NONRIGID REGISTRATION METHODS FOR MYOCARDIAL PERFUSION MRI AND CEREBRAL DIFFUSION TENSOR MRI LI CHAO NATIONAL UNIVERSITY OF SINGAPORE 2012 NONRIGID REGISTRATION METHODS FOR MYOCARDIAL PERFUSION MRI AND CEREBRAL DIFFUSION TENSOR MRI LI CHAO (B.Sc.), University of Science and Technology of China a thesis submitted for the degree of doctor of philosophy DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2012 Acknowledgments First and foremost, I would like to express my sincere appreciation to my supervisor, Asst Prof Sun Ying This dissertation is definitely not possible without her guidance and persistent help I would also like to thank my mentor during the exchange in the Chinese University of Hong Kong, Asst Prof Wang Xiaogang, for his advice Second, I would like to thank my thesis committee, Prof Ong Sim Heng and Asst Prof Yan Shuicheng and anonymous reviewers for their valuable comments Third, I thank Mahapatra Dwarikanath, Jia Xiao, Hiew Litt Teen for their enlightening suggestions during our discussions, and I thank Francis Hoon Keng Chuan and other friends in the Vision and Machine Learning Lab who have helped me in my study Last but surely not the least, I would express my heartfelt thanks to my parents and my wife for their precious support and encouragement i ii ACKNOWLEDGMENTS Contents Acknowledgments i Contents iii Summary vii List of Tables ix List of Figures xi List of Abbreviations and Symbols xv Introduction § 1.1 Motivation § 1.2 Scope and Contributions § 1.2.1 Pseudo Ground Truth Based Perfusion Sequence Registration § 1.2.2 Contour-Image Registration and Its Application to Diffusion MRI § 1.3 Thesis Organization iii iv CONTENTS Background § 2.1 Magnetic Resonance Imaging (MRI) § 2.2 Ischemic Heart Disease and Perfusion MRI 10 § 2.3 Small Vessel Disease and Diffusion MRI 14 § 2.4 Introduction to Image Registration 19 § 2.4.1 Similarity Measures 20 § 2.4.2 Transformation Models 28 § 2.5 Registration in Myocardial Perfusion MRI 35 § 2.6 Registration in Diffusion Tensor MRI 38 The Pseudo Ground Truth Method 41 § 3.1 Introduction 41 § 3.2 PGT-based Registration for General Perfusion MRI 44 § 3.2.1 Data Fidelity Term 45 § 3.2.2 Spatial Smoothness Constraint 45 § 3.2.3 Temporal Smoothness Constraint 48 § 3.2.4 Energy Minimization 49 § 3.2.5 Preliminary Results 52 § 3.3 Registration of Myocardial Perfusion MRI 55 § 3.3.1 Initial Alignment 55 § 3.3.2 Heart Ventricle Segmentation 57 § 3.3.3 Nonrigid Registration 63 The Contour-Image Registration Method 67 § 4.1 Introduction 67 § 4.2 Active Image 71 CONTENTS v § 4.2.1 B-spline FFD 71 § 4.2.2 Energy Functional 72 § 4.2.3 Energy Minimization 73 § 4.2.4 Preliminary Results 74 § 4.3 Free-form Fibers 78 § 4.3.1 Fiber Model 81 § 4.3.2 Fiber-to-DTI Registration 82 Results 95 § 5.1 Data Acquisition 95 § 5.2 Perfusion MRI 96 § 5.3 Diffusion MRI 116 Conclusion and Future Work 127 § 6.1 Conclusion and Discussion 127 § 6.1.1 Cardiac Perfusion MRI 128 § 6.1.2 Cerebral Diffusion MRI 130 § 6.2 Future Work 132 § 6.2.1 Cardiac Perfusion MRI 132 § 6.2.2 Cerebral Diffusion MRI 134 Bibliography 135 List of Publications 149 vi CONTENTS § 5.2 Perfusion MRI 103 18 24 47 18 24 47 18 24 47 18 24 47 Figure 5.3: Contour propagation for one pre-contrast frame and three postcontrast frames from a real patient cardiac MR perfusion scan: contours before applying nonrigid registration (top row), contours propagated by our method (second row), serial demons registration (third row), and NMI-based registration (bottom row) 104 RESULTS Figure 5.4: Comparison of the estimated pseudo ground truth sequences (left) and the propagated contours (right) obtained without segmentation (top), and with segmentation information (bottom) § 5.2 Perfusion MRI 105 For quantitative evaluation, a cardiologist manually drew myocardial contours for the slices in which the endocardium and/or epicardium are visible, and then measured the root mean square (RMS) distance from the manually drawn contours to the propagated contours similar as in (Jolly et al., 2009) As shown in Table 5.1, our method improves the accuracy of the propagated contours for both the endocardial and epicardial boundaries and outperforms serial demons and NMI-based FFD approaches Compared to the contour propagation using global translation only, our nonrigid registration method decreased the RMS distance from 1.18 pixels (2.11 mm) to 1.04 pixels (1.87 mm), whereas the serial demons and NMI-based FFD methods increased the RMS distance to 1.57 pixels (2.80 mm) and 1.48 pixels (2.77 mm) due to misregistration The inverted cumulative histograms for the four methods and no registration are plotted in Fig 5.6 As stated by Jolly et al (2009), a point (x, y) on the curve indicates that x% of all distances are not greater than y pixels, meaning that the bottom-right curve corresponds to the propagation method providing the best match to the manually drawn contours As shown in Fig 5.6, our registration method generates the best propagation results: 74.39% of the distances are no greater than pixel, as compared with 66.08%, 58.06%, and 53.87%, respectively for global translation, NMI-based FFD, and serial demons The RMS distances for respective data sets are shown in Table 5.2 For 18 out of 20 data sets, contours propagated by our method better match the ground truth than only using global translation Additionally, our method significantly surpassed serial Demons and MI-based FFD approaches for most data sets Tables 5.2 also shows the improvement over the general approach § 3.2, especially for datasets #7 and 106 RESULTS #8 In datasets #6 and #11, distances between the propagated contours and manually drawn ones are slightly increased after nonrigid registration This is mainly due to the inconsistency of the manually drawn contours between the reference frame and other frames In both datasets, there was hardly any visible epicardial fat over the lateral wall, so the epicardial border definition over the lateral wall becomes indistinct as contrast washed out of the myocardium, thus making it difficult to keep manually drawn myocardial boundaries consistent Besides, the myocardial boundaries in dataset #6 are very blurry, which poses further difficulty for both ‘ground truth’ drawing and our nonrigid registration algorithm § 5.2 Perfusion MRI (a) 107 (b) (c) (d) Figure 5.5: Contour propagation for cardiac scans using our method Column (a) shows the static frame, on which the myocardial boundaries are manually drawn; columns (b)-(d) show the propagated myocardial contours before, during, and after the first pass of bolus 108 RESULTS Contour Without Registration Global Translation Proposed Method Without Segmentation Serial Demons NMI-based FFD EndoEpiOverall 2.57/3.80 2.51/4.03 2.54/3.94 1.12/2.00 1.22/2.18 1.18/2.11 0.93/1.70 1.11/1.97 1.04/1.87 0.99/1.81 1.13/2.04 1.08/1.95 1.49/2.56 1.62/2.95 1.57/2.80 1.34/2.53 1.57/2.91 1.48/2.77 Table 5.1: The RMS distances (pixels/mm) between the manually drawn contours and the propagated contours for the endocardium, epicardium, and all the contours The distances are measured in terms of pixels and millimeters (mm) separately § 5.2 Perfusion MRI 109 Data Without Registration Global Translation Proposed Method Without Segmentation Serial Demons NMI-based FFD #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14 #15 #16 #17 #18 #19 #20 3.76/7.06 1.19/3.26 0.93/1.74 0.95/2.75 1.36/2.02 2.06/3.23 2.83/3.98 1.62/3.04 1.26/2.37 1.29/3.52 1.56/2.92 1.43/2.69 1.77/1.85 1.22/1.71 2.27/6.20 2.27/5.38 3.91/4.65 4.58/5.44 1.54/3.86 3.99/4.74 1.26/2.35 0.92/2.51 0.90/1.68 1.00/2.89 1.27/1.89 1.41/2.20 0.87/1.23 1.63/3.05 1.06/1.98 0.79/2.16 1.37/2.56 1.38/2.59 1.29/1.35 0.67/0.94 1.09/2.97 1.22/2.90 1.13/1.34 1.44/1.71 1.05/2.62 1.35/1.60 1.09/2.04 0.73/1.99 0.84/1.58 0.87/2.52 1.13/1.68 1.47/2.29 0.66/0.93 1.25/2.34 0.91/1.70 0.73/2.00 1.41/2.64 1.28/2.41 1.03/1.07 0.57/0.80 1.00/2.73 1.02/2.43 0.95/1.13 1.08/1.28 0.93/2.32 1.21/1.44 1.15/2.15 0.73/1.99 0.85/1.60 0.93/2.70 1.13/1.68 1.41/2.20 0.77/1.08 1.61/3.02 0.98/1.84 0.79/2.16 1.37/2.57 1.23/2.30 1.06/1.10 0.65/0.91 1.05/2.88 1.07/2.54 0.94/1.12 1.14/1.36 0.96/2.40 1.17/1.39 1.21/2.26 1.17/3.20 0.88/1.65 0.98/2.83 1.57/2.33 1.87/2.92 1.48/2.08 2.68/5.03 1.52/2.85 0.90/2.45 1.96/3.67 1.79/3.35 1.48/1.54 0.85/1.20 1.84/5.04 0.92/2.18 1.75/2.08 1.63/1.93 1.16/2.90 1.50/1.78 1.33/2.50 1.25/3.43 1.16/2.18 0.99/2.87 1.19/1.77 1.61/2.52 1.14/1.60 1.80/3.37 2.91/5.45 1.21/3.30 2.86/5.36 1.61/3.03 1.94/2.03 1.07/1.51 1.56/4.27 1.05/2.49 1.26/1.50 0.96/1.14 1.28/3.19 1.17/1.39 Table 5.2: Comparisons of the RMS distances (pixels/mm) for respective data sets Best results for respective data sets are highlighted in Bold RESULTS Proposed Method Without Segmentation NMI−based FFD Serial Demons Global Translation Without Registration Distance [Pixels] 2.5 1.5 0.5 0 10 20 30 40 50 60 Percentage [% ] 70 80 90 100 110 Figure 5.6: The inverted cumulative histogram for distances between the propagated contours and the manually drawn contours Circles highlight the proportions of distances that are not greater than pixel § 5.2 Perfusion MRI 111 Comparison of Intensity-time Curves Fig 5.7 shows the intensity-time curves before and after nonrigid registration for a pixel near the myocardial boundary As shown in Fig 5.7 (b), the perfusion signal after global translation still exhibits significant oscillations due to local deformation In contrast, after compensating for the local deformation by performing nonrigid registration, the intensity-time curve becomes smoother at frames where the LV undergoes noticeable local deformation Note that the remaining small local oscillations are caused by image noise Normalized Intensity 0.5 0.4 0.3 0.2 (a) Without Registration Global Translation Proposed Method 0.1 10 20 30 Frame Number 40 50 (b) Figure 5.7: Comparison of intensity-time curves before and after nonrigid registration (a) the static frame of one perfusion sequence, and (b) comparison of the intensity-time curves for the myocardial pixel marked in (a) 112 RESULTS In addition to the intensity-time curves, we also compare the perfusion maps before and after nonrigid registration to qualitatively validate the registration results Myocardial perfusion maps are often used to visualize the perfusion signals and to assist cardiovascular diagnosis (Panting et al., 2001) If the heart undergoes nonrigid deformation, the intensity-time curves around boundaries would be quite different from true perfusion signals as they exhibit large oscillations (see Fig 3.2), which may result in inhomogeneous regions or ghosting in perfusion maps To be unbiased in the parameter extraction procedure, we adopt the method described in (Breeuwer et al., 2001; Milles et al., 2008) to compute the maximum upslope as a perfusion map Fig 5.8 shows the maximum upslope map before and after nonrigid registration As shown in the second image of each column, although rigid motion has been compensated, the resultant perfusion maps still contain ghost boundaries caused by nonrigid heart deformation, whereas the perfusion maps after nonrigid registration (the third image of each column) contain much less or no ghost boundaries § 5.2 Perfusion MRI 113 (a) (b) (c) (d) (e) (f) (g) (h) Figure 5.8: Myocardial perfusion maps generated using maximum upslope Each column shows from top to bottom the static frame, and perfusion maps generated before and after nonrigid registration 114 RESULTS Fig 5.9 shows the means and the standard deviations of the normalized upslope (Milles et al., 2008) in the subendocardial region before and after nonrigid registration For most data sets, the standard deviation of the upslope is greatly reduced, which indicates that the perfusion parameter in the subendocardial region is less noisy after nonrigid registration We believe such reduction of the standard deviation is due to successful compensation of nonrigid deformation rather than erroneous registration, because the nonrigidly registered sequences are obtained by pure intra-frame warping without temporal smoothing Moreover, no texture distortion of the myocardium is observed in registered sequences, which have been validated by a cardiologist Fig 5.9 also shows that the average normalized upslope before nonrigid registration is greater than that after nonrigid registration This is because without compensating elastic deformations, myocardial perfusion signals are contaminated by LV signals, which have much greater upslopes than normal myocardial signals § 5.2 Perfusion MRI 115 0.8 Global Translation Proposed Method 0.7 0.6 0.5 0.4 0.3 0.2 0.1 10 11 12 13 14 15 16 17 18 19 20 Figure 5.9: Comparison of the statistics of the normalized upslope in subendocardial region before and after nonrigid registration 116 § 5.3 RESULTS Fiber-to-DTI Registration and Group Diffusion MRI Analysis The proposed method is implemented in MATLAB (The MathWorks, Natick, MA, USA) with external C libraries Computation time of a fiber-to-DTI registration is about 10-15 mins on a desktop PC (intel Xeon @ 3.33 GHz, 48 GB RAM) The fiber-to-DTI registrations are successful for all the 64 subjects according to visual verification of the fiber points overlaid onto the MRI slices We first present the results by the basic free-form fibers model using only the nFiT measure as described in Sec § 4.3.2 Fig 5.10 displays the fiber points overlaid on the corresponding FA slices As shown, using the nFiT similarity measure, our methods generally succeeded in aligning the fiber tracts to their corresponding WM (dark region in MD) In addition, as rendered in different colors in Fig 5.10, the anatomical fiber bundles are automatically labeled by this fiber-to-DTI registration Fig 5.11 compares the registration results with and without regional prior As shown, in the middle row for example, due to severe WM lesion, FFFs with only nFiT measure (middle) converged to an incorrect position while incorporating regional prior helps to overcome the WM lesion Additionally, since the regional term is only applied on the fibers affected by WM lesion, the registration in healthy regions is not affected § 5.3 Diffusion MRI 117 Figure 5.10: Fiber points reconstructed by § 4.3.2 From left to right shows the MD images in axial view, and overlaid with the original merged fiber model, and the results of affine and nonrigid registration This figure should be viewed in color ...2 NONRIGID REGISTRATION METHODS FOR MYOCARDIAL PERFUSION MRI AND CEREBRAL DIFFUSION TENSOR MRI LI CHAO (B.Sc.), University of Science and Technology of China a thesis submitted for the... Contributions § 1. 2 Scope and Contributions This thesis studies the nonrigid registration problems in myocardial perfusion MRI and cerebral diffusion MRI For myocardial perfusion MRI, the goal is... Cardiac Perfusion MRI 12 8 § 6 .1. 2 Cerebral Diffusion MRI 13 0 § 6.2 Future Work 13 2 § 6.2 .1 Cardiac Perfusion MRI 13 2