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ALGORITHMS FOR FUNCTIONAL AND ANATOMICAL BRAIN ANALYSIS
The development of high dimensional brain mapping in the field of computational anatomy (CA) and its integration with other state-of-the-art brain imaging technologies continues to be a unique opportunity to study both the underlying neurobiology of brain structure and its connections, and the relationships between brain structure abnormalities and patterns of cognitive deficits. Such mapping tools permit the precise formulation of hypotheses concerning brain structure and function determined by patterns of connectivity and shape particularly in development and neurodegeneration. Over the past fifteen years, many investigators have been studying the shape and structure of the human brain in multiple anatomies in common coordinates. Further, emerging methodologies that integrate anatomical and functional information from multiple data provide an opportunity to ask detailed anatomical questions in a single set of standard coordinates. It is now possible to perform functional measurements and anatomical measurements at roughly 1.0 mm resolution. Systems now exist in isolation of each other for examining gray matter reconstructions of the neocortex, studying the gyrification, folding and sulcal patterning of the gray/white boundary of the neocortex, as well as the anatomical size and shape of deep nuclei in the brain such as the hippocampus, thalamus and caudate. Our group has been involved in the development of these tools, including surface and volume mapping tools, cortical and surface generation tools, gyral and sulcal curve generation and the analysis of these structural data. These methods are now being used by investigators around the world in structural studies of the neocortex and deep nuclei in a variety of neurodevelopmental and neurodegenerative processes.
Recent developments in observing the activation of brain regions via functional magnetic resonance imagery (fMRI) while different tasks are being processed are now providing a clear look at the working of this marvellous machinery. Such studies using tools developed in TRD1 are expected to reveal an in depth understanding of the intricate and effortless processing humans can perform while they go about in their daily lives. Knowledge gained from such studies is expected to provide better understanding of the normal mechanisms and aberrations to these mechanisms in developmental situations. Furthermore, in TRD3, diffusion tensor magnetic resonance imaging (DT-MRI or DTI) provides useful physiological information noninvasively, not only about the fiber structure of normal tissue, but also about its changes in development, disease and degeneration. It has already been shown to be of value in studies of neuroanatomy, fiber connectivity, and brain development. DT-MRI has been used in the investigation of cerebral ischemia, brain maturation and traumatic brain injury. It also promises to further our understanding of brain disorders and abnormalities such as adhd, autism, stroke, tumors and metabolic disorders, epilepsy, multiple sclerosis, schizophrenia, Alzheimer's disease and cognitive impairment. Our collaborators have now begun to use fMRI and DT-MRI data to understand the intricate functional properties of the whole brain as well as the neocortex. Thus, our CA tools for the neocortex can be extended to the whole brain and additional tools for analyzing functional and connectivity data in brain and cortical structures can be developed. The tools will be made available to the wider scientific community. In particular, the developments should benefit a wide range of clinical disciplines from psychiatry to pediatrics. Our specific aims are to integrate such structural and functional analysis tools into a software system by developing the following algorithms:Aim 1: Large Deformation Diffeomorphic Metric Mapping (LDDMM) for landmarks, curves, surfaces and volumes in whole brain analysis and registration; Aim 2: LDDMM for Diffusion Tensor images (LDDMM-DT) and tensor algebra; Aim 3: LDDMM for longitudinal and developmental analysis; Aim 4: LDDMM and signal processing methods for Functional Anatomy Building a software system that supports the data structures of curves, surfaces, and scalar and tensorial lattices of volumes will be essential in utilizing methods developed in TRD1 and TRD3 in studying brain structure and function as illustrated in Figure 1. The vertical steps illustrate the use of landmark, curves, surface and volume matching via LDDMM in registering fMRI and DTI data. The horizontal steps illustrate the intersubject comparison via a concantenation of rigid matching and LDDMM.
Figure 2 illustrates the basic model for examining fMRI and DTI data in extrinsic atlas coordinates in the compositional approach in which the high resolution structural representation (sMRI) (S) is used as an intermediate substrate to transfer the individuals fMRI/DTI to the common extrinsic atlas coordinate system (A). The arrows represent bijections between coordinates. The mapping labelled FS transforms the functional scan coordinates within the individuals structural scan by constraining anatomically the activation for a given individual to that individual’s high resolution cortical structure. The composition of transforms in the FS SA uses the sMRI for correspondence to extrinsic atlas coordinates first mapping the structural domain within the individual and then onto extrinsic coordinates via large deformation.
A key component of CA is the Large Deformation Diffeomorphic Metric Mapping (LDDMM) algorithm (ref) that provides a framework for a hierarchy of mappings of embedded structures such as landmarks, gyral/sulcal curves, cortical surfaces, scalar and diffusion image volumes. Such a sequence of mappings ensures that connected sets and disjoint sets remain connected and structure and topology remain preserved. LDDMM can be used to study anatomical structures at various scales from brain structures to sub-microscopic structures, and is being used in Morphometry BIRN and Mouse BIRN projects. LDDMM has been extended to LDDMM-Landmark, LDDMM-Curve, LDDMM-Surface and LDDMM-DTI. The following examples demonstrate the impact of LDDMM and its extensions on the precise quantification of anatomical structure and function in disease. Below left shows the dataflow for the shape analysis-processing pipeline: 1) structural MRI data is uploaded from WashU, 2) de-identified locally, 3) semi-automated subcortical segmentation is done at MGH, 3) shape analyses of segmented hippocampus data is done at JHU, and 4) visualization of combined morphometric results is done at BWH. Top right shows analysis of LDDMM generated metric distances between hippocampi in a study of Alzheimer’s via a Linear Discriminant Analysis 2D scatter plot (ref) . Class labels are represented by Nondemented Controls (1), Alzheimer’s Disease (2) and Semantic Dementia (3). Teragrid resources at SDSC and NCSA via GPFS-WAN were used to analyze hippocampi from 101 subjects.
Landmarks (left) and curves (right) placed on template (top) and target (bottom) cingulate surfaces shown below. Increasing sub-voxel accuracy of LDDMM algorithms is indicated by the averaged CDF for surface distances between 130 left cingulate surfaces from a study of schizophrenia (ref) at the laboratory of Dr. Csernansky, Washington University in St Louis.
Target and template planum temporale (PT) cortical surfaces are colored by curvature information while deformed surfaces (ref) are colored by the degree of deformation. Red and blue respectively denote stretched and compressed regions after matching. CDFs indicate sub-voxel accuracy after mapping of 20 surfaces. Distance error maps intuitively show how far original (left) and deformed (right) surfaces are from the template surface respectively. Data from the laboratory of Dr. Barta, Johns Hopkins University School of Medicine.
Tensor distribution of a region in one slice before (left) and after (middle) mapping (blue and red indicate template and target respectively). The graph compares the difference between template and target tensors before and after different matching schemes. LDDMM-DTI (ref) improves quality in areas with low FA values.
Below left shows coronal (left) and sagittal (right) cropped views of segmentations of MTL averaged from 15 subjects with different alignment schemes. Top right shows hemodynamic responses represented by the beta coefficient of functional response from a 39-voxel (609 mm3) cluster within the right perirhinal cortex. Lower panel shows areas of significant functional activity during the recognition memory task associated with incidental encoding (R v F: remembered vs forgotten), showing as colored overlays on coronal slices through the MTL. (ref)
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