Non-identifiability of parameters for a class of shear-thinning rheological models, with implications for haematological fluid dynamics

Assessment of Rheological Models Applied to Blood Flow in Human Thoracic Aorta

PURPOSE

The purpose of this study is to assess the importance of non-Newtonian rheological models on blood flow in the human thoracic aorta.

METHODS

The pulsatile flow in the aorta is simulated using the models of Casson, Quemada and Walburn-Schneck in addition to a case of fixed (Newtonian) viscosity. The impact of the four rheological models (using constant hematocrit) was assessed with respect to (i) magnitude and deviation of the viscosity relative to a reference value (the Newtonian case); (ii) wall shear stress (WSS) and its time derivative; (iii) common WSS-related indicators, OSI, TAWSS and RRT; (iv) relative volume and surface-based retrograde flow; and (v) the impact of rheological models on the transport of small particles in the thoracic aorta.

RESULTS

The time-dependent flow in the thoracic aorta implies relatively large variations in the instantaneous WSS, due to variations in the instantaneous viscosity by as much as an order of magnitude. The largest effect was observed for low shear rates (tens s-1). The different viscosity models had a small impact in terms of time- and spaced-averaged quantities. The significance of the rheological models was clearly demonstrated in the instantaneous WSS, for the space-averaged WSS (about 10%) and the corresponding temporal derivative of WSS (up to 20%). The longer-term accumulated effect of the rheological model was observed for the transport of spherical particles of 2 mm and 2 mm in diameter (density of 1200 kg/m3). Large particles' total residence time in the brachiocephalic artery was 60% longer compared to the smaller particles. For the left common carotid artery, the opposite was observed: the smaller particles resided considerably longer than their larger counterparts.

CONCLUSIONS

The dependence on the non-Newtonian properties of blood is mostly important at low shear regions (near walls, stagnation regions). Time- and space-averaging parameters of interest reduce the impact of the rheological model and may thereby lead to under-estimation of viscous effects. The rheological model affects the local WSS and its temporal derivative. In addition, the transport of small particles includes the accumulated effect of the blood rheological model as the several forces (e.g., drag, added mass and lift) acting on the particles are viscosity dependent. Mass transport is an essential factor for the development of pathologies in the arterial wall, implying that rheological models are important for assessing such risks.

An Iterative Approach for the Parameter Estimation of Shear-Rate and Temperature-Dependent Rheological Models for Polymeric Liquids

Numerical flow simulations play an important role in polymer processing. One of the essential prerequisites for accurate and precise flow simulations is to obtain accurate materials functions. In the framework of the generalized Newtonian fluid model, one needs to obtain shear viscosity as a function of the rate-of-shear and temperature—as determined by rheometry—and then fitted to a mathematical model. Often, many subjectively perform the fitting without paying attention to the relative quality of the estimated parameters. This paper proposes a unique iterative algorithm for fitting the rate-of-shear and temperature-dependent viscosity model under the time–temperature superposition (TTS) principle. Proof-of-concept demonstrations are shown using the five-parameter Carreau–Yasuda model and experimental data from small-amplitude oscillatory shear (SAOS) measurements. It is shown that the newly proposed iterative algorithm leads to a more accurate representation of the experimental data compared to the traditional approach. We compare their performance in studies of the steady isothermal flow of a Carreau–Yasuda model fluid in a straight, circular tube. The two sets of parameters, one from the traditional approach and the other from the newly proposed iterative approach, show considerable differences in flow simulation. The percentage difference between the two predictions can be as large as 10% or more. Furthermore, even in cases where prior knowledge of the TTS shifting factors is not available, the newly proposed iterative approach can still yield a good fit to the experimental data, resulting in both the shifting factors and parameters for the non-Newtonian fluid model.