Pharmacokinetic modelling during long-term anesthesia: minimizing the gap

Surgical procedures exceeding six hours and intensive care for traumatic injuries often require prolonged general anesthesia, commonly maintained via induced coma. Similar protocols are used for COVID-19 patients under mechanical ventilation. These conditions pose challenges such as tissue drug accumulation and overdose risk. Extended supine or prone positioning alters tissue volumes based on their physical properties. Accurate anesthesia management depends on patient-specific models that characterize pharmacokinetics (PK, drug distribution) and pharmacodynamics (PD, drug effects) using compartmental representations. However, comorbidities such as obesity are typically overlooked in existing PK models.

This study augments PK models to investigate the impact of obesity on drug distribution and clearance by incorporating the risk of drug trapping in adipose tissue as a nonlinear function of body mass index (BMI). A theoretical framework links BMI with tissue porosity and permeability, introducing a "trap" compartment to model delayed clearance in obese patients.

The model is validated using in vitro impedance measurements and numerical simulations. Fat tissue properties were characterized via Cole-Cole fractional-order models, with parameters identified using a genetic algorithm. The nonlinear BMI-trapping relationship was estimated using the trust region method. Simulations covered both open-loop (single-bolus) and closed-loop (continuous infusion) scenarios using model predictive control(MPC).

Impedance measurements and identified Cole-Cole fractional-order models confirmed volume-dependent properties of fat tissue. Simulations using clinical data demonstrated delayed drug clearance in high-BMI patients, which support the proposed theoretical background. Open-loop simulations showed prolonged drug retention, while closed-loop control using MPC maintained anesthetic depth with reduced total drug input. Differences in BIS nadir and total drug usage were observed across BMI and age groups, supporting the model's clinical applicability.

The augmented model with MPC minimizes drug trapping and reduces total drug use, lowering overdose risk and supporting safer anesthesia management.