Model Verification and Error Sensitivity of Turbulence-Related Tensor Characteristics in Pulsatile Blood Flow Simulations

Turbulent blood flow in a cerebral artery with an aneurysm

Unruptured intracranial aneurysms are common in the general population, and many uncertainties remain when predicting rupture risks and treatment outcomes. One of the cutting-edge tools used to investigate this condition is computational fluid dynamics (CFD). However, CFD is not yet mature enough to guide the clinical management of this disease. In addition, recent studies have reported significant flow instabilities when refined numerical methods are used. Questions remain as to how to properly simulate and evaluate this flow, and whether these instabilities are really turbulence. The purpose of the present study is to evaluate the impact of the simulation setup on the results and investigate the occurrence of turbulence in a cerebral artery with an aneurysm. For this purpose, direct numerical simulations were performed with up to 200 cardiac cycles and with data sampling rates of up to 100,000 times per cardiac cycle. Through phase-averaging or triple decomposition, the contributions of turbulence and of laminar pulsatile waves to the velocity, pressure and wall shear stress fluctuations were distinguished. For example, the commonly used oscillatory shear index was found to be closely related to the laminar waves introduced at the inlet, rather than turbulence. The turbulence energy cascade was evaluated through energy spectrum estimates, revealing that, despite the low flow rates and Reynolds number, the flow is turbulent near the aneurysm. Phase-averaging was shown to be an approach that can help researchers better understand this flow, although the results are highly dependent on simulation setup and post-processing choices.

The effect of varying degrees of stenosis on transition to turbulence in oscillatory flows

Many complications in physiology are associated with a deviation in flow in arteries due to a stenosis. The presence of stenosis may transition the flow to weak turbulence. The degree of stenosis as well as its configuration whether symmetric or non-symmetric to the parent artery influences whether the flow would stay laminar or transition to turbulence. Plenty of research efforts focus on investigating the role of varying degrees of stenosis in the onset of turbulence under steady and pulsatile flow conditions. None of the studies, however, have focused on investigating this under oscillatory flow conditions as flow reversal is a major occurrence in a number of physiologic flows, and is of particular relevance in cerebrospinal fluid flow research. Following up on the previous work in which a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$75\%$$\end{document}75% stenosis was studied, this contribution is a detailed investigation of the role of degrees of stenosis on transition in an oscillatory flow. A cylindrical pipe with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$25\%$$\end{document}25%, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$50\%$$\end{document}50% and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$60\%$$\end{document}60% reductions in area in axisymmetric and eccentric configurations is studied for transition with 3 different pulsation frequencies of a purely oscillatory flow. Cycle averaged Reynolds numbers between 1800 and 2100 in steps of 100 are studied for each configuration resulting in 72 simulations each conducted on 76,800 CPU cores of a modern supercomputer. It is found that a higher degree of stenosis and eccentricity causes earlier transition to turbulence in oscillatory flow. The results further demonstrate that a higher frequency of oscillation results in larger hydrodynamic instability in the flow, which is more prominent in smaller degrees of stenosis.

Evaluation of Computational Methodologies for Accurate Prediction of Wall Shear Stress and Turbulence Parameters in a Patient-Specific Aorta

Background: Recent studies suggest that blood flow in main arteries is intrinsically disturbed, even under healthy conditions. Despite this, many computational fluid dynamics (CFD) analyses of aortic haemodynamics make the assumption of laminar flow, and best practices surrounding appropriate modelling choices are lacking. This study aims to address this gap by evaluating different modelling and post-processing approaches in simulations of a patient-specific aorta. Methods: Magnetic resonance imaging (MRI) and 4D flow MRI from a patient with aortic valve stenosis were used to reconstruct the aortic geometry and derive patient-specific inlet and outlet boundary conditions. Three different computational approaches were considered based on assumed laminar or assumed disturbed flow states including low-resolution laminar (LR-Laminar), high-resolution laminar (HR-Laminar) and large-eddy simulation (LES). Each simulation was ran for 30 cardiac cycles and post-processing was conducted on either the final cardiac cycle, or using a phase-averaged approach which utilised all 30 simulated cycles. Model capabilities were evaluated in terms of mean and turbulence-based parameters. Results: All simulation types, regardless of post-processing approach could correctly predict velocity values and flow patterns throughout the aorta. Lower resolution simulations could not accurately predict gradient-derived parameters including wall shear stress and viscous energy loss (largest differences up to 44.6% and 130.3%, respectively), although phase-averaging these parameters improved predictions. The HR-Laminar simulation produced more comparable results to LES with largest differences in wall shear stress and viscous energy loss parameters up to 5.1% and 11.6%, respectively. Laminar-based parameters were better estimated than turbulence-based parameters. Conclusion: Our findings suggest that well-resolved laminar simulations can accurately predict many laminar-based parameters in disturbed flows, but there is no clear benefit to running a HR-Laminar simulation over an LES simulation based on their comparable computational cost. Additionally, post-processing "typical" laminar simulation results with a phase-averaged approach is a simple and cost-effective way to improve accuracy of lower-resolution simulation results.