Level set methods for MRE image processing and analysis

LEVEL SET METHODS FOR MRE IMAGE PROCESSING AND ANALYSIS LI BING NAN NATIONAL UNIVERSITY OF SINGAPORE 2011 LEVEL SET METHODS FOR MRE IMAGE PROCESSING AND ANALYSIS LI BING NAN (B.Eng., Southeast University, Nanjing, China) (M.Sc., Ph.D., University of Macau, Taipa, Macau) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY NUS Graduate School for Integrative Sciences and Engineering National University of Singapore 2011 ACKNOWLEDGMENT I would like to express my gratitude to my supervisors, Prof. ONG Sim Heng from the Department of Electrical & Computer Engineering (ECE, NUS) and Dr. CHUI Chee Kong from the Department of Mechanical Engineering (ME, NUS), as well as the other members in my Thesis Advisory Committee, Dr. CHANG K.Y. Stephen from the Department of Surgery, National University Hospital (NUH) and Prof. TEO Chee Leong (ME, NUS). I consulted Dr. VENKATESH Sudhakar (Radiology, NUS) a lot on clinical magnetic resonance elastography (MRE). Without their guidance and mentorship, it would not have been possible for me to accomplish such interdisciplinary work. MRE is an emerging technology and not easily accessible. The generous supports from Prof. KOBAYASHI Etsuko from the University of Tokyo (UT) in Japan are particularly appreciated. Only with her supports, I could network with Dr. WASHIO Toshikatsu from the National Institute of Advanced Industrial Science & Technology (AIST) and Dr. NUMANO Tomokazu from the Tokyo Metropolitan University (TMU) for various MRE experiments. Meanwhile, Dr. OBADA Takayuki from the National Institute of Radiological Sciences (NIRS) in Japan also supported our MRE experiments. In particular, Dr. VENKATESH Sudhakar and Mr. Christopher Au C.C. (Radiology, NUH) helped us a lot for in vivo patient experiments at NUH. Thanks very much! I had a good time with my group members, including Dr. ZHANG Jing (ECE, NUS), Dr. QIN Jing from the Chinese University of Hong Kong (CSE, CUHK), Mr. NGUYEN Phubinh (ECE, NUS), Mr. FU Yabo (ME, NUS) and many others. Of course, many thanks are extended to Mr. HOON Francis from the Vision & Image I Processing Lab (VIP, NUS) for his helps during my attachment to the Biosignal Processing & Instrumentation Lab (Biosignal, NUS). Also, I enjoyed the attachment to the Biomedical Precision Engineering Lab (BMPE) at UT. Besides Prof. Kobayashi, I have to thank Prof. SAKUMAR Ichiro and Prof. LIAO Hongen for their generous supports. Ms. OOBADA Naho, Ms. OOKI Yusuko and Ms. ISHIDA Yuko, the secretaries of BMPE, offered me many helps. Mr. SHEN Zhonghuan and Mr. TAKEI Yoshiyuki also did a lot in MRE experiments. Moreover, the friendship with Mr. WANG Junchen, Mr. LUAN Kuan and Mr. WANG Shuai will be always in my memory. It is really my honor to be with NUS Graduate School for Integrative Sciences and Engineering (NGS, NUS), who offered me the generous scholarship and enabled me to concentrate on the thesis researches during the candidature. NGS also funded my attachment to UT with its generous 2+2 Programme. I really appreciate the directors and the staff from NGS. All of them are so being considerate and easily going along with. Last but not least, special thanks go to my family, in particular my loves, Ms. SHI Mian and Ms. LI Si Yuan. Without their consideration and endless supports, I would not be able to devote myself to this doctoral programme. All honors and achievements belong to them but me! LI Bing Nan 01 September 2011 II TABLE OF CONTENTS Summary . V List of Figures VII List of Tables .IX List of Symbols . X List of Abbreviations . XII Chapter 1.1 1.2 1.3 1.4 INTRODUCTION Background . Research Objectives Contributions . Thesis Organization . Chapter LITERATURE REVIEW 10 2.1 Level Set Methods . 10 2.1.1 Definition . 11 2.1.2 Interface Evolution . 12 2.1.3 Numerical Algorithms . 16 2.2 Magnetic Resonance Elastography . 18 2.2.1 System Overview . 18 2.2.2 MRE Imaging . 21 2.2.3 Elasticity Reconstruction . 24 2.3 LSM for MRE Image Processing 29 Chapter NEW LEVEL SET METHODS FOR MRE . 31 3.1 Level Set Diffusion . 32 3.1.1 Anisotropic Diffusion by Heat Equation . 33 3.1.2 Complex Diffusion by Schrodinger Equation 34 3.1.3 Coherence Diffusion 35 3.2 Level Set Segmentation . 36 3.2.1 Mathematical Modeling . 38 3.2.2 Implementation 40 III 3.3 Level Set Registration . 42 3.4 Experiments . 43 3.4.1 On Level Set Diffusion 43 3.4.2 On the Unified Level Set Formulation . 45 3.5 Summary . 52 Chapter MRE IMAGE ENHANCEMENT 55 4.1 Phase Unwrapping . 56 4.2 Directional Filtering 57 4.3 Level Set Diffusion . 60 4.3.1 Experiments . 61 4.4 Summary . 71 Chapter MRE ELASTOGRAM ANALYSIS . 72 5.1 Elastogram Segmentation 73 5.2 Piecewise Constant Elasticity Modeling . 77 5.2.1 Experimental Datasets . 79 5.2.2 Experimental Results . 81 5.3 Summary . 88 Chapter DISCUSSIONS . 90 6.1 Magnetic Resonance Elastogaphy . 90 6.1.1 Actuation 90 6.1.2 MRE Imaging . 92 6.1.3 Elasticity Reconstruction . 94 6.2 Level Set Methods . 96 6.3 LSM for MRE . 99 Chapter CONCLUSION . 103 7.1 Summary of Contributions 104 7.1.1 Contributions to Magnetic Resonance Elastogaphy 104 7.1.2 Contributions to Level Set Methods 105 7.2 Future Work 106 Bibliography 109 List of Publications 122 IV SUMMARY Manual palpation is a well-established routine in clinical medicine for health evaluation. It is a method of soft tissue discrimination according to their elastic properties. However, manual palpation is constrained by organ accessibility, tangible sensitivity and personal subjectivity. Magnetic resonance elastography (MRE) is an emerging technique for the quantification of soft tissue elasticity. It extends palpation to internal organs and tissues. The resultant shear modulus distributions or elastograms provide useful information complementary to structural magnetic resonance imaging (MRI). We conducted a series of experiments on static and dynamic MRE at the National University Hospital (NUH), Singapore. Dynamic MRE experiments were also conducted at the National Institute of Advanced Industrial Science & Technology (AIST), Japan and the National Institute of Radiological Sciences (NIRS), Japan. In this study, we concentrated on dynamic MRE, hereafter termed as MRE unless otherwise stated. Different from conventional structural images, MRE wave images are not directly interpretable. Sophisticated algorithms are required for MRE elasticity reconstruction. Local frequency estimation, algebraic inversion of differential equations and matched filters have been implemented and evaluated in our study. Some refractory issues, such as wave interference, phase wrapping and imaging noise, were investigated as well. We found that most algorithms for elasticity reconstruction were nonetheless susceptible to these refractory issues. In order to enhance MRE wave images, we developed new algorithms for phase unwrapping and directional spatiotemporal filtering. A numerical platform – level set diffusion – was proposed for unified noise suppression and image enhancement. V Four controlling schemes, namely min/max curvature flow, Perona-Malik diffusion, coherence-enhancing diffusion and complex anisotropic diffusion, were developed and evaluated against traditional Gaussian and median filters. When the extracted wave fields are complex, complex anisotropic diffusion is particularly suitable for MRE image enhancement. There is a good tradeoff between noise suppression and elasticity consistency. In contrast, Gaussian smoothing distorts the values of elasticity, and median filtering is not good for structural similarity. We further investigated level set methods for MRE elastogram analysis, and have made contributions in two aspects. The first contribution is a new level set formulation unifying image gradient, region competition and prior information. It is helpful for robust elastogram segmentation. The other contribution is a hybrid level set model for piecewise constant elasticity modeling . It segments MRE elastograms and registers them to the corresponding magnitude images. Optimization is accomplished by alternating global and local region competitions. The resultant piecewise constant elasticity facilitates MRE analysis and interpretation. In summary, the work presented in this thesis advances the research on MRE image processing and analysis. To the best of our knowledge, this is the first systematical investigation of MRE image enhancement beyond Gaussian or median filtering. Level set diffusion is optimal for noise suppression and image enhancement in MRE. On the other hand, it is common to manually specify regions of interest in MRE images for elasticity evaluation. We proposed to automate this procedure by using level set methods for elasticity modeling and interpretation. Two new level set models have been developed, one for segmentation and the other one for piecewise constant modeling. These new methods have been evaluated on synthetic and/or real MRE datasets. VI LIST OF FIGURES Figure 1–1. Contrast mechanisms of different imaging modalities. Figure 2–1. Examples of interface representation in LSMs. . 12 Figure 2–2. Illustrative image information for level set evolution 13 Figure 2–3. Overview of the MRE systems in our study . 21 Figure 2–4. Schematic of the FLASH-MSG pulse sequence in our study. . 22 Figure 2–5. LFE for MRE elasticity reconstruction. . 26 Figure 2–6. MRE elasticity reconstruction by direct algebraic inversion. 29 Figure 3–1. Illustrative level set segmentation 37 Figure 3–2. Performance of LSD on a synthetic wave image. 44 Figure 3–3. Selected CT liver tumors in our study. . 46 Figure 3–4. Enhancements of level set segmentation. . 48 Figure 3–5. Evaluation of the 2D unified level set formulation for liver tumor segmentation. . 50 Figure 3-6. Evaluation of the 3D unified level set formulation. 52 Figure 4–1. Phase unwrapping for MRE image enhancement. . 57 Figure 4–2. Directional spatiotemporal filtering. 58 Figure 4–3. MRE image enhancement by directional spatiotemporal filtering. 59 Figure 4–4. Synthetic and real MRE datasets. . 61 Figure 4–5. Algorithms for MRE elasticity reconstruction. 62 Figure 4–6. Adverse impact of noise on MRE elasticity reconstruction. 64 Figure 4–7. Er against evolutional iterations on MREsimu. . 67 Figure 4–8. Er against evolutional iterations on MREbench. 68 Figure 4–9. 20-iteration enhancement on MREsimu wave field with 20% noise. 69 Figure 4–10. 20-iteration enhancement on MREbench wave field with 20% noise. 70 VII Figure 5–1. Elasticity reconstruction on a benchmark MRE dataset. 73 Figure 5–2. Elastogram segmentation using two ordinary level set models 74 Figure 5–3. Initial segmentation by FCM. . 75 Figure 5–4. The unified level set model with balanced controlling parameters. . 76 Figure 5–5. Segmentation by the unified level set formulation with regulated controlling parameters. 76 Figure 5–6. MRE simulation 80 Figure 5–7. Patient MRE dataset. 80 Figure 5–8. Elasticity reconstruction on the simulated MRE datasets. . 82 Figure 5–9. Level set modeling of the simulated phantoms. . 83 Figure 5–10. Elasticity reconstruction on the phantom datasets 84 Figure 5–11. Level set modeling of the phantom datasets . 85 Figure 5–12. Elasticity reconstruction on the patient MRE datasets . 86 Figure 5–13. Level set modeling of the patient datasets. . 87 Figure 6–1. One of the actuation systems for dynamic MRE in our study. . 91 Figure 6–2. Some MRE images by different MRE imaging sequences in our study…. 93 Figure 6–3. Influence of the controlling parameters of a specific imaging sequence… . 93 Figure 6–4. Combining MRE elasticity and magnitude images for analysis and interpretation. . 96 Figure 6–5. 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Computers in Biology and Medicine 41(1) 1-10. [2] Li, B.N., C.K. Chui, S.H. Ong, T. Washio, T. Numano, S. Chang, S. Venkatesh, and E. Kobayashi (2011) Modeling shear modulus distribution in magnetic resonance elastography with piecewise-constant level sets. Magnetic Resonance Imaging, in press, DOI: 10.1016/j.mri.2011.09.015. [3] Li, B.N., C.K. Chui, S. Chang, and S.H. Ong (2011) A new unified level set model for semi-automatic liver tumor segmentation on contrast-enhanced CT images. Expert Systems with Applications, submitted. Book Chapters: [1] Li, B.N., C.K. Chui, S.H. Ong, S. Chang, and E. Kobayashi (2010) Level set diffusion for MRE image enhancement. In: H. Liao, et al. (Eds.) Medical Imaging and Augmented Reality (Lecture Notes in Computer Science 6326) 305–313, Springer. [2] Li, B.N., C.K. Chui, S.H. Ong, T. Washio, T. Numano, S. Chang, S. Venkatesh, and E. Kobayashi (2010) Soft tissue discrimination using magnetic resonance elastography with a new elastic level set model. In: F. Wang, et al. (Eds.) Machine Learning in Medical Imaging (Lecture Notes in Computer Science 6357) 76–83, Springer. 122 List of Publications Conference Proceedings: [1] Li, B.N., C.K. Chui, S.H. Ong, and S. Chang (2008) Integrating FCM and level sets for liver tumor segmentation. Proceedings of ICBME 2008: 202–205, Singapore, Dec 2008. [2] Beh, K.B., B.N. Li, J. Zhang, C.H. Yan, S. Chang, R.Q. Yu, S.H. Ong, and C.K. Chui (2008) A research-centric server for medical image processing, statistical analysis and modeling. Proceedings of ICBME 2008: 206–210, Singapore, Dec 2008. [3] Li, B.N., P.B. Nguyen, S.H. Ong, J. Qin, L.J. Yang, and C.K. Chui (2009) Image processing and modeling for active needle steering in liver surgery. Proceedings of CAR 2009: 306–310, Bangkok, Thailand, Feb 2009. [4] Wang, G., B.N. Li, C.K. Chui, S.H. Ong, S. Venkatesh, and S. Chang (2011) Image categorization for combinatorial CT liver tumor segmentation. International Journal of Computer Aided Radiology and Surgery 6(Suppl. 1) S48-S49, Berlin, Germany, Jun 2011. 123 [...]... datasets 7 Chapter 1 1.4 THESIS ORGANIZATION The theme of this thesis is on investigating LSMs for MRE image processing and analysis First, the numerical platform LSD is proposed for MRE image enhancement Second, we propose a new level set formulation for MRE elastogram segmentation by unifying image gradient, region competition and prior information Finally, we propose a hybrid level set model for. .. mechanisms – MCF, PMD, CED and CAD – are integrated for noise suppression and image enhancement The second topic is on the unified level set formulation for image segmentation It integrates image gradient, region competition and prior information as a whole for controllability and reliability The last part is about a recent region-scalable level set model, which is useful for level set registration The preliminary... sciences (Sethian 1999), but rarely for MRE Note that LSMs merely define a general numerical framework for dynamic implicit interfaces, and it is usually necessary to design specific level set models for different applications An objective of this thesis is to examine current level set models and explore their applicability to MRE image processing and analysis It is not easy to obtain perfect MRE wave images... magnitude images for level set registration We propose a new level set formulation to directly process and analyze MRE elastograms The inherent noise and artifacts make conventional level set models inefficient for MRE elastogram segmentation It inspires us to unify image gradient, region competition and prior information together Owing to its enhanced object indication function, bidirectional balloon force... noise suppression and image enhancement, LSD with four controlling mechanisms – MCF, PMD, CED and CAD – is evaluated against Gaussian and median filters Chapter 5 presents our achievements on LSMs for MRE image analysis With a benchmark MRE dataset, we firstly evaluate two common level set models, and find out that they are inefficient for elastogram segmentation The unified level set formulation, after... suppression and image enhancement in MRE On the other hand, it is common to manually specify ROIs on MRE elastograms for reliable evaluation We propose to automate this procedure by using LSMs for elasticity modeling and interpretation Two new level set models are developed, one for segmentation and the other for piecewise constant modeling These new methods have been evaluated on synthetic and/ or real MRE. .. underlying mechanisms of LSMs and MRE respectively Our work on MRE systems and experiments is briefly introduced The opportunities and challenges of using LSMs for MRE image processing and analysis are reviewed in the last part of this chapter 2.1 LEVEL SET METHODS It is possible to model image processing problems, including denoising, smoothing and even segmentation, by partial differential equations (PDEs)... force and regularized region competition, this unified level set formulation is robust for MRE elastogram segmentation In summary, the work presented in this thesis advances the research on MRE image processing and analysis To the best of our knowledge, this is the first systematic investigation of MRE image enhancement beyond Gaussian or median filtering We find that LSD with CAD is optimal for noise... dilemma of penetration and resolution, and sufficiently accurate algorithms are lacking for elasticity reconstruction In this thesis, we concentrate on investigating LSMs for MRE image processing and analysis MRE elasticity reconstruction is susceptible to noise, artifacts and low SNR (Manduca et al 2001, 2003; Papazoglou et al 2006) We derive the numerical framework – level set diffusion (LSD) – from... to now MRE remains an exploratory problem although there have been a good many publications on it For example, two distinct mechanisms, which were established for quasi-static deformation and dynamic wave propagation, respectively, can be used for MRE Static MRE is designed to image and visualize motion or deformation directly Magnetic resonance tagging (MRT), a candidate solution for static MRE, has . LEVEL SET METHODS FOR MRE IMAGE PROCESSING AND ANALYSIS LI BING NAN NATIONAL UNIVERSITY OF SINGAPORE 2011 LEVEL SET METHODS FOR MRE IMAGE PROCESSING. Imaging 21 2.2.3 Elasticity Reconstruction 24 2.3 LSM for MRE Image Processing 29 Chapter 3 NEW LEVEL SET METHODS FOR MRE 31 3.1 Level Set Diffusion 32 3.1.1 Anisotropic Diffusion by Heat. level set methods for MRE elastogram analysis, and have made contributions in two aspects. The first contribution is a new level set formulation unifying image gradient, region competition and prior