1-D blood vessel modeling: vessel area and flow rate control

In this paper, we introduce blood vessel modeling and discuss several methods. We illustrate derivation of the one-dimensional (1-D) model and, using a finite element method for discretizing the spatial derivative, we yield our simplified model to apply control techniques for stabilizing blood flow and vessel area. We linearize the model using classical techniques and apply linear optimal control. We then simulate the nonlinear system and demonstrate nonlinear control. All control techniques were successful in removing steady-state error. The relative benefits of nonlinear control, particularly sliding mode, are also discussed.