| The oxygenation of blood by means of an extra corporeal bubble oxygenator is formulated as an optimal control problem. The system equations are derived from a three-compartment model of the oxygenator-patient circuit. This system is constrained by its physiological and mechanical limits. The optimal trajectory is that feasible solution which meets desired terminal conditions and which minimizes the amount of oxygen bubbled through the blood. This trajectory is found by a sequential gradient-restoration algorithm. This algorithm is a fast version of a more general algorithm and is derived form it by removing stationary controls from consideration and restricting the form of the terminal conditions. The algorithm is designed to determine the control trajectory quickly enough permit its use in real-time surgical or maintenance situations. It is also easily adaptable to various models of oxygenators and patient parameters. Several examples are given of its use with the oxygenation profile of a Bentley BOS-type oxygenator. The sensitivity of the algorithm to its parameters is shown, and the required accuracy of the inputs is found. |
