Physics-informed neural ordinary differential equations for PBPK-based internal dose prediction in environmental health risk assessment

Reliable prediction of internal doses, especially systemic blood concentrations, is crucial for exposure science and environmental health risk assessment. While traditional physiologically based pharmacokinetic (PBPK) models provide mechanistic insights, their fixed parameters often fail to capture nonlinear dynamics at high concentrations, as encountered in acute contamination scenarios. This study introduces a hybrid PBPK-constrained neural ODE framework that combines neural ordinary differential equations with PBPK modeling. By integrating a minimal two-neuron network correction at the liver compartment, this approach maintains mechanistic interpretability while leveraging AI to learn residual nonlinearities. The methodology was evaluated using two volatile organic compounds relevant to environmental and occupational health. Dermal absorption of dibromomethane (DBM) was simulated using an 11-compartment PBPK model incorporating stratum corneum diffusion solved by spectral collocation. Methylchloroform (MCF) inhalation was modeled using a 4-compartment PBPK model. At an extrapolated dose of 10,000 ppm, the hybrid model achieves R² = 0.760 for DBM and R² = 0.813 for MCF, outperforming pure Neural ODEs with R² = 0.421 and -0.399, and the recalibrated traditional PBPK with R² = 0.190 and 0.504. This framework markedly improves extrapolation under the limited-data conditions typical of controlled environmental exposure studies. The resulting models only require 9-10 free parameters for DBM and 4-5 for MCF, making them highly reproducible and clearly defined. This technique provides a transparent computational proof-of-concept for acute high-dose extrapolation when toxicokinetic data are limited to a small number of observations per dose.