Structural Magnetic Resonance Imaging analysis is a vital component in the study of Alzheimer’s Disease pathology and several techniques exist as part of the existing research conducted. In particular, volumetric approaches in this field are known to be beneficial due to the increased capability to express morphological characteristics when compared to manifold methods. To aid in the improvement of the field, this paper aims to propose an intrinsic volumetric conic system that can be applied to bounded volumetric meshes to enable a more effective study of subjects. The computation of the metric involves the use of heat kernel theory and conformal parameterization on genus-0 surfaces extended to a volumetric domain. Additionally, this paper also explores the use of the ’TetCNN’ architecture on the classification of hippocampal tetrahedral meshes to detect features that correspond to Alzheimer’s indicators. The model tested was able to achieve remarkable results with a measured classification accuracy of above 90% in the task of differentiating between subjects diagnosed with Alzheimer’s and normal control subjects.