A one-dimensional fluid dynamic model of the systemic arteries.

The systemic arteries can be modeled as a bifurcating tree of compliant tapering vessels while blood flow and pressure can be predicted by solving Navier-Stokes equations for each of the branches. If all branches are included the computational cost will become prohibitively large. Therefore, the tree must be truncated after a limited number of generations and a suitable outflow boundary condition must be applied. To this end we propose a structured tree in which the root impedance is calculated using a semi-analytical approach. In the structured tree the fluid dynamic equations are linearized giving a wave equation, which can be solved analytically for each vessel. This provides a dynamical boundary condition based on physiological principles which is computationally feasible. It exhibits the actual phase lag between flow and pressure as well as accommodating the wave propagation effects for the entire systemic arterial tree. Finally, the model has been compared with a standard and well established model, where outflow at the terminals are determined by attaching a Windkessel type boundary condition.