Labeling

Section 3.2.1. ASL Introduction In contrast to DCE MRI, Arterial Spin Labeling (ASL) is a technique used to measure perfusion without the injection of contrast agents. Instead, ASL inverts or saturates arterial blood, and these ‘labeled’ water molecules act as a tracer. The labeled blood can then travel from the large proximal arteries into the microvascuature and readily diffuse

37 into the EES of the tissue. The change in MR signal in a tissue distal to the label will be directly proportional to the perfusion of that tissue. The change in MR signal due to the arrival of the label is relatively small (~1%), but it can be measured on clinical scanners and used to quantify perfusion of the tissue of interest (47–49). The ASL endogenous tracer is detectable for a relatively short time span, which is dictated by the longitudinal relaxation rate (T1) of blood and the tissue of interest.

With an ASL experiment, an image is first acquired after labeling a feeding artery proximal to the tissue of interest. After a delay to allow labeled spins to move into the tissue of interest, an image is acquired. Second, an image is acquired after no labeling to serve as a comparison. These two images are then subtracted to generate a perfusion- weighted image. To quantify tissue perfusion, the change in magnetization can be modeled (50).

There are two different methods for labeling in ASL: pulsed and continuous. The pulse sequence for each of these is generally described in Figure 3.4 and Figure 3.5. In pulsed

ASL (PASL), a bolus of labeled blood is used, which results in transient change in signal in the tissue of interest. In continuous or pseudo-continuous ASL (CASL or pCASL), blood is labeled continuously and reaches a steady-state in the tissue of interest. Each has its own methodology and advantages and will be described in Sections 3.2.2 and 3.2.3.

CASL and pCASL exams have a higher SNR, which can be vital in this low SNR exam.

This can make pCASL a preferable approach to ASL data acquisition. However, PASL methods have a lower RF deposition (specific absorption rate, SAR), which could be advantageous at ultra-high field strengths.

Figure 3.4. Overview of ASL pulse sequences. The top row is a schematic of a CASL/pCASL sequence.

CASL acquisitions begin with a period of labeling, which is followed by a post-label delay to allow for spins to travel into the tissue. The bottom row is a schematic of a PASL sequence. PASL has a short labeling pulse that is followed by an inversion time to allow for labeled spins to travel into the tissue.

Figure 3.5. The labeling methods are pictorially described in this figure. The CASL/pCASL labeling occurs as arterial blood moves through the labeling plane (red line). The PASL labeling occurs by inverting a large slab of blood (red box). After the labeling is applied, images are acquired in the brain as noted by the blue box.

Section 3.2.2. CASL/pCASL Methods CASL methods use long labeling pulses to allow the perfusion signal in the tissue of interest to reach a steady state level. This requires a constant gradient and RF pulse to be applied during labeling to achieve a flow-driven inversion of the arterial spins. While

CASL has been successfully implemented, clinical MRI hardware is not optimized for a

continuous RF pulse. Alternatively, recent literature has focused on using an approach

known as pseudo-continuous ASL (pCASL) (51). pCASL mimics the continuous RF

excitation by using many small and short RF pulses in rapid succession. pCASL can be

implemented on existing MRI hardware, and has been shown to provide valid ASL

perfusion measurements (51). Because of its ease of implementation, pCASL has been

suggested as the preferred CASL method (52).

Figure 3.6. Description of labeling and control pCASL pulses and gradients.

pCASL labeling is further described in Figure 3.6. The exact implementation of the

labeling pulses can cause artifacts and have substantial effects on labeling efficiency

(fraction of arterial spins that are inverted), and several studies have optimized the

sequence parameters (53–55). There are several sequence parameters that must be

considered, including: pulse duration, pulse spacing, maximum slice-selective gradient amplitude, mean slice-selective gradient amplitude for each pulse cycle, and the phase of

the RF pulse. The RF pulses are typically designed as Hanning pulses with a short pulse

duration (~1ms), and the spacing of RF pulses is typically kept as small as possible

(~1ms) (51,53). The slice-selective gradient amplitude (Gmax) is typically kept high

(~10mT/m) to achieve good spatial selectivity of the labeling pulses (51,53). It is also

important to note that the gradients during the pCASL labeling pulses are not balanced. A

small mean gradient (Gave) accumulated between each RF pulse is present to achieve the

adiabatic inversion (~1mT/m) (51). Finally, these pCASL labeling RF pulses are played

off-resonant (at the location of a proximal, feeding artery), so the frequency and phase of

the RF pulses must be shifted by:

= [3.9]

∆휔 훾퐺푚푎푥∆푧 and

= [3.10],

∆휑 훾퐺푎푣푒∆푧∆푡 where Δz is the distance from isocenter the labeling plane is applied and Δt is that time between each labeling pulse. For the control pulses, the phase of the RF pulses is additionally shifted by 180 degrees between each pulse, so that no inversion is produced throughout the train of pulses.

In addition to the design of the pCASL pulses, there are several additional sequence parameters that must be determined. The user must select the label duration time and the post-label delay time. Additionally, the user must determine the exact location of the labeling plane.

The label duration is the total time that the pCASL labeling RF is applied prior to the acquisition of each image. This timing affects the duration of the arterial input of labeled

spins. The label duration should be long in order to allow for a constant supply of labeled

spins, which increases the labeling signal. However, the label relaxes with the T1 of blood

and tissue throughout the labeling duration, which reduces the effectiveness of a long

label. Additionally, long label durations can make scan times very long because each

scan is repeated many times to achieve necessary SNR levels. Thus, pCASL scans in

brain tissue typically use a label duration of 1.5-2s.

The post-label delay time (PLD) is the timing gap after the completion of labeling to allow labeled spins to travel to and perfuse into tissue. The PLD determines how much of the label remains in the arteries and how much has perfused into the tissue of interest.

This timing parameter is related to the arterial transit time, which defines how long it takes for the label to arrive in the tissue of interest. The PLD must be longer than this transit time, so that the perfusion estimate is not biased by labeled signals present in the arteries. However, if the PLD is too long, the signal will relax with the T1 of the tissue

and reduce the SNR. Optimally, the PLD would be slightly longer than the transit time in

the tissue being examined. Typical PLD times in pCASL scans of the brain are 1.5-2s

because transit times in gray matter are typically less than 1.5s.

The selection of the labeling plane location can be complicated. The adiabatic inversion

of blood occurs most efficiently if the arteries are perpendicular to the labeling plane.

Additionally, the user must consider that the labeling plane should not be too far from the

imaging plane of interest. At larger distances, the arterial transit time would be longer,

causing greater T1 relaxation and lower ASL signal in the tissue. Another potential

concern with the labeling plane location is if the area selected is near a strong Bo

inhomogeneity. The frequency and phase of the labeling pulses (related to the shifts

described in Equations 3.9 and 3.10) could be set to incorrect values, causing reduced

efficiency of labeling.

Although a successful pCASL sequence can be difficult to design at first, all of these

sequence parameters can be optimized, and several correction methods have been

proposed (52). Regardless, this protocol has been applied in countless applications, and has been shown to successfully provide a quantitative evaluation of perfusion.

Section 3.2.3. PASL Methods Pulsed ASL (PASL) methods have a substantially different labeling approach. Here, a slab of arterial blood is inverted, which travels into the tissue of interest as a bolus with a short duration. Several label and control conditions have been proposed. FAIR uses a combination of selective and non-selective on-resonant pulses for its control and label conditions. This approach avoids any problems associated with off-resonant excitations.

There are several different methods (including EPISTAR, PICORE, and PULSAR

(49,56,57)) that use a labeling slab proximal to the imaging plane for labeling and distal to the labeling plane for control. The distal labeling plane excites at the same frequency

(with opposite sign), so off-resonant excitation effects are compensated.

Regardless of the labeling method, it is important that the inversion slab be as large as possible. Large labeling slabs increase the duration of the labeling bolus and the ASL experiment’s SNR. However, this size is limited for all PASL techniques, which does limit its SNR in comparison to CASL techniques. The slab should not be so large that the

B1 is inhomogenous, which would cause an incomplete inversion. Thus, a 15-20cm labeling slab has been recommended (52).

The inversion pulses used in PASL are typically adiabatic so that the B1 is homogenous across the inversion slab. Additionally, the slab profile should be considered. It is

important that the labeling pulse does not invert or saturate the imaging slices. This is

typically avoided by introducing a gap between the labeling and imaging slabs.

After the labeling pulse in PASL, which is essentially instantaneous, an inversion time

(TI) is introduced to allow labeled spins to move to the imaging plane and perfuse into the tissue. However, most PASL methods do not have a defined bolus timing because it is

dependent on the slab size and the transit time into the tissue. This makes selection of an

optimal TI value difficult. Some approaches acquire data at different TI values, and select

the TI that produces the highest ASL signal. If a single TI approach is used, a TI value

similar to the PLD used in pCASL is selected, although there may be an incomplete

delivery of the bolus. Another approach is to use the QUIPPS II method, which provides a defined bolus duration (and TI timings) (58,59).

Although PASL methods have a lower SNR than pCASL, they have been successfully implemented on clinical scanners, and have been used in several applications.

Section 3.2.4. Data Acquisition Strategies The primary goal of the data acquisition portion of the ASL experiment is to accurately measure the ASL signal change as quickly as possible. Because the ASL signal is so small, the largest consideration for ASL data acquisition is maintaining a high SNR. To achieve this, images are typically acquired at high field strength (3 Tesla) and with a low spatial resolution. Additionally, many averages of the control/label image pairs are acquired, with acquisition times ranging from 2-4 min.

A variety of readout strategies for 2D and 3D acquisitions have been employed in the literature. Most methods have very efficient and fast readouts, such as EPI and spiral.

Several readout schemes have been extensively used throughout the literature including

3D RARE stack-of-spiral, 3D GRASE, 2D EPI, and 2D spiral (60–64).

Section 3.2.5. Perfusion Quantification As stated previously, the difference in signal between the label and control images is directly proportional to perfusion. This perfusion-weighted image can be used to

qualitatively assess perfusion. In order to measure perfusion, a model can be used to

account for the inflow and outflow of labeled spins and T1 relaxation. The model should

also take into account the dynamics of the bolus of labeled spins and the timing

parameters of the acquisition.

The general model for ASL signal can be mathematically described by the Bloch

equations. Here, the change in signal in the tissue of interest is described by accounting

for the inflow of labeled arterial blood (Ma), the T1 relaxation affects, and the outflow of

blood:

( ) ( ) = + ( ) ( ) [3.11], 푑푀 푡 푀표−푀 푡 푓 푑푡 푇1 푓푀푎 푡 − 휆 푀 푡

where M is the longitudinal magnetization of tissue, Mo is the equilibrium magnetization

of tissue, Ma is the longitudinal magnetization of blood, T1 is the T1 of tissue, f is the

perfusion rate, and λ is the partition coefficient of water between tissue and blood. Note

that Ma(t) will contain information about the transit time of the label and relaxation of the

label during the transit time.

Both CASL and PASL methods acquire an image with and without a label. These images

are subtracted to indicate the change in signal due to ASL:

= [3.12],

푙푎푏푒푙 푐표푛푡푟표푙 where Mlabel is the longitudinal훥푀 magnetization푀 − 푀 after labeling pulses and Mcontrol is the

longitudinal magnetization after control pulses. Thus, equation 3.11 is typically solved in terms of ΔM.

Figure 3.7. General kinetic model for ASL. This model assumes an arterial input function that delivers a bolus of labeled spins to a single tissue compartment. The arterial input function in the general kinetic model described by Buxton, et al., only accounts for relaxation, but it can also account for dispersion. The tissue signal is modeled by describing relaxation and retention.

Buxton, et al., described a general kinetic model for ΔM that can be solved for both

CASL and PASL methods. Three separate functions are used to describe the arterial input function (c(t)), the relaxation (m(t)), and the fraction of tagged water in a voxel (r(t), also known as the residue function). These are described pictorially in Figure 3.7, and can be combined using a convolution function to describe ΔM:

( ) = 2 ( ( ) × [ ( ) ( )]) [3.13],

표푎 where Moa is the equilibrium훥푀 푡 arterial푀 magnetization푓 푐 푡 푟 푡and푚 f푡 is perfusion. The relaxation and residue functions are the same for both CASL and PASL. However, the arterial input function is dependent on the labeling. The general kinetic model assumes that the delivery of labeled spins occurs via uniform plug flow, where the arterial input function can be modeled as a rect function scaled by the labeling efficiency and longitudinal relaxation. The standard model can be described as:

( ) = 0 0 < < [3.14a]

푐 푡 푡 훥푡 ( ) = < < + [3.14b] −푡 �푇1푎 푐푃퐴푆퐿 푡 훼푒 훥푡 푡 휏 훥푡

( ) = < < + [3.14c] −훥푡 �푇1푎 퐶퐴푆퐿 푐 푡 훼푒( ) = 0 훥푡+ 푡 < 휏 훥푡 [3.14d]

푐 푡 휏 훥푡 푡 ( ) = [3.15] −푓푡� 휆 푟 푡 푒 ( ) = [3.16], −푡 �푇1 where α is the labeling efficiency,푚 푡 T1a is푒 the arterial T1, T1 is the tissue T1, f is perfusion,

and λ is the tissue/blood partition coefficient. The arterial input function also has two

timing parameters associated with the duration of the label (τ) and the arterial transit time

(Δt). For pulsed ASL, the duration of the label is related to the spatial extent of the

labeling and is generally unknown. For continuous ASL, the label duration is supplied

(and known) sequence parameter. The transit time is dependent on the gap between the

labeling plane and the imaging plane (which is different for PASL and CASL) and the

blood flow.

While this simple arterial input function is used frequently in ASL, it neglects many

physiological properties of tracer flow. For example, this does not account for dispersion

of the bolus. If desired, the arterial input function can be adapted to include terms for

dispersion as shown in Figure 3.7. This has previously been done using a gamma variate

function model, Gaussian kernels, or gamma kernels (65).

In order to solve for f using Equations 3.13-3.16, at least one pair of ASL images at time t

must be acquired and subtracted. In order for perfusion to be accurately quantified, there

are several parameters that would need to be known: T1 of tissue, T1 of blood, transit

time, label duration for PASL, and labeling efficiency. Because there are several

unknowns, perfusion is typically quantified by making several assumptions. First, the time (t) when data is sampled should be selected to be greater than Δt. This ensures that

the label has been delivered to the target tissue. Second, outflow of labeled water is

negligible. Third, the T1 relaxation is dominated by blood, such that T1a=T1. These simplifications allow for perfusion to be defined as:

= 푃퐿퐷 / / [3.17] �푇 휆 훥푀 푒( 1푎 ) 휏 − �푇 푓 2 훼 푇1푎푀표 1−푒 1푎 푚푙 푔 푠 for a CASL or pCASL experiment, and:

= 푇퐼 / / [3.18] �푇 휆 훥푀 푒 1푎 푓 2 훼 푇퐼 푀표 푚푙 푔 푠 for a PASL experiment. For the CASL/pCASL experiment, t is defined as the post-label

delay time (PLD). For PASL, t is defined as the TI time. Mo can be assumed to be 1, or it

can be measured by acquiring a proton density weighted image.

Section 3.2.6. Advantages/Disadvantages of ASL This technique is completely non-invasive and offers many advantages for both neurological research and clinical investigation (20,21). Specifically, this avoids problems with contrast-related contraindications (impaired kidney function).

Additionally, avoiding the administration of contrast agent allows for the ASL experiment to be repeated in the same exam.

However, ASL is infrequently used in the clinical environment largely because the very small signal changes due to perfusion are extremely difficult to measure. The problem can be partially countered by signal averaging and a low image resolution, but the associated increased in scan time is inefficient and can also lead to errors from patient motion. This also limits the potential applications, because ASL has been predominantly applied in areas with relatively high perfusion (where ASL signal would be larger).

Also, as can be seen in Section 3.2.2-3.2.3, proper implementation of an ASL sequence can be difficult. The sequences require exact implementation, and small problems in Bo and B1 homogeneities can cause large inefficiencies in labeling. Furthermore, there are several user-selected parameters that could lead to great variability in quantitative results.

For example, improper selection of the labeling location, labeling duration, and PLD in pCASL could lead to inaccurate perfusion values. A recent review of ASL techniques proposed current suggestions on these sequence parameters, although these may not work in all patients and situations (52).

Modeling the changes in the MR signal to quantify perfusion with ASL is complicated by several sources of error. For example, there are multiple unknown parameters that affect the ASL signal, such as T1 relaxation times and transit times of labeled blood.

Quantifying these parameters requires separate acquisitions that further increase exam time.

While there are several limitations ASL currently faces as a technology, the advantage of avoiding contrast agent can be really important in patients who cannot receive Gd or in patients (such as children) who are less compliant with IV injections. Because of these benefits, several techniques continue to be explored to improve the robustness and ease- of-implementation of ASL.

Chapter 4. Highly Accelerated Data Acquisition and Reconstructions Portions of this chapter were published in an invited review paper in the Journal of Magnetic

Resonance Imaging (66) and in an original research paper in the Journal of Magnetic Resonance

Imaging (67).

As described in Chapter 2, MRI is a relatively slow imaging modality. There are inherent

links between the scan duration, spatial resolution, field-of-view, and SNR. In clinical

MR imaging, high spatial resolution, large field-of-views, and high SNR are typically desirable. However, this leads to long exam times, which increases exam costs and is a large source of patient discomfort. This is also extremely problematic in many applications including DCE MRI and ASL. In the case of DCE MRI, time-resolved images are acquired with a high temporal resolution to accurately capture changes in concentration of contrast agents. Because of the need for a high temporal resolution, spatial resolution and/or volumetric coverage are typically sacrificed. In the case of ASL, many averages are needed in order to achieve the desired SNR, even with low spatial resolution. Thus, fast data acquisition schemes are desired to decrease the total scan duration.

One of the main objectives in this thesis was to explore methods that utilize highly accelerated data acquisition strategies and how these can be used to improve perfusion

MRI techniques. In this chapter, an introduction to several methods for accelerated data acquisition and reconstruction will be presented. These focus on methods employed in

Chapters 5-7, including the following accelerated acquisitions and/or reconstructions:

Partial Fourier and POCS, TWIST and view-sharing, parallel imaging, non-Cartesian trajectories, and non-Cartesian parallel imaging.

Section 4.1. Partial Fourier Acquisition and Reconstruction The Fourier transform of a real-valued image has conjugate symmetry. Thus,

( ) = ( ) [4.1], ∗ where S(-k) is the k-space signal푆 −at푘 location푆 푘 –k and S*(k) is the complex conjugate of

S(k). This symmetry in k-space can be used to accelerate image acquisition by acquiring

only half of the Cartesian phase encoding lines, and applying this property to reconstruct

the unsampled phase encoding lines. This use of conjugate symmetry to undersample and

reconstruct k-space is known as partial Fourier imaging (32–34,68,69).

Figure 4.1. Diagram of a partial Fourier acquisition. Here, k-space is asymmetrically sampled to accelerate

data acquisition. The missing k-space lines can be reconstructed by using the conjugate symmetry property

of k-space. A symmetric central region of k-space is also acquired to estimate the image phase for reconstruction.

In actual implementations, images are not real-valued, and phase information can be introduced from several factors including field inhomogeneities, motion, and coil sensitivies. This non-zero phase must be accounted for in the image reconstruction to avoid artifacts. Thus, a small symmetric region of central k-space lines is acquired to

estimate the unknown phase. A typical partial Fourier acquisition pattern is shown in

Figure 4.1. The acquisition is typically described by the fraction of phase encoding lines

collected. For example, a partial Fourier factor of 6/8 is commonly used, which indicates

that 25% of the phase encoding lines has not been sampled.

The simplest reconstruction of a partial Fourier acquisition is to replace the missing lines

with zeroes prior to performing the Fourier transform, which is referred to as zero

padding. This can provide reasonable image quality at low acceleration factors, but can

result in image blurring and Gibb’s ringing artifacts. In order to avoid these issues, partial

Fourier reconstruction methods use an estimate of the image phase (from the symmetric

central region) in addition to the measured k-space lines to reconstruct the missing lines.

One potential image reconstruction algorithm known as Projection Onto Convex Sets

(POCS) is described below:

1. The symmetrically sampled central region of k-space is used to generate a low

resolution phase estimate.

a. Apply Hanning or Hamming window on central region of k-space to

generate the signal for the phase estimate: Sph(k).

b. Perform inverse Fourier transform of the filtered k-space region to

-1 generate a low-resolution image: Iph(x) = F (Sph(k)).

c. The phase estimate can be calculated as the angle of the low-resolution

image: φ(x) = ph(x).

2. The phase estimate, φ∠I(x), and asymmetrically sampled k-space lines, Sorig(k), are

used to reconstruct the missing k-space data using the iterative POCS algorithm.

a. Initialize the algorithm with a zero-padded image (using Sorig(k)): Iest(x).

b. Multiply image with the estimated phase (from step 1c):

( ) = | ( )| ( ). 푖휑 푥 푒푠푡 푒푠푡 c. Perform퐼 푥 the퐼 푥Fourier∗ 푒 transform of the new estimated image:

Sest(k) = F (Iest(x)).

d. Replace the sampled signal region with the original data:

Sest(1:ksampled) = Sorig(k).

e. Perform the inverse Fourier transform to find a new estimate of the image:

-1 Iest(x) = F (Sest(k)).

f. If converged, Iest(x) is the final image. Otherwise repeat the process

described in steps 2b-2f until convergence is reached.

Figure 4.2 demonstrates a zero-padded and POCS reconstruction of partial Fourier images (partial Fourier factor of 5/8). In this particular reconstruction, one can see a noticeable blurring in the phase-encoding (anterior-posterior) direction of the zero- padded reconstruction. Despite having acquired 5/8ths of the total number of phase encoding lines, the POCS reconstruction better reconstructs the image.

Partial Fourier data acquisition can reduce imaging time and reconstruction methods like

POCS can reduce the related image artifacts. However, a main limitation of asymmetric sampling is that it has an associated loss in SNR. Additionally, if the image phase cannot be accurately estimated in the POCS reconstruction, there may be some residual image artifacts. A more detailed review of constrained partial Fourier reconstructions and a discussion of various reconstruction methods can be found in (32–34,68,69).

Figure 4.2. Reconstruction of an image with a partial Fourier factor of 5/8. The left image is the original fully-sampled image. The central image is reconstructed with POCS. The right image was reconstructed with zero-padding (missing lines replaced with zeros).

Section 4.2. Partial k-space Acquisitions and View-Sharing Reconstructions Many MRI applications, including MR angiography and DCE MRI, utilize time-resolved

data acquisitions. One method for accelerating data acquisition in these time-resolved

scans is to update segments of k-space at varying rates. These methods can be generally

described as ‘partial k-space updating acquisitions’, but are also commonly referred to as

keyhole imaging because the central region of k-space is typically updated more

frequently (34).

Keyhole imaging methods exploit k-space properties to reduce the amount of information

acquired in each individual time frame. Figure 4.3 demonstrates how various regions of

k-space contribute to a MR image (32). In the left column of Figure 4.3, a low frequency

region of k-space is sampled, which results in a low-resolution image that contributes a

majority of the image contrast. In the right column of Figure 4.3, the remaining high

frequency region of k-space is sampled, which provides much of the edge information.

While this high frequency information is important for reconstructing high resolution

images, keyhole imaging assumes that these high frequency regions have slower temporal

dynamics and can be updated less frequently. In certain applications like MRA and DCE

MRI, this assumption can be made because the changes in signal due to the arrival of

contrast agent mostly affect image contrast and therefore the central region of k-space, while the anatomical structure (and thus the edge information) is assumed stable during the acquisition.

Figure 4.3. Description of k-space properties relevant to keyhole acquisition techniques. In the left column,

a low frequency region of k-space is sampled, resulting in a low-resolution image that contributes a

majority of the image contrast. In the right column, the remaining high frequency region of k-space is

sampled, which provides much of the edge information.

Keyhole imaging updates the central region of k-space frequently, and subsamples the outer regions of k-space. This concept can be applied to 2D or 3D imaging, but the description in this chapter will focus on 3D Cartesian acquisitions. An example 3D

keyhole sampling pattern is shown in Figure 4.4. In Figure 4.4, a central region of k-

space readout lines (denoted as A) is acquired frequently. The outer region of k-space

(denoted as B) is undersampled, so only a fraction of the outer region is acquired between

each update of the A region. In the example in Figure 4.4, the outer region is

undersampled by a factor of 3, and 1/3 of the outer k-space lines are acquired between

each A sampling (denoted as B1, B2, B3).

Figure 4.4. This figure shows a schematic for the how data is undersampled in a 3D Cartesian keyhole acquisition. The red k-space region ‘A’ is updated at a high temporal resolution. The outer k-space region is updated less frequently. In this example, 1/3 of the ‘B’ region is acquired in B1, a different 1/3 of ‘B’ is acquired in B2, and the remaining 1/3 is acquired in B3.

Several implementations of keyhole imaging have been reported in the literature (70–74).

Each method uses a slightly different sampling scheme, but they still follow the same

concept of updating regions of k-space at various frequencies. In this section, an example

method known as TWIST (Time-resolved angiography With Stochastic Trajectories)

(75–77) is described, which is used in Chapter 5. This section also covers the use of a

view-sharing image reconstruction to compensate for the sub-sampled k-space regions.

Figure 4.5. Figure 4.5A describes the TWIST method for assigning k-space readout lines to regions ‘A’ and

‘B’. Figure 4.5B shows an example sampling scheme where the black points represent the readout lines in the ‘A’ region that are updated in every frame. The colored points represent the readout lines in the ‘B’ region that are subsampled by a factor 3. Figure 4.5C demonstrates the view-sharing reconstruction where data is copied across frames to fill missing lines.

TWIST data acquisition is described in Figure 4.5. Figure 4.5B displays a diagram that is

a 2D description of a 3D Cartesian trajectory, where each point on this phase encoding

plane represents a readout line. The black points in the center of the phase encoding plane

represent the readout lines in the ‘A’ region that are updated in every frame. The colored

points represent the readout lines in the ‘B’ region that are subsampled. The sampled

readout lines are sorted into ‘A’ and ‘B’ regions based on their radial distance and

angular orientation as shown in Figure 4.5A.

For each Cartesian readout line, a radial distance from the center (kr) and an azimuthal

angle (ϕ) are defined. All readout lines are then sorted first by their kr value and then by

their ϕ value. The user can define the cutoff point (kA) to select how many points will be

fully-sampled in the ‘A’ region of each frame. All readout points with kr ≥ kA will be assigned to the ‘B’ region, which will be undersampled in each frame. The user must also define the undersampling factor (N) used in the ‘B’ region. In each frame, a disjoint and non-overlapping subset of the data will be acquired such that all frames contain 1/N of the readout lines in B. In the TWIST acquisition, this outer region of k-space is sampled in a pseudo-random manner that was designed to maintain relatively even coverage of outer k-space in each frame. To assign points to a B region, the sorted readout points are sequentially assigned to a ‘B’ subset. The example in Figure 4.5B has an undersampling factor of N=3, where 1/3 of the ‘B’ region is acquired in each frame and all k-space

points in ‘B’ are acquired in these 3 neighboring frames. In summary, there are two

sequence parameters (pA and pB) that must be selected to define the total undersampling

in a TWIST acquisition:

= ( , ) [4.2] , 푘퐴 , 푝퐴 max 푘푃퐸 푚푎푥 푘푃푎푟 푚푎푥 58

and

= [4.3]. 1 푝퐵 푁 The missing k-space lines present in Figure 4.5B are reconstructed using a method called

view-sharing. Because each subset of ‘B’ is sampled in a disjoint fashion, the outer k-

space regions do not overlap in neighboring frames and can be shared to generate a fully

sampled k-space. This process is shown in Figure 4.5C, where the ‘B’ regions in frames 1

and 2 are copied into frame 3 to fill in the missing readout lines.

For view-sharing reconstructions, it is important to define the temporal resolution and

temporal footprint of the data. The temporal resolution is defined as the acquisition time

of one frame (time to acquire the ‘A’ region and one ‘B’ subset region). The temporal

footprint is defined as the total time needed to acquire the ‘A’ region and all ‘B’ regions

needed to fully-sample the outer k-space region. For the example in Figure 4.5B-C, the temporal resolution for frame three would be t3, and the temporal footprint would be t1 +

t2 + t3.

A view-sharing reconstruction can be advantageous because the overall image SNR is not

reduced even at higher acceleration factors. However, as mentioned previously, these

keyhole methods emphasize high temporal fidelity in only the central region of k-space.

The view-sharing reconstruction shares data across a large temporal footprint, which can

cause artifacts related to temporal blurring (77). If pA and pB are chosen to be very

small, substantial image artifacts can occur.

Section 4.3. Parallel Imaging

Section 4.3.1. Parallel Imaging Introduction Parallel imaging reconstruction methods were introduced in the late 1990s, and have

since become some of the most effective methods for reducing clinical scan times. These

techniques rely on the use of a multi-channel receive array to acquire images. The additional spatial encoding information from the coil array is then used to reduce the number of acquired phase encoding lines.

More specifically, data are accelerated by skipping k-space lines in the phase encoding direction. Regularly undersampling the k-space data results in aliasing artifacts in the image domain. Parallel imaging techniques use information about the coil sensitivities to reconstruct an unaliased image from undersampled data. While many different methods have been proposed, this section will introduce two of the seminal parallel imaging techniques: SENSE (Sensitivity Encoding) (78) and GRAPPA (Generalized

Autocalibrating Partially Parallel Acquisition) (79). SENSE is applied in the image

domain to unfold aliasing artifacts caused by the undersampling. GRAPPA is applied in

k-space to reconstruct missing k-space lines.

Regardless of the reconstruction method employed, all parallel imaging methods have

several similarities. Data are acquired using an array of multiple independent coils, and

each receiver coil has a different spatial sensitivity over the FoV as shown in Figure 4.6.

Additional knowledge about the coil sensitivities is required for the image reconstruction.

Undersampling the data by a factor R results in a reduction of image SNR by a factor of at least √R.

Figure 4.6. The left image shows the object being imaged (a brain) and a cartoon illustrating a circular array of eight receive coils. Each coil has its own spatially localized sensitivity. For example, the center and right images show single coil images for two neighboring coils. The sensitivity for each coil will be highest near the coil. The resulting single coil image is the product of the coil sensitivity profile and the object.

Section 4.3.2. Sensitivity Encoding (SENSE) SENSE reconstructions use the additional spatial encoding information from a multi-coil array to reconstruct unaliased images in the image domain. SENSE describes a system of equations that relate the coil sensitivities, gradient encoding, and acquired aliased pixels to a vector of unaliased pixels. If the acceleration factor is less than the number of coils used to acquire the images, this relationship is fully-determined and the unaliased pixels can be reconstructed. For instance, if a data acceleration rate of two is used in a Cartesian scan, aliasing occurs along the phase encoding direction, and two pixels in the image fold together. However, if an eight-channel receiver coil is used to collect the data, there are eight separate estimates for each pixel, which can be used to unfold the two aliased pixels from each other. In this case, despite the data undersampling, the system of equations is over-determined by a factor of four, which allows the reconstruction of unaliased images.

Additionally, the more over-determined the system of equations is, the better the reconstruction results will be.

The SENSE formulation uses a system of equations relating the object to be imaged (v),

the acquired k-space data (m), and the encoding matrix which transforms the image to k-

space (E):

= . [4.4]

The acquired data m has size ncnk, where퐸푣 nc is 푚the number of coils and nk is the number of

sampled positions in k-space. The reconstructed image vector v has size N2, where N is the matrix size of the image. The encoding matrix E accounts for all spatial encoding information from gradients and coil sensitivities, and can be described as a combination of the Fourier terms and sensitivity weighting from the array of coils:

E = e C (r ), [4.5] ikκrp th th l p where rp is the p image pixel, kκ is the κ k-space value, and Cl(rp) is the coil sensitivity

of coil l at pixel rp.

In order to solve for the reconstructed image v in Equation 4.4, the system of equations

2 2 must be fully determined, such that ncnk≥ N . If the data are fully-sampled (nk≥ N ), this

relationship is fully-determined, and an image can be generated even when using a single

coil for data collection. If m is undersampled to accelerate data acquisition and nk is reduced to nk/R, this system of equations can still be theoretically solved as long as the

acceleration factor is less than the number of coils used to acquire the data, such that

2 ncnk/R≥ N . With undersampling in Cartesian imaging along one phase encoding

direction, this simplifies to nc ≥ R.

The original SENSE manuscript proposed a general theory to solve for v using Equation

4.4. This general theory can be applied for any arbitrary k-space trajectory, and is

explained in detail in Section 4.5.2. For the Cartesian case, this can be largely simplified

(and easily solved) because the encoding and undersampling are along a single direction

in k-space. With a Cartesian acquisition and an acceleration factor R, each pixel in the aliased image I will contain information from R pixels with equidistant spacing of

FoV/R. Equations 4.4 and 4.5 can be rewritten in terms of the aliased image I:

= , [4.6] where the matrix C represents the coil sensitivities퐶푣 퐼 at the R pixel locations that are aliased together (size nc x R), v represents the reconstructed image pixels (size R x 1), and I

represents the multi-coil pixel values from the aliased image (size nc x 1). Equation 4.6

describes a set of nc linear equations that has R unknowns, and is described pictorially in

Figure 4.7.

Figure 4.7. This figure shows a pictorial representation of Equation 4.6. For a Cartesian scan with R=2 and

4 receive coils, the data from the scanner is shown as a multi-channel aliased image I. Every pixel in I will contain information from two pixels that are spaced by FoV/R in the fully-sampled image v (example marked by yellow squares in I and v), and these two pixels will be weighted by the coil sensitivity profiles

(matrix C). To perform the SENSE reconstruction, the fully-sampled coil sensitivity profiles (C) are measured in addition to I. Because there are four separate estimates of the two pixels aliased in each pixel in I, the two unaliased pixels in v can be solved for by performing the pseudo-inverse (Equation 4.7).

The image can then be reconstructed by performing the Moore-Penrose inversion:

= ( ) . [4.7] 퐻 −1 퐻 SENSE reconstructions have been푣 successfully퐶 퐶 퐶 ∗employed퐼 in countless applications to reduce imaging time. However, they do have some limitations. At high acceleration factors, SENSE reconstructions can have residual aliasing artifacts and noise amplification because Equation 4.4 becomes less overdetermined. Another limitation of

SENSE is the requirement that the coil sensitivities must be accurately measured. This is typically done by using a pre-scan prior to acquisition of the undersampled data. It can be particularly difficult to measure coil sensitivities in tissues with low signal (lung, bowels, etc.), and coil sensitivities may be inaccurate if there is motion between acquisition of the pre-scan and the undersampled data. Inaccuracies in the coil sensitivity measurements can also lead to residual aliasing artifacts.

Section 4.3.3. Generalized Autocalibrating Partially Parallel Acquisition (GRAPPA) GRAPPA is a parallel imaging reconstruction method that mitigates aliasing artifacts by reconstructing the k-space lines that were skipped in order to accelerate data acquisition.

Once these missing k-space lines are computed, an unaliased image can be reconstructed by applying the Fourier transform.

Because GRAPPA is implemented in k-space, it is important to consider coil sensitivity information in the spatial frequency domain. As depicted in Figure 4.6 in the image domain, an image acquired by a single surface coil is equal to the product of the object and the coil sensitivity profile. If this operation is considered in k-space, the Fourier transform of the object is convolved with the Fourier transform of the coil sensitivity profile. This convolution essentially spreads information across neighboring data points throughout k-space. Furthermore, this occurs in the same pattern throughout k-space. The

GRAPPA reconstruction algorithm takes advantage of this property by using the

information from acquired k-space data (S(ky)) to estimate neighboring k-space points that were not acquired (S(ky - mΔky), where m is an index counting from 1 up to R-1).

In GRAPPA, a kernel of acquired points for all coils (source points) are used to estimate a single missing point for a single coil (target point), and this process is repeated for each coil to reconstruct this target point for all coils. Figure 4.8 shows a schematic of the

GRAPPA reconstruction. A kernel of source points (shown with a kernel size of nc x 2

phase encode points x 3 readout points) is linearly combined to estimate a target point for

one kernel. It is important to note that this kernel is exactly replicated in all regions of a

Cartesian k-space. Regardless of the k-space location, the difference in spatial harmonics

between source and target points is the same. Thus, the kernel is moved through k-space

in a raster-like fashion to reconstruct all missing k-space points. This is described by the following equation:

, , + = ( , , , ) , + , + , 푛푐 푇푎푟푔 푗 푥 푦 푦 푙=1 푏푥 푏푦 푥 푦 푆표푢푟푐푒 푙 푥 푥 푦 푦 푆 �푘 푘 훥푘 � ∑ ∑ ∑ 푤 푗 푙 푏 푏 푆 �푘 푏 푘 푏 � [4.8]

where w is the GRAPPA weight, R is our acceleration factor, and l and j are the coil

indices. bx and by are the kernel indices for a 2D GRAPPA kernel, where a 2x3 kernel

size would have bx values of [-1 0 1] and by values of [0 R]. , , + refers

푆푇푎푟푔 푗�푘푥 푘푦 훥푘푦� to a target point for the jth coil, and , + , + refers to a source point

푆표푢푟푐푒 푙 푥 푥 푦 푦 for the lth coil. This can be simplified푆 by describing�푘 this푏 푘in matrix푏 � form:

= . [4.9]

푆푇푎푟푔 푤푆푆표푢푟푐푒

As can be seen in Equations 4.8 and 4.9, the GRAPPA weight set (w) will have size: (nc x nc x kernel size), and R-1 different weight sets will be needed to reconstruct the missing k-space data. So in the example in Figure 4.8, 3 coils are used to acquire the data with an acceleration factor of 2, and the total number of source points in the kernel is 6. Thus, one weight set with a matrix size of 3 x 3 x 6 will be used to reconstruct k-space.

Figure 4.8. This is a pictorial explanation of the GRAPPA reconstruction method. The left column shows how GRAPPA uses a kernel of source points from several neighboring k-space locations and all coils to estimate a single target point for a single coil. These points are linearly combined using the GRAPPA weight sets. These GRAPPA weights are determined by acquiring a region of k-space that is fully-sampled

(as shown on the right). In both data reconstruction and GRAPPA weight estimation, it can be seen here that each kernel is exactly the same in all regions of k-space. Therefore, GRAPPA weights can be determined by rastering the kernel through a fully-sampled region of k-space (shown by small rectangles), and those same weights can be applied to all kernel locations in the undersampled data to reconstruct the missing points.

In order to solve for missing k-space data, the GRAPPA weight sets must be known. To

determine the relationship between neighboring k-space lines, a small region in the center of k-space is typically fully-sampled (known as the auto-calibration signal or ACS). This

is also shown in Figure 4.8 (right). The GRAPPA kernel can be moved through the ACS

region in a raster-like fashion to build the linear system of equations in Equation 4.9

where the source and target points are known. The Moore-Penrose inversion can then be

applied to Equation 4.9 to solve for the GRAPPA weight sets:

( ) = . [4.10]

푆푇푎푟푔 ∗ 푝푖푛푣 푆푆표푢푟푐푒 푤 To solve for the weight sets, Equation 4.10 must be fully-determined. This requires that the ACS region must be sufficiently large to produce many occurrences of the kernel. At minimum, there must be (nc * number of kernel points) occurrences of the fully-sampled

kernel in the ACS region. In the example in Figure 4.8, this would mean that the ACS

data must have at least 18 kernel occurrences. However, if Equation 4.10 is over

determined and the number of kernel occurrences is much larger than 18, the estimate of

the GRAPPA weight sets will be more accurate and more stable.

The GRAPPA reconstruction method has been heavily used to reduce image acquisition

time clinically over the last decade. However, it does have some limitations. Similarly to

SENSE, it also has suffers from residual aliasing artifacts at high acceleration factors. In

contrast to SENSE, GRAPPA does not require estimation of the coil sensitivity profiles.

This can be an advantage for GRAPPA in situations where the coil sensitivities can be

difficult to measure such as in areas with low signal.

Section 4.4. Non-Cartesian Trajectories Almost all clinical MR imaging is performed by acquiring k-space along a Cartesian, or

rectilinear, trajectory. Data are sampled line-by-line on a rectangular grid as shown in

Figure 4.9. A benefit of this sampling trajectory is that the data are uniformly sampled,

and images can be easily and quickly reconstructed using a fast Fourier transform (FFT).

However, k-space can also be sampled in an arbitrary non-Cartesian manner, and different sampling trajectories will have different properties and implications for the reconstructed image. Many non-Cartesian trajectories have been explored, including but not limited to radial/projection (80,81), spiral (82,83), rosette (84),

BLADE/PROPELLER (85), and stochastic (86) trajectories. Figure 4.9 depicts a radial and a variable-density spiral acquisition.

Sampling along a non-Cartesian trajectory can have many benefits based on the unique

properties of these trajectories. One of the most important properties of non-Cartesian

trajectories is their potential for efficient use of MR gradient hardware and therefore

rapid coverage of k-space. For example, spiral trajectories are able to collect a larger

portion of k-space for a given readout duration. With more k-space coverage per readout

(a spiral readout can also be called a ‘shot’), the total number of shots acquired can be

decreased in order to reduce the total scan time.

Another important property of non-Cartesian trajectories is that they contain fewer

coherent artifacts from undersampling (87). This means that aliasing artifacts are less

destructive to image quality than in the Cartesian case, and mild undersampling can be

used without a specialized reconstruction (87). This is demonstrated in Figure 4.9, where

an undersampling factor of 3 is shown for Cartesian, radial, and spiral acquisitions. While

all images have aliasing artifacts, the non-Cartesian sampled data has less coherent

aliasing than the Cartesian.

Figure 4.9. The left column shows three undersampled trajectories: Cartesian (top), radial (center), spiral

(bottom). The right column demonstrates aliasing artifacts for these trajectories in a head image.

Additionally, many non-Cartesian trajectories have application-specific benefits. They

are less affected by motion (81,88) and allow image contrast to be updated throughout

data acquisition (89). Non-Cartesian acquisitions can also enable motion correction (85),

self-navigation (90,91), ultra-short TE acquisitions (92), spectrally selective imaging

(84), and chemical shift imaging (93).

While non-Cartesian trajectories have many advantages, it is considerably more difficult to reconstruct images from non-Cartesian data because the non-Cartesian data points do

not fall on a grid in k-space. There are many approaches for reconstructing non-Cartesian data (94–100). All non-Cartesian reconstructions performed in this Chapters 6-7

employed the non-uniform fast Fourier transform (NUFFT) (94), which has been made

available in an open-source toolbox (101).

Section 4.5. Non-Cartesian Parallel Imaging

Section 4.5.1. Non-Cartesian Parallel Imaging Introduction As described above, non-Cartesian trajectories can be used to increase acquisition speed

by sampling k-space more efficiently, and data acquisition can be further accelerated by

undersampling these non-Cartesian trajectories. While low levels of undersampling can

often be tolerated (87), the resulting aliasing artifacts from highly undersampled data

must be mitigated to achieve clinically acceptable image quality. As described in Section

4.3, parallel imaging algorithms have been applied to undersampled Cartesian data

(78,79,102) to reduce aliasing artifacts by using the additional spatial information

provided by an array of receiver coils. Combining parallel imaging reconstruction

algorithms with highly accelerated non-Cartesian trajectories would combine the benefits

of both methods, allowing much faster imaging speed than is possible with either method

alone.

Non-Cartesian parallel imaging uses the same general approach as Cartesian parallel

imaging by taking advantage of additional spatial information from coil sensitivities for

the reconstruction of undersampled non-Cartesian data. However, applying these

algorithms to undersampled non-Cartesian data is not trivial. As described above, the

aliasing is more complicated with trajectories such as radial and spiral. As will be seen

later, this more complex aliasing can complicate SENSE reconstructions, and the non-

uniform undersampling throughout k-space can complicate GRAPPA reconstructions.

Thus, traditional parallel imaging techniques must be adapted for use with undersampled

non-Cartesian trajectories. The most commonly-used non-Cartesian parallel imaging

algorithms are similar to existing Cartesian parallel imaging methods in approach and

general properties, and thus a complete review of these basic methods is beneficial to

understanding non-Cartesian parallel imaging and can be found in Section 4.3 or in

review papers such as: (103–105).

In addition to increased imaging speed, non-Cartesian parallel imaging offers a number of other potential advantages over Cartesian approaches. The g-factor, which describes the noise enhancement resulting from the use of a parallel imaging algorithm, is significantly lower for non-Cartesian trajectories than for Cartesian data at the same data reduction factor (106). The relative retention of SNR is due to the fact that the acceleration is divided between two directions in 2D non-Cartesian imaging, whereas acceleration is performed in one direction (the phase encoding direction) in Cartesian imaging. The division of acceleration among several directions enables the coil sensitivities to be used more effectively. Additionally, because typically employed non-

Cartesian trajectories are oversampled in the center of k-space, the full acceleration is only realized at the periphery of k-space. As the high-signal k-space center is completely captured even in undersampled datasets, less noise enhancement is seen in highly accelerated non-Cartesian parallel imaging reconstructions. These factors allow higher data reduction rates to be employed with non-Cartesian trajectories than when using standard Cartesian parallel imaging, warranting the use of more complex non-Cartesian approaches.

It is instructive to briefly examine the various types of non-Cartesian parallel imaging algorithms and to categorize them for comparison. Non-Cartesian parallel imaging reconstructions can be performed in the image domain (107–110) or in k-space (110–

119), use direct (108,111,112,114–119) or iterative (109,110) algorithms, and employ coil sensitivity information (108,109,111,112) or k-space autocalibration data

(110,114,115,117–119). While there are many effective reconstruction algorithms, two

representative methods will be reviewed in this section, namely Conjugate Gradient

SENSE (CG SENSE) (109) and non-Cartesian GRAPPA (117–120). CG SENSE works in the image domain using an iterative algorithm and requires coil sensitivity information.

Non-Cartesian GRAPPA techniques reconstruct missing data in k-space using a direct reconstruction approach, and require autocalibration data.

Section 4.5.2. Conjugate Gradient SENSE (CG SENSE) The SENSE algorithm was introduced in Section 4.3.2. This algorithm can be adapted for use with non-Cartesian data (109,121) and is summarized in-depth below. CG SENSE is

based on the SENSE algorithm, and is used to unfold aliasing artifacts resulting from

undersampled non-Cartesian data using explicit knowledge of coil sensitivity information

(78).

As mentioned previously, the difficulty in performing non-Cartesian parallel imaging

with a SENSE reconstruction stems from the complicated aliasing that must be unfolded.

Theoretically, any of the image pixels can be aliased with any other pixel, which makes

the unfolding matrices extremely large. While the original mathematical concepts in

SENSE still apply to non-Cartesian data, solving the unfolding problem directly would be

extremely computationally intensive. Thus, Pruessmann et al. proposed using the

conjugate gradient (CG) algorithm (122) as an iterative approach for the reconstruction.

The mathematical basis of this algorithm has been previously described in references

(105,109), and is summarized below.

Recall the general SENSE formalism described in Equations 4.4 and 4.5 in Section 4.3.2.

CG SENSE will also be solving for the reconstructed image v by using the encoding

matrix E and the acquired undersampled image m. In this case, we have a non-Cartesian

or arbitrary trajectory that has undersampling in more than one k-space direction. The

2 system of equations must be fully determined, such that ncnk≥ N .

To more easily formulate the CG SENSE reconstruction problem, a matrix F is

introduced to ‘undo’ the encoding, such that:

FE = , [4.11]

where F is the reconstruction matrix and Id isId the identity matrix. An unaliased image can be found by multiplying both sides of Equation 4.4 by the F matrix, which can be expressed by:

v = F m. [4.12]

The reconstruction matrix F can be computed by using Equations 4.5 and 4.11 and a

Moore-Penrose inversion:

F = (E E) E , [4.13] H −1 −1 H −1 where ψ is the sampling noise matrix, whichψ can obtainedψ from noise measurement data

as described in reference (109). While this formulation gives the reconstruction matrix

for the optimal SNR reconstruction, the equations can be simplified by approximating the

noise matrix ψ by the identity matrix:

F = (E E) E . [4.14] H −1 H

With this version of the reconstruction matrix, Equation 4.12 can be rewritten to avoid

the computationally inefficient matrix inversion:

(E E)v = E m. [4.15] H H This set of equations can now be solved using CG without the need to explicitly write out

or invert the E matrix. Instead, the function of the encoding matrix can be replicated by

applying the Fourier transform and coil sensitivity matrices (or their inverses). Because

the data in the v matrix are non-Cartesian, the FFT cannot be used to transition between k-space and the image domain. Thus, a gridding step or some additional interpolation

must be performed so that data are on a Cartesian grid prior to applying the FFT.

The CG SENSE reconstruction process can also be made more efficient by utilizing preconditioning. Here, pre-conditioning involves including terms for density and intensity compensation. Density compensation is applied by including a matrix D, which is a diagonal matrix containing the values of the DCF, to account for differences in the density of the sampling trajectory. Intensity compensation corrects for the sum-of-square weighting that exists due to coil sensitivity variations. A diagonal matrix I containing the inverse square-root of the coil weightings (known from the coil maps) is used to compensate for these intensity differences. Including these terms to Equation 4.15 leads to the following formulation:

( )( v) = E D m . [4.16] H −1 H A summary of the CG SENSE algorithmIE DEI isI depictedI in the diagram shown in Figure 4.10.

Figure 4.10. A summary of the CG SENSE algorithm, which reconstructs an image from undersampled non-Cartesian data. Undersampled, multi-channel k-space data (m1, m2,…,mnc) are acquired and fed into the algorithm. These data are density compensated, gridded, the inverse Fourier transform calculated, and the multi-coil images are multiplied by the conjugate of the coil sensitivities. The multi-coil images are summed and intensity corrected to produce a single image, which is fed into the CG algorithm. The CG algorithm finds a new estimate for the reconstructed image. If the reconstruction has not converged, intensity correction is applied, the image is multiplied by the coil sensitivities, the Fourier transform is calculated, the data are degridded, the original data replaced, and the next iteration begins. This process continues until the reconstruction converges and a stopping criterion has been met. Once the stopping criteria are met, intensity correction is applied, and the result is an unaliased image.

CG SENSE has many advantages including that it does not require alterations based on the sampling trajectory, which is simply supplied as an input to the algorithm for the gridding process. Additionally, the output of the algorithm is a reconstructed Cartesian image where the coils have been combined. Thus, no additional reconstruction steps, such as a NUFFT or coil combination, are necessary after the parallel imaging algorithm is complete.

While CG SENSE is a commonly-used parallel imaging reconstruction method, it does have some limitations. One challenge when applying CG SENSE is the need for coil

75 sensitivity maps, which are required for all SENSE reconstructions. Accurate coil maps can be difficult to obtain in certain applications, which can negatively impact the resulting image quality. For example, it can be difficult to estimate coil sensitivity maps in image areas with low signal or in applications where patient motion may occur. These errors will manifest as residual aliasing artifacts in the reconstructed image.

Section 4.5.3. Non-Cartesian GRAPPA Similar to the development of CG SENSE, non-Cartesian GRAPPA reconstruction algorithms have also been proposed to combine the benefits of parallel imaging reconstructions with non-Cartesian sampling. The basic principles of non-Cartesian

GRAPPA are very similar to those in Cartesian GRAPPA (Section 4.3.3), where missing non-Cartesian k-space data are reconstructed by performing a linear combination of acquired non-Cartesian data. For both Cartesian and non-Cartesian data, Equations 4.9-

4.10 are used to estimate a missing target point using acquired source points and

GRAPPA weights.

As noted in Section 4.3.3, Cartesian undersampling results in a uniform GRAPPA kernel geometry in all parts of k-space. Therefore, the same GRAPPA weights can be applied everywhere, and GRAPPA weights only need to be computed for a single kernel geometry. In contrast, non-Cartesian undersampling results in kernels that no longer have a uniform geometry throughout k-space. The kernel geometry is dependent on both its location along a projection and its angular orientation as seen in Figure 4.11. The change in spatial harmonic information is no longer the same in all kernels, so GRAPPA weights are different for each target point and would theoretically need to be calculated separately. Additionally, calibration of GRAPPA weights must be adapted because the kernel geometry appears only once in each fully-sampled non-Cartesian dataset. Thus, in

order for Equation 4.10 to be fully determined for each target point, different strategies

for GRAPPA weight calibration and acquisition of ACS data must be considered.

The first implementation of non-Cartesian GRAPPA used a radial acquisition, and was used to reconstruct missing radial projections (120). In order to calibrate the GRAPPA weights, a single, fully-sampled radial dataset was acquired as ACS data in addition to the accelerated data. The calibration approach proposed in (120) took advantage of the fact that the change in kernel geometry is small throughout k-space. Therefore, one can approximate a small k-space region as Cartesian. In these Cartesian-like regions, multiple similar kernel replicas can be extracted by moving the kernel through a segment of the fully-sampled ACS radial k-space, as shown in Figure 4.11 (117,120). For example, in a

segment size of 1 projection x 4 read points, the kernel is shifted along a single projection

to four different readout points such that there are a total of four kernel occurrences per

receiver coil.

It is important to note that this method has an inherent tradeoff during GRAPPA weight calibration. If a large segment is used, many kernel occurrences can be found by shifting the kernel through k-space (Equation 4.10 is more over-determined). However, a large

segment can no longer be approximated as Cartesian. Thus, when selecting the size of the

segment, the user must balance the improvement in weight accuracy by increasing the

number of kernel occurrences by using a large segment and the degradation of accuracy

when kernel geometries are too dissimilar within that large segment.

Figure 4.11. This figure is a pictorial description of non-Cartesian GRAPPA calibration (shown for a radial acquisition). The top row shows an example of three kernels from different k-space locations. Although they have the same size (2 projections x 3 readout points), their geometry is dependent on their respective location along the projection and their angular orientation. While each kernel has its own unique geometry, kernels located next to each other (shown in second row) have a more similar geometry. Assuming that these geometries are the same, a small segment can be used for through k-space GRAPPA weight calibration (third row, left). The k-space segment for through k-space calibration is shown by a dashed line, and the red kernel can be shifted within the segment to generate multiple kernel occurrences to solve for the

GRAPPA weights. Alternatively, more than one fully-sampled k-space can be acquired, and the kernel geometry is exactly replicated in each frame (third row, right). Here, the kernel can be selected in each frame to generate multiple kernel occurrences to solve for GRAPPA weights.

Recently, a new approach to non-Cartesian GRAPPA weight calibration was proposed

that used more than one fully-sampled non-Cartesian dataset as ACS data (117,118).

Instead of acquiring a single, fully-sampled dataset for calibration, multiple time frames

can be acquired for through-time calibration, as shown in Figure 4.11. This through-time

calibration data contains exact replications of kernel geometries in each temporal

repetition. These can be used to accurately estimate GRAPPA weights, and has been

shown to provide excellent image quality (117). The main drawback to through-time

calibration is that it requires additional calibration time, and thus there is always interest

in minimizing this calibration time while preserving the highest image quality.

Chapter 5. Simultaneous MR Angiography Exam and Perfusion Measurement The work described in this chapter was published as original research in the Journal of

Magnetic Resonance Imaging (123).

Section 5.1. MRAP Introduction Vascular pathologies can affect large and small vessels, and can manifest as perfusion

deficits from downstream effects of large vessel disease or directly from small vessel

disease. Thus, for comprehensive vascular evaluation, both large and small vessels should

be assessed. Magnetic Resonance Angiography (MRA) depicts large arteries and has

been widely used to assess arterial pathology (76,124–126). However, the

microvasculature cannot be assessed on MRA images, as the spatial resolution is

insufficient to depict sub-millimeter vessels. Instead, quantitative perfusion

measurements provide evaluation of the microvasculature as an aggregate over the voxel volume. MR perfusion measurements are most commonly performed using dynamic

contrast-enhanced (DCE) techniques (30,44,127), in which pharmacokinetic analysis of

the administered contrast agent is used to quantify perfusion. With these techniques,

noninvasive vascular MR imaging, specifically MRA and DCE MRI perfusion, can be

used to separately assess the macro- and microvasculature. For example, perfusion has

been used along with renal MR angiography to grade the effect of renal artery stenosis on

parenchymal perfusion using two gadolinium injections (13). Since most MRA and

perfusion exams each use a separate, full-dose contrast bolus, the two studies may need to

be performed on different days to avoid contamination of the second exam and contrast

double-dosing. These factors effectively preclude the use of MRI to evaluate both

microvascular and macrovascular components of disease simultaneously. Thus, the

multifactorial etiologies of vascular pathologies such as peripheral arterial disease (PAD)

have been incompletely explored.

Time-resolved magnetic resonance angiography (trMRA) techniques are performed by

acquiring 3D images at several time points to dynamically visualize arterial anatomy at

different phases of contrast arrival. These images also contain high spatial resolution data on tissue enhancement. In this study, it was hypothesized that this tissue enhancement

can be used for direct, quantitative, DCE perfusion analysis. However, trMRA image

acquisitions are optimized for visualizing vascular anatomy and not DCE analysis. The

challenge in a simultaneous approach is maintaining high spatial resolution needed to

visualize the vasculature while also achieving high temporal resolution and sufficient

tissue signal-to-noise ratio (SNR) to accurately capture changes in contrast agent

concentration needed to estimate perfusion. In this study, a technique is introduced (MR

Angiography and Perfusion, MRAP), which attempts to meet the stringent needs of both

exams. By simultaneously acquiring angiography images and calculating a quantitative

perfusion parameter, MRAP accomplishes both small and large vessel assessment in a

single exam and contrast dose. MRAP is applied in the legs, and the feasibility of

robustly acquiring both an MRA and measuring quantitative physiological perfusion

differences are demonstrated in asymptomatic volunteers.

Section 5.2. TWIST Data Acquisition and Reconstruction To maintain high spatial resolution and 3D coverage while achieving high temporal

resolution, a view-sharing method known as Time-resolved angiography With

Interleaved Stochastic Trajectories (TWIST) can be employed (76). As described in

section 4.2, TWIST utilizes differential sampling of central and outer regions of k-space

(referred to as "A" and "B" regions, respectively) with a view-sharing reconstruction.

Because this is a 3D Cartesian acquisition, it can also be combined with a partial Fourier acquisition and parallel imaging to generate time-resolved 3D images with high spatial and temporal resolution.

Each of these undersampling and reconstruction techniques has a different effect on the image quality. With parallel imaging, there is an associated loss of SNR, and images can contain residual aliasing artifacts. While view-sharing does not have these problems, the resulting images use information from a longer time period, which causes temporal blurring and related artifacts. Because TWIST combines these techniques, the degree of undersampling from each technique should be optimized to meet the acquisition requirements while balancing their respective limitations.

A brief study was performed to select a sampling strategy for MRAP using TWIST combined with parallel imaging and partial Fourier (128). Sequence parameter selection was evaluated via simulation and experiment to make the acquisition more sensitive to perfusion changes in the muscle while preserving MRA quality. The effects of undersampling and reconstruction techniques on image quality and the accuracy of perfusion quantification were optimized to determine an acceptable range of parameters to be utilized.

Section 5.2.1. Methods The effects of varying the TWIST, GRAPPA, and partial Fourier undersampling parameters on the image acquisition and perfusion measurements were studied. A simulated 4D phantom was generated with dynamic signal intensity that is similar to the contrast dynamics seen in vivo in skeletal muscle. Simulated coil sensitivities for 21 total coils (which mimic those seen in a Siemens peripheral coil set-up) were applied.

TWIST acquisition parameters were varied such that the fractional size of the center

region (pA) was 20, 25, 33, and 50% and the outer k-space region was shared across 2-5

frames. GRAPPA acceleration factors of R=1, 2, and 3 were used in the phase and

partition encoding directions. A partial Fourier acquisition was applied in the phase

encoding direction using a factor of 6/8.

The undersampled simulated data were reconstructed using view-sharing, GRAPPA, and

POCS (see Chapter 4). The resulting images can be compared to the original reference

images to calculate the errors from the reconstruction algorithms. Here, error is reported

in terms of artifact power (AP), which can be defined as:

( ) = , [5.1] ( ) 2 푎푏푠�푖푚푎푔푒푇푊퐼푆푇−푖푚푎푔푒푟푒푓� 2 퐴푃 푎푏푠�푖푚푎푔푒푟푒푓� where imageTWIST are the undersampled and reconstructed images and imageref are the

original fully-sampled simulated images. The reconstructed images were then segmented

to generate regions simulating blood and muscle tissues, and the pharmacokinetic

analysis was performed (for details on the pharmacokinetic analysis, see section 5.3.1) to

evaluate errors in perfusion. The error in Ktrans was estimated for each simulation.

Because the simulation results are heavily dependent on the simulated images and the simulated coil sensitivities, two selected parameter settings were tested in vivo to select the final acquisition parameters. One set of parameters used a higher parallel imaging factor with less view-sharing (R=6, pA =0.25, pB=0.5), and the second set used a slightly lower parallel imaging factor and moderate view-sharing (R=4, pA=0.2, pB=0.333).

Section 5.2.2. Results Figure 5.1 depicts results from the subset of simulations in which temporal resolution was less than 5 s/frame. Whether accelerating with GRAPPA or view-sharing, a higher

83 temporal resolution leads to higher artifact power. For this application, the trade-off between the two TWIST parameters was less important than the choice between acceleration using GRAPPA or view-sharing. In these simulations, R=6 with GRAPPA reconstruction led to a lower artifact power than R=4 with more view-sharing for a given temporal resolution; however, when moving to R=9, accuracy decreased due to inaccurate GRAPPA reconstructions. The simulations where Ktrans error was less than

10% are circled in Figure 5.1.

Figure 5.1: Artifact power vs. Temporal Resolution for the TWIST simulations. Different TWIST parameters are shown using different shapes, and different GRAPPA factors are shown in different colors.

Reconstructions with Ktrans errors of less than 10% are circled, and parameters used for in vivo acquisitions are circled in bold.

Two parameter sets were chosen from the simulation (bold circles in Figure 5.1) for in vivo experiments. These two parameters sets had Ktrans errors that were below 10%.

Additionally, the temporal resolution of approximately 4 seconds for these two parameter sets matched the previously published temporal resolution requirements for DCE MRI in skeletal muscle (129). One set of parameters used a higher parallel imaging factor with less view-sharing (R=6, pA =0.25, pB=0.5), and the second set used a slightly lower parallel imaging factor and moderate view-sharing (R=4, pA=0.2, pB=0.333).

Figure 5.2. The left column shows a coronal and axial image of the distal lower extremities using a fully- sampled 3D Cartesian acquisition. The center column shows the same images acquired using parallel imaging (R=4), TWIST (pA=0.2, pB=0.333), and pF=6/8. The right column shows the images using parallel imaging (R=6), TWIST (pA=0.25, pB=0.5), and pF=6/8. The bottom row shows subtractions of the fully-sampled axial image and the undersampled axial images.

Figure 5.2 shows a coronal and axial slice from 3D images of the distal lower extremity.

In the left column, a fully-sampled dataset is shown for reference. The center and right columns show representative images acquired using the two parameters sets selected from the simulations. The center column was acquired using a lower parallel imaging acceleration factor and moderate view-sharing (R=4, pA=0.2, pB=0.333), and the right column was acquired using a higher parallel imaging acceleration factor and low view-

85 sharing (R=6, pA =0.25, pB=0.5). Although the datasets with R=6 had the lowest artifact power in simulation, the images here show residual aliasing artifacts at this high acceleration factor.

Section 5.2.2. Discussion The goal of this study was to use a simulation-based approach to evaluate the use of

TWIST with DCE MRI. Here, TWIST was combined with parallel imaging and partial

Fourier to enable the acquisition of high spatiotemporal resolution 3D data. However, each of these acquisition and reconstruction techniques has its own benefits and limitations that could affect image quality, temporal fidelity of the contrast dynamics, or both. Regardless of the reconstruction technique, a high temporal resolution would allow for a more accurate sampling of the contrast enhancement, but eventually artifacts from highly accelerated data will deteriorate the quality of the signal. Each of these three techniques can result in different types of artifacts at high levels of undersampling: 1.

View-sharing in TWIST results in temporal blurring artifacts, 2. Acceleration with parallel imaging results in a decreased SNR and residual aliasing artifacts, 3. A partial

Fourier acceleration results in decreased SNR and potential blurring. In order to balance the limits of each of these methods while maintaining resolution requirements, this study created a simulated phantom that mimicked contrast kinetics seen in skeletal muscle. A simulated coil was also applied to allow for reconstruction with parallel imaging.

Because the true images and perfusion (Ktrans) parameters are known, these simulations could allow for a better understanding of image artifacts and how these would results in error in Ktrans. A similar approach was used to study only TWIST sampling parameters for renal DCE MRI (77).

Using simulation results, optimal TWIST parameters and GRAPPA undersampling were

selected to minimize image artifact power and resulting errors in Ktrans. The parallel

imaging acceleration factor had a greater effect on the artifact power than the TWIST

parameter settings. The simulations showed that parallel imaging factors greater than 6

would result in strong residual aliasing artifacts (and higher artifact power). These data

also showed that R=6 achieved the lowest artifact power. For a given parallel imaging

acceleration factor, it can be seen that higher acceleration with TWIST (smaller pA and pB) would give a higher artifact power.

Additionally, errors in the images would propagate to error in perfusion quantification,

which can be evaluated by calculating the percent error in Ktrans for each reconstruction.

A cut-off value of 10% error in Ktrans was selected, and simulations with error below the

cut-off are circled in Figure 5.1. Generally, images with higher artifact power also had

higher error in Ktrans.

We chose to select two sets of sequence parameters for testing. As mentioned in the

Results section, the selected sets had low Ktrans error and had similar temporal resolutions

(~4s). The key difference was a different combination in parallel imaging and TWIST view-sharing parameters. Parallel imaging reconstruction performance can be highly influenced by the object being imaged and the coil arrangement. Therefore, the artifact power experience on the scanner may not perfectly match our simulated results. As can be seen in Figure 5.2, higher levels of residual aliasing artifacts can be seen in the data using a parallel imaging factor of R=6. These artifacts were seen consistently in volunteers, so the R=4 parameters sets were selected for the MRAP study described in

Section 5.3.

Using results from the simulation study and in vivo validation scans, the obtained

parameters settings from this study were: A region 20%, B region 33%, GRAPPA factor

2 in the phase encoding and partition directions, and partial Fourier 6/8 along the phase

encoding direction (128). Chosen TWIST parameters coincide with previous studies that

investigated the trade-offs involved in using view sharing techniques for DCE-MRI (77).

This study demonstrates the ability to combine these k-space undersampling and

reconstruction techniques to achieve a high spatiotemporal resolution 3D dataset that

could be used to simultaneously acquire an angiography image and perform

pharmacokinetic analysis to make a perfusion measurement.

Section 5.3. Application for MRAP in Skeletal Muscle

Section 5.3.1 Methods

Study Participants In this IRB-approved, HIPAA compliant study, experiments were performed on asymptomatic, non-smoking volunteers after written informed consent. Ten volunteers

participated (male/female 5/5, age 26.3±10.4 years, and weight 77.9±17.2 kg).

Study Protocol Each subject performed unilateral plantar flexion exercise using a resistance band for

three minutes while in the MR scanner, creating a physiological perfusion difference between legs. The contralateral leg remained at rest to serve as a baseline comparison. An underlying assumption was that resting perfusion in both legs without exercise would be similar, and therefore differences in perfusion between legs after unilateral exercise

would be due to the stimulus. This can be expected to be true in asymptomatic

volunteers. Imaging was initiated immediately after exercise. The experiment was

performed on each subject on two separate days at least one week apart to study

repeatability of the MRAP perfusion measurement. The leg that was exercised was

randomly selected, and the volunteer exercised the same leg on both days.

Image Acquisition Imaging was performed at 3.0T (Magnetom Verio, Siemens Healthcare, Erlangen,

Germany) with a peripheral angiography matrix coil and spinal array coil. Prior to

exercise and the MRAP exam, a baseline T1 measurement was performed using an inversion recovery experiment (32) with the following parameters: TurboFLASH;

TR/TE 5s/1.33-1.39ms; flip angle 8°;inversion times 150-2000 ms.

Contrast-enhanced MRAP exams were performed on volunteers after administration of

0.1 mmol/kg Gd-DTPA (Magnevist; Bayer, Berlin, Germany) followed by 25 ml saline at

3 ml/s. The injection of contrast was initiated approximately 2 min after cessation of

exercise, following collection of pre-injection baseline images. Other MRAP imaging

parameters were: TR/TE 2.97/1.48ms; resolution: 1.34x1.6x1.5 mm3; 90 temporal

repetitions; and FoV 430x403x96 mm3. The flip angle of 10° was chosen for MRAP to balance the optimal flip angle for tissue signal for the perfusion measurement and contrast-enhanced blood signal for the MRA. The acquisition time for each frame was

3.99 s, which is within the suggested range for analyzing muscle tissue enhancement

curves in the lower extremities (129) and also sufficiently fast for diagnostic MRA in the

legs (130).

Evaluation of Angiography Images Because a combined method such as MRAP may result in two suboptimal exams, both

the angiographic and perfusion exams were analyzed to ensure that the technique could

provide high quality MRA images while also providing perfusion information. To

analyze MRA images, SNR measurements were made. As SNR values in images

processed using techniques such as parallel imaging are not uniform across the image,

SNR calculations cannot be made using spatially-varying regions-of-interest (ROIs)

(131). Instead, the SNR at baseline was measured by taking the ratio of signal in the popliteal artery averaged over the pre-contrast images and the averaged noise over the same ROI obtained from serial baseline subtraction images. An SNR in the maximally enhanced popliteal artery was also obtained as a ratio of the signal at maximal enhancement in the same ROI to the noise as obtained from baseline measurements.

Additionally, two MR-trained attending radiologists were asked to rate their confidence level for assessing lumen patency (0-100%) in the MRAP exam in the right and left legs for the popliteal, anterior tibial, posterior tibial, and peroneal arteries.

Perfusion Measurement Perfusion calculations were performed offline using MATLAB (The MathWorks,Natick,

Massachusetts). Time courses of signal intensity in the muscle were generated over

13.4x16 mm2 (10 voxels2) ROIs in three muscle groups: the tibialis anterior, soleus, and

gastrocnemius. ROIs were placed centrally within the muscle group in a single axial slice.

As mentioned previously, the intrinsic T1 of the tissue was measured using an inversion

recovery experiment, allowing for the calculation of concentration of contrast agent (32).

To convert signal intensity values from the MRAP exam to concentration, the following

equation was used (32):

= + , [5.2] 1 1, 푇1 푇1 표 푟퐶 where T1,o is the intrinsic T1 of the tissue, T1 is its shortened value in the presence of

contrast agent, r is the relaxivity of the contrast agent, and C is the concentration of the

contrast agent. T1,o was measured prior to the MRAP exam, and T1 was computed using

MRAP signal values and the FLASH signal intensity relationship (32).

Gadolinium-based contrast agents are known to passively diffuse between the vascular

space and the extravascular, extracellular space (EES) and are excluded from the

intracellular space. The pharmacokinetics of Gd-DTPA can be described by a one

compartment model with the following equation (44):

= , [5.3] 푑푐푡 푡푟푎푛푠 푑푡 퐾 푐푝 − 푘푒푝푐푡 where cp is the concentration of contrast agent in the plasma, ct is the concentration of

trans contrast agent in the tissue, and K and kep are rate constants. The time-varying

concentration cp was obtained by measuring the arterial input function (AIF) in a region of interest selected within the popliteal artery. The AIF signal time-course was then fit to a gamma variate function (132,133).

For both exercise and rested muscle, this study assumes flow-limited conditions, i.e., high permeability and low flow. In this case (44), the transfer constant is a function of perfusion (F), density (ρ), and hematocrit (Hct):

= (1 ) [5.4], 푡푟푎푛푠 퐾 퐹휌 − 퐻푐푡 assuming a ρ of 1.05 kg/l and Hct of 0.4.

Using these equations, the tissue compartment signal can be converted to contrast agent

concentration (Equation 5.2) and can then be modeled using Equation 5.3 to yield fitted

trans trans parameters kep and K (and by extension, F). As established in prior studies, K is a

direct quantitative measure of perfusion (5). A nonlinear least squares fit was used to

trans estimate kep and K .

In addition to the ROI perfusion analysis, pixelwise perfusion maps were also generated.

Due to SNR considerations, this was performed at a lower spatial resolution by down-

sampling to double the voxel size (to 2.7x3.2x3 mm3), and spatial and temporal averaging

filters were applied (using 2x2 spatial and a three-point temporal convolution kernel with uniform weighting, respectively).

trans The accuracy of the measured K is dependent on the SNR of the DCE and T1

quantification acquisitions. Simulations were performed to estimate the propagated error

trans in measured K caused by noise in the image acquisition. The noise in the T1 mapping

was quantified by measuring the standard deviation of T1 over 10 repetitions. Noise in the

DCE-MRI acquisition was quantified from the first 30 frames acquired prior to contrast

injection. After quantification of the SNR for both acquisitions, Monte Carlo simulations

were performed by adding normally distributed random noise to an 'ideal' enhancement

curve and the resulting data were fit using the modeling process described above. The

ideal arterial enhancement data were generated using a fitted AIF from a volunteer scan,

trans and the ideal muscle enhancement data were generated using known kep and K values.

These simulations estimate the propagated error in measured Ktrans caused by noise from

image acquisition. Physiological variation in measured Ktrans was estimated as the

standard deviation in the measured Ktrans in each muscle over the 10 subjects.

Statistical Analysis The significance of the effect of exercise on Ktrans was evaluated using a paired t-test

(α=0.05, two-tailed). The Bland-Altman method was used to compare intrasubject variability between the two imaging sessions (134). Good agreement between

measurements on separate days indicates repeatability across the two days. Bland Altman

analysis was performed for each muscle group (ROI measurements) at rest and after

exercise across the two scanning sessions.

Section 5.3.2. Results 3D MRAP images were acquired for all volunteers. Maximum Intensity Projection

(MIPs) images generated after baseline subtraction are displayed in Figure 5.3 from three representative datasets. MRA images yielded SNR values of 38±8 at baseline and 110±28

at peak enhancement. A summary of the results of the radiologists' assessments of the angiographic images is presented in Table 5.1. These results showed a high confidence in the evaluation of the angiographic images, i.e., a score approaching 100 for the confidence level of assessing lumen patency.

Table 5.1. Summary of results of radiologists' assessments of the MRA MIPs. Confidence Level in Assessing Lumen Confidence Level in Assessing Lumen Patency in Right Leg Patency in Left Leg Popliteal ATA PTA Peroneal Popliteal ATA PTA Peroneal Mean 96% 94% 97% 99% 98% 95% 97% 99% Maximum 100% 100% 100% 100% 100% 100% 100% 100% Minimum 70% 80% 50% 90% 75% 80% 50% 90% ATA, anterior tibial artery; PTA, posterior tibial artery.

Figure 5.4 shows a representative ROI signal intensity time series and model fits for both

the AIF (Figure 5.4a) and the gastrocnemius (Figure 5.4b) of exercising and resting legs

in a single volunteer. Note the exercised muscle shows both a higher rate of signal change

during contrast arrival, and an increased difference in signal intensity between baseline and plateau.

Figure 5.3. MIPs of a single time frame from three representative trMRA exams of the distal lower extremities. The subject in Figure 3c has bilateral hypoplastic posterior tibial arteries, and peroneal

continuation into the hindfoot. For this subject, note also the higher signal in left, exercised leg musculature

(arrow) in this frame than in the rested leg.

Figure 5.4. Representative signal intensity curves and model fits for the AIF (5.2a) and the muscle

enhancement (5.2b) in a single volunteer. Signal intensity curves were adjusted so that the mean baseline

signal intensities for exercised and rested curves were equivalent for direct comparison. Red 'x' - Exercise

data. Red line - Exercise model fit. Blue points - Rest data. Blue line - Rest model fit.

Table 5.2. Ktrans (min-1) and calculated perfusion (ml/100g/min) values for resting and exercised muscles. Rest Exercise

variation variation across variation across variation subjects across subjects subjects across subjects Ktrans (std, Perfusion (std, Ktrans (std, Perfusion (std, Muscle (min-1) min-1) (ml/100g/min) ml/100g/min) (min-1) min-1) (ml/100g/min) ml/100g/min) Tibialis Anterior 0.14±0.01 0.13 22±1 21 0.29±0.02 0.24 46±3 38 Gastroc- nemius 0.15±0.01 0.14 23±2 19 0.27±0.02 0.16 43±3 25

Soleus 0.19±0.01 0.14 30±2 22 0.34±0.02 0.15 54±3 24 Ktrans (min-1) mean measurement error: from simulation evaluating noise propagation in the images. Variation across subjects: standard deviation in the measured parameter across the 10 subjects.

In Table 5.2, perfusion measurements are summarized for each muscle at rest and after

exercise. The paired t-test results show a strong effect of exercise on Ktrans with p=0.008,

<0.0001, and <0.0001 in the tibialis anterior, gastrocnemius, and soleus, respectively.

Bland-Altman plots are shown in Figure 5.5. No point falls outside two standard deviations of mean measured differences in Ktrans for soleus (Figure 5.5c and 5.5f), and one point for each of the rested and exercised muscles analyzed falls outside the limits of agreement in the Bland-Altman plots for gastrocnemius and tibialis anterior (Figure

5.5a,b,d,e).

Figure 5.5.Bland Altman plots of Ktrans in resting tibialis anterior, gastrocnemius, and soleus muscle (A, B, and C respectively) and exercised tibialis anterior, gastrocnemius, and soleus muscle (D, E, and F respectively). The solid lines represent the mean difference between sessions in all volunteers. Dashed lines represent ± 2 standard deviations from the mean.

Coronal and axial slices from a 3D Ktrans perfusion map are shown in Figure 5.6 (right

column) for a volunteer whose right leg was exercised. For ease of viewing, pixels

outside of the body and those in fat and solid bone structures have been removed by

thresholding and manual segmentation. The resulting higher perfusion in the exercised leg is clearly seen as higher Ktrans values in the right leg compared to the rested left leg.

For reference, the source images for both slices are shown in Figure 5.6 (left column).

These images also demonstrate typical image quality and resolution.

Figure 5.6. In Figure 5.6 (left), original axial and coronal source images are shown that correspond to the parameter map in Figure 5.6 (right). In Figure 5.6 (right), pixel-wise Ktrans (min-1) axial and coronal parameter map. The right leg was exercised while the left leg remained at rest. Note the perfusion was higher in the exercised muscle than in the rested muscle.

Section 5.3.3. Discussion This study demonstrates the feasibility of the MRAP technique, which allows for the

simultaneous acquisition of three-dimensional trMRA images and DCE perfusion

measurements with a single gadolinium dose. While non-contrast techniques are

available for both MRA and for perfusion (47–50,135,136), these are less robust than

contrast-enhanced techniques, and in the case of perfusion, these are often performed on

single, thick slices, limiting the clinical applicability. It follows that currently contrast-

enhanced MRA and perfusion methods have found much more widespread clinical use in

many applications (30).

The MRA images from MRAP maintain high SNR and were rated highly for lumen

assessment by both radiologists, indicating that MRA examination quality was high for

the MRAP experiments. The measurement standard error in Ktrans (perfusion) due to

image noise was in the range of 6-8% of the measured Ktrans, and is much smaller than the

physiological variation in perfusion at rest and with exercise. The large physiological

variation in perfusion across the volunteer population is likely due to factors such as the

subject's effort during exercise, activity level prior to imaging, caffeine intake, and fitness

level, which were not controlled in this study.

The temporal resolution of approximately 4 s/volume was sufficient for accurate

characterization of the tissue enhancement curves as previously described by Lutz et al.

(129). While a better temporal resolution may be desirable for AIF characterization,

Monte Carlo simulations (not included for brevity) showed that when modeling the AIF with a gamma variate function, the temporal resolution used here provided sufficient accuracy for estimating Ktrans given both the physiology of the lower extremities and the

injection protocol used here. Model fits also showed low residual errors between the

model and the obtained data for both the AIF and the time course in the muscle.

Previous MR perfusion studies have been performed in skeletal muscle using contrast-

enhanced and non-contrast methods (129,137–140). The resting perfusion measurements

98 reported here (22 - 30 ml/(100 g∙min)) are in close agreement with those reported when using arterial spin labeling (137,138), which show a range between 20 and 30 ml/(100 g∙min)). Lutz et al. reported DCE perfusion measurement in human skeletal muscle in resting and post-ischemic hyperemic conditions (129). The resting perfusion values in that study (median values of 4.7-5.6 ml/100 g∙min) were much smaller than the measurements reported here and elsewhere (137,138), while the measurements in post- ischemic reactive hyperemia (25.4-26.7 ml/100 g∙min) were similar to those after exercise in this study. The discrepancy in measurements at rest between Lutz et al. and the current study may relate to differences in the two study designs (contralateral legs being exercised versus post ischemic hyperemic), and uncontrolled effects such as exercise and caffeine intake. Measurements during near maximal post-ischemic hyperemic conditions have also been reported by Thompson et al. (102-208 ml/100 g*min) (140), which are larger than those by Lutz et al., or the exercise conditions reported here. The reason for these differences is not clear.

Perfusion in the exercised leg was significantly greater than in the non-exercised leg, demonstrating the ability of MRAP to quantify physiological perfusion differences. The perfusion in normal volunteers increased by a factor of 2.1-2.5 between rest and exercise, which is lower than the 20 to 1 maximal flow reserve measured with ultrasound (141).

This is likely due to the volunteers in the present study performing a relatively modest exercise (not exercise to exhaustion) and the two minute delay between exercise and contrast injection (during baseline data collection). The resting leg could also have slightly elevated perfusion in comparison to true rest due to cardiovascular effects from the exercise. The main limitation of this study is that the level of rest prior to performing

the exercise was uncontrolled, and the effort during the exercise was not quantified.

Nevertheless, the measured perfusion of 43-53 ml/100 g∙min post-exercise were similar to the post-exercise perfusion values in human skeletal muscle previously reported by several groups (137,142,143).

Assuming that the perfusion in the same volunteers is similar on two separate days,

Bland-Altman analysis should show good agreement between the perfusion measurements on those two days. This was observed in each muscle group both at rest and after exercise, with at most one volunteer falling outside the 95% confidence interval commonly used to demonstrate agreement between two measurements. Thus, these data indicate a good repeatability for the MRAP method.

MRAP represents a significant improvement in DCE perfusion of muscle. The double use of the MRAP data means that a single gadolinium injection makes both small and large vessel evaluation possible in a single exam. This may prove to be a clinical and/or investigational advantage. Even in these asymptomatic subjects, the MRAP experiments are exemplars of the possibilities opened up by this technique, in settings where 3D perfusion measurement may be of interest. For example, although MRA exams are often performed to evaluate PAD, perfusion is not routinely measured. This is also in part due to the non-robust, thick, single-slice perfusion measurements available by both non- contrast and contrast-enhanced measurements, which reduce their diagnostic utility for assessing small or spatially varying abnormalities. The data on normal volunteers are suggestive of the usefulness of a higher resolution approach. For example, the resting perfusion in the soleus muscle is higher than in tibialis anterior or gastrocnemius, and the

100 perfusion difference due to exercise is higher in the tibialis anterior than in the gastrocnemius and soleus muscles (214% versus 185% and 178%, respectively).

In some studies, a semi-quantitative approach has been reported in which the rapid increase of the signal intensity curves in an artery (slice 1) and in muscle (slice 2) following contrast agent injection is fit to a line, and the ratio of slopes is termed the perfusion index (1,2). Using this semi-quantitative perfusion index, significant differences were seen between normal subjects and patients with PAD, showing that perfusion mapping (and thus MRAP) could be an important diagnostic tool in PAD (1,2).

The currently used contrast-enhanced, perfusion methods would require a second contrast dose and a second scanning session if both MRA and perfusion acquisitions were to be performed, adding time, cost, inconvenience, and risk of nephrogenic systemic fibrosis

(45,144,145). Thus, although symptoms of PAD, i.e. leg weakness and claudication, result from a constellation of physiological changes secondary to reduced tissue perfusion, the clinical benefits of measuring perfusion in the setting of PAD are still relatively poorly explored. An important recent study which investigated the semi- quantitative perfusion index correlated to a 6-minute walk distance in PAD patients, indicated a relationship between disease status and perfusion (2). The results strongly suggest that high-quality perfusion measurements could be useful in the setting of PAD.

As MRAP is based on a high resolution, 3D acquisition, rather than on a single, thick slice exam, regional alterations in perfusion, or changes in various muscle groups due to intervention/treatment can be better assessed based on such an acquisition. Systematic studies are needed to explore MRAP in the setting of PAD. In addition to a MRAP examination of the distal lower extremities, a MRA exam in the proximal stations may be

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necessary to evaluate large vessels in the proximal station. Non-contrast methods could be considered for these proximal stations. Future studies could also investigate the use of

MRAP with a lower dose of contrast agent, which may allow for a proximal station MRA and a distal lower extremity MRAP exam without an increase in total contrast agent dose.

In conclusion, MRAP provides simultaneous high-resolution MRA and quantitative DCE exams to assess large and small vessels with a single contrast dose. Application in skeletal muscle shows quantitative, repeatable perfusion measurements, and the ability to measure physiological differences. While a first application of MRAP is demonstrated in skeletal muscle, the method is general and can be applied to other organs/tissues to obtain simultaneous perfusion and MRA measurements in, for example, brain or kidney. Tissue- specific factors such as necessary temporal resolution, motion correction or image registration would need to be considered and the acquisition adjusted accordingly.

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Chapter 6. Free-breathing, High Spatiotemporal Resolution Renal

Perfusion Measurements

The work described in Section 6.2 of this chapter was published as original research in the

Journal of Magnetic Resonance Imaging (67). The work described in Sections 6.1 and 6.3 of this

chapter was published as original research in Investigative Radiology (146).

Section 6.1. Renal Perfusion Measurement Introduction

Quantitative DCE MRI exams of the kidneys can be used to provide valuable information

on both renal perfusion and filtration by employing pharmacokinetic modeling of

gadolinium-based contrast agents to obtain measurements of these physiologically

relevant model parameters (147–153). This quantitative evaluation of the kidney has a broad potential for impact in clinical care, including evaluation of renal artery stenosis, renal transplants, and tumor characterization (10,11,13,17,154). Furthermore, it can be

combined with other MR imaging methods, such as an MR angiography exam, for

comprehensive assessment of the kidneys (7,9,12,154–156).

However, acquisition of DCE MRI data is not trivial, particularly if 3D and high

resolution analysis is desired. These methods require high temporal resolution to

appropriately sample the arterial input function and the enhancement of renal

parenchyma tissue (157), and thus spatial resolution or volumetric coverage is typically

sacrificed. View-sharing methods have been utilized to achieve 3D coverage

(77,158,159), but a broad temporal footprint across the shared time frames could affect the accuracy of the pharmacokinetic analysis (77). In addition to the resolution requirements, DCE MRI scans also require sampling of the entire enhancement process, requiring scan times that exceed four minutes (157). This long enhancement time course

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means that respiratory motion is unavoidable and thus problematic. Repeated breath- holds can be employed but there is significant potential for motion due to incomplete breath-holds, especially as the patient tires. Moreover, the necessary rest phases between breath-holds result in data gaps that deleteriously affect the modeling.

In this Chapter, we address all of these problems by performing a free-breathing, 3D high resolution renal perfusion exam. In Section 6.2, we begin by using a highly-accelerated non-Cartesian stack-of-stars trajectory and exploring a novel 3D through-time radial

GRAPPA reconstruction (67,117) to achieve high spatiotemporal resolution acquisition

with full volumetric coverage of the kidneys. Specifically, this section will focus on the

proper calibration of this reconstruction method. This new reconstruction technique is

demonstrated and compared to existing non-Cartesian parallel imaging methods and the

TWIST technique used in Chapter 5. In Section 6.3, this fast acquisition strategy and

reconstruction technique is used to acquire the free-breathing, 3D renal DCE MRI data with a high spatiotemporal resolution. The high temporal resolution free-breathing images are registered to correct for inter-frame motion, and then a separable two compartment renal pharmacokinetic model (153,160) is applied to estimate perfusion and filtration parameters.

Section 6.2. 3D Through-time Radial GRAPPA

Section 6.2.1. Introduction Accelerated image acquisition and reconstruction techniques are frequently employed in

MRI, and are particularly important for time-resolved, 3D acquisitions, in which

volumetric coverage and temporal and spatial resolution requirements cannot be met

without the use of fast imaging methods. This work focuses on combining parallel

104 imaging methods with non-Cartesian trajectories for rapid 3D data acquisition. Alone, parallel imaging reconstructions can be used for acceleration in both phase and partition encoding directions (161–165), and have been shown to provide reduction factors of up to eight for these 3D acquisitions (164). Similarly, used on their own, non-Cartesian k- space trajectories such as radial have many benefits, including robustness to deleterious effects from motion and less detrimental undersampling artifacts in comparison to

Cartesian sampling (87,166). The combination of non-Cartesian acquisitions and parallel imaging techniques has been shown to provide high spatial and/or temporal resolution images (109,112,115–120,167) from highly accelerated datasets. In addition to the aforementioned benefits of each of these techniques, non-Cartesian parallel imaging could allow higher acceleration factors than either non-Cartesian trajectories or parallel imaging alone. Unlike when using view-sharing, or even some compressed sensing methods, the resulting images have well-defined, short temporal footprints, and the techniques are easy to implement. However, non-Cartesian data acquisitions necessitate the use of modified parallel imaging techniques (109,112,113,115–120,168–170). For example, special formulations of the GRAPPA reconstruction method must be used when working with undersampled non-Cartesian trajectories (113,117–120,169,170). In the case of a radial acquisition, GRAPPA weights are applied to the acquired radial projections to estimate missing projections. The challenge in performing radial GRAPPA reconstructions is the calibration of the GRAPPA weights, which can be calculated using through-k-space information as in Cartesian scans (33), or using through-time information as shown in (39,40). The aim of this study is to explore methods for the calibration of 3D through-time radial GRAPPA for a stack-of-stars trajectory.

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Section 6.2.2. Theory The principles of radial GRAPPA reconstruction are similar to those used when

performing GRAPPA on Cartesian data, and have been previously described in detail in

Section 4.3.3 and in (117). In a radial acquisition, the calibration of GRAPPA weights

must be adapted for the radial trajectory, since the kernel geometry is dependent on both

its location along a projection and its angular orientation. As described in Section 4.5.3, non-Cartesian GRAPPA weights can be estimated by shifting the kernel through a small k-space segment as shown in Figure 6.1A. However, this method has an inherent tradeoff between the improvement in weight accuracy by increasing the number of kernel occurrences by using a large segment and the degradation of accuracy when kernel geometries are too dissimilar within that large segment.

Section 4.5.3 also introduced the use of through-time non-Cartesian GRAPPA weight calibration. Here, instead of acquiring a single, fully-sampled dataset for calibration, multiple time frames can be acquired for through-time calibration, as shown in Figure

6.1C. This method creates exact replications of kernel geometries in each temporal repetition, which has been shown to provide excellent image quality (117). During the through-time calibration acquisition, patient motion can occur, leading to differences in calibration information in identical partitions acquired at different times. The motion is negligible during acquisition of neighboring projections, so points within a single

GRAPPA calibration kernel are unaffected. However, one drawback to through-time

calibration is that it requires additional calibration time, and thus there is always interest

in minimizing this calibration time while preserving the highest image quality.

In a 3D stack-of-stars acquisition, the data are acquired using a radial trajectory in the kx-

ky plane and with Cartesian encoding steps in the kz direction. The rectilinear Cartesian

106 encoding steps will be referred to as partitions in this work. As depicted in Figure 6.1B, the 2D GRAPPA kernel can be replicated in each partition to increase the number of kernel occurrences for calibration. Unlike through-k-space calibration using segmentation, through-partition calibration allows for exact replication of kernel geometries, but partitions located far away from the k-space center suffer from decreased

SNR, especially in the outer portions of the radial trajectory, and may not provide the full benefit compared to the time spent collecting this data.

Figure 6.1. Three different 3D non-Cartesian GRAPPA weight calibration methods are shown separately

(A-C) and in combination for an example 3D through-time radial GRAPPA calibration (D). Figure 6.1A depicts through-k-space calibration using segmentation, where kernel occurrences are accumulated by shifting a small kernel (solid block) through a segment of a radial trajectory (indicated by the dashed line).

Figure 6.1B demonstrates through-partition calibration, where kernel occurrences are accumulated by shifting the kernel along the partition dimension. Figure 6.1C depicts through-time calibration, where kernel occurrences are accumulated by shifting the kernel through temporal repetitions of the trajectory.

Because these methods are independent of each other, these can be combined for 3D through-time radial

GRAPPA calibration, and a simple example of this is shown in Figure 6.1D.

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In order to minimize the total time needed for calibration, each of these three different

calibration options (through-k-space with segmentation, through-k-space through-

partition, and through-time) must be combined in an efficient way, as shown

schematically in Figure 6.1D. Here, several fully-sampled partitions are acquired over multiple time points (all projections are acquired in each partition and at each time point), and all radial data are segmented for through-k-space calibration. However, this is not necessarily the most efficient way to acquire calibration data. For example, the use of several different partitions may provide more unique calibration information than using multiple repetitions of the same partition, as partition encoding provides additional variety beyond relying on image differences through-time. However, despite being a potential source of unique information for calibration, using many outer, lower signal partitions may also decrease accuracy of GRAPPA weights. In this study, the trade-off between through-k-space, through-partition, and through-time calibration and the overall accuracy of these GRAPPA weight calibration methods will be explored, and the results applied to undersampled in vivo renal DCE MRI data.

Section 6.2.3. Methods

Simulations The goal of the simulations was to assess the effect of using different amounts of through-time and partition calibration data for the 3D through-time radial GRAPPA

reconstruction. Optimization of this calibration scheme for 3D renal contrast-enhanced

exams cannot be explored directly due to the limitations of in vivo acquisitions, so a

simulation-based approach was implemented (similar to that used in (117)), and the

reconstruction results were used to select the GRAPPA calibration scheme for in vivo

acquisitions/reconstructions. The simulations also explored calibration efficiency; the

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acquisition of each partition and repetition for calibration adds to the total scan time

equally, so the simulations were designed to evaluate which calibration scheme provides

lower reconstruction error for a given amount of calibration acquisition time. A modified

3D Shepp-Logan phantom with random, continuous motion similar to that designed in

(117) was used to generate calibration and undersampled data. This phantom was

sampled in-plane to have 144 projections and 256 oversampled read points with a base

matrix size of 1282. The phantom had a total of 64 partitions, different numbers of which

were used in the calibration process to explore the effects of this parameter.

For the undersampled data, a similarly constructed randomly moving 3D Shepp-Logan

phantom with 16 partitions and an in-plane matrix size of 1282 was generated. The object

was varied to mimic in vivo data such that object information changed continuously for

each time frame and each partition. A total of 64 different frames were generated for the

calibration data and 5 frames for the undersampled data, and the contrast for those five undersampled frames was altered in comparison to the calibration data. Finally, coil sensitivities obtained from the combination of a 6-channel Siemens body array and 6 channels of a spine array were applied to the data to simulate a multi-coil acquisition similar to that used for the renal DCE MRI exam. As the undersampling only occurs in- plane in the angular direction (no undersampling is performed in the partition direction), all reconstructions used a 2D kernel with 2 x 3 points (projection x read) as in (117), and the calibration segment size was set at 1 projection x 4 read points and 4 projection x 8 read points (where the kernel is shifted along the read direction such that there are a total of four kernel occurrences and thirty-two occurrences, respectively). The calibration data was varied by adjusting the number of partitions and repetitions used for calibration; each

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ranged between 1 and 64. For calibration schemes using fewer than the maximum

number of partitions, the central k-space partitions were used for calibration. Only

simulations that had a fully-determined system of equations for GRAPPA weight

estimation were performed, meaning that at least 72 kernel occurrences (6 source kernel points x 12 coils) must be present in the calibration data for each point in the reconstruction. Data were undersampled such that 24 projections were used, which is a radial acceleration factor of 6 and an acceleration of 8.8 with respect to Nyquist sampling criterion. 3D through-time GRAPPA reconstructions were performed where the weights

were determined with these different calibration possibilities, and the resulting root mean

squared error (RMSE) values were computed in comparison to the fully-sampled dataset. in vivo Imaging In this IRB approved, HIPAA compliant study, contrast-enhanced data were acquired in four asymptomatic volunteers after obtaining informed consent. Imaging was performed at 3T (Magnetom Verio, Siemens Healthcare, Erlangen, Germany) with a standard 6- channel body matrix receive coil and spinal array coil (using between 9 and 12 channels), similar to that used in the simulations but with additional spine coils. All data were collected using a FLASH sequence with a stack-of-stars trajectory in order to acquire a time-resolved contrast-enhanced exam after injection of a single dose (0.1 mmol/kg) of gadobenate dimeglumine (Multihance, Bracco Diagnostics Inc., Princeton, NJ). While the overall application of interest was to use 3D through-time radial GRAPPA in the setting of renal DCE MRI, our initial evaluation of the reconstruction technique was performed by acquiring images only during the early phases of contrast arrival and enhancement.

This shorter acquisition allowed the contrast-enhanced exam to be breath-held, but a quantitative pharmacokinetic analysis could not be performed on this limited data. A

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complete exploration of the application of 3D through-time radial GRAPPA to renal DCE

MRI will be described in the following section (Section 6.3).

A dataset was acquired for one subject to confirm the effects of using different calibration schemes tested in simulations for the reconstructions of in vivo data with 3D through- time radial GRAPPA. Calibration data were acquired during free breathing after contrast injection (more than 2 minutes after injection), and a single, breath-held, fully-sampled volume was acquired and retrospectively undersampled for reconstruction. These axial data were acquired with the scanning parameters shown in Table 6.1 for Figure 6.3.

These data were retrospectively undersampled to 40 projections/partition, and were reconstructed with 3D through-time radial GRAPPA using a segment size of 1 projection x 4 read points, and varying numbers of partitions and repetitions. Note that various amounts of calibration data were used to simulate different calibration acquisition times.

The calibration acquisition time was 22 seconds when the product of partitions and repetitions was 32 (i.e. partitions x repetitions = 32), 43 seconds when partitions x repetitions = 64, and 87 seconds when partitions x repetitions = 128. The fully-sampled and retrospectively undersampled data were also reconstructed for a comparison of image quality, and RMSE values were calculated using the fully-sampled data as the reference.

In order to compare the performance of 3D through-time radial GRAPPA with existing non-Cartesian parallel imaging techniques, a dataset was acquired using the parameters listed under Figure 6.4 in Table 6.1, and reconstructed using both the CG SENSE algorithm (109) (2x oversampling, four iterations, Tikhonov regularization with a regularization parameter of 0.1) and 3D through-time radial GRAPPA. Density compensation weights using the Voronoi method (171) were used for preconditioning of

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the CG algorithm and to preserve image resolution. The coil maps were calculated using

the adaptive combination method (172) by averaging over the 16 fully-sampled

calibration frames.

A second comparison was also performed between 3D through-time radial GRAPPA and

the TWIST (time-resolved imaging with stochastic trajectories) technique that was

explored in Chapter 5 (75,76). The same volunteer was scanned on two different dates

spaced one week apart on a 3T scanner using an 18-channel body array and 20 channels

of the spine array (Magnetom Skyra, Siemens Healthcare, Erlangen Germany). Data for

the first exam were acquired with the undersampled stack-of-stars trajectory, and

reconstructed with 3D through-time radial GRAPPA (acquisition and reconstruction parameters shown in Table 6.1 for Figure 6.5-6.6). The second exam utilized the TWIST acquisition and reconstruction. Where possible, the TWIST acquisition matched the acquisition parameters in the 3D through-time radial GRAPPA scan (including FoV, temporal and spatial resolution, bandwidth/pixel, repetition time, echo time, and flip angle). However, to achieve the desired frame rate of 3.5 s, acceleration in the TWIST scan was achieved by using a combination of view-sharing (pA=0.16, pB=0.2), a

Cartesian GRAPPA undersampling factor of 3, and partial Fourier of 6/8 in the slice direction. With this acquisition, the TWIST reconstruction used data from four neighboring frames, yielding a temporal footprint of 17.5 s/frame. The TWIST acquisition does not use view-sharing in the first time point, resulting in a longer acquisition time of 10.1 seconds.

Finally, an additional dataset was acquired to demonstrate the use of 3D through-time radial GRAPPA to reconstruct highly accelerated data in vivo. Renal contrast-enhanced

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exams were acquired coronally with volumetric coverage of the kidneys, renal arteries,

and aorta. These were performed with sequence parameters described in Table 6.1 for

Figures 6.7 and 6.8. Free-breathing calibration scans were performed with the calibration parameters determined using the simulations studies prior to contrast injection.

Table 6.1. Parameters for in vivo experiments performed in Section 6.2.

Figure 6.3 Figure 6.4 Figure 6.5-6.6 Figures 6.7-6.8 Fully-sampled Projections 240 224 224 224 Undersampled Projections 40 28 28 28 Partitions 32 36 36 40 Partition Oversampling 25% 22.2% 25% 10% Acceleration Factor (with respect to Nyquist) 8.8 12.6 12.6 12.6 Partial Fourier (Partition) None 6/8 6/8 6/8 Matrix Size 224 x 224 224 x 224 224 x 224 224 x 224 TR (ms) 2.82 3.91 3.68 3.71 TE (ms) 1.26 1.58 1.49 1.49 Flip Angle 8° 20° 20° 20° BW (Hz/pixel) 890 600 740 720 FoV (mm3) 380x380x64 335x335x108 330x330x108 340x340x120 Spatial Resolution (mm3) 1.7x1.7x4 1.5x1.5x3 1.5x1.5x3 1.5x1.5x3 Temporal Resolution (s) 13.5 3.8 3.5 3.5 Segment Size (proj x read) 1 x 4 4 x 8 4 x 8 4 x 8 Calibration Varied Varied Repetitions (Max: 32) 16 16 (Max: 20) Calibration Varied Partitions (Max: 32) 8 8 8

Undersampled radial data were reconstructed offline in MATLAB (MathWorks, Natick,

MA) with 3D through-time radial GRAPPA using a calibration segment size of 4

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projections x 8 read out points, 16 calibration repetitions, and 8 calibration partitions for data shown in Figures 6.4, 6.5, and 6.6 as suggested by the results of the simulation studies. The images shown in Figures 6.7 and 6.8 were reconstructed using the same

parameters except for the calibration repetitions, which were varied (20, 16, 8, 4, and 2

repetitions were used) to demonstrate the robustness of the reconstruction even when

using fewer repetitions in order to decrease the calibration time. Data were reconstructed

to compensate for the partial Fourier acquisition using projection onto convex sets

(POCS) prior to applying the Fourier transform along the partition direction. Density

compensation and NUFFT (94) were then applied to in-plane radial data to generate the

reconstructed images. Images are displayed in Figures 6.5-6.8 as subtracted maximum

intensity projection (MIP) images, and Figure 6.7 shows MIP images at multiple time

points during contrast enhancement.

Section 6.2.3. Results Simulations were performed to evaluate the effect of adding through-time calibration

information when performing 3D through-time radial GRAPPA. This simulation showed

that increasing the number of calibration repetitions from 1 to 16 decreased the RMSE (as

expected from the 2D through-time calibration results (117)). Once the amount of

calibration data becomes large (in this example, beyond 8 repetitions), additional

temporal repetitions have a diminishing improvement on reconstruction errors.

Figure 6.2 explores in simulation how to efficiently acquire calibration data to achieve

low RMSE by varying the number of partitions or repetitions within a constant

calibration time. The plots show RMSE values for two segment sizes (1x4 and 4x8) when

using different numbers of partitions to perform the calibration, and each data point

represents a different number of repetitions to maintain a constant calibration time (large

114 number of calibration partitions indicates that a small number of calibration repetitions were used and vice versa). In the plot showing the 1x4 segment size reconstructions, these results show that for a set amount of calibration time, the use of more calibration partitions decreases the error until approximately 8 partitions are used. At this point, error begins to increase for a higher number of partitions and fewer repetitions. These results also show that by increasing the total calibration time, reconstruction error decreases (this can be seen by looking at the triangles, with a high RMSE and short calibration time, vs. the diamonds, with a low RMSE and a long calibration time). In the plot showing the 4x8 segment size reconstructions, the general trends in RMSE are similar to those in the 1x4 segment size, but there is an overall decrease in RMSE.

Figure 6.2. This figure shows root mean squared error (RMSE) values for simulations with a radial undersampling factor of 6. These reconstructions were calibrated using a segment size of 1 projection x 4 read (on left) and 4 projections x 8 read (on right), a varied number of partitions, and a varied number of repetitions. The calibration acquisition time for each curve was held constant, meaning that at a low number of partitions, a high number of repetitions are acquired, and vice versa. Calibration time is noted in the legend, where the total acquisition time is equal to 144 projections x TR x C. The RMSE is high at low number of partitions, reaches a minimum at 8 partitions, and begins to gradually increase at high number of partitions.

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To confirm the effects of the calibration scheme on the reconstruction results using in vivo renal contrast-enhanced data, Figure 6.3 shows the results when varying the number of partitions and repetitions for a late contrast-enhanced renal scan. Figure 6.3A shows an example partition generated using the fully-sampled data and Figure 6.3E shows the same undersampled partition for comparison. Figures 6.3B-D were reconstructed using 3D through-time radial GRAPPA with a segment sizes of 1 projection x 4 read points, 16 calibration partitions, and a varied number of repetitions. As the number of repetitions increases from 2 to 8, the image quality improves, and the RMSE decreases. Figures

6.3F-H were calibrated with a segment size of 1 projection x 4 read points, 16 repetitions, and a varied number of partitions. Increasing the amount of calibration data by increasing the number of partitions also improves image quality and decreases RMSE. Additionally, each column is reconstructed with the same amount of calibration data. Similar to the simulation results, very few calibration partitions and a large number of repetitions results in the highest error, and the minimum RMSE is found when using 8 calibration partitions, although visually the image quality is very similar in Figures 6.3C-D and G-H.

The same behavior is observed when a segment size of 4 projections x 8 read points is used for the in vivo reconstructions, although as in the simulations, the RMSE values and thus visual appearance are similar with different numbers of repetitions and partitions. As in the simulation data, the lowest RMSE value was found when using a calibration scheme with 8 partitions, 16 repetitions, and a 4 projection x 8 read point segment size

(RMSE = 16.4%).

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Figure 6.3. A contrast-enhanced, breath-held dataset was acquired fully sampled, retrospectively undersampled to have a radial in-plane acceleration factor of 6, and reconstructed with different calibration schemes. Figure 6.3A shows the fully-sampled image, and Figure 6.3E shows an image after retrospective undersampling. Figures 6.3B-D and 6.3F-H were reconstructed with 3D through-time radial GRAPPA with calibration parameters noted in the upper right hand corner (partitions x repetitions). RMSE was calculated using the fully-sampled image as the comparison and was noted for each reconstruction in the lower right hand corner. Calibration time increases from left to right along both rows and is the same for each column.

The lowest RMSE is found when 8 partitions are used with 16 repetitions (6.3H), although calibration schemes with similar parameters (6.3C, D, and G) also yield good results.

Figure 4 demonstrates reconstruction results of two sets of source images from single partitions using different reconstruction algorithms. The same undersampled data are shown after applying density compensation and the NUFFT (left column), after reconstruction using the 3D through-time radial GRAPPA algorithm (middle column)

(with a 4x8 segment size and a total of eight partitions and 16 repetitions for calibration, as suggested by the simulations and in vivo data) and after the CG SENSE algorithm

(right column). The gridded images demonstrate that these data are highly undersampled

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with a high level of residual streaking artifacts, which are reduced in both the 3D

through-time radial GRAPPA and CG SENSE reconstructions. By visual inspection, the

radial GRAPPA method offers a better overall image quality.

Figure 6.4. Two example partitions from a contrast-enhanced, breath-held dataset acquired with a radial in-

plane acceleration factor of 8 reconstructed with NUFFT (6.4A,D), 3D through-time radial GRAPPA

(6.4B,E), and CG SENSE (6.4C,F). Note the improved image quality of both the parallel imaging reconstructions in comparison to the undersampled data, and the reduced streaking artifacts and noise level in the 3D through-time radial GRAPPA reconstruction.

Figure 6.5 shows full volume subtracted MIP reconstructions from successive frames for the renal trMRA using TWIST (Figure 6.5 top row) and 3D through-time radial

GRAPPA (Figure 6.5 bottom row), for the same subject. The depicted volumes were

acquired at nearly identical time points after contrast injection. The spatial and nominal

temporal resolutions of both datasets are identical (3.5 s/frame, 1.5x1.5x3mm3). The

TWIST dataset has a temporal footprint of 17.5s, while the 3D through-time radial

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GRAPPA has a temporal footprint of 3.5s. Cropped and zoomed images from sub-

volume MIP reconstructions centered on the renal arteries are shown in Figure 6.6. The

maximally enhanced renal arteries seen at the peak of aortic enhancement in the through

time radial GRAPPA exam are shown in the leftmost image. To the right of this image is

the TWIST frame taken with near identical timing after contrast administration.

Successive frames after this point as the peak of arterial enhancement is reached in the

TWIST exam are shown in the next two images. The peak of aortic enhancement is

reached in the third TWIST frame shown (rightmost image). The arrows in Figure 6.6

point to some problematic features of the TWIST exam. The straight solid arrows point to

second and third order branches of the renal arteries that are not as clear visualized with

TWIST. The curved arrows point to parenchymal enhancement, and the open arrows

show locations of venous contamination.

Figures 6.7 and 6.8 depict reconstruction results from a contrast-enhanced trMRA exam acquired with an undersampling factor of 12.6 with respect to Nyquist sampling criterion.

Figure 6.7 displays three frames of sub-volume, subtracted MIPs in the coronal view,

where 20 calibration repetitions and 8 partitions, along with a segment size of 4x8, were

used for the reconstruction. These data demonstrate various stages of contrast

enhancement that can be imaged with this high temporal resolution. Figure 6.8 shows

reconstruction results for a single frame of a sub-volume, subtracted MIP in the coronal

view for four different calibration schemes. Most calibration parameters were held

constant (calibration segment size of 4 projections x 8 read points and 8 calibration

partitions), while the number of calibration repetitions was set to 16, 8, 4, and 2. These

correspond to a decreasing calibration acquisition time of 1.8 min, 0.9 min, 0.44 min, and

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0.22 min, respectively. This figure shows the stability in the reconstruction quality despite the use of significantly less calibration data (and thus a much faster calibration acquisition time).

Figure 6.5. A time resolved, contrast-enhanced renal MRA exam. Images in the top row were acquired with a commercially available Cartesian TWIST sequence that utilizes Cartesian GRAPPA, view-sharing, and partial Fourier. Images in the bottom row were acquired with an undersampled stack-of-stars trajectory with an in-plane acceleration of 12.6 with respect to Nyquist, and reconstructed using a 3D through-time radial GRAPPA. Coronal subtracted MIP images for two neighboring time frames are shown for each of these acquisition/reconstruction methods. The spatial and temporal resolution of both datasets is nominally the same (3.5 s/frame, 1.5x1.5x3mm3). Note that the TWIST dataset has a temporal footprint of 17.5s, while the 3D through-time radial GRAPPA has a temporal footprint of 3.5s.

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Figure 6.6. Zoomed sub-volume MIP images of the time resolved contrast-enhanced renal MRA exams for the same subject using through-time radial GRAPPA acceleration (left) and TWIST acceleration (right 3 frames). The leftmost image shows the renal arteries and aorta at peak aortic/arterial enhancement for the radial GRAPPA exam. The corresponding TWIST image obtained from a near-identical timepoint is shown to the right of the first image. The aorta and arteries continue to enhance further into the subsequent two frames, reaching peak enhancement in the rightmost image, an effect caused by the view-sharing reconstruction. The first and second order branches of the renal arteries (solid, straight arrows in TWIST images) are better depicted in the single, peak enhancement frame of the radial GRAPPA exam. As the view-shared TWIST exam reaches peak aortic enhancement in the two rightmost frames, parenchymal enhancement (curved arrows) and venous enhancement (open arrows) complicate visualization of the small branch vessels.

Figure 6.7. A time resolved, contrast-enhanced, breath-held renal MRA exam was reconstructed using 3D through-time radial GRAPPA with a calibration time of 2.2 min. This data was accelerated in-plane with a factor of 12.6 with respect to Nyquist, and a partial Fourier acquisition was used along the partitions direction. Three time-resolved, coronal frames are shown here as MIPs. These images have spatial resolution of 1.5mm x 1.5mm x 3mm and a temporal resolution of 3.5 s/frame.

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Figure 6.8. A time resolved, contrast-enhanced, breath-held renal exam was reconstructed using 3D through-time radial GRAPPA. This data was accelerated in-plane with a factor of 12.6 with respect to

Nyquist, and a partial Fourier acquisition was used along the partition direction. The same coronal frame is shown here as MIPs for four different GRAPPA weight calibration schemes: 8 calibration partitions with

16, 8, 4, and 2 calibration repetitions (A, B, C, and D). Calibration acquisition times are noted in the lower left corner (Cal time). These images have a spatial resolution of 1.5mm x 1.5mm x 3mm and a temporal resolution of 3.5 s/frame.

Section 6.2.4. Discussion In this study, simulations and in vivo experiments were performed to explore through-

partition and through-time calibration for 3D through-time radial GRAPPA. Similar to the previously reported results for 2D imaging (117), through-time calibration can

improve reconstruction results in 3D data. However, this alone is not the best way to

allocate calibration time since different partitions and different time points do not provide

equivalent information quality to the GRAPPA weight solution. In fact, our simulations

and acquired data show that the lowest RMSE was reported for 8 partitions. At a higher

number of partitions, the reconstruction error levels off, and even begins to increase. This

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is likely due to the low signal content in the outer regions of k-space; these outer

partitions do not provide as much information as partitions closer to the center of k-space.

At lower a number of partitions (≤2), the reconstruction error increases. This is most likely due to the fact that the central partition appears similar at different points in time

(as it is simply the projection of the 3D volume, which appears similar despite motion), and adding additional repetitions of just the center partition do not provide significant new information for the calibration. By encoding more partitions, more different calibration data is available than when simply performing through-time calibration using one or two central partitions. As expected, increasing the calibration time reduces the overall error at all partition/repetition combinations. Additionally, these simulations describe results for two segment sizes for through-k-space calibration. As mentioned in the theory section and in previously published results for 2D reconstructions (117), there

is a trade-off in segment size selection, and a large segment size can introduce

inaccuracies in the GRAPPA weights. Therefore, both segment sizes were selected to be

relatively small, and the 4x8 segment size has a lower RMSE, which is due to the larger

number of kernel occurrences.

In summary, simulations show that multiple low spatial resolution partitions with as

many calibration repetitions as can be performed within a given exam time offer the

lowest RMSE for a given calibration time. For this particular simulation set-up, which

was meant to mimic the in vivo renal contrast-enhanced acquisition, eight partitions

resulted in the lowest RMSE. It is important to note that these recommendations are

based on the kernel size, the acceleration factor, the coil array, and the object used in

these simulations, and therefore may be different in other applications. However, an

123 examination of the in vivo data reconstructed with different parameters shows good agreement of the results obtained from the simulations despite these differences.

In order to compare the 3D through-time radial GRAPPA reconstruction to existing non-

Cartesian parallel imaging techniques, CG SENSE was also used to reconstruct this highly accelerated data. While both reconstructions show improved results over the undersampled data, the GRAPPA reconstruction produces fewer residual aliasing artifacts and lower noise than the CG SENSE reconstruction. It is hypothesized that this difference in image quality is due to potential mismatches between the coil sensitivity maps used and the actual undersampled images, which can lead to errors in the CG

SENSE reconstruction that would not be found in the 3D through-time radial GRAPPA reconstructions. Thus, in such dynamic studies, the use of a technique that does not require coil sensitivity maps, such as through-time radial GRAPPA, may be beneficial. It is important to note that the regularization used in the CG SENSE reconstruction was not optimized in this study, and different regularization methods or parameters result in improved reconstructions.

The 3D through-time radial GRAPPA method was also compared to an exam that was acquired with a commercially available Cartesian TWIST acquisition. These images illustrate how the short temporal footprint of 3D through-time radial GRAPPA can lead to improved image quality. While the spatial and temporal resolutions of the two scans were nominally similar, the overall temporal footprint for the TWIST dataset is 17.5s, while that of the 3D through-time radial GRAPPA data set is 3.5 s. The absence of view- sharing and short temporal footprint in the radial GRAPPA examination reduces edge blurring. Edges and fine details in the second and third order branches of the renal

124 arteries can be better visualized in the first frame of the 3D through-time radial GRAPPA images in comparison with the view-shared TWIST exam. The hepatic and splenic branches of the celiac artery are better depicted in the 3D through-time radial GRAPPA exam in the same frame. Similarly small branches of the superior mesenteric artery were better visualized in the 3D through-time radial GRAPPA exam. While a single optimal frame depicts the arterial enhancement for the 3D through-time radial GRAPPA exam, the small vessels difficult to see in the corresponding TWIST frame. Subsequent TWIST frames at peak aortic/arterial enhancement start to show parenchymal enhancement and venous enhancement, thus also precluding optimal evaluation of the small arteries.

As mentioned above, motion or changes in signal are expected to occur during the through-time calibration. This motion will provide different calibration data for repetitions of the same partition. If the motion experienced is correlated with the calibration acquisition time or the motion is minimal, this may potentially limit the amount of different calibration data provided by through-time calibration. A potential solution could be to randomize the partition encoding order and spacing, which may improve the uniqueness of the calibration data by randomizing the timing of each repetition of the same partition. While this was not likely (or experienced) in renal contrast-enhanced exams, it may be an additional calibration methodology to be considered in some applications such as cardiac imaging.

The primary drawback of this method is the additional scan time needed for GRAPPA weight calibration. However, it can be seen here that with a hybrid approach of combining through-k-space (within plane and through-partition) and through-time calibration, good reconstruction quality can be achieved at clinically acceptable scan

125 times. Furthermore, the improvement in image quality of highly accelerated data may justify an increase in overall scan time for many applications, especially when the additional scans place no additional burden on a patient. A period of less than two minutes of free-breathing scan time is a minimal addition to the overall study, especially when this time is used to produce robust, high quality, high spatio-temporal resolution imaging for the contrast-enhanced exam. Additionally, when performing multiple scans with the same coverage but different contrast, the same calibration data can be employed, allowing for the acceleration of several different scans during a single examination. If a reduced calibration time is desired, the simulations show that for this application, only eight calibration partitions should be acquired with a reduced number of calibration repetitions. While this will increase the reconstruction error, our results demonstrate the robustness of the 3D through-time radial GRAPPA reconstruction when smaller amounts of calibration data are used. When calibration time decreased to below 15 seconds, image quality in these subtracted MIP images is affected by an increase in noise, but remains clinically acceptable.

This implementation of 3D through-time radial GRAPPA has been demonstrated with in- plane, radial undersampling and partial Fourier applied in the partition direction. Further acceleration could be explored in future works by implementing parallel imaging along the partition direction (173,174), applying a CAIPIRINHA-type acquisition where undersampling in each partition is rotated with respect to neighboring partitions (173), using an asymmetric field-of-view (175), or by using more efficient trajectories as was shown with 2D through-time spiral GRAPPA (118).

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In conclusion, 3D through-time radial GRAPPA can be used to successfully reconstruct

highly accelerated non-Cartesian data. In simulation, the hybrid calibration scheme with

the lowest reconstruction error was found to be a moderate number of high signal central

partitions combined with as many temporal repetitions as exam time permits. These

findings were then applied by acquiring in vivo calibration data with eight partitions and

16-20 repetitions to reconstruct data with an in-plane acceleration factor as high as 12.6

with respect to Nyquist criterion in addition to partial Fourier along the partition direction

to achieve a time-resolved, renal contrast-enhanced exam with a temporal resolution of less than 4 s/frame and a spatial resolution of approximately 1.5 mm x 1.5 mm x 3 mm.

Section 6.3. Free-breathing, High Spatiotemporal Resolution Renal Perfusion

Imaging

Section 6.3.1. Introduction In this study, a free-breathing, 3D high resolution renal perfusion exam is explored. We

utilize a highly-accelerated non-Cartesian stack-of-stars trajectory with a 3D through- time radial GRAPPA reconstruction that was fully described in Section 6.2 (67,117) to achieve high spatiotemporal resolution acquisition with full volumetric coverage of the kidneys. The high temporal resolution free-breathing images are registered to correct for inter-frame motion, and then a separable two compartment renal pharmacokinetic model

(153,160) is applied to estimate perfusion and filtration parameters.

Section 6.3.2. Methods

Image Acquisition and Reconstruction In this IRB-approved, HIPAA compliant study, ten asymptomatic volunteers (20 kidneys) were scanned after written informed consent. Volunteers were given no instructions

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regarding water, food, or caffeine intake prior to the study. Imaging was performed at 3.0

T (Magnetom Skyra, Siemens Healthcare, Erlangen, Germany) with a 18 channel body

matrix receive coil and spinal array coil (12-16 channels). The DCE MRI exam was

initiated immediately following injection of a half (in five volunteers) or quarter (in five

volunteers) dose by weight, of Gadopentetate Dimeglumine (Gd-DTPA, Magnevist, 0.05

and 0.025mmol/kg, Bayer, Berlin, Germany).

A spoiled gradient echo acquisition was performed with a stack-of-stars k-space

trajectory. For this cylindrical-shaped trajectory, data were sampled in-plane with a radial trajectory that is replicated along the partition direction using Cartesian encoding. To accelerate the acquisition, only radial undersampling was used (as described in (66)). The

in-plane radial trajectory was undersampled by a factor of eight such that 20 radial

projections were acquired for each partition. This yields an acceleration factor of 12.6

with respect to the Nyquist sampling criterion. This highly accelerated acquisition yielded

a temporal resolution of less than 3 seconds/frame. Scanning parameters were tailored to

fit the anatomy of each volunteer while maintaining a scan time of less than 3 seconds per

volume. Other scanning parameters include: oblique coronal slab orientation, repetition

time: 3.02-3.78 ms, echo time: 1.3 ms, flip angle: 12°, field-of-view (FoV): 350-370mm2

x 79.2-92 mm, spatial resolution: 2.2-2.3 mm3, bandwidth: 710 Hz/pixel, partial Fourier in partition direction: 6/8, acquisition time: 2.1-2.9 s/frame, number of frames: 135, total

DCE MRI acquisition time: 4.7-6.5 min.

As described in section 6.2, the stack-of-stars data were undersampled in-plane in every partition to meet the stringent needs of the renal DCE MRI exam. This results in poor image quality with noise amplification and radial aliasing artifacts. To mitigate these

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artifacts, images were reconstructed with 3D through-time radial GRAPPA (67,117). In this reconstruction, GRAPPA weights are applied to the acquired radial projections to reconstruct the missing radial projections. These GRAPPA weights are calibrated for small segments of the radial trajectory using fully-sampled, 3D time-resolved calibration data (67,117). To perform the 3D through-time calibration, an additional fully-sampled dataset was acquired with the following parameters after the renal DCE-MRI exam: 160 projections/partition, 8 low resolution partitions with the same field-of-view as the undersampled data, 16 temporal repetitions, segment size of 4 projections x 8 readout points, and a calibration acquisition time of approximately 1-1.3 minutes. Data were further accelerated with a partial Fourier acquisition along the partition encoding direction, and were reconstructed using projection onto convex sets (POCS) prior to performing a Fourier transform along the partition direction. Density compensation and the non-uniform fast Fourier transform (94) were then applied to the in-plane radial data to provide reconstructed images.

All reconstructions were performed offline using MATLAB (The Mathworks, Inc.,

Natick, MA). The 3D through-time radial GRAPPA reconstruction is entirely automated, and only requires the user to select calibration parameters (segment size, number of calibration repetitions and partitions) that have been previously optimized (67,117).

Further reconstruction details can be found in (67,117) and open-source code for through- time radial GRAPPA can be found in (66).

Image Registration All data were acquired without breath-holds, and volunteers were asked to breathe normally during data acquisition. Because of the free-breathing acquisition, respiratory motion between frames must be compensated prior to DCE MRI analysis. Here, a

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registration technique was implemented based on work by Chen, et al. (176), which was

previously applied to free-breathing, dynamic contrast-enhanced liver data.

Registration algorithms typically produce better results when applied to images with similar contrast or appearance. For example, registering images during the corticomedullary phase of enhancement to images during the nephrographic phase can be difficult due to the markedly different appearance of the kidneys at these times. To avoid this problem, this method utilizes several reference frames where the kidney is at the same spatial location but at different points in enhancement. The algorithm can then select the reference frame that is temporally nearest to each frame for registration.

This strategy requires that all reference frames have negligible motion between them.

Thus, a canny edge filter was applied to a single coronal slice, and an automated algorithm detected the top edge of the liver throughout the acquisition to track motion.

From these data, the most frequently occurring location was selected, and these frames were monitored to ensure that negligible motion occurred between the selected references. After the references were identified, the open-source FNIRT software

(FMRIB's Non-linear Image Registration Tool) was utilized to register each frame to the temporally nearest reference frame (177,178).

DCE-MRI Analysis A separable two-compartment pharmacokinetic model was used to quantitatively evaluate perfusion and filtration in the kidneys (153). This model describes the perfusion

(FP, mL/100mL/min) of gadolinium from the arteries to the tissue, where it disperses over

the tissue compartment volume (VP, mL/100mL). The model additionally considers the

filtration rate (FT, mL/100mL/min) of gadolinium from the tissue into the renal tubules,

where it disperses over tubular volume (VT, mL/100mL). The mean transit time (MTT) of

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the tracer in the tissue and renal tubular compartments are also denoted as TP and TT,

respectively. As previously described by Sourbron, et al. (153), the concentration of

contrast agent that is transferred to the tissue compartment can be described by the following equation:

( ) = × ( ) [6.1], −푡 −1 �푇푃 퐶푃 푡 푇푃 푒 퐶퐴 푡 where CA(t) is the arterial input function and CP(t) is the concentration of gadolinium in

the tissue compartment. Note that the arterial input function is normalized to account for

the hematocrit Hct (by a factor of (1-Hct), where Hct is assumed to be 0.45).

The contrast agent will be filtered from the renal tissue compartment to the tubular compartment as described in the following equation:

= (1 ) [6.2], 푑퐶푇 푉푇 푑푡 퐹푇퐶푃 − − 푓 퐹푇퐶푇 where CT is the concentration of gadolinium in the tubular compartment. This model also

accounts for reabsorption of the contrast agent, which is denoted in the equation above as

a fraction that is reabsorbed f. Note that the mean transit time of the tubular compartment

will be normalized by the amount of concentration that is not reabsorbed (1-f), such that

= . ( ) 푉푇 푇푇 퐹푇 1−푓 It is important to note that the tissue and tubular compartments cannot be separately

measured, and thus a weighted sum of the two compartments reflects the concentration

changes in acquired renal DCE MRI data:

( ) = ( ) + × ( ) [6.3], −푡⁄푇푇 퐶 푡 푉푃퐶푃 푡 퐹푇푒 퐶푃 푡

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where C(t) describes concentration of gadolinium for the whole kidney or the renal

cortex. Because the arterial input function is used directly in this model, recirculation

effects are accounted for. Using this model, four parameters can be independently

estimated: FP (Perfusion rate), TP (MTT in the plasma compartment), FT (Filtration rate),

and TT (MTT in the tubular compartment). Complete details of this model have been described previously (153,157).

In this study, an ROI in the aorta proximal to the renal arteries was used for the arterial input function. Based on the assumptions of the model (153), a ROI analysis was

performed using a whole kidney ROI. Pixelwise parameter mapping was also performed

on the renal cortex, which was segmented by thresholding signal intensity values in a

frame during corticomedullary enhancement.

To convert signal intensity values to concentration of Gd-DTPA, the following equation

was used (32):

= + [6.4] 1 1, 푇1 푇1 표 푟퐶

where T1,o is the baseline T1 of the tissue (used literature value (39)), T1 is its shortened

value in the presence of Gd-DTPA, r is the relaxivity of the contrast agent (used literature

value (37)), and C is the concentration of the contrast agent. T1 was computed using

signal values and the FLASH signal intensity relationship (32). When converting signal to T1, it was assumed that there were no substantial changes in coil sensitivities (or other

scaling factors) during the concentration time-courses. The resulting concentration time courses were used to estimate perfusion and filtration parameters (FP, TP, FT, and TT) with

132 a non-linear least squares fit using MATLAB (‘fminsearch’ algorithm, The Mathworks,

Inc., Natick, MA).

The accuracy of the perfusion and filtration parameter estimation is dependent on the

SNR of the acquisition. To evaluate how acquisition noise may propagate to errors in parameter estimation, the noise level of the acquisition was measured using the bootstrapping method (179). In one volunteer, a noise scan was acquired in addition to the undersampled data (where the noise scan had the same acquisition parameters but no

RF excitation). The contrast-enhanced scan was acquired after administration of a quarter dose of Gd-DTPA to evaluate noise propagation in the lower SNR case. The randomly reordered noise was added to the undersampled data, which were then reconstructed as described above. This process was repeated to generate 20 datasets. The ROI pharmacokinetic analysis described above was performed on each dataset, and FP, TP, FT, and TT were quantified.

Section 6.3.3. Results Using the 3D through-time radial GRAPPA reconstruction algorithm, highly undersampled data were acquired and successfully reconstructed to achieve a high spatiotemporal resolution. In Figure 6.9, a single partition from a 3D data set is shown at two time points during contrast enhancement. The top row in Figure 6.9 shows the reconstructed undersampled data to demonstrate the level of aliasing artifacts and noise amplification present in the underlying date. The second row shows these same images after reconstruction with 3D through-time radial GRAPPA, where the aliasing artifacts are successfully removed. The successful reconstruction of highly accelerated data with

3D through-time radial GRAPPA is also shown in Figure 6.10 for a second dataset. Here, three partitions of the 36 acquired partitions are shown at 3 different times during contrast

133 enhancement. From these data, image details can be seen, such as corticomedullary differentiation during the arterial phase, despite using a highly undersampled and free- breathing exam. Furthermore, these data have a high spatiotemporal resolution without sacrificing 3D coverage.

Figure 6.9. This figure demonstrates the successful reconstruction of highly accelerated stack-of-stars data with 3D through-time radial GRAPPA. These data were acquired at an acceleration of 12.6 with respect to

Nyquist sampling criterion with a spatial resolution of 2.2mm3 and a temporal resolution of 2.3s/frame. The top row shows the original undersampled data with a gridding reconstruction to show the level aliasing artifacts and noise amplification present in the acquired data. The bottom row shows reconstructed images with the 3D through-time radial GRAPPA reconstruction. The undersampled and reconstructed images are shown for a single partition (from the 40 acquired partitions) at two different time points during contrast enhancement at the corticomedullary phase (23s post injection) and at the nephrographic phase (98.9s post injection).

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Figure 6.10. This figure shows reconstructed images for 3 partitions from the 36 acquired partitions and 3 time points during the corticomedullary, nephrographic, and excretory phases of enhancement. These data were acquired at an acceleration of 12.6 with respect to Nyquist sampling criterion with a spatial resolution of 2.2mm3 and a temporal resolution of 2.1s/frame. Despite the high level of acceleration and free- breathing nature of the acquisition, the images maintain excellent image quality.

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Figure 6.11. Images are acquired with a free-breathing acquisition. Respiratory motion is observed by tracking motion at the top of the liver, which provides a pixel position over time as shown in Figure 6.11A.

Images at the most frequently occurring position (marked by red ‘x’) are used as references for image registration. It is assumed that no motion occurs between these reference images. All other time frames are registered to their temporally adjacent neighbor. The motion observed during data acquisition and the successful registration of this data is shown in Figure 6.11B. The top row of images shows a single partition over fiver adjacent time points that were acquired during a deep inhale (time points noted by red circles in Figure 6.11A). The bottom row shows these images after registration. The last column shows a subtraction of the first and last source images. Figure 6.11B demonstrates that there can be problematic renal motion during the acquisition, and that this motion can be successfully compensated with the registration algorithm. Finally, Figure 6.11C shows a single pixel’s signal intensity time course before and after image registration (pixel located at the top of the right renal cortex). By comparing these two plots, it is clear that oscillations due to respiratory motion are largely removed.

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After image reconstruction, the registration algorithm began by detecting motion that occurred at the top of the liver, which provides a pixel position over time as shown in

Figure 6.11A. The most frequent position (marked by red ‘x’) are all used as reference images for image registration, and all other images are registered to the temporally nearest reference. Figure 6.11B shows images before and after registration is applied.

Five adjacent time points during the excretory phase of enhancement were selected during a deep inhale by the volunteer (shown by red circles in Figure 6.11A). Source images are shown in the first five columns of Figure 6.11B before (top row) and after

(bottom row) registration. The final column in Figure 6.11B shows a subtraction of the last time point from the first time point to demonstrate the change in signal. While respiratory motion of the kidney is relatively small, it can be seen in both the source and subtracted images in Figure 6.11B (top row). Figure 6.11B (bottom row) demonstrates the non-rigid 3D registration’s ability to mitigate respiratory motion. Because the respiratory motion of the kidney is relatively small, an ROI analysis that evaluates the whole kidney is not substantially degraded by respiratory motion. However, this motion does degrade the quality of a pixelwise analysis as shown in Figure 6.11C. This figure shows the change in signal intensity in a single pixel at the edge of the renal cortex. The registration algorithm clearly reduces signal fluctuations due to respiratory motion in that pixel, which would affect the resulting pharmacokinetic analysis.

After reconstruction and registration, pharmacokinetic analysis was performed both with pixelwise mapping and using ROIs, to quantify perfusion, filtration rates and mean transit times. The measured arterial input and renal concentration time courses from ROIs in aorta and in a single slice of the renal parenchyma are shown in Figure 6.12A and 6.12B

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for data acquired after a half and quarter dose, respectively, and a representative model fit

of the data is shown in Figures 6.12A-D. These data show typical concentration ranges that were seen across our population and also good model fit of the data. For each ROI analysis in 20 kidneys, an average root mean squared error of 1.7% was seen between the data and the model fit. The quantitative parameter estimation results from this analysis using an ROI on a single slice around the whole kidney can be seen in Table 6.2 where

10 kidneys were analyzed separately in five asymptomatic volunteers for each dose (total of 20 kidneys in ten volunteers). The bootstrap simulations resulted in a standard deviation of 7.6 ml/min/100ml for Fp, 0.09s for Tp, 0.7 ml/min/100ml for FT, 6.5s for TT.

Table 6.2. Summary of renal perfusion and filtration parameters using the separable compartment model

for a whole kidney ROI analysis. Each column reports Mean ± Standard Deviation. A range of average

values found in the literature for normal kidneys is also provided for reference.

Quarter Literature Half Dose Dose Pooled Data Values Refs. (n=10 kidneys) (n=10 (n=20 kidneys) (17,153,154) kidneys) Renal Perfusion 212.5 ± 218.1 ± 57.1 215.3 ± 51.3 ~ 171.5-229.0 (FP, ml/min/100ml) 47.6 MTT in Plasma 4.8 ± 2.2 3.3 ± 0.8 4.0 ± 1.8 ~6.5 (TP, seconds) Renal Filtration 28.7 ± 10.0 25.8 ± 9.0 27.2 ± 9.4 ~21.3-31.0 (FT, ml/min/100ml) MTT in Tubules 124.2 ± 131.1 ± 60.2 127.6 ± 48.5 ~125 (TT, seconds) 36.3

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Figure 6.12. Figure 6.12A shows a representative arterial input function (AIF) and renal enhancement

curves from ROIs placed in the aorta and around the whole kidney. Figures 6.12A and 6.12B also show the

model fit of this data. This model fits the renal enhancement data well with very low residuals between the

model and the data.

Figures 6.13 and 6.14 show perfusion rate, filtration rate, and mean transit time pixelwise

parameter maps for several partitions from two different volunteers after administration

of a half and quarter dose of Gd-DTPA. These parameters maps are overlaid on the anatomical images for reference. Although only 4 partitions are shown here, more than

36 partitions were actually acquired for these high spatial resolution 3D acquisitions.

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Figure 6.13. Figure 6.13 shows pixelwise parameter maps of the four parameters (perfusion, filtration, and mean transit times of the plasma and tubule compartments) from the pharmacokinetic renal model in 4 of the 36 acquired slices. These data were acquired after administration of a half-dose (by weight) of Gd-

DTPA.

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Figure 6.14. Figure 6.14 shows pixelwise parameter maps of the four parameters (perfusion, filtration, and mean transit times of the plasma and tubule compartments) from the pharmacokinetic renal model in 4 of the 40 acquired slices. These data were acquired after administration of a quarter-dose (by weight) of Gd-

DTPA.

Section 6.3.4. Discussion While much of present clinical MRI focuses on anatomical imaging, techniques including

DCE MRI are promising because they could add a quantitative underlay to renal imaging

(10,11,13,17,154). The combination of perfusion quantification with anatomical imaging could provide complete renal assessment in a single comprehensive MRI exam

(7,9,12,154–156). However, in order for perfusion measurements to find widespread utility in the clinical environment, the exams must be easy to implement, robust to patient compliance issues such as problems with breath-holding, and should be performed at clinically relevant resolutions with complete volumetric coverage. In this study, we

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aimed to provide a high spatiotemporal resolution exam with full coverage of the kidneys

without breath-holding. To achieve the desired resolution and volumetric coverage, the

data were acquired with a highly undersampled non-Cartesian trajectory and were

reconstructed with 3D through-time radial GRAPPA (67,117). Furthermore, it can be

easily implemented with real-time reconstructions (180). In addition, this entire technique

is performed without breath-holds, which simplifies the exam for use in patients who

have difficulty holding their breath, in and of itself a critical improvement in renal

imaging.

3D through-time radial GRAPPA was used to successfully reconstruct data with a

temporal resolution of better than 3s/frame using an acceleration factor of 12.6 with

respect to the Nyquist criterion and partial Fourier in the partition direction. Despite this

high degree of undersampling, the images retain excellent quality, as can be seen in

Figures 6.9 and 6.10. In contrast to other reconstruction techniques, an advantage of 3D

through-time radial GRAPPA reconstruction is that the temporal footprint is the same as

the temporal resolution, which for these exams ranged between 2.1 and 2.9s/frame. No

view-sharing or temporal filtering was employed to reconstruct the data, thus

guaranteeing a high fidelity reconstruction. This short, well-defined temporal footprint allowed for accurate pharmacokinetic analysis of renal enhancement, with obtained parameters in good agreement with the published literature.

For quantification of renal perfusion and filtration, images are acquired for several

minutes after contrast administration. In order to avoid errors due to motion, image

registration must be performed prior to pharmacokinetic analysis (181). While a lot of

research has been explored for registration of dynamic data, the additional challenge of

142 changing contrast throughout the acquisition must also be considered. Previous approaches have successfully utilized a wide range of registration techniques (153,182–

189). Respiratory motion can be minimized by performing multiple breath-holds

(148,159,183,190), but patient fatigue could affect compliance, and the exam is complex for both the patient and the clinical technologists. Moreover, motion between the multiple breath-holds is still problematic, and missing data between breath-holds could affect quantitative accuracy. In order to alleviate these problems, data acquisition in this study was completely free-breathing, and images were retrospectively registered using FNIRT.

This approach has many advantages. First, because this is exam is completely free- breathing, patient comfort and compliance is greatly improved, and the scans are very easily performed. Second, the registration algorithm can be easily implemented offline using a canny edge detection algorithm (MATLAB) and open-source non-rigid registration methods.

Because respiratory motion is relatively small for the kidneys, the effect of motion on signal intensity curves in the ROI analysis is minimal. However, motion is more problematic when generating a pixelwise parameter map as seen in Figure 3C. The registration results demonstrated in Figure 3 show that the algorithm works well despite large changes in contrast and non-rigid motion throughout the acquisition, which allowed for improved pixelwise quantitative analysis. Respiratory motion during the 2-3s acquisition of each individual frame was not corrected. However, as seen in the images in

Figures 6.9-11, intra-frame respiratory motion was minimal and did not cause deleterious image artifacts.

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Functional evaluation of both kidneys in ten volunteers was performed using a pharmacokinetic analysis that included renal perfusion and filtration parameters. Results shown in Figure 6.12 show a good model fit with low residual error with this ROI analysis. The bootstrap error analysis shows that measurement errors in FP, TP, FT, and TT are 6.5-20 times smaller than the physiological variations in these parameters (Table 6.2) seen across the study population. The resulting estimated perfusion parameters (as shown in Table 6.2) are in good agreement with those previously reported in the literature (153).

The filtration rate parameter (FT) is directly proportional to GFR (referred to here as estimated GFR or GFRest) (153). In order to determine GFRest values, a typical single kidney weight of 200g and a tissue density of 1g/ml were assumed. For the half dose data, the mean (±standard deviation) single kidney GFRest was 57.4ml/min±20.0, and the mean (±standard deviation) GFRest per subject was 114.9ml/min±38.4. For the quarter dose data, the mean (±standard deviation) single kidney GFRest was 51.5ml/min±17.9, and the mean (±standard deviation) GFRest per subject was 103.0ml/min±36.5.

High resolution parameter mapping was also demonstrated in Figures 6.13-6.14. It should be noted that only a half-dose (by weight) of gadolinium contrast was utilized in Figure 5 and only a quarter-dose of gadolinium contrast was utilized in Figure 6.14. While previous studies have explored a low dose approach to renal DCE MRI, these results demonstrate that a low dose exam can still be used for a pixelwise analysis with this highly accelerated 3D non-Cartesian parallel imaging acquisition and reconstruction. This opens the door for developing a low dose comprehensive renal exam, or alternatively, using a second half-dose of contrast for other purposes such as a high resolution breath- held angiography study.

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A potential limitation for this methodology is that both the reconstruction and registration

methods are computationally demanding and must be implemented properly to avoid

clinically prohibitive durations. For this work, all image reconstructions and registrations were performed offline, and no parallelization or GPU processing was used. However, this implementation was too slow for clinical use, so a low-latency through-time radial

GRAPPA reconstruction using GPU programming was also implemented. This method has previously been used to perform real-time reconstructions with 2D data (180), and was adapted to work with the 3D stack-of-stars data. With the GPU-based reconstruction,

GRAPPA weight calculation took approximately 38.6 seconds, and reconstruction of each frame took approximately 15.6 seconds. Offline registration of the reconstructed data using FNIRT was approximately 9 min/frame using a single CPU core. The registration of each individual frame can be performed independent of all other frames, so registration could also benefit from parallelization.

In conclusion, 3D through-time radial GRAPPA was used to reconstruct data with a high temporal (2.1-2.9 s/frame) and spatial (approximately 2.2 mm3) resolutions with full 3D

coverage of both kidneys and the aorta (350-370 mm2 x 79-92 mm). The acquisition was

completely free-breathing, and the images were registered to compensate for respiratory

motion. This allowed for accurate high resolution 3D quantitative renal functional

mapping of perfusion and filtration parameters.

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Chapter 7. Magnetic Resonance Fingerprinting and Arterial Spin Labeling The work described in Section 7.2 of this chapter was presented as an oral presentation

at the International Society for Magnetic Resonance in Medicine (191).

Section 7.1. MRF Introduction Magnetic Resonance Fingerprinting (MRF) was recently introduced as a framework for quantifying multiple tissue properties simultaneously using MRI (192). The MRF moniker was selected because the measurement process in MRF is analogous to using fingerprinting for personal identification; a unique sample (fingerprint or MR signal) is acquired and is matched to an entry in a database that contains all possible samples. By matching the sample to a database entry, multiple parameters linked to that sample can be identified (personal information in fingerprinting or tissue parameters in MRF).

There are two main components of designing and implementing an MRF technique. First, the MRF pulse sequence must be designed to generate unique signal evolutions for each tissue type. The MRF pulse sequence should produce signals that are different in tissues with different combinations of parameters. In an ideal situation, these signals would be orthogonal, although this is not realizable in practice. In recent MRF techniques, the sequence is typically designed using pseudo-randomly varied sequence parameters. Once the pulse sequence has been determined, the second step in MRF is accurately modeling the resulting signals in order to create a dictionary of all possible signals. Signal modeling requires incorporating knowledge of MR physics and/or physiology, the pseudo-randomly varied sequence parameters, and all possible combinations of tissue properties. Once a sequence is designed and a dictionary is created, a pattern recognition

146 algorithm can be used to match acquired tissue signals to a single dictionary entry, which will provide access to all of the incorporated tissue properties.

Figure 7.1. MRF relaxometry pulse sequence and parameter quantification (192). These plots were generated from an actual experiment using a phantom that contains structures with different parameter values. (A) Pseudo-randomly varied TR time for MRF relaxometry sequence. (B) Pseudo-randomly varied

FA for MRF relaxometry sequence. (C) Signals from two different tissues. Note that these signals have different temporal evolutions. (D) Matching the acquired signal to a single dictionary entry.

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Figure 7.2. Parameter maps of Mo, T1, T2, and off-resonance of the brain acquired simultaneously using an

MRF experiment (192).

In its initial application, MRF was designed to quantify MR tissue parameters M0, T1, T2,

and the off-resonance frequency (192). A series of images are acquired with a balanced

steady-state free precession sequence and a constantly varied set of sequence parameters

(including but not limited to the TR, flip angle, and RF pulse phase) to generate unique

signals that do not reach a steady-state and that are temporally incoherent (192). An example set of sequence parameters and the resulting signal evolution over this series of images is displayed in Figure 7.1A-C. Figure 7.1C also demonstrates the different signal evolutions for two tissues with different parameter values. In order to generate a dictionary of signals, the Bloch equations are used to model the signal evolution of all possible tissues types with the known randomized sequence parameters and all parameter values (Mo, T1, T2, and off-resonance) over the known physiological ranges (192). The best matched entry can then be selected using a maximum inner product value (as seen in

Figure 2D), which then indicates the corresponding parameter values. In a previous

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study, these four parameters were quantified simultaneously using an approximately ten

second acquisition time, which yielded the in vivo parameter maps of the brain shown in

Figure 7.2.

One of the most important advantages of using the MRF approach is that it provides very accurate quantitative estimates of multiple tissue parameters with a very fast acquisition.

Furthermore, this approach to quantitative MR is a broad concept that could be applied to

many different properties. For example, Christen, et al. has shown that cerebral blood

volume, vessel radius, and oxygenation mapping can also be quantified with an MRF

approach (193). Here, a proof-of-principle study is described, showing an MRF approach

to measuring perfusion parameters with ASL. This project focuses on the adaptation of

the MRF framework to ASL, allowing a simultaneous quantification of perfusion, T1 and

transit time.

Section 7.2. MRF ASL

Section 7.2.1. Introduction ASL is an important MRI method that can provide perfusion measurements without the

use of contrast agents (47,48,194). As described in Chapter 3, ASL methods use protons

in arterial blood as endogenous tracers by manipulating their magnetization proximal to a

tissue of interest. The labeled protons flow from the location of labeling into the tissue of

interest during a user-selected post-label delay time (PLD), and freely diffuse into the tissue. Perfusion (f) is defined as the rate of flow from the vasculature into the tissue compartment. The perfusion of the labeled arterial blood flowing into the tissue of interest changes the MR signal, which can be detected and quantified. ASL is completely

non-invasive and offers many advantages for both neurological research and clinical

investigation (20,21). However, ASL is infrequently used in the clinical environment

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largely because the very small signal changes due to perfusion are extremely difficult to

measure. The problem can be partially countered by signal averaging, but the associated

increased in scan time is inefficient and can also lead to errors from patient motion.

Another difficulty in performing ASL exams in the clinical environment is selecting the

several sequence timing parameters (label duration and post-label delay times). The ideal label duration and post-label delay time can vary based on the patient’s age and condition. While some parameters can be generally prescribed (52), these do not necessarily work for all patients. Because these parameters are linked to the resulting

ASL signal, they must be selected carefully, which may lead to failed or inconsistent scan results.

Furthermore, modeling the changes in the MR signal to quantify perfusion with ASL is complicated by several sources of error. In traditional ASL techniques, a pair of images is acquired with and without a labeling pulse, and the change in signal between labeled and non-labeled (or control) images can be modeled (see Chapter 3 for details). There are several additional parameters that are needed in order to quantify perfusion. These additional considerations include knowing MR tissue properties (T1) and modeling the

arterial input function. Modeling the input function requires knowledge of another

parameter: the transit time of labeled spins (the time at which labeled spins arrive at the

tissue). These additional parameters each affect the accuracy of ASL measurements (50).

Quantifying these parameters would improve the accuracy of perfusion quantification and

may provide additional quantitative tissue information, but it would require separate

acquisitions that further increase exam time. Because of the need for efficient clinical

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exams, current ASL protocols make several assumptions to avoid additional quantitative

scans (52), which may decrease the quantitative accuracy.

To provide a clinically viable ASL exam, these limitations must be overcome. Ideally, the

ASL exam should be efficient, require limited user input, and quantify all ASL tissue parameters accurately and simultaneously. In this work, the MRF framework (192) is explored to improve the ASL experiment.

Section 7.2.2. Theory This project focuses on adapting the MRF framework to measure perfusion and other

ASL-relevant parameters including T1 and transit time (Δt). In order to use a MRF approach, a sequence must be designed that is sensitive to the parameters of interest and results in signals that are different for tissues with different parameters. The MRF ASL pulse sequence can achieve this goal by including a pseudo-random labeling scheme, which provides a non-uniform delivery of labeled arterial spins to the tissue of interest.

Once a sequence is a designed, the MRF ASL signals must be accurately modeled to generate a dictionary of all possible signals. The general kinetic model for ASL signals

(50,195) can be adapted to evaluate the pseudo-random signals generated by the MRF

ASL sequence. Using this dictionary, the unique signal for each spatial location is matched to a single dictionary entry using a pattern recognition algorithm, which provides access to our parameters of interest (f, T1, and Δt).

Figure 7.3. Simplified pulse sequence diagram for MRF ASL. Each sequence block contains a pair of label

and control images. Each block has pseudo-randomly varied label duration and post-label delay times, which are followed by data acquisition using a fully-sampled, single-shot spiral readout (RO).

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In this work, labeling is performed using a pseudo-continuous arterial spin labeling

(pCASL) scheme (51,53). In traditional pCASL, the sequence typically uses a constant, long label duration to provide maximal ASL signal change and a constant, long post-label delay time (PLD) to ensure complete delivery of labeled spins to the tissue (52). In contrast to previous works, MRF ASL applies these labeling/control pulses with a pseudo-random duration to vary the timing of the arterial input function. Additionally, it is known that varying the post-label delay time (PLD) allows for quantification of the transit time (196–198). For MRF ASL, the PLD is randomly varied to gain sensitivity to transit time. By varying the label duration and PLD times, the MRF ASL sequence produces a random in-flow of labeled spins to the tissue over time. Several other sequence parameters can also be changed similar to the original MRF sequence (such as flip angle, TR, TE) (192), although these are not explored in this study. The MRF ASL pulse sequence is described in a simplified sequence diagram in Figure 7.3. Figure 7.3 also shows that label and control pulses are alternated and sequence parameters are held constant for each pair of images. This allows for signal modeling and dictionary creation to explore using pairwise subtraction (as is done in traditional ASL), although this is not required for MRF ASL. The occurrence of labeling and control pulses could also be randomly varied, and the non-subtracted could also be analyzed.

Using the MRF ASL sequence and knowledge of the range of possible tissue parameters, the resulting signals must be accurately modeled to generate a dictionary of all signals.

Here, the single tissue compartment model described in Chapter 3 is used, but the solution must be adjusted to account for the random sequence and dynamic sampling of

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the ASL signal. First, a labeling function, L(t), is introduced to describe pseudo-random sequence timings:

( ) = 1, [7.1A]

퐿(푡) = 1푑푢푟푖푛푔, 푙푎푏푒푙푖푛푔 푝푢푙푠푒푠 [7.1B]

( ) =퐿 0푡, − 푑푢푟푖푛푔 푐표푛푡푟표푙 푝푢푙푠푒푠 [7.1C].

When L(t)=1, the 퐿arterial푡 labeling푑푢푟푖푛푔 function푃퐿퐷 푎푛푑 A(t)=1.푑푎푡푎 This푎푐푞푢 is푖 then푠푖푡푖표푛 used to model the arterial input function, Ma(t):

( ) = (1 2 ( ( ) , × ( ))) [7.2], −훥푡 �푇1 푎 푎 표 where × is the convolution푀 푡 푀 function,− 훼 M푘o is푡 −proton훥푡 푒 density, T퐴1,a 푡is the T1 of arterial blood,

α is labeling efficiency, Δt is the transit time of labeled blood, and k(t – Δt) is function

that affects for the dispersion of the label. The dispersion function k(t – Δt) is a gamma

shaped function as described in (199).

The tissue magnetization can then be described using the Bloch equation:

( ) ( ) = + ( ) ( ) [7.3]. 푑푀 푡 푀표−푀 푡 푓 푑푡 푇1 푓푀푎 푡 − 휆 푀 푡 Figure 7.4 provides plots of an example labeling function, arterial input function, and tissue response signal. It can be seen that the variations in the labeling function provide a variable input of labeled spins, which creates a unique change in tissue signal over time.

The tissue magnetization is then be sampled with an ASL data acquisition scheme.

Equations 7.1-7.3 can be used to model the MRF ASL signal. As described in Figure 7.5, the tissue and sequence parameters must be supplied as inputs to this Bloch equation model. Using all combinations of tissue parameters, a dictionary can then be created that contains all possible MRF ASL signal evolutions.

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Figure 7.4. Plots of an example labeling function (L(t)), arterial input function (Ma(t)), and tissue signal

(M(t)) using equations 7.1-7.3.

Figure 7.5. Diagram describing dictionary creation in MRF ASL.

Section 7.2.3. Methods In this proof-of-principle implementation, an MRF ASL experiment was designed using a

2D acquisition with 25 imaging blocks as described in Figure 7.3. Each block contained a label and control image, so a total of 50 images were acquired. All data were collected

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with constant acquisition parameters including acquisition TR and FA. As described in

the Theory section, a much more flexible sequence could be designed, which may offer

some benefits in generating unique MRF ASL signals. This work serveed as a starting point for exploring the MRF ASL experiment and its feasibility, and the sequence uses only pseudo-randomly varied label duration and post-label delay times. Figure 7.6 shows plots of the label duration and PLD timings in the MRF ASL pulse sequence. Using these sequence timings, the complete dictionary of signals was modeled using Equations 7.1-

7.3.

Figure 7.6. These plots detail the label duration times and post-label delay times for 25 sequence blocks

that each have one label and one control image. These will result in 25 labeled images and 25 control

images for a total of 50 images.

Parameter quantification was performed using a two-step process to find the best match

between the data and the dictionary. Signal changes related to T1 are substantially larger

in magnitude than those related to changes in transit time and perfusion. Therefore, a first

dictionary was constructed using a range of T1 values and neglecting perfusion and transit time (f=0, Δt=0) with non-subtracted signal. A first match was performed by finding the

maximum inner product between the acquired non-subtracted signal and this first

dictionary. A second dictionary was constructed using the quantified T1 value and a range

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of perfusion and transit time values with a pairwise subtracted signal. A second match

was performed by finding the maximum inner product between the acquired pairwise

subtracted signal and the second dictionary.

In order to test how MRF ASL will perform in the presence of noise, Monte Carlo

simulations were performed. A single dictionary entry was selected with parameter

values similar to grey matter (f=0.01 ml/g/s, Δt=1.2s, T1=1.4s). Random noise was then

added to this ideal signal at various SNR values, and the noisy signal was then matched

to the dictionaries by performing the two-step process described above. This is performed

for 1000 repetitions for several different SNR values. For each SNR level, the mean

percent error and standard deviation of percent error was calculated for each parameter.

In an MRF acquisition, image SNR can be difficult to define because the signal is not

constant and does not reach a steady-state. In this work, SNR was defined using the signal and noise levels from the first pairwise subtracted image:

( ) = ( ) [7.4]. 푎푏푠 푆푖푔푛푎푙퐼푀1−푆푖푔푛푎푙퐼푀2 푆푁푅푀푅퐹 휎 푁표푖푠푒퐼푀1−푁표푖푠푒퐼푀2 In order to insure that the Monte Carlo simulations are performed at realistic noise levels,

an SNR measurement was made using in vivo brain data and Equation 7.4. A small ROI

was placed in region of grey matter, and the mean signal from the first pairwise

subtracted image was measured. Noise level was measured using the standard deviation

of an ROI outside of the head.

The sequence was then tested on a 3T MRI scanner (Siemens, Skyra) using a 32 channel

head coil. Data acquisition was performed using a FISP sequence with a 2D single-shot

spiral readout and the following sequence parameters: TR/TE=20/2.5ms, FA=70°,

300mm2 FoV, and 64x64 matrix size. The total scan duration was 1.7 minutes. All

156 collected data were reconstructed using a non-uniform fast Fourier transform (94,101).

The spiral trajectory was measured for image reconstruction (200), and density compensation was performed using the method by Pipe, et al. (96,101). The first MRF

ASL dictionary was simulated using a range of T1 values from 0.02s to 3 s with a step size of 0.02s and assuming that perfusion and transit time were negligible. The second

MRF ASL dictionary was simulated using the quantified T1 value, perfusion values with a range of 0.001 ml/g/s to 0.02 ml/g/s with a step size of 0.0005 ml/g/s, and transit time values with a range of 0.5s to 2s with a steps size of 0.05s.

Section 7.2.4. Results Figure 7.7 shows a labeling function that describes the sequence timings that were defined in Figure 7.6. Using this labeling function, Figure 7.7 also shows the arterial input function and a representative tissue magnetization curve. The simulated tissue signals for two dictionary entries are also shown in Figure 7.8 for parameter values similar to white and grey matter. Despite having very different perfusion and transit time parameters, Figure 7.8 also shows that the non-subtracted signals are mainly affected by the differences in tissue T1. However, the pairwise subtracted curves demonstrate the signal differences due to the perfusion and transit time parameters.

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Figure 7.7. Labeling function, arterial input function, and tissue magnetization using the pseudo-random sequence parameters described in Figure 7.6. The red stars indicate where data is sampled. Note that the tissue magnetization also accounts the change in magnetization due to the RF pulse during data acquisition.

Figure 7.8. Plots of non-subtracted and pairwise subtracted MRF ASL signals simulated using tissue parameters similar to those in grey (black curve) and white (red curve) matter.

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Figure 7.9. Results from Monte Carlo simulations. Each plot shows the mean percent error and standard

deviation percent error for quantification of a parameter at different SNR levels. The red ‘x’ marks the

measured MRF ASL SNR level.

The results of the Monte Carlo simulation are shown in Figure 7.9. The mean and

standard deviation percent error in parameter quantification is shown for perfusion,

transit time, and T1. The simulations were performed at several SNR levels (as defined in

Equation 7.4). The measured SNR was 47.8, which is marked on each plot (red ‘x’).

Perfusion was the parameter most affected by noise. However, the mean percent error in

parameter quantification was low (8.8%) at an SNR of ~48. Error in transit time and T1

were very small at SNR values greater than 20. Mean percent error in transit time and T1

were less than 1% at an SNR of ~48.

Figure 7.10 shows the first nine pairwise subtracted images acquired in an axial 2D slice

of the brain in an asymptomatic volunteer. The change in signal due to variations in

labeling can be seen. In some frames, the label will be predominately in the blood

vessels, while others have more signals in the tissue.

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Figure 7.10. The first nine pairwise subtracted images in the MRF ASL sequence.

ROI analyses of the data shown in Figure 7.10 are shown in Figure 7.11. A small ROI was placed in a white matter and a grey matter region. Plots are shown for both the non- subtracted and pairwise subtracted matches between the data and dictionary. These plots demonstrate low error between the data and the selected dictionary entry. In the grey matter ROI analysis, the T1 was estimated to be 1.42s, the perfusion was estimated to be

0.0145 ml/g/s, and transit time was estimated as 1.55s. In the white matter ROI analysis, the T1 was estimated as 0.98s, the perfusion was estimated to be 0.001 ml/g/s, and transit

160 time was estimated as 2s. In addition to the ROI analysis, Figure 7.12 shows quantitative parameter maps for T1, perfusion, and transit time.

Figure 7.11. Plots of data and the matched dictionary entry from ROIs in grey matter (top row) and white matter (bottom row).

Figure 7.12. Parameters maps of T1, perfusion, and transit time quantified simultaneously with MRF ASL.

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Section 7.2.5. Discussion As described in Chapters 3 and 7, ASL provides perfusion measurements without the use of Gadolinium based contrast agents, which offers many advantages. However, widespread clinical adoption has been hampered by the low sensitivity of ASL, which results in heavy averaging and long imaging times. Additionally, many imaging parameters must be selected by the user, and these can differ across the patient population due to age and disease. This makes the exam very complicated for MR technologist and less robust in the clinical environment. Finally, quantifying perfusion with ASL is also dependent on several other parameters including tissue T1 and transit time. Most recommended techniques for clinical use make several assumptions to avoid performing further quantitative scans (52), but these can have effects on the quantitative accuracy of the resulting perfusion value (50,52).

In this study, a new approach to ASL data acquisition and parameter quantification was proposed by using the MRF framework. A proof-of-principle sequence was designed by pseudo-randomly varying the timings in the pCASL labeling. These variable timings produced different signals for tissues with different parameters, as seen in the simulated signals in Figure 7.8. The MRF ASL signals were then matched to a single dictionary entry using a pattern recognition algorithm. By selecting a single dictionary entry, MRF

ASL provided access to the quantitative tissue parameters that have been modeled. By quantifying the ASL tissue parameters of interest in a single acquisition, the perfusion quantification can improve perfusion accuracy with a single two minute acquisition.

Furthermore, the exam required no user selected parameter adjustment. Overall, this approach seeks to mitigate many problems that ASL currently faces in clinical translation.

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To explore the use of the MRF framework with ASL, simulations were performed to test the ability of MRF ASL to quantify the parameters of interest at several SNR levels. The

Monte Carlo simulation results in Figure 7.9 showed promising results with low error at

SNR levels measured in MRF ASL experiments.

The MRF ASL experiment was then tested in an asymptomatic volunteer on a 3T scanner. Figures 7.10-7.12 demonstrated promising initial results of this technique in a

2D brain scan. The ROI data in Figure 7.11 had a good fit to the matched dictionary entry with low residual error. Additionally, the parameter values seen in the grey and white matter ROI analyses and in the parameter maps were similar to those reported in the literature (39,52). Expected variations in tissue parameters were seen in these maps. For example, grey matter had higher perfusion and lower transit times than in white matter.

Also, the grey matter in posterior regions of the brain had a higher transit time than other grey matter regions.

Although these results are encouraging for simultaneous quantification of perfusion, transit time, and tissue T1, this initial evaluation should be expanded in future works to validate the quantitative values against standard methods. For example, T1 values should match those found in the standard inversion recover spin echo experiment. There is no gold standard perfusion or transit time quantitative method, but the parameters should correlate with those found in traditional pCASL methods. Additionally, the study should be expanded to include a larger group of asymptomatic volunteers, and could be further validated in patients whose diseases are known to have an effect perfusion.

In conclusion, the MRF framework was combined with ASL to provide simultaneous quantification of perfusion, transit time, and T1. The MRF ASL scan used a total

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acquisition time of 1.7 minute acquisition, which is less than the currently recommended

clinical ASL scan protocol (using a 2 - 4 minute acquisition) (52). The acquisition required limited user input (only for selection of the imaging volume and labeling planes) because all timing parameters are pre-selected to be pseudo-randomly varied. Promising initial results were seen in simulations and in initial in vivo tests in the brain.

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Chapter 8. Conclusions

Section 8.1. Summary Tissue perfusion is an important metric that can provide valuable information for

diagnosis of disease, treatment planning, and treatment follow-up. MRI can quantify

perfusion both with and without Gd-based contrast agents, and can provide spatially-

localized perfusion maps. However, these techniques are rarely used in the clinical environment. The works in this thesis focused on providing novel data acquisition and/or reconstruction techniques to overcome limitations in DCE MRI and ASL in order to provide clinically-viable perfusion quantification exams (67,123,146,191).

DCE MRI faces several challenges in clinical implementation. One of the biggest challenges in all DCE MRI applications is balancing the need for large volumetric coverage at relevant spatial resolutions and the need for a high temporal resolution.

Chapters 5 and 6 describe two different strategies to reconstruct undersampled DCE MRI data. Both of these techniques provided high spatiotemporal resolutions, and were able to provide good image quality.

Because many diseases require evaluation of large vessels using a contrast-enhanced

MRA exam, DCE MRI exams to evaluate the microvasculature cannot be performed in the same exam session because this would require doubling the dose of gadolinium based contrast agents. Thus, DCE MRI exams are not typically performed to avoid multiple MR exams. The MRAP exam (Chapter 5) provided a solution by simultaneously performing an MRA and perfusion measurement with a single dose of Gd-based contrast. This was discussed in the context of peripheral arterial disease, although this is not the only setting in which this limitation is encountered. The general methodology for designing an MRAP acquisition and evaluating the resulting MRA images and perfusion measurements could

165 be extended to other highly-accelerated data acquisition and reconstruction strategies and other clinical applications.

In abdominal imaging, DCE MRI also faces problems with respiratory motion. Most exams require multiple breath-holds with long durations and very few short breaks. The use of non-Cartesian parallel imaging methods (Chapter 6) allowed for data to be collected very quickly, so that respiratory motion does not corrupt data acquisition. In combination with retrospective image registration, renal DCE MRI exams can be performed without breath holds.

ASL exams are also not yet implemented in clinical exams due to current limitations.

ASL is inherently a low SNR technique, and in order to measure the very small signal changes due to perfusion, very long exam times are required. Furthermore, modeling the changes in the MR signal to quantify perfusion with ASL is complicated by several sources of error. For example, there are multiple unknown parameters that affect the ASL signal, such as T1 relaxation times and transit times of labeled blood. Quantifying these parameters requires separate acquisitions that further increase exam time. In Chapter 7, the use of a novel quantitative MR framework MR Fingerprinting (MRF) is proposed

(192) to improve the ASL experiment. It is shown that the unique signal evolution is less sensitive to noise, and can quantify parameters even at low SNR values. The proof-of- principle implementation in Chapter 7 showed promising results for simultaneously quantifying three parameters with an acquisition time of less than two minutes.

Section 8.2. Future Directions

Section 8.2.1. MRAP The implementation of MRAP proposed in Chapter 5 was targeted to the application of imaging the distal lower extremities. However, there are several applications that could

166 benefit from this type of exam, for example renal artery stenosis and downstream evaluation of perfusion (154), and simultaneous evaluation of large and small vessel pathologies in ischemic events such as stroke. To use MRAP for a different exam type, the sequence parameters would need to be adjusted to meet application-specific requirements including spatial resolution, temporal resolution, field-of-view, and the data undersampling parameters. However, as was shown in Chapter 6, the TWIST data acquisition may not be able to achieve the acceleration factors necessary for all applications, and alternative data acquisition and reconstruction techniques should be considered.

Using MRAP in the distal lower extremities has been explored in asymptomatic volunteers (123). In order to translate this exam to clinical use, the exam will need to be tested in patients with peripheral arterial disease to show the added clinical value of provided the MRA and perfusion measurements using MRAP. In a small study, MRAP was performed in patients with peripheral arterial disease, and the perfusion measurements showed a statistically significant correlation to currently used clinical metrics for disease severity (201). However, both the MRA and perfusion measurements will need to be compared to the current standard clinical exams. In future clinical translation studies, MRAP should be evaluated in a large patient population, and a full validation study should be performed.

Section 8.2.2. Renal Perfusion and Filtration Quantification using 3D Through-time Radial GRAPPA One of the remaining technical challenges of using 3D Through-time Radial GRAPPA clinically is that reconstruction time can become clinically prohibitive for DCE MRI data.

Additionally, image registration time can also be very long. In order to implement these

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in a clinical exam, both reconstruction and registration times must be greatly reduced.

Both of these operations could benefit from parallel computing because the

reconstruction and registration of each time frame is independent from all other time

frames. Image reconstruction with GPUs has already been demonstrated for 2D and 3D

through-time radial GRAPPA and has reduced reconstruction times (146,180,202).

Once the image reconstruction and registration algorithms have been efficiently

implemented, the renal exam must be demonstrated and validated in a patient population.

Currently, all renal perfusion exams have been performed in asymptomatic volunteers.

The exam should be validated in all renal applications of interest. Although there is no

gold standard renal perfusion metric, the results should match perfusion values in the

literature for the disease. Additionally, the DCE MRI filtration rate parameters should

match traditionally measured GFR values. Finally, the resulting DCE image should be

compared to standard contrast-enhanced, breath-held images (that are currently the clinical standard) to ensure image quality has not been degraded by using the high degree of non-Cartesian undersampling and by using a free-breathing acquisition.

Section 8.2.3. MRF ASL The MRF ASL results described in Chapter 7 demonstrate an initial feasibility for using this methodology to simultaneously quantify perfusion, transit time and T1. However,

further validation is still required to show quantitative accuracy of all estimated

parameters. T1 values can be compared to standard spin echo sequences in a static

phantom and to traditional MRF in vivo. Perfusion and transit time values can be compared to those measured with traditional pCASL methods. However, these values are only expected to correlate to one another, as traditional pCASL is not a defined gold

168 standard and may have inaccuracies due to each parameter being measured separately over long exam times.

Another important development will be to extend data acquisition to a 3D volume. The labeling duration and post-label delay times in ASL data acquisition are much longer than data acquisition. Thus, overall scanning efficiency will be increased by acquiring a 3D volume after each label.

In addition to further validation and technical development studies, MRF ASL must also be performed in a larger population of both normal and patient volunteers. Both of these will help demonstrate the robustness of this technique and its ability to quantify these parameters in the brain in healthy and diseased tissue.

Section 8.3. Conclusions This thesis explored novel strategies for measuring perfusion with MRI in order to overcome limitations that have previously reduced clinical utility. In the first project, large and small vessels in the distal lower extremities were simultaneously evaluated with the MRAP exam and a single dose of contrast agent. The MRAP exam provided the opportunity to measure perfusion in exams that would have previously only evaluated large vessels with an MRA exam. In the second project, a 3D non-Cartesian GRAPPA reconstruction with a through-time calibration was optimized and used to successfully reconstruct highly accelerated data in the kidneys. This acquisition and reconstruction method provided a sufficiently high temporal resolution to acquire a free-breathing renal

DCE exam, which maintained sufficient SNR to perform the exam with a low dose of contrast agent. Finally, a novel perfusion technique was introduced by using the MRF framework with ASL. This proof-of-concept implementation demonstrated the first MRF

169 perfusion measurement and described a general methodology for how to integrate ASL into the MRF framework.

170

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