(148g) The Importance of Rheology in Blood Flow Modeling

Authors: 
Horner, J. S. - Presenter, University of Delaware
Wagner, N. J., University of Delaware
Beris, A., University Of Delaware
Woulfe, D. S., University of Delaware
Understanding blood flow has been an area of active research for centuries dating back to the first description of the circulatory system and discovery of capillaries. Currently, blood flow models are designed and implemented for various purposes ranging from drug delivery to cardiovascular disease diagnosis and treatment. Despite the numerous uses for computational models of blood flow throughout the circulatory system, many of these models are currently limited due to an oversimplified treatment of blood as a uniform Newtonian fluid with the most sophisticated models addressing only the steady shear behavior.

In reality, blood is a complex, continuously changing fluid containing red blood cells, white blood cells, and platelets suspended in plasma. At low shear rates, the red blood cells will reversibly form stacked aggregates, or rouleaux, as a result of intercellular interactions facilitated by macromolecules, such as fibrinogen, within the plasma. This aggregation and subsequent breakup of red blood cell rouleaux results in a viscosity that can decrease several orders of magnitude with increasing shear rate. In addition to a shear thinning behavior under steady shear, blood demonstrates other interesting rheological phenomena including a nonzero yield stress, viscoelasticity, and thixotropy – a time dependent change in viscosity.

Coupled with the complex rheological behavior that blood demonstrates are additional complexities associated with measuring blood rheology. As blood is a living fluid, the sampling protocol as well as time from withdrawal can significantly affect the results. Moreover, the proper measurement devices and conditions must be used to avoid interactions happening within the blood sample which are not characteristic of the bulk behavior such as red blood cell sedimentation or formation of red blood cell free layers near the walls of the measurement device. Due to these handling and measurement difficulties, much of the previous data on blood rheology are plagued with inaccuracies and inconsistencies. Furthermore, many previous works fail to document the full physiological profile of the blood which is critical in developing models which can provide insight into how different components of blood affect the flow behavior.

In this work, we present new data on fully profiled human blood with a focus on careful measurement and handling protocol of the blood samples as well as novel transient tests which can best represent the in vivo pulsatile nature of blood flow. Using these data, we show the significance of blood rheology and how it contributes to the bulk flow behavior of blood throughout the circulatory system. In doing so, a new thixotropic model is proposed which can represent the transient shear stress response of blood for various flow conditions. This model incorporates several parameters which can enable insight into the microscopic interactions between red blood cells. In addition to proposing a new thixotropic model for blood that can be implemented in computational fluid simulations through various arteries, a bicontinuous representation of blood near arterial walls is discussed which can better account for the migration of red blood cells. Lastly, future potential for using blood rheology as not only a modeling tool, but also as a diagnostics tool is presented through investigation of possible correlations between the rheological modeling parameters and the physiological properties for the various blood samples.

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