Medical imaging and brain research are among the most challenging and fascinating topics of contemporary science. Exciting possibilities exist to improve both the state of the art in medicine and our understanding of the human brain. These opportunities have motivated many researchers to use powerful computational methods to analyze brain structure and function, applying them to key questions in medicine and neuroscience. Algorithms can now uncover disease-specific patterns of brain structure and function in whole populations. These tools now chart how the brain grows in childhood, detect abnormalities in disease, and visualize how genes, medication, and demographic factors affect the brain. Image analysis methods can also identify and monitor systematic patterns of altered anatomy in diseases such as Alzheimer’s, tumor growth, epilepsy, and multiple sclerosis, and psychiatric disorders such as schizophrenia, autism, and dyslexia.
We briefly review recent developments in brain image analysis, focusing on (1) current mathematical and computational challenges in the field, and (2) areas where data mining and information-theoretic tools are likely to advance the field in the future. We introduce a range of new tools that compare, contrast, and average imaging data in large human populations. We describe our construction of statistical brain atlases that store detailed information on how the brain varies across age and gender, across time, in health and disease, and over time. Specifically, we introduce a mathematical framework to analyze variations in brain organization, cortical patterning, asymmetry and tissue distribution in several collaborative studies of brain development and disease (N>1000 scans). Mathematics based on Grenander’s pattern theory, covariant partial differential equations (PDEs), pull-backs of mappings under harmonic flows, and high-dimensional random tensor fields are employed to encode anatomic variations in population-based brain image database. We use this reference information to detect disease-specific abnormalities in Alzheimer's disease and schizophrenia, including dynamic changes and medication response over time. We use illustrative examples to show how population patterns of cortical organization, asymmetry, and disease-specific trends can be resolved that are not apparent in individual brain images. Specialized approaches are used to identify generic features of brain organization. These encode cortical pattern variations that complicate comparisons of brain data from one individual to another. We also discuss four-dimensional (4D) maps that store probabilistic information on the dynamics of brain change in development and disease. Digital atlases that generate these maps show considerable promise in identifying general patterns of structural and functional change in diseased populations, and linking them to cognitive, clinical and therapeutic parameters. Finally, we introduce a framework to map how genes affect brain structure. The resulting genetic brain maps can be used in data mining applications, to help investigate inheritance patterns in diseases with known genetic risks.
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