Modeling, control and response surface analysis of anesthesia

Anesthesia practice is unique in the sense that an anesthetist must target profound drug effect during any surgical stimulus and then reverse the effect rapidly when the procedure is over. This can only be achieved when the anesthetist has in depth knowledge of the relationship between concentration and effect and thus facilitate the transition between anesthetic state and awake state in a smooth way. The parameter which is used to define the right amount of anesthesia is `Depth of Anesthesia´ (DoA). A situation involving overdosing or under dosing of anesthetic drug can lead to increased costs incurred, prolonged post-operative stay in the hospitals and in extreme conditions may even lead to death. Earlier larger doses of a single anesthetic agent were used to achieve anesthesia. But it had profound side effects. As such a combination of an anesthetic agent like propofol and an opioid like remifentanil is used, and the modeling is done by a technique which is known as `Three compartment PK-PD model´. The controller used to control the process is `Proportional-Integral-Derivative Controller (PID)´. The interaction between the anesthetic drug and the opioid is then studied, so as to determine the compatibility between the two drugs. The technique which is used in this context is `Response Surface Methodology´. In this paper Response Surface is generated using mat lab and the entire spectrum of drug effect is studied.