One of the leading causes of death and more expensive health care issues is that of cardiovascular disease.  In particular, it is atherosclerosis whose onset has eluded most physicians, but it is the acute coronary episodes which contribute to the mortality of this condition.  Within the last decade, an interesting relationship has been identified relating the persistence of low/oscillatory flow regions in vessels to contribute to the development of this disease.

In order to approach this fluid dynamic problem from a biophysical perspective, please note that the arterial network is a set of bifurcating elastic vessels, where transient pressure and flow waveforms are transduced (and reflected).  The fluid, blood, is in itself a complex fluid which has a sophisticated rheology.  A 1D in space and time model has been developed in Matlab to assess the local hydrodynamic and frequency dependent impedances of the arterial network.  The model uses literature reported measurements for 45 of the main arteries leaving the heart and distributing blood across the body, and includes the tapering effect of vessel segments by implementing a lubrication approximation.  At the outlets of the large arteries, sub-networks of smaller arteries, arterioles, and capillaries have been approximated using scaling relationships developed for vessel bifurcations (and trifurcations).  The impedance calculations are separated into steady and transient components, where the steady component uses the tapering effects and the more complex rheology of blood, which are correlated to the vessel diameters using the Fahraeus-Lindquist effect.  Transient calculations use the Womersley solution for pulsatile flow in thin elastic tubes, where a linear superposition of pressure and flow are related through the characteristic impedance.  The model itself works by using data from literature (or measured) of pressure from any point of the arterial network, and reconstructing the pressure and flow profiles across the rest of the network.  The impedance solution shows good agreement with literature, and even with measurements made on a healthy volunteer, good comparison between the model predictions and measured data has been seen.

For the purposes of cardiovascular disease modeling, detailed 3D computational fluid dynamic (CFD) modeling has been performed with Fluent to better assess the local velocity and shear profiles.  One benefit provided by the 1D model, is that it allows for using more in vivo boundary conditions with 3D CFD.  In the case of 3D modeling in Fluent, there are several factors to be considered: 1) the local fluid dynamics have two more dimensions than the 1D model, 2) the solutions are numerically solved (not analytical or exact), and 3) the simulations are rigid (not of elastic vessels).  To better couple the 1D model predictions with the 3D CFD simulations, a 0D simulant has been developed to represent the 3D calculations (using the lubrication approximation), and it is simultaneously and iteratively solved with the 1D sub-network impedances to develop new boundary conditions which maintain the pressure/flow relationship of the sub-networks and the local CFD of Fluent.  We have successfully completed this iteration technique for various local conditions of the vessels, and it has shown different local effects compared to the typical simulations that would occur if one was blind to the outlet boundary conditions.