Benchmark Problem: A PK/PD Model and Safety Constraints for Anesthesia Delivery

Abstract

Hypnosis, or depth of unconsciousness, is one of the goals of general anesthesia. In this brief paper we provide a differential equation model of how propofol, a commonly used intravenous anesthetic drug, leads to hypnosis. The model has two components: the pharmacokinetics (PK) describing how the drug is metabolized by the body, and the pharmacodynamics (PD) describing how the drug effects the depth of hypnosis. This standard PK/PD model is a compartmental model, and is linear except for an internal time delay and a nonlinear output mapping. We discuss how this model can be simplified and/or complexified so as to take best advantage of the capabilities of a particular analysis method. One goal of developing such a model is to ensure patient safety during surgery, so we describe an example safety verification problem. Finally, in order to demonstrate that this benchmark is operational, we provide code to simulate one version of the system.

Infinite horizon safety controller synthesis through disjunctive polyhedral abstract interpretation

“…The goal is to keep an inverted pendulum upright by providing forces in appropriate directions at appropriate times. Different instances of this benchmark consider different values for the safe set S. Propofol Delivery This benchmark was proposed recently by Maidens et al [22], and detailed by Gan et al [14] the patient is modeled as a 4 variables linear delay differential equation that is approximated using a standard Padé approximation. The input is the infusion rate of the Propofol and the goal is concentration of the Propofol in the effect chamber of the pharmacokinetic model.…”

ARCH-COMP18 Category Report: Stochastic Modelling

“…• Anaesthesia delivery system benchmark : this benchmark is based on an automated anaesthesia delivery problem, with a human (an anaesthesiologist) in the loop [21,5]. The model is described in the form of a discrete-time stochastic hybrid system [1] that depends both the current state of the model and a history of the past input actions by the anaesthesiologist.…”

“…This section proposes a benchmark problem for stochastic verification techniques. Past benchmarks and work exist for automated anaesthesia delivery systems [21,5]. We consider the problem of providing probabilistic guarantees of safety for the automated anaesthesia delivery problem with a human (anaesthesiologist) in the loop.…”

“…Propofol concentration in the patient with external drug administration The concentration of a drug administered to a patient is often represented by a multi-compartment model [26]. The concentration of Propofol in different compartments of the body are modelled using the three-compartment pharmacokinetic system [32,30,21]:…”

ARCH-COMP19 Category Report: Stochastic Modelling

“…We consider the problem of providing probabilistic guarantees of safety for the automated anaesthesia delivery problem with a human (anaesthesiologist) in the loop [22,6,1]. We use the well-studied multi-compartment model for delivery of Propofol (anaesthetic) in paediatrics.…”