James Chun Yip Chan1,4, Kenneth Hor Cheng Koh1, Sheng Yuan Chin1, Zhao Wei2, Jian Cheng Wong3, Chin Chun Ooi2,3
1Singapore Institute of Food and Biotechnology Innovation, 2Centre for Frontier AI Research , 3Institute of High Performance Computing, 4A*STAR Skin Research Labs
Introduction: A key fundamental challenge in physiologically-based pharmacokinetic (PBPK) modelling is the derivation of appropriate parameter values due to the data-driven nature of PBPK modelling and the comparatively small amount of observed data available in literature [1]. In a mechanistic PBPK model, most parameters are fixed to a single value derived from previously observed clinical data from known physiology or in vitro and in vivo experiments while all remaining unknown parameters are concurrently empirically obtained using global fitting [2]. However, this approach poses two issues: (1) estimated values for certain well-established physiological or systems parameters may be physiologically unrealistic if constraints are poorly defined [2]; and (2) the parameter optimization algorithm may converge to a local minimum instead of a global minimum resulting in a suboptimal model. Physics-informed neural network (PINN) is a robust neural network machine learning technique for solving forward and inverse problems that incorporates physical laws into the neural network training process [3]. We hypothesized that the learning capability and physical constraints imposed by PINNs may help resolve the current challenges of parameter acquisition in PBPK modelling. Objectives: The objective of this work is to test the accuracy and performance of a novel framework incorporating PBPK modelling with PINN for parameter discovery as a working proof-of-concept. Methods: A whole-body PBPK model for paracetamol was constructed using the SimBiology module in MATLAB before integration with the PINN architecture. The in vitro metabolic clearance of paracetamol by UGT2B15 (Vmax and Km) was subsequently chosen to be masked since it is the major pathway for paracetamol clearance and has the greatest impact on simulation performance. We first pre-trained a multilayer perceptron (MLP) using simulation data generated by SimBiology, providing a strong initialization for subsequent parameter inference. To ensure good prediction accuracy across all compartments while maintaining fast prediction speed, we also formulated the physical rules the MLP output must obey as a least-squares problem. This formulation ensures minimization of the PBPK model’s prescribed ordinary differential equation (ODE) and initial condition (IC) via the pseudo-inverse method, ensuring consistency with necessary known physiology in the PINN’s output. Leveraging the learned parameters from the first stage, we then utilized the PBPK-PINN to perform joint gradient descent optimization with provided experimental data, thereby unveiling the masked UGT2B15 enzyme kinetics. Results: Prediction results under the inverse setting using pre-trained network parameters as the initialization demonstrated an excellent fit to observed clinical data for plasma concentration-time profile of paracetamol. Prediction performance for our PINN-PBPK model was essentially identical to the conventional ODE solver with near perfect overlap in predicted PK profiles between the two approaches, with simulated area-under-the-curve from time 0 to t h (AUC0-t) for paracetamol plasma concentration-time profile within 1.5-fold of observed clinical data. When masked, the predicted UGT2B15 Vmax and Km obtained using the in-built Suite of Nonlinear and Differential/Algebraic Equation Solvers (SUNDIALS) was 147,632 pmol/min/mg and 100 mM respectively versus the observed 30,016 pmol/min/mg and 23.0 mM reported in vitro from human liver microsomes metabolism experiments. Conversely, our PINN-PBPK model predicted UGT2B15 Vmax and Km of 24,197 pmol/min/mg and 19.1 mM respectively, which were much closer to the actual reported values despite constraining to similar upper and lower bounds for the parameter estimation. The total metabolic clearance of Vmax/Km (CLint) for UGT2B15 between the predicted and observed value was comparable at 1.27 µL/min/mg vs 1.31 µL/min/mg. Conclusions: We present a working proof-of-concept for performing parameter estimation through the successful integration of a deep learning architecture with PBPK modelling. We demonstrated that this framework is able to achieve similar simulated PK profile as conventional ODE solvers but with estimation of unknown parameters that is closer to the actual reported values. By incorporating physical laws to achieve accurate predictions across all compartments, this process required only 10 experimental venous blood time-points to obtain reasonable inferred parameters, thereby demonstrating the efficiency of the proposed PBPK-PINN under limited data constraints. We envision great potential for integrating machine learning techniques such as PINNs with PBPK modelling for more advanced parameter estimation and discovery scenarios to yield more physiologically accurate models.
[1] Tsamandouras et al. Combining the ‘bottom up’ and ‘top down’ approaches in pharmacokinetic modelling: fitting PBPK models to observed clinical data. Br J Clin Pharmacol. 2013 Sep 3;79(1):48–55; https://doi.org/10.1111/bcp.12234 [2] Woodruff et al. Optimization issues in physiological toxicokinetic modeling: a case study with benzene. Toxicol Lett. 1993 Aug;69(2):181-96; https://doi.org/10.1016/0378-4274(93)90103-5 [3] Farea et al. Understanding Physics-Informed Neural Networks: Techniques, Applications, Trends, and Challenges. AI 2024, 5(3), 1534-1557; https://doi.org/10.3390/ai5030074
Reference: PAGE 33 (2025) Abstr 11365 [www.page-meeting.org/?abstract=11365]
Poster: Drug/Disease Modelling - Absorption & PBPK