Nonlinear dynamics in pulse-modulated feedback drug dosing

TL;DR

This paper explores complex nonlinear behaviors in pulse-modulated feedback drug dosing systems, emphasizing the need for bifurcation analysis to ensure safety in hybrid control paradigms.

Contribution

It demonstrates the existence of nonlinear phenomena like multistability and chaos in pulse-modulated drug dosing models, highlighting the importance of bifurcation analysis for safe design.

Findings

Existence of high-multiplicity periodic solutions

Presence of multistability and deterministic chaos

Need for bifurcation analysis in feedback drug dosing

Abstract

Pulse-modulated feedback is utilized in drug dosing to mimic sustained over a longer period of time manual discrete dose administration, the latter is in contrast with continuous drug infusion. The intermittent mode of dosing calls for a hybrid (continuous-discrete) modeling of the closed-loop system, where the pharmacokinetics and pharmacodynamics of the drug are captured by differential equations whereas the control law is described by difference equations. Hybrid dynamics are highly nonlinear which complicates formal design of pulse-modulated feedback. This paper demonstrates complex nonlinear dynamical phenomena arising in a simple control system of dosing a neuromuscular blockade agent in anesthesia. Along with the nominal periodic regimen, undesirable nonlinear behaviors, i.e. periodic solutions of high multiplicity, multistability, as well as deterministic chaos, are shown to exist. It is concluded that design of feedback drug dosing algorithms based on a hybrid paradigm has to be informed by a thorough bifurcation analysis in order to secure patient safety.