Nonlinear dynamics in closed-loop anesthesia: Pharmacokinetic/pharmacodynamic model under PID-feedback

The problem of finding admissible tunings for a PID-controller for automatic neuromuscular blockade drug administration in closed-loop anesthesia is considered. A conventional compartmental pharmacokinetic/pharmacodynamic model with Wiener structure under a PID feedback is analyzed in order to discern the safe intervals of the controller parameters that are free of complex dynamics phenomena. The analysis shows that the closed-loop system undergoes Andronov-Hopf bifurcation at a point in the model parameter space giving rise to nonlinear oscillations, as previously observed in surgical practice. For higher, but still feasible values of the Hill function parametrizing the static nonlinearity, deterministic chaos can arise in the closed loop for lower concentrations of the anesthetic drug.