Kristian Valen-Sendstad

Variability of Computational Fluid Dynamics Solutions for Pressure and Flow in a Giant Aneurysm: The ASME 2012 Summer Bioengineering Conference CFD Challenge

Stimulated by a recent controversy regarding pressure drops predicted in a giant aneurysm with a proximal stenosis, the present study sought to assess variability in the prediction of pressures and flow by a wide variety of research groups. In phase I, lumen geometry, flow rates, and fluid properties were specified, leaving each research group to choose their solver, discretization, and solution strategies. Variability was assessed by having each group interpolate their results onto a standardized mesh and centerline. For phase II, a physical model of the geometry was constructed, from which pressure and flow rates were measured. Groups repeated their simulations using a geometry reconstructed from a micro-computed tomography (CT) scan of the physical model with the measured flow rates and fluid properties. Phase I results from 25 groups demonstrated remarkable consistency in the pressure patterns, with the majority predicting peak systolic pressure drops within 8% of each other. Aneurysm sac flow patterns were more variable with only a few groups reporting peak systolic flow instabilities owing to their use of high temporal resolutions. Variability for phase II was comparable, and the median predicted pressure drops were within a few millimeters of mercury of the measured values but only after accounting for submillimeter errors in the reconstruction of the life-sized flow model from micro-CT. In summary, pressure can be predicted with consistency by CFD across a wide range of solvers and solution strategies, but this may not hold true for specific flow patterns or derived quantities. Future challenges are needed and should focus on hemodynamic quantities thought to be of clinical interest.

Mind the Gap: Impact of Computational Fluid Dynamics Solution Strategy on Prediction of Intracranial Aneurysm Hemodynamics and Rupture Status Indicators

BACKGROUND AND PURPOSE: Computational fluid dynamics has become a popular tool for studying intracranial aneurysm hemodynamics, demonstrating success for retrospectively discriminating rupture status; however, recent highly refined simulations suggest potential deficiencies in solution strategies normally used in the aneurysm computational fluid dynamics literature. The purpose of the present study was to determine the impact of this gap. MATERIALS AND METHODS: Pulsatile flow in 12 realistic MCA aneurysms was simulated by using both high-resolution and normal-resolution strategies. Velocity fields were compared at selected instants via domain-averaged error. We also compared wall shear stress fields and various reduced hemodynamic indices: cycle-averaged mean and maximum wall shear stress, oscillatory shear index, low shear area, viscous dissipation ratio, and kinetic energy ratio. RESULTS: Instantaneous differences in flow and wall shear stress patterns were appreciable, especially for bifurcation aneurysms. Linear regressions revealed strong correlations (R2 > 0.9) between high-resolution and normal-resolution solutions for all indices except kinetic energy ratio (R2 = 0.25) and oscillatory shear index (R2 = 0.23); however, for most indices, the slopes were significantly <1, reflecting a pronounced underestimation by the normal-resolution simulations. Some high-resolution simulations were highly unstable, with fluctuating wall shear stresses reflected by the poor oscillatory shear index correlation. CONCLUSIONS: Typical computational fluid dynamics solution strategies may ultimately be adequate for augmenting rupture risk assessment on the basis of certain highly reduced indices; however, they cannot be relied on for predicting the magnitude and character of the complex biomechanical stimuli to which the aneurysm wall may be exposed. This impact of the computational fluid dynamics solution strategy is likely greater than that for other modeling assumptions or uncertainties.

Direct numerical simulation of transitional flow in a patient-specific intracranial aneurysm

In experiments turbulence has previously been shown to occur in intracranial aneurysms. The effects of turbulence induced oscillatory wall stresses could be of great importance in understanding aneurysm rupture. To investigate the effects of turbulence on blood flow in an intracranial aneurysm, we performed a high resolution computational fluid dynamics (CFD) simulation in a patient specific middle cerebral artery (MCA) aneurysm using a realistic, pulsatile inflow velocity. The flow showed transition to turbulence just after peak systole, before relaminarization occurred during diastole. The turbulent structures greatly affected both the frequency of change of wall shear stress (WSS) direction and WSS magnitude, which reached a maximum value of 41.5Pa. The recorded frequencies were predominantly in the range of 1-500Hz. The current study confirms, through properly resolved CFD simulations that turbulence can occur in intracranial aneurysms.

A study of wall shear stress in 12 aneurysms with respect to different viscosity models and flow conditions.

Recent computational fluid dynamics (CFD) studies relate abnormal blood flow to rupture of cerebral aneurysms. However, it is still debated how to model blood flow with sufficient accuracy. Common assumptions made include Newtonian behaviour of blood, traction free outlet boundary conditions and inlet boundary conditions based on available literature. These assumptions are often required since the available patient specific data is usually restricted to the geometry of the aneurysm and the surrounding vasculature. However, the consequences of these assumptions have so far been inadequately addressed. This study investigates the effects of 4 different viscosity models, 2 different inflow conditions and 2 different outflow conditions in 12 middle cerebral artery aneurysms. The differences are quantified in terms of 3 different wall shear stress (WSS) metrics, involving maximal WSS, average WSS, and proportion of aneurysm sac area with low WSS. The results were compared with common geometrical metrics such as volume, aspect ratio, size ratio and parent vessel diameter and classifications in terms of sex and aneurysm type. The results demonstrate strong correlations between the different viscosity models and boundary conditions. The correlation between the different WSS metrics range from weak to medium. No strong correlations were found between the different WSS metrics and the geometrical metrics or classifications.

High-resolution CFD detects high-frequency velocity fluctuations in bifurcation, but not sidewall, aneurysms

High-frequency flow fluctuations in intracranial aneurysms have previously been reported in vitro and in vivo. On the other hand, the vast majority of image-based computational fluid dynamics (CFD) studies of cerebral aneurysms report periodic, laminar flow. We have previously demonstrated that transitional flow, consistent with in vivo reports, can occur in a middle cerebral artery (MCA) bifurcation aneurysm when ultra-high-resolution direct numerical simulation methods are applied. The object of the present study was to investigate if such high-frequency flow fluctuations might be more widespread in adequately-resolved CFD models. A sample of N=12 anatomically realistic MCA aneurysms (five unruptured, seven ruptured), was digitally segmented from CT angiograms. Four were classified as sidewall aneurysms, the other eight as bifurcation aneurysms. Transient CFD simulations were carried out assuming a steady inflow velocity of 0.5m/s, corresponding to typical peak systolic conditions at the MCA. To allow for detection of clinically-reported high-frequency flow fluctuations and resulting flow structures, temporal and spatial resolutions of the CFD simulations were in the order of 0.1 ms and 0.1 mm, respectively. A transient flow response to the stationary inflow conditions was found in five of the 12 aneurysms, with energetic fluctuations up to 100 Hz, and in one case up to 900 Hz. Incidentally, all five were ruptured bifurcation aneurysms, whereas all four sidewall aneurysms, including one ruptured case, quickly reached a stable, steady state solution. Energetic, rapid fluctuations may be overlooked in CFD models of bifurcation aneurysms unless adequate temporal and spatial resolutions are used. Such fluctuations may be relevant to the mechanobiology of aneurysm rupture, and to a recently reported dichotomy between predictors of rupture likelihood for bifurcation vs. sidewall aneurysms.

Sex differences in intracranial arterial bifurcations

BACKGROUND Subarachnoid hemorrhage (SAH) is a serious condition, occurring more frequently in females than in males. SAH is mainly caused by rupture of an intracranial aneurysm, which is formed by localized dilation of the intracranial arterial vessel wall, usually at the apex of the arterial bifurcation. The female preponderance is usually explained by systemic factors (hormonal influences and intrinsic wall weakness); however, the uneven sex distribution of intracranial aneurysms suggests a possible physiologic factor-a local sex difference in the intracranial arteries. OBJECTIVE The aim of this study was to explore sex variation in the bifurcation anatomy of the middle cerebral artery (MCA) and internal carotid artery (ICA), and the subsequent hemodynamic impact. METHODS Vessel radii and bifurcation angles were measured in patients with MCA and ICA bifurcations. Data from a previously published study of 55 patients undergoing diagnostic cerebral digital subtraction angiography at Dalcross Private Hospital in Sydney, Australia, between 2002 and 2003, were available for analysis. The measurements were used to create idealized, averaged bifurcations of the MCA and ICA for females and males. Computational fluid dynamics simulations were performed to calculate hemodynamic forces in the models. RESULTS The vessel radii and bifurcation angles of 47 MCA and 52 ICA bifurcations in 49 patients (32 females, 17 males; mean age, 53 years; age range, 14-86 years) were measured. Statistically significant sex differences were found in vessel diameter (males larger than females; P < 0.05), but not in bifurcation angle. Computational fluid dynamics simulations revealed higher wall shear stress in the female MCA (19%) and ICA (50%) bifurcations compared with the male bifurcations. CONCLUSIONS This study of MCA and ICA bifurcations in female and male patients suggests that sex differences in vessel size and blood flow velocity result in higher hemodynamic forces acting on the vessel wall in females. This new hypothesis may partly explain why intracranial aneurysms and SAH are more likely to occur in females than in males.

High-resolution computational fluid dynamics detects flow instabilities in the carotid siphon: Implications for aneurysm initiation and rupture?

The carotid siphon is by nature a tortuous vessel segment with sharp bends and large area variations, and of relevance to the study of intracranial aneurysm initiation and rupture. The aim of this paper was to determine whether the siphon might harbor flow instabilities, if care is taken to resolve them. This study focused on five consecutive internal carotid artery (ICA) aneurysm cases from the open-source Aneurisk dataset. The aneurysm, always downstream of the siphon, was digitally removed using previously developed and verified tools. Computational fluid dynamic (CFD) models included long cervical segments upstream, and middle and anterior cerebral arteries downstream. High-resolution pulsatile simulations were performed using the equivalent of ~24 million linear tetrahedra on average (range 16-32 M) and 30,000 time-steps/cycle. Two of the five cases were laminar with mild flow instabilities right after peak systole. One of the cases experienced strong periodic vortex shedding at a frequency of around 100 Hz. The remaining two cases harbored higher frequency flow instabilities and complex 3D vortical structures, extending to the cerebral arteries downstream. Our findings suggest that the carotid siphon, a conduit to the majority of anterior intracranial aneurysms, may experience flow instabilities, consistent with in vitro reports, but seemingly at odds with the majority of CFD studies, which have been done at lower resolutions. This has obvious implications for elucidating the forces involved in aneurysm initiation; and propagation of flow instabilities into ICA or downstream aneurysms could also impact understanding of the forces involved in aneurysm rupture.

Narrowing the Expertise Gap for Predicting Intracranial Aneurysm Hemodynamics: Impact of Solver Numerics versus Mesh and Time-Step Resolution

BACKGROUND AND PURPOSE: Recent high-resolution computational fluid dynamics studies have uncovered the presence of laminar flow instabilities and possible transitional or turbulent flow in some intracranial aneurysms. The purpose of this study was to elucidate requirements for computational fluid dynamics to detect these complex flows, and, in particular, to discriminate the impact of solver numerics versus mesh and time-step resolution. MATERIALS AND METHODS: We focused on 3 MCA aneurysms, exemplifying highly unstable, mildly unstable, or stable flow phenotypes, respectively. For each, the number of mesh elements was varied by 320× and the number of time-steps by 25×. Computational fluid dynamics simulations were performed by using an optimized second-order, minimally dissipative solver, and a more typical first-order, stabilized solver. RESULTS: With the optimized solver and settings, qualitative differences in flow and wall shear stress patterns were negligible for models down to ∼800,000 tetrahedra and ∼5000 time-steps per cardiac cycle and could be solved within clinically acceptable timeframes. At the same model resolutions, however, the stabilized solver had poorer accuracy and completely suppressed flow instabilities for the 2 unstable flow cases. These findings were verified by using the popular commercial computational fluid dynamics solver, Fluent. CONCLUSIONS: Solver numerics must be considered at least as important as mesh and time-step resolution in determining the quality of aneurysm computational fluid dynamics simulations. Proper computational fluid dynamics verification studies, and not just superficial grid refinements, are therefore required to avoid overlooking potentially clinically and biologically relevant flow features.

On the quantification and visualization of transient periodic instabilities in pulsatile flows

Turbulent-like flows without cycle-to-cycle variations are more frequently being reported in studies of cardiovascular flows. The associated stimuli might be of mechanobiological relevance, but how to quantify them objectively is not obvious. Classical Reynolds decomposition, where the flow is separated into mean and fluctuating velocity components, is not applicable as the phase-average is zero. We therefore expanded on established techniques and present the idea, analogous to Reynolds decomposition, to decompose a flow with transient instabilities into low- versus high frequency components, respectively, to discriminate flow instabilities from the underlying cardiac pulsatility. Transient wall shear stress and velocity signals derived from computational fluid dynamic simulations were transferred to the frequency domain. A high-pass filter was applied to subtract the 99% most-energy-containing frequencies, which gave a cut-off frequency of 25Hz. We introduce here the spectral power index, and compute the fluctuating kinetic energy, based on the high-pass filtered velocity components, both being frequency-based operators. The efficacy was evaluated in an aneurysm model for multiple flow rates demonstrating transition to turbulent-like flows. The frequency-based operators were found to better correlate with the qualitatively observed flow instabilities compared to conventional descriptors, like time-averaged wall shear stress or oscillatory shear index. We demonstrate how the high frequencies beyond the physiological range could be analyzed and/or transferred back to the time domain for quantification and visualization purposes. We have introduced general frequency-based operators, easily extendable to other cardiovascular territories based on a posteriori heuristic filtering that allows for separation, isolation, and quantification of cycle-invariant turbulent-like flows.

Improved reduced-order modelling of cerebrovascular flow distribution by accounting for arterial bifurcation pressure drops

Reduced-order modelling offers the possibility to study global flow features in cardiovascular networks. In order to validate these models, previous studies have been conducted in which they compared 3D computational fluid dynamics simulations with reduced-order simulations. Discrepancies have been reported between the two methods. The loss of energy at the bifurcations is usually neglected and has been pointed out as a possible explanation for these discrepancies. We present distributed lumped models of cerebrovasculatures created automatically from 70 cerebrovascular networks segmented from 3D angiograms. The outflow rate repartitions predicted with and without modelling the energy loss at the bifurcations are compared against 3D simulations. When neglecting the energy loss at the bifurcations, the flow rates though the anterior cerebral arteries are overestimated by 4.7±6.8% (error relative to the inlet flow rate, mean ± standard deviation), impacting the remaining volume of flow going to the other vessels. When the energy loss is modelled, this error is dropping to 0.1±3.2%. Overall, over the total of 337 outlet vessels, when the energy losses at the bifurcations are not modelled the 95% of agreement is in the range of ±13.5% and is down to ±6.5% when the energy losses are considered. With minimal input and computational resources, the presented method can estimate the outflow rates reliably. This study constitutes the largest validation of a reduced-order flow model against 3D simulations. The impact of the energy loss at the bifurcations is here demonstrated for cerebrovasculatures but can be applied to other physiological networks.