Periklis Tsiros1, Vasilis Minadakis1, Haralambos Sarimveis1
1National Technical University of Athens
Introduction/Objectives: Often in the literature, instead of exhaustively reporting all observations of a state variable, these observations are summarized through the use of statistical measures. A common example of this practice is the way concentration – time profiles of patients are reported in pharmacokinetic studies. By utilizing comprehensive information through statistical modeling, that is, by incorporating all available statistical measures of a variable, we can effectively propagate the reported uncertainty and interindividual variability observed at the state variable level to parameter estimation, and vice versa. Here, we developed a methodology that learns the mean and standard deviation of an ODE state variable through the PINNs framework [1], by comparing the mean and variance resulting from the automatic differentiation of a neural network (NN), with the corresponding mean and variance stemming out of the ODE system. Methods: A 3-compartment pharmacokinetic model was employed to demonstrate the utility of D-PINNs in forward and inverse problems. The model included three parameters, namely k12, k21 and ke, to describe the transfer rates among the central, peripheral and excreta compartments. The ODE system was used to simulate 20 virtual patients with varying drug biodistribution parameters. These parameters were sampled from a predefined population-level distribution. For each virtual patient, the sampled parameters were used as input into the ODE system to generate concentration-time profiles across the three compartments. To mimic a physical drug sampling procedure, ten time points were selected, and the concentrations in all three compartments were recorded for each patient. The data were then summarized by calculating the mean and variance at each time point, simulating a typical reporting format in pharmacokinetic studies. Following simulated data generation, a simple feed forward NN architecture was selected to model the problem. The NN used time and initial dose as input and predicted the mean and variance of each of the three state variables of the ODE system. In the inverse problem, the goal was to predict parameters k12, k21 and ke,while the forward problem included predicting the 95% confidence intervals (CI) for a new “unseen” dose. Results: The NN’s predictions compared to actual sampled observations revealed exceptional accuracy in capturing data trends across all three compartments for both the mean and variance. The model managed to estimate with high accuracy the population mean and variance of each parameter. For the forward problem, the predicted CI by the model was almost identical to the one obtained by ODE bootstrapping. Importantly, the CI of the concentration-time profile was generated in 0.28 seconds in comparison to 30 seconds required for bootstrapping. Conclusions:The obtained results demonstrate the ability of the proposed algorithm to infer statistical information about population parameters by using only statistical information related to the state of the ODE system. Additionally, the model could predict the CI of the concentration-time profiles in a fraction of the time needed by traditional approaches. This study highlights the potential of new ML-driven methodologies to improve parameter estimation and minimize the time needed to run mechanistic simulations. 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.
[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.
Reference: PAGE 33 (2025) Abstr 11710 [www.page-meeting.org/?abstract=11710]
Poster: Methodology – AI/Machine Learning