Optimizing target control of the vessel rich group with volatile anesthetics

The ability to monitor the inspired and expired concentrations of volatile anesthetic gases in real time makes these drugs implicitly targetable. However, the end-tidal concentration only represents the concentration within the brain and the vessel rich group (VRG) at steady state, and very poorly approximates the VRG concentration during common dynamic situations such as initial uptake and emergence. How should the vaporization of anesthetic gases be controlled in order to optimally target VRG concentration in clinical practice? Using a generally accepted pharmacokinetic model of uptake and redistribution, a transfer function from the vaporizer setting to the VRG is established and transformed to the time domain. Targeted actuation of the vaporizer in a time-optimal manner is produced by a variable structure, sliding mode controller. Direct mathematical application of the controller produces rapid cycling at the limits of the vaporizer, further prolonged by low fresh gas flows. This phenomenon, known as "chattering", is unsuitable for operating real equipment. Using a simple and clinically intuitive modification to the targeting algorithm, a variable low-pass boundary layer is applied to the actuation, smoothing discontinuities in the control law and practically eliminating chatter without prolonging the time taken to reach the VRG target concentration by any clinically significant degree. A model is derived for optimum VRG-targeted control of anesthetic vaporizers. An alternate and further application is described, in which deliberate perturbation of the vaporization permits non-invasive estimation of parameters such as cardiac output that are otherwise difficult to measure intra-operatively.