Mapping cortical change in Alzheimer's disease, brain development, and schizophrenia

This paper describes algorithms that can identify patterns of brain structure and function associated with Alzheimer's disease, schizophrenia, normal aging, and abnormal brain development based on imaging data collected in large human populations. Extraordinary information can be discovered with these techniques: dynamic brain maps reveal how the brain grows in childhood, how it changes in disease, and how it responds to medication. Genetic brain maps can reveal genetic influences on brain structure, shedding light on the nature–nurture debate, and the mechanisms underlying inherited neurobehavioral disorders. Recently, we created time-lapse movies of brain structure for a variety of diseases. These identify complex, shifting patterns of brain structural deficits, revealing where, and at what rate, the path of brain deterioration in illness deviates from normal. Statistical criteria can then identify situations in which these changes are abnormally accelerated, or when medication or other interventions slow them. In this paper, we focus on describing our approaches to map structural changes in the cortex. These methods have already been used to reveal the profile of brain anomalies in studies of dementia, epilepsy, depression, childhood- and adult-onset schizophrenia, bipolar disorder, attention-deficit/hyperactivity disorder, fetal alcohol syndrome, Tourette syndrome, Williams syndrome, and in methamphetamine abusers. Specifically, we describe an image analysis pipeline known as cortical pattern matching that helps compare and pool cortical data over time and across subjects. Statistics are then defined to identify brain structural differences between groups, including localized alterations in cortical thickness, gray matter density (GMD), and asymmetries in cortical organization. Subtle features, not seen in individual brain scans, often emerge when population-based brain data are averaged in this way. Illustrative examples are presented to show the profound effects of development and various diseases on the human cortex. Dynamically spreading waves of gray matter loss are tracked in dementia and schizophrenia, and these sequences are related to normally occurring changes in healthy subjects of various ages.

Introduction

Brain imaging continues to provide new and remarkable insights on how disease impacts the human brain. Large-scale brain mapping initiatives are charting brain structure and function in hundreds or even thousands of human subjects across the life span (e.g., Good et al., 2001, N = 465; Mazziotta et al., 2001; N = 7000). The individuals surveyed include twin populations and patients with Alzheimer's disease, schizophrenia, and other neurological and psychiatric disorders. At the cutting edge of this research are mathematical and computational strategies to compare and contrast imaging information from large populations, and to map disease effects on the brain. Such techniques are now revealing dynamic waves of brain change in development, dementia, and psychosis. Mathematical models are also identifying how drug treatments, risk genes, and demographic factors modulate these dynamic processes. Another related type of brain map—a genetic brain map—can also reveal how heredity and environmental factors influence cortical development and disease (Cannon et al., 2002, Thompson et al., 2001a, Thompson et al., 2001b). These brain mapping techniques empower disease detection, exploration, and intervention, and offer new insights in clinical trials assessing drugs that slow degenerative brain changes (Ashburner et al., 2003, Jack et al., 2003, Zijdenbos et al., 1996).

Many brain imaging studies focus on the cerebral cortex, which changes profoundly during development and disease. Nonetheless, cortical geometry is complex and varies widely from individual to individual. This presents a challenge for all brain mapping efforts that aim to pool neuroimaging data across subjects. Unless mathematical tactics are developed to model the structural and functional variation of the human brain, efforts to detect group differences in brain structure are limited considerably, and disease effects on cortical anatomy are difficult to identify.

As imaging studies expand into ever-larger populations, we and others have developed techniques that have mapped unsuspected patterns of brain changes in childhood (Giedd et al., 1999, Gogtay et al., 2004, Paus et al., 1999, Sowell et al., 2001, Sowell et al., 2002a, Thompson et al., 2004b, Sowell et al., 2004b, Thompson et al., 2000a, Thompson et al., 2001b) and dynamic waves of tissue loss in dementia and schizophrenia (Rapoport et al., 1999, Thompson et al., 2001a, Thompson et al., 2001b, Thompson et al., 2003). Maps of disease effects on the brain, computed from serial magnetic resonance imaging (MRI) scans of patients (Janke et al., 2001) or those at genetic risk (Cannon et al., 2002), can clarify disease progression and transmission, and can also provide therapeutic targets (cf. Fox et al., 2001). All these efforts draw on methods from the rapidly growing field of computational anatomy (see e.g., Ashburner et al., 2003, Bankman, 1999, Bookstein, 2001, Chung, 2001, Csernansky et al., 1998, Davatzikos, 1996, Davatzikos et al., 2001, Drury and Van Essen, 1997, Evans et al., 1994, Fischl and Dale, 2000, Fitzpatrick and Sonka, 2000, Gee and Bajcsy, 1998, Gerig et al., 2001, Grenander and Miller, 1998, Leahy and Insana, 2001, Miller et al., 2002, Sereno et al., 1996, Thompson and Toga, 2003a, Thompson and Toga, 2003b, Thompson et al., 2000a, Thompson et al., 2000b, Thompson et al., 2001a, Thompson et al., 2001b, cf. Toga, 1998, Toga and Mazziotta, 2002; see other papers in this issue for recent developments and reviews).

The methods described in this paper represent one set of approaches used in computational anatomy today. Computational anatomy uses mathematical techniques from differential geometry, numerical analysis, and the theory of partial differential equations (Sapiro, 2001) to model objects and processes in brain images. Geometrical surfaces, for example, are often used to represent the shape of brain structures such as the cerebral cortex (Fischl et al., 2001, Thompson and Toga, 1996, van Essen, 2004). Techniques to analyze and compare cortical structure have advanced through many years of research in computer vision, artificial intelligence, image analysis, and computer graphics. Neuroscience studies applying these methods typically aim to uncover patterns of altered structure and function in healthy and diseased populations using novel mathematics to identify new features, to compare brain measures, or to increase the sensitivity to detect statistically significant differences. Detecting systematic effects of disease on brain structure is challenging as it requires: (1) computational techniques to generate average patterns of brain structure in human populations (see Fig. 1); (2) statistical methods that work with scalar or vector fields to encode individual variations in brain structure and identify significant group differences or changes over time (Fig. 2, Fig. 3); and (3) large and richly characterized image databases, with related cognitive, clinical, demographic, and often genetic, data on patients and healthy controls.

One of the most fundamental challenges in brain mapping is how to average and compare brain structure across subjects. The anatomy of different subjects varies widely, especially the gyral patterns of the cortex, and this presents a problem when averaging brain images together, as can be seen in an example (Fig. 1).

Many diseases affect cortical anatomy, but there have been major difficulties in developing average and statistical representations of the effects of disease on the cortex, given the extreme variations in cortical patterning across subjects. One solution to this, proposed here, is to build explicit geometric models of the cortex using parametric surfaces and to build deformation maps on the geometric models that explicitly associate corresponding cortical regions across subjects. A similar ‘surface-based’ approach has also been taken by other groups developing frameworks to visualize or analyze cortical data (e.g., Hurdal and Stephenson, 2004, Mangin et al., 2004, Tosun et al., 2004, van Essen, 2004, this volume).

A clear benefit of this approach is that it can be used to create average models of cortical anatomy that retain anatomic features (e.g., sulcal landmarks) found consistently across subjects. Templates of cortical anatomy can be built retaining detailed information about individual variability. Functional or structural data from many subjects can then be transferred to a common neuroanatomical template while adjusting for individual differences in gyral patterning. Features that have a consistent relation to the gyral anatomy are then greatly reinforced in the group average models (Fig. 1). The explicit matching of anatomy eliminates much of the confounding anatomical variance when pooling data across subjects and makes consistent functional and structural patterns easier to identify (Rasser et al., 2004, Thompson et al., 2001a, Thompson et al., 2001b).

When matching cortical anatomy between subjects, mathematical criteria can be applied to enforce the matching of key functional or anatomic landmarks from one data set to another. 3D deformation maps can be computed to match these features exactly, while deforming one surface onto another. These deformation algorithms often draw on methods from continuum mechanics, extending concepts to brain images that were originally developed to model the deformation of 3D elastic and fluid media (these tools are described later).

A second benefit of surface-based cortical modeling is that the anatomical variability of the cortex can be studied by constructing mappings that deform one cortex onto another. If these deformation mappings are analyzed statistically, group differences in cortical anatomy, or hemispheric asymmetries, can be pinpointed and mapped. Their anatomical profile can also be visualized. Regions with significant differences in cortical thickness, gyral patterning, or other cortical attributes can be visualized in color on a graphically rendered anatomical surface. Systematic differences or changes in cortical organization, gray matter distribution, cortical thickness, or asymmetry can then be distinguished from normal variations, and statistical criteria can be developed to assess if cortical anatomy is abnormal by referring to normative data on anatomical variation (Thompson et al., 1997).

This paper gives an overview of methods we have developed to analyze cortical anatomy. Illustrative data from various neuroscience projects are presented, as well as the mathematics used to compute them. We describe the types of maps and models that can be constructed, and how they can be compared across individuals and groups. We discuss three key steps in creating statistical maps of cortical anatomy: (i) cortical parameterization, or creating geometrical models of the cortical surface; (ii) matching cortical features across individuals, which requires warping one brain surface onto another; and (iii) statistical comparisons to understand effects of disease, aging, or development on anatomy, which can also be used to map group differences or identify correlations between brain structure and genetic or cognitive differences. We show how these methods can be applied to reveal hitherto unknown features of Alzheimer's disease, schizophrenia, and normal development, suggesting their potential in biomedical and clinical research. Finally, we suggest areas where additional mathematical research is likely to speed the pace of discovery in these areas of neuroscience.