Stress-Constrained Physics-Informed UNet for Voxel-Wise Multiparameter Hyperelastic Inversion in Volumetric Medical Imaging

Purpose. To develop a physics-informed computational framework for voxel-wise, multiparameter hyperelastic characterization of heterogeneous soft tissues from volumetric displacement data, with the goal of improving spatially resolved biomechanical imaging and enabling mechanically informed detection of pathological regions.

Methods. A physics-informed UNet estimates spatial distributions of Mooney–Rivlin material parameters from strain-derived volumetric inputs. The framework uses finite-element datasets representing a spherical inclusion, an anatomically realistic gray/white-matter brain, and a brain with a tumor-like inclusion. Its physics-informed loss enforces mechanical equilibrium through the divergence of the first Piola–Kirchhoff stress and incorporates boundary-traction constraints.

Results. The PI-UNet reconstructs heterogeneous material fields across the benchmark configurations, captures stiffness contrasts and anatomical structure, and remains robust under displacement noise when moderate smoothing is applied. In the tumor model, clustering of the reconstructed mechanical fields localizes the lesion with high spatial agreement to the ground truth.

Conclusion. The framework provides a scalable and physically grounded approach for three-dimensional voxel-wise hyperelastic inversion from imaging-derived data and establishes a foundation for spatially resolved tissue characterization and mechanically informed lesion detection.