Enhancing Alzheimer's Diagnosis: Leveraging Anatomical Landmarks in Graph Convolutional Neural Networks on Tetrahedral Meshes

Alzheimer's disease (AD) is a major neurodegenerative condition that affects millions around the world. As one of the main biomarkers in the AD diagnosis procedure, brain amyloid positivity is typically identified by positron emission tomography (PET), which is costly and invasive. Brain structural magnetic resonance imaging (sMRI) may provide a safer and more convenient solution for the AD diagnosis. Recent advances in geometric deep learning have facilitated sMRI analysis and early diagnosis of AD. However, determining AD pathology, such as brain amyloid deposition, in preclinical stage remains challenging, as less significant morphological changes can be observed. As a result, few AD classification models are generalizable to the brain amyloid positivity classification task. Blood-based biomarkers (BBBMs), on the other hand, have recently achieved remarkable success in predicting brain amyloid positivity and identifying individuals with high risk of being brain amyloid positive. However, individuals in medium risk group still require gold standard tests such as Amyloid PET for further evaluation. Inspired by the recent success of transformer architectures, we propose a geometric deep learning model based on transformer that is both scalable and robust to variations in input volumetric mesh size. Our work introduced a novel tokenization scheme for tetrahedral meshes, incorporating anatomical landmarks generated by a pre-trained Gaussian process model. Our model achieved superior classification performance in AD classification task. In addition, we showed that the model was also generalizable to the brain amyloid positivity prediction with individuals in the medium risk class, where BM alone cannot achieve a clear classification. Our work may enrich geometric deep learning research and improve AD diagnosis accuracy without using expensive and invasive PET scans.

Geometry-Aware Hierarchical Bayesian Learning on Manifolds

Bayesian learning with Gaussian processes demonstrates encouraging regression and classification performances in solving computer vision tasks. However, Bayesian methods on 3D manifold-valued vision data, such as meshes and point clouds, are seldom studied. One of the primary challenges is how to effectively and efficiently aggregate geometric features from the irregular inputs. In this paper, we propose a hierarchical Bayesian learning model to address this challenge. We initially introduce a kernel with the properties of geometry-awareness and intra-kernel convolution. This enables geometrically reasonable inferences on manifolds without using any specific hand-crafted feature descriptors. Then, we use a Gaussian process regression to organize the inputs and finally implement a hierarchical Bayesian network for the feature aggregation. Furthermore, we incorporate the feature learning of neural networks with the feature aggregation of Bayesian models to investigate the feasibility of jointly learning on manifolds. Experimental results not only show that our method outperforms existing Bayesian methods on manifolds but also demonstrate the prospect of coupling neural networks with Bayesian networks.