Annals of Biomedical Engineering (2026). DOI: 10.1007/s10439-026-04321-4.
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.
Inverse elastography aims to infer tissue mechanical properties from measured motion or deformation. Instead of returning only a single stiffness-like quantity, this framework estimates multiple nonlinear Mooney–Rivlin parameters at every voxel, creating spatially resolved constitutive maps aligned with volumetric medical-imaging data.
The network receives a multi-loading volumetric strain stack and predicts voxel-wise material parameters. During optimization, the predicted fields are inserted into the nonlinear constitutive equations. The loss penalizes violations of static equilibrium through the divergence of first Piola–Kirchhoff stress and penalizes mismatch with accessible boundary reaction information.
The study evaluates synthetic three-dimensional benchmarks containing a spherical inclusion, gray and white matter, and a tumor-like mechanical inclusion. The reconstructed parameter maps preserve heterogeneous anatomy and provide mechanically meaningful features for future elastography, phantom validation, and mechanics-informed lesion analysis.
Move through the saved optimization iterations—or press Play—to compare the evolving C10, C01, and shear-modulus predictions with ground truth. The axial, coronal, and sagittal slices and the three-dimensional context are all adjustable.
For a consistent scientific comparison, each field uses a fixed ground-truth-based color scale across all iterations. Saturation in early frames therefore represents a large prediction error rather than a changing display scale.
Open the full-screen viewer ↗This work was supported by the National Institutes of Health through NIBIB Trailblazer Award R21EB032187 and NINDS Grant 1R01NS131554-01.
Use the published DOI as the authoritative identifier.
@article{Asadi2026StressConstrainedPIUNet,
author = {Asadi, Amirreza and Laksari, Kaveh},
title = {Stress-Constrained Physics-Informed UNet for Voxel-Wise Multiparameter Hyperelastic Inversion in Volumetric Medical Imaging},
journal = {Annals of Biomedical Engineering},
year = {2026},
doi = {10.1007/s10439-026-04321-4},
url = {https://doi.org/10.1007/s10439-026-04321-4}
}