Pulsatile flow in the abdominal aorta and the renal arteries of three patients was studied numerically. Two of the patients had renal artery stenosis. The aim of the study was to assess the use of four types of indicators for determining the risk of new stenosis after revascularization of the affected arteries. The four indicators considered include the time averaged wall shear stress (TAWSS), the oscillatory shear index (OSI), the relative reference time (RRT) and a power law model based in platelet activation modeling but applied to the endothelium, named endothelium activation indicator (EAI). The results show that the indicators can detect the existing stenosis but are less successful in the revascularized cases. The TAWSS and, more clearly, the EAI approach seem to be better in predicting the risk for stenosis relapse at the original location and close to the post-stenotic dilatation. The shortcomings of the respective indicators are discussed along with potential improvements to endothelial activation modeling and its use as an indicator for risks of restenosis.

Patient specific (PS) blood flow studies have become popular in recent years but have thus far had limited clinical impact. This is possibly due to uncertainties and errors in the underlying models and simulations set-up. This study focuses on the sensitivity of simulation results due to in- and outflow boundary conditions (BC:s). Nine different inlet- and seven different outlet BC:s were applied to two variants of a healthy subject’s thoracic aorta. Temporal development of the flow is essential for the formation and development of helical/spiralling flow where the commonly observed clockwise helical motion may change direction during the heart-cycle. The sensitivity to temporal and spatial variations in the inlet conditions is significant both when expressed in terms of mean and maximal wall shear stress (WSS) and its different averaged variables, e.g. Time-Averaged WSS (TAWSS), Oscillating Shear Index (OSI) and Relative Residence Time (RRT). The simulation results are highly sensitive to BC. For example, the maximal WSS may vary over 3 orders of magnitude (1 to 1000 Pa) depending on particular combinations of BC:s. Moreover, certain formulations of outlet boundary conditions may be inconsistent with the computed flow field if the underlying assumptions of the space-time dependence are violated. The results of this study show that CFD simulations can reveal flow details that can enhance understanding of blood flows. However, the results also demonstrate the potential difficulties in mimicking blood flow in clinical situations.

Arterial blood flow contains structures known to be associated with arterial wall pathologies (such as atherosclerosis and aneurysms) but also with helical motion reported to be atheroprotective. Numerical simulation of the flow in a typical human thoracic aorta model was carried out for several heart- and flow-rates. The aim was to explore the presence and the underlying mechanism of the formation of helical flow, retrograde motion and the formation of smaller scale unsteady flow structures. The main findings of the paper are as follows:

- Retrograde flow is induced during flow deceleration. Reversed flow may persist throughout the cardiac cycle in parts of the descending aorta. Retrograde flow may lead enhanced risk of upstream transport of thrombi from the descending aorta to the branches of the aortic arch.

- Helical flows are induced by bend and torsion of the aorta and through non-uniformity in the spatial distribution of the inlet flow (aortic valve plane).

- Amplification of axial vorticity was shown to occur in the thoracic aorta. This convective instability is enhanced in the descending aorta.

- Transitional and turbulent flow may occur in the thoracic aorta under elevated flow- and heart-rate conditions also in healthy individuals.

- Under normal conditions, healthy individuals do not develop turbulent flow in the thoracic aorta.

A hypothesis for a possible mechanism for the atheroprotective effect of helical flow is suggested.

Purpose: The purpose of the study is to determine the effects of heart rate (HR) and cardiac output(CO), in the temporal variation of CO on flow structures and related biomechanical markers.

Methods: The pulsatile flow in the thoracic aorta was simulated for 15 combinations of HR (60-150 beats per minutes, BPM), CO and cardiac temporal profiles. In all cases, the Quemada viscositymodel was used. The results were analyzed in terms of biomechanical markers such as extent ofretrograde flow in the lumen and close to the wall, helicity parameters, commonly used wall shearstress (WSS) indicators along with proposed Endothelial Activation Indices (EAIs).

Results: The simulations demonstrated the presence of helical motion in all cases. The helicalmotion depends on the spatial distribution of the flow by the aortic valve. Time- and space-averagedhelicity indices were found to have smallest values in the aortic arch and largest in the descendingpart of the aorta. For all cases, retrograde flow was observed. The extent of separated flow close tothe aortic wall depended strongly on the rate of decelerating CO during late systole as well aspossible axial flow deceleration periods during diastole. At high HR and CO, small scale flowstructures developed, indicating transition to turbulence. Time averaged WSS-related indicatorswere less distinctive in assessing the spatial and temporal impact as compared to the EAI indicators(EAI_Nobili and EAI_Soares) accounting for both accumulated stress and the temporal behavior of thestress.

Conclusions: The results underpin the importance of temporal variation of the cardiac flowrate andthe impact of the deceleration phase of systole on retrograde flow and formation of helical flowstructures. As retrograde and helical flow has been found to be related to atherosclerosis, thetemporal contribution of the flowrate must be maintained, since time averaged biomechanicalindicators filter out information of potential diagnostic importance. Temporal flow behavior, up tocell response frequency, needs to be reflected by the biomechanical indicators as in the proposed EAI_Soares indicator.

Purpose: The purpose of the study is to assess the importance of non-Newtonian rheological models onblood 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 wasassessed with respect to the following quantities:

i. Magnitude of the viscosity relative to a reference value (the Newtonian case) and the relative mean deviation from that value.

ii. Mechanical kinetic energy,vorticity, viscous dissipation rate.

iii. WSS and its time derivative.

iv. WSS-related indicators; OSI, TAWSS and RRT.

Results: The flow in the thoracic aorta is characterized by shear-rates leading to an increase in viscosity by afactor of up to six. The different models had negligible impact on the kinetic energy and viscous dissipationrate. The effect on WSS related parameters was quantified and was found to be modest. Largest effect wasobserved for low shear-rates (below 100 s-2).

Conclusions: The choice of a non-Newtonian model is important whenever the flow is viscosity dominated.Blood flow in larger arteries is weakly dependent on viscosity and can be handled by a model with weakdependence on shear-rate (e.g. Quemada or Newtonian). Blood flows with regions with low shear-rate andstrong temporal variation requires rheological models that better account for low shear and explicitlyincludes temporal variation effects.

Purpose: The purpose of the study is to compare and assess modeling of transport cells and lipoproteins by the blood in the human thoracic aorta.

Methods: In the continuum framework, three flux models were considered; Fickian, Zydney-Colton (Z-C) and Leighton-Acrivos (L-A). The transport of spherical particles (cells and lipoprotein of different sizes and densities) under pulsatile flow condition were simulated. The effect of local red blood cell (RBC) concentration (hematocrit) on blood viscosity wasconsidered through Quemada’s model. Lagrangian particle transport (LPT) was assessed and compared to the continuum models. Contribution to RBC flux (diffusion) due to gradients inhematocrit, mixture density and viscosity was assessed. Results were extracted in terms ofmean and variations in concentrations, residence time and path lengths of RBC and six othercells and lipoproteins.

Results: The effects of local hematocrit variations on the local blood viscosity is large (a factor of more than 2) but the effect on wall shear stress (WSS) indicators is much more modest (few percent). In terms of mean concentration, the three continuum transport modelsyield local viscosity that deviate by a factor between about 1.3 to 2, as compared to a constantviscosity case. The main contribution to the mass (RBC) flux in the L-A model is from the shear-rate gradient term, followed by the viscosity gradient term and least by the RBC concentration gradient term (low flow rate). The inflow and wall boundary conditions play an important role on the details of the mass transport. The LPT result do converge to the expected concentration at the different outflow boundaries. However, the convergence rate isslow and require more than 30 cardiac periods to get below 2% in outflow hematocrit.Detailed analysis of the RBC paths shows large variations. For the outlet from the thoracicaorta RBC path length and residence time ranging from 0.333 m to 0.0.791 m and from lessthan one to about four cardiac cycles, respectively. The corresponding values for the LCCA are about 0.2 m to more than 0.5 m and about a quarter to about four cardiac cycles,respectively. The LPT results also show that particles are subject to a lift force driven bystrong path curvature and particle to fluid density difference. A simulation with injection ofparticles in the descending aorta indicated the possibility of upstream transport of particlesinto the three main arteries branching from the aortic arch.

Conclusions: Continuum transport models depend strongly on calibrated model parametersand the imposed boundary conditions. Counter gradient diffusion may occur as the fluxes aredependent on gradients of shear rate, concentration, and viscosity. LPT has the advantage ofaccounting for temporal effect and are most appropriate for dilute particle suspensions such ascells (except for RBC) and lipoproteins. LPT though, may require substantially longercomputational time when statistical data is sought.