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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. Category: academic. Difficulty: medium

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