Modelling Pharmacokinetic Variability with Physics-Informed Neural Networks

Modelling Pharmacokinetic Variability with Physics-Informed Neural Networks Periklis Tsiros, Vasileios Minadakis and Haralambos Sarimveis School of Chemical Engineering, National Technical University of Athens, 157 80 Athens, Greece CONTACT INFORMATION: ptsir[email protected], [email protected], [email protected] BACKGROUND In many studies, individual measurements of a state variable are not reported; instead, summary statistics such as the mean and variance are provided. This is common in pharmacokinetic studies, where concentration–time profiles are often summarized across subjects. To incorporate this aggregated information into parameter estimation, we propose a methodology that leverages Physics-Informed Neural Networks (PINNs) [1] to learn the parameters of a predefined distribution. Our approach compares the differentials of the mean and variance obtained via automatic differentiation of the neural network (NN) with those derived analytically from the underlying ordinary differential equation (ODE) system through sampling, enabling the propagation of population-level uncertainty into the parameter inference process. OBJECTIVES ✔Develop a methodology based on PINNs to estimate the parameters of a predefined distribution of model parameters, using observed time-series data of the state variable’s mean and variance. ✔Demonstrate the effectiveness of the proposed approach through a proof-of-concept study using synthetic data. ✔Using a simple one-compartment pharmacokinetic model and assuming the correct form of the underlying distribution, show that the framework can accurately recover the parameters of that distribution. ✔A simple feed forward NN architecture with time as the only input was employed to predict the mean and variance of the serum concentration. The structure of the network consisted of 2 hidden layers with 5 nodes each. This simple structure was sufficient to predict the observed concentration means and variances across time with high precision. ✔The model managed to estimate with high accuracy the underlying population distributions of the parameters, as well as the variance of the residual error. ✔The results demonstrate the ability of the proposed PINNs methodology to infer statistical information about population parameters by using only statistical information related to the state of the ODE system. ✔This study highlights the potential of integrating novel machine learning–driven methodologies into pharmacokinetic parameter estimation. REFERENCES [1] Raissi, M., Perdikaris, P. and Karniadakis, G.E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, pp.686–707. doi:https://doi.org/10.1016/j.jcp.2018.10.045 ACKNOWLEDGEMENTS The authors acknowledge financial support by the SCENARIOS project (Grant Agreement 101037509) which has been funded by the European Commission under the Horizon 2020 Programme. METHODS RESULTS and CONCLUSIONS National Technical University of Athens A. Synthetic Data Generation Figure 1: Schematic representation of the PINNs framework used to infer the parameters of the ODE system leveraging the the mean and variance of the state variable of the . Figure 2: Goodness-of-fit on the observed data. Figure 3: Predicted vs. population parameter distributions generated by 1,000 samples . B. PINNs