Parcellation of Human Amygdala Subfields Using Orientation Distribution Function and Spectral K-means Clustering

Amygdala plays an important role in fear and emotional learning, which are critical for human survival. Despite the functional relevance and unique circuitry of each human amygdaloid subnuclei, there has yet to be an efficient imaging method for identifying these regions in vivo. A data-driven approach without prior knowledge provides advantages of efficient and objective assessments. The present study uses high angular and high spatial resolution diffusion magnetic resonance imaging to generate orientation distribution function, which bears distinctive microstructural features. The features were extracted using spherical harmonic decomposition to assess microstructural similarity within amygdala subfields are identified via similarity matrices using spectral k-mean clustering. The approach was tested on 32 healthy volunteers and three distinct amygdala subfields were identified including medial, posterior-superior lateral, and anterior-inferior lateral

Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel regression is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. Unlike many previous partial differential equation based approaches involving diffusion, our approach represents the solution of diffusion analytically, reducing numerical inaccuracy and slow convergence. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, we have applied the method in characterizing the localized growth pattern of mandible surfaces obtained in CT images from subjects between ages 0 and 20 years by regressing the length of displacement vectors with respect to the template surface.Comment: Accepted in Medical Image Analysi

Shape analysis of the human brain.

Autism is a complex developmental disability that has dramatically increased in prevalence, having a decisive impact on the health and behavior of children. Methods used to detect and recommend therapies have been much debated in the medical community because of the subjective nature of diagnosing autism. In order to provide an alternative method for understanding autism, the current work has developed a 3-dimensional state-of-the-art shape based analysis of the human brain to aid in creating more accurate diagnostic assessments and guided risk analyses for individuals with neurological conditions, such as autism. Methods: The aim of this work was to assess whether the shape of the human brain can be used as a reliable source of information for determining whether an individual will be diagnosed with autism. The study was conducted using multi-center databases of magnetic resonance images of the human brain. The subjects in the databases were analyzed using a series of algorithms consisting of bias correction, skull stripping, multi-label brain segmentation, 3-dimensional mesh construction, spherical harmonic decomposition, registration, and classification. The software algorithms were developed as an original contribution of this dissertation in collaboration with the BioImaging Laboratory at the University of Louisville Speed School of Engineering. The classification of each subject was used to construct diagnoses and therapeutic risk assessments for each patient. Results: A reliable metric for making neurological diagnoses and constructing therapeutic risk assessment for individuals has been identified. The metric was explored in populations of individuals having autism spectrum disorders, dyslexia, Alzheimers disease, and lung cancer. Conclusion: Currently, the clinical applicability and benefits of the proposed software approach are being discussed by the broader community of doctors, therapists, and parents for use in improving current methods by which autism spectrum disorders are diagnosed and understood

Shape-based detection of cortex variability for more accurate discrimination between autistic and normal brains.

Introduction: Autism is a complex developmental disability that typically appears during the first three years of life, and is the result of a neurological disorder that affects the normal functioning of the brain, impacting development in the areas of social interaction and communication skills. According to the Centers for Disease Control and Prevention (CDC) in 2009, about 1 in 110 American children will fall somewhere in the autistic spectrum. Although the cause of autism is still largely not clear, researchers have suggested that genetic, developmental, and environmental factors may be the cause or the predisposing effects towards developing autism. While shape based statistical analysis methods for autism are still in their early stages, current results show positive outlooks on the ability to detect differences between autistic and normal patients. Methods: The goal of this thesis is to construct a complete package that is capable of taking 2-dimensional images from a standard medical scanner, and be able to construct a three-dimensional representation of the object and examine it through combination of its weighted linear spherical harmonics. The desired outcome is that a distinction can be made between the analysis of autistic and normal brain data. The analysis package created is divided into three distinct components that are capable of performing the complete analysis on a subject. The components included in the package in order of runtime are: volumetric extraction and mesh generation from 2-dimensional medical scanner data, spherical deformation of the constructed mesh, and weighted spherical harmonic representation and analysis. Results: The minimum error for each brain following spherical harmonic reconstruction was calculated along with the fastest iteration at which the brain converged below the error thresholds of 11% and 10%. It was expected that due to the complexity of an Autistic brain these would require more iterations to converge to the same error level as a normal brain. It was also likely that within the number of iterations tested the autistic brains would record a larger final error due to this slower convergence rate. This was confirmed by the data. A global result was examined as well for the autistic and normal data groups. The overall minimum error for normal brain data was significantly lower than the autistic brain data. The average error for autistic brain data was significantly higher in both convergence measurements, but was dramatically higher in the 10% category. Conclusion: Using this method of analyzing data can demonstrate accurate differences in normal and autistic brains. The research that has been generated in this thesis can clearly demonstrate that the normal brain data converged both faster and with a lower rate of error level than the Autistic brain data. This result proves that the autistic brain is a more complex structure, and would be more difficult to reconstruct using this Shape- Based Detection of Cortex Variability process

Hippocampal shape analysis in Alzheimer’s disease using Functional Data Analysis

The hippocampus is one of the first affected regions in Alzheimer's disease. The left hippocampi of control subjects, patients with mild cognitive impairment and patients with Alzheimer's disease are represented by spherical harmonics. Functional data analysis is used in the hippocampal shape analysis. Functional principal component analysis and functional independent component analysis are defined for multivariate functions with two arguments. A functional linear discriminant function is also defined. Comparisons with other approaches are carried out. Our functional approach gives promising results, especially in shape classification. Copyright © 2013 John Wiley & Sons, Ltd

Age-related differences in the structural complexity of subcortical and ventricular structures

It has been well established that the volume of several subcortical structures decreases in relation to age. Different metrics of cortical structure (e.g., volume, thickness, surface area, and gyrification) have been shown to index distinct characteristics of interindividual differences; thus, it is important to consider the relation of age to multiple structural measures. Here, we compare age-related differences in subcortical and ventricular volume to those differences revealed with a measure of structural complexity, quantified as fractal dimensionality. Across 3 large data sets, totaling nearly 900 individuals across the adult lifespan (aged 18–94 years), we found greater age-related differences in complexity than volume for the subcortical structures, particularly in the caudate and thalamus. The structural complexity of ventricular structures was not more strongly related to age than volume. These results demonstrate that considering shape-related characteristics improves sensitivity to detect age-related differences in subcortical structures

Using high angular resolution diffusion imaging data to discriminate cortical regions

Brodmann's 100-year-old summary map has been widely used for cortical localization in neuroscience. There is a pressing need to update this map using non-invasive, high-resolution and reproducible data, in a way that captures individual variability. We demonstrate here that standard HARDI data has sufficiently diverse directional variation among grey matter regions to inform parcellation into distinct functional regions, and that this variation is reproducible across scans. This characterization of the signal variation as non-random and reproducible is the critical condition for successful cortical parcellation using HARDI data. This paper is a first step towards an individual cortex-wide map of grey matter microstructure, The gray/white matter and pial boundaries were identified on the high-resolution structural MRI images. Two HARDI data sets were collected from each individual and aligned with the corresponding structural image. At each vertex point on the surface tessellation, the diffusion-weighted signal was extracted from each image in the HARDI data set at a point, half way between gray/white matter and pial boundaries. We then derived several features of the HARDI profile with respect to the local cortical normal direction, as well as several fully orientationally invariant features. These features were taken as a fingerprint of the underlying grey matter tissue, and used to distinguish separate cortical areas. A support-vector machine classifier, trained on three distinct areas in repeat 1 achieved 80-82% correct classification of the same three areas in the unseen data from repeat 2 in three volunteers. Though gray matter anisotropy has been mostly overlooked hitherto, this approach may eventually form the foundation of a new cortical parcellation method in living humans. Our approach allows for further studies on the consistency of HARDI based parcellation across subjects and comparison with independent microstructural measures such as ex-vivo histology

Detecting and visualizing differences in brain structures with SPHARM and functional data analysis

A new procedure for classifying brain structures described by SPHARM is presented. We combine a dimension reduction technique (functional principal component analysis or functional independent component analysis) with stepwise variable selection for linear discriminant classification. This procedure is compared with many well-known methods in a novel classification problem in neuroeducation, where the reversal error (a common error in mathematical problem solving) is analyzed by using the left and right putamens of 33 participants. The comparison shows that our proposal not only provides outstanding performance in terms of predictive power, but it is also valuable in terms of interpretation, since it yields a linear discriminant function for 3D structures

Hitting the right target : noninvasive localization of the subthalamic nucleus motor part for specific deep brain stimulation

Deep brain stimulation of the subthalamic nucleus (STN) has gained momentum as a therapy for advanced Parkinson’s disease. The stimulation effectively alleviates the patients’ typical motor symptoms on a long term, but can give rise to cognitive and psychiatric adverse effects as well. Based on primate studies, the STN has been divided into three functionally different parts, which were distinguished by their afferent and efferent connections. The largest part is the motor area, followed by an associative and a limbic area. The serious adverse effects on cognition and behavior occurring after deep brain stimulation are assumed to be caused by electrical current spread to the associative and limbic areas of the STN. Therefore, selective stimulation of the motor part of the STN seems crucial, both to obtain the best possible therapeutic effect on the motor symptoms and to minimize the debilitating effects on cognition and behavior. However, current medical imaging techniques do not yet facilitate the required accurate identification of the STN itself, let alone its different functional areas. The final target for DBS is still often adjusted using intraoperative electrophysiology. Therefore, in this thesis we aimed to improve imaging for deep brain stimulation using noninvasive MRI protocols, in order to identify the STN and its motor part. We studied the advantages and drawbacks of already available noninvasive methods to target the STN. This review did not lead to a straightforward conclusion; identification of the STN motor part remained an open question. In follow-up on this question, we investigated the possibility to distinguish the different functional STN parts based on their connectivity information. Three types of information were carefully analyzed in this thesis. First, we looked into the clustering of local diffusion information within the STN region. We visually inspected the complex diffusion profiles, derived from postmortem rat brain data with high angular resolution, and augmented this manual segmentation method using k-means and graph cuts clustering. Because the weighing of different orders of diffusion information in the traditionally used L2 norm on the orientation distribution functions (ODFs) remained an open issue, we developed a specialized distance measure, the so-called Sobolev norm. This norm does not only take into account the amplitudes of the diffusion profiles, but also their extrema. We showed it to perform better than the L2 norm on synthetic phantom data and real brain (thalamus) data. The research done on this topic facilitates better classification by clustering of gray matter structures in the (deep) brain. Secondly, we were the first to analyze the STN’s full structural connectivity, based on probabilistic fiber tracking in diffusion MRI data of healthy volunteers. The results correspond well to topical literature on STN projections. Furthermore, we assessed the structural connectivity per voxel of the STN seed region and discovered a gradient in connectivity to the premotor cortex within the STN. While going from the medial to the lateral part of the STN, the connectivity increases, confirming the expected lateral location of the STN motor part. Finally, the connectivity analysis produced evidence for the existence of a "hyperdirect" pathway between the motor cortex and the STN in humans, which is very useful for future research into stimulation targets. The results of these experiments indicate that it is possible to find the motor part of the STN as specific target for deep brain stimulation using structural connectivity information acquired in a noninvasive way. Third and last, we studied functional connectivity using resting state functional MRI data of healthy volunteers. The resulting significant clusters provided us with the first complete description of the STN’s resting state functional connectivity, which corresponds with the expectations based on available literature. Moreover, we performed a reverse regression procedure with the average time series signals in motor and limbic areas as principal regressors. The results were analyzed for each STN voxel separately and also showed mediolateral gradients in functional connectivity within the STN. The lateral STN part exhibited more motor connectivity, while the medial part seemed to be more functionally connected to limbic brain areas, as described in neuronal tracer studies. These results show that functional connectivity analysis also is a viable noninvasive method to find the motor part of the STN. The work on noninvasive MRI methods for identification of the STN and its functional parts, as presented in this thesis, thus contributes to future specific stimulation of the motor part of the STN for deep brain stimulation in patients with Parkinson’s disease. This may help to maximize the motor effects and minimize severe cognitive and psychiatric side effects