Oscillations-free PID control of anesthetic drug delivery in neuromuscular blockade

The PID-control of drug delivery or the neuromuscular blockade (NMB) in closed-loop anesthesia is considered. The NMB system dynamics portrayed by a Wiener model can exhibit sustained nonlinear oscillations under realistic PID gains and for physiologically feasible values of the model parameters. Such oscillations, also repeatedly observed in clinical trials, lead to under- and over-dosing of the administered drug and undermine patient safety. This paper proposes a tuning policy for the proportional PID gain that via bifurcation analysis ensures oscillations-free performance of the control loop. Online estimates of the Wiener model parameters are needed for the controller implementation and monitoring of the closed-loop proximity to oscillation.

The nonlinear dynamics of the PID-controlled NMB system are studied by bifurcation analysis. A database of patient models estimated under PID-controlled neuromuscular blockade during general anesthesia is utilized, along with the corresponding clinical measurements. The performance of three recursive algorithms is compared in the application at hand: an extended Kalman filter, a conventional particle filter (PF), and a PF making use of an orthonormal basis to estimate the probability density function from the particle set.

It is shown that with a time-varying proportional PID gain, the type of equilibria of the closed-loop system remains the same as in the case of constant controller gains. The recovery time and frequency of oscillations are also evaluated in simulation over the database of patient models. Nonlinear identification techniques based on model linearization yield biased parameter estimates and thus introduce superfluous uncertainty. The bias and variance of the estimated models are related to the computational complexity of the identification algorithms, highlighting the superiority of the PFs in this safety-critical application.

The study demonstrates feasibility of the proposed oscillation-free control strategy combining bifurcation theory based design and online parameter estimation by PF.