Towards a Holistic Cortical Thickness Descriptor: Heat Kernel-Based Grey Matter Morphology Signatures

Abstract

In this paper, we propose a heat kernel based regional shape descriptor that may be capable of better exploiting volumetric morphological information than other available methods, thereby improving statistical power on brain magnetic resonance imaging (MRI) analysis. The mechanism of our analysis is driven by the graph spectrum and the heat kernel theory, to capture the volumetric geometry information in the constructed tetrahedral meshes. In order to capture profound brain grey matter shape changes, we first use the volumetric Laplace-Beltrami operator to determine the point pair correspondence between white-grey matter and CSF-grey matter boundary surfaces by computing the streamlines in a tetrahedral mesh. Secondly, we propose multi-scale grey matter morphology signatures to describe the transition probability by random walk between the point pairs, which reflects the inherent geometric characteristics. Thirdly, a point distribution model is applied to reduce the dimensionality of the grey matter morphology signatures and generate the internal structure features. With the sparse linear discriminant analysis, we select a concise morphology feature set with improved classification accuracies. In our experiments, the proposed work outperformed the cortical thickness features computed by FreeSurfer software in the classification of Alzheimer’s disease and its prodromal stage, i.e., mild cognitive impairment, on publicly available data from the Alzheimer’s Disease Neuroimaging Initiative. The multi-scale and physics based volumetric structure feature may bring stronger statistical power than some traditional methods for MRI-based grey matter morphology analysis.

A Tetrahedron-Based Heat Flux Signature for Cortical Thickness Morphometry Analysis

“…For comparisons, we select the surface-based thickness morphometry method used in FreeSurfer [6] and a lumped tetrahedron-based method [17]. In [17], the lumped discrete volumetric LBO is defined as: L p = D −1 S , where D = diag ( d 1 , …, d n ).…”

“…In [17], the lumped discrete volumetric LBO is defined as: L p = D −1 S , where D = diag ( d 1 , …, d n ). d n is the weighted volume sum of all the tetrahedrons sharing vertex i: d n =Σ T l ∈ N ( i ) Volume ( T l )/4.…”

“…The folded gyri and sulci also make it harder to generate multi-layer tetrahedral meshes. Repeated smoothing is a commonly used method to remove geometric errors[17], but may cause data integrity loss. Our solution here is a minimally invasive surgery over intersection regions.…”

“…Tetrahedron-based volumetric morphometry (TBVM) approach is a representative new method for cortical analyses [17, 18]. It deals with the measurement of brain structure and changes on tetrahedral mesh.…”

Multi-task sparse screening for predicting future clinical scores using longitudinal cortical thickness measures

“…Mild Cognitive Impairment (MCI)), and facilitate early interventions [5]. A number of cortical thickness estimation methods have been developed [4, 11, 8, 17, 19] and they were well adopted in neuroimaging research. Despite advances in cortical thickness estimation used to track symptomatic patients, there is still a lack of accurate and reliable brain imaging systems that can predict future clinical decline by analyzing longitudinal cortical thickness changes.…”