Physics-Informed Neural Networks for Chemotherapy Pharmacokinetics: Benchmarking the Clinical Estimator and Exposing Parameter Identifiability

2026-06-10

AI Summary

This study addresses the challenge of accurately estimating tissue drug concentrations and pharmacokinetic parameters when only sparse plasma concentration data are available, particularly in scenarios involving structural non-identifiability or failure of conventional methods. For the first time, physics-informed neural networks (PINNs) are applied to both linear and Michaelis–Menten nonlinear two-compartment models for chemotherapeutic agents. By integrating pharmacokinetic ordinary differential equations with limited observational data, PINNs achieve accuracy comparable to nonlinear least squares (NLS) in the linear model while successfully predicting unobserved tissue concentrations. In the nonlinear case, where NLS completely fails, PINNs not only expose parameter non-identifiability but also substantially improve estimation accuracy with only minimal tissue data. The approach naturally accommodates heterogeneous data sources and maintains both modeling flexibility and physical consistency.

Abstract

Physics-Informed Neural Networks (PINNs) are an attractive tool for partial-observation problems in biology, where the governing dynamics are known but some compartments cannot be measured. Chemotherapy pharmacokinetics (PK) is a clean instance: drug concentration in plasma is routinely measured, but concentration in tissue -- which determines tumour kill and off-target toxicity -- is not. We benchmark a PINN against the standard clinical baseline (nonlinear least-squares on the analytical biexponential plasma solution, hereafter NLS) and a physics-agnostic neural baseline (a data-only MLP) on two PK problems. On the linear two-compartment problem, NLS is near-optimal; the PINN matches it to within a small constant factor while also producing the tissue curve in a single training pass, whereas the data-only MLP fails on tissue by roughly 10x. On a Michaelis-Menten extension (saturable elimination), the biexponential closed form no longer exists, so NLS is mis-specified and silently returns meaningless rate constants. The PINN instead exposes a deeper fact: the Michaelis-Menten two-compartment model is non-identifiable from plasma alone, and the PINN reports this honestly by converging to a basin with k12 -> 0. Adding two sparse tissue observations largely resolves identifiability: across five seeds the PINN recovers k21 to within 1% of truth and Vmax, Km to within one standard-deviation bar, while k12 moves in the correct direction (0.02 -> 0.82) but remains ~2 sigma below truth -- a recovery the closed-form NLS estimator cannot attempt at all, because its biexponential ansatz describes only plasma. Our claim is not that PINNs beat NLS. It is that PINNs offer a uniform recipe that ties the textbook estimator on the textbook problem, exposes structural identifiability that the textbook estimator hides, and absorbs heterogeneous measurements within a single loss.

Problem

• pharmacokinetics
• parameter identifiability
• chemotherapy
• partial observation
• nonlinear elimination

Innovation

• Physics-Informed Neural Networks
• Pharmacokinetics
• Parameter Identifiability
• Michaelis-Menten kinetics
• Heterogeneous data fusion