A differential-algebraic equation (DAE) formulation of arterial hemodynamics

A nonlinear distributed mathematical model of arterial hemodynamics is presented. This model is elegantly formulated as a PDAE (a set of partial differential algebraic equations). Starting from two individually developed models for each of the interacting domains, the coupled model is systematically formulated, with minimal algebraic manipulation of each of the single domain models: the nonlinear dynamic equations of the fluidic and the structural domains are concatenated. They are supplemented with algebraic constraints to ensure kinematic and dynamic compatibility between the two domains at the interface of interaction. The advantages of such a formulation are examined. The resulting distributed model takes into account taper and viscoelasticity of the arterial wall and the two-dimensional nature of the fluid flow. It is semi-discretized in space, resulting in an index 2 DAE. Required boundary conditions are identified. The DAE system is realized using a recently emerging approach that converts the higher index realization problem into an equivalent control problem