QUANTIFYING BRAIN WHITE MATTER STRUCTURAL CHANGES IN NORMAL AGING USING FRACTAL DIMENSION by LUDUAN ZHANG Submitted in partial fulfillment of the requirements For the degree of Doctor of Philosophy Dissertation Advisor: Guang H. Yue, Ph.D. Department of Biomedical Engineering CASE WESTERN RESERVE UNIVERSITY January, 2006 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the dissertation of ______________________________________________________ candidate for the Ph.D. degree *. (signed)_______________________________________________ (chair of the committee) ________________________________________________ ________________________________________________ ________________________________________________ ________________________________________________ ________________________________________________ (date) _______________________ *We also certify that written approval has been obtained for any proprietary material contained therein. Copyright © 2006 by Luduan Zhang All rights reserved I grant to Case Western Reserve University the right to use this work, irrespective of any copyright, for the University’s own purposes without cost to the University or to its students, agents and employees. I further agree that the University may reproduce and provide single copies of the work, in any format other than in or from microforms, to the public for the cost of reproduction. Luduan Zhang To my loving parents, my brother, Yuanheng, and my sister, Hongying. Table of Contents Table of Contents ............................................................................................................. vi List of Tables ..................................................................................................................... x List of Figures................................................................................................................... xi Acknowledgements ........................................................................................................ xiv List of Abbreviations ..................................................................................................... xvi Abstract………………………………………………………………………………..xvii 1. Introduction and Background .................................................................................. 1 1.1. Introduction......................................................................................................... 1 1.2. Brain Anatomy and Histology ............................................................................ 3 1.2.1. Nerve Cells and Function............................................................................ 3 1.2.2. White Matter and Gray Matter.................................................................... 5 1.3. Aging of White Matter........................................................................................ 6 1.3.1. Overview..................................................................................................... 6 1.3.2. Imaging of White Matter Changes.............................................................. 7 1.3.3. Histopathologic Correlates of White Matter Changes on MR.................... 8 1.3.4. Clinical Correlates of White Matter Changes............................................. 8 1.4. Skeleton – Shape Medial Representation ........................................................... 9 1.5. Fractal Dimension – Shape Complexity Descriptor ......................................... 12 1.5.1. The Concept of the “Fractal” .................................................................... 12 1.5.2. Fractal Dimension..................................................................................... 13 1.5.2.1. Fractal Dimension Definition ........................................................... 13 1.5.2.2. Measurement of Fractal Dimension.................................................. 15 vi 1.6. Dissertation Objectives and Organization ........................................................ 16 1.6.1. Objectives ................................................................................................. 16 1.6.2. Specific Aims............................................................................................ 16 1.6.3. Dissertation Organization ......................................................................... 18 1.7. References......................................................................................................... 21 2. Fractal Dimension in Human Cerebellum Measured by Magnetic Resonance Imaging ............................................................................................................................ 25 2.1. Abstract............................................................................................................. 25 2.2. Introduction....................................................................................................... 26 2.3. Materials and Methods...................................................................................... 29 2.3.1. Subjects..................................................................................................... 29 2.3.2. Collection of MR Head Images ................................................................ 29 2.3.3. Segmentation and Resampling of CB Images .......................................... 30 2.3.4. Segmentation of WM and GM.................................................................. 31 2.3.5. Extraction of WM Skeleton ...................................................................... 31 2.3.6. Measurement of CB Fractal Dimension ................................................... 32 2.3.7. Statistical Analysis.................................................................................... 33 2.4. Results............................................................................................................... 33 2.5. Discussion......................................................................................................... 35 2.6. References......................................................................................................... 40 3. A Three-dimensional Fractal Analysis Method for Quantifying White Matter Structure in Human Brain ............................................................................................. 44 3.1. Abstract............................................................................................................. 44 vii 3.2. Introduction....................................................................................................... 45 3.3. Materials and Methods...................................................................................... 48 3.3.1. MR Images................................................................................................ 48 3.3.2. Image Processing ...................................................................................... 49 3.3.3. Fractal Analysis Methods ......................................................................... 51 3.3.3.1. Box-counting Method in HarFA....................................................... 52 3.3.3.2. Fractal Analysis Methods of the Present Study ................................ 53 3.3.4. Accuracy and Sensitivity Assessment ...................................................... 56 3.4. Results............................................................................................................... 58 3.4.1. Phantom Results........................................................................................ 58 3.4.2. MR Results................................................................................................ 59 3.4.3. Box Size.................................................................................................... 61 3.5. Discussion......................................................................................................... 63 3.5.1. Importance of Shape Descriptor (Skeleton) in FD Analysis .................... 66 3.5.2. Comparison with HarFA and Pseudo-3D Method.................................... 66 3.5.3. Accuracy Assessment ............................................................................... 68 3.5.4. Sensitivity Assessment.............................................................................. 70 3.5.5. Summary................................................................................................... 71 3.6. References......................................................................................................... 72 4. Quantifying Brain White Matter Changes in Normal Aging using Fractal Dimension ........................................................................................................................ 76 4.1. Abstract............................................................................................................. 76 4.2. Introduction....................................................................................................... 77 viii 4.3. Materials and Methods...................................................................................... 79 4.3.1. Subjects..................................................................................................... 79 4.3.2. Head Images Acquisition.......................................................................... 79 4.3.3. Image Processing ...................................................................................... 80 4.3.4. Measurement of Fractal Dimension.........................................................