Pharmacometrics Modeling via Physics-Informed Neural Networks: Integrating Time-Variant Absorption Rates and Fractional Calculus for Enhancing Prediction Accuracy

We present a novel method to improve pharmacokinetic and pharmacodynamic (PK&PD) modeling, an essential step of drug development. Conventional models frequently fail to fully comprehend the intricacies of drug absorption and distribution, which limits their predictive abilities required for personalized treatment strategies. Our methodology introduces two innovations to enhance modeling accuracy: 1. Time-varying parameters: this approach is designed to accommodate the dynamic nature of drug absorption rates. It offers a nuanced mathematical formulation that goes beyond traditional models with constant absorption rate assumptions. 2. Fractional calculus in explaining delayed drug response: we simplify complex multi-compartment models into more manageable forms, such as two-compartment models or a single equation by incorporating fractional and ordinary derivatives. This approach effectively captures anomalous diffusion phenomena, surpassing traditional models in describing drug delayed response without the need for extensive compartmentalization. These extensions introduce significant complexities, particularly in achieving accurate and analytically solvable models. This study presents a novel approach that leverages physic-informed neural network to address these challenges. By simultaneously solving the equations and identifying the optimal model, this neural network-based solution offers a potentially analytical expression, streamlining the model simplification process.