Non-Newtonian Endothelial Shear Stress Simulation: Does It Matter?

FIGURE 1. Normal and abnormal viscosity profiles. (A) In a straight unobstructed artery, blood velocity takes on a parabolic profile with low shear rate (high viscosity) in the centre of the artery and low viscosity at the wall. (B) In the presence of stenoses, curvatures, or bifurcations, the blood velocity profile becomes distorted. Localized regions of low shear rate can develop at the wall, resulting in high viscosity near the endothelial surface.

FIGURE 2. An idealized stenotic model with an artery’s diameter of 3mm and 40% DS. Segment 1: at least 1 diameter from the proximal stenotic segment; Segment 2: 1 diameter from the proximal shoulder of the stenosis to minimal lumen diameter; Segment 3: minimal lumen diameter to 1 diameter distal to the stenosis shoulder; Segment 4: remaining distal segment.

FIGURE 3. Qualitative differences in ESS from (A) Newtonian and (B) non-Newtonian models. Although the distribution of high and low ESS is similar, the non-Newtonian model predicts higher ESS throughout the artery. This is visually most apparent from the larger areas exposed to high ESS (white arrows). ESS, endothelial shear stress.

FIGURE 4. Quantitative difference in ESS between Newtonian and non-Newtonian models (Single Representative Case). (A) Coronary flow rate, systole is indicated in black, diastole is indicated in green. (B,C) The % difference and absolute difference are calculated as (non-Newtonian ESS – Newtonian ESS), thus positive values indicate non-Newtonian results were higher whereas negative values indicate higher Newtonian results. The non-Newtonian results show consistently higher percent normalized difference and absolute difference in ESS over the cardiac cycle, except during the momentary transition between systole and diastole at approximately 0.35s. (D) Newtonian simulations predict more of the vessel is exposed to atherogenic levels of ESS over the cardiac cycle.

FIGURE 5. ESS and local blood viscosity. (A) Multiple areas of low ESS (<1Pa) are identified (white arrows). (B) Non-Newtonian simulation detects regions of high LBV (>1.45) in the centre of the vessel and at the wall (orange arrows). ESS, endothelial shear stress; LBV, local blood viscosity.