Abstract

The Physiologically Based Pharmacokinetic (PBPK) modeling is a mathematical tool that has emerged as a powerful instrument to describe the absorption, distribution, metabolism, and elimination of therapeutic compounds in biological systems. This study conducts a sensitivity and stability analysis of a PBPK model with consideration of nonlinear saturable cellular uptake behavior to assess the impact of physiological and biochemical parameters on drug transport behavior and system equilibrium. The model is composed of various interconnected compartments with the plasma, liver, kidney, tumor tissue, and peripheral organs, and drug transfer between the compartments is based on mass balance principles. Michaelis–Menten kinetics is used to model cellular uptake to include saturation effects in the target tissue. The governing equations are nonlinear and are written as coupled ODEs for the variations in concentration with time. The results show that in comparison with assuming linear drug accumulation, uptake saturation markedly changes the drug accumulation pattern, residence time, and tissue exposure. The overall results show that these saturable uptake parameters can vary by a small amount and significantly alter the intracellular concentrations of the drug and the systemic pharmacokinetics. The targeted drug delivery applications are especially sensitive to the efficiency of the receptor-mediated transport, making the accurate estimation of the parameters. The numerical simulations also indicate the model's ability to simulate the nonlinear pharmacokinetic responses at different doses. The system is almost linear at low doses and saturated at high doses, causing accumulation in the system and delayed clearance. Stability regions derived from the analysis validate that the balance of physiological parameters is required to achieve controlled therapeutic behavior and avoid excessive tissue toxicity. The research study founded that the inclusion of saturable uptake mechanisms in PBPK can be important for better prediction of drug biodistribution and treatment optimization. The suggested sensitivity and stability framework offers useful evidences in the pharmaceutical design, personalized medicine, and clinical optimization of therapeutic strategies based on nanoparticles.