Energy-Based Tissue Manifolds for Longitudinal MRI Analysis
A novel geometric framework for analyzing longitudinal multi-parametric MRI leverages patient-specific energy modeling within sequence space. Each voxel is characterized by its multi-sequence intensity vector (T1, T1c, T2, FLAIR, ADC), and an implicit neural representation is compactly trained through denoising score matching to derive an energy function from a single baseline scan. This learned energy landscape offers a differential-geometric perspective of tissue regimes without the need for segmentation labels. Tissue basins are defined by local minima, gradient magnitude indicates closeness to regime boundaries, and local constraint structure is described by Laplacian curvature. The baseline energy manifold serves as a stable geometric reference, reflecting contrast combinations noted at diagnosis and remaining unchanged at follow-up.
Key facts
- Framework uses patient-specific energy modeling in sequence space
- Each voxel represented by multi-sequence intensity vector (T1, T1c, T2, FLAIR, ADC)
- Implicit neural representation trained via denoising score matching
- Energy function learned from single baseline scan
- Local minima define tissue basins
- Gradient magnitude indicates proximity to regime boundaries
- Laplacian curvature characterizes local constraint structure
- Baseline manifold is fixed geometric reference not retrained
Entities
Institutions
- arXiv