In order to optimize the design of a Fontan we must minimize the energy loss across the connection while maintaining as close to normal physiological function as possible. All the energy input into the circulation by the right ventricle is lost when it is bypassed. This will have a large effect on the patient's endurance if the energy loss across the connection is very large. Design variables are constrained variables that can be directly manipulated. In the pulmonary system there are only a few variables that the surgeon can affect.
State variables are variables which are constrained but can only be manipulated indirectly.
In this case there is only one state variable, namely the flow fraction between the left and right pulmonary arteries. For our purpose, the energy loss through the system is what we want to minimize. In this form, the objective function is unconstrained. Optimization is achieved by finding the local minimum of the unconstrained objective function. This is accomplished by performing a least squares polynomial curve fit to the data and finding an estimate of the minimum on the resulting equation.