Solving SPDEs for Multi-Dimensional Shape Analysis

161945-Thumbnail Image.png
Description
Statistical Shape Modeling is widely used to study the morphometrics of deformable objects in computer vision and biomedical studies. There are mainly two viewpoints to understand the shapes. On one hand, the outer surface of the shape can be taken

Statistical Shape Modeling is widely used to study the morphometrics of deformable objects in computer vision and biomedical studies. There are mainly two viewpoints to understand the shapes. On one hand, the outer surface of the shape can be taken as a two-dimensional embedding in space. On the other hand, the outer surface along with its enclosed internal volume can be taken as a three-dimensional embedding of interests. Most studies focus on the surface-based perspective by leveraging the intrinsic features on the tangent plane. But a two-dimensional model may fail to fully represent the realistic properties of shapes with both intrinsic and extrinsic properties. In this thesis, severalStochastic Partial Differential Equations (SPDEs) are thoroughly investigated and several methods are originated from these SPDEs to try to solve the problem of both two-dimensional and three-dimensional shape analyses. The unique physical meanings of these SPDEs inspired the findings of features, shape descriptors, metrics, and kernels in this series of works. Initially, the data generation of high-dimensional shapes, here, the tetrahedral meshes, is introduced. The cerebral cortex is taken as the study target and an automatic pipeline of generating the gray matter tetrahedral mesh is introduced. Then, a discretized Laplace-Beltrami operator (LBO) and a Hamiltonian operator (HO) in tetrahedral domain with Finite Element Method (FEM) are derived. Two high-dimensional shape descriptors are defined based on the solution of the heat equation and Schrödinger’s equation. Considering the fact that high-dimensional shape models usually contain massive redundancies, and the demands on effective landmarks in many applications, a Gaussian process landmarking on tetrahedral meshes is further studied. A SIWKS-based metric space is used to define a geometry-aware Gaussian process. The study of the periodic potential diffusion process further inspired the idea of a new kernel call the geometry-aware convolutional kernel. A series of Bayesian learning methods are then introduced to tackle the problem of shape retrieval and classification. Experiments of every single item are demonstrated. From the popular SPDE such as the heat equation and Schrödinger’s equation to the general potential diffusion equation and the specific periodic potential diffusion equation, it clearly shows that classical SPDEs play an important role in discovering new features, metrics, shape descriptors and kernels. I hope this thesis could be an example of using interdisciplinary knowledge to solve problems.
Date Created
2021
Agent

A T1 and DTI Fused 3D Corpus Callosum Analysis in MCI Subjects With High and Low Cardiovascular Risk Profile

128175-Thumbnail Image.png
Description

Understanding the extent to which vascular disease and its risk factors are associated with prodromal dementia, notably Alzheimer's disease (AD), may enhance predictive accuracy as well as guide early interventions. One promising avenue to determine this relationship consists of looking

Understanding the extent to which vascular disease and its risk factors are associated with prodromal dementia, notably Alzheimer's disease (AD), may enhance predictive accuracy as well as guide early interventions. One promising avenue to determine this relationship consists of looking for reliable and sensitive in-vivo imaging methods capable of characterizing the subtle brain alterations before the clinical manifestations. However, little is known from the imaging perspective about how risk factors such as vascular disease influence AD progression. Here, for the first time, we apply an innovative T1 and DTI fusion analysis of 3D corpus callosum (CC) on mild cognitive impairment (MCI) populations with different levels of vascular profile, aiming to de-couple the vascular factor in the prodromal AD stage. Our new fusion method successfully increases the detection power for differentiating MCI subjects with high from low vascular risk profiles, as well as from healthy controls. MCI subjects with high and low vascular risk profiles showed differed alteration patterns in the anterior CC, which may help to elucidate the inter-wired relationship between MCI and vascular risk factors.

Date Created
2016-12-28
Agent

Mapping the Basal Ganglia Alterations in Children Chronically Exposed to Manganese

128529-Thumbnail Image.png
Description

Chronic manganese (Mn) exposure is associated with neuromotor and neurocognitive deficits, but the exact mechanism of Mn neurotoxicity is still unclear. With the advent of magnetic resonance imaging (MRI), in-vivo analysis of brain structures has become possible. Among different sub-cortical

Chronic manganese (Mn) exposure is associated with neuromotor and neurocognitive deficits, but the exact mechanism of Mn neurotoxicity is still unclear. With the advent of magnetic resonance imaging (MRI), in-vivo analysis of brain structures has become possible. Among different sub-cortical structures, the basal ganglia (BG) has been investigated as a putative anatomical biomarker in MR-based studies of Mn toxicity. However, previous investigations have yielded inconsistent results in terms of regional MR signal intensity changes. These discrepancies may be due to the subtlety of brain alterations caused by Mn toxicity, coupled to analysis techniques that lack the requisite detection power. Here, based on brain MRI, we apply a 3D surface-based morphometry method on 3 bilateral basal ganglia structures in school-age children chronically exposed to Mn through drinking water to investigate the effect of Mn exposure on brain anatomy. Our method successfully pinpointed significant enlargement of many areas of the basal ganglia structures, preferentially affecting the putamen. Moreover, these areas showed significant correlations with fine motor performance, indicating a possible link between altered basal ganglia neurodevelopment and declined motor performance in high Mn exposed children.

Date Created
2017-02-03
Agent

A Multivariate Surface-Based Analysis of the Putamen in Premature Newborns: Regional Differences Within the Ventral Striatum

128812-Thumbnail Image.png
Description

Many children born preterm exhibit frontal executive dysfunction, behavioral problems including attentional deficit/hyperactivity disorder and attention related learning disabilities. Anomalies in regional specificity of cortico-striato-thalamo-cortical circuits may underlie deficits in these disorders. Nonspecific volumetric deficits of striatal structures have been

Many children born preterm exhibit frontal executive dysfunction, behavioral problems including attentional deficit/hyperactivity disorder and attention related learning disabilities. Anomalies in regional specificity of cortico-striato-thalamo-cortical circuits may underlie deficits in these disorders. Nonspecific volumetric deficits of striatal structures have been documented in these subjects, but little is known about surface deformation in these structures. For the first time, here we found regional surface morphological differences in the preterm neonatal ventral striatum. We performed regional group comparisons of the surface anatomy of the striatum (putamen and globus pallidus) between 17 preterm and 19 term-born neonates at term-equivalent age. We reconstructed striatal surfaces from manually segmented brain magnetic resonance images and analyzed them using our in-house conformal mapping program. All surfaces were registered to a template with a new surface fluid registration method. Vertex-based statistical comparisons between the two groups were performed via four methods: univariate and multivariate tensor-based morphometry, the commonly used medial axis distance, and a combination of the last two statistics. We found statistically significant differences in regional morphology between the two groups that are consistent across statistics, but more extensive for multivariate measures. Differences were localized to the ventral aspect of the striatum. In particular, we found abnormalities in the preterm anterior/inferior putamen, which is interconnected with the medial orbital/prefrontal cortex and the midline thalamic nuclei including the medial dorsal nucleus and pulvinar. These findings support the hypothesis that the ventral striatum is vulnerable, within the cortico-stiato-thalamo-cortical neural circuitry, which may underlie the risk for long-term development of frontal executive dysfunction, attention deficit hyperactivity disorder and attention-related learning disabilities in preterm neonates.

Date Created
2013-07-03
Agent

Genetic Influence of Apolipoprotein E4 Genotype on Hippocampal Morphometry: An N=725 Surface-Based Alzheimer's Disease Neuroimaging Initiative Study

129539-Thumbnail Image.png
Description

The apolipoprotein E (APOE) e4 allele is the most prevalent genetic risk factor for Alzheimer's disease (AD). Hippocampal volumes are generally smaller in AD patients carrying the e4 allele compared to e4 noncarriers. Here we examined the effect of APOE

The apolipoprotein E (APOE) e4 allele is the most prevalent genetic risk factor for Alzheimer's disease (AD). Hippocampal volumes are generally smaller in AD patients carrying the e4 allele compared to e4 noncarriers. Here we examined the effect of APOE e4 on hippocampal morphometry in a large imaging database—the Alzheimer's Disease Neuroimaging Initiative (ADNI). We automatically segmented and constructed hippocampal surfaces from the baseline MR images of 725 subjects with known APOE genotype information including 167 with AD, 354 with mild cognitive impairment (MCI), and 204 normal controls. High-order correspondences between hippocampal surfaces were enforced across subjects with a novel inverse consistent surface fluid registration method. Multivariate statistics consisting of multivariate tensor-based morphometry (mTBM) and radial distance were computed for surface deformation analysis. Using Hotelling's T2 test, we found significant morphological deformation in APOE e4 carriers relative to noncarriers in the entire cohort as well as in the nondemented (pooled MCI and control) subjects, affecting the left hippocampus more than the right, and this effect was more pronounced in e4 homozygotes than heterozygotes. Our findings are consistent with previous studies that showed e4 carriers exhibit accelerated hippocampal atrophy; we extend these findings to a novel measure of hippocampal morphometry. Hippocampal morphometry has significant potential as an imaging biomarker of early stage AD.

Date Created
2014-08-01
Agent