Quantitative analysis of shape changes in the cerebral cortex across the adult human lifespan

Neurodegenerative diseases are an increasing health care problem in the United States. Quantitative neuroimaging provides a noninvasive method to illuminate individual variations in brain structure to better understand and diagnose these disorders. The overall objective of this research is to develop novel clinical tools that summarize and quantify changes in brain shape to not only help better understand age-appropriate changes but also, in the future, to dissociate structural changes associated with aging from those caused by dementing neurodegenerative disorders. Because the tools we will develop can be applied for individual assessment, achieving our goals could have a significant clinical impact. An accurate, practical objective summary measure of the brain pathology would augment current subjective visual interpretation of structural magnetic resonance images. Fractal dimension is a novel approach to image analysis that provides a quantitative measure of shape complexity describing the multiscale folding of the human cerebral cortex. Cerebral cortical folding reflects the complex underlying architectural features that evolve during brain development and degeneration including neuronal density, synaptic proliferation and loss, and gliosis. Building upon existing technology, we have developed innovative tools to compute global and local (voxel-wise and regional) cerebral cortical fractal dimensions and voxel-wise cortico-fractal surfaces from high-contrast MR images. Our previous research has shown that fractal dimension correlates with cognitive function and changes during the course of normal aging. We will now apply unbiased diffeomorphic atlasing methodology to dramatically improve the alignment of complex cortical surfaces. Our novel methods will create more accurate, detailed geometrically averaged images to take into account the intragroup differences and make statistical inferences about spatiotemporal changes in shape of the cerebral cortex across the adult human lifespan.

iv QUANTITATIVE ANALYSIS OF SHAPE CHANGES IN THE CEREBRAL CORTEX ACROSS THE ADULT HUMAN LIFESPAN by Sourav Ranjan Kole A dissertation submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Bioengineering The University of Utah December 2015 iv Copyright © Sourav Ranjan Kole 2015 All Rights Reserved iv The University of Utah Graduate School STATEMENT OF DISSERTATION APPROVAL The dissertation of Sourav Ranjan Kole has been approved by the following supervisory committee members: Richard Daniel King , Chair 08/10/15 Date Approved Alan Dale Dorval II , Member 08/25/15 Date Approved Preston Thomas Fletcher , Member 08/10/15 Date Approved Norman Foster , Member 08/10/15 Date Approved Sarang Joshi , Member Date Approved and by Patrick Tresco , Chair/Dean of the Department/College/School of Bioengineering and by David B. Kieda, Dean of The Graduate School. ABSTRACT Neurodegenerative diseases are an increasing health care problem in the United States. Quantitative neuroimaging provides a noninvasive method to illuminate individual variations in brain structure to better understand and diagnose these disorders. The overall objective of this research is to develop novel clinical tools that summarize and quantify changes in brain shape to not only help better understand age-appropriate changes but also, in the future, to dissociate structural changes associated with aging from those caused by dementing neurodegenerative disorders. Because the tools we will develop can be applied for individual assessment, achieving our goals could have a significant clinical impact. An accurate, practical objective summary measure of the brain pathology would augment current subjective visual interpretation of structural magnetic resonance images. Fractal dimension is a novel approach to image analysis that provides a quantitative measure of shape complexity describing the multiscale folding of the human cerebral cortex. Cerebral cortical folding reflects the complex underlying architectural features that evolve during brain development and degeneration including neuronal density, synaptic proliferation and loss, and gliosis. Building upon existing technology, we have developed innovative toolsiv to compute global and local (voxel-wise and regional) cerebral cortical fractal dimensions and voxel-wise cortico-fractal surfaces from high-contrast MR images. Our previous research has shown that fractal dimension correlates with cognitive function and changes during the course of normal aging. We will now apply unbiased diffeomorphic atlasing methodology to dramatically improve the alignment of complex cortical surfaces. Our novel methods will create more accurate, detailed geometrically averaged images to take into account the intragroup differences and make statistical inferences about spatiotemporal changes in shape of the cerebral cortex across the adult human lifespan. v Family 6 TABLE OF CONTENTS ABSTRACT .................................................................................................... iii LIST OF TABLES ............................................................................................ x LIST OF FIGURES ......................................................................................... xi ACKNOWLEDGMENTS .............................................................................. xiii Chapters 1. INTRODUCTION ........................................................................................ 1 1.1 Motivation and Significance ............................................................... 1 1.2 Summary of Innovation and Overview of Forthcoming Chapters .... 4 1.3 References ........................................................................................... 5 2. BACKGROUND .......................................................................................... 6 2.1 Fractal Dimension, Measure of Cerebral Cortical Shape Complexity .......................................................................................... 6 2.2 Validating the Clinical Need .............................................................. 8 2.3 Advantages of Fractal Dimension Analysis ....................................... 8 2.4 Computation of Global Fractal Dimension ...................................... 10 2.5 Computation of Local Fractal Dimension ........................................ 13 2.6 References ......................................................................................... 13 3. GLOBAL FRACTAL ANALYSIS OF THE CEREBRAL CORTICAL RIBBON ACROSS THE ADULT HUMAN LIFESPAN ............................ 21 3.1 Abstract ............................................................................................. 21 3.2 Introduction ...................................................................................... 22 3.3 Methodology ...................................................................................... 24 3.3.1 Participants ............................................................................. 24 3.3.2 MRI Acquisition ...................................................................... 25 3.3.3 MRI Processing ...................................................................... 26vii 3.3.4 Data Analysis ......................................................................... 27 3.4 Results ............................................................................................... 28 3.4.1 Frequency Distribution Plot of DLBS Data ........................... 28 3.4.2 Cortical Ribbon Complexity Differences Across the Lifespan ........................................................................... 28 3.4.3 Cortical Ribbon Complexity and Demographic Factors ........ 29 3.4.4 Cortical Ribbon Complexity Versus Other Structural Measures of the Cortex ........................................................... 30 3.4.5 General Linear Model Incorporating Other Structural Measures of the Cortex ........................................................... 31 3.5 Discussion ......................................................................................... 31 3.6 Conclusion ......................................................................................... 35 3.7 Acknowledgments ............................................................................. 36 3.8 References ......................................................................................... 36 4. USE OF AGE-WEIGHTED AND FRACTAL DIMENSION-WEIGHTED ATLASES TO CHARACTERIZE AGE-RELATED CEREBRAL CORTICAL ATROPHIC CHANGES .................................................................................. 49 4.1 Abstract ............................................................................................. 49 4.2 Introduction ...................................................................................... 50 4.3 Methodology ...................................................................................... 53 4.3.1 Participants ............................................................................. 53 4.3.2 Image Analysis Pipeline ......................................................... 54 4.3.3 Atlas Construction Using LDDMM Framework ................... 54 4.3.3.1 Intensity Normalization .............................................. 54 4.3.3.2 Affine Alignment to Common Coordinate Space ........ 54 4.3.3.3 Gaussian Binning ......................................................... 54 4.3.3.4 Age-Weighted and Fractal Dimension-Weighted Atlas Construction ....................................................... 55 4.4 Results ............................................................................................... 58 4.4.1 Results for Age-Weighted Atlases Analyses .......................... 58 4.4.1.1 Age-Weighted Atlases Quantitatively Characterize Age-Related Atrophic Changes .................................... 59 4.4.1.2 Intraatlas Analysis for Age-Weighted Atlases ............ 59 4.4.1.3 Interatlas Analysis for Age-Weighted Atlases ............ 60 4.4.2 Results for Fractal Dimension-Weighted Atlases Analyses .................................................................................. 61 4.4.2.1 Fractal Dimension-Weighted Atlases Quantitatively Characterize Age-Related Atrophic Changes ............. 61 4.4.2.2 Intraatlas Analysis for FD-Weighted Atlases ............. 62 4.4.2.3 Interatlas Analysis for FD-Weighted Atlases ............. 63 4.5 Discussion ......................................................................................... 63 4.6 Conclusion ......................................................................................... 66 viii 4.7 Acknowledgments ............................................................................. 67 4.8 References ......................................................................................... 68 5. CHARACTERIZATION OF SPATIOTEMPORAL CHANGES IN SHAPE COMPLEXITY OF THE CEREBRAL CORTEX ON A LOBAR AND REGIONAL SCALE ACROSS THE ADULT HUMAN LIFESPAN ............... 78 5.1 Abstract ............................................................................................. 78 5.2 Introduction ...................................................................................... 80 5.3 Methodology ...................................................................................... 81 5.3.1 Participants ............................................................................. 81 5.3.2 MRI Acquisition ...................................................................... 82 5.3.3 MRI Processing ...................................................................... 82 5.3.4 Computing Local Fractal Dimension ..................................... 83 5.4 Results ............................................................................................... 84 5.4.1 Lobar Results .......................................................................... 84 5.4.2 ROI Results ............................................................................. 85 5.4.2.1 Changes Across the Regions ........................................ 85 5.4.2.2 Changes Between the Hemispheres: Left versus Right ......................................................... 87 5.4.2.3 Changes Between the Surfaces: Lateral versus Medial ................................................. 88 5.5 Discussion ......................................................................................... 88 5.6 Conclusion ......................................................................................... 91 5.7 Acknowledgments ............................................................................. 91 5.8 References ......................................................................................... 92 6. CONCLUSION ......................................................................................... 105 6.1 Summary of Contributions and Impact to Medical Imaging and Clinical Neurology .................................................................. 105 6.2 Unpublished Results ...................................................................... 107 6.3 Future Work .................................................................................... 109 6.3.1 Validation and Comparison of Normal Aging Characterization Data ............................................... 109 6.3.2 Evaluation of Age-Calibrated FD as a Neuroimaging Biomarker for AD ......................................... 110 6.3.3 Dissociation of Shape Changes with Normal Aging from AD ................................................................................. 111 6.3.4 Classification of Cognitively Normal Individuals and Individuals with AD Using Local FD .......................... 112 6.3.5 Evaluation of the Effects of Common Co-Morbidities on Age-Calibrated FD ................................................................ 113 6.3.5 Integration of Structural, Metabolic, and ix Pathological Information Evaluation ................................... 114 6.4 References ....................................................................................... 116 LIST OF TABLES 3.1 Subject demographics .................................................................................. 47 3.2 Summary statistics and differences per decade ......................................... 48 3.3 General linear model ................................................................................... 35 4.1 Student's t-test for half-decades ................................................................. 76 4.2 Student's t-test for decades ......................................................................... 76 4.3 Student's t-test for two-decades .................................................................. 77 4.4 Student's t-test with Atlas 20 as gold standard ......................................... 77 5.1 Average lobar values ................................................................................. 103 5.2 Average region-of-interest values ............................................................. 103 LIST OF FIGURES 2.1 Visual correlates of cortical fractal dimension ........................................... 20 3.1 Color-coded frequency distribution plot ..................................................... 44 3.2 Fractal dimension across the lifespan ........................................................ 45 3.3 Selected volumetric properties as a function of age ................................... 46 4.1 Pipeline for construction of weighted atlases ............................................. 70 4.2 Sagittal and axial slices of age-weighted atlases ....................................... 70 4.3 Vector energy from individual image to age-weighted atlas ..................... 71 4.4 Intraatlas analysis of age-weighted atlases ............................................... 71 4.5 Interatlas analysis of age-weighted atlases ............................................... 72 4.6 Sagittal and axial slices of fractal dimension-weighted atlases ................ 73 4.7 Vector energy from individual image to fractal dimension-weighted atlas .............................................................................................................. 74 4.8 Intraatlas analysis of fractal dimension-weighted atlases ........................ 74 4.9 Interatlas analysis of fractal dimension-weighted atlases ........................ 75 5.1 Fractal dimension on a lobar scale across the lifespan ............................. 99 5.2 Asymmetry in local fractal dimension on a lobar scale ........................... 100 5.3 Change in FD across the lifespan for local ROIs ..................................... 101 5.4 Asymmetry in FD across the lifespan for local ROIs ............................... 102xii 6.1 Construction of voxel-based cortico-fractal surface mean ....................... 117 6.2 Example of application of Z-score for AD ................................................. 118 ACKNOWLEDGMENTS First and foremost, I would like to offer my gratitude to my advisor, Dr. Richard King. While being under the tutelage of Dr. King over the past five years, I have come to know him not only as an intellectual powerhouse at our lab and at the clinic, but more importantly, as a genuinely kind and compassionate individual. His steady encouragement and support throughout this time has allowed me to flourish as an independent scientific researcher and has led me to have a well-rounded experience during my graduate studies. For all of this, and more, Dr. King, I thank you. I offer my gratitude to the members of my Supervisory Committee, Drs. Alan Dorval, P. Thomas Fletcher, Norman Foster, and Sarang Joshi for their guidance, support, and thoughtful, incisive questions during group and one-on-one meetings, all of which has immeasurably increased the quality of my research and experience. The research presented in this dissertation could not have been accomplished without the essential contributions of several of my fellow students and co-workers at our lab, the Center for Alzheimer's Care Imaging and Research (CACIR), and the Scientific Computing and Imaging Institute (SCI) at the University of Utah. I thank Carena Kole, my wife and with xiv whom I jubilantly share my life, for her meticulous and diligent work as a researcher in our lab. The innumerable hours that she has spent on almost every aspect of the projects that she has worked on have been instrumental to the success of each one of those projects. I thank Dr. Angela Wang for being a cogent soundboard throughout my graduate work, and for her generous help on many projects. I thank Dr. Nikhil Singh for the numerous constructive discussions that I have had with him and particularly for helping me to learn how to use and the tailor the use of Altaswerks for my applications. I thank Sam Preston and the SCI Support team for their help in solving several computational challenges that I had encountered. Special thanks to Dr. Denise Park, PI of the Center for Vital Longevity at the University of Texas at Dallas, for providing access to the Dallas Lifespan Brain Study database, upon which much of this work has been built. Finally, I thank my family, Phullara Kole, Dr. Chittaranjan Kole, Devleena Kole, and Carena Kole, to whom this dissertation is dedicated. Their deeply held conviction in my abilities continues to empower my strides in life. Thank you for your love, support, and sacrifice. This work has been supported in part by CACIR, and grants from the Robert Wood Johnson Foundation, National Institute of Aging (5-R37-AG006265-27, 5-P30-AG012300-15, and K23-AG03835), and the Alzheimer's Association. 2 CHAPTER 1 INTRODUCTION This dissertation aims to outline the independent research conducted to develop novel clinical tools that summarize and quantify age-related changes in the shape of the human cerebral cortex across the adult human lifespan. 1.1 Motivation and Significance Neurodegenerative diseases are an increasing health care problem in the United States. Alzheimer's disease (AD) is the most common neurodegenerative disease and the 6th leading cause of death in the United States of America with 84,767 deaths (not including deaths from complications caused by AD) in 2013 [1]. There are over 5 million individuals over the age of 65 living with AD today, and the estimated prevalence is expected to range from 11 million to 16 million by 2050 [1]. Furthermore, estimates from Medicare data suggests that one in every three seniors dies with Alzheimer's disease or another neurodegenerative disease [2,3]. 2 In 2015, an American develops AD every 67 seconds. In 2050, an American will develop the disease every 33 seconds [1]. The total annual payments for health care, long-term care, and hospice care for individuals with AD and other dementias are estimated to increase from $226 billion in 2015 to more than $1 trillion in 2050 (both metrics are in 2015 dollars). This growth in health care payments includes a five-fold increase in government spending under Medicare and Medicaid and approximately five-fold increase in out-of-pocket spending [1]. Furthermore, deaths from Alzheimer's disease increased 71% between 2000 and 2013, while deaths from other major diseases such as heart disease (the number one cause of death in the U.S.), stroke, and prostate cancer decreased by 14%, 23%, and 11%, respectively [1]. Currently, there is no treatment to prevent, slow the progression of, or cure Alzheimer's disease. The prevalence, mortality, impact on family members/caregivers, and cost to society combined make this one of the gravest worldwide human health problems of our time. In order to find treatments that prevent, slow the progression of, or cure Alzheimer's disease, we need to diagnose the presence of AD reliably. In order to diagnose AD reliably, we need tools to understand the pathophysiology of the disease and to be able to evaluate and monitor the progression of the disease. 3 To evaluate a possible neurodegenerative condition, neuroimaging, such as a Magnetic Resonance (MR) Images or Computed Tomography (CT) scans, is commonly performed to noninvasively observe structural atrophy patterns associated with such degenerative diseases. The current standard in the radiological assessment of structural information of brain images is to make a visual assessment such as "mild age-appropriate atrophy". This assessment is qualitative and therefore, highly subjective. The subtle changes in anatomy cannot be identified by broad, subjective terms such as "mild" atrophy. Furthermore, the large changes in structure, due to normal aging, present concomitantly with the structural changes due to disease, which confounds the diagnosis of neurodegenerative diseases. Therefore, we have developed tools that summarize and quantify changes in cerebral cortical shape on a global-, lobar-, regional-level. We have applied these tools to characterize normal aging across the adult human lifespan to establish a baseline of cortical shape change with normal aging. Because these tools can be applied for individual assessment, achieving our goals could have a significant clinical impact by aiding to not only understand age-appropriate changes but also, in the future, to dissociate structural changes associated with aging from those caused by dementing neurodegenerative disorders. An accurate, practical objective summary measure of the brain physiology, and subsequently pathology, would augment current subjective visual interpretation of structural magnetic resonance images. 4 1.2 Summary of Innovation and Overview of Forthcoming Chapters Chapter 2 provides background information on fractal dimension, its applications and computation methods of global and local fractal dimension, for understanding the studies described in the subsequent chapters. The methodological aspects that make this research unusually innovative go hand-in-hand with the chapters in this dissertation and have been outlined below. 1) The use of global fractal dimension as an integrative marker of cerebral cortical shape to quantitatively characterize the age-related changes in the shape of cerebral cortex from age 20 to 89 (Chapter 3). 2) The construction of age-weighted diffeomorphic atlases per age-group (half-decade and decade) from age 20 to 89 to account for the intra-age group variability to improve the sensitivity and specificity of the shape analysis (Chapter 4). 3) The use of vector energy to quantify the variability and the difference in shape of the cerebral cortex between each decade and half-decade from age 20 to 89 (Chapter 4). 4) The development of novel techniques to create global fractal dimension-weighted diffeomorphic atlases to improve the shape analysis (Chapter 4). 5 5) The use of local fractal dimension as a marker of cerebral cortical shape to quantitatively characterize the lobar and regional spatiotemporal changes in the shape of cerebral cortex with normal aging from age 20 to 89 (Chapter 5). 6) The development of novel techniques to apply diffeomorphic atlasing methodology to voxel-based cortico-fractal surfaces to characterize regional spatiotemporal changes in the shape of cerebral cortex (Chapter 6). 1.3 References [1] "2015 Alzheimer"s disease facts and figures," Alzheimer's & Dementia, vol. 11, no. 3, pp. 332-384, 2015. [2] J. Bynum, "Tabulations based on data from the National 20% Sample Medicare Fee-for-Service Beneficiaries for 2009," Unpublished raw data, 2011. [3] J. Bynum, "Unpublished tabulations based on data from the Medicare Current Beneficiary Survey for 2008," Unpublished raw data, 2011. 6 CHAPTER 2 BACKGROUND 2.1 Fractal Dimension, a Measure of Cerebral Cortical Shape Complexity, as a Neuroimaging Biomarker The human cerebral cortex undergoes numerous structural changes over the lifespan. Even in healthy adults with a normal performance with standard neuropsychologic screening measures, there are significant age-related decreases noted in regional brain volumes and cortical thickness patterns [1-3]. In Alzheimer's disease, the loss of neurons and subsequent axonal degeneration leads to cerebral atrophy; the structural effects on the cerebral cortex include widening of sulci and thinning of the cortical ribbon [4]. Several cross-sectional imaging studies have quantified volumetric changes in cortical and sub-cortical structures as a function of healthy aging as well as pathological processes such as hypertension, cerebrovascular disease, and neurodegenerative diseases. However, the assessment of cerebral cortical shape has been less well explored. Analysis of shape is a complementary approach to volumetric analysis, which quantifies other 7 important structural properties beyond the standard measurement of area. Neuroimaging studies in recent years have highlighted the numerous important properties of the human cerebral cortex. One of the more interesting characteristics of the cortex is that it displays fractal properties (i.e., statistical similarity in shape) over a range of spatial scales [5-11]. Fractal dimension analysis was first made popular by a series of works by Benoit Mandelbrot in the late 1970s and early 1980s [12,13]. These analytic techniques can capture very complicated structures using relatively simple computational algorithms. Scientists have used fractal analysis for many years to quantify geologic phenomena such as decay of coastlines, analyzing cracks in crystal structure, botanical simulation, and atmospheric modeling [14]. It had been proposed that these same principles could be used to quantify the spatial properties of the surface of the brain. Studies using anatomical data from either gross specimens [15] or magnetic resonance images [9-11,16] have demonstrated that the human cerebral cortex exhibits fractal properties, such as being statistically self-similar (magnification of smaller scale structure resembles the large-scale structure). The complexity of the cerebral cortex can be quantified by a numerical value known as fractal dimension [12,13]. The underlying cerebral white matter, as well as the cerebellum and supporting white matter tracts, are amenable to study using fractal approaches [17-21]. 8 2.2 Validating the Clinical Need for a Structural Neuroimaging Biomarker Cerebral cortical shape complexity assessment is important because it provides a clinically useful and applicable method to quantify shape change. The numerical value of fractal dimension has a definite visual correlate, as seen in Figure 2.1. Cortical complexity is otherwise difficult to reliably assess in clinical practice. The current standard in the radiological assessment of brain images is to make a subjective visual assessment such as "mild age-appropriate atrophy". This type of assessment is very limited because the evaluation varies significantly between individuals, there is no definition of the terms (what does "mild" mean), and because subtle changes cannot be identified using such broad terms. Quantification of these age-related changes will enable currently subjective measures of "age-appropriate" atrophy to be objectively quantified, and thus improve our understanding of atrophic changes on an individual basis. 2.3 Advantages of Fractal Dimension Analysis Currently, there exist several techniques for assessment of cerebral morphology, such as manual ROI-based volumetric approaches [22], hippocampal shape analysis [23], voxel-based morphometry [24,25], cortical pattern matching [26,27], brain boundary shift integral [28], cortical thickness [29-31], and regional cortical segmentation [32]. These techniques 9 can reliably differentiate patients with AD from controls by demonstrating decreases in brain volumes [33-36]. But volumetric characterization is one of many aspects of human anatomical structure and some of these techniques are overly simplistic. Additional information not available by volumetric analysis may be gained using other analysis techniques, such as shape analysis [37]. Shape characterization has proven be a useful method for identifying clinically relevant information on neuroimaging scans [23,36,38]. The folding of the human cerebral cortex reflects the complex underlying architectural features that evolve during brain development and degeneration including neuronal density, synaptic proliferation and loss, and gliosis. The shape complexity of cerebral cortical folding changes with normal aging as well as with neurodegenerative diseases and cortical properties such as gyrification index, cortical thickness, and sulcal depth are altered. The fractal properties of the cerebral cortex arise secondary to folding [15]; diseases that alter cortical properties, such as gyrification index, cortical thickness, and sulcal depth, will become a natural target for fractal analysis. Fractal analysis integrates information over a range of spatial scales (two orders of magnitude from 0.5 mm to ~30 mm) [24]. The range over which the fractal analysis is valid can be determined by measuring the consistency (scale invariance) in the cube count/size slope [20]. Given the range, this unique approach to shape analysis can integrate several aspects of structural change associated with disease, i.e., both subtle changes in cortical thickness 10 associated with synaptic and neuronal loss as well as larger scale changes in the width and depth of sulci. Also, fractal dimension is a direct measure of gray matter atrophy and underlying cytoarchitectural changes, as compared to other shape metrics derived from secondary image processing methods [39,40]. Therefore, fractal dimension provides a quantitative, aggregate measure of shape complexity describing this multiscale folding of the human cerebral cortex from neuroradiological scans. Furthermore, fractal dimension analysis has been proven to be complementary, and in some cases, a more advantageous methodology, to several existing methodologies, such as volumetric studies [23,20,41], voxel-based morphometry [19,42-45], traditional MR morphometric analysis [46], and cortical thickness and gyrification [45,47]. 2.4 Computation of Global Fractal Dimension Fractal dimension analysis has been used to study epilepsy [16], schizophrenia [38,46,48,49], and cortical development [50,51], but our lab was the first to demonstrate practical application in AD [47,42]. We have demonstrated that changes in the fractal dimension in the cortex occur in Alzheimer's disease using 2D slicing methods [47]. Furthermore, we have also demonstrated that the fractal analysis method is more effective when applied to the entire cortical ribbon instead of just the inner or outer surfaces, and that the cortical ribbon does a better job of distinguishing 11 Alzheimer's disease from healthy controls than cortical thickness or gyrification index [42]. Additionally, the pattern of loss of cerebral cortical complexity differs between diseases reflecting selective neuronal vulnerability and/or regional disease expression. Therefore, we have written custom software to perform a global and local (voxel-wise and regional) fractal analysis and create cortico-fractal surfaces (discussed in Chapter 6) in the original 3D image space. There are several approaches for computing the fractal dimension of objects, such as caliper methods [13,52,53], box-counting algorithms [13,54], dilation methods [55], and spatial frequency analysis [9]. We selected a box-counting algorithm because of the simplicity of implementation as well as for comparison to other studies that use this method to examine fractal properties of the human brain [7,10,11,16,17,18,20,21]. The fractal dimension (FD) of the cortical surfaces was computed using a custom software program called Cortical Complexity Calculator (C3), which is based on a 3D cube-counting algorithm. This algorithm has been described by [13,54], and used by several previous investigators [7,8]. Furthermore, this algorithm has been shown to be a robust and accurate method of computing cortical complexity [8]. The implementation of this algorithm that has been applied for this study is very similar to [8]. C3 uses a 3D cube-counting algorithm, which tiles the tessellated triangles (~200,000 per surface per hemisphere) with cubes of varying sizes. 12 This approach is derived from the Minkowski-Bouligand dimension with an extrapolation using 3D cubes instead of 2D boxes. The cube count for each hemisphere covers the entire cortical ribbon, including the pial surface, gray-white surface, and all necessary intermediate surfaces (temporary 3D meshes spatially contained between the pial surface and gray-white surface. Intermediate surfaces can be dynamically generated as needed to create a full model of the entire cortical ribbon, as described in a previous study [42]. The intersection of each triangle (including the edges) with a cube matrix covering the entire brain is computed using standard geometry. Each cube is counted only once, resulting in a cube count of the total number of intersections. The cube size is then changed, and the intersection computation is repeated. The fractal dimension of an object, also known as the Hausdorf-Besikovich dimension, is computed as the change in the log of the cube count divided by the change in the log of the cube size (see Equation (2.1)).  FD    log(cube count)  log(cube size) (2.1) The version of C3 used in this study was written on Mac OS X (10.5) using the XCode environment in Objective C with graphic implementation using OpenGL. 13 2.5 Computation of Local Fractal Dimension Most studies of the fractal properties of the cerebral cortex have focused on computing whole-brain measures (i.e., generating one number which summarizes the entire hemisphere). It is well established that aging has differential effects on the cerebral cortex, with some regions being more selectively prone to age-related atrophy and this is true for progressive neurodegenerative diseases, such as Alzheimer's disease, as well [1-3,56]. Furthermore, the local pattern of cortical complexity loss with aging likely differs from alterations associated with neurodegenerative disease such as Alzheimer's disease or Frontotemporal dementia. Thus, a local analysis of the cortical complexity of regions more prone to change will likely increase the sensitivity and specificity of the analysis. To compute local values of fractal dimension, the process of cube-counting was performed at every voxel that was labeled as belonging to the cerebral cortex. Instead of including the entire cortex in the counting, only those voxels located within a cubic region of 30mm were included. For details of this process, see [57]. 2.6 References [1] K. Walhovd, L. Westlye, I. Amlien, T. Espeseth, I. Reinvang, N. Raz, I. Agartz, D. Salat, D. Greve, B. Fischl, A. Dale and A. Fjell, "Consistent neuroanatomical age-related volume differences across multiple samples," Neurobiology of Aging, vol. 32, no. 5, pp. 916-932, 2011. 14 [2] N. 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Local curvature is mapped to the color scale (green = highest curvature, gray = lowest curvature) to allow better visualization of the 3D properties. Visually, the decreased complexity is associated with widened sulci and smaller gyri. All of these subjects had normal cognition. 2.5992.6212.6562.68821 CHAPTER 3 FRACTAL ANALYSIS OF THE CEREBRAL CORTICAL RIBBON ACROSS THE ADULT HUMAN LIFESPAN 3.1 Abstract Fractal dimension analysis of high-resolution magnetic resonance images is a method for quantifying the complexity of the human cerebral cortex. In order to use cortical fractal dimension as a biomarker for age-related diseases, it is critical to establish the influence of aging on cortical complexity. The purpose of this paper is to examine age-related differences in cortical complexity across the adult lifespan in a large cross-sectional cohort of well-characterized, cognitively normal, healthy adults. MR images of the brain from 301 subjects in the Dallas Lifespan Brain Study (age range 20-89, ~43 per decade) were analyzed using FreeSurfer to segment volumetric parameters and generate 3D surface models of the cortex. The global cortical fractal dimension was computed from the surface models using customized cube-counting software. Additionally, the volumes of subcortical and cortical regions were calculated along with cortical 22 thickness, surface area, and gyrification index measures. Global fractal dimension of the cortex decreases precipitously with age (r = -0.801, R2 = 0.642). Significant differences (p < 0.05) in average cortical complexity occur between all successive decades except for between the 40s and 50s (p = 0.08). Cortical thickness had the strongest age-related effect (r = -0.662, R2 = 0.438), followed by gyrification index (r = -0.546, R2 = 0.298) and brain volume (r = -0.455, R2 = 0.298). Cortical surface area was weakly correlated with age (r = -.296, R2 = 0.087). Cortical thickness and gyrification index were the strongest drivers of cortical fractal dimension. Significant alterations in the shape of the cerebral cortex occur throughout the adult lifespan, and these changes can be quantified using global cortical fractal dimension. Now that the normal range of age-related complexity values have been identified, this tool can be used to identify structural changes not associated with normal aging. 3.2 Introduction The human cerebral cortex undergoes a number of structural changes over the lifespan. Even in healthy adults with a normal performance on standard neuropsychologic screening measures, there are significant age-related decreases noted in regional brain volumes and cortical thickness patterns [1-3]. Many cross-sectional imaging studies [4-6] have quantified volumetric changes in cortical and sub-cortical structures as a function of 23 healthy aging as well as in pathological processes such as hypertension, cerebrovascular disease, and neurodegenerative diseases [7]. While cortical volumetric properties have been well characterized, the assessment of cortical shape has been less well explored. Analysis of shape is a complementary approach to volumetric analysis, which quantifies other important structural properties beyond the standard measurement of area. In particular, the folding of the cerebral cortex creates shapes that are statistically similar over a range of spatial scales. The complexity of these folding patterns can be characterized using a measure known as fractal dimension. Studies using anatomical data from either tissue specimens and magnetic resonance images have demonstrated that the human cerebral cortex exhibits fractal properties [8-15]. Fractal dimension analysis was first made popular by a series of works by Benoit Mandelbrot in the late 1970s and early 1980s [16,17]. These analytic techniques can capture very complicated structures using relatively simple computational algorithms [18]. Mathematically created fractal objects exhibit a property called "self-similarity", which means that magnification of smaller scale features exactly duplicate a larger scale structure. This approach has been applied to the analysis of brain structure several times in recent years. The underlying cerebral white matter, as well as the cerebellum and supporting white matter tracts, are amenable to study using fractal approaches [19-23]. The approach has been used to study epilepsy [24], 24 schizophrenia [25-28], cortical development [29,30], and Alzheimer's disease [31,32]. Recent methodological advancements in cortical fractal analysis include a technique to analyze the entire cortical ribbon as derived from 3D tessellated polygon models of cortex segmented from high-resolution high-contrast T1 weighted images [32]. This technique offers significant improvements over using models of the pial (outer cortical) surface or gray-white (inner cortical) surface in terms of differentiating healthy aging from neurodegenerative processes on a group-comparison basis. However, the effects of aging on the complexity of the cortical ribbon have not yet been explored. The purpose of this paper is to examine age-related differences in cortical complexity across the adult lifespan in a large cross-sectional cohort of cognitively normal adults. These complexity differences will be also compared to currently used volumetric assessments of the cerebral cortex (thickness, volume, surface area, and gyrification index). 3.3 Methodology 3.3.1 Participants Participants consisted of 301 individuals aged 20-88 (mean 52.8 ± 19.6 years; uniform age distribution with ~43 subjects per decade; 192 women, 109 men) from the Dallas Lifespan Brain Study (DLBS). DLBS is a large-scale longitudinal research project designed to characterize neural and cognitive 25 aging across the adult lifespan from age 20 to 89. These participants were recruited through media advertisements and flyers and underwent health history screening via a health questionnaire as well as telephone and personal interviews. All participants were screened against cardiovascular, neurological, and psychiatric disorders, head injury with loss of consciousness > 10 min, and drug/alcohol abuse. Additional exclusion criteria for our study were irregularities in the MR image and inability to produce cortical surfaces via the FreeSurfer pipeline (discussed below). Participants were native English speakers and strongly right-handed (on the Edinburgh Handedness Questionnaire [33]. The participants were well educated (mean 16.58 ± 2.66 years) and scored highly (28.31 ± 1.31) on the Mini Mental State Examination (MMSE; [34]). All participants provided written informed consent and were debriefed in accord with university human investigations committee guidelines. 3.3.2 MRI Acquisition All participants were scanned on a single 3T Philips Achieva scanner equipped with an 8-channel head coil. High-resolution anatomical images were collected with a T1-weighted MP-RAGE sequence with 160 sagittal slices, 1×1×1mm3 voxel; 204×256×160 matrix, TR=8.1ms, TE=3.7ms, flip-angle=12°. See Table 3.1 for a demographic summary of the subjects. 26 3.3.3 MRI Processing Segmentation of the brain images was performed using a semiautomated segmentation software suite called FreeSurfer (version 4.4.0, Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Boston). FreeSurfer contains a set of tools for analysis and visualization of structural and functional brain imaging data. FreeSurfer has been described in detail in prior publications [35-43]. FreeSurfer was also used to generate three-dimensional tessellated polygon models of the inner (gray-white) and outer (pial) cortical surfaces. Preliminary segmentation of the gray matter from the white matter was generated based on intensity differences and geometric structure differences in the gray/white junction [44]. The pial surface was generated using outward deformation of the gray/white surface with a second-order smoothness constraint [36,44]. The smoothness constraint allowed the pial surface to be extended into otherwise ambiguous areas. The resulting surfaces have sub-voxel accuracy. Manual editing was performed to correct for errors in the gray-white boundary (e.g., subcortical T1 hypointense regions improperly included as cortex or white matter boundaries incorrectly drawn due to improper intensity normalization) and the pial boundary (e.g., meningeal dural tissue not fully removed by the skull-stripping procedure). 27 The fractal dimension (FD) of the cortical ribbon was computed using a custom software program called the Cortical Complexity Calculator, which is based on a 3D cube-counting algorithm (described in Chapter 2). The software directly imports the FreeSurfer surface models to perform the complexity analysis in native space. 3.3.4 Data Analysis A mean FD value was extracted for each subject and the values of cortical fractal dimension between successive decade-wide cohorts were compared using a Student's t-test (one-tailed, α < 0.05 considered significant) to determine between which decades FD differences were most apparent. To determine whether there are significant differences in the variance of fractal dimension as a function of age, an F-statistic was computed to compare the variance across decades. Critical values were determined for each decade pairing at the α = 0.05 significance level. To examine relationships between cortical fractal dimension and population demographic factors, we performed a general linear model (GLM) using gender, age, education, MMSE scores, and intracranial volume (ICV) as predictive factors. To explore relationships between cortical fractal dimension and other commonly used measures of brain structure, values for average cortical thickness (CT), total segmented brain volume (BV), total cortical surface area (SA), and gyrification index (GI, a ratio of the total cortical 28 surface area to the surface area of a tightly-wrapping smoothed cortical surface) were extracted from the FreeSurfer data files. A GLM was created (using SPSS Statistics, IBM, version 21.0.0.0) entering CT, BV, SA, GI, and age as independent variables to determine which structural factors best predicted FD. 3.4 Results 3.4.1 Frequency Distribution Plot of DLBS Data The frequency distribution plot of the 301 cognitively normal subjects in the Dallas Lifespan Brain study database has been created (Figure 3.1). We have presented two subjects (MR image and 3D surface model generated by FreeSurfer for each subject) on either side of the spectrum, one which is of a 78-year-old subject with a FD of 2.599 (bottom) and one which is of a 24-year-old subject with a FD of 2.688 (top) to visualize the differences in shape of the cerebral cortex across the spectrum. 3.4.2 Cortical Ribbon Complexity Differences Across the Lifespan On average, we found that the fractal dimension of the cortex decreased with age, and there was a strong correlation between the two, with age alone accounting for 64% of the variance in cortical complexity (Pearson r = -0.801, R2 = 0.642). Whole brain fractal dimension as a function of age is 29 shown in Figure 3.2 and summarized in Table 3.2 by decade. The most significant age-related differences in cortical complexity occurred earlier in the adult lifespan. The difference between the 20s and 30s and between the 30s and 40s were highly significant (p < 0.0001). In contrast, no statistically significant decrease in average cortical fractal dimension was observed between the 40s and 50s, (p = 0.08), where the smallest absolute difference in average FD was seen. Significant differences were again seen between older cohorts (60s, 70s, and 80s, p < 0.02). All cohorts separated by at least 20 years differed significantly (p < 0.0001 for all pairwise t-tests). The degree of significance was smaller among older cohorts than younger cohorts, possibly due to the increased variability observed in the older cohorts. The variance for each decade was compared using F-test for homoscedastisticy between decades. We found the degree of variability in cortical complexity increases with age, with significant difference in variance observed between the youngest and oldest cohorts (F-Test p < 0.05 for 20s vs. 80s, 30s vs. 70s, 30s vs. 80s, and 40s vs. 80s; see Table 3.2). 3.4.3 Cortical Ribbon Complexity and Demographic Factors Zero-order Pearson correlations indicated that cortical fractal dimension was significantly associated with age (R2 = 0.642, p < 0.001), years of education (R2 = 0.021, p = 0.047), MMSE (R2 = 0.105, p < 0.001), but not with 30 ICV (R2 = 0.006, p = 0.18) or gender (average FD for Females = 2.649, Males 2.648, p = 0.477). To consider the combined effects of these demographic characteristics, we conducted a GLM with age, gender, MMSE, education, and ICV as predictors of FD. We found a significant effect of age (F [1, 294]= 440.85, p < 0.001) and education (F [1, 294]= 3.98, p = 0.047) on FD, where older age and fewer years of education were associated with less cortical complexity. We found no significant effect on global cortical fractal dimension between genders (F < 1, p = 0.546), MMSE scores (F < 1, p = 0.704), or ICV in this sample (F < 1, p = 0.698) after controlling for the effects of each other. 3.4.4 Cortical Ribbon Complexity Versus Other Structural Measures of the Cortex We also examined separately the effect of age on common volumetric properties: cortical thickness, cortical surface area, brain volume, and gyrification index. As shown in Figure 3.3, all four of these measurements demonstrated significant decreases over the adult lifespan. Of these four indices, cortical thickness had the highest correlation with age (r = -0.662), followed by gyrification index (r = -0.546) and brain volume (r = -0.455). Cortical surface area was weakly correlated with age (r = -0.296). 31 3.4.5 General Linear Model Incorporating Other Structural Measures of the Cortex To consider the relative association of these structural variables with FD, a general linear model including age, thickness, gyrification index, surface area, and volume were entered as predictors of FD (see Table 3.3). Both cortical thickness (F[1,295] = 44.4, p < 0.001, η = 0.28) and gyrification index (F[1,295] = 40.1, p < 0.001, η = 0.36) were significant factors in predicting cortical fractal dimension. Note that cortical thickness and gyrification index were not strongly correlated with each other (r = 0.226). Intracranial Volume (F[1,295] = -2.0, p = 0.31, η < 0.001) has no predictive value for fractal dimension. Cortical surface area (F[1,295] = -11.0, p < 0.001, η = 0.05) has a small effect on predicting fractal dimension. Age (F[1,295] = -13.0, p < 0.001, η = 0.03) also has a small effect, and is no longer a strong predictor of FD once cortical thickness and gyrification index are accounted for in the model. 3.5 Discussion To the best of our knowledge, this is the first large, cross-sectional study to report on quantitative characterization of changes in cerebral cortical complexity through the adult human lifespan for a cognitively normal population. A previous study explored cortical complexity changes across the lifespan, but had a scantily distributed population, particularly with a low 32 sampling of older adults (only 9 out of 93 subjects over the age of 40) [45]. The current data suggest a linear decrease in cerebral cortical complexity with age across the adult human lifespan. This study benefits from using a 3-dimensional technique that incorporates the entire thickness of the cortex when computing cerebral cortical fractal dimension [31]. Previous researchers reported both linear decreases with aging in other measurements of brain area, such as cortical thickness [54,55], and volumetric measures [56-58], as well as a structural changes that accelerate with aging using tools such as voxel-based morphometry [46,59], gray matter density [60], and volumetric measures [2,47,61-65]. We speculate that one reason that structural changes do not accelerate with aging in the population for this study is that this is a highly selected healthy research population with advantageous demographic factors (i.e., education, ethnicity, socioeconomic status, etc.), and may not represent the population at large. Cortical fractal dimension reflects a combination of volumetric factors (cortical thickness) and spatial factors (gyrification index). The findings in this paper are consistent with studies performed on images of normal adults and subjects with Alzheimer's disease [30]. The integration of multiple aspects of brain morphometry results in fractal dimension metrics having a larger effect size than either cortical thickness or gyrification index. The fact that fractal dimension is independent of head size (intracranial volume) is expected given that fractal dimension is a scale invariant measure. This may 33 also explain why there is not much of a gender effect on fractal dimension. This study identified significant age-related differences in complexity occurring in the 20s and 30s, well before subjects complain of cognitive slowing and well before typical age-related diseases such as Alzheimer's disease or recurrent microvascular insults are manifested. There are certainly still changes in synaptic connectivity occurring during this earlier period in life, and perhaps a decreasing complexity reflects more specificity in cortical wiring. The clinical significance of these differences needs further exploration. We found an increase in variability of cortical fractal dimension with older age. This increased variability occurs despite the fact that all subjects maintained normal cognition and no subjects had a significant burden of microvascular disease (which was an exclusion criteria). Understanding the sources of this variability and the long-term clinical significance are important next steps. It remains to be determined if age-related differences in cortical complexity are linked with the commonly observed cognitive changes in normal aging. In these data, we saw a glimpse of this possibility in a significant correlation of FD with the MMSE scores (although nonsignificant after accounting for age), suggesting that there may be neuropsychological correlates of these cortical changes that should be further explored with detailed cognitive assessments. Additionally, this method may be useful in 34 distinguishing normal from pathological aging. There are visual correlates to the computed fractal dimension, with decreased dimension being associated with widened sulci and thinner cortex. This technique provides a quantitative method for measuring complexity, which currently is assessed by radiologists using imprecise qualitative terms such a "mild age-appropriate atrophy". The fractal analysis method described in this paper can replace such qualitative terms with a quantitative and precise measure. Another useful extension of the approach used in this paper is to enable a regional analysis of cortical fractal dimension (which could be analyzed locally at thousands of locations across the cortex) rather than generating a single number that summarizes the complexity of the entire cerebrum. It is well established that aging has differential effects on the cerebral cortex, with some regions being more selectively prone to age-related atrophy [58]. Furthermore, the local pattern of cortical complexity loss with aging likely differs from alterations associated with neurodegenerative disease such as Alzheimer's disease or Frontotemporal dementia. Thus, a local analysis of the cortical complexity of regions more prone to change will likely increase the sensitivity and specificity of the analysis. There are a number of important future analyses that can come from this study. Certainly obtaining longitudinal data on the subjects in the database (along with corresponding neuropsychological testing) will be important for understanding the trajectory of cortical complexity on an 35 individual basis. Given that the older subjects in this study grew up in a very different environment than the current younger subjects, the natural history may very well be changing and is a known limitation of cross-sectional designs. Following subjects who subsequently proceed to develop age-related neurodegenerative diseases such as Alzheimer's may also help to identify early cortical complexity changes that might indicate impending disease. Epidemiologic factors such as a history of hypertension, stroke, or diabetes, are also important factors to consider, but will require a different population than was used for this study. Finally, correlating complexity changes with other imaging biomarkers (such as the presence of cortical beta-amyloid protein deposition) may yield additional insight into cortical complexity changes across the lifespan, as will utilizing cortical complexity as a predictor of cognitive performance in normal aging and in dementia. 3.6 Conclusions The results of this study demonstrate that complexity of the cerebral cortex linearly decreases during the course of even normal aging, quantified by computing the global fractal dimension of the cortical ribbon. As fractal dimension is a direct measure of gray matter atrophy and underlying cytoarchitectural changes, this is an important finding in regards to shape complexity of the cerebral cortex. 36 3.7 Acknowledgements I thank Dr. Denise Park, the PI of the Center for Vital Logevity at University of Texas-Dallas, for providing access to the Dallas Lifespan Brain study database. Also, I would like to acknowledge contributions of Dr. Kristen Kennedy and Dr. Karen Rodrigue at the University of Texas-Dallas and Dr. Richard King, Brandon Brown, and Jeanette Berberich at the Alzheimer's Image Analysis Lab at the University of Utah. This research was supported by the Center for Alzheimer's Care, Imaging and Research and grants from the National Institute of Aging (5R37AG006265-27, K23AG03835). 3.8 References [1] K. Walhovd, L. Westlye, I. Amlien, T. Espeseth, I. Reinvang, N. Raz, I. Agartz, D. Salat, D. Greve, B. Fischl, A. Dale and A. 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One is of a 24-year-old person with a FD of 2.688 (top) and one is a 78-year-old person with a FD of 2.599 (bottom). 45 Figure 3.2 Fractal dimension across the lifespan. The scatter plot shows the age and cortical ribbon fractal dimension for each subject. The value of cortical fractal dimension tends to decrease as subjects age, but the variability in dimensionality for any give age rage increases as subjects age. The linear regression shows a high correlation. 46 Figure 3.3 Selected volumetric properties as function of age. Each subject is represented as a point on the scatter plots. A. Cortical Thickness B. Cortical Surface Area. C. Brain Volume. D. Gyrification Index. 47 Table 3.1 Subject Demographics: All subjects are free from history of neurological disease or brain injury, claustrophobia, uncontrollable shaking, use of medications that affect cognitive function or vascular response, foreign metallic objects in the body, and any conditions which would contraindicate MRI. There is not a significant difference in the education, gender %, or MMSE score between any of the decade groups. Age Number Gender (%M) Education MMSE 20-29 47 36.2% 16.4 29.0 30-39 42 38.1% 17.5 28.5 40-49 42 35.7% 16.0 28.5 50-59 47 30.4% 17.3 28.8 60-69 47 37.5% 16.9 28.2 70-79 41 34.1% 15.9 27.7 80-89 35 42.9% 15.9 27.1 48 Table 3.2 Summary statistics and differences per decade. The average values and standard deviations for each decade patients are shown in the table. The p values for the difference between the fractal dimensions of successive decade cohorts are shown in the right column. Significant differences (p < 0.05) are highlighted. Table 3.3 General linear model: Cortical thickness and gyrification index were the factors with the highest predictive power of fractal dimension. Model Beta Error 95% Lower bound 95% Upper bound Cortical Thickness 0.088 0.004 0.080 0.096 Gyrification Index 0.071 0.004 0.062 0.079 Brain Volume < 0.00001 0.000 -0.001 -0.120 Age < 0.00001 0.000 0.000 -0.007 Surface Area < 0.00001 0.000 -0.007 0.005 Decade n FD ± st. dev p vs. previous decade Sig. variance difference (F-test p < 0.05) 20s 47 2.670 ± 0.0090 vs. 80s 30s 42 2.662 ± 0.0092 <0.0001 vs. 70s, 80s 40s 42 2.652 ± 0.0091 <0.0001 vs. 80s 50s 46 2.649 ± 0.0113 0.0806 60s 47 2.643 ± 0.0111 0.0004 70s 41 2.636 ± 0.0119 0.0178 80s 35 2.626 ± 0.0151 0.0012 49 CHAPTER 4 USE OF AGE-WEIGHTED AND FRACTAL DIMENSION- WEIGHTED ATLASES TO CHARACTERIZE AGE- RELATED CEREBRAL CORTICAL ATROPHIC CHANGES ACROSS THE ADULT HUMAN LIFESPAN 4.1 Abstract To assess cerebral cortical shape changes across the human lifespan by generating atlases, which are variably-weighted, geometrically averaged images of cerebral anatomy of a given population, age and global cerebral cortical fractal dimension (FD) were used as weighting variables. The purpose of this study was 1) to compare interatlas and intraatlas differences for age-weighted atlases and global cerebral cortical fractal dimension-weighted atlases and 2) to compare age-weighted atlases and global cerebral cortical fractal dimension-weighted atlases as biomarkers for cerebral cortical shape changes. Magnetic resonance images of the brain from 314 subjects in the Dallas Lifespan Brain Study (age range 20-89, ~45 per decade) were 50 analyzed using FreeSurfer to segment volumetric parameters and generate 3D surface models of the cortex. The cortical fractal dimension was computed from the surface models using customized cube-counting software. The Large Deformation Diffeomorphic Metric Mapping framework was used to construct atlases and to assign metric distances on the space of anatomical images to quantify similarity/dissimilarity in the shape of the cerebral cortex. Variability in cerebral cortical structure is highest in brains of higher age and lower fractal dimension. There is less variance in cerebral cortical structure for brains of equivalent fractal dimension as compared to brains of equivalent age. There is more variance in cerebral cortical structure between fractal dimension-weighted cohorts as compared to variance in cerebral cortical structure between age-weighted cohorts. Atlases weighted by fractal dimension capture more of the variance in cortical shape than atlases based upon age (R2FD = 0.62 & R2Age = 0.48). Atlases weighted by fractal dimension is a novel concept that can capture cerebral cortical shape change better than age-weighted atlases. 4.2 Introduction It is well established that during the normal aging process significant changes in the size and shape of the brain occur, which are not associated with cognitive dysfunction [1,2]. Additionally, there is a great amount of variability between different individuals within similar age groups in the 51 normal aging process. Different individuals "age" differently, i.e., at different rates of degeneration and at different regions within the brain [1,3]. These age-related changes, between different age groups and within similar age groups, in the shape of the brain with normal aging make age-appropriateness difficult to reliably assess and confound diagnoses in clinical practice. Therefore, quantification of these age-related changes and calibration for age using a large database of brains from cognitively normal subjects across the adult human lifespan will enable currently subjective measures of "age-appropriate" atrophy to be objectively quantified, and thus improve our understanding of age-related atrophic changes on an individual basis and across the lifespan. Also, we have created fractal dimension-weighted atlases and analyzed its use to capture cerebral cortical shape changes. AtlasWerks was used to generate age-weighted and global fractal dimension-weighted atlases. The AtlasWerks suite is an open-source software package developed by the Scientific Computing and Imaging Institute at the University of Utah, as an implementation of the deformation algorithms based on the well-established Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework. The Large Deformation Diffeomorphic Metric Mapping framework has been used to estimate geodesics in the diffeomorphic space, where the optimal diffeomorphisms are the shortest metric distances between images [4-9]. Also, the LDDMM framework has 52 been used to measure interpopulation [10,11] and intrapopulation [12] variability. Please see [8,13] to review use of diffeomorphic mappings for modeling anatomical shape changes. AtlasWerks simultaneously and reversibly deforms a set of images into a geometric average, an atlas. The influence of each image on the atlas has been weighted by age and fractal dimension, using a sliding Gaussian Kernel, to generate age-weighted and global fractal dimension-weighted atlas. Here, we used AtlasWerks to construct age-weighted atlases for every half-decade from age 20 to 89 and fractal dimension-weighted atlases in increments of FD= 0.01 from FD of 2.60 to 2.69, using a database of 314 cognitively normal brains collected by the Dallas Lifespan Brain Study. Each cortical voxel of an atlas has a unique set of statistical values based upon location and age and fractal dimension. Also, we used the concept of "vector energy" within the LDDMM framework to assign metric distances on the space of anatomical images to quantify interatlas differences and intraatlas variability in the shape of the cerebral cortex. To the best of our knowledge, this is the first large, cross-sectional study to 1) apply age-weighted atlases to quantitatively characterize age-related atrophic changes through the adult human lifespan (age: 20-89) for a cognitively normal cohort, 2) apply fractal dimension-weighted atlases to quantitatively characterize atrophic changes for a cognitively normal cohort, 3) apply vector energy to quantify the variability in the shape of the cerebral 53 cortex within atlases of age and global fractal dimension (intraatlas analysis), and 4) apply vector energy to quantify the difference in shape of the cerebral cortex between successive atlases of age and global fractal dimension (interatlas analysis). 4.3 Methodology The methodology that has been used in this paper to construct age-weighted and global cerebral cortical complexity-weighted atlases has been outlined in Figure 4.1. All preprocessing steps have used Mac OS X version 10.5.8. 4.3.1 Participants For this study, 314 subjects from DLBS were analyzed. Subjects have at least a high school education, a Mini-Mental State Exam (MMSE) of 26 or greater, and corrected vision of 20/30. Subjects are free from history of neurological disease or brain injury, claustrophobia, uncontrollable shaking, use of medications that affect cognitive function or vascular response, foreign metallic objects in the body, and any conditions which would contraindicate MRI. For more information on DLBS see Chapter 3 Sections 3.3.1 and 3.3.2. 54 4.3.2 Image Analysis Pipeline Image analysis steps are the same as outlined in Section 3.3.3 in Chapter 3. 4.3.3 Atlas Construction Using LDDMM Framework 4.3.3.1 Intensity Normalization All 314 images have been intensity normalized via a semiautomated process. Each image has been normalized based on binning of the intensity ranges of gray matter, white matter, and cerebrospinal fluid. Subsequently, the intensity histograms have been manually corrected for these different tissue classes in the brain. This second intensity normalization is performed to standardize intensity for this particular cohort of 314 images. 4.3.3.2 Affine Alignment to Common Coordinate Space Prior to atlas construction, in order to remove artifacts due to scanner positions and pose, all the images were aligned to one image in the population. 4.3.3.3 Gaussian Binning To construct age-weighted and FD-weighted atlases, the subjects were binned using a Gaussian kernel to create age-weighted and FD-weighted cohorts. Age-weighted cohorts were created for every half-decade from ages 55 20-89 using a Gaussian kernel to bin with sigma=5. Fractal dimension-weighted cohorts were created from fractal dimension 2.60-2.69 using a Gaussian kernel to bin with sigma=0.01. The following is the kernel that was used:  w(ti ,t)  1 2 exp (ti ,t)2 2 2 (4.1) 4.3.3.4 Age-weighted and Fractal Dimension- Weighted Atlas Construction Using LDDMM Framework Atlases were constructed using AtlasWerks, which is based on the well-established Large Deformation Diffeomorphic Metric Mapping framework. Under the LDDMM framework, brain shape changes are modeled by diffeomorphisms acting on the underlying coordinate space of images [10]. Diffeomorphisms are one-to-one, smooth, and invertible transformations that preserve topology and form a group structure under compositions. Any two images can be represented by a diffeomorphism that registers them. This group of diffeomorphisms is a manifold with a Riemannian metric. This metric defines the notion of similarity and alternatively, the difference between brain shapes. A convenient and natural machinery for generating diffeomorphic transformations is by the integration of ordinary differential equations (ODE) on the underlying coordinate space,  defined via the smooth time-indexed 56 velocity vector fields v(t, y) : (t ∈ [0, 1], y ∈ Ω) → R3. The function φv (t, x) given by the solution of the ODE dy/dx = v(t, y) with the initial condition y(0) = x defines a diffeomorphism of . One defines a Riemannian metric on a space of diffeomorphisms by inducing an energy on these velocity fields. The distance between the identity transformation and a diffeomorphism ψ is defined as the minimization  d(id, )2  min{ Lv(t,),v(t,)dt : v (1,)   () 0 1  } (4.2) The distance between any two diffeomorphisms is defined as d(φ, ψ) = d(id, ψ ◦φ−1). This Riemannian metric defined on the space of diffeomorphisms can now be used to compute a deformation that matches two images. If the problem is to register an image I1 over the target image I2, then image at time t is defined as It = I1 ◦φ −1, i.e., I0 = I1. The deformation φ is defined as the ‘optimal' time-varying velocity field vˆ, based on minimizing the energy functional, E (v):  (v)  Lv(t,),v(t,)2 dt 0 1   1  2 I1 o 1  I 2 L2 2 , (4.3) i.e.,  vˆ  argmin(v), v :Ý t  vt ( t ) (4.4) where the second term in Equation 3 allows inexact matching, and σ is a free parameter controlling the tradeoff between exactness of the match and smoothness of the velocity fields. 57 Notice that the above metric induces a distance metric between two images, I1 and I2 written as a minimizer of the form:  d(I1,I2 )2 min{Vector energy + Image energy} (4.5) The metric defines the notion of similarity and alternatively, the difference between brain shapes. Notice, the first term, vector energy, can be also be interpreted as the minimum amount of energy it takes to deform one brain in a smooth and invertible fashion to match another and the second term, image mismatch, allows for inexact matching of images. The empirical estimate of weighted Fréchet mean of images,  I can now be presented using this distance metric on images. The goal is to compute the unbiased weighted atlas image,  I that minimizes the sum of squared distances to the given population of images [10]. Given a collection of N anatomical images and corresponding normalized weights, {Ii, wi} for i = 1, · · · , N , the atlas can be defined as a solution to the minimum mean square energy criteria  I  argmin I 1 N wid(I,I i )2  i1 N (4.6) The minimum mean squared energy atlas construction problem is that of jointly estimating an image  I and N individual deformations. We use the above framework to create age-weighted  I age l and FD-weighted  I age m atlas where  l and  m indexes over the chosen age and FD grid points. Furthermore, we have calculated the amount of vector energy it takes 58 to deform an individual constituent image to the respective atlas for all age-weighted and FD-weighted atlases. This is used to calculate intraatlas variability in shape of the images for both sets of atlases. The values of vector energies required to deform an individual image to the respective atlas between successive half-decade-wide cohorts have been compared using a Student's t-test (2 tailed, model 3, p < 0.05 considered significant). 4.4 Results 4.4.1 Results for Age-Weighted Atlases Analyses 4.4.1.1 Age-Weighted Atlases Quantitatively Characterize Age-Related Atrophic Changes Through the Adult Human Lifespan Age-weighted atlases have been constructed for every half-decade from ages 20-89 using a Gaussian kernel to bin with sigma=5. Each age-weighted atlas is a statistical representation of that population, i.e., age-weighted atlas 20 (binned with a Gaussian kernel of mean=20 and sigma=5) represents the shapes of all the cerebral cortices of individuals that are of age 25. Figure 4.2 illustrates the changes in the shape of the cerebral cortex with normal aging for every two decades from 20 to 80. 59 The amount of vector energy it takes to deform each image to its respective atlas has been calculated and plotted for all age-weighted atlases in the DLBS database (Figure 4.3). Each datum represents the images of each atlas, keeping in mind a Gaussian kernel was used for binning. The amount of vector energy it takes to deform each image to its respective atlas increases with age and there is more variability in the shape of the cerebral cortex in younger individuals and older individuals. 4.4.1.2 Intraatlas Analysis for Age- Weighted Atlases The amount of vector energy it takes to construct each atlas quantifies the variability in the shape of the cerebral cortex within each decade and half-decade. We found that the amount of vector energy it takes to construct each atlas remains approximately constant until age 55 and then increases with age (see Figure 4.4). The increase vector energy necessary to construct each atlas after age 55 indicates greater variability in the shape of the cerebral cortex within the age groups (half-decade and decade after age 55). A Student's t-test (2 tailed, model 3) to compare the amount of vector energy to deform each image to its respective atlas for successive half-decade atlases has been performed. We found that there is no significant difference in the amount of vector energy it takes to deform an image to its respective atlas for successive atlases from 20-55. Significant differences (p<0.05) in vector energy to deform each image to its respective atlas for successive half-60 decade atlases have been highlighted in yellow. There was significant difference in the amount of vector energy it takes to deform each image to its respective atlas from 55-60, 60-65, 65-70, & 75-80 (Table 4.1). Here, a Student's t-test (2 tailed, model 3) to compare the amount of vector energy to deform each image to its respective atlas for successive decade atlases has been performed. We found similar results as the aforementioned half-decade analysis, with significant difference in the amount of vector energy it takes to deform each image to its respective atlas from 50-60, 60-70, & 70-80 (Table 4.2). A Student's t-test (2 tailed, model 3) to compare the amount of vector energy to deform each image to its respective atlas for successive two-decade atlases has been performed. We found significant difference in the amount of vector energy it takes to deform each image to its respective atlas from 30-50, 40-60, 50-70, & 60-80 (Table 4.3). The intraatlas analyses indicate that the amount of vector energy it takes to construct each atlas remains approximately constant until age 55 and then increases with age. 4.4.1.3 Interatlas Analysis for Age- Weighted Atlases Vector energy quantifies the difference in the shape of the cerebral cortex between each decade and half-decade. Here, we have plotted the 61 amount of vector energy it takes to deform each atlas to the successive decade atlas (Figure 4.5). In this interatlas analysis, we found that the amount of vector energy it takes to deform each atlas to the successive decade-atlas increases with age, i.e., the difference in the shape of the cerebral cortex between decades increases with age. Also, we found similar results with lower sampling, i.e., with deforming each atlas to the successive half-decade atlas (data not shown). Here, we use age-weighted Atlas 20 as a gold standard of cognitively normal and compare the vector energy required for each image in Atlas 20 to be deformed to the Atlas 20 image as compared to the vector energy required for each image to be deformed to its respective atlas. We found that there is a significant difference in the shape of the cerebral cortex between the atlases from age 55 onwards for the analysis with half-decades and from age 60 onwards for the analysis with decades (Table 4.4). 4.4.2 Results for Fractal Dimension-Weighted Atlases Analyses 4.4.2.1 Fractal Dimension-Weighted Atlases Quantitatively Characterize Age-Related Atrophic Changes Fractal dimension-weighted cohorts were constructed from fractal dimension 2.60-2.69 using a Gaussian kernel to bin with sigma=0.01. Figure 62 4.6 illustrates the changes in the shape of the cerebral cortex with increase in global fractal dimension for every 0.03 FD from FD of 2.60 to 2.69. The amount of vector energy it takes to deform an individual constituent image to its respective atlas has been calculated and plotted for all FD-weighted atlases in the DLBS database (Figure 4.7). We found that the amount of vector energy it takes to deform each image to its respective atlas decreases with increase in global cerebral cortical FD and there is more variability in the shape of the cerebral cortex in individuals with lower global cerebral cortical FD. In comparison to age-weighted atlases, we see that atlases weighted by global fractal dimension capture more of the variance in cortical shape than atlases weighted by age, R2=0.48 & R2= 0.62, respectively. 4.4.2.2 Intraatlas Analysis for FD- Weighted Atlases Vector energy quantifies the variability in the shape of the cerebral cortex within each decade and half-decade. We found that the amount of vector energy it takes to construct each atlas decreases with an increase in cortical FD (see Figure 4.8). The decrease vector energy necessary to construct each atlas indicates lesser variability in the shape of the cerebral cortex within the age groups (half-decade and decade). 63 4.4.2.3 Interatlas Analysis for FD- Weighted Atlases Vector energy quantifies the difference in the shape of the cerebral cortex between each decade and half-decade. Here, we have plotted the amount of vector energy it takes to deform each global fractal dimension-weighted atlas to the successive atlas. In our interatlas analysis, we found that the amount of vector energy it takes to deform each atlas to the successive decade-atlas decreases with an increase in global cerebral cortical FD, i.e., the difference in the shape of the cerebral cortex between decades decreases with an increase in FD (Figure 4.9). Also, we found that there is significant difference in the amount of vector energy it takes to deform each image to its respective atlas from 2.61-2.62, 2.62-2.63, 2.63-2.64, 2.64-2.65, 2.65-2.66, 2.66-2.67, & 2.68-2.69. Therefore, there is a significant difference in the shape of the cerebral cortex between the aforementioned FD-weighted atlases. 4.5 Discussion In Chapter 3, we had used fractal dimension to quantify the shape of the cerebral cortex and the change in the fractal dimension metric to characterize the change in the shape of the cerebral cortex across the adult human lifespan. In this chapter, we have used vector energy to quantify and characterize the change in the shape of the cerebral cortex. We have 64 confirmed our previous finding of variability of the shape of the cerebral cortex increasing with normal aging. However, in this study with vector energy, we did not find a significant difference in the shape of the cerebral cortex between cohorts earlier than age 55, whereas we had reported significant difference in the shape of the cerebral cortex between 20s and 30s cohorts and between the 30s and 40s cohorts in Chapter 3, using fractal dimension. Furthermore, we found an acceleration of the difference in the shape of the cerebral cortex between atlases of higher age cohorts. Although, the assessment of trajectory of different measures with aging across the human lifespan is mixed in extant literature, our nonlinear trajectory assessment is in accord with findings by other groups [1,11,14]. Obtaining longitudinal data on the subjects in the database, along with corresponding neuropsychological testing, may help to understand the sources of the variability within and acceleration between age groups and the long-term clinical significance thereof. In the process of deforming a population of images into a weighted atlas, some individual outliers were identified that required significantly more energy to deform from the native space into the atlas space. It is important to note that these outliers were the same individuals in the age-weighted and fractal-dimension weighted atlases (see Figures 4.3 and 4.7). Upon closer visual inspection, these individuals do appear to be structurally different from the rest of the population. For example, in creating the 65 weighted atlas centered around 75 years old, one individual had required much more vector energy (~800) to be deformed to the 75-year-old Atlas than the rest of the population (average energy ~250). When compared to the 75-year-old Atlas, this individual showed wider sulci, larger ventricles, and a thinner cortical ribbon diffusely. Note that despite the evidence for greater cerebral atrophy, the cognitive performance on screening tests was still within the normal range. The visual confirmation of structural differences helps to substantiate the notion that vector energy under the LDDMM framework is capturing the intended structural variability. A useful extension of the approach used in the chapter is to create other biomarker-weighted atlases. Other than the structural changes due to normal aging and neurodegenerative disease, there are biochemical, metabolical, and pathological changes that occur as well. Atlases may be constructed by being weighted these other clinically relevant biomarkers. This may be more reliable as an indicator of intrapopulation variability and interpopulation differences and to augment clinical diagnosis. Moreover, there are a number of important future analyses that can come from this study. Age-weighted atlases across the human lifespan can be used as a baseline to quantitatively characterize the normal aging process. Also, age-weighted atlases can be used to quantify and characterize changes due to different neurodegenerative diseases. Currently, the variability in structure due to normal aging, which is present concomitantly with the 66 structural changes due to neurodegenerative disease, confounds the diagnosis of neurodegenerative diseases. Having age-weighted atlases for normal aging and for neurodegenerative disease, we can then quantitatively delineate normal aging changes from changes due to a specific neurodegenerative disease and create quantitative characteristic plots for each neurodegenerative disease, without the confounding effects of normal aging. 4.6 Conclusions Age-weighted atlases can quantitatively characterize age-related atrophic changes in the cerebral cortex and provide a baseline for and improve our understanding of cortical shape change with normal aging across the adult human lifespan. By accounting for the variability in the shape of the cortex between different individuals within specific age groups and quantifying differences between age groups, age-appropriateness on an individual basis becomes easier to assess. Fractal dimension is a novel neuromaging biomarker that summarizes and quantifies clinically relevant changes in brain shape, which are a reflection of underlying physiological changes, which occur due to normal aging or neurodegenerative disease. Also, fractal dimension-weighted atlases capture the variance in cerebral cortical shape and shape change progression better than age-weighted atlases. Therefore, fractal dimension may be a better surrogate biomarker for cerebral cortical shape changes than age and 67 a better predictor of cerebral cortical shape change. As a quantitative and reliable measure that can characterize shape changes in the cerebral cortex that accrue with normal aging and neurodegenerative diseases, global fractal dimension can provide a quantitative interpretation of structural data in neuroradiological scans that is complementary or not available by standard volumetric analyses. Consequently, using this quantitative metric, we may dissociate structural changes associated with aging from those caused by dementing neurodegenerative diseases. Furthermore, cerebral cortical FD, as a measure of structural changes, in addition to other quantitative markers, such as volumetric, metabolic, and pathological measures, may augment/replace the current standard of care of qualitative and subjective clinical diagnosis and may significantly improve clinical diagnosis of neurodegenerative disorders. 4.7 Acknowledgements I thank Dr. Sarang Joshi for developing Atlaswerks and the seminal work supporting it. I thank Dr. Nikhil Singh's guidance in helping to learn how to use Atlaswerks. This study would not have been realized without the constructive discussions with and contributions from Carena Kole, Dr. P. Thomas Fletcher and Dr. Richard King. Finally, I thank Kyle Hansen, Jeanette Berberich, and Brandon Brown for their assistance. 68 This study was supported by the Center for Alzheimer's Care Imaging and Research at the University of Utah, and grants from the Robert Wood Johnson Foundation, National Institute of Aging (5-R37-AG006265-27 and 5-P30-AG012300-15), and the Alzheimer's Association. 4.8 References [1] N. Raz, "Regional brain changes in aging healthy adults: general trends, individual differences and modifiers," Cerebral Cortex, vol. 15, no. 11, pp. 1676-1689, 2005. [2] K. Walhovd, L. Westlye, I. Amlien, T. Espeseth, I. Reinvang, N. Raz, I. Agartz, D. Salat, D. Greve, B. Fischl, A. Dale and A. Fjell, "Consistent neuroanatomical age-related volume differences across multiple samples," Neurobiology of Aging, vol. 32, no. 5, pp. 916-932, 2011. [3] N. Raz, P. Ghisletta, K. Rodrigue, K. Kennedy and U. Lindenberger, "Trajectories of brain aging in middle-aged and older adults: regional and individual differences," NeuroImage, vol. 51, no. 2, pp. 501-511, 2010. [4] M. I. Miller, L. Younes, "Group actions, homeomorphisms, and matching: a general framework," International Journal of Computer Vision, vol. 41, no. 1-2, pp. 61-84, 2001. [5] A. Trouvé and L. Younes, "Metamorphoses through lie group action," Found Comput Math, vol. 5, no. 2, pp. 173-198, 2005. [6] M. Beg, M. Miller, A. Trouvé and L. Younes, "Computing large deformation metric mappings via geodesic flows of diffeomorphisms," International Journal of Computer Vision, vol. 61, no. 2, pp. 139-157, 2005. [7] L. Younes, A. Qiu, R. Winslow and M. Miller, "Transport of relational structures in groups of diffeomorphisms," Journal of Mathematical Imaging and Vision, vol. 32, no. 1, pp. 41-56, 2008. [8] L. Younes, F. Arrate and M. Miller, "Evolutions equations in computational anatomy," NeuroImage, vol. 45, no. 1, pp. S40-S50, 69 2009. [9] M. Miller, A. Trouvé and L. Younes, "On the metrics and Euler-Lagrange equations of computational anatomy," Annual Review of Biomedical Engineering, vol. 4, no. 1, pp. 375-405, 2002. [10] S. Joshi, B. Davis, M. Jomier and G. Gerig, "Unbiased diffeomorphic atlas construction for computational anatomy," NeuroImage, vol. 23, pp. S151-S160, 2004. [11] J. Allen, J. Bruss, C. Brown and H. Damasio, "Normal neuroanatomical variation due to age: the major lobes and a parcellation of the temporal region," Neurobiology of Aging, vol. 26, no. 9, pp. 1245-1260, 2005. [12] M. Miller, A. Trouvé and L. Younes, "Geodesic shooting for computational anatomy," Journal of Mathematical Imaging and Vision, vol. 24, no. 2, pp. 209-228, 2006. [13] L. Younes, "Shapes and diffeomorphisms," Applied Mathematical Sciences, vol. 171, 2010. [14] A. Fjell, L. Westlye, H. Grydeland, I. Amlien, T. Espeseth, I. Reinvang, N. Raz, A. Dale and K. Walhovd, "Accelerating cortical thinning: unique to dementia or universal in aging?," Cerebral Cortex, vol. 24, no. 4, pp. 919-934, 2012. 70 Figure 4.1 Pipeline showing overall methodology to construct age-weighted and cortical complexity weighted atlases. Figure 4.2 Sagittal (top panel) and axial (bottom panel) slices of age-weighted atlases for every two decades from 20 to 80 illustrate the changes in the shape of the cerebral cortex with normal aging. 71 Figure 4.3 Amount of vector energy it takes to deform an individual constituent image to the respective atlas has been plotted for all age-weighted atlases in the DLBS database. Figure 4.4 Intraatlas analysis of age-weighted atlases. Amount of vector energy it takes to deform each atlas to the successive decade-atlas increases with age, i.e., the difference in the shape of the cerebral cortex between decades increases with age. 72 Figure 4.5 Interatlas analysis of age-weighted atlases. The amount of vector energy it takes to deform each atlas to the successive decade atlas increases linearly but with greater slopes between certain age groups. 73 Figure 4.6 Sagittal (top panel) and axial (bottom panel) slices of fractal dimension-weighted atlases for every 0.03 FD from FD of 2.60 to 2.69 illustrate the changes in the shape of the cerebral cortex with increase in global FD. 74 Figure 4.7 Amount of vector energy it takes to deform an individual constituent image to its respective atlas has been plotted for all global fractal dimension-weighted atlases in the DLBS database. Figure 4.8 Intraatlas analysis of FD-weighted atlases. Amount of vector energy it takes to deform each atlas to the successive decade atlas decreases with an increase in global cerebral cortical FD, i.e., the difference in the shape of the cerebral cortex between decades decreases with an increase in FD. 75 Figure 4.9 Interatlas analysis of FD-weighted atlases. Amount of vector energy it takes to deform each global fractal dimension-weighted atlas to the successive atlas has been plotted. A significant difference was found in the amount of vector energy it takes to deform each image to its respective atlas from 2.61-2.62, 2.62-2.63, 2.63-2.64, 2.64-2.65, 2.65-2.66, 2.66-2.67, & 2.68-2.69. 76 Table 4.1 Student's t-test for half-decades. Student's t-test (2 tailed, model 3) to compare the amount of vector energy to deform each image to its respective atlas for successive half-decade atlases was performed. There was significant difference in the amount of vector energy it takes to deform each image to its respective atlas from 55-60, 60-65, 65-70, & 75-80. Table 4.2 Student's t-test for decades. Student's t-test (2 tailed, model 3) to compare the amount of vector energy to deform each image to its respective atlas for successive decade atlases has been performed. Significant differences (p < 0.05) have been highlighted in yellow. We found similar results as the aforementioned half-decade analysis. 77 Table 4.3 Student's t-test for two-decades. Student's t-test (2 tailed, model 3) to compare the amount of vector energy to deform each image to its respective atlas for successive two-decade atlases has been performed. Significant differences (p < 0.05) have been highlighted in yellow. Significant difference in the amount of vector energy it takes to deform each image to its respective atlas from 30-50, 40-60, 50-70, & 60-80 was found. Table 4.4 Student's t-test with Atlas 20 as gold standard. Student's t-test (2 tailed, model 3) to compare the vector energy required for each image in Atlas 20 to be deformed to the Atlas 20 image as compared to the vector energy required for each image to be deformed to its respective half-decade atlas (top) and decade-atlas (bottom). Significant differences (p < 0.05) have been highlighted in yellow. A significant difference was found in the shape of the cerebral cortex between the atlases from age 55 onwards for the analysis with half-decades and from age 60 onwards for the analysis with decades. 78 CHAPTER 5 CHARACTERIZATION OF SPATIOTEMPORAL CHANGES IN SHAPE COMPLEXITY OF THE CEREBRAL CORTEX ON A LOBAR AND REGIONAL SCALE ACROSS THE ADULT HUMAN LIFESPAN 5.1 Abstract Advances in postimaging analysis of human brain MR images have enabled the quantification of fractal dimension (a measure of shape complexity) on the human cerebral cortex at a local level. The purpose of this paper is to characterize the spatiotemporal distribution of changes in cortical fractal dimension on a lobar and regional scale across the adult human lifespan in a large, healthy, cross-sectional database (N=301, age range: 20-88). High-contrast MR scans (MP-RAGE format) were downloaded from the Dallas Lifespan Brain Study. Each scan was processed using FreeSurfer to semiautomatically generate a cortical/subcortical segmentation and cortical parcellation. Cortical labels were applied by FreeSurfer based upon the 79 Desikan-Killiany atlas. The fractal dimension for a 30mm local region was computed independently for every cortical voxel using custom software (C3). The cortical labels were aligned with the fractal dimension maps, and aggregate statistics on regions of interest were generated using a MATLAB script. A linear decrease in cerebral cortical complexity across the adult human lifespan at both the lobar- and regional-level was observed. Variable effects on the cerebral cortex, with some regions being more selectively prone to age-related atrophy, varied across age ranges. On the regional level, the inferior temporal, inferior parietal, lateral occipital, middle temporal, entorhinal, fusiform, and temporal pole regions of the left hemisphere had the least amount of change in cortical complexity across the adult human lifespan. In contrast, the superior frontal, isthmus cingulate, posterior cingulate, and lingual regions had the greatest amount of change in cortical complexity across the adult human lifespan. This study highlights the variable effects of normal aging on the cerebral cortex based upon local complexity changes. Having established this reference of normal could serve as important comparative biomarker when trying to identify individuals at risk for disease, such as Alzheimer's disease, that are known to affect cortical complexity. 80 5.2 Introduction The structure of the human cerebral cortex undergoes significant changes throughout the adult lifespan. Even in the absence of any measurable or symptomatic cerebral disease, there are measurable changes in the properties of the cerebral cortex (e.g., thickness, volume, curvature, gyrification index, complexity). Numerous studies have documented volumetric and shape changes. These studies of normal aging can serve as reference biomarkers when trying to distinguish the effects of normal aging from those of progressive neurodegenerative disease. In a recent large study of normal aging, global fractal dimension (a measure of shape complexity) was recently found to steadily decrease across the lifespan in healthy individuals aged 20-89, as seen in Chapter 3. However, it is also clear that normal aging (and neurodegenerative diseases) have variable effects on the cerebral cortex, with some regions being more selectively prone to age-related atrophy [1-3]. Additionally, several groups have reported on the acceleration of atrophy with normal aging for particular regions [1,4-6]. Given that cortical atrophy is a focal process, additional information will be gained by performing the characterization of cortical complexity changes due to normal aging at a local scale. Another motivation is that the local pattern of cortical complexity loss with aging differs from alterations associated with neurodegenerative disease, such as Alzheimer's disease or Frontotemporal dementia. A robust 81 analysis at a local scale will lead to the characterization of spatial and temporal pattern signatures of cerebral cortical fractal dimension associated with normal aging and our understanding of the patterns and trajectories of change with normal aging will help us to characterize change with neurodegenerative diseases, without the effects of normal aging, better. Advances in postimaging analysis have enabled the ability to compute the fractal cerebral dimension of the cortex on a local region of predefined size. The value for a region of interest can then be calculated by aggregating individual values of all cortical voxels that share a particular property (i.e., are contained in a particular lobe, or are located in a particular gyrus). The labels of the cerebral cortex are generated using semiautomatic cortical segmentation and parcellation software (FreeSurfer). The purpose of this paper is to characterize local cerebral cortical complexity changes on a lobar and ROI level and to report on the laterality, linearity, and spatiotemporal distribution of change in the shape complexity of the cerebral cortex across the adult human lifespan, by a large cross-sectional examination. 5.3 Methodology 5.3.1 Participants Participants for this study were 301 individuals aged 20-88 (mean 52.8 ± 19.6 years; uniform age distribution with ~44 subjects per decade; 192 82 women, 109 men) from the Dallas Lifespan Brain Study. For more information on DLBS see Chapter 3, Sections 3.3.1 and 3.3.2. 5.3.2 MRI Acquisition All participants were scanned on a single 3T Philips Achieva scanner equipped with an 8-channel head coil. High-resolution anatomical images were collected with a T1-weighted MP-RAGE sequence with 160 sagittal slices, 1×1×1mm3 voxel; 204×256×160 matrix, TR=8.1ms, TE=3.7ms, flip-angle=12°. The raw data used in this study were extracted from high-resolution high contrast magnetic resonance images (MP-RAGE, resolution of 1 x 1 x 1.25mm, TR =9.7 ms, TE= 4 ms, flip angle = 10 degrees, T1 = 20 msec, and TD = 200 msec). 5.3.3 MRI Processing Segmentation of the brain images was performed using a semiautomated segmentation software suite called FreeSurfer (Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Boston). FreeSurfer contains a set of tools for analysis and visualization of structural and functional brain imaging data. FreeSurfer has been described in detail in prior publications [9-17] and our pipeline for image segmentation with FreeSurfer with subsequent manual editing has been described in Chapter 3. 83 The cortical parcellation is created by labeling each cortical voxel based on registration to a spherical atlas [18]. By the parcellation of the cerebral cortex into units with respect to gyral and sulcal structure [13,19] cortical parcellation regions for each hemisphere were identified. 5.3.4 Computing Local Fractal Dimension The fractal dimension (FD) of the cortical ribbon was computed using a custom software program called the Cortical Complexity Calculator. The version of C3 used in this study was written on Mac OS X (10.5) using the XCode environment in Objective C with graphic implementation using OpenGL. Computation of local fractal dimension has been described in Chapter 2. The cortical parcellation image generated by FreeSurfer was then co-registered with the local fractal dimension image using a MATLAB script. To compute regional values for each cortical region, for each hemisphere, we grouped all cortical voxels that shared the same parcellation label as determined by FreeSurfer. The regions were then grouped to form larger regions (lobes) based upon the FreeSurfer predetermined scheme. 84 5.4 Results 5.4.1 Lobar Results For both hemispheres, the mean fractal dimension of the lobes across the lifespan was consistently in the following order: temporal > occipital > parietal > frontal. The average data for subjects in their 20s and 80s are summarized in Table 5.1. Fractal dimension values for each lobe (Frontal, Parietal, Temporal, and Occipital)<