Accounting for residence-time in blood rheology models: do we really need non-Newtonian blood flow modelling in large arteries?

Abstract

Patient-specific computational fluid dynamics (CFD) is a promising tool that provides highly resolved haemodynamics information. The choice of blood rheology is an assumption in CFD models that has been subject to extensive debate. Blood is known to exhibit shear-thinning behaviour, and non-Newtonian modelling has been recommended for aneurysmal flows. Current non-Newtonian models ignore rouleaux formation, which is the key player in blood's shear-thinning behaviour. Experimental data suggest that red blood cell aggregation and rouleaux formation require notable red blood cell residence-time (RT) in a low shear rate regime. This study proposes a novel hybrid Newtonian and non-Newtonian rheology model where the shear-thinning behaviour is activated in high RT regions based on experimental data. Image-based abdominal aortic and cerebral aneurysm models are considered and highly resolved CFD simulations are performed using a minimally dissipative solver. Lagrangian particle tracking is used to define a backward particle RT measure and detect stagnant regions with increased rouleaux formation likelihood. Our novel RT-based non-Newtonian model shows a significant reduction in shear-thinning effects and provides haemodynamic results qualitatively identical and quantitatively close to the Newtonian model. Our results have important implications in patient-specific CFD modelling and suggest that non-Newtonian models should be revisited in large artery flows.

Keywords: Lagrangian particle tracking; aneurysm; computational fluid dynamics; haemodynamics; rouleaux formation; wall shear stress.

Figure 1.

The three-dimensional computer models, corresponding computational mesh and the waveforms used as inlet boundary condition are shown (AAA model on the left and cerebral aneurysm model on the right). The highlighted red region shows the region of interest (aneurysmal region) where the RT calculation is done.

Figure 2.

Tracers are seeded on the computational nodes in the region of interest (aneurysmal region). The tracers are integrated backward in time until they leave the region of interest. Subsequently, backward RT is calculated and mapped to tracer initial location. The red dots demonstrate tracers that are initially densely seeded in the aneurysm and subsequently integrated backward in time.

Figure 3.

TAWSS contours for the AAA (top row) and ICA aneurysm (bottom row) models. The τ_m value in the colour bar range is set to 0.7 and 20 Pa for the AAA and ICA aneurysm models, respectively. The different rheology models are shown in the figure.

Figure 4.

OSI contours for the AAA (top row) and ICA aneurysm (bottom row) models. The different rheology models are shown in the figure.

Figure 5.

Velocity vectors for the AAA (top row) and ICA aneurysm (bottom row) models at the shown cross sections and intra-cardiac time-points. Surface streamlines of the velocity vectors projected to the cross section are shown. The streamlines are coloured based on the total velocity vector. The V_m value in the colour bar range is set to 4 and 10 m s⁻¹ for the AAA and ICA aneurysm models, respectively. The different rheology models are shown in the figure.

Figure 6.

Box plots of the relative point-wise change (|τ₁ − τ₂|/τ₂) between the Newtonian model (reference model) and the other rheological models for the OSI and TAWSS results in the AAA (top row) and ICA aneurysm (bottom row) models. The median, first and third quartiles are shown in the box plots. The whiskers correspond to the minimum and 99th percentile of the data. The plots are created based on all of the computational nodes in the aneurysmal region. (Online version in colour.)

Figure 7.

Probability density histograms of the strain rate history (integrated Frobenius norm of the strain rate tensor along each trajectory) and average velocity (average velocity experienced by each trajectory) for tracers that meet the RT threshold (left panels) and do not meet the RT threshold (right panels). The histograms are based on all of the tracers released at different time-points. The AAA (top row) and ICA aneurysm (bottom row) results are shown. The RT threshold used is RT_th = 5 s for the AAA and RT_th = 1.5 s for the ICA aneurysm model. Strain rate history () is dimensionless and the unit for velocity is cm s⁻¹. (Online version in colour.)