Transitional flow in aneurysms and the computation of haemodynamic parameters

Abstract

Haemodynamic forces appear to play an influential role in the evolution of aneurysms. This has led to numerous studies, usually based on computational fluid dynamics. Their focus is predominantly on the wall shear stress (WSS) and associated derived parameters, attempting to find correlations between particular patterns of haemodynamic indices and regions subjected to disease formation and progression. The indices are generally determined by integration of flow properties over a single cardiac cycle. In this study, we illustrate that in some cases the transitional flow in aneurysms can lead to significantly different WSS distributions in consecutive cardiac cycles. Accurate determination of time-averaged haemodynamic indices may thus require simulation of a large number of cycles, which contrasts with the common approach to determine parameters using data from a single cycle. To demonstrate the role of transitional flow, two exemplary cases are considered: flow in an abdominal aortic aneurysm and in an intracranial aneurysm. The key differences that are observed between these cases are explained in terms of the integral timescale of the transitional flows in comparison with the cardiac cycle duration: for relatively small geometries, transients will decay before the next cardiac cycle. In larger geometries, transients are still present when the systolic phase produces new instabilities. These residual fluctuations serve as random initial conditions and thus seed different flow patterns in each cycle. To judge whether statistics are converged, the derived indices from at least two successive cardiac cycles should be compared.

Effects of Reynolds and Womersley Numbers on the Hemodynamics of Intracranial Aneurysms

“…We have assumed rigid walls similar to previous simulations [2, 14, 17, 19] because the displacement of aneurysm's wall is typically small and the flow patterns of small distensible and rigid models in the carotid region are very similar [32]. In addition, we have assumed Newtonian fluid in our simulations because the non-Newtonian effects are negligible in larger (>500  μ m) arteries [33] and previous simulations of both Newtonian and non-Newtonian fluids have shown similar flow patterns [19].…”

“…Computational fluid dynamics (CFD) holds an important position in the investigation of hemodynamic factors in aneurysms because of its higher resolution near the walls relative to experimental methods such as laser Doppler velocimetry, particle image velocimetry, and magnetic resonance imaging, which is required to compute hemodynamic factors such as shear stress correctly [8, 9]. Many investigations have been carried out on the hemodynamics of IAs using experimental methods [10–12] and CFD [7, 13, 14]. …”

Wall shear stress exposure time: a Lagrangian measure of near-wall stagnation and concentration in cardiovascular flows

“…The effect of WSS divergence on WSSET can become important in higher Reynolds numbers where the WSS divergence can become very high. In the present study, we only used one cardiac cycle of WSS data and assumed periodicity to generate WSS trajectories, although cycle-to-cycle variations in WSS exist in some cardiovascular flows such as AAAs [46]. However, our aim in this study was to demonstrate the applicability of our approach and comparison to existing methods.…”

A comparison of hemodynamic metrics and intraluminal thrombus burden in a common iliac artery aneurysm

“…[5,35,36]). However, in light of a recent study by Poelma et al [54], we investigated the statistical convergence of these variables, as it had become clear that the systolic pulses were creating fluctuations within the CIAA that continued through diastole. When similar behaviour was present in a model of Poelma et al [54], they showed that 28 cycles of data did not lead to complete convergence at a particular location.…”

“…With this in mind, we approximated the blood flow as laminar and considered the blood to be an incompressible fluid with a density of 1050 kg/m 3 . The walls of the arteries were characterised by no-slip, rigid wall boundary conditions [5,6,32,35,54,55] and the viscosity was modelled using a non-Newtonian approximation (Carreau-Yasuda, as implemented by Biasetti et al [44]; [56]). By using a non-Newtonian model, as opposed Newtonian, we can capture the macro-scale shear-thinning of the blood, allowing a one-way Lagrangian particle transport model to provide a good prediction of individual blood-cell trajectories within the continuous phase (blood).…”