Abstract
The pharmacokinetic literature is rich in aggregated concentration data that contain valuable information, yet tools to extract this information remain limited. This work introduces distributional physics-informed neural networks (D-PINNs), a novel algorithm designed to enable statistical modelling within the PINN framework, allowing recovery of pharmacokinetic parameter distributions at the population level from published concentration means and variances. Unlike traditional PINNs, which often focus on point estimates, D-PINNs incorporate distributional assumptions directly into the optimisation process. The framework utilises neural networks for predicting the mean and variance of the concentration over time. These predictions are then incorporated into a sampling-based procedure within the residual network, which uses the governing ordinary differential equation (ODE) system to compute the physics-informed loss term. The methodology accounts for both interindividual variability through the parameter distribution and measurement noise through a residual error model. The capability of D-PINNs to infer population-level parameter distributions from concentration summary statistics was demonstrated through a simple proof-of-concept using simulated data from a one-compartment pharmacokinetic model of intravenous drug administration. The model achieved high accuracy in estimating both the parameter distribution and the residual error. Hyperparameter tuning highlighted important aspects of model development. The modelling framework was then applied to real-world data to demonstrate its ability to recover information on the distribution of kinetic parameters in the studied population. Specifically, a minimal physiologically-based pharmacokinetic (mPBPK) model for monoclonal antibodies (mAbs) was fitted to aggregated plasma concentration data reported in the literature using D-PINNs. The same aggregated data were also analysed using a Markov chain Monte Carlo (MCMC) analogue to benchmark the proposed methodology.