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

Construction of 4D high-definition cortical surface atlases of infants: Methods and applications

In neuroimaging, cortical surface atlases play a fundamental role for spatial normalization, analysis, visualization, and comparison of results across individuals and different studies. However, existing cortical surface atlases created for adults are not suitable for infant brains during the first two years of life, which is the most dynamic period of postnatal structural and functional development of the highly-folded cerebral cortex. Therefore, spatiotemporal cortical surface atlases for infant brains are highly desired yet still lacking for accurate mapping of early dynamic brain development. To bridge this significant gap, leveraging our infant-dedicated computational pipeline for cortical surface-based analysis and the unique longitudinal infant MRI dataset acquired in our research center, in this paper, we construct the first spatiotemporal (4D) high-definition cortical surface atlases for the dynamic developing infant cortical structures at 7 time points, including 1, 3, 6, 9, 12, 18, and 24 months of age, based on 202 serial MRI scans from 35 healthy infants. For this purpose, we develop a novel method to ensure the longitudinal consistency and unbiasedness to any specific subject and age in our 4D infant cortical surface atlases. Specifically, we first compute the within-subject mean cortical folding by unbiased groupwise registration of longitudinal cortical surfaces of each infant. Then we establish longitudinally-consistent and unbiased inter-subject cortical correspondences by groupwise registration of the geometric features of within-subject mean cortical folding across all infants. Our 4D surface atlases capture both longitudinally-consistent dynamic mean shape changes and the individual variability of cortical folding during early brain development. Experimental results on two independent infant MRI datasets show that using our 4D infant cortical surface atlases as templates leads to significantly improved accuracy for spatial normalization of cortical surfaces across infant individuals, in comparison to the infant surface atlases constructed without longitudinal consistency and also the FreeSurfer adult surface atlas. Moreover, based on our 4D infant surface atlases, for the first time, we reveal the spatially-detailed, region-specific correlation patterns of the dynamic cortical developmental trajectories between different cortical regions during early brain development

Novel Approaches to the Representation and Analysis of 3D Segmented Anatomical Districts

Nowadays, image processing and 3D shape analysis are an integral part of clinical practice and have the potentiality to support clinicians with advanced analysis and visualization techniques. Both approaches provide visual and quantitative information to medical practitioners, even if from different points of view. Indeed, shape analysis is aimed at studying the morphology of anatomical structures, while image processing is focused more on the tissue or functional information provided by the pixels/voxels intensities levels. Despite the progress obtained by research in both fields, a junction between these two complementary worlds is missing. When working with 3D models analyzing shape features, the information of the volume surrounding the structure is lost, since a segmentation process is needed to obtain the 3D shape model; however, the 3D nature of the anatomical structure is represented explicitly. With volume images, instead, the tissue information related to the imaged volume is the core of the analysis, while the shape and morphology of the structure are just implicitly represented, thus not clear enough. The aim of this Thesis work is the integration of these two approaches in order to increase the amount of information available for physicians, allowing a more accurate analysis of each patient. An augmented visualization tool able to provide information on both the anatomical structure shape and the surrounding volume through a hybrid representation, could reduce the gap between the two approaches and provide a more complete anatomical rendering of the subject. To this end, given a segmented anatomical district, we propose a novel mapping of volumetric data onto the segmented surface. The grey-levels of the image voxels are mapped through a volume-surface correspondence map, which defines a grey-level texture on the segmented surface. The resulting texture mapping is coherent to the local morphology of the segmented anatomical structure and provides an enhanced visual representation of the anatomical district. The integration of volume-based and surface-based information in a unique 3D representation also supports the identification and characterization of morphological landmarks and pathology evaluations. The main research contributions of the Ph.D. activities and Thesis are: \u2022 the development of a novel integration algorithm that combines surface-based (segmented 3D anatomical structure meshes) and volume-based (MRI volumes) information. The integration supports different criteria for the grey-levels mapping onto the segmented surface; \u2022 the development of methodological approaches for using the grey-levels mapping together with morphological analysis. The final goal is to solve problems in real clinical tasks, such as the identification of (patient-specific) ligament insertion sites on bones from segmented MR images, the characterization of the local morphology of bones/tissues, the early diagnosis, classification, and monitoring of muscle-skeletal pathologies; \u2022 the analysis of segmentation procedures, with a focus on the tissue classification process, in order to reduce operator dependency and to overcome the absence of a real gold standard for the evaluation of automatic segmentations; \u2022 the evaluation and comparison of (unsupervised) segmentation methods, finalized to define a novel segmentation method for low-field MR images, and for the local correction/improvement of a given segmentation. The proposed method is simple but effectively integrates information derived from medical image analysis and 3D shape analysis. Moreover, the algorithm is general enough to be applied to different anatomical districts independently of the segmentation method, imaging techniques (such as CT), or image resolution. The volume information can be integrated easily in different shape analysis applications, taking into consideration not only the morphology of the input shape but also the real context in which it is inserted, to solve clinical tasks. The results obtained by this combined analysis have been evaluated through statistical analysis

3D Shape Similarity Through Structural Descriptors

Due to the recent improvements to 3D object acquisition, visualization and modeling techniques, the number of 3D models available is more and more growing, and there is an increasing demand for tools supporting the automatic search for 3D objects and their sub-parts in digital archives. Whilst there are already techniques for rapidly extracting knowledge from massive volumes of texts (like Google [htt]) it is harder to structure, filter, organize, retrieve and maintain archives of digital shapes like images, 3D objects, 3D animations and virtual or augmented reality. This situations suggests that in the future a primary challenge in computer graphics will be how to find models having a similar global and/or local appearance. Shape descriptors and the methodologies used to compare them, occupy an important role for achieving this task. For this reason a first contribution of this thesis is to provide a critical analysis of the most representative geometric and structural shape descriptors with respect to a set of properties that shape descriptors should have. This analysis is targeted at highlighting the differences between descriptors in order to better understand where a descriptor fails and another succeed. As a second contribution, the thesis investigates the problem of using a structural descriptor for shape comparison purposes. A large class of structural shape descriptors can be easily encoded as directed, a-cyclic and attributed graphs, thus the problem of comparing structural descriptors is approached as a graph matching problem. The techniques used for graph comparison have an exponential computational complexity and it is therefore necessary to define an algorithmic approximation of the optimal solution. The methods for structural descriptors comparison, commonly used in the computer graphics community, consist of heuristic graph matching algorithms for specific application tasks, while it is lacking a general approach suitable for incorporating different heuristics applicable in different application tasks. The second contribution presented in this thesis is aimed at defining a framework for expressing the optimal algorithm for the computation of the maximal common subgraph in a formalization which makes it straightforward usable for plugging heuristics in it, in order to achieving different approximations of the optimal solution according to the specific case. Implemented heuristics for robust graph matching with respect to graph structural noise are discussed and experimented on sub-part correspondence between similar 3D objects, and shape retrieval application with respect to different structural graph descriptors

The functional neuroanatomy of auditory sensory gating and its behavioural implications

Auditory sensory gating (ASG) is the ability in individuals to suppress incoming irrelevant sensory input, indexed by evoked response to paired auditory stimuli. ASG is impaired in psychopathology such as schizophrenia, in which it has been proposed as putative endophenotype. This study aims to characterise electrophysiological properties of the phenomenon using MEG in time and frequency domains as well as to localise putative networks involved in the process at both sensor and source level. We also investigated the relationship between ASG measures and personality profiles in healthy participants in the light of its candidate endophenotype role in psychiatric disorders. Auditory evoked magnetic fields were recorded in twenty seven healthy participants by P50 ‘paired-click’ paradigm presented in pairs (conditioning stimulus S1- testing stimulus S2) at 80dB, separated by 250msec with inter trial interval of 7-10 seconds. Gating ratio in healthy adults ranged from 0.5 to 0.8 suggesting dimensional nature of P50 ASG. The brain regions active during this process were bilateral superior temporal gyrus (STG) and bilateral inferior frontal gyrus (IFG); activation was significantly stronger in IFG during S2 as compared to S1 (at p<0.05). Measures of effective connectivity between these regions using DCM modelling revealed the role of frontal cortex in modulating ASG as suggested by intracranial studies, indicating major role of inhibitory interneuron connections. Findings from this study identified a unique event-related oscillatory pattern for P50 ASG with alpha (STG)-beta (IFG) desynchronization and increase in cortical oscillatory gamma power (IFG) during S2 condition as compared to S1. These findings show that the main generator for P50 response is within temporal lobe and that inhibitory interneurons and gamma oscillations in the frontal cortex contributes substantially towards sensory gating. Our findings also show that ASG is a predictor of personality profiles (introvert vs extrovert dimension)

New Directions for Contact Integrators

Contact integrators are a family of geometric numerical schemes which guarantee the conservation of the contact structure. In this work we review the construction of both the variational and Hamiltonian versions of these methods. We illustrate some of the advantages of geometric integration in the dissipative setting by focusing on models inspired by recent studies in celestial mechanics and cosmology.Comment: To appear as Chapter 24 in GSI 2021, Springer LNCS 1282

Faculty Publications and Creative Works 2004

Faculty Publications & Creative Works is an annual compendium of scholarly and creative activities of University of New Mexico faculty during the noted calendar year. Published by the Office of the Vice President for Research and Economic Development, it serves to illustrate the robust and active intellectual pursuits conducted by the faculty in support of teaching and research at UNM

2014 Update of the Alzheimer's Disease Neuroimaging Initiative: A review of papers published since its inception

The Alzheimer's Disease Neuroimaging Initiative (ADNI) is an ongoing, longitudinal, multicenter study designed to develop clinical, imaging, genetic, and biochemical biomarkers for the early detection and tracking of Alzheimer's disease (AD). The initial study, ADNI-1, enrolled 400 subjects with early mild cognitive impairment (MCI), 200 with early AD, and 200 cognitively normal elderly controls. ADNI-1 was extended by a 2-year Grand Opportunities grant in 2009 and by a competitive renewal, ADNI-2, which enrolled an additional 550 participants and will run until 2015. This article reviews all papers published since the inception of the initiative and summarizes the results to the end of 2013. The major accomplishments of ADNI have been as follows: (1) the development of standardized methods for clinical tests, magnetic resonance imaging (MRI), positron emission tomography (PET), and cerebrospinal fluid (CSF) biomarkers in a multicenter setting; (2) elucidation of the patterns and rates of change of imaging and CSF biomarker measurements in control subjects, MCI patients, and AD patients. CSF biomarkers are largely consistent with disease trajectories predicted by β-amyloid cascade (Hardy, J Alzheimer's Dis 2006;9(Suppl 3):151-3) and tau-mediated neurodegeneration hypotheses for AD, whereas brain atrophy and hypometabolism levels show predicted patterns but exhibit differing rates of change depending on region and disease severity; (3) the assessment of alternative methods of diagnostic categorization. Currently, the best classifiers select and combine optimum features from multiple modalities, including MRI, [(18)F]-fluorodeoxyglucose-PET, amyloid PET, CSF biomarkers, and clinical tests; (4) the development of blood biomarkers for AD as potentially noninvasive and low-cost alternatives to CSF biomarkers for AD diagnosis and the assessment of α-syn as an additional biomarker; (5) the development of methods for the early detection of AD. CSF biomarkers, β-amyloid 42 and tau, as well as amyloid PET may reflect the earliest steps in AD pathology in mildly symptomatic or even nonsymptomatic subjects and are leading candidates for the detection of AD in its preclinical stages; (6) the improvement of clinical trial efficiency through the identification of subjects most likely to undergo imminent future clinical decline and the use of more sensitive outcome measures to reduce sample sizes. Multimodal methods incorporating APOE status and longitudinal MRI proved most highly predictive of future decline. Refinements of clinical tests used as outcome measures such as clinical dementia rating-sum of boxes further reduced sample sizes; (7) the pioneering of genome-wide association studies that leverage quantitative imaging and biomarker phenotypes, including longitudinal data, to confirm recently identified loci, CR1, CLU, and PICALM and to identify novel AD risk loci; (8) worldwide impact through the establishment of ADNI-like programs in Japan, Australia, Argentina, Taiwan, China, Korea, Europe, and Italy; (9) understanding the biology and pathobiology of normal aging, MCI, and AD through integration of ADNI biomarker and clinical data to stimulate research that will resolve controversies about competing hypotheses on the etiopathogenesis of AD, thereby advancing efforts to find disease-modifying drugs for AD; and (10) the establishment of infrastructure to allow sharing of all raw and processed data without embargo to interested scientific investigators throughout the world