Overview
Forward simulations are only as useful as the parameters that drive them. In the clinical setting, material parameters such as myocardial stiffness cannot be measured directly — they must be inferred from observable quantities like strain fields and pressure-volume data. Inverse modeling is the mathematical framework for recovering these parameters, turning clinical measurements into patient-specific inputs for the digital twin.
Technical Formulation
We pose the inverse problem as a PDE-constrained optimization, where a clinical objective function $J$ is minimized with respect to material parameters $\mathbf{p}$ subject to the governing mechanics equations. Gradients of $J$ with respect to $\mathbf{p}$ are computed via the adjoint-state method, which provides exact sensitivities at a cost independent of the number of parameters. In the JAX framework this corresponds to a vector-Jacobian product (VJP), computed automatically through reverse-mode differentiation. The primary target is passive myocardial stiffness, though the framework generalizes naturally to other parameters as the model complexity grows toward growth and remodeling.
Clinical Application
Non-invasive recovery of regional myocardial stiffness from clinical measurements provides a quantitative, patient-specific biomarker that standard imaging cannot directly supply. This is the core capability that makes a cardiac digital twin clinically actionable rather than just a simulation tool.
References & Resources
- Learning physics-based models from data: perspectives from inverse problems and model reduction - Introduction to inverse problems and model reduction
- Computational Methods for Inverse Problems - Practical treatment of regularization and optimization for inverse problems.