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

PURPOSE: To develop and evaluate a stress-constrained physics-informed UNet framework for voxel-wise, multiparameter hyperelastic characterization of heterogeneous soft tissues from volumetric displacement data and accessible boundary reaction information in controlled synthetic 3D benchmarks. METHODS: We introduce a physics-informed UNet (PI-UNet) that estimates voxel-wise Mooney-Rivlin parameter maps from multi-loading, strain-derived volumetric inputs. Synthetic finite-element data were generated for three benchmarks: a stiff spherical inclusion in a homogeneous matrix, an anatomically realistic gray/white matter brain embedded in a homogeneous matrix, and an embedded brain containing a synthetic tumor-like inclusion. The loss enforces static equilibrium through the divergence of the first Piola-Kirchhoff stress and incorporates boundary reaction information as face-averaged stress or an equivalent resultant force. Noise robustness was assessed using displacement perturbations and Gaussian smoothing within the loss formulation. RESULTS: PI-UNet reconstructed heterogeneous Mooney-Rivlin fields with high spatial fidelity across the tested synthetic configurations. In the spherical-inclusion benchmark, moderate smoothing reduced noise sensitivity while preserving inclusion geometry. In the gray/white matter benchmark, the framework recovered distinct material signatures for matrix, gray matter, and white matter. In the tumor-like benchmark, scalar fields derived from reconstructed material parameters improved unsupervised identification of the mechanically distinct lesion-like region compared with deformation-derived invariant fields alone. CONCLUSION: The proposed stress-constrained PI-UNet provides a scalable computational framework for controlled voxel-wise 3D multiparameter hyperelastic inversion from volumetric deformation fields and accessible boundary reaction measurements, supporting future experimental phantom validation, richer constitutive models, uncertainty quantification, and eventual in vivo elastography studies.