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Reduction of Noise Due to Task Correlated Motion in Event Related Overt Word Generation Functional Magnetic Resonance Im...


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REDUCTION OF NOISE DUE TO TASK CORRELATED MOTION IN EVENT RELATED OVERT WORD GENERATION FUNCTIONAL MAGNETIC RESONANCE IMAGING PARADIGMS By KAUNDINYA S. GOPINATH A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2003

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Copyright 2003 by Kaundinya S. Gopinath

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There are more things in heaven and earth Horatio, Than are dreamt of in your philosophy. William Shakespeare, in Hamlet: Act 1, Scene 5

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ACKNOWLEDGMENTS This work would not have been possible without the active help and blessings of a number of people. Firstly, I would like to acknowledge my advisor, Dr. Richard Briggs, for his constant support and encouragement throughout the duration of my Ph.D. Dr. Briggs introduced me to the concepts of magnetic resonance imaging and functional MRI. I remember, like it was just yesterday, how he explained the concepts of relaxation and MR signal detection in the lab on the tenth floor of the dental sciences building. Dr. Briggs has always impressed me by his tremendous insights into MR physics. He has the ability to explain recondite concepts in concise laymans terms, which helped me greatly in my learning process. Dr. Briggs gave me freedom to go explore the world of MR, a field that amazes me with its scope and potential everyday. I remember, early in my first years with the group, how I used to come back from the library or some other place flush with excitement at some new idea I had or some new application of MR I had just encountered in some journal, and when I told Dr. Briggs he would give me more insight into the new idea or application, give me a few papers on it and even sometimes have some stories about some of the early MR personnel who had worked on it. I realized quickly that it was not easy to surprise him with a MR discovery. Apart from his academic influences, Dr. Briggs and Mrs. Dorothy Briggs have always been warm and generous and I enjoyed all the times when I had the occasion to mingle with them socially. iv

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I would like to acknowledge Dr. Bruce Crossons help in my education in FMRI. Dr. Crosson has an encyclopedic knowledge of brain function and anatomy and it always amazes me how he is able to describe the name and function of any obscure (to me) gyrus or sulcus one points to in the brain. Dr. Crosson always impressed me by his problem-solving approach of attacking FMRI issues. Whenever I have a discussion with him regarding data analysis and FMRI, I seem to come away with a new insight into the issue I have been discussing with him. Dr. Crosson has always been generous with his support and encouragement for my work. Dr. Crosson constantly impresses me with his energy and drive. It seems just as easy to come upon him at work at 1am at night or 8am in the morning. Also I have always enjoyed the parties at Dr. Crossons place. There is always something interesting happening when we have a function at his place. I would like to acknowledge the help Dr. Wesley Bolch provided in advancing my academic future. He took me into the department when my academic career was floundering after some lackluster years in the uninspiring Physics Department. I will eternally be indebted to him for giving me a second chance. In the future, I hope to live up to the trust he put in me. I enjoyed all the classes I took with Dr. Bolch. I was very impressed by his energy and attention to detail. I remember the marathon sessions he used to hold over the weekends going over the presentations of the whole class. At the end of these sessions, when everybody else seemed tired, he looked like he could go for a couple of sessions more. Dr. Bolch always has time for the students and his commitment to students well-being is unstinting. I consider myself fortunate to be in his department. I would also like to acknowledge my advisors Dr. David Hintenlang and Dr. John Harris. I have had the fortune to take some classes under Dr. Hintenlang and he always v

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impressed by the ease with which he taught. I remember sitting through his lectures and wondering at the easy pace only to look down at my work and see five or six pages of notes. And I always thought I did not take much notes. Dr. Hintenlang has the knack of relating recondite concepts (in say radiation shielding) to everyday events, which makes it easy to understand the subject. Dr. Harris has been very accommodating in sparing time for me at short notice. His academic engagements seem numerous and I appreciate him taking time off from his exciting pursuits at CNEL for me. The work conducted at his hybrid computation group seems very exciting. The advances being made in DSP will surely be of use in MRI/FMRI soon. I still marvel as how he and his collaborators can make a monkey move an artificial limb by just thinking about it. I would also like to acknowledge the help of my MR physics colleagues Dr. Kyung Peck and Dr. David Soltysik for useful discussions in physics. Also, I would like to thank our neuropsychologists Dr. Anna Moore, Dr. Keith White, Dr. Tim Conway, Dr. Allison Cato, Christina Wierenga, Megan Gaiefsky, Christy Milsted and Ashley Wabnitz for useful discussions, subject coding and neuro-psychological input. This work was conducted with the help of NIH grants P50-DCO388 and RO1-DCO3455, Department of Nuclear and Radiological Engineering and the Brain Rehabilitation Research Center, VA RR &D, Gainesville, Fl. Lastly, I would like to thank my family members: my parents who stand by me though I have not been always there for them, my sisters Radha and Kalli who have been a guiding force in my life and God for blessing me with a life I am happy to lead. vi

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TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF FIGURES.............................................................................................................x ABSTRACT.......................................................................................................................xv CHAPTER 1 BASICS OF MAGNETIC RESONANCE IMAGING................................................1 Origins of Magnetic Resonance Imaging.....................................................................1 Concepts of Magnetic Resonance Imaging..................................................................1 Spin Physics and Magnetization............................................................................2 Resonance..............................................................................................................3 Electro-Magnetic Induction...................................................................................3 Relaxation.....................................................................................................................4 Longitudinal Relaxation, T 1 ...................................................................................4 Transverse Relaxation, T 2 ......................................................................................5 Gradients, Spatial Encoding and K-Space....................................................................6 Basic MR Pulse Sequences...........................................................................................7 Spin-Echo Pulse Sequence.....................................................................................7 Gradient-Echo Pulse Sequence..............................................................................9 Contrast and Resolution.......................................................................................10 Fast Imaging Sequences.............................................................................................10 Echo-Planar Imaging...........................................................................................11 Spiral Imaging......................................................................................................12 2 FUNCTIONAL MAGNETIC RESONANCE IMAGING........................................14 Origins of Functional Magnetic Resonance Imaging.................................................14 Principles of BOLD Functional MRI.........................................................................15 BOLD Hemodynamic Response.................................................................................16 Spatio-Temporal Characteristics of BOLD FMRI.....................................................18 Spatial Specificity................................................................................................18 Temporal Resolution...........................................................................................18 Linearity of BOLD Response..............................................................................19 FMRI Experiment Design...........................................................................................20 Blocked Paradigms..............................................................................................21 vii

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Event-Related Paradigms....................................................................................21 FMRI Data Analysis...................................................................................................22 Overview.............................................................................................................22 Image Registration...............................................................................................23 FMRI Noise Characteristics................................................................................24 Parametric Methods and General Linear Model.................................................26 Inference..............................................................................................................29 ROC Analysis......................................................................................................31 3 MOTION AND FMRI................................................................................................32 Introduction.................................................................................................................32 Major Sources of Motion Artifacts and Deterministic Solutions...............................33 Static Magnetic Field Effects..............................................................................34 Spin History Effects............................................................................................37 Inter-Shot Motion................................................................................................38 Remarks...............................................................................................................41 Mechanistic Solutions.................................................................................................41 Motion Parameter Regression.............................................................................42 Stimulus-Correlated Motion................................................................................43 SCM-Ignoring Images.........................................................................................45 SCM-Detrending.................................................................................................46 Other Mechanistic Methods................................................................................46 4 TASK CORRELATED MOTION NOISE REDUCTION METHODS....................48 Selective Detrending...................................................................................................48 Selective Detrending: Methods...................................................................................50 Subjects and Task................................................................................................51 Image Acquisition...............................................................................................51 Data Analysis.......................................................................................................52 Deconvolution and Regression............................................................................53 Estimation of the TCM Signal Changes..............................................................53 Choosing Representative BOLD HRFs...............................................................55 Selective Detrending Algorithm..........................................................................55 Analysis of Detrended Time-Series.....................................................................60 Implementation of Motion Parameter Regression......................................................61 Implementation of the Screening Images Method......................................................62 Implementation of Non-Selective Detrending............................................................62 Receiver Operating Characteristics............................................................................63 Reduction of False Positives...............................................................................63 Retention of True Positives.................................................................................64 5 RESULTS AND DISCUSSION.................................................................................68 Results.........................................................................................................................68 Patient 1 (Pre-Treatment)....................................................................................70 viii

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Patient 1 (Post-Treatment)...................................................................................75 Patient 2 (Pre-Treatment)....................................................................................80 Patient 2 (Post-Treatment)...................................................................................84 Control Subject 1.................................................................................................90 Control Subject 2.................................................................................................93 Control Subject 3.................................................................................................97 Control Subject 4...............................................................................................102 Discussion.................................................................................................................106 6 CONCLUSION AND FUTURE WORK.................................................................112 Conclusion................................................................................................................112 Future Work..............................................................................................................115 APPENDIX SELECTED PUBLICATIONS........................................................................................117 Conference Abstracts................................................................................................117 ISMRM Proceedings: Oral Sessions.................................................................117 ISMRM Proceedings: Poster Sessions..............................................................117 Full Papers................................................................................................................119 LIST OF REFERENCES.................................................................................................122 BIOGRAPHICAL SKETCH...........................................................................................132 ix

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LIST OF FIGURES Figure page 1.1 Timing diagram of a 2-D Spin Echo Sequence..........................................................8 1.2 K-space diagram of a 2-D Spin Echo Sequence.........................................................9 1.3 Timing diagram of an Echo-Planar Imaging Sequence............................................11 1.4 K-Space diagram of an Echo-Planar Imaging sequence..........................................12 1.5 Timing diagram (left) and k-space diagram (right) of a 1-shot spiral EPI sequence...................................................................................................................13 2.1 Schematic representation of a BOLD hemodynamic response................................17 2.2 The estimated impulse responses for a auditory cortex voxel activated at F(16,470) = 30, p-val 0 (left) and a voxel with F(16,470) = 2.5 (right). The signal has been normalized to a unit maximum......................................................31 3.1 Two-shot spiral FMRI time series image of a mid sagittal slice showing swirl-like patterns arising from inter-shot motion. The image has been detrended of its time-series mean to better portray the effects of motion................39 4.1 Activation map overlaid on a low-resolution spiral FMR image. The red voxels correspond to R 2 > 0.2 and the yellow voxels denote R 2 > 0.3. The yellow arrow points to the voxel IRFs. The central voxel in the grid shows a selected TCM IRF....................................................................................................54 4.2 Activation map of the maximal absolute cross-correlation coefficient with TCM CC TCM thresholded by R 2 > 0.1. The yellow voxels correspond to max(CC TCM ) > 0.7 and the red denotes max(CC TCM ) > 0.5..............................................................58 4.3 Distribution of number of voxels undergoing non-selective detrending for a given max(CC BOLD ) as a fraction of the number of voxels at that max(CC BOLD ) for three different levels of separability, 0.2 (blue), 0.1 (green) and 0.0 (magenta) (a). Similar distributions for max(abs(CC TCM )) (b)....................60 4.4 Estimated hemodynamic response of a true positive right medial frontal voxel of patient 1 (pre-therapy) dataset (blue) and the corresponding fit to a generic hemodynamic response (green)...................................................................66 x

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5.1 Activation maps thresholded at R 2 > 0.2 for patient-1 (pre-scan) with no TCM noise-reduction (a), with selective detrending (b), with motion parameter regression (c), with ignoring 2 images after speech (d) and with non-selective detrending (e). The blue arrows indicate TCM voxel IRFs and the green arrows BOLD voxel IRFs....................................................................................................69 5.2 Fraction of voxels detected as a function threshold R 2 for (a) the false-positives test-bed and (b) the true-positives test-bed for aphasia patient 1 (pre-therapy scan). The blue curve (ML0) represents the case of no motion correction, the black curve (ML2) represents the method of ignoring the first 2 images after speech, the green curve (MPR) represents the motion-parameter regression method, the magenta curve (dtsel) represents the selective detrending method and the red curve (dt) represents the non-selective detrending method......72 5.3 Some representative TCM-related voxel IRFs (a); Some representative BOLD HRFs (b) from aphasia patient 1 (pre-therapy scan) data............................73 5.4 The effect of the methods of noise correction on a right medial-frontal voxel BOLD HRF exhibiting an early response for patient 1 pre-therapy scan (a). The effect of the methods of noise correction on a right inferior sulcus voxel, exhibiting both BOLD and TCM signal changes (b) for the same scan. The no-correction curve is hidden by the selective detrending curve in both figures.......................................................................................................................73 5.5 Activation maps thresholded at R 2 > 0.2 for patient 1 (post-therapy scan) with no TCM noise-reduction (a), with selective detrending (b), with motion parameter regression (c), with ignoring 2 images after speech (d) and with non-selective detrending (e). The blue arrows indicate TCM voxel IRFs and the green arrows BOLD voxel IRFs........................................................................................76 5.6 Some representative TCM-related voxel IRFs from patient 1 post-therapy scan (a). The effect of the methods of noise correction on a right medial-frontal voxel BOLD HRF exhibiting an early response for the same dataset (b). The no-correction curve is hidden by the selective detrending curve............................78 5.7 Fraction of voxels detected as a function threshold R 2 for (a) the false-positives test-bed and (b) the true-positives test-bed for aphasia patient 1 (post-therapy scan). The blue curve (ML0) represents the case of no motion correction, the black curve (ML2) represents the method of ignoring first 2 images after speech, the green curve (MPR) represents the motion-parameter regression method, the magenta curve (dtsel) represents the selective detrending method and the red curve (dt) represents the non-selective detrending method......................................................................................................................78 xi

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5.8 Activation maps thresholded at R 2 > 0.2 for patient-2 (pre-therapy scan) with no TCM noise-reduction (a), with selective detrending (b), with motion parameter regression (c), with ignoring 2 images after speech (d) and with non-selective detrending (e). The blue arrows indicate TCM voxel IRFs and the green arrows BOLD voxel IRFs...............................................................................81 5.9 Some representative TCM-related voxel IRFs from patient 2 pre-therapy scan (a). The effect of the methods of noise correction on a right medial-frontal voxel BOLD HRF exhibiting an early response for the same dataset (b). The no-correction curve is hidden by the selective detrending curve............................83 5.10 Fraction of voxels detected as a function threshold R2 for (a) the false-positives test-bed and (b) the true-positives test-bed for aphasia patient 2 (pre-therapy scan). The blue curve (ML0) represents the case of no motion correction, the black curve (ML2) represents the method of ignoring first 2 images after speech, the green curve (MPR) represents the motion-parameter regression method, the magenta curve (dtsel) represents the selective detrending method and the red curve (dt) represents the non-selective detrending method......83 5.11 Activation maps thresholded at R 2 > 0.2 for patient 2 (post-therapy scan) with no TCM noise-reduction (a), with selective detrending (b), with motion parameter regression (c), with ignoring 2 images after speech (d) and with non-selective detrending (e). The blue arrows indicate TCM voxel IRFs and the green arrows BOLD voxel IRFs...............................................................................85 5.12 Some representative TCM-related voxel IRFs from patient 2 post-therapy scan (a). The effect of the methods of noise correction on a right medial-frontal voxel BOLD HRF exhibiting an early response for the same dataset (b). The no-correction curve is hidden by the selective detrending curve............................87 5.13 Fraction of voxels detected as a function threshold R2 for (a) the false-positives test-bed and (b) the true-positives test-bed for aphasia patient 2 (post-therapy scan). The blue curve (ML0) represents the case of no motion correction, the black curve (ML2) represents the method of ignoring first 2 images after speech, the green curve (MPR) represents the motion-parameter regression method, the magenta curve (dtsel) represents the selective detrending method and the red curve (dt) represents the non-selective detrending method......87 5.14 Activation maps thresholded at R 2 > 0.2 for control subject 1 with no TCM noise-reduction (a), with selective detrending (b), with motion parameter regression (c), with ignoring 2 images after speech (d) and with non-selective detrending (e). The blue arrows indicate TCM voxel IRFs and the green arrows BOLD voxel IRFs........................................................................89 xii

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5.15 Some representative TCM-related voxel IRFs from control subject 1. The effect of the methods of noise correction on a right medial-frontal voxel BOLD HRF exhibiting an early response for the same dataset (b). The no-correction curve is hidden by the selective detrending curve.............................................................91 5.16 Fraction of voxels detected as a function threshold R2 for (a) the false-positives test-bed and (b) the true-positives test-bed for control subject 1. The blue curve (ML0) represents the case of no motion correction, the black curve (ML2) represents the method of ignoring first 2 images after speech, the green curve (MPR) represents the motion-parameter regression method, the magenta curve (dtsel) represents the selective detrending method and the red curve (dt) represents the non-selective detrending method......................................................91 5.17 Activation maps thresholded at R 2 > 0.2 for control subject-2 with no TCM noise-reduction (a), with selective detrending (b), with motion parameter regression (c), with ignoring 2 images after speech (d) and with non-selective detrending (e). The blue arrows indicate TCM voxel IRFs and the green arrows BOLD voxel IRFs........................................................................94 5.18 Some representative TCM-related voxel IRFs from control subject 2 (a). The effect of the methods of noise correction on a right medial-frontal voxel BOLD HRF exhibiting an early response for the same dataset (b). The no-correction curve is hidden by the selective detrending curve..................................96 5.19 Fraction of voxels detected as a function threshold R2 for (a) the false-positives test-bed and (b) the true-positives test-bed for control subject 2. The blue curve (ML0) represents the case of no motion correction, the black curve (ML2) represents the method of ignoring first 2 images after speech, the green curve (MPR) represents the motion-parameter regression method, the magenta curve (dtsel) represents the selective detrending method and the red curve (dt) represents the non-selective detrending method.....................................96 5.20 Activation maps thresholded at R 2 > 0.2 for control subject 3 with no TCM noise-reduction (a), with selective detrending (b), with motion parameter regression (c), with ignoring 2 images after speech (d) and with non-selective detrending (e). The blue arrows indicate TCM voxel IRFs and the green arrows BOLD voxel IRFs....................................................................................................98 5.21 Some representative TCM-related voxel IRFs from control subject 3 (a). The effect of the methods of noise correction on a right medial-frontal voxel BOLD HRF exhibiting an early response for the same dataset (b). The no-correction curve is hidden by the selective detrending curve................................100 xiii

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5.22 Fraction of voxels detected as a function threshold R2 for (a) the false-positives test-bed and (b) the true-positives test-bed for control subject 3. The blue curve (ML0) represents the case of no motion correction, the black curve (ML2) represents the method of ignoring first 2 images after speech, the green curve (MPR) represents the motion-parameter regression method, the magenta curve (dtsel) represents the selective detrending method and the red curve (dt) represents the non-selective detrending method....................................................100 5.23 Activation maps thresholded at R 2 > 0.2 for control subject 4 with no TCM noise-reduction (a), with selective detrending (b), with motion parameter regression (c), with ignoring 2 images after speech (d) and with non-selective detrending (e). The blue arrows indicate TCM voxel IRFs and the green arrows BOLD voxel IRFs..................................................................................................103 5.24 Some representative TCM-related voxel IRFs from control subject 4 (a). The effect of the methods of noise correction on a right medial-frontal voxel BOLD HRF exhibiting an early response for the same dataset. The nocorrection curve is hidden by the selective detrending curve................................105 5.25 Fraction of voxels detected as a function threshold R2 for (a) the false-positives test-bed and (b) the true-positives test-bed for control subject 4. The blue curve (ML0) represents the case of no motion correction, the black curve (ML2) represents the method of ignoring first 2 images after speech, the green curve (MPR) represents the motion-parameter regression method, the magenta curve (dtsel) represents the selective detrending method and the red curve (dt) represents the non-selective detrending method................105 xiv

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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy REDUCTION OF NOISE DUE TO TASK CORRELATED MOTION IN EVENT RELATED OVERT WORD GENERATION FUNCTIONAL MAGNETIC RESONANCE IMAGING PARADIGMS By Kaundinya S. Gopinath December, 2003 Chair: Wesley Bolch Cochair: Richard W. Briggs Major Department: Nuclear and Radiological Engineering Event-related overt word generation functional magnetic resonance imaging paradigms play an important role in the understanding of brain function. The necessity for monitoring the subject responses in functional magnetic resonance imaging of patients requires use of overt word generation paradigms. Speech-related task-correlated motion acts as a major confound in the analysis of overt word-generation paradigms. Task-correlated motion artifacts in event-related overt word generation paradigms have been treated with three main methods: motion parameter regression, ignoring/screening signal changes during speech and detrending functional magnetic resonance imaging datasets of components proportional to the task-correlated motion time-series chosen from false-positive task-correlated motion voxels. In this work a new selective detrending method for reduction of noise associated with task-correlated motion in event-related overt word generation functional magnetic resonance imaging paradigms is introduced. xv

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The performance of this method is compared with the other three methods of task-correlated motion noise reduction. The selective detrending method outperforms the other three methods in terms of reduction of task-correlated motion false-positives as well as retention of blood oxygenation level dependent signal true-positives. xvi

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CHAPTER 1 BASICS OF MAGNETIC RESONANCE IMAGING Chapter 1 discusses the basic concepts of magnetic resonance imaging (MRI). The origins of nuclear magnetic resonance (NMR), principles of magnetic resonance imaging, and development of fast imaging sequences are discussed. Origins of Magnetic Resonance Imaging The idea of nuclear magnetic resonance owed its birth to the discovery of the proton spin by Stern and Gerlach (1) in 1933, through an extension of methods which helped them discover electron spin in 1921. Rabi and colleagues were the first to predict and observe nuclear magnetic resonance in 1937 (2). Bloch and Purcell extended these concepts to measure the proton spin precessional signal from samples, using radiofrequency methods (3, 4). All of the above-mentioned luminaries were awarded Nobel Prizes for their work. MRI had its beginnings in the seminal work of Mansfield and Grannell and Lauterbur in the 1970s (5, 6). They discovered that if a known spatially varying magnetic field is introduced across a sample, the precession of spins within the sample will depend on their spatial locations. Concepts of Magnetic Resonance Imaging The NMR or MRI signal has its basis in quantum mechanics. The quantity spin angular momentum has no exact analog in classical mechanics. The signal observed at the imaging end, however, can be visualized in terms of aggregate magnetization of a population of spins and is a classical regime manifestation. Thus, depending on the 1

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2 physical quantity examined, the concepts of magnetic resonance imaging are most easily elucidated by taking recourse to quantum mechanics, classical mechanics or semi-classical approximations. Spin Physics and Magnetization The nuclei of atoms consist of fermions, protons and neutrons, with half integer spins. The nuclide as a whole has a spin quantum number, I. The spin of the nucleus is an inherently quantum mechanical entity. The energy states that the nucleus can have, called energy levels, are quantized. In the presence of a static D.C. magnetic field, B 0 the nuclide can inhabit 2I+1 energy levels given by (7) 02BmcegSEz [1] where S z can take values from I to +I, e is the electronic charge, is the Plancks constant, m is the mass of the nucleus and c is the velocity of light in gauss-ergian units and g is the Lande g-factor. A hydrogen nuclide (which consists of a proton) has spin I = 1/2 and can occupy two states, aligned either with or against the field. 021E [2] where 00B [3] is the expression for angular frequency in which the constant termed the gyro-magnetic ratio, can be evaluated from equation [1] and is equal to 42 MHz/Tesla for a proton. In an ensemble of water protons in a magnetic field, the relative population of nuclear spins in the two states is given by

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3 kTEENNexp [4] where N + and N are the number of nuclear spins in E + and E energy levels respectively, k is the Boltzmans constant and T is the temperature. Thus there is a net magnetization M 0 in the B 0 direction. The magnetization vector M 0 precesses around the applied magnetic field B 0 with an angular frequency 0 called the Larmor frequency, which is the same as the one obtained in equation [3]. Resonance If a magnetic field B 0 is applied to a population of nuclear spins in a laboratory, they precess around the applied field. The reference frame in which the spins are staionary is rotating with respect to the laboratory frame with the angular frequency of the spins. Now, if a magnetic field, B 1 is applied in this rotating frame at right angles to the spins, they can be tipped, i.e., start precessing around the field B 1 It can be shown (8) and is intuitively obvious that the applied magnetic field B 1 should oscillate with an angular frequency equal to the Larmor frequency of precession of the spins in the laboratory frame. This desired resonance condition between the oscillation frequency of the B 1 field and the precession frequency supplies the R in the acronym MRI. For water protons and all other MR imaging nuclides this frequency is in the radio range, hence the term radio-frequency (RF) magnetic field. Electro-Magnetic Induction When the RF magnetic field B 1 is switched off, the will start precessing about the permanent field, B 0 Thus, the magnetic flux through a coil, with axis aligned perpendicular to B 0 will change resulting in an electro-motive force (e.m.f) induced in the coil according to Faradays law of electro-magnetic induction.

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4 Mdtd [5] where M is flux associated with the changing magnetization field passing through the coil after removal of the RF transmit field B1. This is the basis of MRI signal generation. Relaxation The e.m.f and hence the MR signal derived in the last section depend on the rate of change of the magnetization in the plane transverse to the B 0 field. This evolution of the magnetization of the sample depends on two types of interactions involving the nuclear spins in the sample. Both these interactions tend to the virialization of the system and are hence termed relaxations. Longitudinal Relaxation, T 1 A spin = 1/2 system has two allowed energy states. In the absence of an applied magnetic field, the two states are more or less equally populated. The transition from equi-population of states, in the absence of a field, to a preferential occupation of the lower energy state in the presence of an applied field, described in equation [4], is caused by the relaxation mechanism called longitudinal relaxation (9). The transition in states for a given spin is achieved by resonant absorption of a quantum of energy by the spin from the molecular environment (lattice). Thus, the term resonant is the operative word here. Only energy transactions (e.g., arising from rotation/translation of nuclear moments within the molecule) which lead to the transfer of energy E = 0 from the lattice to the nuclear spin or vice-versa lead to longitudinal relaxation. If B 0 is applied along the z-direction, the time evolution of longitudinal magnetization, i.e., magnetization parallel to the z-direction, after the removal of the 90 spin flipping field, B 1 is given by (10) ))/exp(1()(10TtMtMz [10]

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5 where, M z is the magnetization at time t, M 0 is the equilibrium magnetization and T 1 is called the longitudinal relaxation time. The value of T 1 for proton imaging will depend on the molecular environment of the sample. For water (H 2 0) protons, T 1 is about 1000 msec. T 1 increases with the strength of the B 0 field in liquid samples at typical NMR field strengths. Transverse Relaxation, T 2 In a physical MR sample the local magnetic field experienced by a given spin is a combination of the B 0 field and the fields generated by its neighbors. After a 90 tip of a set of spins, the net transverse magnetization decays with time. This is because the different spins constituting the net transverse magnetization fan out or dephase as they experience different time-dependent local magnetic fields. Thus, the MR signal which depends on the transverse magnetization goes to zero. The evolution of the transverse magnetization is given by (10) )/exp()0()(2TtMtM [11] where M is the transverse magnetization and T 2 is called the transverse relaxation time. T 2 relaxation is caused by both slow and fast molecular motions, in contrast with T 1 relaxation, which can be caused only by fast molecular motions at the Larmor frequency. Hence T 2 is always lesser than or equal to T 1 In practical situations, there are inhomogeneities in the permanent magnetic field B 0 which cause increased dephasing of the spins leading to a shortening of the transverse relaxation time. This leads to an effective transverse relaxation time T given by *2 1 [12] 222/1/1/TTT

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6 where the second term in equation [12] refers to the T 2 shortening due to the B 0 inhomogeneities. Gradients, Spatial Encoding and K-Space The ability to spatially separate the signal comes from a simple, yet brilliant extension of the Larmor relation, equation [3], first discovered by Lauterbur (6). If the z-component of the magnetic field is varied along the x-direction, the spins in the x-y plane will precess at different frequencies depending on their x-coordinates. 0)( xGxx [13] where G x is the applied linear x-gradient to the z-component of the magnetic field. Thus by demodulating the signal at different frequencies, (x), a representation of MR spin density at different points along the x-axis can be obtained. The signal along the y and z-axes can be spatially encoded in an analogous fashion. For an isochromat of spins seeing a constant background field over which a linear x-gradient field is superimposed, after demodulation of the signal, the phase is given by [14] xkdttGxxx2)( where [15] dttGkxx)( is the spatial frequency component of the phase. The MR signal can be considered to be the sum of all isochromat signals, each weighted by the local spin density (x) and the phase term from equation [14]. dxxkixksxx)2exp()()( [16]

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7 Hence, the effective spin density (x) can be estimated from an inverse Fourier transform of the signal s(k x ). In three dimensions zyxzyxzyxdkdkdkzkykxkikkkszyx))(2exp(),,(),,( [17] where is an estimation of the effective spin density which becomes equal to the exact value when the reconstruction is perfect. In equation [17], the Fourier inverse of the reconstructed image space is the k-space, which is obtained after demodulating the signal. The k-space contains all the information regarding the manner in which the magnetic field gradients were played out to spatially encode the image. All MRI sequences can be succinctly represented by their acquisition k-space diagrams. Since the MR image is obtained as an inverse Fourier transform estimate of the demodulated signal k-space, the latter, in principle, contains more information about the image. Basic MR Pulse Sequences The vast majority of MRI pulse sequences are a variation on two basic image acquisition methods, the spin-echo sequence and the gradient echo sequence. The most popular rapid image acquisition sequences in conventional use, the echo-planar imaging (EPI) sequences, are variations on the gradient echo sequence. EPI as well as spiral-EPI sequences have the capability of acquiring the whole image in one acquisition. Spin-Echo Pulse Sequence Figure 1.1 shows a timing diagram of a simple spin echo sequence (11). A 90 RF pulse is first applied (period 1) in conjunction with a slice selective gradient Gz to create a transverse magnetization in the slice encoded by Gz. During period 2, spins which dephase as a result of the slice selective gradient are rephrased by a negative

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8 compensating gradient. Also a programmable phase encoding gradient Gy is applied which encodes spins in the y-direction. In addition, a readout direction gradient Gx is applied which serves the purpose of compensating for phase that will be accrued due to the readout gradient in period 4. In period 3 a slice-selective 180 RF pulse is applied. The purpose of this pulse is to generate a spin-echo in period 4, when all the spins which have been dispersed by the applied and background gradients will come back in phase. The readout gradient G x is played out during collection of the echo in period 4, to encode spins in the x-direction. The above sequence is repeated for different values of the phase encoding gradient, G y to encode the y-axis. The time interval between the application of the RF pulse and the acquisition of the center of the echo is called the echo time (TE). The time-interval between two successive phase-encoding steps is called repetition time (TR). 90 180 RF Gz n Gy Gx Signal TE 1 2 3 4 TR Figure 1.1: Timing diagram of a 2-D Spin Echo Sequence

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9 In terms of k-space (Figure 1.2) each repetition (echo) of the sequence generates one line of the k-space. After acquisition of all the echoes a two-dimensional k-space image is generated, which upon inverse Fourier transformation generates a 2-D image of the slice. Figure 1.2: K-space diagram of a 2-D Spin Echo Sequence Gradient-Echo Pulse Sequence The gradient echo sequence differs from the spin echo sequence in the manner in which the echo is generated during readout. While the spin echo sequence generates the echo by the use of a 180 refocusing pulse, in the gradient echo sequence, the echo is generated by the gradient reversal in going from the refocusing G x gradient to the readout G x gradient. Thus, the echo is created when the spins dispersed by the initial negative G x are brought back in phase during readout by the positive G x This form of echo generation can not compensate for the phase dispersal due to background gradients. Thus the signal decays faster (through T decay) in a gradient echo sequence when compared to a spin echo sequence (through T *2 2 decay). Both the gradient echo sequence and the spin echo sequence are examples of 2-D FT spin warp imaging.

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10 Contrast and Resolution The MR signal for a 2-D FT spin warp sequence is given by )/exp(cos)/exp()/exp()/exp(1sin))/exp(1(),,,(2121100TTETTRTTRTTRTTRTETRS [18] where S is the signal as a function of repetition time (TR), echo time (TE), effective spin density 0 and RF flip angle By judicious choice of the parameters of the scan, image contrast can be achieved by enhancing the differences in T 1 T 2 (T) or spin density between different constituents in the sample. These three constitute the most basic contrast generating mechanisms. Other contrast parameters in vogue include flow, magnetic susceptibility difference and diffusion (to name just a few). *2 The image resolution is dictated by the number of phase-encoding steps N y the number of acquisition samples in the readout N x and the field of view (FOV) in the x and y-directions. For brain imaging applications the FOV ranges from 20-24 cm and the image matrix is 256 by 256, giving an in-plane resolution of about 1mm by 1mm. Fast Imaging Sequences The scanning time required for the 2D-FT spin warp sequences mentioned above can be quite long. Roughly, the scanning time will be given by TR times N y the number of phase encode steps. For TR = 1sec, a 64 x 64 matrix image will take 64 seconds. For many MR applications faster acquisition times are required. One major advance in shortening acquisition times was performed by Mansfields group (12) in Nottingham when they invented the Echo-Planar Imaging (EPI) sequence. Mansfield himself had introduced the concepts of EPI a decade or so back (13). The Stanford group (14-15)

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11 subsequently devised a different version of EPI called the spiral-EPI (or just spiral) sequence. Echo-Planar Imaging Figure 1.3 shows a timing diagram of a conventional single-shot EPI sequence. The whole of k-space (Figure 1.4) is acquired in a single application of the RF pulse. An oscillatory gradient G x is applied along the frequency encoding direction and a train of gradient echoes is collected. Each echo is then phase encoded independently by blipped G y gradient and the whole k-space matrix is covered. The blips in G y gradient occur at during each zero crossing of the G x gradient. Figure 1.3: Timing diagram of an Echo-Planar Imaging Sequence Thus each echo corresponds to one line of k-space as in Figure 1.2. While each k-space line in Figure 1.2 was acquired in one TR, all the k-space lines in Figure 1.4 are

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12 acquired in a single TR. Modern EPI sequences can acquire one slice in as low as 30 milli-seconds (16). Figure 1.4: K-Space diagram of an Echo-Planar Imaging sequence Spiral Imaging An extension of the conventional EPI sequence is the spiral sequence (17-19). Figure 1.5 shows the timing diagram and corresponding k-space diagram of a spiral fast imaging sequence. In a spiral sequence, both the G x and G y gradients oscillate with increasing amplitude as a function of time during readout. There is no phase-encoding gradient. The k-space is acquired in a spiral-fashion, hence the name. The gradient slew rate (the maximal rate of change of the gradients in the pulse sequence) requirements for spiral imaging are not as high as for conventional EPI sequences (18, 19). Scan times per slice are comparable to that of standard EPI sequences. Spiral sequences are inherently self-refocussed and do not have geometric distortions that plague EPI sequences. However, they require off-line reconstruction which can take much longer than EPI sequences.

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13 Figure 1.5: Timing diagram (left) and k-space diagram (right) of a 1-shot spiral EPI sequence.

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CHAPTER 2 FUNCTIONAL MAGNETIC RESONANCE IMAGING Chapter 2 discusses concepts of functional magnetic resonance imaging (FMRI). The origins of this functional imaging modality, the principles of blood oxygenation level dependent (BOLD) FMRI and the spatio-temporal properties of the BOLD FMRI signal are discussed. Finally, salient features in FMRI experiment design and data analysis are reviewed. Origins of Functional Magnetic Resonance Imaging Until the late 1980s, the decay of signal due to local magnetic field inhomogeneities due toTrelaxation was considered a nuisance and sought to be minimized. Among the first to realize that the presence of a paramagnetic substance in the blood stream acts as a vascular marker, giving useful contrast, were researchers of the MGH group (20), who pioneered the application of contrast agents to study brain perfusion in animals. In the early 1990s, Belliveau and collaborators (21) first extended these principles to image functional brain activation in humans with MR contrast agents. Subsequently Ogawa, working with laboratory animals, in a seminal paper (22), demonstrated that similar changes of MR image contrast can be obtained by changing the oxygenation state of blood. This observation was rooted in the fact [first measured by Pauling in 1936 (23)] that deoxyhemoglobin is more paramagnetic than oxyhemoglobin, which itself has a very similar magnetic susceptibility to that of brain tissue. Brain activation leads to creation of imbalances between the oxygen uptake and blood flow leading to blood oxygenation level dependent (BOLD) MRI signal contrast around *2 14

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15 cortical vessels, which can be mapped non-invasively with MR sequences optimizing T contrast. The first human subject BOLD FMRI was performed in 1992 by Kwong (24) and Ogawa (25), using gradient-echo MR images. BOLD FMRI accounts for most functional imaging studies of the brain with MRI, though another method involving the labeling of arterial spins with a preparatory RF pulse, first advocated by the Pittsburgh group (26), is fast gaining currency. This is a cerebral blood flow monitoring technique for functional MRI. *2 Principles of BOLD Functional MRI BOLD FMRI, like other functional neuroimaging methods such as positron emission tomography (27) and optical imaging (28) is based on physiological responses related to brain activation. Brain function is spatially segmented and compartmentalized. This can be mapped through measuring secondary changes in metabolism and hemodynamics in response to neuronal activity. The MRI signal acquired with a single pulse sequence is given by )()(21TATMS [2.1] where M is the sampled magnetization, determined by (T 1T 1 with inflow) and A is the signal attenuation, governed by the T decay of the in-plane magnetization. The activation-induced MRI signal change in the capillary bed is given by *2 AAMMSS/// [2.2] The first term in equation [2.2] is the change in signal due to inflow and is (at steady state attained after repetitive pulsing) very small (29), M/M ~ 0.0035. The second term in equation [2.2], when described by a simple T decay is given by *2 )/1(/2TTEAA [2.3]

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16 for echo-time TE and activation induced change in transverse relaxation, (1/T). BOLD contrast is solely due to the susceptibility difference of red cells with paramagnetic deoxyhemoglobin relative to their surrounding. The bulk susceptibility of red cells, which is due to the hemoglobin deoxygenation level, changes the field shift inside and outside the red cells. The change in due to brain activation can be written in terms of the blood oxygenation level Y, change in cerebral blood flow, CBF, magnetic field, B *2 *2T 0 and echo-time, TE (23). ))1((/0YvBTEaAA [2.4] where a is a constant and v is the blood volume fraction. Equation [2.4] is actually a simplification. The exact dependence of the MRI signal change due to activation on the hemodynamic and MRI parameters is still a subject of research. BOLD Hemodynamic Response Figure 2.1 shows a schematic representation of a BOLD hemodynamic response to an applied neuronal stimulus. The response can be characterized by segmenting it into four epochs. First, there is a delay which could range from 2 to 4 seconds (30) between the application of the stimulus and the onset of hemodynamic response. This delay could be both due to delay in neuronal firing in response to the stimulus or sluggishness associated with the neurovascular coupling. The second feature, shown as a dotted curve is often called the initial dip. This event, which can last up to 2 seconds (31) is the result of a local increase in cerebral metabolic rate of oxygen consumption (CMRO2) at the site of neuronal firing, leading to an increase in the local deoxyhemoglobin concentration, which results in decrease in MR signal intensity. This phenomenon is not often observed (for instance initial dip is seen

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17 only B0 3T and at temporal resolutions around or less than 1 second), and hence designated by the dashed curve. Figure 2.1: Schematic representation of a BOLD hemodynamic response The next epoch is the positive BOLD response. This happens due to an increase in cerebral blood flow (CBF) which occurs after neuronal firing. This results in hyperoxygenation of the neural tissue which leads to a decrease in the deoxyhemoglobin concentration and thus an increase in MR signal. The positive BOLD response to a neuronal impulse consists of a relatively sharp increase (about 4-6 seconds) to maximum and a slower decrease characterized by fall-times of about 7 seconds or more (32). This epoch is the classical BOLD response, which is utilized to quantify brain activation in most instances of FMRI analysis. Sometimes a positive overshoot (dashed curve) is seen at the start of the positive BOLD response. One plausible reason for the overshoot is the mismatch in the rates of adjustment of CBF and the cerebral blood volume (CBV) (33) during changes in stimulation state. Soon after neuronal stimulation, the CBF exhibits an abrupt jump to its elevated level while the CBV adjustment is more gradual. This results in a hump in the BOLD response when there is an short-lived increase in the oxygenation of the tissue due to the mismatch between CBF and CBV. The reverse happens at the end of the positive BOLD response, when elevated CBV levels persist even as CBF and hence the

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18 oxygenation decreases leading to a decrease in MR signal. This incompletely understood post-stimulus undershoot can take up to tens of seconds to recover (34). Spatio-Temporal Characteristics of BOLD FMRI It is profitable to explore the relationship between brain activation and the corresponding BOLD hemodynamic response. In particular, it would be remunerative to examine in detail how the BOLD response is related to the underlying brain activation in time and space. Spatial Specificity Apart from the BOLD response changes originating in the capillaries embedded within the cortex and localized to site of neural activity, the hemodynamics that give rise to observed FMRI signal changes originate from a number of sources on both the supply (arterial) and draining (venous) side which can be as much as a centimeter away from site of neural activity (35-36). To get around the loss of specificity due to the draining vein effect, which is a byproduct of the hyperoxic phase of the BOLD response, some authors (37) have hypothesized that use be made of the initial dip part of the BOLD response which is a corollary of the early hypoxic phase. This is thought to be more localized to the site of neural activity. But as mentioned before, the initial dip can be elusive to image and requires high temporal resolution too. Methods involving MR phase images (38-39) show more promise in discriminating large vessel effects. Temporal Resolution The neuronal processes associated with brain function range do not extend over a few hundred milliseconds even for the more complex cognitive tasks (40). In contrast, the BOLD hemodynamic response to a neural stimulus could extend over tens of seconds. To answer the question of how separated in time, neuronal events have to be, in order to be

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19 resolved with BOLD FMRI, it is necessary to understand the exact mechanism of coupling between brain activity and the vascular response. At present the nature of neurovascular coupling is not well understood. Studies involving measurements of evoked potentials and BOLD MR signals (41) have claimed that temporal dynamics of brain can be measured indirectly by observed correlations between the BOLD response signal parameters and dynamics of underlying brain function. But the observations are open to interpretation in terms of their generalization to all brain functions and locations as well as how consistently the measured electrical activity reflects brain function (42). Linearity of BOLD Response Optimal design of FMRI experiments requires knowledge of the nature of the relationship between stimulus presentation and evoked BOLD hemodynamic response. Early ventures into FMRI signal analysis assumed a linear relationship between stimulus duration and evoked BOLD FMRI signal change (43). Subsequent studies have demonstrated significant departures from linearity for stimulus durations less than 4-6 seconds (45, 46). Another manifestation of this nonlinearity is the dependence in the amplitude and latency of the hemodynamic response to a neural stimulus on the timing of preceding stimuli. At inter-stimulus-intervals (ISI) of 5-6 seconds or greater, the hemodynamic responses of multiple stimuli sum in a roughly linear fashion (47). However at shorter intervals (e.g. less than 2 seconds), there are significant departures from linearity, in that the hemodynamic response to the second stimulus in a pair is reduced in amplitude and increased in latency compared to that evoked by a single stimulus. This phenomenon has been observed in auditory (48), motor (47) and visual cortices (49). The aforementioned studies on nonlinearity of the BOLD hemodynamic response were done on lower level cognitive systems. Gopinath et al. (50) noticed

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20 refractoriness at longer ISIs (3seconds and more) in the hemodynamic response of voxels in the supplementary motor area (SMA) under a higher level cognitive task, a semantic word generation paradigm. Extending on this work Gopinath et al. (51) subsequently found an increase in the nonlinearity of the BOLD hemodynamic response along a functionally connected neural pathway. In this study the change in the linearity of the relationship between stimulus pattern and BOLD response along the receptive and expressive language processing network was observed. Under an overt word repetition task, an increase in the nonlinearity of the BOLD response was observed in the output (motor cortex) of the language processing network compared to the input (auditory cortex). The above discussion leads one to explore the neural basis of FMRI signal. Questions of importance are does the FMRI signal reflect axonal firing output as does EEG? (52) or does it reflect postand pre-synaptic signals? (53, 54). A recent review on this subject (55) suggests that the BOLD effect should be interpreted as a reflection of neuronal signaling and not as a locus of increased energy utilization. Much work needs to be done on this subject to get a clear picture of the neural basis of FMRI signal. Design and analysis of FMRI experiments will clearly benefit from a better understanding of the neurovascular coupling. FMRI Experiment Design FMRI is rapidly gaining currency as a preferred method for imaging brain function. FMRI has been used to image brain activation in simple brain functions stimulating the auditory areas of the brain (56), motor areas (57) and visual areas (58). With the success of these experiments FMRI has quickly graduated to imaging higher level cognitive processes in the brain dealing with language (59), pain (60) and perception (61) among a

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21 host of other systems. It has also found application in treatment of pathologies (62) and pre-surgical planning (63). FMRI study designs can be broadly classified into two types: 1) blocked paradigms and 2) event-related paradigms. Blocked Paradigms Blocked paradigms were the first approach to be employed in FMRI studies (25, 26). Blocked paradigms involve application of FMRI stimuli for finite durations ranging from ~10 sec to ~ 1 min interspersed with rest intervals of about the same durations. Regions in the brain which show significant signal change between the active and rest conditions can be considered activated. Blocked paradigms have flexibility, allowing use of multi-factorial designs (64) as well as parametric designs (65). The rest intervals may be of uniform size (boxcar stimulus order) or varied (randomized block designs). Optimization of blocked paradigms has been studied with regard to both neuropsychological and statistical terms (66), though further refinement of the optimization procedures is in order to account for variability in hemodynamic response, brain activation and noise of the associated FMRI signal time-series. With the knowledge at hand (66), one can surmise that the length of the active and rest intervals should be such that the BOLD FMRI signal will be at activation frequencies in the range 0.08-0.15 Hz. This is because the hemodynamic response acts as a low-pass filter and attenuates the signal at frequencies greater than ~ 0.2 Hz and also the FMRI time-series noise has been known to exhibit disproportionate spectral power at frequencies (67) below 0.05 Hz. Event-Related Paradigms The blocked paradigms of the previous section offer the highest efficiency among the currently used designs in FMRI (68) in detecting activated areas. However, the inherent characteristics of blocked paradigms prevent them from being able to estimate

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22 the hemodynamic responses of each individual stimulus in a block (69). Also, blocked designs cannot readily accommodate behavioral constraints imposed by some event sequences, such as those occurring infrequently, randomly or discretely, those not having precise time-locking to known stimuli, or mixing of events from fundamentally different tasks (70). Event-related FMRI (ER-FMRI) designs overcome all the above-mentioned obstacles and also provide means of examining questions regarding the dynamics and time course of neural activity as well as neurovascular coupling. Early ventures in ER-FMRI (70, 67) involved application of periodic single-trial stimuli. Subsequent developments in ER-FMRI have demonstrated that pseudo-random ordered single-trial stimulus sequences are more optimal in terms of both detection and estimation efficiency of the signal changes in ER-FMRI (69, 71, 72). FMRI Data Analysis The BOLD signal changes in FMRI at 3T are typically 2-10 %. Tasks involving higher level cognitive systems (like language) tend to exhibit a smaller signal change (2-4%) than those involving activation of the primary cortices. The role of FMRI data analysis is to extract this signal from the background noise. Overview The data analysis methods can be categorized into 1) hypothesis independent methods and 2) hypothesis driven methods. Hypothesis independent methods such as ICA (73), fuzzy-cluster analysis (74) have yet to be perfected for FMRI and are not widely used. Hypothesis driven methods can be categorized into a) parametric methods and b) nonparametric methods.

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23 Image Registration Proper image registration (aligning the time series images) is imperative to minimize the effect of motion on the FMRI signal. Image registration is the first step in the post-processing of acquired FMRI images. Image registration is usually performed with image-intensity-based methods (75-77). The guiding principle in all intensity-based image registration methods is the minimization of some quantity related to the voxel-wise image-to-image intensity differences. Conventional intensity-based image registration methods consist of two steps (75-77). The first step is the estimation of the rotation and translation parameters required to align a given image with the base image, usually obtained as best-fit rigid body rotation and translation parameters in the global optimization algorithm used to re-align the images. The second step is the assignment of intensity values to the voxels in the rotated image grid. This resampling is done by means of polynomial (77) or Fourier interpolation (78). Polynomial interpolation is local (band-limited). This can introduce blurring in the resampled images (i.e. correlation between the signal values at nearby pixels). Fourier interpolation is more desirable, albeit slower. In Fourier interpolation the image is resampled globally in the reconstructed k-space, which upon inverse Fourier transform gives the registered image. The blurring introduced is much reduced. There is a separate class of feature-based registration methods which have been proposed for FMRI (79, 80, 81). These methods segment a known anatomic contour in all the images of the FMRI time-series and use the contour as a reference for tracking and compensating for head motion. Gopinath et al. (80) proposed one such method which is now available in a more refined form (81) to implement a 2D feature-based image registration. This method endeavors to segment an anatomic shape prior (e.g. the corpus

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24 callosum) in each of the images in the FMRI time-series and estimate the motion parameters involved in aligning the prior in all the images in the time-series. These methods are still in their infancy and are not in general use. The main drawback lies in the difficulty in segmentation of low resolution FMRI images. FMRI Noise Characteristics The preponderance of FMRI studies in the literature use parametric methods of data analysis. The characterization of the noise structure is critical to parametric analyses of FMRI time-series. The earliest FMRI data analysis methods assumed the underlying noise structure to be wide sense stationary (WSS) Gaussian white noise (43). More detailed inspections have revealed significant colored (67, 82), non-Gaussian (83) as well as non-stationary (84) features in the FMRI noise. Most methods of parametric data analysis handle the FMRI noise in one of the following three ways. Some neuroimaging softwares (85) assume the noise structure to be WSS and Gaussian white. They typically fit a polynomial trend to the baseline to reduce the power of low-frequency noise components in the time-series. This method has some merit in that the FMRI time-series is believed to have a strong white noise component. For example, Purdon et al. (82), using a WSS Gaussian white noise plus a first order auto-regressive (AR(1)) model, estimated a 3:1 ratio for the power of the white noise component to that of the colored noise component in their model for FMRI noise time-series for TR = 2 sec. The second prescription for treating the underlying noise structure is called pre-coloring. In this method (86) the FMRI time-series (with unknown intrinsic color) is swamped with a known amount of auto-correlation by smoothing with a Gaussian filter. The time-series is then analyzed with the assumption that it is WSS Gaussian with a pre-determined auto-correlation function (ACF). The third noise-treatment method (82, 87) relies on pre

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25 whitening the time-series before analysis. This involves estimation of the color by auto-regressive moving average (ARMA) time series analysis. The presence of a dominant white noise component makes estimation of the color of the time-series particularly difficult (88). One can take recourse to the frequency domain and try estimating the color using non-parametric spectral analysis (67, 89). However spectral estimation involves an inherent trade-off between bias and consistency of the power spectrum estimate (88). Gopinath et al. (90) proposed a technique to overcome the obstacles in conventional methods of frequency domain FMRI signal analysis. Using a result from statistical signal processing (91), for broadband signals in noise of unknown power spectral densities (provided WSS), the authors demonstrated that judicious design of event-related FMRI experiments can result in broadband hemodynamic response signals in FMRI time-series. In such a case, only an estimate of the power spectrum is needed to construct a detector for broadband FMRI signals in unknown colored FMRI noise time-series, without the need for exact determination of the color of the noise. The preceding discussion has focused on the stochastic properties of FMRI noise. In practice, the changes in FMRI signal due to physiological processes like cardiac and respiration are also included in the noise term (92). Techniques have been introduced (93-94) to correct for the noise introduced by physiological processes. For whole-brain FMRI studies with long TR (~ 2 sec) the respiration and cardiac noise components are not very significant (95), especially when the stimulus order is aperiodic and are hence ignored. The origin of FMRI noise is of interest. If the features in the noise can be ascribable to physical/physiological process(es) the task of FMRI signal analysis would be

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26 simplified. Some groups (44, 87) have suggested that the low frequency features of the FMRI noise are related to physiological sources like resting state neural activity. Others (67, 96) are skeptical, pointing to the fact that disproportionate spectral power at low frequencies has been observed in phantoms and cadavers also. Recently Gopinath et al. (97) showed that some regions in the brain which exhibited 1/f-like features in the image-magnitude FMRI noise time-series also exhibited similar behavior in the image-phase FMRI noise time-series. These findings would also preclude resting state neural activity as a source of the color in FMRI noise as the neuro-vascular coupling which relates neural activity to the BOLD signal at the capillary level does not leave a signature in the voxel-phase. Gopinath et al. also showed (98) presence of more voxels exhibiting disproportionate spectral at low frequencies (f < 0.01 Hz) in diseased brain tissue than intact brain tissue; a finding difficult to reconcile with the resting state neural activity as a source of /f FMRI noise, since there is significantly less neural activity in diseased tissue when compared to healthy brain tissue. Parametric Methods and General Linear Model The first attempts at FMRI data analysis utilized parametric methods (43, 44). Most parametric methods can be expressed in the form of General Linear Models (GLMs). The brief review of FMRI signal processing presented here will focus on deconvolution analysis under the framework of a GLM. This is also instructive in that it is the main method of analysis followed throughout this thesis. This method (99, 100) relies on the assumption that the observed FMRI time series, Z(t) is the result of a convolution of the applied task stimulus-impulse time-series, f(t) and the impulse response function (IRF) h(t). This signal is over and above a baseline and is in the

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27 presence of a Gaussian white noise process (t). In the discrete-time domain indexed by n, 1,...1,010NppnfhnZnmnpmmn [2.5] where 0 and 1 are the baseline parameters (corresponding to mean and linear trend) and the summation denotes the discrete-time finite-lag convolution of the f(t) and h(t) over p lags and N is the number of time-points in the time-series. The baseline of FMRI time-series often exhibit a global linear or polynomial drift and have to be included in the model for optimal signal detection and estimation. The constant p is determined by the duration of the anticipated hemodynamic response function (HRF). In matrix formulation [2.5] becomes XZ [2.6] where Z is the observed time-series vector, X is the deconvolution matrix and is the white noise matrix. The linear regression problem expressed by equation [2.6] can be solved for estimates of Z and andby minimizing the error sum of squares between the estimated (fitted) time-series and observed time-series: Z [2.7] 210)()(iNiiZZQSSE which gives the least squares estimate for through [2.8] ZXXXTT1)( The parameter vector is composed of the estimated parameter for the mean (), linear trend () and the IRF parameter estimates (h). 0 1 ph..0 The significance of the regression can be evaluated by constructing the following hypothesis test,

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28 nmnpmmnannfhnZHnZH 010100:: [2.9] where H 0 and H a are the null and alternate hypothesis (same as equation [2.5]) respectively and 0 and 1 are the parameters corresponding respectively to the mean and linear trend of the noise (baseline) model. A test of the null hypothesis is made by determining the parameters which yield a least squares fit for the baseline model as well as the parameters that provide the least squares fit for the signal plus noise (full) model of H a. Next the residual sums of squares between the observed time-series and the fitted time-series for the baseline model, SSE(B) and that of the full model, SSE(F) are evaluated. The null hypothesis can then be tested through the test statistic F*, FFBdfFSSEdfdfFSSEBSSEerrorMSregressionMSF)()()()()(* [2.10] where df B and df F are the degrees of freedom of the baseline model and full model respectively given by [2.11] 1)1(22pdfdfpNdfNdfFBFB where is the number of usable data points. The test statistic F* has the F(df pNN B df F df F ) distribution under the null hypothesis. The coefficient of multiple determination R 2 can be used as an indicator of the goodness of fit between the full model and the data, as given by )()(12BSSEFSSER [2.12] and can be regarded as the proportion of the variation in the data that is explained by the full regression model.

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29 Inference Once a statistical parametric map of voxels in the brain is obtained, the next step is to decide how to threshold the data, in order to be able to say a certain voxel (or area of the brain) is activated at a given level of significance (p-value). This task is complicated by the multiple comparison problem. Typically, for a whole brain FMRI study with resolution ~ 3 mm, a large number of voxels ( ~40,000) are tested simultaneously for rejection of the null hypothesis. Thus, even with a p-value of 0.01, one can end up with a significant number (~ 400) of false positive voxels, which get declared active, assuming all the voxels are independent. The simplest procedure to control for multiple comparisons is the Bonferroni correction (101). Here, for a desired significance threshold, p, the voxels are declared active if they possess p-values less than p/N, where N is the number of voxels in the map. This procedure can be considered overly conservative (102), even in the case where all the voxels are independent (as is not the case in FMRI), and can lead to loss of power (declaring voxels to be inactive when they are active). Recently, some groups (102, 103) have advanced a less conservative procedure for controlling multiple comparison false positives. Instead of correcting the family-wise error rates (FWER), as is done in Bonferroni correction, they control for the false discovery rates (FDR), the proportion of false positives. FDR theory (102,103), also allows for non-independent voxel families, as opposed to the Bonferroni method, where one has to estimate the number of independent voxels. In practice, a lot of groups do not control for multiple comparisons, opting instead to threshold the data at low p-values. This procedure is surprisingly effective at the individual subject level. The reason can be surmised as follows; at conventional FMRI sites, with B 0 ~1.5-4T, even the relatively small magnitude of BOLD signal changes of 3

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30 10 % lead can to very low p-values in support of the null hypothesis, in the regions of interest. Thus, the SPMs are thresholded at high levels of significance, erring if anything on the side of specificity. In fact, when estimation of the HRF is also critical to the analysis over and above the detection of activation, one might need to threshold the SPMs at a higher level of significance, in order to eliminate voxels whose estimated IRF (or HRF) is not well defined. Figure 2.2 shows the IRF for a voxel with F(16,470) = 30 as well as a voxel with F(16,470) = 2.5, for an event-related silent word generation study (90). Although the F = 2.5 voxel is significant at p < 0.001, the corresponding IRF is not well defined unlike that of the F = 30 voxel. The signal in the figure has been normalized to a unit maximum to show the shape better. The voxel IRF on the right has a substantially lower raw amplitude compared to the one on the left. The post stimulus undershoot seems pronounced in the voxel (from the auditory cortex) hemodynamic response on the left. The distribution of the test statistic can vary between subjects and also between different sessions of the same subject (104, 105). Thus, it may be beneficial to threshold each session separately and use procedures like conjunction analyses (106) to make between-session inferences.

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31 Figure 2.2: The estimated impulse responses for a auditory cortex voxel activated at F(16,470) = 30, p-val 0 (left) and a voxel with F(16,470) = 2.5 (right). The signal has been normalized to a unit maximum. ROC Analysis Receiver operating characteristics (ROC) curves are used to test the performance of a detector, imaging modality, or technique (107). The application of ROC analysis to test different image processing techniques, statistical data analysis methods, preprocessing steps prior to statistical analysis, and experiment design in FMRI has been attempted by a few groups (90, 108, 109, 110, 111). Ventures into ROC analysis have consisted of using synthetic data (90, 110, 111) or real data under test-retest conditions (108, 109). The major drawbacks in using synthetic data are the hitherto incompletely understood nature of the noise structure in FMRI time-series as well as the unpredictability of the BOLD FMRI signal (84, 104, 105). The problem with using test-retest methods is the unpredictable variations between sessions in the BOLD signal (104-105) as well as the multivariate nature, within session, of the BOLD signal change (84).

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CHAPTER 3 MOTION AND FMRI The artifacts produced by subject motion are a major confound in the analysis of functional magnetic resonance imaging (FMRI) time series data. In this chapter the major sources of motion-related artifacts in FMRI time series are described. Some of the existing methods for dealing with motion artifacts in the literature are also reviewed. Introduction FMRI signal changes are of the order of 1-8% of the baseline signal intensity in conventional MR systems (1.5T and 3T). As a result, it is very important that the signal changes from sources other than functional activation be eliminated as far as possible. In living subjects, movement is unavoidable. Even small motions can impact the FMRI time series adversely. For instance (75 Cox, et al., 1999), it has been seen that typical T-weighted brain images show 10-20% intensity changes between adjacent voxels in the parenchyma and 70-80% changes at the edge of the brain. Thus, motions of the order of a tenth of a voxel can produce 1-2% signal changes in the parenchyma and 7-8% signal change at the edges of the brain, of the same size as changes occurring from brain activation that are to be detected. For a 20 cm field of view (FOV) 128 X 128 image the above statement implies that motions of the order of 150 m can have a significant impact on the FMRI signal. Motion can impair the detection of real functional activation in several ways. Random motions of the subject will appear as additive noise in the voxel time-series and decrease the detectability of functional activation. Stimulus-correlated *2 32

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33 motion can mask real activation in cortical regions and also appear as false-positive activation in the brain edges and high-contrast regions of the brain. Proper image registration (aligning the time series images) is imperative to minimize the effect of motion on the FMRI signal. As mentioned in Chapter 2, conventional intensity-based image registration methods consist of two steps (75-77). The first step is the estimation of the rotation and translation parameters required to align a given image with the base image. The second step is the assignment of intensity values to the voxels in the rotated image grid. Motion artifacts can creep into the time-series from errors encountered in both of the above steps, i.e. misalignment or misinterpolation. Grootnik et al. (112) have characterized the artifacts introduced into the time-series by intensity-based image-registration methods using a brain phantom. They attribute these artifacts to interpolation errors introduced by the resampling inherent within realignment. Most intensity-based methods fail when the motion is large more than a voxel (75). Feature-based methods (80-81) use features in the image as landmarks in the registration method. These methods, however, need the identification (or segmentation) of some feature which is not always possible in low resolution FMRI images. Often this is the only motion correction step performed in FMRI studies. However, it would be optimal if image registration were but a first step in the treatment of motion artifacts in FMRI. As mentioned before, conventional image registration programs can give rise to unintended errors. Major Sources of Motion Artifacts and Deterministic Solutions In fact, even after perfect alignment of the time-series, the deleterious effects of motion on the FMRI time series persist to some extent. These effects can be due to a

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34 number of sources. The following paragraphs will point out the major sources of motion-related artifacts and review the methods that exist in the literature to treat them. Static Magnetic Field Effects Head motion in inhomogeneous magnetic field causes local distortions in the static magnetic field (B 0 ), which are not unwarped in standard image-registration schemes. Ideally, the B 0 field should be homogeneous throughout the sample (head). This is hard to achieve in practice since the head distorts the magnetic field (113). To a certain extent the B 0 field can be made homogeneous by adjusting the current in the shim coils. The shim field will depend on the orientation of the head with respect to the B 0 field. The shim fields are set up before the acquisition of the images. Residual inhomogeneities which exist after the shimming will be modulated by head motion, producing time-dependent magnetic field distortions. Consequently there will be a non-zero field difference between the before-movement and after-movement-after-realignment images, for a given point in the sample. Jezzard et al. (113) demonstrated this by acquiring phase images in addition to magnitude images with an echo planar imaging (EPI) sequence while a controlled flexion of the subjects head was performed. They showed that even after re-alignment a substantial field difference existed between the before motion and after motion images. Even a 1 rotation will result in local distortions of the order of one pixel. Quantitatively, the resonant frequency of the 2D FMRI image at a point, in the absence of magnetic field inhomogeneities, is given by )(),(0yGxGyxyx [3.1]

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35 where 0 = B 0 is the central frequency, -being the gyromagnetic ratio (42.575 MHz/T). The presence of magnetic field inhomogeneities leads to introduction of a spatially varying off-resonance (8H, 113, 114) term into equation [3.1] which becomes ),()(),(0yxyGxGyxyx [3.2] where (x,y) is the off-resonance term. The off-resonance has different effects on different methods of image acquisition used in FMRI. In EPI, where the k-space data is acquired in rectangular fashion, the off-resonance causes geometric distortion. The spatial encoding, which depends on the resonant frequency, is compromised, resulting in pixels being mis-located. In spiral imaging, where the k-space is acquired in a spiral fashion, the off-resonance causes blurring. In FMRI, magnetic field environment at a point can differ from image-to-image due to motion. This time dependence will manifest as apparent noise in the FMRI time-series. Some remedies have been proposed to ameliorate this effect. Jezzards group (113), working with EPI data, pointed out that the off-resonance term can be calculated by TEyxyx/),(),( [3.3] where is the field distortion caused by motion and is the phase difference between the given image and the first image, x and y specify the in-plane Cartesian co-ordinates of the position and TE is the echo-time. Thus, the pixel-shifts can be calculated from a temporal sequence of phase images and corrected. This method assumes that offresonance of the first image is either negligible or is corrected by other methods. Also, this method is applicable to EPI FMRI but not to spiral FMRI.

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36 The manifestation of off-resonance related artifacts is different in spiral imaging. The off-resonance leads to blurring in spiral images (114-115). In conventional spiral reconstruction programs the off-resonance due to field inhomogeneity is calculated by constructing a field map for the first image in the time-series. All the images are then reconstructed by incorporating the phase conjugate of the inhomogeneity dependent phase error in the kernel of the Fourier transform. All the images in the time series are deblurred using the off-resonance term of the first image. However, in the case of motion, just like in EPI, an analogous method to perform time dependent off-resonance deblurring in spiral imaging is needed. It must be stressed that these methods will only correct for geometric distortions (in the case of EPI) and blurring (in the case of spiral) images. The signal loss due to dephasing within voxels cannot be recovered. The extent to which the time-dependent distortions affect the FMRI time series has not been studied. It would be desirable to look at the effects of the distortion correction in order to assess their significance. Ward and collaborators (116) have looked at the feasibility of real-time auto-shimming, wherein they compute the change in magnetic field due to motion in real-time and correct the shim by applying compensating gradients accordingly. The changes in magnetic field due to motion are measured by a navigator pulse sequence. The advantage of this method is that it compensates for the magnetic field distortions at image acquisition, which is more desirable since this could also alleviate the intravoxel signal dephasing that occurs due to the inhomogeneities. Post-processing methods have to work with the irreversible loss of signal that occurs due to increased inhomogeneity. The main drawback of this method is that it can only compensate for first-order changes in the

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37 field. The susceptibility artifacts which cause the most dephasing involve inhomogeneity gradients of higher order. Thus the need for a post-processing off-resonance compensation method will still exist. There is also the practical difficulty that not all FMRI centers have access to hardware and software needed for pulse-sequence-based correction methods. Spin History Effects In conventional 2D multi-slice multi-excitation image acquisitions encountered in FMRI, the signal or magnetization from a small volume of the object will depend on the interaction of the B 0 field with the slice-selective RF electromagnetic field B 1 (117-118) and the recovery of magnetization due to longitudinal relaxation during TR. The electromagnetic field environment will change considerably with small displacements of the sample (head) around the inferior and superior edges of an axial slice, the right and left edges of a sagittal slice and the anterior and posterior edges of a coronal slice. Thus even small motions of the order of a few mm in a plane orthogonal to that of the image will result in a different magnetization from one excitation to the next. This effect will be considerable in cases where the recovery of longitudinal magnetization is incomplete between two excitations (which is the case when the TR is comparable to T 1 as is the case in FMRI). Thus the signal from a given volume is a function of its current position as well as it spin excitation history. It should be noted that post-hoc image registration of the images cannot compensate for intensity anomalies caused by this effect. Retrospective correction for through plane motion effects on signal intensity would require detailed knowledge of a number of physical properties, such as the spatial variation of relaxation times within the head, a seemingly intractable problem at best, unsolvable at worst. Prospective image acquisition correction methods offer the best solution for through

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38 plane motion. Two such methods have been proposed. One method (119) estimates the motion parameters from one image to the next by conventional image registration schemes. This is done in real-time and the slice gradients are upgraded accordingly such that the measurement coordinate system is kept at a fixed orientation relative to the patients head during the scan. Thus, in principle, the motion artifacts caused by spin history disruptions can be alleviated. The main drawback of this method is that due to constraints of computing power and gradient hardware requirements, the gradient upgrade interval is currently limited, leading to whole-brain TR of 3-4 seconds or more. Thus, the temporal resolution offered is not sufficient for most current FMRI needs. Another method that has been proposed (120-121) measures the inter-image head motion by employing navigator pulses. The slice gradients are subsequently updated real-time, enabling the relative orientation of the head and the measurement co-ordinate system to remain fixed during the scan. The main drawback of this method is that it takes up to 160 msec per slice, thus requiring a gradient upgrade interval and hence TR of 4 sec or more for a whole-brain study. This is not sufficient for most current FMRI studies. It would be better to use faster methods of encoding motion, such as an optical monitoring device, independent of MR signal acquisition, which would lead to faster update times and improved motion correction. Inter-Shot Motion Often, in FMRI studies, it is desirable to use a multi-shot spiral/EPI sequence to have enough spatial resolution to attenuate the signal drop-offs in high susceptibility contrast regions, or to resolve small anatomic features such as cortical columns or to study physiological mechanisms. For whole-brain study, image TR of the order of 2 seconds is the norm. Thus the time between the two shots for a given slice in a 2D

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39 acquisition sequence is about 2 seconds. In multi-shot spiral imaging, the motion that occurs in between the shots leads to inconsistencies in the collection of the k-space data (115, 19). Inconsistencies in the low spatial frequencies leads to intensity distortions in the image. Inconsistencies in the high spatial frequencies leads to swirl like patterns in the image (Figure 3.1). Figure 3.1 Two-shot spiral FMRI time series image of a mid sagittal slice showing swirl-like patterns arising from inter-shot motion. The image has been detrended of its time-series mean to better portray the effects of motion. In FMRI these motion-induced signal variations may fluctuate from image to image in the time-series, leading to increased variance in the voxel time-series, thereby decreasing the ability to detect brain activation. Low frequency image intensity distortions can be treated by the application of navigator techniques (92-122) or k-space regression (93) to ensure that all the interleaves of a multi-shot spiral image have the k = 0 point common. Essentially these methods force the k= 0 point in the k-space to have the same magnitude and phase in all the shots. Since low spatial frequencies contain most of the information related to image intensity, these methods succeed in minimizing the image distortions due to motion. These methods are aimed primarily at decreasing the effects of physiological fluctuations, which tend to cause global signal intensity changes.

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40 Higher spatial frequencies do not contain much intensity information. Thus the methods to eliminate low frequency intensity modulations due to physiological fluctuations ignore high k-space inter-shot inconsistencies. However, subject motion between shots does lead to swirl-like patterns in the image due to high k-space fluctuations. These swirls vary from image to image depending on the motion. This manifests as additive noise in the FMRI time series. Oftentimes these motions are also stimulus-correlated, which increases false positives and can also mask real activation. This adds extra constraints in designing FMRI experiments. Researchers are often forced to settle for low-resolution one-shot spiral images for studies like overt word generation, which involve significant motion. In order to attenuate the high frequency artifacts in FMRI images acquired with a 2-shot spiral sequence; it is useful to understand the origins of the artifact. Suppose, in the time TR elapsed between the acquisition of the first and second shots, the image rotates by an angle, about the axis normal to the image plane. Then the image space as well as the k-space of the second shot needs to be rotated by the amount in order for the two acquisitions to be aligned. If the image space of the second shot is translated by a distance, r, given by jyixr [3.4] with respect to that of the first shot (where x and y are the translations along the two orthogonal axes, denoted by unit vectors, and ), then by the Fourier shift theorem, every point on the k-space accrues a phase, i j k given by ykxkrkyxk [3.5] Thus, in order to reconstruct the image properly, the data-points in the k-space matrix acquired with the second shot need to be multiplied by a phase term, e ik.r It is obvious

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41 that the prescribed method is limited to in-plane motion corrections. This is because the image acquisition is in 2D and there is no phase encode along the third cardinal axis. The extent to which the k-space distortions produced by inter-shot motions affect the FMRI time series has not been studied. It would be desirable to look at the effects of the distortion correction in order to assess their significance. Remarks The methods mentioned up till now are deterministic in the sense that they isolate the cause of different motion-related artifacts and then correct for them. They are mutually exclusive in that ideally all the three different classes (off-resonance distortion compensation, spin-history correction and inter-shot motion correction) should be performed to properly detrend motion-related noise in the FMRI time series. The order of the execution of the steps is also important. Obviously prospective methods used during image acquisition should be performed before applying retrospective correction methods. The relative importance of these methods depends on the FMRI protocol used. For example, if one-shot imaging methods are used, the high spatial frequency related artifact would hardly be an issue. Also if the task (e.g. overt word generation with coronal/sagittal acquisition) were such that the motion is mainly in-plane, off-resonance correction would be more important than spin-history effects. Mechanistic Solutions Another class of methods can be employed to reduce noise associated with motion in the FMRI time-series. These methods are mechanistic in the sense that they do not explicitly attempt to account for the physical processes that relate motion to the artifactual noise produced. They endeavor to phenomenologically model the signal changes in the FMRI time series due to motion and separate out or detrend the motion

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42 related signal changes from the BOLD signal changes. These artifacts could arise from any of the motion-related sources mentioned in the previous section. Motion Parameter Regression Friston and collaborators (117) proposed a method to account for motion artifacts in the FMRI time-series. They posit that the movement related effects can be divided into those that are a function of the position of the object in the frame of reference of the scanner in the current scan and those that are due to movement in the previous scans. The first component is posited to include changes in signal intensity as the position of the voxel changes with respect to inhomogeneous background magnetic field (e.g. susceptibility induced high image contrast boundaries) as well as signal changes due to displacements around the slice boundaries in the slice excitation direction, which result in changes in the RF excitation profile. The second component is theorized to reflect the signal fluctuations due to changes in the spin excitation history, which are caused by movement in the previous scans. Invoking arguments which pin the dependence of motion-related signal changes on first-order perturbations of the longitudinal magnetization arising from movement in present and previous scans, they argue that artifactual motion-related signal changes at a given instant can be modeled with a second order polynomial in the displacements of the object in the present and the preceding scans in the FMRI time-series. The displacements are encoded by the estimated motion parameters in the re-alignment of the present and preceding scans to the last scan of the FMRI time-series. The signal time series can be written as titititiititititiittYxbxaxbxaS2111611261)()()()( [3.6]

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43 where S t is the signal at time t, x it is the value of the estimated motion parameter of the x i th of the six degrees of freedom in the rigid body realignment of the t th scan to the last scan of the FMRI time-series, a it and b it are coefficients to be estimated by ordinary least squares along with the model parameters of Y t the part of the FMRI time-series free of motion-related signal changes through a multiple linear regression procedure. There are some drawbacks to this approach of motion artifact reduction. The model assumes that head motion affects all the voxels in a similar linear fashion. It has been noted that FMRI voxels on brain-edges and high-contrast boundaries are much more sensitive to motion than voxels away from such features (118, 123, 124, 125, 126). Also the model assumes that the movement-related signal changes are independent of hemodynamic brain activation signal changes. Bullmore and collaborators (118) demonstrated that this last assumption is violated by stimulus-correlated motion. In such cases they also demonstrated that Fristons correction (117) can reduce the power of detecting true-positive brain activation voxels. Finally, equation [3.6] assumes that most of the signal changes due to motion arise from spin-history effects. Stimulus-correlated motion in overt word generation experiments have been shown to cause susceptibility-induced magnetic field changes (123-125). The resulting signal changes in the FMRI time-series are an order of magnitude larger than movement-induced spin-history signal changes and may not be linearly dependent on the motion parameters. Regardless, this method of motion correction enjoys widespread acceptance. Stimulus-Correlated Motion Some FMRI paradigms require overt word generation in response to auditory or visual stimuli (127, 128). Speech involves movement of pharyngeal muscles, especially

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44 tongue and jaw, which have been demonstrated to change the susceptibility-induced magnetic field distribution of the brain (124). The greatest magnetic field changes due to speaking occur in the inferior and frontal regions of the brain, decreasing rapidly towards the superior and dorsal edges. The changes in the magnetic field cause pixel shifts in EPI FMRI time-series images (113) and blurring in spiral FMRI time-series images (114). The effects of pixel-shifts (or blurring) are more pronounced at the brain edges and other high image contrast boundaries, where large spatial gradients in image intensity exist. Voxels at these regions may exhibit as much as 100 % stimulus-correlated signal changes. Thus, after statistical signal processing they might show false positive activation with statistical significance similar to or higher, than voxels exhibiting BOLD signal change. These changes in magnetic field can occur even if the part of the head being imaged is perfectly still. In fact, Yetkin and collaborators (123) found changes in the magnetic field distribution of a homogenous copper sulfate (CuSO 4 ) solution phantom when a separate CuSO 4 solution phantom was moved in its vicinity but outside the field of view (FOV) of the RF coil. Thus signal changes due to speech-engendered stimulus-correlated motions (SCMs) will not be compensated by conventional image registration algorithms (75-77). Also SCM associated with speech can be dependent on what is generated overtly. For instance, Birn observed (124) that the generation of the word one caused almost double the change in the magnetic field distribution when compared to the word two for a normal human control brain at B 0 = 1.5T. Thus methods involving motion-parameter-regression (117) also may not adequately correct for SCM signal changes associated with overt word generation. This is because such methods assume a

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45 linear relationship between motion and corresponding signal changes and are also predicated on the assumption that most of the signal changes due to motion are due to changes in the spin-excitation history and not local magnetic field distribution changes. SCM-Ignoring Images The major portion of signal changes due to speech-related SCM occurs in the first 4 or 5 seconds after speech (124-125). The BOLD hemodynamic response to cognitive processes typically exhibit a delay of 3-6 seconds before onset and the peak is reached only after 4-6 seconds after that (30). Thus, assuming one is interested in studying the brain activation signal changes subsequent to overt production, the inherent difference in the time scales of BOLD and SCM-related signal changes can be used to mitigate the effects of SCM. This argument has been used by certain groups (127-128) to ignore (127) or screen using temporal phase (128) signal changes during the first few images after speech. This method may not be optimal if there is a significant overlap between the time-courses of SCM and BOLD related signal changes (125, 129). In FMRI studies involving patients with language deficits, the time lag between stimulus delivery and overt production can be much longer and more unpredictable than in controls (130). For these cases patient response-locked data analyses are more suitable than language-stimulus-cue-locked timing (131). In such cases, ignoring (or screening) images after speech can lead to sub-optimal detection and estimation of BOLD signal changes, especially in brain regions where the cognitive processes start before overt production. With respect to ignoring a few images after overt word generation, there is also the caveat that for whole-brain FMRI with nearly isotropic voxels, the imaging constraints restrict the minimum allowable TR to between 1.5 and 2 seconds. Consequently the desirability of imaging the complete BOLD HRF might necessitate adoption of a protocol

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46 where only one or two images after enunciation are ignored (screened). This length of time may not be sufficient to eliminate all the effects of SCM. SCM-Detrending As mentioned before the voxels most affected by the SCM lie on the brain edges and other high-contrast boundaries. Birn and collaborators (125) performed single event FMRI studies of speaking, swallowing, jaw clenching and tongue movement and found SCM-related signal changes at voxels near the brain edge of similar statistical significance to BOLD activation voxels in the areas of motor cortex involved in the above-mentioned tasks. They found that orthogonalizing all the voxel time-series in the FMRI dataset with respect to SCM signal changes resulted in functional activation maps with reduced SCM artifacts. This method is sensitive to the time evolution of the SCM-related and hemodynamic responses. If the BOLD HRF and the SCM signal changes are not well resolved, the application of this method has been shown, by our group (129) to result in loss of sensitivity for detecting brain activation. This situation can arise, for example, at voxels in brain areas responsible for preparation for the word generation task. FMRI studies of patients with language deficits require adoption of a data analysis protocol based on patient responses. The time lag between stimulus delivery and patient response is much greater in such patients. Use of a non-selective global detrending procedure as described above (125) can result in loss of information about brain processes related to preparation of the overt response in such cases. Other Mechanistic Methods There are a few other methods for dealing with stimulus-correlated motion in FMRI time-series. Some authors have argued that the SCM artifacts can be somewhat

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47 idiosyncratic and vary across individual participants (118, 127). Thus the effects of the SCM will be mitigated if the FMRI data are averaged across a group of participants. This method may not have the generalized applicability it is purported to posses (118, 127). Salvador and collaborators (126) have suggested that masking all activated voxels which lie on regions of high image intensity gradients. This method can have the effect of eliminating cortical activation along with SCM-related activation since a significant amount of cortical regions in the brain lie near high-contrast boundaries.

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CHAPTER 4 TASK CORRELATED MOTION NOISE REDUCTION METHODS In this chapter a new selective detrending method for reducing noise due to stimulus-correlated motion in FMRI time-series of overt word-generation paradigms is advanced. A framework is introduced to evaluate this method as well as compare its performance with three other methods of SCM-related artifact reduction in event-related overt word-generation FMRI paradigms: 1) motion parameter regression (117, 118), 2) ignoring images during speech (127) and 3) non-selective detrending (125). Since there is generally a significant delay between the presentation of neuronal stimulus and the performance of a overt word generation task among patients, the speech-related artifacts in the FMRI time-series should be more appropriately termed task-correlated (instead of task-correlated). Also, since the patients and the control subjects data analysis are presented in the same framework the term task-correlated motion (TCM) will be adopted instead of the term more commonly used in FMRI literature, stimulus-correlated motion (SCM). Selective Detrending Task-correlated motion due to movements involved in verbalizing lead to significant changes in the FMRI signal (123-125). These artifactual increases/decreases in signal intensity are manifested as false-positive activations in high contrast boundaries in or outside the brain. Since the origin of signal changes due to speech related TCM is mainly attributed to susceptibility profile fluctuations, the shapes of the time courses of the signal changes in the brain due to speech-related TCM and of the signal evolution at 48

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49 high-contrast boundaries characteristic of large magnetic susceptibility gradients should have some similarities (123-125). Thus it should be possible to adequately represent most of the TCM-related signal changes in the dataset with the signal changes from a few representative voxels selected from high contrast boundaries outside or on the brain. The signal changes due to speech-related TCM in all affected voxels should be representable as a whole or in part by the selected set of voxels. The method of Birn et al. (125) detrends all the voxel time-series in the FMRI dataset of components proportional to all the selected TCM voxel time-series, using a linear least-squares method. This has the undesirable effect of detrending brain activation related BOLD MR signal along with TCM-related signal in voxels where the BOLD signal has a significant overlap with net TCM-related signal change of all chosen TCM voxels. The selective detrending method introduced here endeavors to overcome this drawback by examining voxels for TCM-related signal changes and performing the detrending only if certain criteria (developed to maximize false-positive TCM noise reduction as well as true-positive BOLD signal retention) are satisfied. It would be remunerative to recall that the magnetic field changes due to speech-related TCM are strongest in the inferio-frontal regions of the brain and decrease rapidly along the inferior-superior direction as well as anterior-posterior direction (124). Thus, detrending all voxels, non-selectively, of components proportional to all the representative TCM time-series will tend to be overly conservative. A more attractive approach would be to examine each voxel for presence of significant corruption due to task-correlated motion (as characterized by the representative set of TCM time-series) and detrend selectively.

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50 Both the non-selective detrending method as well as the method of ignoring images have the potential to decrease the significance of activation of true-positive BOLD MR voxels along with the false-positive TCM corrupted voxels. There are two instances when this situation can arise. The first case is encountered in voxels which do not exhibit a significant delay to onset in their hemodynamic response. There is some recent literature citing that voxels exhibiting capillary BOLD activation localized to brain activation sites exhibit smaller delays while voxel HDRs having a significant venous BOLD component tend to have a more delayed and sluggish response (132). The second situation arises in language FMRI paradigms in aphasic patients using subject response-locked stimuli. Since aphasia patients, before therapy, tend to exhibit long pauses of up to 10 seconds before generating a word to a semantic cue, the BOLD signal changes driven by the brain processes involving response preparation may significantly overlap with subject response correlated speech related TCM signal changes. Thus a good detrending procedure should have the property of decreasing TCM signal changes as much as possible while leaving BOLD MR signal changes largely intact. This can be accomplished by selecting an adequate set of (phase offset) BOLD MR signal change voxels, examining each voxel time-series for presence of BOLD MR signal changes characterized by the representative voxels, and taking care not to decrease the BOLD component in them if and when selective detrending is performed on them. The next section describes the implementation of the detrending procedure. Selective Detrending: Methods In this section the methods used in the application of the selective detrending to reduce TCM noise in event-related overt FMRI paradigms in controls as well as patients

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51 will be explained. The paradigm is slightly different for aphasia patients due to their inability to generate words fluently. Subjects and Task Two aphasia patients (one female and one male: ages 60 and 70) with left hemisphere stroke were scanned twice, once before rehabilitation therapy and once after therapy. This yielded four FMRI datasets to which the noise reduction methods could be applied. The patients performed an event-related overt word-generation task, for which they were asked to provide single-word responses to semantic category cues. The inter-stimulus interval between category cues was 24.9, 26.6, 28.2 or 29.8 sec, corresponding to 15, 16, 17 or 18 images, assigned in a pseudo-random manner. The patients underwent rehabilitation treatment in between the preand post-therapy scans. The rehabilitation treatment was designed to engage right-hemisphere intention mechanisms to facilitate word finding and consisted of patients naming pictures shown on a computer monitor, under the tutelage of therapists. In addition to the aphasia patients, four healthy control subjects (three female and one male: ages 50-70) were also scanned with a similar event-related overt language FMRI paradigm. The subjects were asked to provide single-word responses to semantic category cues. The inter-stimulus interval between category cues was 16.6, 18.3, 19.9 or 21.6 sec, corresponding to 10, 11, 12 or 13 images, assigned in a pseudo-random manner. Image Acquisition For patients, low resolution functional MR images were obtained using a 1-shot forward spiral sequence (18). Thirty-two 4-4.5 mm thick sagittal slices covering the whole brain were acquired. The repetition-time (TR) was 1660 msec, the echo-time (TE) was 18 msec, the flip angle (FA) was 70 and the field of view (FOV) was 200 mm. The

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52 image matrix size after interpolation was 64 x 64 and spatial resolution was 3.1 mm x 3.1 mm x 4-4.5 mm. Five functional runs were acquired with 161 images in each run, 1.66 sec per image. For anatomic reference, a high resolution T1-weighted 3D spoiled gradient recalled (SPGR) sequence was acquired with scanning parameters: 240 mm FOV, 256 x 256 image matrix, 0.9 mm x 0.9 m x 1.3 mm resolution, TR = 23 msec, TE = 7.7 msec and FA = 25. For angiographic reference, a 2D SPGR time-of-flight (TOF) MR angiogram was obtained with scanning parameters: 200 mm FOV, 256 x 256 image matrix, 0.78 mm x 0.78 m x 4-4.5 mm resolution, TR = 170 msec, TE = 4.9 msec and FA = 50. The subject responses were monitored and coded with Cool Edit software into two categories, correct and other responses. The data analysis was performed with AFNI (85) and Matlab software. The image acquisition parameters were the same for the normal subjects, the only change being that the functional runs were each 111 images long. Also, the categorization of the subject overt responses into correct or other was moot since the patients were able to answer all the semantic queries correctly. Data Analysis The five functional runs were registered to a common base-image (the last image of the last run), detrended of linear trends and concatenated to give a 805-image time-series (555-image time-series for controls). To estimate the TCM-related signal changes, all the subject responses (both correct and other) were pooled together and an overt-response locked stimulus vector was constructed. This vector had 805 (555 for controls) data-points, all zero except the ones corresponding to images in which there was an overt response.

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53 Deconvolution and Regression For each voxel, the signal was considered to be the result of a convolution of the overt-response locked stimulus vector with the voxel impulse response (IRF) plus a constant baseline and a white-noise term. Fifteen lag impulse responses were deconvolved for each voxel from the knowledge of the observed voxel FMRI time-series and the stimulus vector. The deconvolution analysis was performed as described in Chapter 2. The significance of activation at each voxel was assessed through the use of a General Linear Model (GLM). The details of the GLM are as follows: nmnpmmnannfhZHZH 0000:: [4.1] where Z n is the voxel time-series, 0 is the constant baseline parameter under the baseline model, 0 is the constant baseline parameter under the full model, and the summation denotes the discrete-time finite-lag convolution of the f(t), the stimulus vector and h(t), the IRF over p = 15 lags (p = 12 lags for controls), n is the white noise component and N is the number of time-points in the time-series. The significance of activation (i.e. rejection of the null hypothesis) was assessed through the calculation of the F-statistic for regression. The coefficient of determination R 2 was also calculated. R 2 expresses the goodness of fit and can be thought of as the ratio of the variance in the time-series that can be ascribed to the full model to the total variance of the time-series. Estimation of the TCM Signal Changes Speech-related false positive activation due to TCM occurs at/near high contrast boundaries on or outside the brain (124, 125). They are also more pronounced in the inferior and frontal regions of the brain (124) and have some distinct characteristics in

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54 that most of the noise due to TCM occurs in the first few images during and after speech (123-125). The fluctuations are generally a sharp increase/decrease in signal during and just after speech. Thus, examining voxel IRFs on or near high contrast boundaries on or outside the brain, for sudden signal changes, above the threshold selected for inferring brain activation will lead to characterizations of different forms the TCM-related signal changes take. Since signal changes due to TCM have a common origin, it is reasonable to expect that a handful of selected TCM voxels can form an adequate representation of TCM-related signal changes in the brain. Ten to fifteen (depending on the situation) distinct voxel impulse responses at/near high contrast boundaries, on/outside the brain, showing signal changes above the threshold selected for inferring brain activation, were selected to adequately characterize TCM IRFs in the FMRI dataset. Figure 4.1 illustrates this procedure for the case of a few TCM IRFs. The chosen TCM IRFs were convolved with the overt response-locked event vector to form the corresponding 805-image (555-image for controls) TCM time-series. Figure 4.1: Activation map overlaid on a low-resolution spiral FMR image. The red voxels correspond to R 2 > 0.2 and the yellow voxels denote R 2 > 0.3. The yellow arrow points to the voxel IRFs. The central voxel in the grid shows a selected TCM IRF.

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55 Choosing Representative BOLD HRFs In order to optimize the retention of true-positives capability of the selective detrending method, a few (3 or 4) representative estimated BOLD hemodynamic responses were selected from the FMRI dataset. The chosen BOLD HRFs activated above the threshold selected for inferring brain activation and spanned the possible delays (phase of onset of hemodynamic responses) in the dataset. The criterion used in selecting the voxels for detrending involved computation of cross-correlation coefficients of the voxel IRFs with the selected representative BOLD HRFs. The computed cross-correlation coefficients acted as a test of whether BOLD MR signal was being reduced (as is explained in the next section). Hence 3-4 representative BOLD HRFs were sufficient to characterize true positive BOLD voxels. Selective Detrending Algorithm For each 16-image voxel IRF (13-image IRF for controls) in the FMRI dataset, the cross-correlation coefficient CC TCM of the voxel IRF with each of the representative TCM IRFs was calculated. Also the representative TCM IRF for which the absolute value of the CC TCM was a maximum was found. This value was employed as an indicator of false-positive TCM corruption in the voxel time-series. For each 16-image voxel IRF (13-image IRF for controls) in the FMRI dataset, the cross-correlation coefficient CC BOLD of the voxel IRF with each of the representative BOLD HRFs was also calculated. Also the representative BOLD HRF for which the value of the CC BOLD was a maximum was found. This value was employed as an indicator of true positive BOLD MR signal in the voxel time-series. The selective detrending algorithm endeavored to maximize the reduction of false positive TCM signal as well as the retention of true positive BOLD MR signal. To achieve this, each voxel time-series was detrended of components

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56 proportional to the maximally correlated representative TCM time-series in one of three different ways depending on the voxel IRFs correlation with the representative TCM time-series and the selected BOLD time-series: Case 1: if max(abs(CC TCM )) > 0.5 and max(abs(CC TCM )) > CC BOLD + 0.2 then the voxel time-series was detrended of components proportional to the corresponding representative TCM time-series using linear least-squares fit (100). The implicit assumption is that if the voxel time-series satisfies these criteria most of the task-correlated signal changes in it are TCM-related. Case 2: if max(abs(CC TCM )) > 0.5 and CC BOLD + 0.2 > max(abs(CC TCM )) > CC BOLD then the voxel time-series was detrended of components proportional to a corresponding more temporally localized representative TCM time-series formed by considering only the first three images in the representative TCM IRF during construction. The detrending was performed only if the norm of the residuals of the fit of the first three images of the voxel IRF with those of the representative TCM IRF was less than a set value resnorm TCM The implicit assumption here is that if the voxel time-series satisfies these criteria, there is enough likelihood of presence of both BOLD MR signal and TCM signal in it to merit a more localized examination of its epochal signal changes. Since the TCM signal changes occur mostly in the first three images after speech, detrending components proportional to the more localized TCM time-series (given there exists the requisite fit between the voxel IRF and the TCM IRF) is anticipated to reduce the motion corrupted parts of the BOLD MR signal changes in case of presence of both BOLD and TCM signal changes or decrease the major fluctuations in signal due to TCM in case the voxel time-series mainly consist of TCM signal changes. For the datasets studied resnorm TCM =

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57 0.15, corresponding to a p-value for the fit more than 0.95 between the voxel IRF and TCM IRF, was adequate in achieving the mentioned goals. Case 3: if max(abs(CC TCM )) > 0.5 and max(abs(CC TCM )) < CC BOLD then the voxel time-series was detrended of components proportional to a corresponding more localized representative TCM time-series formed by considering only the first three images in the representative TCM IRF during construction. The detrending was performed only if the norm of the residuals of the fit of the first three images of the voxel IRF with those of the representative TCM IRF was less than a set value resnorm BOLD The assumption here is that if the voxel time-series satisfies these criteria it mainly consists of BOLD signal changes, the retention of which outweighs the need for reduction of TCM signal changes (if they exist). Hence, the criterion for the fit is more stringent. For the datasets studied resnorm BOLD = 0.003, corresponding to a p-value of more than 0.999 (133) was adequate to achieve the set goals. The above criteria were chosen to maximize the elimination of TCM-related signal as well as the retention of BOLD MR signal. They rely on prior empirical observations on BOLD MR signal and TCM-related signal (30,123-125). The first part of the algorithm seeks voxels which are presumably affected by TCM alone. These voxel time-series are detrended of components proportional to the maximally correlated representative TCM time-series. The selection criteria used to detect these voxels require a minimum threshold of 0.5 (corresponding to a p-value of 0.05) for max(abs(CC TCM )) as well as a degree of separability between max((abs(CC TCM )) and max(CC BOLD )). The choice of 0.5 for the minimum threshold for cross-correlation is conservative. From the datasets studied voxels exhibiting significant TCM corruption generally posses much

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58 higher values for CC TCM Figure 4.2 shows the activation map formed by max(CC TCM ) overlaid on the IRF dataset. It is apparent that voxels exhibiting significant TCM possess high values of max(CC TCM ). Most of the activated voxels seem to have a max(CC TCM ) > 0.7. Figure 4.2: Activation map of the maximal absolute cross-correlation coefficient with TCM CC TCM thresholded by R 2 > 0.1. The yellow voxels correspond to max(CC TCM ) > 0.7 and the red denotes max(CC TCM ) > 0.5. Case 1 also mentions the requirement of the presence of more correlation between the voxel IRF with the TCM IRF than that with the BOLD HRF. This requirement was introduced to ensure that voxels selected by this criteria possess mainly TCM signal changes even if the max(abs(CC TCM )) and max(CC BOLD ) are both more than 0.5. The choice of 0.2 for separability between CC TCM and CC BOLD was conservative. Figure 4.3 (a) shows the distribution of the ratio of number of voxels undergoing non-selective detrending for a given max(CC BOLD ) threshold to the total number of voxels in the dataset activated above the same threshold, for 3 different levels of separability between max(abs(CC TCM )) and max(CC BOLD ); 0.0, 0.1 and 0.2, on top of the criteria that the voxel

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59 be more correlated with the TCM responses than the BOLD responses. Figure 4.3 (b) shows the ratio of number of voxels undergoing non-selective detrending for a given max(abs(CC TCM )) threshold to the total number of voxels in the dataset activated above the same threshold, for the same levels of separability as Fig 4.3 (a). Examining Figure 4.3 (a), the curve for separability = 0.2 seems to indicate that roughly 10% of the voxels with max(CC BOLD ) 0.7 will undergo global detrending, where the voxels will be detrended of components proportional to the maximally correlated TCM time-series. But this corresponds to max(abs(CC TCM )) > 0.9, at which level the voxel has a strong probability to be a TCM false-positive. At this level of separability, the Fig 4.3 (b) shows that around 10% of voxels with max(abs(CC TCM )) 1 are detrended of components to the TCM time-series formed by considering only the first three images of the TCM IRFs. The local detrending is by nature of its conception, less successful in reducing TCM signal changes than the global detrending. Thus, examining the curves, it is apparent that separability = 0.2 condition, if anything enhances the probability of retaining true-positive BOLD signal at the expense of diminished capacity to reduce false-positives. The second criteria regarding temporally localized detrending is expected to compensate for any attenuation in the false-positive reduction capacity. The results in the next chapter support this assertion. The second part of the algorithm examines voxels that show sufficient correlation between both TCM and BOLD responses. These voxels are detrended only if the fit between the first 3 images of their impulse response and the selected TCM IRFs is lower than a set limit. The set limit is more stringent for those voxels which are sufficiently correlated to both TCM and BOLD responses and in addition show more correlation with

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60 the chosen BOLD HRFs. From the description, it is apparent that the proper characterization of the BOLD and TCM responses is critical to the success of the method. (a) (b) Figure 4.3: Distribution of number of voxels undergoing non-selective detrending for a given max(CC BOLD ) as a fraction of the number of voxels at that max(CC BOLD ) for three different levels of separability, 0.2 (blue), 0.1 (green) and 0.0 (magenta) (a). Similar distributions for max(abs(CC TCM )) (b). Analysis of Detrended Time-Series The analysis of the detrended time-series proceeded in the same way as the undetrended time-series analysis. For each voxel the signal was considered to be the result of sum of convolutions of the correct response-locked stimulus vector and other response-locked stimulus vector and their corresponding impulse responses, plus a constant baseline and a white noise component. Fifteen lag impulse responses (12 for normal control subjects) for each of the conditions were estimated from the knowledge of the observed voxel FMRI time-series and the stimulus vectors. For the GLM, the baseline model was considered to include a constant baseline and the fitted signal due to other responses plus white noise, whereas the full model was considered to include a constant baseline, the fitted signal due to other responses and

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61 the fitted signal due to the correct responses plus white noise. In this way, the test-statistics F and R 2 quantified significance of correct response related signal alone. Implementation of Motion Parameter Regression Motion parameter regression (MPR) has been introduced in Chapter 3. Here the methods to implement MPR in a GLM based deconvolution analysis framework are described. The motion parameters for each image in the 805-image (555-image for controls) time-series were obtained from the image-registration program. For each voxel, the rigid-motion related signal at each scan was modeled as a quadratic function of the motion parameters in that scan and the preceding scan (117, 118).The motion-related signal was modeled as part of the baseline, along with the other response related signal changes, so that the regression statistic reflected the activation due to correct responses alone. The regression model (for patients) used is as follows: a: [4.2] oocchshs1515 pp6600 noppopnrnrrrnrrnrrrnrnnppnppnrnrrrnrrnrrrnrnhsMMMMbZHMMMMbZH15021,02,1,0,0021,602,1,60,0: where M r,n is the motion parameter for the r th degree of freedom at the n th image, , and are fitted constants, s c and s o are the correct and other response-locked stimulus vectors and h c and h o are the corresponding estimated impulse response functions. The impulse responses are estimated to 12 lags for the normal controls. The regression F and R 2 statistics were calculated for each voxel to quantify the significance of activation related to the correct response stimulus.

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62 Implementation of the Screening Images Method The method of screening images during speech (127) uses the observation (123-125) that most of the signal fluctuations due to speech occur in the first few images during and after speech. This method was implemented in the context of a GLM based deconvolution analysis by ignoring the zeroth and first lags while estimating the voxel IRF. The regression model (for patients) used was as follows: [4.3] pp noppopnnnopopncpcpnnahsbZHhshsbZH150001501520:: The other response related signal was modeled as part of the baseline. For the case of normal controls the IRFs were estimated up to 12 lags. The activation statistics R 2 and F, quantify the significance of activation due to correct responses. It should be noted that the signal changes occurring during the first two images after overt production do not contribute to the activation statistic in this method, whether it is TCM-related or BOLD-related. Implementation of Non-Selective Detrending The non-selective detrending method proposed by Birn et al. (125) also assumes that the TCM-related signal changes are temporally resolved from BOLD MR signal changes. This method has been described in Chapter 3. In the present context, the implementation of the non-selective detrending method followed that of the selective detrending method up to the part regarding estimation of TCM IRFs. The difference is in the detrending procedure. In the non-selective detrending all the voxels in the FMRI dataset are detrended of components proportional to all the representative TCM time series using a linear least-squares method (100). Since this is

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63 equivalent to detrending all the voxels in the FMRI dataset of components proportional to sum of all the chosen TCM time-series only a few (5-6 as opposed to 10-15) representative TCM time-series suffice. The detrended FMRI datasets were analyzed in exactly the same manner as described in the selective detrending method. Receiver Operating Characteristics The difficulties in conducting conventional ROC analysis have been mentioned in Chapter 2. Here the performance of the selective detrending method and its comparison with the other three methods as well as the case of no noise reduction is conducted through a modified ROC analysis procedure. The ROC procedure was used to measure two complementary indications of efficacy 1) the reduction of the false positive voxels outside the brain in the real FMRI datasets and 2) the retention of the true-positive voxels inside the brain, with IRFs satisfying strict criteria for BOLD hemodynamic responses. Reduction of False Positives The voxels outside the brain that possess R 2 or F values above the threshold selected to infer brain activation can be trivially considered to be false-positive voxels at that threshold. This is reinforced by considering voxels a sufficient distance outside the brain such that there are no effects due to large veins at the boundaries of the brain. The signal intensities in a low-resolution spiral MR image decrease rapidly away from the brain edge. By constructing signal-intensity histograms, the high intensity intra-cerebral voxels can be separated from the extra-cerebral voxels. Since TCM-related signal changes are accentuated at high contrast boundaries outside the brain created by CSF, cranium, air cavities, and scalp (134), the chosen test-bed can be considered to contain a fair population of TCM voxels. A further reduction of the test-bed, using the knowledge that TCM-corrupted voxels show more fluctuation in the early part of the IRF, can

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64 increase the proportion of TCM-corrupted voxels in the test-bed. Thus, the distribution of number of detected voxels as a function of threshold R 2 or F-statistic can be used to compare the efficacy of motion correction of all the four methods. For each FMRI dataset, an intensity-based brain mask was created using an iterative outlier-reduction method. This is implemented as a program in the AFNI software. This program also allows for dilating the brain mask by the requisite number of voxels to include regions just outside the brain which are low-intensity but exhibit venous activation arising from large peripheral veins. Voxel IRFs (a sufficient distance outside the brain to preclude venous effects) exhibiting larger fluctuation in the first 5 images relative to the last 11 (7 for controls) images were chosen to form the test-bed of false-positive activation. The distribution of the number of voxels in the test-bed detected as a function of threshold R 2 was constructed for all the four methods as well as for the case of no motion correction. An important property of the test-bed of false positives is that the method of obtaining the test-bed is independent of the algorithm to estimate false positive TCM signal changes. An assumption implicit in construction of the test-bed is that TCM signal changes in false-positive voxels outside the brain are representative of the TCM signal changes at high contrast boundaries on the brain. This assumption is valid when the TCM signal changes of voxels in the brain are not corrupted by BOLD signal changes. Retention of True Positives The intra-cerebral voxel IRFs, specified by the brain masking method, were fitted to a generic hemodynamic response curve. This curve, which is included as part of the AFNI software, is parameterized in terms of amplitude, delay-time, rise-time and fall-time. The functional form of the curve is given by

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65 otherwisethtttttttttttAthtttttttAthFRDRDFDRFRDDRD0)(18.06.12tantanh2)(18.06.12tantanh2)( [4.4] where A is the amplitude, t D t R and t F are delay-time, rise-time and fall-time of the hemodynamic response respectively. This function is more malleable to be fitted to estimated IRFs than gamma-variate functions (especially at low temporal resolutions). It also has the advantage of being parameterized in terms of temporal aspects of the HRF, a useful feature that comes of use while screening IRFs. The IRF of each voxel was fit to the generic hemodynamic response function (HRF) by means of a nonlinear optimization method using Matlab. 222),()(),( iiitIthtIthaa [4.5] where 2 is the cost function that was minimized by varying the parameter set a which consists of the parameters amplitude, t D t R and t F t is time discretized by the index i, h is the generic HDR described in Equation 4.4 and I is the voxel IRF. The parameters were varied iteratively till the cost function was minimized using a large-scale algorithm. This fitting was carried out with the lsqcurvefit function of Matlab. Figure 4.4 shows the estimated hemodynamic response of a true-positive BOLD voxel in the right medial frontal region of patient 1 (pre-therapy) dataset (blue) and the corresponding fit (green) from employing the non-linear optimization method. The graph shows the evolution of

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66 the curves over the first 20 seconds (which is the part of the IRFs relevant to the selection criteria). Figure 4.4: Estimated hemodynamic response of a true positive right medial frontal voxel of patient 1 (pre-therapy) dataset (blue) and the corresponding fit to a generic hemodynamic response (green). The maxima of the first 4 images of each voxel IRF, max(IRF 1-4 ) and the corresponding minima, min(IRF 1-4 ) were also calculated. Intra-cerebral voxel IRFs satisfying the following criteria formed the test-bed for hemodynamic-like voxels. )min(2.1)max(41,411604141IRFIRFttttttttttADRFFRRDFRD [4.6] where the terms are as defined above. Time is expressed in units of image TR (i.e. 1 1.66 sec). The set of criteria relating to amplitude and time were chosen so as to eliminate TCM-related IRFs. The penalty paid in terms of screening some BOLD HRFs was compensated by the fact that the chosen test-bed was devoid of TCM voxels. The

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67 distribution of the number of voxels in the selected test-bed detected as a function of threshold R 2 was constructed for all the four methods as well as for the case of no motion correction. The distributions were constructed to provide a means of comparing the true-positives retention capabilities of the four methods to retain true positive voxels.

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CHAPTER 5 RESULTS AND DISCUSSION In this chapter the results of the application of the selective detrending method as well as the other methods of reducing noise arising from task-correlated motion are presented and compared. The implications of the results on data analysis of event-related overt word-generation FMRI paradigms are discussed. Results In the following pages the omnibus results from the application of the four methods of TCM noise reduction reviewed, on FMRI datasets involving event-related overt generation paradigms in four patient datasets (two patients scanned twice, pre and post treatment) and four control subject datasets, are presented in the form of statistical activation maps parameterized by the coefficient of determination, R 2 The case of no noise correction is also provided for reference. In addition the results from the modified ROC analysis, i.e., the false-positives reduction capacity as well as true-positives retention capacity, examined based on separate voxel test-beds, are also provided for all the four patient datasets and the four control subject datasets. In the figures of the R 2 -activation maps green arrows point to selected BOLD HRF AFNI-grabs and blue arrows point to selected TCM IRF AFNI-grabs. In the graphs for the modified ROC analysis, the symbols ML0 and ML2 stand for min-lag (the lowest lag to which the impulse response is estimated) set to 0 and 2 respectively. Also all the activated voxels (in red) in the selective detrending activation maps posses BOLD hemodynamic-like responses. 68

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69 (a) (c) (b) (d) (e) Figure 5.1 Activation maps thresholded at R 2 > 0.2 for patient-1 (pre-scan) with no TCM noise-reduction (a), with selective detrending (b), with motion parameter regression (c), with ignoring 2 images after speech (d) and with non-selective detrending (e). The blue arrows indicate TCM voxel IRFs and the green arrows BOLD voxel IRFs.

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70 Patient 1 (Pre-Treatment) The Figure 5.1(a) shows a lateral sagittal slice of a high-resolution T1-weighted anatomic image with the R 2 -activation map overlay for the aphasia-patient-I (under pre-treatment condition), without TCM noise reduction. Some of the estimated TCM IRFs and BOLD HRF for selected voxels are also shown. Figure 5.1(b) shows the map with selective detrending. All the voxels shown activated in the selective detrending map exhibited BOLD HRF responses. The green arrow in the figure points away from activation at the inferior frontal sulcus (IFS), which is implicated in word-generation. The selective detrending method is able to attenuate the motion-corrupted portion of the IFS hemodynamic response. Figures 5.1 (c-e) show the R 2 -activation map for the same patient under the same scan after motion parameter regression, ignoring two images after speech and non-selective detrending. All the voxels activated above a threshold R 2 > 0.20 (corresponding to p-value < 10 -20 ) shown in red. All the activated voxels in the selective detrending map (Figure 5.1 (b)) exhibited BOLD HRF similar to the one shown by the green arrow in Figure 5.1 (b). Figure 5.1 (a) shows a lot of TCM corrupted false-positive voxels, particularly in the inferior and frontal regions. A few representative TCM impulse responses are shown by the blue arrows. From the figures (5.1 (a-e)) for the 5 cases it can be noted that for this subject the motion-parameter regression (MPR) method performs poorly with regard to TCM noise reduction. The method of ignoring the first two images during speech (Figure 5.1 (d)) performs better than the MPR method. However it still exhibits some false-positive TCM voxels as marked by the blue arrows. The non-selective detrending method (Figure 5.1 (e)) is sub-optimal in this case. This method seems to reduce the true-positive BOLD hemodynamic signals in the inferior frontal sulcus.

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71 The selective detrending method performs better than all other techniques. Not only is it able to reduce TCM-related false positive activation, but also it is also able to retain the brain activation voxels corrupted by motion artifacts, and to remove parts of the signal time course originating from motion. Figure 5.1 (b) shows one such example for the case of an inferior frontal sulcus voxel (which is implicated in semantic word generation). The sudden large fluctuation in the signal at the onset of the response caused by task-correlated motion is attenuated to give a more regularized hemodynamic response as shown by the green arrow. The above statement is quantified in the modified ROC analyses illustrated in Figures 5.2 (a-b). The efficiency of TCM noise reduction of all the four methods as well as for the case of no motion correction is shown in Figure 5.2 (a) for aphasia patient-1 (pre-scan). Ideally, all the voxels in the false-positives test-bed should go to zero (or more accurately go towards the null distribution values). The selective detrending method (denoted dtsel and represented by the magenta curve) performs almost as well as the non-selective detrending method (denoted dt and represented by the red curve) in terms of reducing TCM false-positives. The method of ignoring images (ML2; black) is less optimal whereas the motion-parameter regression method (MPR; green) seems to have very little effect on TCM voxels. The case with no motion correction (ML0; blue) is also shown for reference. Figure 5.2 (b) shows the effect of each of the TCM noise reduction treatments on the test-bed of the true-positive BOLD HRF-like voxels. Since the criteria for inclusion into the test-bed precludes the occurrence of speech-related TCM voxels, ideally a given treatment should have the same distribution as for the case of no noise correction. There

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72 does not seem to be much difference in the true-positives retention capacity between the MPR, ML2 and selective detrending methods. The non-selective detrending method seems to suffer from a loss of sensitivity to BOLD MR signal. By considering this graph along with the TCM noise reduction graph of Figure 5.2 (a) one can state that the selective detrending method performs the best in terms of TCM noise reduction and true positive BOLD HRF retention. (a) (b) Figure 5.2: Fraction of voxels detected as a function threshold R 2 for (a) the false-positives test-bed and (b) the true-positives test-bed for aphasia patient 1 (pre-therapy scan). The blue curve (ML0) represents the case of no motion correction, the black curve (ML2) represents the method of ignoring the first 2 images after speech, the green curve (MPR) represents the motion-parameter regression method, the magenta curve (dtsel) represents the selective detrending method and the red curve (dt) represents the non-selective detrending method. The superior performance of the selective detrending method when compared to the method of ignoring images and the non-selective detrending method can be comprehended by examining Figure 5.3. The figure on the left, 5.3 (a), shows some representative TCM corrupted impulse responses chosen from voxels outside the brain for aphasia patient 1 (pre-therapy scan).

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73 ggg (a) (b) Figure 5.3: Some representative TCM-related voxel IRFs (a); Some representative BOLD HRFs (b) from aphasia patient 1 (pre-therapy scan) data. (a) (b) Figure 5.4: The effect of the methods of noise correction on a right medial-frontal voxel BOLD HRF exhibiting an early response for patient 1 pre-therapy scan (a). The effect of the methods of noise correction on a right inferior sulcus voxel, exhibiting both BOLD and TCM signal changes (b) for the same scan. The no-correction curve is hidden by the selective detrending curve in both figures.

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74 Some of the TCM IRFs (e.g. the red curve) are shifted relative to the time of onset. Some of responses (blue) have significant longer lasting effects. Thus the method of ignoring two images after speech may not adequately attenuate the effects of TCM in these voxels and false-positive activation may remain even after the correction algorithm is executed. Increasing the number of ignored images is not an attractive option, in that this may lead to loss of sensitivity to true-positive BOLD responses (as can be inferred from Figure 5.3). In fact one perceives a potential loss of sensitivity to some true-positive BOLD HRFs (especially the green and red curves in Figure 5.3 (b)) even for the ML2 method. An analogous analysis can be made for the case of the non-selective detrending method. Attenuating the effects of TCM in the voxel IRFs shown in Figure 5.3 (a) may lead to attenuation in true-positive BOLD signal in some voxels as represented by the curves in Figure 5.3 (b). This is the source of the sub-optimal true-positives retention capacity of the non-selective detrending method. Figure 5.4 (a) shows the effect of applying the reviewed methods of TCM noise reduction on a BOLD activation voxel in the right medial-frontal region of aphasia patient 1 (pre-therapy scan). This voxels hemodynamic response has an early onset. This could be due to the overt response-locked stimulus vector used in the analysis. Presumably this voxel covers neuronal sources that activate prior to the overt-response, or the voxel HRF has zero delay to onset and the resolution of the stimulus vector and image acquisition is not sufficient to extract the early response. The blue dashed curve (ML0-2) in Figure 5.4 (a) (which has been generated by shifting the response-locked stimulus vector back by two images) suggests that the HRF has started prior to word-enunciation. It is obvious from the Figure 5.4 (a) that the method of ignoring two images

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75 during speech (ML2, black) suffers from a lack of sensitivity to the early portion of the hemodynamic response, since the method ignores the first two images. The non-selective detrending method (dt, red) removes BOLD MR signal in this voxel and hence is sub-optimal. The selective detrending method (dtsel, magenta) does not perform any detrending on this voxel and leaves the putative early-onset BOLD signal intact. The motion parameter regression method (MPR, green) also does not suffer from loss of sensitivity to BOLD MR signal in this case. An added advantage of the selective detrending method is that it has the capacity to at least partially tease apart TCM and BOLD signal changes in a brain activation voxel that has been affected by both. Figure 5.4 (b) shows the voxel HRFs of an inferior frontal sulcus voxel of patient 1 (pre-therapy scan). (This voxel has been marked by the green arrow in the Figure 5.1 (b)). From the graph, in the curve representing no noise correction (ML0, blue), one perceives a large initial fluctuation in signal (caused by TCM) and a subsequent smooth hemodynamic response (caused by brain activation) The selective detrending method (dtsel, magenta) is able to attenuate the TCM-related signal changes resulting in a more regularized hemodynamic response. The motion parameter regression method (MPR, green) does not have much affect on the voxel IRF. The non-selective detrending method (dt, red) removes a lot of BOLD signal along with the TCM signal. The method of ignoring two images during speech (ML2, black) performs almost as well as the selective detrending method in this case. Patient 1 (Post-Treatment) The Figure 5.5 (a) shows a lateral sagittal slice of a high-resolution T1-weighted anatomic image with the R 2 -activation map overlay for the aphasia-patient-I (under post-treatment condition), without TCM noise reduction.

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76 (a) (b) (c) (d) (e) Figure 5.5: Activation maps thresholded at R 2 > 0.2 for patient 1 (post-therapy scan) with no TCM noise-reduction (a), with selective detrending (b), with motion parameter regression (c), with ignoring 2 images after speech (d) and with non-selective detrending (e). The blue arrows indicate TCM voxel IRFs and the green arrows BOLD voxel IRFs.

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77 Some of the estimated TCM IRFs and BOLD HRF for selected voxels are also shown. Figure 5.5(b) shows the map with selective detrending. All the voxels shown activated in the selective detrending map exhibited BOLD HRF responses. Figures 5.5 (c-e) show the R 2 -activation map for the same patient under the same scan after motion parameter regression, ignoring two images after speech and non-selective detrending. All the voxels activated above a threshold R 2 > 0.20 (corresponding to p-value < 10 -20 ) shown in red. All the activated voxels in the selective detrending map (Figure 5.5 (b)) exhibited BOLD HRF similar to the one shown by the green arrow in Figure 5.5 (b) (which shows activation in the motor strip). Figure 5.5 (a) shows a lot of TCM corrupted false-positive voxels, particularly in the inferior and frontal regions. A few representative TCM impulse responses are shown by the blue arrows. From the figures (5.5 (a-e)) for the 5 cases it can be noted that for this subject the motion-parameter regression (MPR) method and the ML2 method do not perform well with regard to TCM noise reduction. The non-selective detrending method seems to reduce true-positive BOLD MR signal along with TCM noise. The selective detrending method seems to work the best in terms of retention of true-positives and reduction of false-positives. Figure 5.6 (a) shows some representative TCM IRFs extracted from the patient 1 (post-therapy scan) dataset. There are a lot of similarities in the motion responses. Some of the TCM IRFs (e.g. the red curve) are shifted relative to the time of onset. Some of responses (blue) have significant longer lasting effects. Figure 5.6 (b) shows the effect of applying the reviewed methods of TCM noise reduction on a BOLD activation voxel in the right lateral-frontal region of aphasia patient 1 (post-therapy scan). This voxels hemodynamic response has an early onset.

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78 (a) (b) Figure 5.6: Some representative TCM-related voxel IRFs from patient 1 post-therapy scan (a). The effect of the methods of noise correction on a right medial-frontal voxel BOLD HRF exhibiting an early response for the same dataset (b). The no-correction curve is hidden by the selective detrending curve. (a) (b) Figure 5.7: Fraction of voxels detected as a function threshold R 2 for (a) the false-positives test-bed and (b) the true-positives test-bed for aphasia patient 1 (post-therapy scan). The blue curve (ML0) represents the case of no motion correction, the black curve (ML2) represents the method of ignoring first 2 images after speech, the green curve (MPR) represents the motion-parameter regression method, the magenta curve (dtsel) represents the selective detrending method and the red curve (dt) represents the non-selective detrending method.

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79 The blue dashed curve (ML0-2) in Figure 5.6 (b) (which has been generated by shifting the response-locked stimulus vector back by two images) suggests that the HRF has started prior to word-enunciation. It is obvious from the Figure 5.6(b) that the method of ignoring two images during speech (ML2, black) suffers from a lack of sensitivity to the early portion of the hemodynamic response, since the method ignores the first two images. The non-selective detrending method (dt, red) removes BOLD MR signal in this voxel and hence is sub-optimal. The selective detrending method (dtsel, magenta) does not perform any detrending on this voxel and leaves the BOLD signal intact. The motion parameter regression method (MPR, green) also seems to leave the BOLD MR signal intact in this voxel. The modified ROC analyses for this FMRI dataset is illustrated in Figures 5.7 (a-b). The efficiency of TCM noise reduction of all the four methods as well as for the case of no motion correction is shown in Figure 5.7(a) for aphasia patient 2 (post-therapy scan). The non-selective detrending method (dt; red curve) performs the best in terms of reducing TCM false-positives. The selective detrending method (dtsel; magenta) performs better than the method of ignoring images (ML2; black) as well as the motion-parameter regression method (MPR; green). The MPR and ML2 method curves look similar. The case with no motion correction (ML0; blue) is also shown for reference. Figure 5.7 (b) shows the effect of each of the TCM noise reduction treatments on the test-bed of the true-positive BOLD HRF-like voxels. There does not seem to be much difference in the true-positives retention capacity between the MPR, ML2 and selective detrending methods. The non-selective detrending method seems to suffer from a loss of

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80 sensitivity to BOLD MR signal. By considering this graph along with the TCM noise reduction graph of Figure 5.7 (a) one can state that the selective detrending method performs the best in terms of TCM noise reduction and true positive BOLD HRF retention. Patient 2 (Pre-Treatment) The Figure 5.8(a) shows a medial sagittal slice of a high-resolution T1-weighted anatomic image with the R 2 -activation map overlay for the aphasia-patient-2 (under pre-treatment condition), without TCM noise reduction. Some of the estimated TCM IRFs and BOLD HRF for selected voxels are also shown. Figure 5.8(b) shows the map with selective detrending. All the voxels shown activated in the selective detrending map exhibited BOLD HRF responses. The green arrow in the figure points away from activation in the right anterior putamen region, which is implicated in word-generation. The selective detrending method is able to attenuate the motion-corrupted portion of the hemodynamic response. Figures 5.8 (c-e) show the R 2 -activation map for the same patient under the same scan after motion parameter regression, ignoring two images after speech and non-selective detrending. All the voxels activated above a threshold R 2 > 0.20 (corresponding to p-value < 10 -20 ) shown in red. All the activated voxels in the selective detrending map (Figure 5.8 (b)) exhibited BOLD HRF similar to the one shown by the green arrow in Figure 5.8 (b). Figure 5.8 (a) shows a lot of TCM corrupted false-positive voxels, particularly in the inferior and frontal regions. A few representative TCM impulse responses are shown by the blue arrows. From the figures (5.8 (a-e)) for the 5 cases it can be noted that for this subject the motion-parameter regression (MPR) method as well as the ignoring images method (ML2) show residual TCM-related false-positives event after noise-reduction. The non-selective detrending method seems to reduce true-positive

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81 (a) (b) (c) (d) (e) Figure 5.8: Activation maps thresholded at R 2 > 0.2 for patient-2 (pre-therapy scan) with no TCM noise-reduction (a), with selective detrending (b), with motion parameter regression (c), with ignoring 2 images after speech (d) and with non-selective detrending (e). The blue arrows indicate TCM voxel IRFs and the green arrows BOLD voxel IRFs.

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82 BOLD MR signal along with TCM noise. The selective detrending method seems to work the best in terms of retention of true-positives and reduction of false-positives. Figure 5.9 (a) shows some representative TCM IRFs extracted from the patient 2 (pre-therapy scan) dataset. There are a lot of similarities in the TCM responses. Some of the TCM IRFs are shifted relative to the time of onset and some have significant longer lasting effects. Figure 5.9 (b) shows the effect of applying the reviewed methods of TCM noise reduction on a right medial-frontal BOLD activation voxel in aphasia patient 2 (pre-therapy scan). This voxels hemodynamic response has an early onset. The blue dashed curve (ML0-2) in Figure 5.9 (b) (which has been generated by shifting the response-locked stimulus vector back by two images) suggests that the HRF has started prior to word-enunciation. It is obvious from the Figure 5.9 (b) that the method of ignoring two images during speech (ML2, black) suffers from a lack of sensitivity to the early portion of the hemodynamic response, since the method ignores the first two images. There also seems to be a slight decrease in the amplitude of the response for the ML2 curve. This could be due to the use of an unbiased estimator in deconvolution analysis. The non-selective detrending method (dt, red) removes BOLD MR signal in this voxel and hence is sub-optimal. The selective detrending method (dtsel, magenta) does not perform any detrending on this voxel and leaves the BOLD signal intact. The motion parameter regression method (MPR, green) also leads to a reduced HRF amplitude.

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83 (a) (b) Figure 5.9: Some representative TCM-related voxel IRFs from patient 2 pre-therapy scan (a). The effect of the methods of noise correction on a right medial-frontal voxel BOLD HRF exhibiting an early response for the same dataset (b). The no-correction curve is hidden by the selective detrending curve. (a) (b) Figure 5.10: Fraction of voxels detected as a function threshold R2 for (a) the false-positives test-bed and (b) the true-positives test-bed for aphasia patient 2 (pre-therapy scan). The blue curve (ML0) represents the case of no motion correction, the black curve (ML2) represents the method of ignoring first 2 images after speech, the green curve (MPR) represents the motion-parameter regression method, the magenta curve (dtsel) represents the selective detrending method and the red curve (dt) represents the non-selective detrending method.

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84 The modified ROC analyses for this study is illustrated in Figures 5.10 (a-b). The efficiency of TCM noise reduction of all the four methods as well as for the case of no motion correction is shown in Figure 5.10 (a). The selective detrending method (dtsel; magenta) performs almost as well as the non-selective detrending method (dt; red) in terms of reducing TCM false-positives. The method of ignoring images (ML2; black) and the motion-parameter regression method (MPR; green) look similar and are less optimal. The case with no motion correction (ML0; blue) is also shown for reference. Figure 5.10 (b) shows the effect of each of the TCM noise reduction treatments on the test-bed of the true-positive BOLD HRF-like voxels. The distributions look similar except for the non-selective detrending method. The non-selective detrending method seems to suffer from a loss of sensitivity to BOLD MR signal. By considering this graph along with the TCM noise reduction graph of Figure 5.10 (a) one can state that the selective detrending method performs the best in terms of TCM noise reduction and true positive BOLD HRF retention. Patient 2 (Post-Treatment) The Figure 5.11 (a) shows a lateral sagittal slice of a high-resolution T1-weighted anatomic image with the R 2 -activation map overlay for the aphasia-patient-2 (under post-treatment condition), without TCM noise reduction. Some of the estimated TCM IRFs and BOLD HRF for selected voxels are also shown. Figure 5.11(b) shows the map with selective detrending. All the voxels shown activated in the selective detrending map exhibited BOLD HRF responses. The green arrow in the figure points away from activation in the motor strip, which is implicated in word-generation. Figures 5.11 (c-e) show the R 2 -activation map for the same patient under the same scan after motion parameter regression, ignoring two images after speech and non-selective

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85 (a) (c) (b) (d) (e) Figure 5.11: Activation maps thresholded at R 2 > 0.2 for patient 2 (post-therapy scan) with no TCM noise-reduction (a), with selective detrending (b), with motion parameter regression (c), with ignoring 2 images after speech (d) and with non-selective detrending (e). The blue arrows indicate TCM voxel IRFs and the green arrows BOLD voxel IRFs.

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86 detrending. All the voxels activated above a threshold R 2 > 0.20 (corresponding to p-value < 10 -20 ) shown in red. All the activated voxels in the selective detrending map (Figure 5.11 (b)) exhibited BOLD HRF similar to the one shown by the green arrow in Figure 5.11 (b). Figure 5.11 (a) shows a lot of TCM corrupted false-positive voxels, particularly in the inferior and frontal regions. A few representative TCM impulse responses are shown by the blue arrows. From the figures (5.11 (a-e)) for the 5 cases it can be noted that for this subject the motion-parameter regression (MPR) method as well as the ignoring images method (ML2) show residual TCM-related false-positives event after noise-reduction. The non-selective detrending method seems to reduce true-positive BOLD MR signal along with TCM noise. The selective detrending method seems to work the best in terms of retention of true-positives and reduction of false-positives. Figure 5.12 (a) shows some representative TCM IRFs extracted from the patient 2 (pre-therapy scan) dataset. There are a lot of similarities in the TCM responses. Some of the TCM IRFs are shifted relative to the time of onset and some have significant longer lasting effects. Figure 5.12 (b) shows the effect of applying the reviewed methods of TCM noise reduction on a right medial-frontal BOLD activation voxel in aphasia patient 2 (post-therapy scan). This voxels hemodynamic response has an early onset. The blue dashed curve (ML0-2) in Figure 5.12 (b) (which has been generated by shifting the response-locked stimulus vector back by one image) suggests that the HRF has started prior to word-enunciation. It is obvious from the Figure 5.12 (b) that the method of ignoring two images during speech (ML2, black) suffers from a lack of sensitivity to the early portion of the hemodynamic response, since the method ignores the first two images. There also

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87 (a) (b) Figure 5.12: Some representative TCM-related voxel IRFs from patient 2 post-therapy scan (a). The effect of the methods of noise correction on a right medial-frontal voxel BOLD HRF exhibiting an early response for the same dataset (b). The no-correction curve is hidden by the selective detrending curve. (a) (b) Figure 5.13: Fraction of voxels detected as a function threshold R2 for (a) the false-positives test-bed and (b) the true-positives test-bed for aphasia patient 2 (post-therapy scan). The blue curve (ML0) represents the case of no motion correction, the black curve (ML2) represents the method of ignoring first 2 images after speech, the green curve (MPR) represents the motion-parameter regression method, the magenta curve (dtsel) represents the selective detrending method and the red curve (dt) represents the non-selective detrending method.

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88 seems to be a slight decrease in the amplitude of the response for the ML2 curve. This could be due to the use of an unbiased estimator in deconvolution analysis. The non-selective detrending method (dt, red) removes BOLD MR signal in this voxel and hence is sub-optimal. The selective detrending method (dtsel, magenta) does not perform any detrending on this voxel and leaves the BOLD signal intact. The motion parameter regression method (MPR, green) also leads to a reduced HRF amplitude. The modified ROC analyses for the aphasia patient 2 (post-therapy scan) is illustrated in Figures 5.13 (a-b). The efficiency of TCM noise reduction of all the four methods as well as for the case of no motion correction is shown in Figure 5.13 (a). The non-selective detrending method (dt; red curve) performs the best in terms of reducing TCM false-positives. The selective detrending method (dtsel; magenta) performs better than the method of ignoring images (ML2; black) as well as the motion-parameter regression method (MPR; green). The ML2 method performs slightly better than the MPR method. The case with no motion correction (ML0; blue) is also shown for reference. Figure 5.13 (b) shows the effect of each of the TCM noise reduction treatments on the test-bed of the true-positive BOLD HRF-like voxels. The distributions look similar except for the non-selective detrending method. The non-selective detrending method seems to suffer from a loss of sensitivity to BOLD MR signal. By considering this graph along with the TCM noise reduction graph of Figure 5.13 (a) one can state that the selective detrending method performs the best in terms of TCM noise reduction and true positive BOLD HRF retention.

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89 (a) (c) (b) (d) (e) Figure 5.14: Activation maps thresholded at R 2 > 0.2 for control subject 1 with no TCM noise-reduction (a), with selective detrending (b), with motion parameter regression (c), with ignoring 2 images after speech (d) and with non-selective detrending (e). The blue arrows indicate TCM voxel IRFs and the green arrows BOLD voxel IRFs.

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90 Control Subject 1 The Figure 5.14 (a) shows a medial sagittal slice of a high-resolution T1-weighted anatomic image with the R 2 -activation map overlay for the control subject 1, without TCM noise reduction. Some of the estimated TCM IRFs and BOLD HRF for selected voxels are also shown. Figure 5.14(b) shows the map with selective detrending. All the voxels shown activated in the selective detrending map exhibited BOLD HRF responses. The green arrow in the figure points away from activation in the right medial frontal region, which is implicated in word-generation. Figures 5.14 (c-e) show the R 2 -activation map for the same subject under the same scan after motion parameter regression, ignoring two images after speech and non-selective detrending. All the voxels activated above a threshold R 2 > 0.20 (corresponding to p-value < 10 -20 ) shown in red. All the activated voxels in the selective detrending map (Figure 5.14 (b)) exhibited BOLD HRF similar to the one shown by the green arrow in Figure 5.14 (b). Figure 5.14 (a) shows a lot of TCM corrupted false-positive voxels, particularly in the inferior and frontal regions. A few representative TCM impulse responses are shown by the blue arrows. From the figures (5.14 (a-e)) for the 5 cases it can be noted that for this subject the motion-parameter regression (MPR) method as well as the ignoring images method (ML2) show residual TCM-related false-positives event after noise-reduction. The non-selective detrending method seems to reduce true-positive BOLD MR signal along with TCM noise. The selective detrending method seems to work the best in terms of retention of true-positives and reduction of false-positives.

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91 (b) (a) Figure 5.15: Some representative TCM-related voxel IRFs from control subject 1. The effect of the methods of noise correction on a right medial-frontal voxel BOLD HRF exhibiting an early response for the same dataset (b). The no-correction curve is hidden by the selective detrending curve. (a) (b) Figure 5.16: Fraction of voxels detected as a function threshold R2 for (a) the false-positives test-bed and (b) the true-positives test-bed for control subject 1. The blue curve (ML0) represents the case of no motion correction, the black curve (ML2) represents the method of ignoring first 2 images after speech, the green curve (MPR) represents the motion-parameter regression method, the magenta curve (dtsel) represents the selective detrending method and the red curve (dt) represents the non-selective detrending method.

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92 Figure 5.15 (a) shows some representative TCM IRFs extracted from the control subject 1 dataset. There are a lot of similarities in the TCM responses. Some of the TCM IRFs are shifted relative to the time of onset and some have significant longer lasting effects. Figure 5.15 (b) shows the effect of applying the reviewed methods of TCM noise reduction on a right medial-frontal BOLD activation voxel in control subject 1. This voxels hemodynamic response has an early onset. It is obvious from the Figure 5.15 (b) that the method of ignoring two images during speech (ML2, black) suffers from a lack of sensitivity to the early portion of the hemodynamic response, since the method ignores the first two images. The non-selective detrending method (dt, red) removes BOLD MR signal in this voxel and hence is sub-optimal. The selective detrending method (dtsel, magenta) does not perform any detrending on this voxel and leaves the BOLD signal intact. The motion parameter regression method (MPR, green) leads to a slightly reduced HRF amplitude. The modified ROC analyses for the control subject 1 is illustrated in Figures 5.16 (a-b). The efficiency of TCM noise reduction of all the four methods as well as for the case of no motion correction is shown in Figure 5.16 (a). The selective detrending method (dtsel; magenta) performs almost as well as the non-selective detrending method (dt; red) in terms of reducing TCM false-positives. The method of ignoring images (ML2; black) is less optimal. The motion-parameter-regression method (MPR; green) does not show much improvement over the no-correction case (ML0; blue). Figure 5.16 (b) shows the effect of each of the TCM noise reduction treatments on the test-bed of the true-positive BOLD HRF-like voxels. The distributions look similar

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93 except for the non-selective detrending method. The non-selective detrending method seems to suffer from a loss of sensitivity to BOLD MR signal. By considering this graph along with the TCM noise reduction graph of Figure 5.16 (a) one can state that the selective detrending method performs the best in terms of TCM noise reduction and true positive BOLD HRF retention. Control Subject 2 The Figure 5.17 (a) shows a lateral sagittal slice of a high-resolution T1-weighted anatomic image with the R 2 -activation map overlay for the control subject 2, without TCM noise reduction. Some of the estimated TCM IRFs and BOLD HRF for selected voxels are also shown. Figure 5.17(b) shows the map with selective detrending. All the voxels shown activated in the selective detrending map exhibited BOLD HRF responses. The green arrow (pointing right in Figure 5.17 (a)) points away from activation in the right middle frontal region, which is implicated in word-generation. The green arrow in Figure 5.17 (b) points away from a brocas area voxel which exhibits an early response. The activation maps of the other 3 methods do not exhibit this voxel. Figures 5.17 (c-e) show the R 2 -activation map for the same subject under the same scan after motion parameter regression, ignoring two images after speech and non-selective detrending. All the voxels activated above a threshold R 2 > 0.20 (corresponding to p-value < 10 -20 ) shown in red. All the activated voxels in the selective detrending map (Figure 5.17 (b)) exhibited BOLD HRF similar to the one shown by the green arrow in Figure 5.17 (a). Figure 5.17 (a) shows a lot of TCM corrupted false-positive voxels, particularly in the inferior and frontal regions. A few representative TCM impulse responses are shown by the blue arrows. From the figures (5.17 (a-e)) for the 5 cases it can be noted that for this subject the motion-parameter regression (MPR) method as well

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94 (a) (c) (b) (d) (e) Figure 5.17: Activation maps thresholded at R 2 > 0.2 for control subject-2 with no TCM noise-reduction (a), with selective detrending (b), with motion parameter regression (c), with ignoring 2 images after speech (d) and with non-selective detrending (e). The blue arrows indicate TCM voxel IRFs and the green arrows BOLD voxel IRFs.

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95 as the ignoring images method (ML2) show residual TCM-related false-positives event after noise-reduction. The non-selective detrending method seems to reduce true-positive BOLD MR signal along with TCM noise. The selective detrending method seems to work the best in terms of retention of true-positives and reduction of false-positives. Figure 5.18 (a) shows some representative TCM IRFs extracted from the control subject 2 dataset. There are a lot of similarities in the TCM responses. Some of the TCM IRFs are shifted relative to the time of onset and some have significant longer lasting effects. Figure 5.18 (b) shows the effect of applying the reviewed methods of TCM noise reduction on a right medial-frontal BOLD activation voxel in control subject 2. This voxels hemodynamic response has an early onset. It is obvious from the Figure 5.18 (b) that the method of ignoring two images during speech (ML2, black) suffers from a lack of sensitivity to the early portion of the hemodynamic response, since the method ignores the first two images. There seems to be a slight decrease in the amplitude of the response for the ML2 curve. This could be due to the use of an unbiased estimator in deconvolution analysis. The non-selective detrending method (dt, red) removes BOLD MR signal in this voxel and hence is sub-optimal. The selective detrending method (dtsel, magenta) does not perform any detrending on this voxel and leaves the BOLD signal intact. The motion parameter regression method (MPR, green) also leads to a slightly reduced HRF amplitude. The modified ROC analyses for the control subject 2 is illustrated in Figures 5.19 (a-b). The efficiency of TCM noise reduction of all the four methods as well as for the case of no motion correction is shown in Figure 5.19 (a). The non-selective detrending

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96 (a) (b) Figure 5.18: Some representative TCM-related voxel IRFs from control subject 2 (a). The effect of the methods of noise correction on a right medial-frontal voxel BOLD HRF exhibiting an early response for the same dataset (b). The no-correction curve is hidden by the selective detrending curve. (a) (b) Figure 5.19: Fraction of voxels detected as a function threshold R2 for (a) the false-positives test-bed and (b) the true-positives test-bed for control subject 2. The blue curve (ML0) represents the case of no motion correction, the black curve (ML2) represents the method of ignoring first 2 images after speech, the green curve (MPR) represents the motion-parameter regression method, the magenta curve (dtsel) represents the selective detrending method and the red curve (dt) represents the non-selective detrending method.

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97 method (dt; red curve) performs the best in terms of reducing TCM false-positives. The selective detrending method (dtsel; magenta) performs better than the method of ignoring images (ML2; black) as well as the motion-parameter regression method (MPR; green). The ML2 method performs slightly better than the MPR method. The no-correction curve (ML0; blue) is also given for reference. Figure 5.19 (b) shows the effect of each of the TCM noise reduction treatments on the test-bed of the true-positive BOLD HRF-like voxels. The distributions look similar except for the non-selective detrending method. The non-selective detrending method seems to suffer from a loss of sensitivity to BOLD MR signal. By considering this graph along with the TCM noise reduction graph of Figure 5.19 (a) one can state that the selective detrending method performs the best in terms of TCM noise reduction and true positive BOLD HRF retention. Control Subject 3 The Figure 5.20 (a) shows a lateral sagittal slice of a high-resolution T1-weighted anatomic image with the R 2 -activation map overlay for the control subject 3, without TCM noise reduction. Some of the estimated TCM IRFs and BOLD HRF for selected voxels are also shown. Figure 5.20(b) shows the map with selective detrending. All the voxels shown activated in the selective detrending map exhibited BOLD HRF responses. The green arrow (pointing right in Figure 5.20 (b)) points away from activation in the motor strip, which is implicated in word-generation. The green arrow (pointing left) in Figure 5.20 (b) points away from an inferior frontal sulcus voxel which exhibits an early response. The activation maps of the other 3 methods do not exhibit this voxel. Figures 5.20 (c-e) show the R 2 -activation map for the same subject under the same scan after motion parameter regression, ignoring two images after speech and non-selective

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98 (a) (c) (b) (d) (e) Figure 5.20: Activation maps thresholded at R 2 > 0.2 for control subject 3 with no TCM noise-reduction (a), with selective detrending (b), with motion parameter regression (c), with ignoring 2 images after speech (d) and with non-selective detrending (e). The blue arrows indicate TCM voxel IRFs and the green arrows BOLD voxel IRFs.

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99 detrending. All the voxels activated above a threshold R 2 > 0.20 (corresponding to p-value < 10 -20 ) shown in red. All the activated voxels in the selective detrending map (Figure 5.20 (b)) exhibited BOLD HRF similar to the one shown by the green arrows in Figure 5.20 (a). Figure 5.20 (a) shows a lot of TCM corrupted false-positive voxels, particularly in the inferior and frontal regions. A few representative TCM impulse responses are shown by the blue arrows. From the figures (5.20 (a-e)) for the 5 cases it can be noted that for this subject the motion-parameter regression (MPR) method as well as the ignoring images method (ML2) show residual TCM-related false-positives event after noise-reduction. The non-selective detrending method seems to reduce true-positive BOLD MR signal along with TCM noise. The selective detrending method seems to work the best in terms of retention of true-positives and reduction of false-positives. Figure 5.21 (a) shows some representative TCM IRFs extracted from the control subject 3 dataset. There are a lot of similarities in the TCM responses. Some of the TCM IRFs are shifted relative to the time of onset and some have significant longer lasting effects. Figure 5.21 (b) shows the effect of applying the reviewed methods of TCM noise reduction on a right lateral pre-frontal BOLD activation voxel in control subject 3. This voxel is indicated by the green arrow (pointing left) in Figure 5.20 (b). This voxels hemodynamic response has an early onset. The blue dashed curve (ML0-2) in Figure 5.21 (b) (which has been generated by shifting the response-locked stimulus vector back by one image) suggests that the HRF has started prior to word-enunciation. It is obvious from the Figure 5.21 (b) that the method of ignoring two images during speech (ML2; black) suffers from a lack of sensitivity to the early portion of the hemodynamic response

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100 (a) (b) Figure 5.21: Some representative TCM-related voxel IRFs from control subject 3 (a). The effect of the methods of noise correction on a right medial-frontal voxel BOLD HRF exhibiting an early response for the same dataset (b). The no-correction curve is hidden by the selective detrending curve. (a) (b) Figure 5.22: Fraction of voxels detected as a function threshold R2 for (a) the false-positives test-bed and (b) the true-positives test-bed for control subject 3. The blue curve (ML0) represents the case of no motion correction, the black curve (ML2) represents the method of ignoring first 2 images after speech, the green curve (MPR) represents the motion-parameter regression method, the magenta curve (dtsel) represents the selective detrending method and the red curve (dt) represents the non-selective detrending method.

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101 since the m ethod ignores the first two images. There also seems to be a slight decrease in the amplitude of the response for the ML2 curve. This could be due to the use of an unbiased estimator in deconvolution analysis. The non-selective detrending method (dt, red) removes BOLD MR signal in this voxel and hence is sub-optimal. The selective detrending method (dtsel, magenta) does not perform any detrending on this voxel and leaves the BOLD signal intact. The motion parameter regression method (MPR, green) also seems to leave much of the BOLD MR signal intact. The modified ROC analyses for the control subject 3 is illustrated in Figures 5.22 (a-b). The efficiency of TCM noise reduction of all the four methods as well as for the case of no motion correction is shown in Figure 5.22 (a). The non-selective detrending method (dt; red curve) performs the best in terms of reducing TCM false-positives. The selective detrending method (dtsel; magenta) performs better than the method of ignoring images (ML2; black) as well as the motion-parameter regression method (MPR; green). The curves for the ML2 and the MPR methods look similar. The no-correction curve (ML0; blue) is also given for reference. Figure 5.22 (b) shows the effect of each of the TCM noise reduction treatments on the test-bed of the true-positive BOLD HRF-like voxels. The distributions for the ML2, selective detrending method and the no-correction case look similar. The non-selective detrending method seems to suffer from a loss of sensitivity to BOLD MR signal. The MPR method too seems to be less sensitive to true-positive BOLD MR signal when compared to the selective detrending and the ML2 methods. By considering this graph along with the TCM noise reduction graph of Figure 5.22 (a) one can state that the

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102 selective detrending method performs the best in terms of TCM noise reduction and true positive BOLD HRF retention. Control Subject 4 The Figure 5.23 (a) shows a lateral sagittal slice of a high-resolution T1-weighted anatomic image with the R 2 -activation map overlay for the control subject 4, without TCM noise reduction. Some of the estimated TCM IRFs and BOLD HRF for selected voxels are also shown. Figure 5.23(b) shows the map with selective detrending. All the voxels shown activated in the selective detrending map exhibited BOLD HRF responses. The green arrow in Figure 5.23 (a) points away from activation in the inferior parietal region which is implicated in word-generation. The green arrow in Figure 5.23 (b) points away from activation in the primary auditory region. Figures 5.23 (c-e) show the R 2 -activation map for the same subject under the same scan after motion parameter regression, ignoring two images after speech and non-selective detrending. All the voxels activated above a threshold R 2 > 0.20 (corresponding to p-value < 10 -20 ) shown in red. All the activated voxels in the selective detrending map (Figure 5.23 (b)) exhibited BOLD HRF similar to the one shown by the green arrows in Figure 5.23 (a). Figure 5.23 (a) shows a lot of TCM corrupted false-positive voxels, particularly in the inferior and frontal regions. A few representative TCM impulse responses are shown by the blue arrows. From the figures (5.23 (a-e)) for the 5 cases it can be noted that for this subject the motion-parameter regression (MPR) method performs poorly in reducing noise arising from TCM. The ML2 method performs better than the MPR method, but it also exhibits some residual TCM voxels after TCM noise-reduction. The non-selective detrending method seems to reduce true-positive BOLD MR signal along with TCM

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103 (a) (c) (b) (e) (d) Figure 5.23: Activation maps thresholded at R 2 > 0.2 for control subject 4 with no TCM noise-reduction (a), with selective detrending (b), with motion parameter regression (c), with ignoring 2 images after speech (d) and with non-selective detrending (e). The blue arrows indicate TCM voxel IRFs and the green arrows BOLD voxel IRFs.

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104 Figure 5.24 (a) shows some representative extra-cerebral TCM IRFs extracted from the control subject 4 dataset. There are a lot of similarities in the TCM responses. Some of the TCM IRFs are shifted relative to the time of onset and some have significant longer lasting effects. Figure 5.24 (b) shows the effect of applying the reviewed methods of TCM noise reduction on a right medial-frontal BOLD activation voxel in control subject 4. This voxels hemodynamic response has an early onset. It is obvious from the Figure 5.24 (b) that the method of ignoring two images during speech (ML2, black) suffers from a lack of sensitivity to the early portion of the hemodynamic response, since the method ignores the first two images. The non-selective detrending method (dt, red) removes BOLD MR signal in this voxel and hence is sub-optimal. The selective detrending method (dtsel, magenta) does not perform any detrending on this voxel and leaves the BOLD signal intact. The motion parameter regression method (MPR, green) also seems to leave the BOLD MR signal more or less intact. The modified ROC analyses for the control subject 4 is illustrated in Figures 5.25 (a-b). The efficiency of TCM noise reduction of all the four methods as well as for the case of no motion correction is shown in Figure 5.25 (a). The non-selective detrending method (dt; red curve) performs the best in terms of reducing TCM false-positives. The selective detrending method (dtsel; magenta) performs better than the method of ignoring images (ML2; black) as well as the motion-parameter regression method (MPR; green). The curves for the ML2 and the MPR methods look similar (though the ML2 method seems to perform slightly better). The no-correction curve (ML0; blue) is also given for reference.

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105 (a) (b) Figure 5.24: Some representative TCM-related voxel IRFs from control subject 4 (a). The effect of the methods of noise correction on a right medial-frontal voxel BOLD HRF exhibiting an early response for the same dataset. The no-correction curve is hidden by the selective detrending curve. (a) (b) Figure 5.25: Fraction of voxels detected as a function threshold R2 for (a) the false-positives test-bed and (b) the true-positives test-bed for control subject 4. The blue curve (ML0) represents the case of no motion correction, the black curve (ML2) represents the method of ignoring first 2 images after speech, the green curve (MPR) represents the motion-parameter regression method, the magenta curve (dtsel) represents the selective detrending method and the red curve (dt) represents the non-selective detrending method.

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106 Figure 5.25 (b) shows the effect of each of the TCM noise reduction treatments on the te st-bed of the true-positive BOLD HRF-like voxels. The distributions look similar except for the non-selective detrending method. The non-selective detrending method seems to suffer from a loss of sensitivity to BOLD MR signal. By considering this grapalong with the TCM noise reduction graph of Figure 5.25 (a) one can state that the selective detrending method performs the best in terms of TCM noise reduction andpositive BOLD HRF retention. h true Discussion From the results shown, the supe selective detrending method is appareter the MPR method (117-118) on the datasets is interesting. Table 1 expres tion d of riority of the ent over the other three methods of TCM noise reduction: 1) the motion-paramregression method (MPR), 2) the method of ignoring 2 images during speech (ML2) and 3) the non-selective detrending method. It would be remunerative to examine the source of this superiority. The effect of sses the average maximum rigid rotation and translation of the head during epochof speech production. These values have been obtained by considering the first four images after every overt response, finding the absolute maximum of each of the 6 moparameters during those four images and constructing a mean of all the epochal maxima. Thus, the values in the table refer to the rigid-body TCM during speech. It should be noted that the maximum rotation consistently through all the epochs is less than a thira degree for the most motion-prone dataset (patient 2 pre-therapy scan), corresponding to less than 3 Hz disturbance in background magnetic field, and leading to less than a sixth of a pixel shift consistently through all the epochs. The maximal TCM rigid-rotation in other datasets is much less. Contrast to that the jaw movement TCM related changes in

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107 background field can be up to 10 Hz. Thus for the datasets examined, the rigid movement of the head is probably not a major contributing factor in the TCM related signal changes. Examining the modified MPR ROC curves of all the subjects reveals that, the cases in which the MPR method leads to attenuation TCM false-positives (e.g. control subject 3also reflect loss of sensitivity to true-positives. This illustrates the throwing the baby with the bath water effect of the MPR method which has been observed in the literatu(117-118). Subject ) re roll (deg) pitch (deg) yaw (deg) dS (mm) dL (mm) dP (mm) Pat 1 pre -tx 7 0.061 0.0777 0.0856 0.1462 0.0795 0.0633 0.1136 0.1448 0.1466 0.2820 0.0968 0.0992 Pat 2 pre-tx 0.0880 0.1581 0.2486 0.4188 0.1783 0.0576 Pat 2 post-tx 0.0972 0.1472 0.2914 0.2674 0.1557 0.0804 Control 1 0.0666 0.1910 0.0683 0.1310 0.0609 0.0663 Control 2 0.0523 0.1619 0.1281 0.2005 0.0680 0.0555 Control 3 0.0506 0.1763 0.1467 0.2312 0.1066 0.1053 Control 4 0.0346 0.0915 0.0812 0.1151 0.0704 0.0588 Pat 1 post-tx T able 1: The mean of the epochal maxima of the 3 rigid rotational motion parameters, roll, pitch and yaw (degrees) and of the 3 rigid translational motion g the first he method of ignoring first two images during and after speech (ML2) has been put foo it parameters, displacements towards the superior direction, to the left and towards the posterior (mm). Each epoch represents the motion durin4 images after each overt response. T rward as a potential means to reduce TCM false-positives (127). This method assumes that all the TCM signal changes occur in the first 2 images after speech. Alsworks when the BOLD hemodynamic signal changes are temporally resolvable from the TCM signal changes. All the datasets exhibit some TCM responses which are shifted (i.e.start after the first couple of images) as well as some longer lasting ones. The basis of the delay to onset of the TCM IRF could lie in the constraints of whole-brain image

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108 acquisition. In multi-slice whole-brain studies, the latter acquired slices are temposhifted with respect to the slices imaged first. Thus, the IRFs of voxels in the latter slicewill be shifted in time with respect to the voxels in the first acquired slices. The longer lasting TCM responses could be due to slow magnetic field changes, like during swallowing (125) or due to relaxation to steady state effects. The ML2 method wable to sufficiently attenuate such shifted and longer lasting TCM signal changes. The dataset from patient 1 (post-therapy scan) seems especially corrupted by shifted and longer lasting TCM signal changes. The ML2 method does not perform well in such conditions. The selective detrending method outperforms the ML2 method in terms oTCM false-positives reduction in all cases studied. The ML2 method may also suffer from loss of sensitivity to true-positive BOLD signal changes which do not exhibit a delay to onset or start prior to word-enunciation. The results section illustrates exampof such voxels for all the eight datasets. The non-selective detrending metho rally s ill not be f les d (125) assumes that the TCM signal changes are tehe time-g mporally resolvable from the BOLD signal changes. Application of this method involves detrending all the voxels in the FMRI dataset of components proportional to tchosen TCM time-series. From the results section, it is apparent that there is a good deal of similarities between the TCM time-series (within a dataset and even between datasets).In addition since the non-selective detrending method detrends components proportional to all the TCM time-series from a given voxel (which is effectively the same as detrending components proportional to the modulus sum of all the chosen TCM series) a handful would suffice for an adequate representation. The selective detrendinmethod on the other hand only detrends components proportional to the maximally

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109 correlated TCM time-series (given the detrending criteria are satisfied) from a givenvoxel. Thus it requires more representative TCM time-series to adequately characterizthe effects of TCM. The magnetic fi e eld disturbances due speech-related TCM are more pronounced at the in m D MR tive the three TCM noise reduction methods: ignoring images (ML2), non-selective detrending and selective detrending would benefit from ferior and frontal regions of the brain (124). The field disturbances rapidly fall off in the inferior-to-superior and anterior-to-posterior direction. Thus, the effects of TCM are not uniform throughout the brain. The activation maps of the no-correction cases in the datasets examined illustrate this point. There is more false-positive extra-cerebral TCM voxels in the frontal and inferior regions of the head. Thus, the non-selective detrending of all the voxels in the dataset of components proportional to all the TCMtime-series may be superfluous. More importantly, if there is an overlap between the BOLD hemodynamic response of a given voxel and the TCM IRF being detrended frothe voxel, the non-selective detrending method reduces true-positive BOLD MR signal. Such a case arises in situations analogous to the ones mentioned in the discussion of the ML2 method. The results section illustrates examples of voxels in which the non-selective detrending method results in substantial attenuation of true-positive BOLsignal for all the eight datasets. Thus, though the nonselective detrending method performs the best in terms of reduction of TCM false-positives in all the datasets examined, it is also the least optimal in terms of true-positives retention. The selecdetrending method performs as well as (or comparable to) the nonselective method in terms of false-positives reduction. The results also indicate that

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110 increa sed temporal resolution. The ML2 method would benefit from the greater flexibility afforded in choosing the number of images screened with increased temporaresolution. The selective detrending method would benefit from the increased nuimages available in the fitting/detrending procedure allowing for a more robust fit. The process of selecting which voxels to detrend will also benefit from increased temporal resolution. The attendant additional images available will make the cross-correlation as well as the 2-norm estimates more robust. In this context, it must be mentioned that values for resnormTCM and resnormBOLD chosen for the selective detrending method should be viewed more as a prescription than a rule. The values used in this thesis wearrived at by exam l mber of re lues g he non-stion tly. Even the same subject scanned under different conditions can be affected differently by motion. From Table 1 it may be noticed that the average epochal maxima inin g what was o ptim al for the first two datasets. These chosen vaof resnormTCM and resnormBOLD were found to perform adequately in the subsequent six datasets studied. These values may not have general application and it would be remunerati ve t o find the opt ima l limits for each dataset studied on an individual basis. The argument regarding the scope for improvement of the fitting/detrendinprocedure with increased temporal resolution, mentioned above, is also applicable for t elective detrending procedure. The influence on temporal resolution on the moparameter regression method is less certain. Regression estimates robustness scale with the number of data-points available. However, our results indicate that there does not seem to a direct benefit in using the MPR method in TCM noise reduction in the first place. Motion in FMRI is idiosyncratic in nature. It can affect different subjects differen

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111 of the r igid-motion parameters in the post-treatment scan for aphasia patient-1 is adouble that of the pre-scan. The effects of TCM are also different between preand potherapy scans for patient 1. The post-therapy scan seems less responsive to the ML2 method of TCM noise-reduction, indicating more shifted and longer lasting TCM signal changes in the post-therapy scan. Finally it would be remunerative to examine the similarities and the differencebetween the aphasia patients and normal control subjects with regards to task-correlated motion. It can be noted from examining Tabl lmost st-s e 1 that, in general the control subjects exhibit nts ed less task-correlated rigid-body motion when compared to the patient datasets. This is understandable as the controls are more motivated and also understand and followthe instructions better. The ischemic stroke which causes brocas aphasia in the patiealso may lead to impairment of motor function. The patients thus have less control over their movements and speech. The results show a little more TCM corrupted voxels in patients compared to controls. The TCM responses, in general, look similar across different subjects, indicating that the TCM signal changes have a similar physical origin.

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CHAPTER 6 CONCLUSION AND FUTURE WORK In this chapter the conclusions reached after analysis of the data presented in the previous chapter are discussed. Improvements on the method and future directions of TCM noise-reduction research are conjectured. Conclusion Event-related overt word generation paradigms play an important role in the understanding of brain function (127, 130). The necessity for monitoring the subject responses in FMRI of patients (130) requires use of overt word generation paradigms. Task-correlated motion acts as a major confound in the analysis of overt word-generation paradigms (125). TCM artifacts in event-related overt word generation paradigms have been treated with three main methods: motion parameter regression (117), ignoring/screening signal changes during speech (127, 128) and detrending FMRI datasets of components proportional to the TCM time-series chosen from false-positive TCM voxels (125). In Chapter 4, a new selective detrending method was introduced. The results from the Chapter 5 indicate that the selective detrending method performs better than the other three main methods of TCM noise reduction in vogue. The selective detrending method performs almost as well as the non-selective detrending method in terms of TCM noise reduction and better than all other methods in terms of capacity to retain BOLD MR signals. Moreover, the results of the previous chapter point out the inadequacies of using the motion parameter regression method (MPR), the 112

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113 ignoring images during speech method (ML2) and the non-selective detrending method in whole-brain event-related overt word generation paradigms. The MPR method assumes a linear relationship between the rigid motion parameters and related FMRI signal changes and tries to eliminate motion-related signal changes by regressing out components of the FMRI time-series proportional the motion parameter time-series. Depending upon the regression fit between the motion parameter time-series and the FMRI time-series, this method may either have little effect on TCM noise reduction or might have a deleterious effect on BOLD MR signal along with TCM noise. The method of ignoring the first two images (ML12) after speech assumes that the TCM signal changes are temporally resolvable from BOLD MR signal changes. The ML2 method fails to attenuate TCM signals which are shifted relative to the overt response stimulus. This can be a significant issue in whole-brain FMRI, where the slices acquired last are delayed by about an image TR off with respect to the stimulus vector. The ML2 method also suffers from a loss of sensitivity to early hemodynamic responses that either start before the overt-response stimulus or exhibit minimal delay to onset. The non-selective detrending method makes the same assumption regarding temporal resolvability of BOLD and TCM signal changes as the ML2 method. Since this method effectively detrends the components of all the voxel time-series in the FMRI dataset proportional to the sum of the selected TCM time-series, the penalty of temporally unresolved BOLD and TCM signal changes is the loss of sensitivity to true-positive brain activation. The selective detrending method is to some extent able to

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114 overcome these and other confounds by examining for TCM related signal changes and detrending accordingly. The success of the selective detrending method is critically dependent on the proper and adequate characterization of the TCM and BOLD signal changes in the dataset. This can be accomplished with a good deal of certainty for voxels activated above the threshold selected for inferring brain activation through visual inspection. In fact the efficacy of all the methods used can be determined for voxels activated above the selected threshold by visual inspection. Although, in theory data driven/modeled methods of inspection are more objective, in fact proper modeling of the TCM and BOLD responses can be difficult and sensitive to modeling error. Visual inspection can however be time consuming. It is also subjective (though not entirely so in that TCM and BOLD patterns can oftentimes be more easily told apart by visual inspection than data modeling). All the phenomenological methods of TCM noise reduction suffer to an extent from subjective inferrals and interpretation of data. This situation is unappealing to the Physicists mind which is always looking for elegant solutions. One other conclusion that can be generalized to all overt word-generation studies is the finding that magnetic field disturbances that produce signal fluctuations during speech seem to act as the main source of TCM signal changes. This is borne out by Table 1 in Chapter 5 which suggests that with proper padding rigid-rotation can be restricted to less than a third of a degree leading to less than a sixth of pixel-shifts. Speech-related field disturbances are an order of magnitude higher. Since the field disturbances are known to propagate from inferior to superior regions of the brain (124, 125) use of sagittal or coronal acquisitions will by and large keep the field shifts in-plane and the

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115 resulting artifacts can be attenuated by distortion correction methods (113). Use of axial slices will result in the added confound of non-uniform slice excitation from image to image as well as through-plane dephasing, neither of which is easily treatable. Future Work The selective detrending method introduced in this study works in a univarate general linear model framework. Whenever detrending is executed it essentially removes a fixed amount of TCM signal at each epoch (formed by overt response and located in time by the stimulus vector). Thus since the overall GLM statistic, whether it be F-statistic or the coefficient of determination, R 2 relies on the convolution (with the stimulus vector) of the estimated IRF, which can be considered as an average across the epochs, the detrended time-series results in a TCM denoised estimate of the test-statistic. To perform a more thorough TCM detrending one could examine for the presence of TCM related signal changes at each epoch and detrend selectively in a time-dependent manner. Such a detrended time-series would be amenable to more probing forms of analysis like randomization tests and paradigm independent methods. The time and hardware penalty in conducting this detrending scales linearly as the number of epochs. Thus for the present study which had up to 45 epochs, this proposed detrending of each individual stimulus presentation could take 45 times longer (which comes out to about one day per dataset) than the current implementation. A different approach to TCM noise reduction would be to utilize the correlated changes in voxel phase during speech. Essentially, background magnetic field disturbances during speech will leave a signature in the image-phase of the voxels. Changes in voxel phase can be utilized to undistort the attendant pixel shifts (113) in a time-dependent fashion. Real-time auto-shimming methods which do first-order linear

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116 distortion correction already exist (116). Alternately phase-correlated magnitude signal changes can be regressed out of the FMRI time-series (38). One major difficulty in distortion correction using voxel phase is that the unwarp is a first order correction and the magnitude TCM related field disturbances will probably lead to non-linear distortions in the image. This confound will also affect the voxel-phase regression method as the relation between phase changes and the resultant signal changes maybe nonlinear. However these difficulties may not be insurmountable and there is hope that more elegant solutions to TCM related noise in FMRI time-series will be found.

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APPENDIX SELECTED PUBLICATIONS In this appendix a few selected publications of Kaundinya S. Gopinath are listed. Conference Abstracts ISMRM Proceedings: Oral Sessions K.S. Gopinath, K.K. Peck, D.A. Soltysik, B.A. Crosson, and R.W. Briggs, "A Selective Detrending Method to Reduce Noise Due to Event-Correlated Motion in fMRI Time-Series for an Event-Related Overt Word Generation Paradigm, Proc. Intl. Soc. Mag. Res. Med. 11, 388(2003). 11th ISMRM (International Society for Magnetic Resonance in Medicine) meeting, Toronto, Ontario, Canada, May 10-16, 2003. K.S. Gopinath and R.W. Briggs, "Fourier Method for Detection of FMRI Signal in Noise of Unknown Power Spectral Density, Proc. Intl. Soc. Mag. Res. Med. 10, Vol. 1, abstract 750 (2002). 10th ISMRM (International Society for Magnetic Resonance in Medicine) meeting, Honolulu, Hawaii, May 18-24, 2002. Kaundinya Gopinath, Richard W. Briggs, David Soltysik, Nathan Himes, and Bruce A. Crosson, "Reduction of Noise Associated With Stimulus Correlated Motion in Event Related Overt Word Production fMRI Studies, Proc. Intl. Soc. Mag. Res. Med. 9, 297 (2001). 9th ISMRM (International Society for Magnetic Resonance in Medicine) meeting, Glasgow, Scotland, April 21 27, 2001. Nathan C. Himes, Richard W. Briggs, Kaundinya S. Gopinath, Michael E. Robinson, Donald D. Price, and G. Nicholas Verne, "fMRI Studies of Visceral and Cutaneous Pain in IBS Patients and Normal Subjects, Proc. Intl. Soc. Mag. Res. Med. 9, 530 (2001). 9th ISMRM (International Society for Magnetic Resonance in Medicine) meeting, Glasgow, Scotland, April 21 27, 2001. ISMRM Proceedings: Poster Sessions K.S. Gopinath, K.K. Peck, D.A. Soltysik, and R.W. Briggs, "Similarities in the Low Frequency Noise Characteristics between the Magnitude and Phase Time-Series, Proc. Intl. Soc. Mag. Res. Med. 11, 1890 (2003). 11th ISMRM (International Society for Magnetic Resonance in Medicine) meeting, Toronto, Ontario, Canada, May 10-16, 2003. 117

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118 K.S. Gopinath, K.K. Peck, D.A. Soltysik, B.A. Crosson, and R.W. Briggs, "Comparison of the Low Frequency Noise Characteristics between Diseased and Healthy Brain Regions, Proc. Intl. Soc. Mag. Res. Med. 11, 1892 (2003). 11th ISMRM (International Society for Magnetic Resonance in Medicine) meeting, Toronto, Ontario, Canada, May 10-16, 2003. D.A. Soltyisk, K. Gopinath, K.K. Peck, B.A. Crosson, and R.W. Briggs, "A Quantitative Analysis of the Nonlinearity of the BOLD Response in Different Cortices, Proc. Intl. Soc. Mag. Res. Med. 11, 1887 (2003). 11th ISMRM (International Society for Magnetic Resonance in Medicine) meeting, Toronto, Ontario, Canada, May 10-16, 2003. K. Peck, A. Bacon Moore, B. Crosson, K. Gopinath, D. Soltysik, and R.W. Briggs, "Reduction in Time to Peak of Hemodynamic Response Functions After Therapy Demonstrated by BOLD fMRI Studies of Aphasia Patients, Proc. Intl. Soc. Mag. Res. Med. 11, 2025 (2003). 11th ISMRM (International Society for Magnetic Resonance in Medicine) meeting, Toronto, Ontario, Canada, May 10-16, 2003. K.S. Gopinath, K.K.Peck, T.W. Conway, and R.W. Briggs, "Increase in Linearity of the BOLD Response Along a Functionally Connected Neural Pathway, Proc. Intl. Soc. Mag. Res. Med. 10, Vol. 2, abstract 1388 (2002). 10th ISMRM (International Society for Magnetic Resonance in Medicine) meeting, Honolulu, Hawaii, May 18-24, 2002. Kyung K.Peck, Kaundinya Gopinath, David Soltysik, Anna Moore, Christina Wierenga, Bruce Crosson, and Richard W. Briggs, "Comparison of Functional Time Course Patterns in Broca's Area and Supplementary Motor Area during Silent Sentence Generation Task in fMRI, Proc. Intl. Soc. Mag. Res. Med. 10, Vol. 2, abstract 1491 (2002). 10th ISMRM (International Society for Magnetic Resonance in Medicine) meeting, Honolulu, Hawaii, May 18-24, 2002. Kaundinya Gopinath, Yunmei Chen, Richard W. Briggs, Feng Huang, and T. Sheshadri, "Feature Based Image Registration for FMR Images, Proc. Intl. Soc. Mag. Res. Med. 9, 1201 (2001). 9th ISMRM (International Society for Magnetic Resonance in Medicine) meeting, Glasgow, Scotland, April 21 27, 2001. Kaundinya Gopinath, Richard W. Briggs, and Nathan Himes, "Examination of the Linearity of BOLD FMRI Responses in a Higher Level Cognitive System, Proc. Intl. Soc. Mag. Res. Med. 9, 1189 (2001). 9th ISMRM (International Society for Magnetic Resonance in Medicine) meeting, Glasgow, Scotland, April 21 27, 2001.

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119 Richard W. Briggs, Iona Dy-Liacco, Kaundinya S. Gopinath, Nathan C. Himes, David A. Soltysik, Paul Browne, and Roger Tran-Son-Tay, "A New Vibrotactile Device for fMRI, Proc. Intl. Soc. Mag. Res. Med. 9, 1227 (2001). 9th ISMRM (International Society for Magnetic Resonance in Medicine) meeting, Glasgow, Scotland, April 21 27, 2001. J.M. Anderson, R.W. Briggs, B. Crosson, K.S. Gopinath, D. Gokcay, J.R. Sadek, L.J. Gonzalez Rothi, E.J. Auerbach, D.A. Soltysik and K.M. Heilman, "Evidence of Right Hemisphere Engagement during the Production of Overt Emotional Prosody: An Event Related fMRI Study, Abstract 899, 8th ISMRM (International Society for Magnetic Resonance in Medicine) meeting, Denver, Colorado, April 1 7, 2000. R.W. Briggs, J.M. Anderson, B. Crosson, L.M. Maher, H.L. Roth, K.S. Gopinath, D. Gokcay, L.J. Gonzalez Rothi, E.J. Auerbach, and D.A. Soltysik, "Preliminary Evidence of Language Reorganization After Left Hemispheric Injury: A Whole Brain, Event Related fMRI Study of Sentence Production, Abstract 862, 8th ISMRM (International Society for Magnetic Resonance in Medicine) meeting, Denver, Colorado, April 1 7, 2000. R.W. Briggs, K.S. Gopinath, M.A. Cato, and B.A. Crosson, "Deconvolution Analysis in Emotional Word Generation Monitored by Random Block and Event Related fMRI, Abstract 836, 8th ISMRM (International Society for Magnetic Resonance in Medicine) meeting, Denver, Colorado, April 1 7, 2000. Full Papers M.A. Cato, B. Crosson, D. Gokcay, D. Soltysik, C. Wierenga, K. Gopinath, N. Himes, H.Belanger, R.M. Bauer, I.S. Fischler, L. Gonzalez-Rothi, and R.W. Briggs, J. Cog. Neurosciece (accepted for publication). "Processing Emotional Connotation during Word Generation: Laterality and Effects on Rostral Frontal and Retrosplenial Cortices." G. N. Verne, N.C. Himes, M.E. Robinson, K.S. Gopinath, R.W. Briggs, B.A. Crosson, and D.D. Price, Pain (in press). "Central Representation of Visceral and Cutaneous Hypersensitivity in the Irritable Bowel Syndrome." B. Crosson, H. Benefield, M.A. Cato, J.R. Sadek, A.B. Moore, C.E. Wierenga, K. Gopinath, D. Soltysik, R.M. Bauer, E.J. Auerbach, D. Gkay, C.M. Leonard, and R.W. Briggs, J. Intl. Neurophysch. Soc. (in press). Left and Right Basal Ganglia and Frontal Activity during Word Generation: The Nature of Lexical-Semantic Retrieval. B. Crosson, M.A. Cato, J.R. Sadek, D. Gokcay, R.M. Bauer, I.S. Fischler, L. Maron, K.S. Gopinath, E.J. Auerbach, S.R. Browd, and R.W. Briggs, J. Intl. Neurophysch. Soc., 8,

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120 607-622 (2002). "Semantic Monitoring of Words with Emotional Connotation during fMRI: Contribution of Anterior Left Frontal Cortex." Y. Chen, H.D. Tagare, S. Thiruvenkadam, F. Huang, D. Wilson, K.S. Gopinath, R.W. Briggs, and E.A. Geiser, Intl. J. Computer Vision, 50(3), 315-328 (2002). Using Prior Shapes in Geometric Active Contours in a Variational Framework. J.M. Gelb, K.S. Gopinath, D.C. Kennedy, International Journal of Modern Physics D, 8(2), 229-250 (1999). Relativistic electrons on a rotating spherical magnetic dipole: surface orbitals. J.M. Gelb, K.S. Gopinath, D.C. Kennedy, International Journal of Modern Physics D, 8(2), 251-270 (1999). Relativistic electrons on a rotating spherical magnetic dipole: localized three-dimensional states. K.S. Gopinath, D.C. Kennedy, Technical Report, UFIFT-HEP-97-06 (1997). Relativistic charged particle in magnetic dipole-spherical geometry : II. general tiled surface orbits. K.S. Gopinath, D.C. Kennedy, J.M. Gelb, Technical Report, UFIFT-HEP-97-11 (1997). Relativistic charged particle in magnetic dipole-spherical geometry :III. Local three-dimensional states. K.S. Gopinath, Thesis (M.S.)--University of Florida, (1997), Relativistic charged particle in dipole-sphere configuration. K.S. Gopinath, Thesis (M.Sc)University of Poona (1993), Large-Scale Structures in the Universe. Y. Chen, S. Thiruvenkadam, F. Huang, K.S. Gopinath, and R.W. Briggs, in preparation for submission to IEEE Trans. Med. Imaging. Feature Based Image Registration for Functional MR Images. R.W. Briggs, I. Dy-Liacco, M.P. Malcolm, H. Lee, K.K. Peck, K.S. Gopinath, N.C. Himes, D.A. Soltysik, P. Browne, and R. Tran-Son-Tay, Magn. Reson. Med. (under revision) "A Pneumatic Vibrotactile Stimulation Device for fMRI."

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121 K.S. Gopinath, Thesis (Ph.D) University of Florida (expected August 2003). Reduction of Noise Associated with Stimulus-Correlated Motion in FMRI time-series. K.S. Gopinath, K.K. Peck, D.A. Soltysik, B.A. Crosson, and R.W. Briggs, in preparation, "A Selective Detrending Method to Reduce Noise Due to Event-Correlated Motion in fMRI Time-Series for an Event-Related Overt Word Generation Paradigm." K.S. Gopinath, K.K. Peck, D.A. Soltysik, K. D. White, B.A. Crosson, and R.W. Briggs, in preparation, Sensitivity Compensation Analysis for Comparison of Preand Post-treatment Scans of Aphasia Patients Under a Language FMRI Paradigm.

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BIOGRAPHICAL SKETCH Kaundinya Srinivasan Gopinath was born on Valentines Day, 1969. He had his early schooling in Jabalpur and Madras. He graduated from Ramnarain Ruia College, Bombay University, with a B.Sc. in physics. He subsequently attended the University of Poona and the Inter-University Center for Astronomy and Astrophysics, Poona, under a Universities Grants Commission Scholarship. After graduating in 1993 with a M. Sc. in physics and astrophysics he joined the Department of Physics, University of Florida. After graduating in 1998 with a MS in physics he joined the Department of Nuclear and Radiological Engineering, University of Florida. Currently he is a doctoral candidate in medical physics at the University of Florida. 132


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Title: Reduction of Noise Due to Task Correlated Motion in Event Related Overt Word Generation Functional Magnetic Resonance Imaging Paradigms
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Title: Reduction of Noise Due to Task Correlated Motion in Event Related Overt Word Generation Functional Magnetic Resonance Imaging Paradigms
Physical Description: Mixed Material
Copyright Date: 2008

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Source Institution: University of Florida
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REDUCTION OF NOISE DUE TO TASK CORRELATED MOTION IN EVENT
RELATED OVERT WORD GENERATION FUNCTIONAL MAGNETIC
RESONANCE IMAGING PARADIGMS















By

KAUNDINYA S. GOPINATH


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2003

































Copyright 2003

by

Kaundinya S. Gopinath

































There are more things in heaven and earth Horatio, Than are dreamt of in your
philosophy.
-William Vlhlkelpe, e, in Hamlet: Act 1, Scene 5















ACKNOWLEDGMENTS

This work would not have been possible without the active help and blessings of a

number of people. Firstly, I would like to acknowledge my advisor, Dr. Richard Briggs,

for his constant support and encouragement throughout the duration of my Ph.D. Dr.

Briggs introduced me to the concepts of magnetic resonance imaging and functional

MRI. I remember, like it was just yesterday, how he explained the concepts of relaxation

and MR signal detection in the lab on the tenth floor of the dental sciences building. Dr.

Briggs has always impressed me by his tremendous insights into MR physics. He has the

ability to explain recondite concepts in concise layman's terms, which helped me greatly

in my learning process. Dr. Briggs gave me freedom to go explore the world of MR, a

field that amazes me with its scope and potential everyday. I remember, early in my first

years with the group, how I used to come back from the library or some other place flush

with excitement at some "new" idea I had or some "new" application of MR I had just

encountered in some journal, and when I told Dr. Briggs he would give me more insight

into the "new" idea or application, give me a few papers on it and even sometimes have

some stories about some of the early MR personnel who had worked on it. I realized

quickly that it was not easy to surprise him with a MR "discovery." Apart from his

academic influences, Dr. Briggs and Mrs. Dorothy Briggs have always been warm and

generous and I enjoyed all the times when I had the occasion to mingle with them

socially.









I would like to acknowledge Dr. Bruce Crosson's help in my education in FMRI.

Dr. Crosson has an encyclopedic knowledge of brain function and anatomy and it always

amazes me how he is able to describe the name and function of any obscure (to me) gyms

or sulcus one points to in the brain. Dr. Crosson always impressed me by his 'problem-

solving' approach of attacking FMRI issues. Whenever I have a discussion with him

regarding data analysis and FMRI, I seem to come away with a new insight into the issue

I have been discussing with him. Dr. Crosson has always been generous with his support

and encouragement for my work. Dr. Crosson constantly impresses me with his energy

and drive. It seems just as easy to come upon him at work at lam at night or 8am in the

morning. Also I have always enjoyed the parties at Dr. Crosson's place. There is always

something interesting happening when we have a function at his place.

I would like to acknowledge the help Dr. Wesley Bolch provided in advancing my

academic future. He took me into the department when my academic career was

floundering after some lackluster years in the uninspiring Physics Department. I will

eternally be indebted to him for giving me a second chance. In the future, I hope to live

up to the trust he put in me. I enjoyed all the classes I took with Dr. Bolch. I was very

impressed by his energy and attention to detail. I remember the marathon sessions he

used to hold over the weekends going over the presentations of the whole class. At the

end of these sessions, when everybody else seemed tired, he looked like he could go for a

couple of sessions more. Dr. Bolch always has time for the students and his commitment

to students' well-being is unstinting. I consider myself fortunate to be in his department.

I would also like to acknowledge my advisors Dr. David Hintenlang and Dr. John

Harris. I have had the fortune to take some classes under Dr. Hintenlang and he always









impressed by the ease with which he taught. I remember sitting through his lectures and

wondering at the easy pace only to look down at my work and see five or six pages of

notes. And I always thought I did not take much notes. Dr. Hintenlang has the knack of

relating recondite concepts (in say radiation shielding) to everyday events, which makes

it easy to understand the subject.

Dr. Harris has been very accommodating in sparing time for me at short notice. His

academic engagements seem numerous and I appreciate him taking time off from his

exciting pursuits at CNEL for me. The work conducted at his hybrid computation group

seems very exciting. The advances being made in DSP will surely be of use in

MRI/FMRI soon. I still marvel as how he and his collaborators can make a monkey

move an artificial limb by just thinking about it.

I would also like to acknowledge the help of my MR physics colleagues Dr. Kyung

Peck and Dr. David Soltysik for useful discussions in physics. Also, I would like to thank

our neuropsychologists Dr. Anna Moore, Dr. Keith White, Dr. Tim Conway, Dr. Allison

Cato, Christina Wierenga, Megan Gaiefsky, Christy Milsted and Ashley Wabnitz for

useful discussions, subject coding and neuro-psychological input. This work was

conducted with the help of NIH grants P50-DC0388 and RO1-DC03455, Department of

Nuclear and Radiological Engineering and the Brain Rehabilitation Research Center, VA

RR &D, Gainesville, Fl.

Lastly, I would like to thank my family members: my parents who stand by me

though I have not been always there for them, my sisters Radha and Kalli who have been

a guiding force in my life and God for blessing me with a life I am happy to lead.
















TABLE OF CONTENTS
page

A C K N O W L E D G M E N T S ................................................................................................. iv

LIST OF FIGURES ................................... ...... ... ................. .x

A B S T R A C T .......................................... ..................................................x v

CHAPTER

1 BASICS OF MAGNETIC RESONANCE IMAGING...............................................1

Origins of Magnetic Resonance Imaging ........................................... .................
Concepts of Magnetic Resonance Imaging ........................................... .................1
Spin Physics and M agnetization..................... ...... .......................... 2
R e so n an ce ................... ...................3.............................
E lectro-M agnetic Induction............................................ ........................... 3
R relaxation ............................... ............................................. 4
Longitudinal R elaxation, T ........................................................ ............... 4
Transverse R elaxation, T2 ...................... .. .. ......... ...................... ............... 5
Gradients, Spatial Encoding and K-Space....... ........... ................... .............6
B asic M R Pulse Sequences......................................... ................................. 7
Spin-E cho Pulse Sequence.......................................................... ............... 7
Gradient-Echo Pulse Sequence .............................................9
C contrast and R solution ...................... .. .. ......... ....................... ............... 10
F ast Im aging Sequences ........................................... ....................................... 10
Echo-Planar Im aging ................................... ........ .... .... .......... .... 11
Spiral Im aging.................................................... 12

2 FUNCTIONAL MAGNETIC RESONANCE IMAGING ........................................14

Origins of Functional M agnetic Resonance Imaging ................................................14
Principles of BOLD Functional M RI ........................................ ...... ............... 15
BOLD Hemodynamic Response......................... ............................. 16
Spatio-Temporal Characteristics of BOLD FMRI ............................................. 18
Sp atial Sp ecificity ............................................ ................. 18
Tem poral Resolution ............ ...................... ........ ... ..... .......... .... 18
Linearity of BOLD Response........................................................................ 19
FM R I Experim ent D esign............. ................................. .................. ............... 20
Blocked Paradigm s ....... .............................. ............ .. ........ .... 21









Event-R elated Paradigm s ............................................................................. 21
FM RI D ata Analysis ........ ...... ... .... ........ ........................ 22
O v erv iew ....................................................... 2 2
Im age R egistration............ ...................................... ...... ...23
FM RI N oise Characteristics ................................... ... ....................... 24
Parametric Methods and General Linear Model ...........................................26
Inference ............... ......... .......................29
R O C A naly sis ................................................... 3 1

3 M OTION AND FM RI ................................................................. ............... 32

Introduction .......... ... ....... ..... .........................32
Major Sources of Motion Artifacts and Deterministic Solutions............. ...............33
Static M agnetic Field Effects ........................................ ......................... 34
Spin H history E effects ........................ .. ...................... .. ...... .... ..... ...... 37
Inter-Shot M otion ........................ .............. ............... .... ....... 38
R e m a rk s ......................................................................................................... 4 1
M echanistic Solutions ..................... .......................................... ..41
M otion Param eter R egression ........................................ ......... ............... 42
Stim ulus-Correlated M otion...................................................... ..... .......... 43
SCM -Ignoring Im ages ................................... ......... ..... ............... 45
SCM -D etrending ....................... .................. ................. .... ....... 46
O their M echanistic M ethods ........................................ .......................... 46

4 TASK CORRELATED MOTION NOISE REDUCTION METHODS ....................48

S elective e D etren d in g ........................................................................ .................... 4 8
Selective D etrending: M ethods........................................................ ............... 50
Subjects and Task ......... ..... .... .................... ........ ........ .. .. .. ........ .... 51
Im ag e A cqu isition .............................. .... ...................... .. ........ .... ............5 1
D ata A n aly sis................................................ ................ 52
D econvolution and R egression....................................... ......................... 53
Estimation of the TCM Signal Changes.................................... 53
Choosing Representative BOLD HRFs............................................................55
Selective D etrending Algorithm ....................................................................... 55
Analysis of Detrended Time-Series................................................ ............... 60
Implementation of Motion Parameter Regression.....................................................61
Implementation of the Screening Images Method.....................................................62
Implementation of Non-Selective Detrending.........................................................62
Receiver Operating Characteristics ........................................ ........................ 63
R education of False Positives ........................................ .......... ............... 63
R detention of True Positives ........................................ ........................... 64

5 RESULTS AND DISCU SSION ........................................... .......................... 68

R e su lts ................................................................................................................... 6 8
Patient 1 (Pre-Treatm ent) ............................................................................. 70


viii










Patient 1 (Post-Treatm ent).............................................................. ............... 75
Patient 2 (Pre-Treatm ent) ............................................................................. 80
Patient 2 (Post-Treatm ent).............................................................. .. ............. 84
C control Subject 1 ...................................................... 90
C o n tro l S u object 2 ........................................................................................... 9 3
C o n tro l S u object 3 ........................................................................................... 9 7
C control Subject 4 ...........................................................102
D isc u ssio n ........................................................................................1 0 6

6 CONCLUSION AND FUTURE WORK ...... .............................................112

C o n c lu sio n .......................................................................................................... 1 1 2
Future W ork ............................................................................. 115

APPENDIX

SELE C TED PU B LIC A TIO N S .................................................................................. 117

Conference A bstracts ..................................... ..... .. .................. .. ............... 117
ISM RM Proceedings: Oral Sessions .............................................................. 117
ISMRM Proceedings: Poster Sessions ........................................................117
F u ll P a p e rs ............. ..... ............ ................................. .............................................1 1 9

LIST OF REFERENCES .................. ........ .................122

BIOGRAPHICAL SKETCH ............... ......... ........ ........132















LIST OF FIGURES


Figure pge

1.1 Timing diagram of a 2-D Spin Echo Sequence ......................................................8

1.2 K-space diagram of a 2-D Spin Echo Sequence.............................. .....................9

1.3 Timing diagram of an Echo-Planar Imaging Sequence............................... 11

1.4 K-Space diagram of an Echo-Planar Imaging sequence .......................................12

1.5 Timing diagram (left) and k-space diagram (right) of a 1-shot spiral EPI
sequence. ............................................................................13

2.1 Schematic representation of a BOLD hemodynamic response.............................17

2.2 The estimated impulse responses for a auditory cortex voxel activated at
F(16,470) = 30, p-val z 0 (left) and a voxel with F(16,470) = 2.5 (right). The
signal has been normalized to a unit maximum. ............................................ 31

3.1 Two-shot spiral FMRI time series image of a mid sagittal slice showing
swirl-like patterns arising from inter-shot motion. The image has been
detrended of its time-series mean to better portray the effects of motion ...............39

4.1 Activation map overlaid on a low-resolution spiral FMR image. The red voxels
correspond to R2 > 0.2 and the yellow voxels denote R2 > 0.3. The
yellow arrow points to the voxel IRFs. The central voxel in the grid shows a
selected TCM IR F ........................................... ............... .... ....... 54

4.2 Activation map of the maximal absolute cross-correlation coefficient with TCM
CCrcm, thresholded by R2 > 0.1. The yellow voxels correspond to max(CCTcM) >
0.7 and the red denotes max(CCTcM) > 0.5. .................................. ..................58

4.3 Distribution of number of voxels undergoing non-selective detrending
for a given max(CCBoLD) as a fraction of the number of voxels at that
max(CCBoLD) for three different levels of separability, 0.2 (blue), 0.1 (green)
and 0.0 (magenta) (a). Similar distributions for max(abs(CCTcM)) (b). ..................60

4.4 Estimated hemodynamic response of a true positive right medial frontal
voxel of patient 1 (pre-therapy) dataset (blue) and the corresponding fit to a
generic hemodynamic response (green). ........................................ ............... 66









5.1 Activation maps thresholded at R2 > 0.2 for patient-1 (pre-scan) with no
TCM noise-reduction (a), with selective detrending (b), with motion parameter
regression (c), with ignoring 2 images after speech (d) and with non-selective
detrending (e). The blue arrows indicate TCM voxel IRFs and the green arrows
B O L D voxel IR F s. ........................ ........................ .. .. ........ ............... 69

5.2 Fraction of voxels detected as a function threshold R2 for (a) the false-positives
test-bed and (b) the true-positives test-bed for aphasia patient 1 (pre-therapy scan).
The blue curve (MLO) represents the case of no motion
correction, the black curve (ML2) represents the method of ignoring the first 2
images after speech, the green curve (MPR) represents the motion-parameter
regression method, the magenta curve (dtsel) represents the selective detrending
method and the red curve (dt) represents the non-selective detrending method......72

5.3 Some representative TCM-related voxel IRFs (a); Some representative
BOLD HRFs (b) from aphasia patient 1 (pre-therapy scan) data............................73

5.4 The effect of the methods of noise correction on a right medial-frontal
voxel BOLD HRF exhibiting an 'early' response for patient 1 pre-therapy
scan (a). The effect of the methods of noise correction on a right inferior sulcus
voxel, exhibiting both BOLD and TCM signal changes (b) for the same scan.
The no-correction curve is hidden by the selective detrending curve in both
figures ................................................................ .. ...... ........... 73

5.5 Activation maps thresholded at R2 > 0.2 for patient 1 (post-therapy scan)
with no TCM noise-reduction (a), with selective detrending (b), with motion
parameter regression (c), with ignoring 2 images after speech (d) and with non-
selective detrending (e). The blue arrows indicate TCM voxel IRFs and the green
arrow s B OLD voxel IRFs. ............................................. .............................. 76

5.6 Some representative TCM-related voxel IRFs from patient 1 post-therapy
scan (a). The effect of the methods of noise correction on a right medial-frontal
voxel BOLD HRF exhibiting an 'early' response for the same dataset (b). The
no-correction curve is hidden by the selective detrending curve ..........................78

5.7 Fraction of voxels detected as a function threshold R2 for (a) the false-positives
test-bed and (b) the true-positives test-bed for aphasia patient 1
(post-therapy scan). The blue curve (MLO) represents the case of no motion
correction, the black curve (ML2) represents the method of ignoring first 2
images after speech, the green curve (MPR) represents the motion-parameter
regression method, the magenta curve (dtsel) represents the selective
detrending method and the red curve (dt) represents the non-selective detrending
m eth o d ........................................................................... 7 8









5.8 Activation maps thresholded at R2 > 0.2 for patient-2 (pre-therapy scan)
with no TCM noise-reduction (a), with selective detrending (b), with motion
parameter regression (c), with ignoring 2 images after speech (d) and with
non-selective detrending (e). The blue arrows indicate TCM voxel IRFs and the
green arrow s B O LD voxel IR F s.................................................... ..................... 81

5.9 Some representative TCM-related voxel IRFs from patient 2 pre-therapy
scan (a). The effect of the methods of noise correction on a right medial-frontal
voxel BOLD HRF exhibiting an 'early' response for the same dataset (b). The
no-correction curve is hidden by the selective detrending curve ..........................83

5.10 Fraction of voxels detected as a function threshold R2 for (a) the false-positives
test-bed and (b) the true-positives test-bed for aphasia patient 2 (pre-therapy scan).
The blue curve (MLO) represents the case of no motion
correction, the black curve (ML2) represents the method of ignoring first 2
images after speech, the green curve (MPR) represents the motion-parameter
regression method, the magenta curve (dtsel) represents the selective detrending
method and the red curve (dt) represents the non-selective detrending method.....83

5.11 Activation maps thresholded at R2 > 0.2 for patient 2 (post-therapy scan)
with no TCM noise-reduction (a), with selective detrending (b), with motion
parameter regression (c), with ignoring 2 images after speech (d) and with non-
selective detrending (e). The blue arrows indicate TCM voxel IRFs and the
green arrow s B O LD voxel IR Fs........................................ ................................85

5.12 Some representative TCM-related voxel IRFs from patient 2 post-therapy scan (a).
The effect of the methods of noise correction on a right medial-frontal voxel
BOLD HRF exhibiting an 'early' response for the same dataset (b). The
no-correction curve is hidden by the selective detrending curve ..........................87

5.13 Fraction of voxels detected as a function threshold R2 for (a) the false-positives
test-bed and (b) the true-positives test-bed for aphasia patient 2
(post-therapy scan). The blue curve (MLO) represents the case of no motion
correction, the black curve (ML2) represents the method of ignoring first 2
images after speech, the green curve (MPR) represents the motion-parameter
regression method, the magenta curve (dtsel) represents the selective detrending
method and the red curve (dt) represents the non-selective detrending method .....87

5.14 Activation maps thresholded at R2 > 0.2 for control subject 1 with no
TCM noise-reduction (a), with selective detrending (b), with motion
parameter regression (c), with ignoring 2 images after speech (d) and with
non-selective detrending (e). The blue arrows indicate TCM voxel IRFs and
the green arrows BOLD voxel IRFs............................................................. 89









5.15 Some representative TCM-related voxel IRFs from control subject 1. The effect
of the methods of noise correction on a right medial-frontal voxel BOLD HRF
exhibiting an 'early' response for the same dataset (b). The no-correction curve
is hidden by the selective detrending curve. .................................. ............... 91

5.16 Fraction of voxels detected as a function threshold R2 for (a) the false-positives
test-bed and (b) the true-positives test-bed for control subject 1. The
blue curve (MLO) represents the case of no motion correction, the black curve
(ML2) represents the method of ignoring first 2 images after speech, the green
curve (MPR) represents the motion-parameter regression method, the magenta
curve (dtsel) represents the selective detrending method and the red curve (dt)
represents the non-selective detrending method. ............. ...................... ......... 91

5.17 Activation maps thresholded at R2 > 0.2 for control subject-2 with no
TCM noise-reduction (a), with selective detrending (b), with motion
parameter regression (c), with ignoring 2 images after speech (d) and with
non-selective detrending (e). The blue arrows indicate TCM voxel IRFs and
the green arrows BOLD voxel IRFs............................................................. 94

5.18 Some representative TCM-related voxel IRFs from control subject 2 (a).
The effect of the methods of noise correction on a right medial-frontal voxel
BOLD HRF exhibiting an 'early' response for the same dataset (b). The no-
correction curve is hidden by the selective detrending curve. ................................96

5.19 Fraction of voxels detected as a function threshold R2 for (a) the false-positives
test-bed and (b) the true-positives test-bed for control subject 2.
The blue curve (MLO) represents the case of no motion correction, the black
curve (ML2) represents the method of ignoring first 2 images after speech, the
green curve (MPR) represents the motion-parameter regression method, the
magenta curve (dtsel) represents the selective detrending method and the red
curve (dt) represents the non-selective detrending method...............................96

5.20 Activation maps thresholded at R2 > 0.2 for control subject 3 with no
TCM noise-reduction (a), with selective detrending (b), with motion parameter
regression (c), with ignoring 2 images after speech (d) and with non-selective
detrending (e). The blue arrows indicate TCM voxel IRFs and the green arrows
B O L D voxel IR F s. ......................... ........................ .. .. ........ ............... 98

5.21 Some representative TCM-related voxel IRFs from control subject 3 (a).
The effect of the methods of noise correction on a right medial-frontal voxel
BOLD HRF exhibiting an 'early' response for the same dataset (b). The no-
correction curve is hidden by the selective detrending curve. ............................100









5.22 Fraction of voxels detected as a function threshold R2 for (a) the false-positives
test-bed and (b) the true-positives test-bed for control subject 3. The
blue curve (MLO) represents the case of no motion correction, the black curve
(ML2) represents the method of ignoring first 2 images after speech, the green
curve (MPR) represents the motion-parameter regression method, the magenta
curve (dtsel) represents the selective detrending method and the red curve (dt)
represents the non-selective detrending method. ............ .................................. 100

5.23 Activation maps thresholded at R2 > 0.2 for control subject 4 with no
TCM noise-reduction (a), with selective detrending (b), with motion parameter
regression (c), with ignoring 2 images after speech (d) and with non-selective
detrending (e). The blue arrows indicate TCM voxel IRFs and the green arrows
B O L D voxel IR F s. ........................ ...................... ... .. .. .... ............... 103

5.24 Some representative TCM-related voxel IRFs from control subject 4 (a).
The effect of the methods of noise correction on a right medial-frontal voxel
BOLD HRF exhibiting an 'early' response for the same dataset. The no-
correction curve is hidden by the selective detrending curve. ............................105

5.25 Fraction of voxels detected as a function threshold R2 for (a) the false-positives
test-bed and (b) the true-positives test-bed for control subject 4.
The blue curve (MLO) represents the case of no motion correction, the
black curve (ML2) represents the method of ignoring first 2 images after
speech, the green curve (MPR) represents the motion-parameter regression
method, the magenta curve (dtsel) represents the selective detrending method
and the red curve (dt) represents the non-selective detrending method..............105















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

REDUCTION OF NOISE DUE TO TASK CORRELATED MOTION IN EVENT
RELATED OVERT WORD GENERATION FUNCTIONAL MAGNETIC
RESONANCE IMAGING PARADIGMS

By

Kaundinya S. Gopinath

December, 2003

Chair: Wesley Bolch
Cochair: Richard W. Briggs
Major Department: Nuclear and Radiological Engineering

Event-related overt word generation functional magnetic resonance imaging

paradigms play an important role in the understanding of brain function. The necessity

for monitoring the subject responses in functional magnetic resonance imaging of

patients requires use of overt word generation paradigms. Speech-related task-correlated

motion acts as a major confound in the analysis of overt word-generation paradigms.

Task-correlated motion artifacts in event-related overt word generation paradigms have

been treated with three main methods: motion parameter regression, ignoring/screening

signal changes during speech and detrending functional magnetic resonance imaging

datasets of components proportional to the task-correlated motion time-series chosen

from false-positive task-correlated motion voxels. In this work a new selective detrending

method for reduction of noise associated with task-correlated motion in event-related

overt word generation functional magnetic resonance imaging paradigms is introduced.









The performance of this method is compared with the other three methods of task-

correlated motion noise reduction. The selective detrending method outperforms the

other three methods in terms of reduction of task-correlated motion false-positives as well

as retention of blood oxygenation level dependent signal true-positives.














CHAPTER 1
BASICS OF MAGNETIC RESONANCE IMAGING

Chapter 1 discusses the basic concepts of magnetic resonance imaging (MRI). The

origins of nuclear magnetic resonance (NMR), principles of magnetic resonance imaging,

and development of fast imaging sequences are discussed.

Origins of Magnetic Resonance Imaging

The idea of nuclear magnetic resonance owed its birth to the discovery of the

proton spin by Stern and Gerlach (1) in 1933, through an extension of methods which

helped them discover electron spin in 1921. Rabi and colleagues were the first to predict

and observe nuclear magnetic resonance in 1937 (2). Bloch and Purcell extended these

concepts to measure the proton spin precessional signal from samples, using

radiofrequency methods (3, 4). All of the above-mentioned luminaries were awarded

Nobel Prizes for their work.

MRI had its beginnings in the seminal work of Mansfield and Grannell and

Lauterbur in the 1970s (5, 6). They discovered that if a known spatially varying magnetic

field is introduced across a sample, the precession of spins within the sample will depend

on their spatial locations.

Concepts of Magnetic Resonance Imaging

The NMR or MRI signal has its basis in quantum mechanics. The quantity spin

angular momentum has no exact analog in classical mechanics. The signal observed at

the imaging end, however, can be visualized in terms of aggregate magnetization of a

population of spins and is a classical regime manifestation. Thus, depending on the









physical quantity examined, the concepts of magnetic resonance imaging are most easily

elucidated by taking recourse to quantum mechanics, classical mechanics or semi-

classical approximations.

Spin Physics and Magnetization

The nuclei of atoms consist of fermions, protons and neutrons, with half integer

spins. The nuclide as a whole has a spin quantum number, I. The spin of the nucleus is an

inherently quantum mechanical entity. The energy states that the nucleus can have, called

energy levels, are quantized. In the presence of a static D.C. magnetic field, Bo, the

nuclide can inhabit 21+1 energy levels given by (7)

eh
E = Sg Bo
2mc [1]
where S can take values from I to +I, e is the electronic charge, A is the Planck's

constant, m is the mass of the nucleus and c is the velocity of light in gauss-ergian units

and g is the Lande g-factor. A hydrogen nuclide (which consists of a proton) has spin I

1/2 and can occupy two states, aligned either with or against the field.


E, = + hA)o [2]
2

where

Co = Bo [3]

is the expression for angular frequency in which the constant y, termed the gyro-

magnetic ratio, can be evaluated from equation [1] and is equal to 42 IMHz/Tesla for a

proton.

In an ensemble of water protons in a magnetic field, the relative population of

nuclear spins in the two states is given by









( E -E -E
N oc exp- [4]
N kT

where N+ andN_ are the number of nuclear spins in E+ and E_ energy levels respectively, k

is the Boltzman's constant and Tis the temperature. Thus there is a net magnetization Mo

in the Bo direction. The magnetization vector Mo processes around the applied magnetic

field Bo with an angular frequency coo, called the Larmor frequency, which is the same as

the one obtained in equation [3].

Resonance

If a magnetic field Bo is applied to a population of nuclear spins in a laboratory,

they process around the applied field. The reference frame in which the spins are

staionary is rotating with respect to the laboratory frame with the angular frequency of

the spins. Now, if a magnetic field, B1, is applied in this rotating frame at right angles to

the spins, they can be tipped, i.e., start processing around the field B1. It can be shown (8)

and is intuitively obvious that the applied magnetic field B1 should oscillate with an

angular frequency equal to the Larmor frequency of precession of the spins in the

laboratory frame. This desired "resonance" condition between the oscillation frequency

of the B1 field and the precession frequency supplies the "R" in the acronym MRI. For

water protons and all other MR imaging nuclides this frequency is in the radio range,

hence the term radio-frequency (RF) magnetic field.

Electro-Magnetic Induction

When the RF magnetic field B1 is switched off, the will start processing about the

permanent field, Bo. Thus, the magnetic flux through a coil, with axis aligned

perpendicular to Bo, will change resulting in an electro-motive force (e.m.f) induced in

the coil according to Faraday's law of electro-magnetic induction.










dt
s-c [5]


where OM is flux associated with the changing magnetization field passing through the

coil after removal of the RF transmit field B This is the basis of MRI signal generation.

Relaxation

The e.m.f and hence the MR signal derived in the last section depend on the rate of

change of the magnetization in the plane transverse to the Bo field. This evolution of the

magnetization of the sample depends on two types of interactions involving the nuclear

spins in the sample. Both these interactions tend to the virialization of the system and are

hence termed relaxations.

Longitudinal Relaxation, T1

A spin = 1/2 system has two allowed energy states. In the absence of an applied

magnetic field, the two states are more or less equally populated. The transition from

equi-population of states, in the absence of a field, to a preferential occupation of the

lower energy state in the presence of an applied field, described in equation [4], is caused

by the relaxation mechanism called longitudinal relaxation (9). The transition in states for

a given spin is achieved by resonant absorption of a quantum of energy by the spin from

the molecular environment (lattice). Thus, the term "resonant" is the operative word here.

Only energy transactions (e.g., arising from rotation/translation of nuclear moments

within the molecule) which lead to the transfer of energy E = hAo from the lattice to the

nuclear spin or vice-versa lead to longitudinal relaxation. IfBo is applied along the z-

direction, the time evolution of longitudinal magnetization, i.e., magnetization parallel to

the z-direction, after the removal of the 90 spin flipping field, B1, is given by (10)

M (t)= M0(1- exp(-t/ T,)) [10]









where, Mz is the magnetization at time t, Mo is the equilibrium magnetization and T1 is

called the longitudinal relaxation time. The value of T1 for proton imaging will depend on

the molecular environment of the sample. For water (H20) protons, T, is about 1000

msec. T, increases with the strength of the Bo field in liquid samples at typical NMR field

strengths.

Transverse Relaxation, T2

In a physical MR sample the local magnetic field experienced by a given spin is a

combination of the Bo field and the fields generated by its neighbors. After a 90 tip of a

set of spins, the net transverse magnetization decays with time. This is because the

different spins constituting the net transverse magnetization fan out or dephase as they

experience different time-dependent local magnetic fields. Thus, the MR signal which

depends on the transverse magnetization goes to zero. The evolution of the transverse

magnetization is given by (10)

M (t)= M O (0)exp(-t /T T) [11]

where M1 is the transverse magnetization and T2 is called the transverse relaxation time.

T2 relaxation is caused by both slow and fast molecular motions, in contrast with T,

relaxation, which can be caused only by fast molecular motions at the Larmor frequency.

Hence T2 is always lesser than or equal to T1. In practical situations, there are

inhomogeneities in the permanent magnetic field Bo, which cause increased dephasing of

the spins leading to a shortening of the transverse relaxation time. This leads to an

effective transverse relaxation time T2 given by

1/T2 =1/2 +1/ T [12]









where the second term in equation [12] refers to the T2 shortening due to the Bo

inhomogeneities.

Gradients, Spatial Encoding and K-Space

The ability to spatially separate the signal comes from a simple, yet brilliant

extension of the Larmor relation, equation [3], first discovered by Lauterbur (6). If the z-

component of the magnetic field is varied along the x-direction, the spins in the x-y plane

will process at different frequencies depending on their x-coordinates.

w(x) = Gx + o) [13]

where Gx is the applied linear x-gradient to the z-component of the magnetic field. Thus

by demodulating the signal at different frequencies, co(x), a representation of MR spin

density at different points along the x-axis can be obtained. The signal along they and z-

axes can be spatially encoded in an analogous fashion.

For an isochromat of spins seeing a constant background field over which a linear

x-gradient field is superimposed, after demodulation of the signal, the phase is given by

p = xG (t)dt [14]
[14]
= 2~dkx

where

k = fG (t)dt [15]

is the spatial frequency component of the phase.

The MR signal can be considered to be the sum of all isochromat signals, each

weighted by the local spin density p(x) and the phase term from equation [14].

s(k) = p(x)exp(-i2;k.x)dx [16]









Hence, the effective spin density p(x) can be estimated from an inverse Fourier

transform of the signal s(kx). In three dimensions

p'(x,y, z) = Js(kx,ky, k) exp(i2r(kx + kyy + k z))dkxdkydk [17]

where p' is an estimation of the effective spin density which becomes equal to the exact

value when the reconstruction is perfect.

In equation [17], the Fourier inverse of the reconstructed image space is the k-

space, which is obtained after demodulating the signal. The k-space contains all the

information regarding the manner in which the magnetic field gradients were played out

to spatially encode the image. All MRI sequences can be succinctly represented by their

acquisition k-space diagrams. Since the MR image is obtained as an inverse Fourier

transform estimate of the demodulated signal k-space, the latter, in principle, contains

more information about the image.

Basic MR Pulse Sequences

The vast majority of MRI pulse sequences are a variation on two basic image

acquisition methods, the spin-echo sequence and the gradient echo sequence. The most

popular rapid image acquisition sequences in conventional use, the echo-planar imaging

(EPI) sequences, are variations on the gradient echo sequence. EPI as well as spiral-EPI

sequences have the capability of acquiring the whole image in one acquisition.

Spin-Echo Pulse Sequence

Figure 1.1 shows a timing diagram of a simple spin echo sequence (11). A 900 RF

pulse is first applied (period 1) in conjunction with a slice selective gradient Gz to create

a transverse magnetization in the slice encoded by Gz. During period 2, spins which

dephase as a result of the slice selective gradient are rephrased by a negative










compensating gradient. Also a programmable phase encoding gradient Gy is applied

which encodes spins in the y-direction. In addition, a readout direction gradient Gx is

applied which serves the purpose of compensating for phase that will be accrued due to

the readout gradient in period 4. In period 3 a slice-selective 1800 RF pulse is applied.

The purpose of this pulse is to generate a "spin-echo" in period 4, when all the spins

which have been dispersed by the applied and background gradients will come back in

phase. The readout gradient Gx is played out during collection of the echo in period 4, to

encode spins in the x-direction. The above sequence is repeated for different values of the

phase encoding gradient, Gy to encode the y-axis. The time interval between the

application of the RF pulse and the acquisition of the center of the echo is called the echo

time (TE). The time-interval between two successive phase-encoding steps is called

repetition time (TR).

900 1800














Signal --

TE
4i 4
1 2 3 4

TR
Figure 1.1: Timing diagram of a 2-D Spin Echo Sequence









In terms of k-space (Figure 1.2) each repetition (echo) of the sequence generates

one line of the k-space. After acquisition of all the echoes a two-dimensional k-space

image is generated, which upon inverse Fourier transformation generates a 2-D image of

the slice.


t-*








Figure 1.2: K-space diagram of a 2-D Spin Echo Sequence

Gradient-Echo Pulse Sequence

The gradient echo sequence differs from the spin echo sequence in the manner in

which the echo is generated during readout. While the spin echo sequence generates the

echo by the use of a 180 refocusing pulse, in the gradient echo sequence, the echo is

generated by the gradient reversal in going from the refocusing Gx gradient to the readout

Gx gradient. Thus, the echo is created when the spins dispersed by the initial negative Gx

are brought back in phase during readout by the positive Gx. This form of echo generation

can not compensate for the phase dispersal due to background gradients. Thus the signal

decays faster (through T, decay) in a gradient echo sequence when compared to a spin

echo sequence (through T2 decay). Both the gradient echo sequence and the spin echo

sequence are examples of 2-D FT spin warp imaging.









Contrast and Resolution

The MR signal for a 2-D FT spin warp sequence is given by

(1 exp(-TR/ T, ))s in /
S(TR, TE, p ,O) = Po exp( exp(-TE/ T )
1- exp(-TR / T)exp(-TR / T) -exp(-TR / T)cos

[18]

where S is the signal as a function of repetition time (TR), echo time (TE), effective spin

density po and RF flip angle 0. By judicious choice of the parameters of the scan, image

contrast can be achieved by enhancing the differences in TI, T2 (T, ) or spin density

between different constituents in the sample. These three constitute the most basic

contrast generating mechanisms. Other contrast parameters in vogue include flow,

magnetic susceptibility difference and diffusion (to name just a few).

The image resolution is dictated by the number of phase-encoding steps Ny, the

number of acquisition samples in the readout Nx and the field of view (FOV) in the x and

y-directions. For brain imaging applications the FOV ranges from 20-24 cm and the

image matrix is 256 by 256, giving an in-plane resolution of about 1mm by 1mm.

Fast Imaging Sequences

The scanning time required for the 2D-FT spin warp sequences mentioned above

can be quite long. Roughly, the scanning time will be given by TR times Ny, the number

of phase encode steps. For TR = Isec, a 64 x 64 matrix image will take 64 seconds. For

many MR applications faster acquisition times are required. One major advance in

shortening acquisition times was performed by Mansfield's group (12) in Nottingham

when they invented the Echo-Planar Imaging (EPI) sequence. Mansfield himself had

introduced the concepts of EPI a decade or so back (13). The Stanford group (14-15)








subsequently devised a different version of EPI called the spiral-EPI (or just spiral)
sequence.
Echo-Planar Imaging
Figure 1.3 shows a timing diagram of a conventional single-shot EPI sequence. The
whole of k-space (Figure 1.4) is acquired in a single application of the RF pulse. An
oscillatory gradient Gx is applied along the frequency encoding direction and a train of
gradient echoes is collected. Each echo is then phase encoded independently by blipped
Gy gradient and the whole k-space matrix is covered. The blips in Gy gradient occur at
during each zero crossing of the Gx gradient.

90,
RF --------------------

/.- -'\________________


U I U u

T2*decay
signal T decay

Figure 1.3: Timing diagram of an Echo-Planar Imaging Sequence
Thus each echo corresponds to one line of k-space as in Figure 1.2. While each k-
space line in Figure 1.2 was acquired in one TR, all the k-space lines in Figure 1.4 are


H [Am -



r\n r\\ n n-









acquired in a single TR. Modern EPI sequences can acquire one slice in as low as 30

milli-seconds (16).


Figure 1.4: K-Space diagram of an Echo-Planar Imaging sequence

Spiral Imaging

An extension of the conventional EPI sequence is the spiral sequence (17-19).

Figure 1.5 shows the timing diagram and corresponding k-space diagram of a spiral fast

imaging sequence. In a spiral sequence, both the Gx and Gy gradients oscillate with

increasing amplitude as a function of time during readout. There is no phase-encoding

gradient. The k-space is acquired in a spiral-fashion, hence the name. The gradient slew

rate (the maximal rate of change of the gradients in the pulse sequence) requirements for

spiral imaging are not as high as for conventional EPI sequences (18, 19). Scan times per

slice are comparable to that of standard EPI sequences. Spiral sequences are inherently

self-refocussed and do not have geometric distortions that plague EPI sequences.

However, they require off-line reconstruction which can take much longer than EPI

sequences.






13



RF ----

--~-AWV



Ox ----- ------------------



Ox ."" .. ...... .......
Oz


Figure 1.5: Timing diagram (left) and k-space diagram (right) of a 1-shot spiral EPI
sequence.


;4: I-~' ;> "i1\'JI














CHAPTER 2
FUNCTIONAL MAGNETIC RESONANCE IMAGING

Chapter 2 discusses concepts of functional magnetic resonance imaging (FMRI).

The origins of this functional imaging modality, the principles of blood oxygenation level

dependent (BOLD) FMRI and the spatio-temporal properties of the BOLD FMRI signal

are discussed. Finally, salient features in FMRI experiment design and data analysis are

reviewed.

Origins of Functional Magnetic Resonance Imaging

Until the late 1980's, the decay of signal due to local magnetic field

inhomogeneities due to T2 relaxation was considered a nuisance and sought to be

minimized. Among the first to realize that the presence of a paramagnetic substance in

the blood stream acts as a vascular marker, giving useful contrast, were researchers of the

MGH group (20), who pioneered the application of contrast agents to study brain

perfusion in animals. In the early 1990's, Belliveau and collaborators (21) first extended

these principles to image functional brain activation in humans with MR contrast agents.

Subsequently Ogawa, working with laboratory animals, in a seminal paper (22),

demonstrated that similar changes of MR image contrast can be obtained by changing the

oxygenation state of blood. This observation was rooted in the fact [first measured by

Pauling in 1936 (23)] that deoxyhemoglobin is more paramagnetic than oxyhemoglobin,

which itself has a very similar magnetic susceptibility to that of brain tissue. Brain

activation leads to creation of imbalances between the oxygen uptake and blood flow

leading to blood oxygenation level dependent (BOLD) MRI signal contrast around










cortical vessels, which can be mapped non-invasively with MR sequences optimizing T2

contrast. The first human subject BOLD FMRI was performed in 1992 by Kwong (24)

and Ogawa (25), using gradient-echo MR images. BOLD FMRI accounts for most

functional imaging studies of the brain with MRI, though another method involving the

labeling of arterial spins with a preparatory RF pulse, first advocated by the Pittsburgh

group (26), is fast gaining currency. This is a cerebral blood flow monitoring technique

for functional MRI.

Principles of BOLD Functional MRI

BOLD FMRI, like other functional neuroimaging methods such as positron

emission tomography (27) and optical imaging (28) is based on physiological responses

related to brain activation. Brain function is spatially segmented and compartmentalized.

This can be mapped through measuring secondary changes in metabolism and

hemodynamics in response to neuronal activity.

The MRI signal acquired with a single pulse sequence is given by

S = M(T,*) A(T2) [2.1]
where Mis the sampled magnetization, determined by T,* (Ti with inflow) and A is the

signal attenuation, governed by the T2 decay of the in-plane magnetization. The

activation-induced MRI signal change in the capillary bed is given by

AS/S = AM /M + AA/ A [2.2]
The first term in equation [2.2] is the change in signal due to inflow and is (at steady state

attained after repetitive pulsing) very small (29), AM/M 0.0035.

The second term in equation [2.2], when described by a simple T2 decay is given

by


A / A = -TEA(1/ T2')


[2.3]









for echo-time TE and activation induced change in transverse relaxation, A(1/ T ). BOLD

contrast is solely due to the susceptibility difference of red cells with paramagnetic

deoxyhemoglobin relative to their surrounding. The bulk susceptibility of red cells, which

is due to the hemoglobin deoxygenation level, changes the field shift inside and outside

the red cells. The change in T2 due to brain activation can be written in terms of the blood

oxygenation level Y, change in cerebral blood flow, ACBF, magnetic field, Bo and echo-

time, TE (23).

AA / A = a TE A(vB (1- Y)) [2.4]
where a is a constant and v is the blood volume fraction. Equation [2.4] is actually

a simplification. The exact dependence of the MRI signal change due to activation on the

hemodynamic and MRI parameters is still a subject of research.

BOLD Hemodynamic Response

Figure 2.1 shows a schematic representation of a BOLD hemodynamic response to

an applied neuronal stimulus. The response can be characterized by segmenting it into

four epochs. First, there is a delay which could range from 2 to 4 seconds (30) between

the application of the stimulus and the onset of hemodynamic response. This delay could

be both due to delay in neuronal firing in response to the stimulus or sluggishness

associated with the neurovascular coupling.

The second feature, shown as a dotted curve is often called the "initial dip". This

event, which can last up to 2 seconds (31) is the result of a local increase in cerebral

metabolic rate of oxygen consumption (CMRO2) at the site of neuronal firing, leading to

an increase in the local deoxyhemoglobin concentration, which results in decrease in MR

signal intensity. This phenomenon is not often observed (for instance initial dip is seen









only BO > 3T and at temporal resolutions around or less than 1 second), and hence

designated by the dashed curve.










Figure 2.1: Schematic representation of a BOLD hemodynamic response

The next epoch is the positive BOLD response. This happens due to an increase in

cerebral blood flow (CBF) which occurs after neuronal firing. This results in

hyperoxygenation of the neural tissue which leads to a decrease in the deoxyhemoglobin

concentration and thus an increase in MR signal. The positive BOLD response to a

neuronal impulse consists of a relatively sharp increase (about 4-6 seconds) to maximum

and a slower decrease characterized by fall-times of about 7 seconds or more (32). This

epoch is the classical BOLD response, which is utilized to quantify brain activation in

most instances of FMRI analysis.

Sometimes a positive overshoot (dashed curve) is seen at the start of the positive

BOLD response. One plausible reason for the overshoot is the mismatch in the rates of

adjustment of CBF and the cerebral blood volume (CBV) (33) during changes in

stimulation state. Soon after neuronal stimulation, the CBF exhibits an abrupt jump to its

elevated level while the CBV adjustment is more gradual. This results in a hump in the

BOLD response when there is an short-lived increase in the oxygenation of the tissue due

to the mismatch between CBF and CBV. The reverse happens at the end of the positive

BOLD response, when elevated CBV levels persist even as CBF and hence the









oxygenation decreases leading to a decrease in MR signal. This incompletely understood

post-stimulus undershoot can take up to tens of seconds to recover (34).

Spatio-Temporal Characteristics of BOLD FMRI

It is profitable to explore the relationship between brain activation and the

corresponding BOLD hemodynamic response. In particular, it would be remunerative to

examine in detail how the BOLD response is related to the underlying brain activation in

time and space.

Spatial Specificity

Apart from the BOLD response changes originating in the capillaries embedded

within the cortex and localized to site of neural activity, the hemodynamics that give rise

to observed FMRI signal changes originate from a number of sources on both the supply

(arterial) and draining (venous) side which can be as much as a centimeter away from site

of neural activity (35-36). To get around the loss of specificity due to the draining vein

effect, which is a by-product of the hyperoxic phase of the BOLD response, some

authors (37) have hypothesized that use be made of the "initial dip" part of the BOLD

response which is a corollary of the early hypoxic phase. This is thought to be more

localized to the site of neural activity. But as mentioned before, the initial dip can be

elusive to image and requires high temporal resolution too. Methods involving MR phase

images (38-39) show more promise in discriminating large vessel effects.

Temporal Resolution

The neuronal processes associated with brain function range do not extend over a

few hundred milliseconds even for the more complex cognitive tasks (40). In contrast, the

BOLD hemodynamic response to a neural stimulus could extend over tens of seconds. To

answer the question of how separated in time, neuronal events have to be, in order to be









resolved with BOLD FMRI, it is necessary to understand the exact mechanism of

coupling between brain activity and the vascular response. At present the nature of

neurovascular coupling is not well understood. Studies involving measurements of

evoked potentials and BOLD MR signals (41) have claimed that temporal dynamics of

brain can be measured indirectly by observed correlations between the BOLD response

signal parameters and dynamics of underlying brain function. But the observations are

open to interpretation in terms of their generalization to all brain functions and locations

as well as how consistently the measured electrical activity reflects brain function (42).

Linearity of BOLD Response

Optimal design of FMRI experiments requires knowledge of the nature of the

relationship between stimulus presentation and evoked BOLD hemodynamic response.

Early ventures into FMRI signal analysis assumed a linear relationship between stimulus

duration and evoked BOLD FMRI signal change (43). Subsequent studies have

demonstrated significant departures from linearity for stimulus durations less than 4-6

seconds (45, 46). Another manifestation of this nonlinearity is the dependence in the

amplitude and latency of the hemodynamic response to a neural stimulus on the timing of

preceding stimuli. At inter-stimulus-intervals (ISI) of 5-6 seconds or greater, the

hemodynamic responses of multiple stimuli sum in a roughly linear fashion (47).

However at shorter intervals (e.g. less than 2 seconds), there are significant departures

from linearity, in that the hemodynamic response to the second stimulus in a pair is

reduced in amplitude and increased in latency compared to that evoked by a single

stimulus. This phenomenon has been observed in auditory (48), motor (47) and visual

cortices (49). The aforementioned studies on nonlinearity of the BOLD hemodynamic

response were done on lower level cognitive systems. Gopinath et al. (50) noticed









refractoriness at longer ISIs (3 seconds and more) in the hemodynamic response of voxels

in the supplementary motor area (SMA) under a higher level cognitive task, a semantic

word generation paradigm. Extending on this work Gopinath et al. (51) subsequently

found an increase in the nonlinearity of the BOLD hemodynamic response along a

functionally connected neural pathway. In this study the change in the linearity of the

relationship between stimulus pattern and BOLD response along the receptive and

expressive language processing network was observed. Under an overt word repetition

task, an increase in the nonlinearity of the BOLD response was observed in the output

(motor cortex) of the language processing network compared to the input (auditory

cortex).

The above discussion leads one to explore the neural basis of FMRI signal.

Questions of importance are does the FMRI signal reflect axonalfiring output as does

EEG? (52) or does it reflect post- andpre-synaptic signals? (53, 54). A recent review on

this subject (55) suggests that the BOLD effect should be interpreted as a reflection of

neuronal signaling and not as a locus of increased energy utilization. Much work needs to

be done on this subject to get a clear picture of the neural basis of FMRI signal. Design

and analysis of FMRI experiments will clearly benefit from a better understanding of the

neurovascular coupling.

FMRI Experiment Design

FMRI is rapidly gaining currency as a preferred method for imaging brain function.

FMRI has been used to image brain activation in simple brain functions stimulating the

auditory areas of the brain (56), motor areas (57) and visual areas (58). With the success

of these experiments FMRI has quickly graduated to imaging higher level cognitive

processes in the brain dealing with language (59), pain (60) and perception (61) among a









host of other systems. It has also found application in treatment of pathologies (62) and

pre-surgical planning (63). FMRI study designs can be broadly classified into two types:

1) blocked paradigms and 2) event-related paradigms.

Blocked Paradigms

Blocked paradigms were the first approach to be employed in FMRI studies (25,

26). Blocked paradigms involve application of FMRI stimuli for finite durations ranging

from -10 sec to 1 min interspersed with rest intervals of about the same durations.

Regions in the brain which show significant signal change between the "active" and rest

conditions can be considered "activated". Blocked paradigms have flexibility, allowing

use of multi-factorial designs (64) as well as parametric designs (65). The rest intervals

may be of uniform size (boxcar stimulus order) or varied (randomized block designs).

Optimization of blocked paradigms has been studied with regard to both

neuropsychological and statistical terms (66), though further refinement of the

optimization procedures is in order to account for variability in hemodynamic response,

brain activation and noise of the associated FMRI signal time-series. With the knowledge

at hand (66), one can surmise that the length of the active and rest intervals should be

such that the BOLD FMRI signal will be at activation frequencies in the range 0.08-0.15

Hz. This is because the hemodynamic response acts as a low-pass filter and attenuates the

signal at frequencies greater than ~ 0.2 Hz and also the FMRI time-series noise has been

known to exhibit disproportionate spectral power at frequencies (67) below 0.05 Hz.

Event-Related Paradigms

The blocked paradigms of the previous section offer the highest efficiency among

the currently used designs in FMRI (68) in detecting activated areas. However, the

inherent characteristics of blocked paradigms prevent them from being able to estimate









the hemodynamic responses of each individual stimulus in a block (69). Also, blocked

designs cannot readily accommodate behavioral constraints imposed by some event

sequences, such as those occurring infrequently, randomly or discretely, those not having

precise time-locking to known stimuli, or mixing of events from fundamentally different

tasks (70). Event-related FMRI (ER-FMRI) designs overcome all the above-mentioned

obstacles and also provide means of examining questions regarding the dynamics and

time course of neural activity as well as neurovascular coupling. Early ventures in ER-

FMRI (70, 67) involved application of periodic single-trial stimuli. Subsequent

developments in ER-FMRI have demonstrated that pseudo-random ordered single-trial

stimulus sequences are more optimal in terms of both detection and estimation efficiency

of the signal changes in ER-FMRI (69, 71, 72).

FMRI Data Analysis

The BOLD signal changes in FMRI at 3T are typically 2-10 %. Tasks involving

higher level cognitive systems (like language) tend to exhibit a smaller signal change (2-

4%) than those involving activation of the primary cortices. The role of FMRI data

analysis is to extract this signal from the background noise.

Overview

The data analysis methods can be categorized into 1) hypothesis independent

methods and 2) hypothesis driven methods. Hypothesis independent methods such as

ICA (73), fuzzy-cluster analysis (74) have yet to be perfected for FMRI and are not

widely used. Hypothesis driven methods can be categorized into a) parametric methods

and b) nonparametric methods.









Image Registration

Proper image registration (aligning the time series images) is imperative to

minimize the effect of motion on the FMRI signal. Image registration is the first step in

the post-processing of acquired FMRI images. Image registration is usually performed

with image-intensity-based methods (75-77). The guiding principle in all intensity-based

image registration methods is the minimization of some quantity related to the voxel-wise

image-to-image intensity differences. Conventional intensity-based image registration

methods consist of two steps (75-77). The first step is the estimation of the rotation and

translation parameters required to align a given image with the base image, usually

obtained as best-fit rigid body rotation and translation parameters in the global

optimization algorithm used to re-align the images. The second step is the assignment of

intensity values to the voxels in the rotated image grid. This resampling is done by means

of polynomial (77) or Fourier interpolation (78). Polynomial interpolation is local (band-

limited). This can introduce blurring in the resampled images (i.e. correlation between the

signal values at nearby pixels). Fourier interpolation is more desirable, albeit slower. In

Fourier interpolation the image is resampled globally in the reconstructed k-space, which

upon inverse Fourier transform gives the registered image. The blurring introduced is

much reduced.

There is a separate class of feature-based registration methods which have been

proposed for FMRI (79, 80, 81). These methods segment a known anatomic contour in all

the images of the FMRI time-series and use the contour as a reference for tracking and

compensating for head motion. Gopinath et al. (80) proposed one such method which is

now available in a more refined form (81) to implement a 2D feature-based image

registration. This method endeavors to segment an anatomic shape prior (e.g. the corpus









callosum) in each of the images in the FMRI time-series and estimate the motion

parameters involved in aligning the prior in all the images in the time-series. These

methods are still in their infancy and are not in general use. The main drawback lies in

the difficulty in segmentation of low resolution FMRI images.

FMRI Noise Characteristics

The preponderance of FMRI studies in the literature use parametric methods of

data analysis. The characterization of the noise structure is critical to parametric analyses

of FMRI time-series. The earliest FMRI data analysis methods assumed the underlying

noise structure to be wide sense stationary (WSS) Gaussian white noise (43). More

detailed inspections have revealed significant colored (67, 82), non-Gaussian (83) as well

as non-stationary (84) features in the FMRI noise. Most methods of parametric data

analysis handle the FMRI noise in one of the following three ways. Some neuroimaging

software (85) assume the noise structure to be WSS and Gaussian white. They typically

fit a polynomial trend to the baseline to reduce the power of low-frequency noise

components in the time-series. This method has some merit in that the FMRI time-series

is believed to have a strong white noise component. For example, Purdon et al. (82),

using a WSS Gaussian white noise plus a first order auto-regressive (AR(1)) model,

estimated a 3:1 ratio for the power of the white noise component to that of the colored

noise component in their model for FMRI noise time-series for TR = 2 sec. The second

prescription for treating the underlying noise structure is called pre-coloring. In this

method (86) the FMRI time-series (with unknown intrinsic color) is swamped with a

known amount of auto-correlation by smoothing with a Gaussian filter. The time-series is

then analyzed with the assumption that it is WSS Gaussian with a pre-determined auto-

correlation function (ACF). The third noise-treatment method (82, 87) relies on pre-









whitening the time-series before analysis. This involves estimation of the color by auto-

regressive moving average (ARMA) time series analysis.

The presence of a dominant white noise component makes estimation of the color

of the time-series particularly difficult (88). One can take recourse to the frequency

domain and try estimating the color using non-parametric spectral analysis (67, 89).

However spectral estimation involves an inherent trade-off between bias and consistency

of the power spectrum estimate (88). Gopinath et al. (90) proposed a technique to

overcome the obstacles in conventional methods of frequency domain FMRI signal

analysis. Using a result from statistical signal processing (91), for broadband signals in

noise of unknown power spectral densities (provided WSS), the authors demonstrated

that judicious design of event-related FMRI experiments can result in broadband

hemodynamic response signals in FMRI time-series. In such a case, only an estimate of

the power spectrum is needed to construct a detector for broadband FMRI signals in

unknown colored FMRI noise time-series, without the need for exact determination of the

color of the noise.

The preceding discussion has focused on the stochastic properties of FMRI noise.

In practice, the changes in FMRI signal due to physiological processes like cardiac and

respiration are also included in the noise term (92). Techniques have been introduced (93-

94) to correct for the noise introduced by physiological processes. For whole-brain FMRI

studies with long TR (- 2 sec) the respiration and cardiac noise components are not very

significant (95), especially when the stimulus order is periodic and are hence ignored.

The origin of FMRI noise is of interest. If the features in the noise can be ascribable

to physical/physiological processes) the task of FMRI signal analysis would be









simplified. Some groups (44, 87) have suggested that the low frequency features of the

FMRI noise are related to physiological sources like resting state neural activity. Others

(67, 96) are skeptical, pointing to the fact that disproportionate spectral power at low

frequencies has been observed in phantoms and cadavers also. Recently Gopinath et al.

(97) showed that some regions in the brain which exhibited "1/f-like" features in the

image-magnitude FMRI noise time-series also exhibited similar behavior in the image-

phase FMRI noise time-series. These findings would also preclude resting state neural

activity as a source of the color in FMRI noise as the neuro-vascular coupling which

relates neural activity to the BOLD signal at the capillary level does not leave a signature

in the voxel-phase. Gopinath et al. also showed (98) presence of more voxels exhibiting

disproportionate spectral at low frequencies (f < 0.01 Hz) in diseased brain tissue than

intact brain tissue; a finding difficult to reconcile with the resting state neural activity as a

source of"l/f" FMRI noise, since there is significantly less neural activity in diseased

tissue when compared to healthy brain tissue.

Parametric Methods and General Linear Model

The first attempts at FMRI data analysis utilized parametric methods (43, 44).

Most parametric methods can be expressed in the form of General Linear Models

(GLMs). The brief review of FMRI signal processing presented here will focus on

deconvolution analysis under the framework of a GLM. This is also instructive in that it

is the main method of analysis followed throughout this thesis. This method (99, 100)

relies on the assumption that the observed FMRI time series, Z(t) is the result of a

convolution of the applied task stimulus-impulse time-series, f(t) and the impulse

response function (IRF) h(t). This signal is over and above a baseline and is in the









presence of a Gaussian white noise process E(t). In the discrete-time domain indexed by

n,

p
Zn= fo+, + A l+ I hf,, + E2.
m=0 [2.5]
n= p, p+1,...N-1
where fo and f/ are the baseline parameters (corresponding to mean and linear trend) and

the summation denotes the discrete-time finite-lag convolution of thef(t) and h(t) over

lags and Nis the number of time-points in the time-series. The baseline of FMRI time-

series often exhibit a global linear or polynomial drift and have to be included in the

model for optimal signal detection and estimation. The constant is determined by the

duration of the anticipated hemodynamic response function (HRF). In matrix

formulation [2.5] becomes

Z= Xp +E [2.6]
where Z is the observed time-series vector, X is the deconvolution matrix and E is the

white noise matrix. The linear regression problem expressed by equation [2.6] can be

solved for estimates of Z and P Z and P by minimizing the error sum of squares

between the estimated (fitted) time-series and observed time-series:

N-1
SSE= Q()= (Z Z,) [2.7]
1=0
which gives the least squares estimate for p through


S=(XTX) IXTZ [2.8]
The parameter vector p is composed of the estimated parameter for the mean (/ o), linear


trend (/ ,) and the IRF parameter estimates (ho..hp).

The significance of the regression can be evaluated by constructing the following

hypothesis test,









Ho :Z =Yo +y0 + n+
P [2.9]
H,:Zn = +,n+ hm fn,, +En
m=0
where Ho and Ha are the null and alternate hypothesis (same as equation [2.5])

respectively and yo and yi are the parameters corresponding respectively to the mean and

linear trend of the noise (baseline) model. A test of the null hypothesis is made by

determining the parameters which yield a least squares fit for the baseline model as well

as the parameters that provide the least squares fit for the signal plus noise (full) model of

H,. Next the residual sums of squares between the observed time-series and the fitted

time-series for the baseline model, SSE(B) and that of the full model, SSE(F) are

evaluated. The null hypothesis can then be tested through the test statistic F*,

SSE(B) SSE(F)
F MS(regression) df, dfF
MS(error) SSE(F)
dfF
where dfB and dfF are the degrees of freedom of the baseline model and full model

respectively given by

df = N'- 2
dfF = N'- 2 -(p+) [2.11]
df -dfF =p+l
where N'= N p is the number of usable data points. The test statistic F* has the F(dfB-

dfF, dfF) distribution under the null hypothesis. The coefficient of multiple determination,

R, can be used as an indicator of the goodness of fit between the full model and the data,

as given by

R= SSE(F) [2.12]
SSE(B)
and can be regarded as the proportion of the variation in the data that is explained by the

full regression model.









Inference

Once a statistical parametric map of voxels in the brain is obtained, the next step is

to decide how to threshold the data, in order to be able to say a certain voxel (or area of

the brain) is activated at a given level of significance (p-value). This task is complicated

by the multiple comparison problem. Typically, for a whole brain FMRI study with

resolution 3 mm, a large number of voxels ( -40,000) are tested simultaneously for

rejection of the null hypothesis. Thus, even with ap-value of 0.01, one can end up with a

significant number (- 400) of false positive voxels, which get declared active, assuming

all the voxels are independent. The simplest procedure to control for multiple

comparisons is the Bonferroni correction (101). Here, for a desired significance

threshold, p, the voxels are declared active if they possess p-values less than p/N, where

Nis the number of voxels in the map. This procedure can be considered overly

conservative (102), even in the case where all the voxels are independent (as is not the

case in FMRI), and can lead to loss of power (declaring voxels to be inactive when they

are active). Recently, some groups (102, 103) have advanced a less conservative

procedure for controlling multiple comparison false positives. Instead of correcting the

family-wise error rates (FWER), as is done in Bonferroni correction, they control for the

false discovery rates (FDR), the proportion of false positives. FDR theory (102,103), also

allows for non-independent voxel families, as opposed to the Bonferroni method, where

one has to estimate the number of independent voxels.

In practice, a lot of groups do not control for multiple comparisons, opting instead

to threshold the data at low p-values. This procedure is surprisingly effective at the

individual subject level. The reason can be surmised as follows; at conventional FMRI

sites, with Bo -1.5-4T, even the relatively small magnitude of BOLD signal changes of 3-









10 % lead can to very lowp-values in support of the null hypothesis, in the regions of

interest. Thus, the SPMs are thresholded at high levels of significance, erring if anything

on the side of specificity. In fact, when estimation of the HRF is also critical to the

analysis over and above the detection of activation, one might need to threshold the

SPMs at a higher level of significance, in order to eliminate voxels whose estimated IRF

(or HRF) is not well defined. Figure 2.2 shows the IRF for a voxel with F(16,470) = 30

as well as a voxel with F(16,470) = 2.5, for an event-related silent word generation study

(90). Although the F = 2.5 voxel is significant atp < 0.001, the corresponding IRF is not

well defined unlike that of the F = 30 voxel. The signal in the figure has been normalized

to a unit maximum to show the shape better. The voxel IRF on the right has a

substantially lower raw amplitude compared to the one on the left. The post stimulus

undershoot seems pronounced in the voxel (from the auditory cortex) hemodynamic

response on the left. The distribution of the test statistic can vary between subjects and

also between different sessions of the same subject (104, 105). Thus, it may be beneficial

to threshold each session separately and use procedures like conjunction analyses (106) to

make between-session inferences.










1 1


0.5
0.5

0)0
C0

-0.5


-0.5 -1
0 10 20 Time sec 10 20
Time (sec)
Figure 2.2: The estimated impulse responses for a auditory cortex voxel activated at
F(16,470) = 30, p-val z 0 (left) and a voxel with F(16,470) = 2.5 (right). The
signal has been normalized to a unit maximum.

ROC Analysis

Receiver operating characteristics (ROC) curves are used to test the performance

of a detector, imaging modality, or technique (107). The application of ROC analysis to

test different image processing techniques, statistical data analysis methods,

preprocessing steps prior to statistical analysis, and experiment design in FMRI has been

attempted by a few groups (90, 108, 109, 110, 111). Ventures into ROC analysis have

consisted of using synthetic data (90, 110, 111) or real data under test-retest conditions

(108, 109). The major drawbacks in using synthetic data are the hitherto incompletely

understood nature of the noise structure in FMRI time-series as well as the

unpredictability of the BOLD FMRI signal (84, 104, 105). The problem with using test-

retest methods is the unpredictable variations between sessions in the BOLD signal (104-

105) as well as the multivariate nature, within session, of the BOLD signal change (84).














CHAPTER 3
MOTION AND FMRI

The artifacts produced by subject motion are a major confound in the analysis of

functional magnetic resonance imaging (FMRI) time series data. In this chapter the major

sources of motion-related artifacts in FMRI time series are described. Some of the

existing methods for dealing with motion artifacts in the literature are also reviewed.

Introduction

FMRI signal changes are of the order of 1-8% of the baseline signal intensity in

conventional MR systems (1.5T and 3T). As a result, it is very important that the signal

changes from sources other than functional activation be eliminated as far as possible. In

living subjects, movement is unavoidable. Even small motions can impact the FMRI time

series adversely. For instance (75 Cox, et al., 1999), it has been seen that typical T2 -

weighted brain images show 10-20% intensity changes between adjacent voxels in the

parenchyma and 70-80% changes at the edge of the brain. Thus, motions of the order of a

tenth of a voxel can produce 1-2% signal changes in the parenchyma and 7-8% signal

change at the edges of the brain, of the same size as changes occurring from brain

activation that are to be detected. For a 20 cm field of view (FOV) 128 X 128 image the

above statement implies that motions of the order of 150 |tm can have a significant

impact on the FMRI signal. Motion can impair the detection of real functional activation

in several ways. Random motions of the subject will appear as additive noise in the voxel

time-series and decrease the detectability of functional activation. Stimulus-correlated









motion can mask real activation in cortical regions and also appear as false-positive

activation in the brain edges and high-contrast regions of the brain.

Proper image registration (aligning the time series images) is imperative to

minimize the effect of motion on the FMRI signal. As mentioned in Chapter 2,

conventional intensity-based image registration methods consist of two steps (75-77). The

first step is the estimation of the rotation and translation parameters required to align a

given image with the base image. The second step is the assignment of intensity values to

the voxels in the rotated image grid. Motion artifacts can creep into the time-series from

errors encountered in both of the above steps, i.e. misalignment or misinterpolation.

Grootnik et al. (112) have characterized the artifacts introduced into the time-series by

intensity-based image-registration methods using a brain phantom. They attribute these

artifacts to interpolation errors introduced by the resampling inherent within realignment.

Most intensity-based methods fail when the motion is large more than a voxel (75).

Feature-based methods (80-81) use features in the image as landmarks in the registration

method. These methods, however, need the identification (or segmentation) of some

feature which is not always possible in low resolution FMRI images.

Often this is the only motion correction step performed in FMRI studies. However,

it would be optimal if image registration were but a first step in the treatment of motion

artifacts in FMRI. As mentioned before, conventional image registration programs can

give rise to unintended errors.

Major Sources of Motion Artifacts and Deterministic Solutions

In fact, even after perfect alignment of the time-series, the deleterious effects of

motion on the FMRI time series persist to some extent. These effects can be due to a









number of sources. The following paragraphs will point out the major sources of motion-

related artifacts and review the methods that exist in the literature to treat them.

Static Magnetic Field Effects

Head motion in inhomogeneous magnetic field causes local distortions in the static

magnetic field (Bo), which are not unwarped in standard image-registration schemes.

Ideally, the Bo field should be homogeneous throughout the sample (head). This is hard to

achieve in practice since the head distorts the magnetic field (113). To a certain extent the

Bo field can be made homogeneous by adjusting the current in the shim coils. The shim

field will depend on the orientation of the head with respect to the Bo field. The shim

fields are set up before the acquisition of the images. Residual inhomogeneities which

exist after the swimming will be modulated by head motion, producing time-dependent

magnetic field distortions. Consequently there will be a non-zero field difference between

the before-movement and after-movement-after-realignment images, for a given point in

the sample. Jezzard et al. (113) demonstrated this by acquiring phase images in addition

to magnitude images with an echo planar imaging (EPI) sequence while a controlled

flexion of the subject's head was performed. They showed that even after re-alignment a

substantial field difference existed between the "before motion" and "after motion"

images. Even a 1 rotation will result in local distortions of the order of one pixel.

Quantitatively, the resonant frequency of the 2D FMRI image at a point, in the absence of

magnetic field inhomogeneities, is given by

o)(x,y)= o) + y(Gx + Gyy) [3.1]









where oao = yBo, is the central frequency, y-being the gyromagnetic ratio (42.575

MHz/T). The presence of magnetic field inhomogeneities leads to introduction of a

spatially varying off-resonance (8H, 113, 114) term into equation [3.1] which becomes

o)(x,y) = o) + y(Gx + Gyy) + Ac(x,y) [3.2]

where Alo(x,y) is the off-resonance term. The off-resonance has different effects on

different methods of image acquisition used in FMRI. In EPI, where the k-space data is

acquired in rectangular fashion, the off-resonance causes geometric distortion. The spatial

encoding, which depends on the resonant frequency, is compromised, resulting in pixels

being mis-located. In spiral imaging, where the k-space is acquired in a spiral fashion, the

off-resonance causes blurring. In FMRI, magnetic field environment at a point can differ

from image-to-image due to motion. This time dependence will manifest as apparent

noise in the FMRI time-series.

Some remedies have been proposed to ameliorate this effect. Jezzard's group

(113), working with EPI data, pointed out that the off-resonance term can be calculated

by

Ao (x, y)= AB(x, y)/ TE [3.3]

where Ao is the field distortion caused by motion and JA is the phase difference

between the given image and the first image, x and y specify the in-plane Cartesian co-

ordinates of the position and TE is the echo-time. Thus, the pixel-shifts can be calculated

from a temporal sequence of phase images and corrected. This method assumes that off-

resonance of the first image is either negligible or is corrected by other methods. Also,

this method is applicable to EPI FMRI but not to spiral FMRI.









The manifestation of off-resonance related artifacts is different in spiral imaging.

The off-resonance leads to blurring in spiral images (114-115). In conventional spiral

reconstruction programs the off-resonance due to field inhomogeneity is calculated by

constructing a field map for the first image in the time-series. All the images are then

reconstructed by incorporating the phase conjugate of the inhomogeneity dependent

phase error in the kernel of the Fourier transform. All the images in the time series are

deblurred using the off-resonance term of the first image. However, in the case of motion,

just like in EPI, an analogous method to perform time dependent off-resonance

deblurring in spiral imaging is needed.

It must be stressed that these methods will only correct for geometric distortions (in

the case of EPI) and blurring (in the case of spiral) images. The signal loss due to

dephasing within voxels cannot be recovered. The extent to which the time-dependent

distortions affect the FMRI time series has not been studied. It would be desirable to look

at the effects of the distortion correction in order to assess their significance.

Ward and collaborators (116) have looked at the feasibility of real-time auto-

shimming, wherein they compute the change in magnetic field due to motion in real-time

and correct the shim by applying compensating gradients accordingly. The changes in

magnetic field due to motion are measured by a navigator pulse sequence. The advantage

of this method is that it compensates for the magnetic field distortions at image

acquisition, which is more desirable since this could also alleviate the intravoxel signal

dephasing that occurs due to the inhomogeneities. Post-processing methods have to work

with the irreversible loss of signal that occurs due to increased inhomogeneity. The main

drawback of this method is that it can only compensate for first-order changes in the









field. The susceptibility artifacts which cause the most dephasing involve inhomogeneity

gradients of higher order. Thus the need for a post-processing off-resonance

compensation method will still exist. There is also the practical difficulty that not all

FMRI centers have access to hardware and software needed for pulse-sequence-based

correction methods.

Spin History Effects

In conventional 2D multi-slice multi-excitation image acquisitions encountered

in FMRI, the signal or magnetization from a small volume of the object will depend on

the interaction of the Bo field with the slice-selective RF electromagnetic field B1 (117-

118) and the recovery of magnetization due to longitudinal relaxation during TR. The

electromagnetic field environment will change considerably with small displacements of

the sample (head) around the inferior and superior edges of an axial slice, the right and

left edges of a sagittal slice and the anterior and posterior edges of a coronal slice. Thus

even small motions of the order of a few mm in a plane orthogonal to that of the image

will result in a different magnetization from one excitation to the next. This effect will be

considerable in cases where the recovery of longitudinal magnetization is incomplete

between two excitations (which is the case when the TR is comparable to T, as is the case

in FMRI). Thus the signal from a given volume is a function of its current position as

well as it spin excitation history. It should be noted that post-hoc image registration of the

images cannot compensate for intensity anomalies caused by this effect. Retrospective

correction for through plane motion effects on signal intensity would require detailed

knowledge of a number of physical properties, such as the spatial variation of relaxation

times within the head, a seemingly intractable problem at best, unsolvable at worst.

Prospective image acquisition correction methods offer the best solution for through-









plane motion. Two such methods have been proposed. One method (119) estimates the

motion parameters from one image to the next by conventional image registration

schemes. This is done in real-time and the slice gradients are upgraded accordingly such

that the measurement coordinate system is kept at a fixed orientation relative to the

patient's head during the scan. Thus, in principle, the motion artifacts caused by spin

history disruptions can be alleviated. The main drawback of this method is that due to

constraints of computing power and gradient hardware requirements, the gradient

upgrade interval is currently limited, leading to whole-brain TR of 3-4 seconds or more.

Thus, the temporal resolution offered is not sufficient for most current FMRI needs.

Another method that has been proposed (120-121) measures the inter-image head motion

by employing navigator pulses. The slice gradients are subsequently updated real-time,

enabling the relative orientation of the head and the measurement co-ordinate system to

remain fixed during the scan. The main drawback of this method is that it takes up to 160

msec per slice, thus requiring a gradient upgrade interval and hence TR of 4 sec or more

for a whole-brain study. This is not sufficient for most current FMRI studies. It would be

better to use faster methods of encoding motion, such as an optical monitoring device,

independent of MR signal acquisition, which would lead to faster update times and

improved motion correction.

Inter-Shot Motion

Often, in FMRI studies, it is desirable to use a multi-shot spiral/EPI sequence to

have enough spatial resolution to attenuate the signal drop-offs in high susceptibility

contrast regions, or to resolve small anatomic features such as cortical columns or to

study physiological mechanisms. For whole-brain study, image TR of the order of 2

seconds is the norm. Thus the time between the two shots for a given slice in a 2D-









acquisition sequence is about 2 seconds. In multi-shot spiral imaging, the motion that

occurs in between the shots leads to inconsistencies in the collection of the k-space data

(115, 19). Inconsistencies in the low spatial frequencies leads to intensity distortions in

the image. Inconsistencies in the high spatial frequencies leads to swirl like patterns in

the image (Figure 3.1).













Figure 3.1 Two-shot spiral FMRI time series image of a mid sagittal slice showing swirl-
like patterns arising from inter-shot motion. The image has been detrended of
its time-series mean to better portray the effects of motion.

In FMRI these motion-induced signal variations may fluctuate from image to

image in the time-series, leading to increased variance in the voxel time-series, thereby

decreasing the ability to detect brain activation. Low frequency image intensity

distortions can be treated by the application of navigator techniques (92-122) or k-space

regression (93) to ensure that all the interleaves of a multi-shot spiral image have the k =

0 point common. Essentially these methods force the k= 0 point in the k-space to have

the same magnitude and phase in all the shots. Since low spatial frequencies contain most

of the information related to image intensity, these methods succeed in minimizing the

image distortions due to motion. These methods are aimed primarily at decreasing the

effects of physiological fluctuations, which tend to cause global signal intensity changes.









Higher spatial frequencies do not contain much intensity information. Thus the

methods to eliminate low frequency intensity modulations due to physiological

fluctuations ignore high k-space inter-shot inconsistencies. However, subject motion

between shots does lead to swirl-like patterns in the image due to high k-space

fluctuations. These swirls vary from image to image depending on the motion. This

manifests as additive noise in the FMRI time series. Oftentimes these motions are also

stimulus-correlated, which increases false positives and can also mask real activation.

This adds extra constraints in designing FMRI experiments. Researchers are often forced

to settle for low-resolution one-shot spiral images for studies like overt word generation,

which involve significant motion. In order to attenuate the high frequency artifacts in

FMRI images acquired with a 2-shot spiral sequence; it is useful to understand the origins

of the artifact. Suppose, in the time TR elapsed between the acquisition of the first and

second shots, the image rotates by an angle, 0, about the axis normal to the image plane.

Then the image space as well as the k-space of the second shot needs to be rotated by the

amount -0 in order for the two acquisitions to be aligned. If the image space of the second

shot is translated by a distance, Ar, given by

Ar = Axi + Ayj [3.4]

with respect to that of the first shot (where Ax and Ay are the translations along the two

orthogonal axes, denoted by unit vectors, i and j), then by the Fourier shift theorem,

every point on the k-space accrues a phase, o given by

S=k Ar = kAx+kyAy [3.5]

Thus, in order to reconstruct the image properly, the data-points in the k-space matrix

acquired with the second shot need to be multiplied by a phase term, e'k-r. It is obvious









that the prescribed method is limited to in-plane motion corrections. This is because the

image acquisition is in 2D and there is no phase encode along the third cardinal axis. The

extent to which the k-space distortions produced by inter-shot motions affect the FMRI

time series has not been studied. It would be desirable to look at the effects of the

distortion correction in order to assess their significance.

Remarks

The methods mentioned up till now are deterministic in the sense that they

isolate the cause of different motion-related artifacts and then correct for them. They are

mutually exclusive in that ideally all the three different classes (off-resonance distortion

compensation, spin-history correction and inter-shot motion correction) should be

performed to properly detrend motion-related noise in the FMRI time series. The order of

the execution of the steps is also important. Obviously prospective methods used during

image acquisition should be performed before applying retrospective correction methods.

The relative importance of these methods depends on the FMRI protocol used. For

example, if one-shot imaging methods are used, the high spatial frequency related artifact

would hardly be an issue. Also if the task (e.g. overt word generation with

coronal/sagittal acquisition) were such that the motion is mainly in-plane, off-resonance

correction would be more important than spin-history effects.

Mechanistic Solutions

Another class of methods can be employed to reduce noise associated with motion

in the FMRI time-series. These methods are mechanistic in the sense that they do not

explicitly attempt to account for the physical processes that relate motion to the

artifactual noise produced. They endeavor to phenomenologically model the signal

changes in the FMRI time series due to motion and separate out or detrend the motion-









related signal changes from the BOLD signal changes. These artifacts could arise from

any of the motion-related sources mentioned in the previous section.

Motion Parameter Regression

Friston and collaborators (117) proposed a method to account for motion

artifacts in the FMRI time-series. They posit that the movement related effects can be

divided into those that are a function of the position of the object in the frame of

reference of the scanner in the current scan and those that are due to movement in the

previous scans. The first component is posited to include changes in signal intensity as

the position of the voxel changes with respect to inhomogeneous background magnetic

field (e.g. susceptibility induced high image contrast boundaries) as well as signal

changes due to displacements around the slice boundaries in the slice excitation direction,

which result in changes in the RF excitation profile. The second component is theorized

to reflect the signal fluctuations due to changes in the spin excitation history, which are

caused by movement in the previous scans. Invoking arguments which pin the

dependence of motion-related signal changes on first-order perturbations of the

longitudinal magnetization arising from movement in present and previous scans, they

argue that artifactual motion-related signal changes at a given instant can be modeled

with a second order polynomial in the displacements of the object in the present and the

preceding scans in the FMRI time-series. The displacements are encoded by the

estimated motion parameters in the re-alignment of the present and preceding scans to the

last scan of the FMRI time-series. The signal time series can be written as

6 6
S, = at, ( x,,) + b, ( )2 + ( ) + b,, ( _, )2 + [3.6]
1=1 1=1









where St is the signal at time t, 6x,t is the value of the estimated motion parameter of the

xth of the six degrees of freedom in the rigid body realignment of the tth scan to the last

scan of the FMRI time-series, a,t and b,t are coefficients to be estimated by ordinary least

squares along with the model parameters of Yt, the part of the FMRI time-series free of

motion-related signal changes through a multiple linear regression procedure.

There are some drawbacks to this approach of motion artifact reduction. The model

assumes that head motion affects all the voxels in a similar linear fashion. It has been

noted that FMRI voxels on brain-edges and high-contrast boundaries are much more

sensitive to motion than voxels away from such features (118, 123, 124, 125, 126). Also

the model assumes that the movement-related signal changes are independent of

hemodynamic brain activation signal changes. Bullmore and collaborators (118)

demonstrated that this last assumption is violated by stimulus-correlated motion. In such

cases they also demonstrated that Friston's correction (117) can reduce the power of

detecting true-positive brain activation voxels.

Finally, equation [3.6] assumes that most of the signal changes due to motion arise

from spin-history effects. Stimulus-correlated motion in overt word generation

experiments have been shown to cause susceptibility-induced magnetic field changes

(123-125). The resulting signal changes in the FMRI time-series are an order of

magnitude larger than movement-induced spin-history signal changes and may not be

linearly dependent on the motion parameters. Regardless, this method of motion

correction enjoys widespread acceptance.

Stimulus-Correlated Motion

Some FMRI paradigms require overt word generation in response to auditory or

visual stimuli (127, 128). Speech involves movement of pharyngeal muscles, especially









tongue and jaw, which have been demonstrated to change the susceptibility-induced

magnetic field distribution of the brain (124). The greatest magnetic field changes due to

speaking occur in the inferior and frontal regions of the brain, decreasing rapidly towards

the superior and dorsal edges. The changes in the magnetic field cause pixel shifts in EPI

FMRI time-series images (113) and blurring in spiral FMRI time-series images (114).

The effects of pixel-shifts (or blurring) are more pronounced at the brain edges and other

high image contrast boundaries, where large spatial gradients in image intensity exist.

Voxels at these regions may exhibit as much as 100 % stimulus-correlated signal

changes. Thus, after statistical signal processing they might show false positive activation

with statistical significance similar to or higher, than voxels exhibiting BOLD signal

change.

These changes in magnetic field can occur even if the part of the head being

imaged is perfectly still. In fact, Yetkin and collaborators (123) found changes in the

magnetic field distribution of a homogenous copper sulfate (CuSO4) solution phantom

when a separate CuSO4 solution phantom was moved in its vicinity but outside the field

of view (FOV) of the RF coil. Thus signal changes due to speech-engendered stimulus-

correlated motions (SCMs) will not be compensated by conventional image registration

algorithms (75-77). Also SCM associated with speech can be dependent on what is

generated overtly. For instance, Bim observed (124) that the generation of the word 'one'

caused almost double the change in the magnetic field distribution when compared to the

word 'two' for a normal human control brain at Bo = 1.5T. Thus methods involving

motion-parameter-regression (117) also may not adequately correct for SCM signal

changes associated with overt word generation. This is because such methods assume a









linear relationship between motion and corresponding signal changes and are also

predicated on the assumption that most of the signal changes due to motion are due to

changes in the spin-excitation history and not local magnetic field distribution changes.

SCM-Ignoring Images

The major portion of signal changes due to speech-related SCM occurs in the first 4

or 5 seconds after speech (124-125). The BOLD hemodynamic response to cognitive

processes typically exhibit a delay of 3-6 seconds before onset and the peak is reached

only after 4-6 seconds after that (30). Thus, assuming one is interested in studying the

brain activation signal changes subsequent to overt production, the inherent difference in

the time scales of BOLD and SCM-related signal changes can be used to mitigate the

effects of SCM. This argument has been used by certain groups (127-128) to ignore (127)

or screen using temporal phase (128) signal changes during the first few images after

speech. This method may not be optimal if there is a significant overlap between the

time-courses of SCM and BOLD related signal changes (125, 129). In FMRI studies

involving patients with language deficits, the time lag between stimulus delivery and

overt production can be much longer and more unpredictable than in controls (130). For

these cases patient response-locked data analyses are more suitable than language-

stimulus-cue-locked timing (131). In such cases, ignoring (or screening) images after

speech can lead to sub-optimal detection and estimation of BOLD signal changes,

especially in brain regions where the cognitive processes start before overt production.

With respect to ignoring a few images after overt word generation, there is also the

caveat that for whole-brain FMRI with nearly isotropic voxels, the imaging constraints

restrict the minimum allowable TR to between 1.5 and 2 seconds. Consequently the

desirability of imaging the complete BOLD HRF might necessitate adoption of a protocol









where only one or two images after enunciation are ignored (screened). This length of

time may not be sufficient to eliminate all the effects of SCM.

SCM-Detrending

As mentioned before the voxels most affected by the SCM lie on the brain edges

and other high-contrast boundaries. Birn and collaborators (125) performed single event

FMRI studies of speaking, swallowing, jaw clenching and tongue movement and found

SCM-related signal changes at voxels near the brain edge of similar statistical

significance to BOLD activation voxels in the areas of motor cortex involved in the

above-mentioned tasks. They found that orthogonalizing all the voxel time-series in the

FMRI dataset with respect to SCM signal changes resulted in functional activation maps

with reduced SCM artifacts.

This method is sensitive to the time evolution of the SCM-related and

hemodynamic responses. If the BOLD HRF and the SCM signal changes are not well

resolved, the application of this method has been shown, by our group (129) to result in

loss of sensitivity for detecting brain activation. This situation can arise, for example, at

voxels in brain areas responsible for preparation for the word generation task. FMRI

studies of patients with language deficits require adoption of a data analysis protocol

based on patient responses. The time lag between stimulus delivery and patient response

is much greater in such patients. Use of a non-selective global detrending procedure as

described above (125) can result in loss of information about brain processes related to

preparation of the overt response in such cases.

Other Mechanistic Methods

There are a few other methods for dealing with stimulus-correlated motion in

FMRI time-series. Some authors have argued that the SCM artifacts can be somewhat






47


idiosyncratic and vary across individual participants (118, 127). Thus the effects of the

SCM will be mitigated if the FMRI data are averaged across a group of participants. This

method may not have the generalized applicability it is purported to posses (118, 127).

Salvador and collaborators (126) have suggested that masking all activated voxels

which lie on regions of high image intensity gradients. This method can have the effect of

eliminating cortical activation along with SCM-related activation since a significant

amount of cortical regions in the brain lie near high-contrast boundaries.














CHAPTER 4
TASK CORRELATED MOTION NOISE REDUCTION METHODS

In this chapter a new selective detrending method for reducing noise due to

stimulus-correlated motion in FMRI time-series of overt word-generation paradigms is

advanced. A framework is introduced to evaluate this method as well as compare its

performance with three other methods of SCM-related artifact reduction in event-related

overt word-generation FMRI paradigms: 1) motion parameter regression (117, 118), 2)

ignoring images during speech (127) and 3) non-selective detrending (125). Since there is

generally a significant delay between the presentation of neuronal stimulus and the

performance of a overt word generation task among patients, the speech-related artifacts

in the FMRI time-series should be more appropriately termed task-correlated (instead of

task-correlated). Also, since the patients' and the control subjects' data analysis are

presented in the same framework the term task-correlated motion (TCM) will be adopted

instead of the term more commonly used in FMRI literature, stimulus-correlated motion

(SCM).

Selective Detrending

Task-correlated motion due to movements involved in verbalizing lead to

significant changes in the FMRI signal (123-125). These artifactual increases/decreases

in signal intensity are manifested as false-positive activations in high contrast boundaries

in or outside the brain. Since the origin of signal changes due to speech related TCM is

mainly attributed to susceptibility profile fluctuations, the shapes of the time courses of

the signal changes in the brain due to speech-related TCM and of the signal evolution at









high-contrast boundaries characteristic of large magnetic susceptibility gradients should

have some similarities (123-125). Thus it should be possible to adequately represent most

of the TCM-related signal changes in the dataset with the signal changes from a few

representative voxels selected from high contrast boundaries outside or on the brain. The

signal changes due to speech-related TCM in all affected voxels should be representable

as a whole or in part by the selected set of voxels.

The method of Birn et al. (125) detrends all the voxel time-series in the FMRI

dataset of components proportional to all the selected TCM voxel time-series, using a

linear least-squares method. This has the undesirable effect of detrending brain activation

related BOLD MR signal along with TCM-related signal in voxels where the BOLD

signal has a significant overlap with net TCM-related signal change of all chosen TCM

voxels.

The selective detrending method introduced here endeavors to overcome this

drawback by examining voxels for TCM-related signal changes and performing the

detrending only if certain criteria (developed to maximize false-positive TCM noise

reduction as well as true-positive BOLD signal retention) are satisfied. It would be

remunerative to recall that the magnetic field changes due to speech-related TCM are

strongest in the inferio-frontal regions of the brain and decrease rapidly along the

inferior-superior direction as well as anterior-posterior direction (124). Thus, detrending

all voxels, non-selectively, of components proportional to all the representative TCM

time-series will tend to be overly conservative. A more attractive approach would be to

examine each voxel for presence of significant corruption due to task-correlated motion

(as characterized by the representative set of TCM time-series) and detrend selectively.









Both the non-selective detrending method as well as the method of ignoring images

have the potential to decrease the significance of activation of true-positive BOLD MR

voxels along with the false-positive TCM corrupted voxels. There are two instances when

this situation can arise. The first case is encountered in voxels which do not exhibit a

significant delay to onset in their hemodynamic response. There is some recent literature

citing that voxels exhibiting capillary BOLD activation localized to brain activation sites

exhibit smaller delays while voxel HDRs having a significant venous BOLD component

tend to have a more delayed and sluggish response (132). The second situation arises in

language FMRI paradigms in aphasic patients using subject response-locked stimuli.

Since aphasia patients, before therapy, tend to exhibit long pauses of up to 10 seconds

before generating a word to a semantic cue, the BOLD signal changes driven by the brain

processes involving response preparation may significantly overlap with subject response

correlated speech related TCM signal changes.

Thus a good detrending procedure should have the property of decreasing TCM

signal changes as much as possible while leaving BOLD MR signal changes largely

intact. This can be accomplished by selecting an adequate set of (phase offset) BOLD

MR signal change voxels, examining each voxel time-series for presence of BOLD MR

signal changes characterized by the representative voxels, and taking care not to decrease

the BOLD component in them if and when selective detrending is performed on them.

The next section describes the implementation of the detrending procedure.

Selective Detrending: Methods

In this section the methods used in the application of the selective detrending to

reduce TCM noise in event-related overt FMRI paradigms in controls as well as patients









will be explained. The paradigm is slightly different for aphasia patients due to their

inability to generate words fluently.

Subjects and Task

Two aphasia patients (one female and one male: ages 60 and 70) with left

hemisphere stroke were scanned twice, once before rehabilitation therapy and once after

therapy. This yielded four FMRI datasets to which the noise reduction methods could be

applied. The patients performed an event-related overt word-generation task, for which

they were asked to provide single-word responses to semantic category cues. The inter-

stimulus interval between category cues was 24.9, 26.6, 28.2 or 29.8 sec, corresponding

to 15, 16, 17 or 18 images, assigned in a pseudo-random manner. The patients underwent

rehabilitation treatment in between the pre- and post-therapy scans. The rehabilitation

treatment was designed to engage right-hemisphere intention mechanisms to facilitate

word finding and consisted of patients naming pictures shown on a computer monitor,

under the tutelage of therapists.

In addition to the aphasia patients, four healthy control subjects (three female and

one male: ages 50-70) were also scanned with a similar event-related overt language

FMRI paradigm. The subjects were asked to provide single-word responses to semantic

category cues. The inter-stimulus interval between category cues was 16.6, 18.3, 19.9 or

21.6 sec, corresponding to 10, 11, 12 or 13 images, assigned in a pseudo-random manner.

Image Acquisition

For patients, low resolution functional MR images were obtained using a 1-shot

forward spiral sequence (18). Thirty-two 4-4.5 mm thick sagittal slices covering the

whole brain were acquired. The repetition-time (TR) was 1660 msec, the echo-time (TE)

was 18 msec, the flip angle (FA) was 70 and the field of view (FOV) was 200 mm. The









image matrix size after interpolation was 64 x 64 and spatial resolution was 3.1 mm x 3.1

mm x 4-4.5 mm. Five functional runs were acquired with 161 images in each run, 1.66

sec per image. For anatomic reference, a high resolution T1-weighted 3D spoiled gradient

recalled (SPGR) sequence was acquired with scanning parameters: 240 mm FOV, 256 x

256 image matrix, 0.9 mm x 0.9 m x 1.3 mm resolution, TR = 23 msec, TE = 7.7 msec

and FA = 250. For angiographic reference, a 2D SPGR time-of-flight (TOF) MR

angiogram was obtained with scanning parameters: 200 mm FOV, 256 x 256 image

matrix, 0.78 mm x 0.78 m x 4-4.5 mm resolution, TR = 170 msec, TE = 4.9 msec and FA

= 50. The subject responses were monitored and coded with Cool EditTM software into

two categories, "correct" and "other" responses. The data analysis was performed with

AFNITM (85) and MatlabTM software.

The image acquisition parameters were the same for the normal subjects, the only

change being that the functional runs were each 111 images long. Also, the categorization

of the subject overt responses into "correct" or "other" was moot since the patients were

able to answer all the semantic queries correctly.

Data Analysis

The five functional runs were registered to a common base-image (the last image of

the last run), detrended of linear trends and concatenated to give a 805-image time-series

(555-image time-series for controls). To estimate the TCM-related signal changes, all the

subject responses (both "correct" and "other") were pooled together and an overt-

response locked stimulus vector was constructed. This vector had 805 (555 for controls)

data-points, all zero except the ones corresponding to images in which there was an overt

response.









Deconvolution and Regression

For each voxel, the signal was considered to be the result of a convolution of the

overt-response locked stimulus vector with the voxel impulse response (IRF) plus a

constant baseline and a white-noise term. Fifteen lag impulse responses were

deconvolved for each voxel from the knowledge of the observed voxel FMRI time-series

and the stimulus vector. The deconvolution analysis was performed as described in

Chapter 2. The significance of activation at each voxel was assessed through the use of a

General Linear Model (GLM). The details of the GLM are as follows:

Ho : Z, = Yo + E,
P [4.1]
H :Z, = + hm fn,, +
m=0

where Zn is the voxel time-series, yo is the constant baseline parameter under the baseline

model, fo is the constant baseline parameter under the full model, and the summation

denotes the discrete-time finite-lag convolution of theftt, the stimulus vector and h(t),

the IRF over = 15 lags (p = 12 lags for controls), en is the white noise component and N

is the number of time-points in the time-series. The significance of activation (i.e.

rejection of the null hypothesis) was assessed through the calculation of the F-statistic for

regression. The coefficient of determination R2 was also calculated. R2 expresses the

goodness of fit and can be thought of as the ratio of the variance in the time-series that

can be ascribed to the full model to the total variance of the time-series.

Estimation of the TCM Signal Changes

Speech-related false positive activation due to TCM occurs at/near high contrast

boundaries on or outside the brain (124, 125). They are also more pronounced in the

inferior and frontal regions of the brain (124) and have some distinct characteristics in









that most of the noise due to TCM occurs in the first few images during and after speech

(123-125). The fluctuations are generally a sharp increase/decrease in signal during and

just after speech. Thus, examining voxel IRFs on or near high contrast boundaries on or

outside the brain, for sudden signal changes, above the threshold selected for inferring

brain activation will lead to characterizations of different forms the TCM-related signal

changes take. Since signal changes due to TCM have a common origin, it is reasonable to

expect that a handful of selected TCM voxels can form an adequate representation of

TCM-related signal changes in the brain.

Ten to fifteen (depending on the situation) distinct voxel impulse responses at/near

high contrast boundaries, on/outside the brain, showing signal changes above the

threshold selected for inferring brain activation, were selected to adequately characterize

TCM IRFs in the FMRI dataset. Figure 4.1 illustrates this procedure for the case of a few

TCM IRFs. The chosen TCM IRFs were convolved with the overt response-locked event

vector to form the corresponding 805-image (555-image for controls) TCM time-series.








1 /







Figure 4.1: Activation map overlaid on a low-resolution spiral FMR image. The red
voxels correspond to R2 > 0.2 and the yellow voxels denote R2 > 0.3. The
yellow arrow points to the voxel IRFs. The central voxel in the grid shows a
selected TCM IRF.









Choosing Representative BOLD HRFs

In order to optimize the 'retention of true-positives' capability of the selective

detrending method, a few (3 or 4) representative estimated BOLD hemodynamic

responses were selected from the FMRI dataset. The chosen BOLD HRFs activated

above the threshold selected for inferring brain activation and spanned the possible delays

(phase of onset of hemodynamic responses) in the dataset. The criterion used in selecting

the voxels for detrending involved computation of cross-correlation coefficients of the

voxel IRFs with the selected representative BOLD HRFs. The computed cross-

correlation coefficients acted as a test of whether BOLD MR signal was being reduced

(as is explained in the next section). Hence 3-4 representative BOLD HRFs were

sufficient to characterize true positive BOLD voxels.

Selective Detrending Algorithm

For each 16-image voxel IRF (13-image IRF for controls) in the FMRI dataset, the

cross-correlation coefficient CCTrc of the voxel IRF with each of the representative TCM

IRFs was calculated. Also the representative TCM IRF for which the absolute value of

the CCrcm was a maximum was found. This value was employed as an indicator of false-

positive TCM corruption in the voxel time-series. For each 16-image voxel IRF (13-

image IRF for controls) in the FMRI dataset, the cross-correlation coefficient CCBOLD of

the voxel IRF with each of the representative BOLD HRFs was also calculated. Also the

representative BOLD HRF for which the value of the CCBOLD was a maximum was

found. This value was employed as an indicator of true positive BOLD MR signal in the

voxel time-series. The selective detrending algorithm endeavored to maximize the

reduction of false positive TCM signal as well as the retention of true positive BOLD MR

signal. To achieve this, each voxel time-series was detrended of components









proportional to the maximally correlated representative TCM time-series in one of three

different ways depending on the voxel IRF's correlation with the representative TCM

time-series and the selected BOLD time-series:

Case 1: if max(abs(CCTcM)) > 0.5 and max(abs(CCTcM)) > CCBOLD + 0.2

then the voxel time-series was detrended of components proportional to the

corresponding representative TCM time-series using linear least-squares fit (100). The

implicit assumption is that if the voxel time-series satisfies these criteria most of the task-

correlated signal changes in it are TCM-related.

Case 2: if max(abs(CCTcM)) > 0.5 and CCBOLD + 0.2 > max(abs(CCTcM)) > CCBOLD

then the voxel time-series was detrended of components proportional to a corresponding

more temporally localized representative TCM time-series formed by considering only

the first three images in the representative TCM IRF during construction. The detrending

was performed only if the norm of the residuals of the fit of the first three images of the

voxel IRF with those of the representative TCM IRF was less than a set value

resnormTcM. The implicit assumption here is that if the voxel time-series satisfies these

criteria, there is enough likelihood of presence of both BOLD MR signal and TCM signal

in it to merit a more localized examination of its epochal signal changes. Since the TCM

signal changes occur mostly in the first three images after speech, detrending components

proportional to the more localized TCM time-series (given there exists the requisite fit

between the voxel IRF and the TCM IRF) is anticipated to reduce the motion corrupted

parts of the BOLD MR signal changes in case of presence of both BOLD and TCM

signal changes or decrease the major fluctuations in signal due to TCM in case the voxel

time-series mainly consist of TCM signal changes. For the datasets studied resnormrcM









0.15, corresponding to a p-value for the fit more than 0.95 between the voxel IRF and

TCM IRF, was adequate in achieving the mentioned goals.

Case 3: if max(abs(CCrcM)) > 0.5 and max(abs(CCrcM)) < CCBOLD

then the voxel time-series was detrended of components proportional to a corresponding

more localized representative TCM time-series formed by considering only the first three

images in the representative TCM IRF during construction. The detrending was

performed only if the norm of the residuals of the fit of the first three images of the voxel

IRF with those of the representative TCM IRF was less than a set value resnormBoLD. The

assumption here is that if the voxel time-series satisfies these criteria it mainly consists of

BOLD signal changes, the retention of which outweighs the need for reduction of TCM

signal changes (if they exist). Hence, the criterion for the fit is more stringent. For the

datasets studied resnormBoLD = 0.003, corresponding to a p-value of more than 0.999

(133) was adequate to achieve the set goals.

The above criteria were chosen to maximize the elimination of TCM-related signal

as well as the retention of BOLD MR signal. They rely on prior empirical observations

on BOLD MR signal and TCM-related signal (30,123-125). The first part of the

algorithm seeks voxels which are presumably affected by TCM alone. These voxel time-

series are detrended of components proportional to the maximally correlated

representative TCM time-series. The selection criteria used to detect these voxels require

a minimum threshold of 0.5 (corresponding to a p-value of 0.05) for max(abs(CCrcM)) as

well as a degree of separability between max((abs(CCrcM)) and max(CCBOLD)). The

choice of 0.5 for the minimum threshold for cross-correlation is conservative. From the

datasets studied voxels exhibiting significant TCM corruption generally posses much









higher values for CCTrc. Figure 4.2 shows the activation map formed by max(CCTcM)

overlaid on the IRF dataset. It is apparent that voxels exhibiting significant TCM possess

high values of max(CCTcM). Most of the activated voxels seem to have a max(CCTcM) >

0.7.



















Figure 4.2: Activation map of the maximal absolute cross-correlation coefficient with
TCM CCTrc, thresholded by R2 > 0.1. The yellow voxels correspond to
max(CCTcM) > 0.7 and the red denotes max(CCTcM) > 0.5.

Case 1 also mentions the requirement of the presence of more correlation between

the voxel IRF with the TCM IRF than that with the BOLD HRF. This requirement was

introduced to ensure that voxels selected by this criteria possess mainly TCM signal

changes even if the max(abs(CCTcM)) and max(CCBoLD) are both more than 0.5. The

choice of 0.2 for separability between CCTrc and CCBOLD was conservative. Figure 4.3

(a) shows the distribution of the ratio of number of voxels undergoing non-selective

detrending for a given max(CCBoLD) threshold to the total number of voxels in the dataset

activated above the same threshold, for 3 different levels of separability between

max(abs(CCTcM)) and max(CCBoLD); 0.0, 0.1 and 0.2, on top of the criteria that the voxel









be more correlated with the TCM responses than the BOLD responses. Figure 4.3 (b)

shows the ratio of number of voxels undergoing non-selective detrending for a given

max(abs(CCTcM)) threshold to the total number of voxels in the dataset activated above

the same threshold, for the same levels of separability as Fig 4.3 (a). Examining Figure

4.3 (a), the curve for separability = 0.2 seems to indicate that roughly 10% of the voxels

with max(CCBOLD) z 0. 7 will undergo global detrending, where the voxels will be

detrended of components proportional to the maximally correlated TCM time-series. But

this corresponds to max(abs(CCrcM)) > 0.9, at which level the voxel has a strong

probability to be a TCM false-positive. At this level of separability, the Fig 4.3 (b) shows

that around 10% of voxels with max(abs(CCrcM)) z 1 are detrended of components to the

TCM time-series formed by considering only the first three images of the TCM IRFs.

The local detrending is by nature of its conception, less successful in reducing TCM

signal changes than the global detrending. Thus, examining the curves, it is apparent that

separability =0.2 condition, if anything enhances the probability of retaining true-

positive BOLD signal at the expense of diminished capacity to reduce false-positives.

The second criteria regarding temporally localized detrending is expected to compensate

for any attenuation in the false-positive reduction capacity. The results in the next chapter

support this assertion.

The second part of the algorithm examines voxels that show sufficient correlation

between both TCM and BOLD responses. These voxels are detrended only if the fit

between the first 3 images of their impulse response and the selected TCM IRFs is lower

than a set limit. The set limit is more stringent for those voxels which are sufficiently

correlated to both TCM and BOLD responses and in addition show more correlation with










the chosen BOLD HRFs. From the description, it is apparent that the proper

characterization of the BOLD and TCM responses is critical to the success of the method.


1 1 --.--
A
A 1 1
S0.8 0.8 __
o0 o0
6 0.6- 0.6
-LO
E
Z E
0.4 0.4

| 0.2 CC >cm>C old+ 0.1 >c \ 0.2





for three different levels of separability, 0.2 (blue), 0.1 (green) and 0.0
.tcm old
02t(hresho%~ma(CB&6o ) 0.8 1 0 O SAreSholi4a(ab -c ))8 1

(a) (b)



Figure 4.3: Distribution of number of voxels undergoing non-selective detrending for a
given max(CCBoLD) as a fraction of the number of voxels at that max(CCBoLD)
for three different levels of separability, 0.2 (blue), 0.1 (green) and 0.0
(magenta) (a). Similar distributions for max(abs(CCTcM)) (b).

Analysis of Detrended Time-Series

The analysis of the detrended time-series proceeded in the same way as the

undetrended time-series analysis. For each voxel the signal was considered to be the

result of sum of convolutions of the "correct" response-locked stimulus vector and

"other" response-locked stimulus vector and their corresponding impulse responses, plus

a constant baseline and a white noise component. Fifteen lag impulse responses (12 for

normal control subjects) for each of the conditions were estimated from the knowledge of

the observed voxel FMRI time-series and the stimulus vectors.

For the GLM, the baseline model was considered to include a constant baseline and

the fitted signal due to "other" responses plus white noise, whereas the full model was

considered to include a constant baseline, the fitted signal due to "other" responses and










the fitted signal due to the "correct" responses plus white noise. In this way, the test-

statistics F and R2 quantified significance of"correct" response related signal alone.

Implementation of Motion Parameter Regression

Motion parameter regression (MPR) has been introduced in Chapter 3. Here the

methods to implement MPR in a GLM based deconvolution analysis framework are

described. The motion parameters for each image in the 805-image (555-image for

controls) time-series were obtained from the image-registration program. For each voxel,

the rigid-motion related signal at each scan was modeled as a quadratic function of the

motion parameters in that scan and the preceding scan (117, 118).The motion-related

signal was modeled as part of the baseline, along with the "other" response related signal

changes, so that the regression statistic reflected the activation due to "correct" responses

alone. The regression model (for patients) used is as follows:
6 6
Ha: Z, = bo+ r,nr +Mf, + Mn aJr r+M, Mr
rO r=O
15, 15 + E [4.2]
nhc + so, + h
p=O p=0
6 6
1 'o +/I-M 2 _M-2
H,: Z = bo + jMrn a +Mr _, r,n 'r rn 1_ /r
r=O r=O
15
+ s, h + En
p=0
where Mr,n is the motion parameter for the rth degree of freedom at the nth image, a, /, a'

and are fitted constants, sc and s are the "correct" and "other" response-locked

stimulus vectors and he and h are the corresponding estimated impulse response

functions. The impulse responses are estimated to 12 lags for the normal controls. The

regression F and R2 statistics were calculated for each voxel to quantify the significance

of activation related to the "correct" response stimulus.









Implementation of the Screening Images Method

The method of screening images during speech (127) uses the observation (123-

125) that most of the signal fluctuations due to speech occur in the first few images

during and after speech. This method was implemented in the context of a GLM based

deconvolution analysis by ignoring the zeroth and first lags while estimating the voxel

IRF. The regression model (for patients) used was as follows:

15 15
H,: Z, =b, + + s, h + sn, hp + E
p-2 p0 [4.3]
15
H0, Z,,=b,+ s h + E,
p=0

The "other" response related signal was modeled as part of the baseline. For the case of

normal controls the IRFs were estimated up to 12 lags. The activation statistics R2 and F,

quantify the significance of activation due to "correct" responses. It should be noted that

the signal changes occurring during the first two images after overt production do not

contribute to the activation statistic in this method, whether it is TCM-related or BOLD-

related.

Implementation of Non-Selective Detrending

The non-selective detrending method proposed by Bim et al. (125) also assumes

that the TCM-related signal changes are temporally resolved from BOLD MR signal

changes. This method has been described in Chapter 3.

In the present context, the implementation of the non-selective detrending method

followed that of the selective detrending method up to the part regarding estimation of

TCM IRFs. The difference is in the detrending procedure. In the non-selective detrending

all the voxels in the FMRI dataset are detrended of components proportional to all the

representative TCM time series using a linear least-squares method (100). Since this is









equivalent to detrending all the voxels in the FMRI dataset of components proportional to

sum of all the chosen TCM time-series only a few (5-6 as opposed to 10-15)

representative TCM time-series suffice. The detrended FMRI datasets were analyzed in

exactly the same manner as described in the selective detrending method.

Receiver Operating Characteristics

The difficulties in conducting conventional ROC analysis have been mentioned in

Chapter 2. Here the performance of the selective detrending method and its comparison

with the other three methods as well as the case of no noise reduction is conducted

through a modified ROC analysis procedure. The ROC procedure was used to measure

two complementary indications of efficacy 1) the reduction of the false positive voxels

outside the brain in the real FMRI datasets and 2) the retention of the true-positive voxels

inside the brain, with IRFs satisfying strict criteria for BOLD hemodynamic responses.

Reduction of False Positives

The voxels outside the brain that possess R2 or F values above the threshold

selected to infer brain activation can be trivially considered to be false-positive voxels at

that threshold. This is reinforced by considering voxels a sufficient distance outside the

brain such that there are no effects due to large veins at the boundaries of the brain. The

signal intensities in a low-resolution spiral MR image decrease rapidly away from the

brain edge. By constructing signal-intensity histograms, the high intensity intra-cerebral

voxels can be separated from the extra-cerebral voxels. Since TCM-related signal

changes are accentuated at high contrast boundaries outside the brain created by CSF,

cranium, air cavities, and scalp (134), the chosen test-bed can be considered to contain a

fair population of TCM voxels. A further reduction of the test-bed, using the knowledge

that TCM-corrupted voxels show more fluctuation in the early part of the IRF, can









increase the proportion of TCM-corrupted voxels in the test-bed. Thus, the distribution of

number of detected voxels as a function of threshold R2 or F-statistic can be used to

compare the efficacy of motion correction of all the four methods.

For each FMRI dataset, an intensity-based brain mask was created using an

iterative outlier-reduction method. This is implemented as a program in the AFNIrM

software. This program also allows for dilating the brain mask by the requisite number of

voxels to include regions just outside the brain which are low-intensity but exhibit venous

activation arising from large peripheral veins. Voxel IRFs (a sufficient distance outside

the brain to preclude venous effects) exhibiting larger fluctuation in the first 5 images

relative to the last 11 (7 for controls) images were chosen to form the test-bed of false-

positive activation. The distribution of the number of voxels in the test-bed detected as a

function of threshold R2 was constructed for all the four methods as well as for the case

of no motion correction.

An important property of the test-bed of false positives is that the method of

obtaining the test-bed is independent of the algorithm to estimate false positive TCM

signal changes. An assumption implicit in construction of the test-bed is that TCM signal

changes in false-positive voxels outside the brain are representative of the TCM signal

changes at high contrast boundaries on the brain. This assumption is valid when the TCM

signal changes of voxels in the brain are not corrupted by BOLD signal changes.

Retention of True Positives

The intra-cerebral voxel IRFs, specified by the brain masking method, were fitted

to a generic hemodynamic response curve. This curve, which is included as part of the

AFNITM software, is parameterized in terms of amplitude, delay-time, rise-time and fall-

time. The functional form of the curve is given by









h(t) = tanh tan f +1 tD < +R
S2 tR

h(t) = tanh tanr 1.6 ( +t tD 0.8 +1 tD + tR < t tD + tR +tF [4.4]
2 2 tF
h(t) = 0 ot//i n iie



where A is the amplitude, tD, tR and tF are delay-time, rise-time and fall-time of the

hemodynamic response respectively. This function is more malleable to be fitted to

estimated IRFs than gamma-variate functions (especially at low temporal resolutions). It

also has the advantage of being parameterized in terms of temporal aspects of the HRF, a

useful feature that comes of use while screening IRFs. The IRF of each voxel was fit to

the generic hemodynamic response function (HRF) by means of a nonlinear optimization

method using MatlabTM.

X = h(t,a)-I(t) 2 (h(t,,a)-I(t,)) [4.5]


where X2 is the cost function that was minimized by varying the parameter set a which

consists of the parameters amplitude, tD, tR and tF, t is time discretized by the index i, h is

the generic HDR described in Equation 4.4 and I is the voxel IRF. The parameters were

varied iteratively till the cost function was minimized using a large-scale algorithm. This

fitting was carried out with the Isqcurvefit function of MatlabTM. Figure 4.4 shows the

estimated hemodynamic response of a true-positive BOLD voxel in the right medial

frontal region of patient 1 (pre-therapy) dataset (blue) and the corresponding fit (green)

from employing the non-linear optimization method. The graph shows the evolution of










the curves over the first 20 seconds (which is the part of the IRFs relevant to the selection

criteria).


20
Voxel IRF
15 -Cox Fit


10


5

0


-5
0 5 Tie (sec) 10 15


Figure 4.4: Estimated hemodynamic response of a true positive right medial frontal voxel
of patient 1 (pre-therapy) dataset (blue) and the corresponding fit to a generic
hemodynamic response (green).

The maxima of the first 4 images of each voxel IRF, max(IRF _4) and the

corresponding minima, min(IRFi_4) were also calculated. Intra-cerebral voxel IRFs

satisfying the following criteria formed the test-bed for hemodynamic-like voxels.

A>0

tD + R + tF > 6
tD + t <11
tR + t > 4 [4.6]

tF, tR >1
tD <4
max(IRFl4 ) > 1.2 min(IRF4 )

where the terms are as defined above. Time is expressed in units of image TR (i.e. 1

1.66 sec). The set of criteria relating to amplitude and time were chosen so as to eliminate

TCM-related IRFs. The penalty paid in terms of screening some BOLD HRFs was

compensated by the fact that the chosen test-bed was devoid of TCM voxels. The






67


distribution of the number of voxels in the selected test-bed detected as a function of

threshold R2 was constructed for all the four methods as well as for the case of no motion

correction. The distributions were constructed to provide a means of comparing the true-

positives retention capabilities of the four methods to retain true positive voxels.














CHAPTER 5
RESULTS AND DISCUSSION

In this chapter the results of the application of the selective detrending method as

well as the other methods of reducing noise arising from task-correlated motion are

presented and compared. The implications of the results on data analysis of event-related

overt word-generation FMRI paradigms are discussed.

Results

In the following pages the omnibus results from the application of the four methods

of TCM noise reduction reviewed, on FMRI datasets involving event-related overt

generation paradigms in four patient datasets (two patients scanned twice, pre and post

treatment) and four control subject datasets, are presented in the form of statistical

activation maps parameterized by the coefficient of determination, R2. The case of no

noise correction is also provided for reference. In addition the results from the modified

ROC analysis, i.e., the false-positives reduction capacity as well as true-positives

retention capacity, examined based on separate voxel test-beds, are also provided for all

the four patient datasets and the four control subject datasets. In the figures of the R2-

activation maps green arrows point to selected BOLD HRF AFNI-grabs and blue arrows

point to selected TCM IRF AFNI-grabs. In the graphs for the modified ROC analysis, the

symbols 'MLO' and 'ML2' stand for min-lag (the lowest 'lag' to which the impulse

response is estimated) set to 0 and 2 respectively. Also all the activated voxels (in red) in

the selective detrending activation maps posses BOLD hemodynamic-like responses.









INI


x,


Figure 5.1 Activation maps thresholded at R2 > 0.2 for patient-1 (pre-scan) with no TCM
noise-reduction (a), with selective detrending (b), with motion parameter
regression (c), with ignoring 2 images after speech (d) and with non-selective
detrending (e). The blue arrows indicate TCM voxel IRFs and the green
arrows BOLD voxel IRFs.









Patient 1 (Pre-Treatment)

The Figure 5.1(a) shows a lateral sagittal slice of a high-resolution T1-weighted

anatomic image with the R2-activation map overlay for the aphasia-patient-I (under pre-

treatment condition), without TCM noise reduction. Some of the estimated TCM IRFs

and BOLD HRF for selected voxels are also shown. Figure 5.1(b) shows the map with

selective detrending. All the voxels shown activated in the selective detrending map

exhibited BOLD HRF responses. The green arrow in the figure points away from

activation at the inferior frontal sulcus (IFS), which is implicated in word-generation. The

selective detrending method is able to attenuate the motion-corrupted portion of the IFS

hemodynamic response. Figures 5.1 (c-e) show the R2-activation map for the same patient

under the same scan after motion parameter regression, ignoring two images after speech

and non-selective detrending. All the voxels activated above a threshold R2 > 0.20

(corresponding to p-value < 10-20) shown in red. All the activated voxels in the selective

detrending map (Figure 5.1 (b)) exhibited BOLD HRF similar to the one shown by the

green arrow in Figure 5.1 (b). Figure 5.1 (a) shows a lot of TCM corrupted false-positive

voxels, particularly in the inferior and frontal regions. A few representative TCM impulse

responses are shown by the blue arrows. From the figures (5.1 (a-e)) for the 5 cases it can

be noted that for this subject the motion-parameter regression (MPR) method performs

poorly with regard to TCM noise reduction.

The method of ignoring the first two images during speech (Figure 5.1 (d))

performs better than the MPR method. However it still exhibits some false-positive TCM

voxels as marked by the blue arrows. The non-selective detrending method (Figure 5.1

(e)) is sub-optimal in this case. This method seems to reduce the true-positive BOLD

hemodynamic signals in the inferior frontal sulcus.









The selective detrending method performs better than all other techniques. Not only

is it able to reduce TCM-related false positive activation, but also it is also able to retain

the brain activation voxels corrupted by motion artifacts, and to remove parts of the

signal time course originating from motion. Figure 5.1 (b) shows one such example for

the case of an inferior frontal sulcus voxel (which is implicated in semantic word

generation). The sudden large fluctuation in the signal at the onset of the response caused

by task-correlated motion is attenuated to give a more regularized hemodynamic response

as shown by the green arrow.

The above statement is quantified in the modified ROC analyses illustrated in

Figures 5.2 (a-b). The efficiency of TCM noise reduction of all the four methods as well

as for the case of no motion correction is shown in Figure 5.2 (a) for aphasia patient-1

(pre-scan). Ideally, all the voxels in the 'false-positives' test-bed should go to zero (or

more accurately go towards the null distribution values). The selective detrending method

(denoted 'dtsel' and represented by the magenta curve) performs almost as well as the

non-selective detrending method (denoted 'dt' and represented by the red curve) in terms

of reducing TCM false-positives. The method of ignoring images (ML2; black) is less

optimal whereas the motion-parameter regression method (MPR; green) seems to have

very little effect on TCM voxels. The case with no motion correction (MLO; blue) is also

shown for reference.

Figure 5.2 (b) shows the effect of each of the TCM noise reduction treatments on

the test-bed of the true-positive BOLD HRF-like voxels. Since the criteria for inclusion

into the test-bed precludes the occurrence of speech-related TCM voxels, ideally a given

treatment should have the same distribution as for the case of no noise correction. There










does not seem to be much difference in the true-positives retention capacity between the

MPR, ML2 and selective detrending methods. The non-selective detrending method

seems to suffer from a loss of sensitivity to BOLD MR signal. By considering this graph

along with the TCM noise reduction graph of Figure 5.2 (a) one can state that the

selective detrending method performs the best in terms of TCM noise reduction and true

positive BOLD HRF retention.


1 1
MLO MLO
ML2 ML2
0.8 MPR 0.8 MPR
Sdtseldtsel
0.6 dt dt
0.6 0.6dt
A
0.4 o 0.4

0.2 0.2

0
0.05 0.1 0.15R2 0.2 0.25 0.3 0.1 0.2 0.3 0.4
thR
(a) (b)



Figure 5.2: Fraction of voxels detected as a function threshold R2 for (a) the false-
positives test-bed and (b) the true-positives test-bed for aphasia patient 1 (pre-
therapy scan). The blue curve (MLO) represents the case of no motion
correction, the black curve (ML2) represents the method of ignoring the first 2
images after speech, the green curve (MPR) represents the motion-parameter
regression method, the magenta curve (dtsel) represents the selective
detrending method and the red curve (dt) represents the non-selective
detrending method.

The superior performance of the selective detrending method when compared to the

method of ignoring images and the non-selective detrending method can be

comprehended by examining Figure 5.3. The figure on the left, 5.3 (a), shows some

representative TCM corrupted impulse responses chosen from voxels outside the brain

for aphasia patient 1 (pre-therapy scan).















150

100

50

S0
2I)
-50

-100

-150

-200
0 5 e ( s15 20
ioIme (sec)


20




-20


-40

_6= 0


25 0


5 Tme (secl


Figure 5.3: Some representative TCM-related voxel IRFs (a); Some representative BOLD
HRFs (b) from aphasia patient 1 (pre-therapy scan) data.


-5 0 5 10 15 20 25
Time (sec)


'ime (sec)


Figure 5.4: The effect of the methods of noise correction on a right medial-frontal voxel
BOLD HRF exhibiting an 'early' response for patient 1 pre-therapy scan (a).
The effect of the methods of noise correction on a right inferior sulcus voxel,
exhibiting both BOLD and TCM signal changes (b) for the same scan. The
no-correction curve is hidden by the selective detrending curve in both
figures.


20 25









Some of the TCM IRFs (e.g. the red curve) are shifted relative to the time of onset. Some

of responses (blue) have significant longer lasting effects. Thus the method of ignoring

two images after speech may not adequately attenuate the effects of TCM in these voxels

and false-positive activation may remain even after the correction algorithm is executed.

Increasing the number of ignored images is not an attractive option, in that this may lead

to loss of sensitivity to true-positive BOLD responses (as can be inferred from Figure

5.3). In fact one perceives a potential loss of sensitivity to some true-positive BOLD

HRFs (especially the green and red curves in Figure 5.3 (b)) even for the ML2 method.

An analogous analysis can be made for the case of the non-selective detrending

method. Attenuating the effects of TCM in the voxel IRFs shown in Figure 5.3 (a) may

lead to attenuation in true-positive BOLD signal in some voxels as represented by the

curves in Figure 5.3 (b). This is the source of the sub-optimal true-positives retention

capacity of the non-selective detrending method.

Figure 5.4 (a) shows the effect of applying the reviewed methods of TCM noise

reduction on a BOLD activation voxel in the right medial-frontal region of aphasia

patient 1 (pre-therapy scan). This voxels hemodynamic response has an 'early' onset.

This could be due to the overt response-locked stimulus vector used in the analysis.

Presumably this voxel covers neuronal sources that activate prior to the overt-response,

or the voxel HRF has zero delay to onset and the resolution of the stimulus vector and

image acquisition is not sufficient to extract the early response. The blue dashed curve

(MLO-2) in Figure 5.4 (a) (which has been generated by shifting the response-locked

stimulus vector back by two images) suggests that the HRF has started prior to word-

enunciation. It is obvious from the Figure 5.4 (a) that the method of ignoring two images









during speech (ML2, black) suffers from a lack of sensitivity to the early portion of the

hemodynamic response, since the method ignores the first two images. The non-selective

detrending method (dt, red) removes BOLD MR signal in this voxel and hence is sub-

optimal. The selective detrending method (dtsel, magenta) does not perform any

detrending on this voxel and leaves the putative "early-onset" BOLD signal intact. The

motion parameter regression method (MPR, green) also does not suffer from loss of

sensitivity to BOLD MR signal in this case.

An added advantage of the selective detrending method is that it has the capacity to

at least partially tease apart TCM and BOLD signal changes in a brain activation voxel

that has been affected by both. Figure 5.4 (b) shows the voxel HRFs of an inferior frontal

sulcus voxel of patient 1 (pre-therapy scan). (This voxel has been marked by the green

arrow in the Figure 5.1 (b)). From the graph, in the curve representing no noise correction

(MLO, blue), one perceives a large initial fluctuation in signal (caused by TCM) and a

subsequent smooth hemodynamic response (caused by brain activation) The selective

detrending method (dtsel, magenta) is able to attenuate the TCM-related signal changes

resulting in a more regularized hemodynamic response. The motion parameter regression

method (MPR, green) does not have much affect on the voxel IRF. The non-selective

detrending method (dt, red) removes a lot of BOLD signal along with the TCM signal.

The method of ignoring two images during speech (ML2, black) performs almost as well

as the selective detrending method in this case.

Patient 1 (Post-Treatment)

The Figure 5.5 (a) shows a lateral sagittal slice of a high-resolution T1-weighted

anatomic image with the R2-activation map overlay for the aphasia-patient-I (under post-

treatment condition), without TCM noise reduction.
























(a)










(b) (c)









(d) (e)






Figure 5.5: Activation maps thresholded at R2 > 0.2 for patient 1 (post-therapy scan) with
no TCM noise-reduction (a), with selective detrending (b), with motion
parameter regression (c), with ignoring 2 images after speech (d) and with
non-selective detrending (e). The blue arrows indicate TCM voxel IRFs and
the green arrows BOLD voxel IRFs.









Some of the estimated TCM IRFs and BOLD HRF for selected voxels are also shown.

Figure 5.5(b) shows the map with selective detrending. All the voxels shown activated in

the selective detrending map exhibited BOLD HRF responses. Figures 5.5 (c-e) show the

R -activation map for the same patient under the same scan after motion parameter

regression, ignoring two images after speech and non-selective detrending. All the voxels

activated above a threshold R2 > 0.20 (corresponding to p-value < 10-20) shown in red.

All the activated voxels in the selective detrending map (Figure 5.5 (b)) exhibited BOLD

HRF similar to the one shown by the green arrow in Figure 5.5 (b) (which shows

activation in the motor strip). Figure 5.5 (a) shows a lot of TCM corrupted false-positive

voxels, particularly in the inferior and frontal regions. A few representative TCM impulse

responses are shown by the blue arrows. From the figures (5.5 (a-e)) for the 5 cases it can

be noted that for this subject the motion-parameter regression (MPR) method and the

ML2 method do not perform well with regard to TCM noise reduction. The non-selective

detrending method seems to reduce true-positive BOLD MR signal along with TCM

noise. The selective detrending method seems to work the best in terms of retention of

true-positives and reduction of false-positives.

Figure 5.6 (a) shows some representative TCM IRFs extracted from the patient 1

(post-therapy scan) dataset. There are a lot of similarities in the motion responses. Some

of the TCM IRFs (e.g. the red curve) are shifted relative to the time of onset. Some of

responses (blue) have significant longer lasting effects.

Figure 5.6 (b) shows the effect of applying the reviewed methods of TCM noise

reduction on a BOLD activation voxel in the right lateral-frontal region of aphasia patient

1 (post-therapy scan). This voxels hemodynamic response has an 'early' onset.











80

60

40


-20



-40

-60 10Time( 20
0 5 10 Time ( c) 20


0 5 T10 ) 15 20 25
Time (sec)


Figure 5.6: Some representative TCM-related voxel IRFs from patient 1 post-therapy
scan (a). The effect of the methods of noise correction on a right medial-
frontal voxel BOLD HRF exhibiting an 'early' response for the same dataset
(b). The no-correction curve is hidden by the selective detrending curve.


1

0.8

S0.6
A

S0.4
L .
0.2


0 ---
0.05 0.1


R2 0.2
th
(a)


0.25 R2 0.35


Figure 5.7: Fraction of voxels detected as a function threshold R2 for (a) the false-
positives test-bed and (b) the true-positives test-bed for aphasia patient 1
(post-therapy scan). The blue curve (MLO) represents the case of no motion
correction, the black curve (ML2) represents the method of ignoring first 2
images after speech, the green curve (MPR) represents the motion-parameter
regression method, the magenta curve (dtsel) represents the selective
detrending method and the red curve (dt) represents the non-selective
detrending method.











The blue dashed curve (MLO-2) in Figure 5.6 (b) (which has been generated by shifting

the response-locked stimulus vector back by two images) suggests that the HRF has

started prior to word-enunciation. It is obvious from the Figure 5.6(b) that the method of

ignoring two images during speech (ML2, black) suffers from a lack of sensitivity to the

early portion of the hemodynamic response, since the method ignores the first two

images. The non-selective detrending method (dt, red) removes BOLD MR signal in this

voxel and hence is sub-optimal. The selective detrending method (dtsel, magenta) does

not perform any detrending on this voxel and leaves the BOLD signal intact. The motion

parameter regression method (MPR, green) also seems to leave the BOLD MR signal

intact in this voxel.

The modified ROC analyses for this FMRI dataset is illustrated in Figures 5.7 (a-b).

The efficiency of TCM noise reduction of all the four methods as well as for the case of

no motion correction is shown in Figure 5.7(a) for aphasia patient 2 (post-therapy scan).

The non-selective detrending method (dt; red curve) performs the best in terms of

reducing TCM false-positives. The selective detrending method (dtsel; magenta)

performs better than the method of ignoring images (ML2; black) as well as the motion-

parameter regression method (MPR; green). The MPR and ML2 method curves look

similar. The case with no motion correction (MLO; blue) is also shown for reference.

Figure 5.7 (b) shows the effect of each of the TCM noise reduction treatments on

the test-bed of the true-positive BOLD HRF-like voxels. There does not seem to be much

difference in the true-positives retention capacity between the MPR, ML2 and selective

detrending methods. The non-selective detrending method seems to suffer from a loss of









sensitivity to BOLD MR signal. By considering this graph along with the TCM noise

reduction graph of Figure 5.7 (a) one can state that the selective detrending method

performs the best in terms of TCM noise reduction and true positive BOLD HRF

retention.

Patient 2 (Pre-Treatment)

The Figure 5.8(a) shows a medial sagittal slice of a high-resolution T1-weighted

anatomic image with the R2-activation map overlay for the aphasia-patient-2 (under pre-

treatment condition), without TCM noise reduction. Some of the estimated TCM IRFs

and BOLD HRF for selected voxels are also shown. Figure 5.8(b) shows the map with

selective detrending. All the voxels shown activated in the selective detrending map

exhibited BOLD HRF responses. The green arrow in the figure points away from

activation in the right anterior putamen region, which is implicated in word-generation.

The selective detrending method is able to attenuate the motion-corrupted portion of the

hemodynamic response. Figures 5.8 (c-e) show the R2-activation map for the same patient

under the same scan after motion parameter regression, ignoring two images after speech

and non-selective detrending. All the voxels activated above a threshold R2 > 0.20

(corresponding to p-value < 10-20) shown in red. All the activated voxels in the selective

detrending map (Figure 5.8 (b)) exhibited BOLD HRF similar to the one shown by the

green arrow in Figure 5.8 (b). Figure 5.8 (a) shows a lot of TCM corrupted false-positive

voxels, particularly in the inferior and frontal regions. A few representative TCM impulse

responses are shown by the blue arrows. From the figures (5.8 (a-e)) for the 5 cases it can

be noted that for this subject the motion-parameter regression (MPR) method as well as

the ignoring images method (ML2) show residual TCM-related false-positives event after

noise-reduction. The non-selective detrending method seems to reduce true-positive




































(b) (c)


(d) (e)


Figure 5.8: Activation maps thresholded at R2 > 0.2 for patient-2 (pre-therapy scan) with
no TCM noise-reduction (a), with selective detrending (b), with motion
parameter regression (c), with ignoring 2 images after speech (d) and with
non-selective detrending (e). The blue arrows indicate TCM voxel IRFs and
the green arrows BOLD voxel IRFs.


--PO


,:"











BOLD MR signal along with TCM noise. The selective detrending method seems to

work the best in terms of retention of true-positives and reduction of false-positives.

Figure 5.9 (a) shows some representative TCM IRFs extracted from the patient 2

(pre-therapy scan) dataset. There are a lot of similarities in the TCM responses. Some of

the TCM IRFs are shifted relative to the time of onset and some have significant longer

lasting effects.

Figure 5.9 (b) shows the effect of applying the reviewed methods of TCM noise

reduction on a right medial-frontal BOLD activation voxel in aphasia patient 2 (pre-

therapy scan). This voxels hemodynamic response has an 'early' onset. The blue dashed

curve (MLO-2) in Figure 5.9 (b) (which has been generated by shifting the response-

locked stimulus vector back by two images) suggests that the HRF has started prior to

word-enunciation. It is obvious from the Figure 5.9 (b) that the method of ignoring two

images during speech (ML2, black) suffers from a lack of sensitivity to the early portion

of the hemodynamic response, since the method ignores the first two images. There also

seems to be a slight decrease in the amplitude of the response for the ML2 curve. This

could be due to the use of an unbiased estimator in deconvolution analysis. The non-

selective detrending method (dt, red) removes BOLD MR signal in this voxel and hence

is sub-optimal. The selective detrending method (dtsel, magenta) does not perform any

detrending on this voxel and leaves the BOLD signal intact. The motion parameter

regression method (MPR, green) also leads to a reduced HRF amplitude.











60

40

20

-Fd 0

a -20

-40

-60

-80
0 5 Time (sec)10


0 5 10
Time (sec)


Figure 5.9: Some representative TCM-related voxel IRFs from patient 2 pre-therapy scan
(a). The effect of the methods of noise correction on a right medial-frontal
voxel BOLD HRF exhibiting an 'early' response for the same dataset (b). The
no-correction curve is hidden by the selective detrending curve.


1

0.8

0.6
A
rr
0 0.4
0.
0.2


0.1 0.15 R 0.2 0.25 0.3 0.04 0.1 0.15 R2 0.2 0.25 0.3
(a (b)
(a) (b)


Figure 5.10: Fraction of voxels detected as a function threshold R2 for (a) the false-
positives test-bed and (b) the true-positives test-bed for aphasia patient 2 (pre-
therapy scan). The blue curve (MLO) represents the case of no motion
correction, the black curve (ML2) represents the method of ignoring first 2
images after speech, the green curve (MPR) represents the motion-parameter
regression method, the magenta curve (dtsel) represents the selective
detrending method and the red curve (dt) represents the non-selective
detrending method.


15 20









The modified ROC analyses for this study is illustrated in Figures 5.10 (a-b). The

efficiency of TCM noise reduction of all the four methods as well as for the case of no

motion correction is shown in Figure 5.10 (a). The selective detrending method (dtsel;

magenta) performs almost as well as the non-selective detrending method (dt; red) in

terms of reducing TCM false-positives. The method of ignoring images (ML2; black) and

the motion-parameter regression method (MPR; green) look similar and are less optimal.

The case with no motion correction (MLO; blue) is also shown for reference.

Figure 5.10 (b) shows the effect of each of the TCM noise reduction treatments on

the test-bed of the true-positive BOLD HRF-like voxels. The distributions look similar

except for the non-selective detrending method. The non-selective detrending method

seems to suffer from a loss of sensitivity to BOLD MR signal. By considering this graph

along with the TCM noise reduction graph of Figure 5.10 (a) one can state that the

selective detrending method performs the best in terms of TCM noise reduction and true

positive BOLD HRF retention.

Patient 2 (Post-Treatment)

The Figure 5.11 (a) shows a lateral sagittal slice of a high-resolution T1-weighted

anatomic image with the R2-activation map overlay for the aphasia-patient-2 (under post-

treatment condition), without TCM noise reduction. Some of the estimated TCM IRFs

and BOLD HRF for selected voxels are also shown. Figure 5.11(b) shows the map with

selective detrending. All the voxels shown activated in the selective detrending map

exhibited BOLD HRF responses. The green arrow in the figure points away from

activation in the motor strip, which is implicated in word-generation. Figures 5.11 (c-e)

show the R2-activation map for the same patient under the same scan after motion

parameter regression, ignoring two images after speech and non-selective