volumetric reconstruction and real-time deformation modeling of biomedical images

VOLUMETRIC RECONSTRUCTION AND REAL-TIME DEFORMATION MODELING OF BIOMEDICAL IMAGES by Pei Chen A dissertation submitted to the Faculty of the University of Delaware in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Electrical Engineering Summer 2006 c  2006 Pei Chen All Rights Reserved UMI Number: 3220796 3220796 2006 Copyright 2006 by Chen, Pei UMI Microform Copyright All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, MI 48106-1346 All rights reserved. by ProQuest Information and Learning Company. VOLUMETRIC RECONSTRUCTION AND REAL-TIME DEFORMATION MODELING OF BIOMEDICAL IMAGES by Pei Chen Approved: Gonzalo R. Arce, Ph.D. Chair of the Department of Electrical and Computer Engineering Approved: Eric W. Kaler, Ph.D. Dean of the College of Engineering Approved: Conrado M. Gempesaw II, Ph.D. Vice Provost for Academic and International Programs I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: Kenneth E. Barner, Ph.D. Professor in charge of dissertation I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: Karl V. Steiner, Ph.D. Professor in charge of dissertation I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: Charles Boncelet, Ph.D. Member of dissertation committee I certify that I have read this dissertation and that in my opinion it meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: Chandra Kambhamettu, Ph.D. Member of dissertation committee ACKNOWLEDGEMENTS I wish to thank the following people; first of all, my advisors, Dr. Kenneth Barner and Dr. Karl Steiner; my committee members, Dr. Charles Boncelet, and Dr. Chandra Kambhamettu; Dr. Javier Garcia-Frias and Dr. Gonzalo R. Arce for invaluable discussions; and Dr. Denny Lee from DirectRadiography Inc. and Dr. Thomas L. Bauer from the Helen F. Graham Cancer Center, Christiana Care Health System for providing original X-ray images and CT data that were utilized to implement my models and algorithms, and invaluable medical guidance; my parents and my sister, Candy Chen; my friends and colleagues, Dr. Yongzhong Shen, Dr. Yao Nie, Dr. Beilei Wang, Dr. Il-Ryeol Kim, Mr. Yu Yuan, Mr. Bingwei Weng, Mr. Simon Ellwanger, Mr. Tuncer C. Aysal, Mr. Steve Krufka, and Dr. Praveen Thiagarajan; and the staff at the Department of Electical and Computer Engineering and at the Delaware Biotechnology Institute. I must also thank my wife, Yan Wen, without whom none of this would ever have been possible. The research presented in this dissertation is funded in part by the National Science Foundation under Grant HRDC9800175 and 9875658 and NIH-NCRR Grant 2 P20 RR 016472-04 iv TABLE OF CONTENTS LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii Chapter 1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Medical Image Acquisition Techniques . . . . . . . . . . . . . . . . . 3 1.2 Medical Modeling and Simulation using Virtual Reality . . . . . . . . 7 1.3 Dissertation Organization . . . . . . . . . . . . . . . . . . . . . . . . 10 2 STATISTICAL RECONSTRUCTION FOR DIGITAL TOMOSYNTHESIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 Statistical Tomosynthetic Reconstructions . . . . . . . . . . . . . . . 16 2.2.1 Maximum A Posteriori (MAP) Reconstruction . . . . . . . . . 18 2.2.2 Statistical Models . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.3 Iterative Optimization of 3D MAP Reconstruction . . . . . . . 21 2.3 Multi-Resolution Statistical Tomosynthesis . . . . . . . . . . . . . . . 23 2.4 Simulation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.5 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.5.1 Comparison of Reconstruction Images . . . . . . . . . . . . . . 32 2.5.2 Convergence of Log-Posteriori and NMSE . . . . . . . . . . . 33 v 2.5.3 Experiments on Interpolation and Down-sampling Algorithms 41 2.6 Reconstructions Using Real X-Ray Image Data . . . . . . . . . . . . 45 2.6.1 The X-Ray Imaging System . . . . . . . . . . . . . . . . . . . 45 2.6.2 The Reconstruction Process and Results . . . . . . . . . . . . 48 2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3 REAL-TIME DEFORMATION MODELING FOR VIRTUAL SURGERY SIMULATION . . . . . . . . . . . . . . . . . . . . . . . . 51 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.1.1 Non-physical modeling . . . . . . . . . . . . . . . . . . . . . . 53 3.1.2 Physical modeling . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.1.2.1 Finite element method . . . . . . . . . . . . . . . . . 54 3.1.2.2 Mass-spring model . . . . . . . . . . . . . . . . . . . 55 3.2 Mass-Spring Deformable Model . . . . . . . . . . . . . . . . . . . . . 59 3.3 Adaptive Spring Constants . . . . . . . . . . . . . . . . . . . . . . . . 67 3.4 Model Convergence And Stability . . . . . . . . . . . . . . . . . . . . 82 3.5 A Surgery Simulation System with PHANToM Haptic Feedback . . . 85 3.6 Implementation and Results . . . . . . . . . . . . . . . . . . . . . . . 90 3.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4 FUTURE WORK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.1 Tomosynthetic Reconstruction . . . . . . . . . . . . . . . . . . . . . . 96 4.1.1 Fast Re-projection . . . . . . . . . . . . . . . . . . . . . . . . 96 4.1.2 Local Tomosynthesis . . . . . . . . . . . . . . . . . . . . . . . 96 4.2 Deformation Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.2.1 Dynamic Simulations . . . . . . . . . . . . . . . . . . . . . . . 97 4.2.2 Collision Detection for Multi-Point Interactions . . . . . . . . 97 4.2.3 Simulation of Virtual Cutting . . . . . . . . . . . . . . . . . . 98 4.2.4 Validation of Haptic Simulations . . . . . . . . . . . . . . . . 98 4.2.5 Evaluation of Surgical Simulations . . . . . . . . . . . . . . . 99 vi 4.2.6 The Distributed Surgical Simulator . . . . . . . . . . . . . . . 99 BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 vii LIST OF FIGURES 1.1 General steps of digital medical imaging procedures. CT = Computed Tomography. MRI = Magnetic Resonance Imaging. PET = Positron Emission Tomography. SPECT = Single Photon Emission Computed Tomography. . . . . . . . . . . . . . . . . . . . 2 1.2 First radiograph of a hand made by W. C. R¨ontgen on December 22, 1895. Original plate is in the Deutsche Museum, Munich, Germany. 4 1.3 (a) An example of the CT image of a human head. (b) An example of the MRI image of the same human head at the same anatomical level. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 (a) A CT scanner in operation. (b) An MRI scanner in operation. 6 1.5 (a) Volume rendering of a CT data set provided by Christiana Care. (b) The surface data extracted from the volume data in (a). . . . . 8 2.1 Example of a circular tomosynthesis geometry. Imaged object is located between a planar detector and an X-ray source. The projections are taken from discrete source/detector locations. Eight (K = 8) projections are captured in this example. . . . . . . . . . . 17 2.2 Definition of weights ω sj for the neighbor voxels of f j . Each weight is the reciprocal of the spatial distance between f j and the corresponding neighbor voxel. . . . . . . . . . . . . . . . . . . . . . 20 2.3 Overview of the proposed M-MAP reconstruction. The reconstruction is performed from the coarsest scale up to the finest scale. As the MAP reconstruction converges at a coarser scale k, the final reconstruction is interpolated up and used to initialize the MAP reconstruction at the next finer scale. . . . . . . . . . . . . . 24 viii 2.4 Three x − y image slices at different depth z of the simulated phantom. The linear attenuation coefficient of each region is indicated by the numbers with unit cm −1 . Brighter color represents higher attenuation coefficient. Black color indicates attenuation coefficient of 0 cm −1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.5 The absolute function and its differentiable approximations. α = √ x 2 + ε with ε = 10 −3 , β = √ x 2 + ε with ε = 10 −5 , and γ = |x|. 32 2.6 Image slices of simulated phantom and reconstructions from eight projections with 200k incident photon count. Images from the first row down are (a) simulated phantom, (b) backprojection, (c) F-MAP initialized to uniform image, (d) M-MAP-2 initialized to uniform image, (e) M-MAP-3 initialized to uniform image. . . . . . 34 2.7 Image slices of simulated phantom and reconstructions from eight projections with 200k incident photon count. Images from the first row down are (a) simulated phantom, (b) backprojection, (c) F-MAP initialized to backprojection, (d) M-MAP-2 initialized to backprojection, and (e) M-MAP-3 initialized to backprojection. . . 35 2.8 Image slices of simulated phantom and reconstructions from eight projections with 20k incident photon count. Images from the first row down are (a) simulated phantom, (b) backprojection, (c) F-MAP initialized to uniform image, (d) M-MAP-2 initialized to uniform image, and (e) M-MAP-3 initialized to uniform image. . . . 36 2.9 Image slices of simulated phantom and reconstructions from eight projections with 20k incident photon count. Images from the first row down are (a) simulated phantom, (b) backprojection, (c) F-MAP initialized to backprojection, (d) M-MAP-2 initialized to backprojection, and (e) M-MAP-3 initialized to backprojection. . . 37 2.10 Image slices of simulated phantom and reconstructions from eight projections with 2k incident photon count. Images from the first row down are (a) simulated phantom, (b) backprojection, (c) F-MAP initialized to uniform image, (d) M-MAP-2 initialized to uniform image, and (e) M-MAP-3 initialized to uniform image. . . . . . . . 38 ix [...]... applying image analysis and image modeling techniques such as volumetric rendering, surface reconstruction and visualization, and feature identification Since the major contributions of this work, statistical tomosynthetic reconstruction and interactive modeling of soft tissues, reside in the domains of medical image acquisition, medical modeling, and medical simulation, the rest of this chapter is focused... features, such as modeling of deformation or cutting of soft tissues, are sacrificed due to the missing interior structures data A trade-off between computational performance and accuracy of modeling is usually made by combining surface data with volumetric data In the latest medical virtual reality applications, the modeling of soft tissue mechanics and deformations for realistic visual and haptic feedback... but related areas of work: 1) a maximum a posterior (MAP) tomosynthetic reconstruction for X-ray imaging, and 2) real-time deformation modeling of soft organs and tissues utilizing an adaptive mass-spring model, which is the basis of a prototype for a virtual surgery simulation system The proposed tomosynthetic reconstruction algorithm described in Chapter 2 is based on Bayes’ theorem and reconstructs... (b)), the brain tissue and other soft tissues of the human head become clearer One essential procedure shared by those three-dimensional volume imaging techniques such at CT, MRI, and SPECT is reconstruction of the final image of a scanned body For instance, a CT scanner uses X-rays to generate cross-sectional, two-dimensional images of the body Images are acquired by rapid rotation of the X-ray tube 360◦... mass-spring models Images on the top row show the FEM model, while images on the bottom row show the mass-spring model From left to right, deformations of the surface contact point (SCP) are assumed to be 5 mm, 10 mm, and 15 mm, which are equivalent to deformations of 10%, 20%, and 30% at the SCP 72 xii 3.10 Comparison of deformations generated by the FEM model and mass-spring... function of node 0’s x-coordinate for different RSC values 70 3.8 A tetrahedral mesh of a cube model and deformations of the cube model generated by the proposed mass-spring model (a) The mesh structure is in its rest shape (b) The deformation with a high kh /ke value (c) The deformation with a low kh /ke value 71 3.9 Deformations of the cube model generated by the finite element model (FEM) and. .. image quality and algorithmic efficiency 1.2 Medical Modeling and Simulation using Virtual Reality Computer-based reconstruction and rendering of three-dimensional medical image data sets is beginning to replace the mental reconstruction from two dimensional image slices However, although volumetric visualization serves a number of important application in basic research, clinical diagnosis, and treatment... Figure 1.5 shows examples of a volume-rendered and a surface-rendered torso of a patient Producing realistic data models and providing real-time interaction with medical data resides in the domain of virtual reality (VR) The use of virtual reality technology opens new realms in the teaching, practice, and investigation of medical 7 (a) (b) Figure 1.5: (a) Volume rendering of a CT data set provided... mass-spring model with a low and a high RSC values 74 3.11 Comparison of deformations generated by the FEM model and mass-spring model with adaptive RSCs For simplicity, only three sets of results are shown here From the first row down, the RSC0 values in equation (3.24) and (3.25) are −0.10, −0.14, and −0.18, and the Poisson’s ratios of the FEM model are 0.10, 0.30, and 0.49 The left column... resolutions are initialized to interpolations of coarser reconstruction data Chapter 3 of the dissertation presents a real-time adaptive deformable graphical model, based on a volumetric tetrahedral mesh, for interactive modeling of such objects as human organs and tissues in a virtual surgery simulation The presented model is a mass-spring model to simulate deformations of a nonrigid object by iteratively solving . Information and Learning Company. VOLUMETRIC RECONSTRUCTION AND REAL-TIME DEFORMATION MODELING OF BIOMEDICAL IMAGES by Pei Chen Approved: Gonzalo R. Arce, Ph.D. Chair of the Department of Electrical and. VOLUMETRIC RECONSTRUCTION AND REAL-TIME DEFORMATION MODELING OF BIOMEDICAL IMAGES by Pei Chen A dissertation submitted to the Faculty of the University of Delaware in partial fulfillment of. meets the academic and professional standard required by the University as a dissertation for the degree of Doctor of Philosophy. Signed: Kenneth E. Barner, Ph.D. Professor in charge of dissertation I