Vertex-wise biomechanical sensitivity mapping of subcortical structures under atrophy in Parkinson's disease

Parkinson's disease (PD) is characterized by progressive neurodegeneration and pronounced subcortical asymmetry, yet the extent to which anatomical geometry modulates mechanical responses to atrophy remains insufficiently understood. We propose a vertex-wise biomechanical framework to quantify structure-specific vulnerability by linking MRI-derived morphology to finite-strain mechanical behavior. First, subject-specific 3D meshes of key subcortical regions are reconstructed from T1-weighted MRI data of 141 PD subjects from the PPMI dataset. Second, finite-strain simulations are implemented using a one-term Ogden hyperelastic model, which is then evaluated against experimental reference data. Third, region-specific atrophy is modeled via an isotropic expansion analogy, inducing mechanical deformation. Finally, we introduce three novel indices SALDI, MechSALDI, and DeformSALDI, which characterize surface-based asymmetry, strain-based sensitivity, and displacement-based sensitivity, respectively. These indices are employed to generate vertex-wise 3D sensitivity maps. The principal component analysis (PCA) reveals a dominant low-dimensional structure across the biomechanical indices, with the first component explaining 89.7% of the total variance, indicating strong coherence among geometry- and deformation-derived measures of mechanical sensitivity. The vertex-wise analysis demonstrates a reproducible hierarchy of regional vulnerability, with the hippocampus and amygdala exhibiting the highest mechanical sensitivity, while the thalamus and pallidum show relative resilience. Comparative analyses between PD and healthy controls reveal systematic region-specific differences in biomechanical sensitivity, particularly in striatal and limbic circuits. Hierarchical regression further demonstrates that several SALDI-derived biomechanical indices retain independent associations with cognitive performance and asymmetric motor manifestations, including hippocampal and amygdalar indices for cognition and thalamic, putaminal, pallidal, and accumbens indices for motor asymmetry measures, even after adjustment for conventional volumetric asymmetry. Overall, the observed subcortical sensitivity in PD follows a structured organization driven by local geometry and material-dependent mechanical behavior rather than uniform atrophy. The proposed framework provides a quantitative basis for characterizing geometry-dependent biomechanical sensitivity beyond conventional volumetric measurements and may facilitate future longitudinal studies of individualized degeneration trajectories, patient stratification, and disease progression in neurodegenerative disorders.