Overview
Research introduces a Physics-Informed Neural Network (PINN) framework designed for a multiphysics continuum model of tumor growth. This framework focuses on chemo-fluidic coupling, addressing the computational demands associated with classical mesh-based solvers in the context of inverse parameter identification and predictive patient-specific pipelines for tumor progression.
Research Context
Tumor progression is characterized as a multiphysical phenomenon involving interactions between interstitial fluid dynamics, biochemical transport, and cellular mechanics across multiple spatiotemporal scales. Traditional mesh-based solvers, while capable of high accuracy, incur substantial computational costs when repeated evaluations are necessary, such as during inverse parameter identification or within future patient-specific predictive pipelines.
Approach
The developed PINN framework targets a tractable chemo-fluidic continuum model for tumor growth. This model couples an advection-diffusion-reaction (ADR) equation, which describes the tumor volume fraction, with a quasi-static Darcy pressure equation, which models the interstitial fluid pressure. The solid-mechanical equilibrium component was intentionally decoupled, resulting in a three-equation system. The gradient structure of this system is stable under automatic differentiation, which facilitated robust deep-learning optimization. The network was engineered to simultaneously learn state variables directly from physics constraints, thereby solving the forward problem. Additionally, it recovers hidden transport parameters from sparse and noisy synthetic measurements, addressing the inverse problem through a Data-Assimilation PINN (DA-PINN) approach.
Findings
- Forward Solver Verification: The forward solver component of the PINN framework was verified against a high-resolution finite-difference (FD) reference. This comparison indicated that the PINN achieved a mean absolute error below 0.002.
- Inverse Problem Performance (DA-PINN): For the inverse problem, the DA-PINN demonstrated its ability to recover hidden parameters. Specifically, starting with an initial permeability estimate of 0.08 (which was four times the true value of 0.02), and utilizing only 5% spatially sparse observations corrupted by 5% Gaussian noise, the DA-PINN successfully recovered the permeability with a relative error below 5%.
Why This Matters
These findings suggest that physics-informed deep learning presents a viable and computationally efficient methodology for multiphysics oncology modeling. The mathematical groundwork laid by this approach is positioned for future integration into clinical data assimilation pipelines.