Energy-based Tissue Manifolds for Longitudinal Multiparametric MRI Analysis
Summary: arXiv:2604.07180v1 Announce Type: cross
Abstract
We propose a geometric framework for longitudinal multi-parametric MRI analysis based on patient-specific energy modelling in sequence space. Rather than operating on images with spatial networks, each voxel is represented by its multi-sequence intensity vector (T1, T1c, T2, FLAIR, ADC), and a compact implicit neural representation is trained via denoising score matching to learn an energy function Eθ(u) over ℝd from a single baseline scan.
The learned energy landscape provides a differential-geometric description of tissue regimes without segmentation labels. Local minima define tissue basins, gradient magnitude reflects proximity to regime boundaries, and Laplacian curvature characterises local constraint structure. Importantly, this baseline energy manifold is treated as a fixed geometric reference: it encodes the set of contrast combinations observed at diagnosis and is not retrained at follow-up.
Longitudinal assessment is therefore formulated as evaluation of subsequent scans relative to this baseline geometry. Rather than comparing anatomical segmentations, we analyse how the distribution of MRI sequence vectors evolves under the baseline energy function.
Case Studies and Findings
In a paediatric case with later recurrence, follow-up scans show progressive deviation in energy and directional displacement in sequence space toward the baseline tumour-associated regime before clear radiological reappearance. In a case with stable disease, voxel distributions remain confined to established low-energy basins without systematic drift.
Conclusion
The presented cases serve as proof-of-concept that patient-specific energy manifolds can function as geometric reference systems for longitudinal multiparametric MRI analysis without explicit segmentation or supervised classification. This innovative approach provides a foundation for further investigation of manifold-based tissue-at-risk tracking in neuro-oncology.
Key Features of the Proposed Framework
- Patient-Specific Energy Modelling: The framework utilizes energy models tailored to individual patient scans.
- Implicit Neural Representation: It employs denoising score matching for training the energy function.
- Geometric Reference System: The baseline energy manifold acts as a stable reference for longitudinal assessment.
- No Need for Segmentation: The analysis is conducted without requiring explicit segmentation or classification, simplifying the workflow.
- Case Study Validation: Real-world cases demonstrate the effectiveness of the approach in detecting disease progression and stability.
Future Directions
As this framework evolves, further research will explore its application in various oncological conditions, potentially leading to enhanced tracking of tissue at risk and improved patient outcomes. The integration of additional MRI sequences and advanced machine learning techniques may further refine the analysis and provide deeper insights into disease dynamics.