Learning Chemotherapy Drug Action via Universal Physics-Informed Neural Networks

TL;DR

This work introduces Universal Physics-Informed Neural Networks (UPINNs) to automatically learn hidden terms in differential-equation models used in quantitative systems pharmacology, focusing on chemotherapy pharmacodynamics. By decomposing dynamics into a known part F and an unknown term G approximated by a neural network, UPINNs recover classic drug actions (Log-kill, Norton-Simon, E_max) from synthetic data and extend to parameter identification across doses and to in-vitro doxorubicin dynamics. The approach enables simultaneous fitting and interpolation of dose-dependent parameters (k_p(D), θ(D)) and reveals time-varying net proliferation rates, offering a data-driven route to refine QSP models without extensive manual literature distillation. While effective, the method currently lacks uncertainty quantification and formal identifiability guarantees, pointing to future work on uncertainty methods and principled identifiability analyses to strengthen practical deployment.

Abstract

Quantitative systems pharmacology (QSP) is widely used to assess drug effects and toxicity before the drug goes to clinical trial. However, significant manual distillation of the literature is needed in order to construct a QSP model. Parameters may need to be fit, and simplifying assumptions of the model need to be made. In this work, we apply Universal Physics-Informed Neural Networks (UPINNs) to learn unknown components of various differential equations that model chemotherapy pharmacodynamics. We learn three commonly employed chemotherapeutic drug actions (log-kill, Norton-Simon, and E_max) from synthetic data. Then, we use the UPINN method to fit the parameters for several synthetic datasets simultaneously. Finally, we learn the net proliferation rate in a model of doxorubicin (a chemotherapeutic) pharmacodynamics. As these are only toy examples, we highlight the usefulness of UPINNs in learning unknown terms in pharmacodynamic and pharmacokinetic models.

Figures (10)

• Figure 1: Overview of the structure of the UPINN method as applied to \ref{['eq:1']}, which shows inputs and outputs of all known and unknown components, as well as losses. The surrogate solution $U$ outputted by the UPINN takes time $t$ as input. Both $F$ (the known component of the differential equation) and $G$ (the unknown component, to be fit by the UPINN) take in time and $\hat{U}$, the prediction of the neural network, as input. $F$ and $G$, along with $U_t$ (the autodifferentiated derivative of $U_{NN}$ w.r.t. time) and is passed as input to the PINN loss. Then, the PINN loss computes the error between $U_t$ and $F+G$. The MSE loss computes the error between the surrogate solution $\hat{U}$ and the data.
• Figure 2: Datasets for the different drug actions (a, b, c) with their respective drug actions learned below them (d, e, f). Data was collected with a fixed time period (0.15 days) elapsing between each data point. The drug actions are the functions $G(N)$ in Eq \ref{['eq:cell_kill_3_types']}, replaced by one of: log-kill, Norton-Simon and $E_{max}$.
• Figure 3: Datasets for the different drug actions (a, b, c) with their respective drug actions learned below them (d, e, f). The data is noiseless but collected such that there is at one datapoint for each 0.05-interval decrease in $N$. Although there are half as many points collected than in the equispaced case, the MSE between the true drug action and the predicted drug action is still on the order of $10^{-4}$ as shown by Table \ref{['tab:section_1_mses']}
• Figure 4: Datasets for the different drug actions (a, b, c) with their respective drug actions learned below them (c, d, f). The data has a noise level of 0.03 added proportionally to the mean of the variables.
• Figure 5: Datasets for the different drug actions (a, b, c) with their respective drug actions learned below them (c, d, f). The data is spaced so that times of high cell decline have proportionally more observations (one datapoint for each 0.05-interval decrease in $N$). It also has a noise level of 0.03 added proportionally to the mean of the variables.