Results under bootstrap.

In oral drug pharmacokinetics (PK), drug-drug interactions are inevitable, yet traditional compartmental models struggle to effectively quantify such processes. This study proposes a linearly coupled two-compartment PK model, where the coupling term is defined as a linear function of another drug’s amount to strike a balance between model simplicity and physiological interpretability. The model introduces parameter heterogeneity and linear interaction terms based on the classical compartmental structure, more accurately capturing concentration-dependent dynamic changes during combined drug administration. To address the model’s nonlinear characteristics and high-dimensional parameters, a hierarchical optimization numerical solution algorithm was developed, enhancing computational efficiency while validating robustness against Gaussian noise. Through systematic analysis of key PK metrics (, , AUC, and ), the study reveals the mechanisms by which absorption and clearance parameter variations influence drug distribution in vivo. Combining numerical simulations, parameter ablation experiments, and real-world data validation, the full model (retaining all linear interaction terms) outperforms the simplified model in both goodness-of-fit and information criteria, demonstrating superior interpretability and predictive performance. Overall, this model offers an intermediate solution between traditional compartmental models and PBPK models, providing a novel methodological framework for quantitative research on drug-drug interactions.