Physics-Informed LSTM Neural Network for Personalized Pharmacokinetic Modeling of Polymyxin B in Critically Ill Patients.

Polymyxin B represents a critical last-resort antibiotic for carbapenem-resistant Gram-negative infections, yet its narrow therapeutic window and substantial inter-individual pharmacokinetic variability present significant challenges for optimal dosing in critically ill patients. Population pharmacokinetic (PopPK) models based on nonlinear mixed-effects modeling (NLMEM) are well-established, flexible frameworks for dose individualization that are fully capable of incorporating complex, nonlinear, and time-varying covariate relationships; however, their individual-level prediction accuracy is fundamentally governed by data availability and model specification, and substantial eta-shrinkage may occur when per-subject observations are sparse. As a complementary approach, we developed a novel physics-informed long short-term memory (PI-LSTM) neural network that synergistically integrates mechanistic pharmacokinetic principles with deep learning for personalized concentration prediction, intended as a complementary approach to established PopPK methods. The model was trained and validated using simulated data from 1,000 septic patients incorporating time-varying renal function and individualized dosing regimens. The PI-LSTM architecture combines bidirectional LSTM layers for temporal modeling, multi-head attention for adaptive covariate weighting, and physics-based constraints enforcing fundamental pharmacokinetic relationships (kel = CL/V). The model achieved good predictive performance with R² = 0.694 for concentration prediction (MAE = 1.398 mg/L, RMSE = 2.211 mg/L), accurately estimating population-level parameters (mean CL: 2.02 vs. 2.03 L/h true; mean V: 44.7 vs. 41.1 L true) with well-calibrated uncertainty quantification (91.5% prediction interval coverage). An ablation study demonstrated that each physics-informed loss component contributed to maintaining pharmacological interpretability, and a head-to-head comparison with a standard PopPK model on the same data provided context for the relative strengths of each approach. This hybrid framework successfully maintains pharmacological interpretability while leveraging deep learning's capacity to model complex nonlinear relationships, offering a promising complementary approach for therapeutic drug monitoring and individualized dosing optimization in precision antimicrobial therapy.