Modeling Adoptive Cell Therapy in Bladder Cancer from Sparse Biological Data using PINNs
Kayode Olumoyin, Katarzyna Rejniak
TL;DR
This work addresses learning time-varying dynamics in sparse oncology data by extending physics-informed neural networks (PINNs) with time-dependent parameters learned from data augmented via spline interpolation. The authors introduce a Modified PINN framework consisting of two coupled surrogates: one for state trajectories $u_{NN}(t)$ and one for time-varying parameters $\Lambda_{NN}(t)$, trained to satisfy the known ODE form $\frac{d\mathbf{u}}{dt}=f(t,\mathbf{u};\Lambda)$ while incorporating biological constraints as regularization. They demonstrate the approach on a bladder cancer ODE model under gemcitabine and adoptive T cell therapy, comparing two interpolation regimes (86 vs 35 points) and showing that Case2 yields better error metrics (MSE, MAE, MAPE) and tighter uncertainty bounds; importantly, spline interpolation preserves convergence of the PINN solution. The results illustrate data-efficient learning of unmodeled temporal effects in multi-population cancer dynamics and highlight the potential of biology-informed regularization to improve predictive fidelity in limited-data settings, with broad applicability to other differential-equation models in biology.
Abstract
Physics-informed neural networks (PINNs) are neural networks that embed the laws of dynamical systems modeled by differential equations into their loss function as constraints. In this work, we present a PINN framework applied to oncology. Here, we seek to learn time-varying interactions due to a combination therapy in a tumor microenvironment. In oncology, experimental data are often sparse and composed of a few time points of tumor volume. By embedding inductive biases derived from prior information about a dynamical system, we extend the physics-informed neural networks (PINN) and incorporate observed biological constraints as regularization agents. The modified PINN algorithm is able to steer itself to a reasonable solution and can generalize well with only a few training examples. We demonstrate the merit of our approach by learning the dynamics of treatment applied intermittently in an ordinary differential equation (ODE) model of a combination therapy. The algorithm yields a solution to the ODE and time-varying forms of some of the ODE model parameters. We demonstrate a strong convergence using metrics such as the mean squared error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE).