(142am) The Effect of the Non-Newtonian Blood Flow Rheology On the Flow Through the Arterial Network

This research has been undertaken as a continuation of our efforts to develop a sophisticated model capable of predicting accurately the time-dependent blood pressure and flow profiles throughout the entire human arterial network, that is from the largest arteries down to the smallest of the capillaries. Even when one is interested on a 3D simulation of a specific component of the human arterial network, the complexity of the human system and the interconnectivity of all the vessels within it dictate the implementation of some type of simplified model for the rest of the network, if in vivo conditions are to be simulated. Thus, our approach so far has been to construct a hybrid model ^[1], involving a combination of a 1D and a 3D simulation.

So far, in our previous 1D model^[2], a simplified description for the blood flow characteristics has been adopted to describe the steady state flow properties. The Casson model was used, but with variable parameters that are dependent to the local environment (local hematocrit, Ht and local vessel diameter) based on empirical preexisting relations. Furthermore, to describe the time-dependent flow, a linearization of the problem into Fourier modes is used, based on a Newtonian behavior that again involved a variable viscosity depending to the local environment.

In this presentation, the effect of non-Newtonian characteristics of human blood upon its flow in the arterial network is discussed. We first examined the empirical relations used to determine the parameters of the Casson model, the yield stress and the viscosity, and evaluated the steady state flow predictions over a large number of literature data. Our analysis shows the previously developed empirical relations to be insufficient. However, we need to note here that albeit the Casson model with properly selected parameters is quite capable in describing observed steady flow vs pressure drop blood flow behavior with a given sample, when samples are changed so do the parameters. This indicates that there are other factors, in addition to the hematocrit, that need to be accounted in order to be able to quantitatively define blood flow behavior (perhaps fibrinogen can play such a role). Second, we performed a sensitivity analysis of the blood pressure and flow in the arterial network against the extreme values of the modeling blood flow parameters.

Funding: Grant Award # NSF CBET 1033296

[1]. : Johnson David A.; Naik Ulhas P.; Beris Antony N., Efficient implementation of the proper outlet flow conditions in blood flow simulations through asymmetric arterial bifurcations, International Journal for Numerical Methods in Fluids, Volume: 66 Issue: 11 Pages: 1383-1408 (2011).

[2]. Johnson David A.; Spaeth Justin R.; Rose William C.; Edwards D.; Naik Ulhas P.; Beris Antony N., An impedance model for blood flow in the human arterial system. Part I: Model development and MATLAB implementation, Computers & Chemical Engineering, Volume: 35 Issue: 7 Pages: 1304-1316 ( 2011).