In vivo estimation of right ventricular biomechanics from hemodynamic data using a physics-informed neural networks approach.

Introduction: : Understanding right ventricular (RV) tissue mechanics is critical for diagnosing and managing pulmonary hypertension and other cardiac conditions. Conventional methods such as inverse finite element (FE) modeling or ex vivo mechanical testing provide accurate material properties but are invasive, labor-intensive, and often constrained by subject-specific geometries. Automated model discovery approaches offer flexible constitutive modeling with high precision but typically lack interpretability and generalizability [1]. To address these challenges, we propose a novel, interpretable, and in vivo framework using physics-informed neural networks (PINNs). Our method estimates the eight parameters of the Holzapfel–Ogden (HO) model, representing isotropic, fiber, collagen, and coupling contributions, directly from imaging-derived hemodynamic data and fiber-collagen orientation features [2].

Materials and

Methods: : Equibiaxial stretch–stress data (λ = 1.0–1.3) were collected from 40 myocardial samples, with measurements of circumferential and longitudinal stresses. Corresponding hemodynamic features were extracted via echocardiography imaging, catheterization, and fiber-collagen orientations were derived from histology (Fig. 1). These paired datasets served as input to a PINN framework that predicts HO parameters through an invariant-based strain energy formulation (Fig. 2). The model enforces biophysical constraints, including zero stress at λ = 1.0 and energy normalization at the reference configuration, to ensure physically plausible outputs. Once trained, the PINN infers material parameters for new samples using only in vivo hemodynamics [3].

Results, Conclusions, and Discussions:: Results and

Discussion: Our PINN-based approach achieved a consistent performance across the test dataset, with a mean relative error below 10% in predicting ensemble first Piola–Kirchhoff stress (summed circumferential and longitudinal stresses) (Fig. 3). The integration of hemodynamic features enabled sample-specific parameter estimation, providing a clinically feasible and scalable solution. Compared to inverse optimization, which yielded the best fit for individual samples but requires direct mechanical data, the PINN offered comparable accuracy without invasive testing [4]. Automated model discovery provided flexible constitutive representations and excellent sample-wise fits but lacked generalization to unseen data. Our results suggest that the PINN balances robustness, interpretability, and generalizability, making it a promising tool for biomechanical phenotyping and personalized diagnostics.

Conclusions: This work presents an in vivo and interpretable approach for estimating myocardial material properties using PINNs. By combining physiological data, histological orientation, and physics-based constraints, we eliminate the dependency on direct mechanical testing and enable generalized application across subjects. Future work will extend this model to incorporate multimodal datasets, including non-invasive estimation of fiber orientations using imaging-based techniques such as diffusion tensor MRI or ultrasound-based speckle tracking and probabilistic uncertainty quantification to address inter-subject variability.

Acknowledgements and/or References (Optional):: Acknowledgments: RRM was supported by the American Heart Association under grant No. 25PRE1377496.

References:
[1] Martonová, D., et al. (2024). Automated model discovery for human cardiac tissue: Discovering the best model and parameters. Computer Methods in Applied Mechanics and Engineering, 428, 117078.
[2] Holzapfel, G. A., & Ogden, R. W. (2009). Constitutive modelling of passive myocardium: A structurally based framework for material characterization. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 367(1902), 3445–3475.
[3] Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, 686–707.
[4] Neelakantan, S., et al. (2025). Right Ventricular Stiffening and Anisotropy Alterations in Pulmonary Hypertension: Mechanisms and Relations to Right Heart Failure. Journal of the American Heart Association, 14(5), e037126.