Characterization of volumetric flow rate waveforms at the carotid bifurcations of older adults

Towards the mechanical characterisation of unruptured intracranial aneurysms: Numerical modelling of interactions between a deformation device and the aneurysm wall

Intracranial aneurysm is a critical pathology related to the arterial wall deterioration. This work is an essential aspect of a large scale project aimed at providing clinicians with a non-invasive patient-specific decision support tool regarding the rupture risk assessment. A machine learning algorithm links the aneurysm shape observed and a database of UIA clinical images associated with in vivo wall mechanical properties and rupture characterisation. The database constitution is derived from a device prototype coupled with medical imaging. It provides the mechanical characterisation of the aneurysm from the wall deformation obtained by inverse analysis based on the variation of luminal volume. Before performing in vivo tests of the device on small animals, a numerical model was built to quantify the device's impact on the aneurysm wall under natural blood flow conditions. As the clinician will never be able to precisely situate the device, several locations were considered. In preparation for the inverse analysis procedure, artery material laws of increasing complexity were studied (linear elastic, hyper elastic Fung-like). Considering all the device locations and material laws, the device induced relative displacements to the Systole peak (worst case scenario with the highest mechanical stimulus linked to the blood flow) ranging from 375 μm to 1.28 mm. The variation of luminal volume associated with the displacements was between 0.95 % and 4.3 % compared to the initial Systole volume of the aneurysm. Significant increase of the relative displacements and volume variations were found with the study of different cardiac cycle moments between the blood flow alone and the device application. For forthcoming animal model studies, Spectral Photon CT Counting, with a minimum spatial resolution of 250 μm, was selected as the clinical imaging technique. Based on this preliminary study, the displacements and associated volume variations (baseline for inverse analyse), should be observable and exploitable.

Development of an in vitro setup for flow studies in a stented carotid artery bifurcation

To investigate flow conditions in a double-layered carotid artery stent, a bench-top in vitro flow setup including a bifurcation phantom was designed and fabricated. The geometry of the tissue-mimicking phantom was based on healthy individuals. Two identical phantoms were created using 3D-printing techniques and molding with PVA-gel. In one of them, a clinically available CGuard double-layer stent was inserted. Measurements were performed using both continuous and pulsatile flow conditions. Blood flow studies were performed using echoPIV: a novel ultrasound-based technique combined with particle image velocimetry. A maximum deviation of 3% was visible between desired and measured flow patterns. The echoPIV measurements showed promising results on visualization and quantification of blood flow in and downstream the stent. Further research could demonstrate the effects of a double-layered stent on blood flow patterns in a carotid bifurcation in detail.

An in silico study of the effects of cardiovascular aging on carotid flow waveforms and indexes in a virtual population

Cardiovascular aging is strongly associated with increased risk of cardiovascular disease and mortality. Moreover, health and lifestyle factors may accelerate age-induced alterations, such as increased arterial stiffness and wall dilation, beyond chronological age, making the clinical assessment of cardiovascular aging an important prompt for preventative action. Carotid flow waveforms contain information about age-dependent cardiovascular properties, and their ease of measurement via noninvasive Doppler ultrasound (US) makes their analysis a promising tool for the routine assessment of cardiovascular aging. In this work, the impact of different aging processes on carotid waveform morphology and derived indexes is studied in silico, with the aim of establishing the clinical potential of a carotid US-based assessment of cardiovascular aging. One-dimensional (1-D) hemodynamic modeling was employed to generate an age-specific virtual population (VP) of N = 5,160 realistic carotid hemodynamic waveforms. The resulting VP was statistically validated against in vivo aging trends in waveforms and indexes from the literature, and simulated waveforms were studied in relation to age and underlying cardiovascular parameters. In our study, the carotid flow augmentation index (FAI) significantly increased with age (with a median increase of 50% from the youngest to the oldest age group) and was strongly correlated to local arterial stiffening (r = 0.94). The carotid pulsatility index (PI), which showed less pronounced age variation, was inversely correlated with the reflection coefficient at the carotid branching (r = -0.88) and directly correlated with carotid net forward wave energy (r = 0.90), corroborating previous literature where it was linked to increased risk of cerebrovascular damage in the elderly. There was a high correlation between corrected carotid flow time (ccFT) and cardiac output (CO) (r = 0.99), which was not affected by vascular age. This study highlights the potential of carotid waveforms as a valuable tool for the assessment of cardiovascular aging.NEW & NOTEWORTHY An age-specific virtual population was generated based on a 1-D model of the arterial circulation, including newly defined literature-based specific age variations in carotid vessel properties. Simulated carotid flow/velocity waveforms, indexes, and age trends were statistically validated against in vivo data from the literature. A comprehensive study of the impact of aging on carotid flow waveform morphology was performed, and the mechanisms influencing different carotid indexes were elucidated. Notably, flow augmentation index (FAI) was found to be a strong indicator of local carotid stiffness.

In silico hemodynamical simulations show additional benefits of artery wall softening induced by antihypertensive drugs

BACKGROUND AND OBJECTIVES

Age-related arterial stiffening increases peripheral resistance and decreases arterial distensibility, thus contributing to hypertension, an important risk factor of atherosclerosis. It causes abnormal blood flow, endothelial dysfunction, higher pulse wave velocity, and consequently elevated pressure wave amplitude.

METHODS

This paper presents the influence of these changes via multiscale 3D-0D transient computational fluid dynamics simulations of blood flow in five patient-specific geometries of human carotid bifurcation using archetypal flow waveforms for young and old subjects.

RESULTS

The proposed model shows a significant decrease in the time-averaged wall shear stress (TAWSS) for the old archetypal flow waveform. This is in good agreement with clinical data on a straight segment of common carotid arteries available for young and old subjects. Moreover, our study showed that the decrease of area-averaged TAWSS related to the old flow waveform is much more pronounced (2.5 ÷ 4.5 times higher) at risk areas (areas showing TAWSS below its threshold value of 0.48 Pa) than in straight segments commonly considered in clinical studies.

CONCLUSIONS

Since arterial stiffness can be lowered through long-term usage of any of the five basic groups of antihypertensives, possible benefits of such medical therapy could be not only lowering blood pressure and peripheral resistance but also in increasing the TAWSS and thus attenuating an important mechanism of the atherosclerotic process.

Understanding intracranial aneurysm sounds via high-fidelity fluid-structure-interaction modelling

BACKGROUND

Since the 1960s, the origins of intracranial aneurysm bruits and musical murmurs have been debated, with proposed mechanisms ranging from self-excitation (i.e., resonance) by stable pulsatile flow, to vibration caused by unstable (laminar vortex shedding or turbulent) flow. This knowledge gap has impeded the use of intracranial sounds a marker of aneurysm remodelling or rupture risk. New computational techniques now allow us to model these phenomena.

METHODS

We performed high-fidelity fluid-structure interaction simulations capable of understanding the magnitude and mechanisms of such flow-induced vibrations, under pulsatile flow conditions. Six cases from a previous cohort were used.

RESULTS

In five cases, underlying flow instabilities present as broad-band, random vibrations, consistent with previously-described bruits, while the sac also exhibits resonance, rocking back and forth in different planes of motion, consistent with previously described musical murmurs. Both types of vibration have amplitudes in the range of 0.1 to 1 μm. The murmurs extend into diastole, after the underlying flow instability has dissipated, and do not exhibit the characteristic repeating frequency harmonics of previously hypothesized vortex-shedding mechanisms. The remaining case with stable pulsatile flow does not vibrate. Spectrograms of the simulated vibrations are consistent with previously reported microphone and Doppler ultrasound recordings.

CONCLUSIONS

Our results provide a plausible explanation for distinct intracranial aneurysm sounds and characterize the mechanical environment of a vibrating aneurysm wall. Future work should aim to quantify the deleterious effects of these overlooked stimuli on the vascular wall, to determine which changes to the wall makeup are associated with vibration.

Cerebral arterial flow dynamics during systole and diastole phases in young and older healthy adults

BACKGROUND

Since arterial flow is the leading actor in neuro-fluids flow dynamics, it might be interesting to assess whether it is meaningful to study the arterial flow waveform in more detail and whether this provides new important information. Few studies have focused on determining the influence of heart rate variation over time on the arterial flow curve. Therefore, this study aimed to evaluate cerebral arterial flow waveforms at extracranial and intracranial compartments in young and elderly healthy adults, also considering systole and diastole phases.

METHODS

Cine phase-contrast magnetic resonance imaging (CINE-PC MRI) was performed on twenty-eight healthy young volunteers (HYV) and twenty healthy elderly volunteers (HEV) to measure arterial blood flows at the extracranial and intracranial planes. A semi-automated protocol using MATLAB scripts was implemented to identify the main representative points in the arterial flow waveforms. Representative arterial profiles were estimated for each group. Moreover, the effects of age and sex on flow times, amplitude-related parameters, and parameters related to systole and diastole phases were evaluated at the extracranial and intracranial compartments. Student's t-test or Wilcoxon's test (depending on the normality of the distribution) was used to detect significant differences.

RESULTS

In HYVs, significant differences were observed between extracranial and intracranial levels in parameters related to the AP1 amplitude. Besides the detected differences in pulsatility index (extracranial: 0.92 ± 0.20 vs. 1.28 ± 0.33; intracranial: 0.79 ± 0.15 vs. 1.14 ± 0.18, p < .001) and average flow (715 ± 136 vs. 607 ± 125 ml/min, p = .008) between HYV and HEV, differences in the amplitude value of the arterial flow profile feature points were also noted. Contrary to systole duration (HYV: 360 ± 29 ms; HEV: 364 ± 47 ms), diastole duration presented higher inter-individual variability in both populations (HYV: 472 ± 145 ms; HEV: 456 ± 106 ms). Our results also showed that, with age, it is mainly the diastolic phase that changes. Although no significant differences in duration were observed between the two populations, the mean flow value in the diastolic phase was significantly lower in HEV (extracranial: 628 ± 128 vs. 457 ± 111 ml/min; intracranial: 599 ± 121 vs. 473 ± 100 ml/min, p < .001). No significant differences were observed in the arterial flow parameters evaluated between females and males in either HYV or HEV.

CONCLUSION

Our study provides a novel contribution on the influence of the cardiac cycle phases on cerebral arterial flow. The main contribution in this study concerns the identification of age-related alterations in cerebral blood flow, which occur mainly during the diastolic phase. Specifically, we observed that mean flow significantly decreases with age during diastole, whereas mean flow during systole is consistent.

The relationship between geometry and hemodynamics of the stenotic carotid artery based on computational fluid dynamics

OBJECTIVE

The purpose of this work was to investigate the relationship between the geometric factors and the hemodynamics of the stenotic carotid artery.

METHODS

We retrospectively reviewed data of patients with carotid stenosis (40%-95%). The Navier-Stokes equations were solved using ANSYS CFX 18.0. Correlation analysis was based on Spearman's test. Geometric variables (p < 0.1 in the univariate analysis) were entered into the logistical regression. A receiver-operating characteristics analysis was used to detect hemodynamically significant lesions.

RESULTS

81 patients (96 arteries) were evaluated. The logistic regression analysis revealed that the translesional pressure ratio was significantly correlated with the stenosis degree (OR = 1.147, p < 0.001) and the angle between internal carotid artery and external carotid artery (angle γ) (OR = 0.933, p = 0.01). The translesional wall shear stress ratio was significantly correlated with stenosis degree (OR = 1.094, p < 0.001), lesion length (OR = 0.873, p = 0.01), lumen area of internal carotid artery (OR = 0.867, p = 0.002), and lumen area of common carotid artery (OR = 1.058, p = 0.01). For predicting low translesional pressure ratio, the AUC was 0.71 (p < 0.001) for angle γ, and was 0.87 (p < 0.001) for stenosis degree. For predicting high translesional wall shear stress ratio, the AUC was 0.62 (p = 0.04) for lumen area of internal carotid artery, and was 0.77 (p < 0.001) for stenosis degree.

CONCLUSIONS

Apart from stenosis degree, other geometric characteristics of lesions may also have an influence on hemodynamics of the stenotic carotid artery.

Onset and nature of flow-induced vibrations in cerebral aneurysms via fluid-structure interaction simulations

Clinical, experimental, and recent computational studies have demonstrated the presence of wall vibrations in cerebral aneurysms, thought to be induced by blood flow instability. These vibrations could induce irregular, high-rate deformation of the aneurysm wall, and potentially disrupt regular cell behavior and promote deleterious wall remodeling. In order to elucidate, for the first time, the onset and nature of such flow-induced vibrations, in this study we imposed a linearly increasing flow rate on high-fidelity fluid-structure interaction models of three anatomically realistic aneurysm geometries. Prominent narrow-band vibrations in the range of 100-500 Hz were found in two out of the three aneurysm geometries tested, while the case that did not exhibit flow instability did not vibrate. Aneurysm vibrations consisted mostly of fundamental modes of the entire aneurysm sac, with the vibrations exhibiting more frequency content at higher frequencies than the flow instabilities driving those vibrations. The largest vibrations occurred in the case which exhibited strongly banded fluid frequency content, and the vibration amplitude was highest when the strongest fluid frequency band was an integer multiple of one of the natural frequencies of the aneurysm sac. Lower levels of vibration occurred in the case which exhibited turbulent-like flow with no distinct frequency bands. The current study provides a plausible mechanistic explanation for the high-frequency sounds observed in cerebral aneurysms, and suggests that narrow-band (vortex-shedding type) flow might stimulate the wall more, or at least at lower flow rates, than broad-band, turbulent-like flow.

Heterogeneous model to evaluate CFD in intracranial bifurcation aneurysms treated with the WEB device to predict angiographic outcome

INTRODUCTION

The Woven EndoBridge device (WEB) was developed as an alternative to treat Wide-Necked bifurcation aneurysms. It has proven to be effective and safe, however, cases of recanalization have been reported. The purpose of this study was to evaluate and quantify hemodynamic parameters and indexes with CFD of the intracranial aneurysms before and after WEB simulation and to establish their relationship to complete occlusion.

MATERIALS AND METHODS

Using the heterogeneous model based on the marching cubes algorithm, we created 3D representations of 27 bifurcated intracranial aneurysms treated with the single-layer WEB device to evaluate hemodynamics parameters with CFD, calculated with and without the WEB.

RESULTS

We observed a lower treatment entry concentration indices (ICI) (2.12 ± 1.31 versus 3.14 ± 0.93, p-value: 0.029) previous to placement of WEB and higher pre-treatment FN (7.56 ± 5.92 versus 3.35 ± 1.51, p-value: 0.018) and post-treatment FN (5.34 ± 5.89 versus 1.99 ± 0.83, p-value: 0.021) for cases with successful occlusions. Lower post-treatment SRa (197.81 ± 221.29 versus 80.02 ± 45.25, p-value: 0.044) and higher pre (0.11 ± 0.07 versus 0.25 ± 0.19, p-value: 0.011) and post-treatment MATT (0.69 ± 1.23 versus 1.02 ± 0.46, p-value: 0.006) were observed in non-occluded cases.

CONCLUSIONS

In our CFD analysis of the hemodynamic parameters of IA, we found lower ICI before the placement of the WEB device and higher FN pre- and post-treatment for cases with successful occlusions. Non-occluded cases had lower post-treatment SRa and higher pre-treatment and post-treatment MATT.

Geometry of intracranial aneurysms and of intrasaccular devices may influence aneurysmal occlusion rates after endovascular treatment

INTRODUCTION

The Woven EndoBridge device (WEB) is used to treat wide-neck bifurcation aneurysms. These devices are deployed inside the sac. Therefore, the mesh structure provides apposition with the aneurysm wall and induces aneurysmal thrombosis. The objective of our study was to evaluate the anatomic and device-related parameters and indexes with Computational Fluid Dynamics (CFD) of the intracranial aneurysms before and after WEB simulation and find their relationship to complete occlusion.

MATERIALS AND METHODS

Using the heterogeneous model based on the marching cubes algorithm, we created 3D representations of 27 bifurcated intracranial aneurysms treated with the single-layer WEB device to evaluate anatomic and device-related parameters with CFD.

RESULTS

In our CFD analysis, we observed higher large volumes (Va) (0.25 ± 0.18 versus 0.39 ± 0.09, p-value= 0.025) and higher volume to neck surface ratio (Ra) (1.32 ± 0.17 versus 1.54 ± 0.14, p-value= 0.021) in cases with occlusion failure.

CONCLUSIONS

Large aneurysm volumes (Va) and higher volume to neck surface ratio (Ra) could be associated with occlusion failure in aneurysms treated with the WEB device.

Hemodynamics of anterior circulation intracranial aneurysms with daughter blebs: investigating the multidirectionality of blood flow fields

Recent advances in diagnostic neuroradiological imaging, allowed the detection of unruptured intracranial aneurysms (IAs). The shape - irregular or multilobular - of the aneurysmal dome, is considered as a possible rupture risk factor, independently of the size, the location and patient medical background. Disturbed blood flow fields in particular is thought to play a key role in IAs progression. However, there is an absence of widely-used hemodynamic indices to quantify the extent of a multi-directional disturbed flow. We simulated blood flow in twelve patient-specific anterior circulation unruptured intracranial aneurysms with daughter blebs utilizing the spectral/hp element framework Nektar++. We simulated three cardiac cycles using a volumetric flow rate waveform while we considered blood as a Newtonian fluid. To investigate the multidirectionality of the blood flow fields, besides the time-averaged wall shear stress (TAWSS), we calculated the oscillatory shear index (OSI), the relative residence time (RRT) and the time-averaged cross flow index (TACFI). Our CFD simulations suggest that in the majority of our vascular models there is a formation of complex intrasaccular flow patterns, resulting to low and highly oscillating WSS, especially in the area of the daughter blebs. The existence of disturbed multi-directional blood flow fields is also evident by the distributions of the RRT and the TACFI. These findings further support the theory that IAs with daughter blebs are linked to a potentially increased rupture risk.

A numerical investigation of the mechanics of intracranial aneurysms walls: Assessing the influence of tissue hyperelastic laws and heterogeneous properties on the stress and stretch fields

Numerical simulations have been extensively used in the past two decades for the study of intracranial aneurysms (IAs), a dangerous disease that occurs in the arteries that reach the brain and affect overall 3.2% of a population without comorbidity with up to 60% mortality rate, in case of rupture. The majority of those studies, though, assumed a rigid-wall model to simulate the blood flow. However, to also study the mechanics of IAs walls, it is important to assume a fluid-solid interaction (FSI) modeling. Progress towards more reliable FSI simulations is limited because FSI techniques pose severe numerical difficulties, but also due to scarce data on the mechanical behavior and material constants of IA tissue. Additionally, works that have investigated the impact of different wall modeling choices for patient-specific IAs geometries are a few and often with limited conclusions. Thus our present study investigated the effect of different modeling approaches to simulate the motion of an IA. We used three hyperelastic laws - the Yeoh law, the three-parameter Mooney-Rivlin law, and a Fung-like law with a single parameter - and two different ways of modeling the wall thickness and tissue mechanical properties - one assumed that both were uniform while the other accounted for the heterogeneity of the wall by using a "hemodynamics-driven" approach in which both thickness and material constants varied spatially with the cardiac-cycle-averaged hemodynamics. Pulsatile numerical simulations, with patient-specific vascular geometries harboring IAs, were carried out using the one-way fluid-solid interaction solution strategy implemented in solids4foam, an extension of OpenFOAM®, in which the blood flow is solved and applied as the driving force of the wall motion. We found that different wall morphology models yield smaller absolute differences in the mechanical response than different hyperelastic laws. Furthermore, the stretch levels of IAs walls were more sensitive to the hyperelastic and material constants than the stress. These findings could be used to guide modeling decisions on IA simulations, since the computational behavior of each law was different, for example, with the Yeoh law being the fastest to converge.

Reliability of using generic flow conditions to quantify aneurysmal haemodynamics: A comparison against simulations incorporating boundary conditions measured in vivo

BACKGROUND AND OBJECTIVES

Initiation, growth, and rupture of intracranial aneurysms are believed to be closely related to their local haemodynamic environment. While haemodynamics can be characterised by use of computational fluid dynamics (CFD), its reliability depends heavily upon accurate assumption of the boundary conditions. Herein, we compared the simulated aneurysmal haemodynamics obtained by use of generic boundary conditions against those obtained under flow conditions measured in vivo.

METHODS

We prospectively recruited 19 patients with intracranial aneurysms requiring 3-dimensional rotational angiography, during which blood pressure at the internal carotid artery was probed by catheter and flowrate measured by a dedicated software tool. Using these flow conditions measured in vivo, we quantified the aneurysmal haemodynamics for each patient by CFD, and then compared the results with those derived from a generic condition reported in the literature, in terms of the time-averaged wall shear stress (TAWSS), oscillatory shear index (OSI), relative residence time (RRT), and percentage of the intra-aneurysmal flow (PIAF). In addition, the effects on aneurysmal haemodynamics of different outflow strategies (splitting method vs. Murray's Law) and simulation schemes (transient vs. steady-state) relative to each flow condition were also assessed.

RESULTS

Differences in the simulated TAWSS (-6.08 ± 10.64 Pa, p = 0.001), OSI (0.06 ± 0.13, p = 0.001), and PIAF (-0.05 ± 0.20, p = 0.012) between the patient-specific and generic boundary conditions were found to be statistically significant, in contrast to that in the RRT (49 ± 307 Pa^-1, p = 0.062). Outflow strategies did not yield statistically significant differences in any of the investigated parameters (all p > 0.05); rather, the resulting parameters were found to be in good correlations (all r > 0.71, p < 0.001). Difference between the aneurysmal TAWSS and the WSS derived from cycle-averaged flowrate condition was found to be minor (0.66 ± 1.36 Pa, p = 0.000), so was that between PIAFs obtained respectively from the transient and steady-state simulations (0.02 ± 0.05, p = 0.000).

CONCLUSIONS

Incorporating into simulation the patient-specific boundary conditions is critical for CFD to characterise aneurysmal haemodynamics, while outflow strategies may not introduce significant uncertainties. Steady-state simulation incorporating the cycle-averaged flow condition may produce unbiased WSS and PIAF compared to the transient analysis.

An Oscillatory Shear Index-Based Model to Describe Progressive Carotid Artery Stenosis

Background and aims: This study describes and demonstrates the applicability of a novel in silico method for modeling progressive carotid artery stenosis using the oscillatory shear index (OSI) as the basis of stenosis. Methods: Three-dimensional reconstructions of 11 carotid arteries were generated using patient-derived magnetic resonance angiography and duplex ultrasound data. Computational fluid dynamic simulations were sequentially generated following computational stenosis assessment, and corresponding changes in OSI were observed and used as measure of morphological stabilization. Results: 6 carotid models showed progressive stenosis with statistically significant increases in regions of high OSI (OSI >.2, P < .05) with eventual carotid occlusion in 1 of the cases. Three models remained free or nearly free of increased OSI, whereas 1 model showed an overall decrease in high OSI regions (P < .05) and another trended in that direction but did not achieve statistical significance (P = .145). Conclusions: To our knowledge, this is the first computational model describing progressive stenosis in any peripheral artery including the carotid. Taken together, this study provides a novel framework for computational hemodynamic investigations on progressive atherosclerosis in the carotid artery.

A heterogeneous model of endovascular devices for the treatment of intracranial aneurysms

Numerical computations of hemodynamics inside intracranial aneurysms treated by endovascular braided devices such as flow-diverters contribute to understanding and improving such treatment procedures. Nevertheless, these simulations yield high computational and meshing costs due to the heterogeneity of length scales between the dense weave of the fine struts of the device and the arterial volume. Homogeneous strategies developed over the last decade to circumvent this issue substitute local dissipations due to the wires with a global effect in the form of a pressure-drop across the device surface. However, these methods cannot accurately reproduce the flow-patterns encountered near the struts, the latter strongly dictating the intra-saccular flow environment. In this work, a versatile theoretical framework which aims at correctly reproducing the local flow heterogeneities due to the wires while keeping memory consumption, meshing and computational times as low as possible is introduced. This model reproduces the drag forces exerted by the device struts onto the fluid, thus producing local and heterogeneous effects on the flow. Extensive validation for various flow and geometric configurations using an idealized device is performed. To further illustrate the method capabilities, a real patient-specific aneurysm endovascularly treated with a flow-diverter is used, enabling quantitative comparisons with classical approaches for both intra-saccular velocities and computational costs reduction. The proposed heterogeneous model endeavors to bridge the gap between computational fluid dynamics and clinical applications and ushers in a new era of numerical treatment planning with minimally costing computational tools.

Simulation of intracranial hemodynamics by an efficient and accurate immersed boundary scheme

We use computational fluid dynamics (CFD) to simulate blood flow in intracranial aneurysms (IAs). Despite ongoing improvements in the accuracy and efficiency of body-fitted CFD solvers, generation of a high quality mesh appears as the bottleneck of the flow simulation and strongly affects the accuracy of the numerical solution. To overcome this drawback, we use an immersed boundary method. The proposed approach solves the incompressible Navier-Stokes equations on a rectangular (box) domain discretized using uniform Cartesian grid using the finite element method. The immersed object is represented by a set of points (Lagrangian points) located on the surface of the object. Grid local refinement is applied using an automated algorithm. We verify and validate the proposed method by comparing our numerical findings with published experimental results and analytical solutions. We demonstrate the applicability of the proposed scheme on patient-specific blood flow simulations in IAs.

Validation of an aging virtual population for the study of carotid hemodynamics

The analysis of carotid ultrasound (US) flow, velocity, and diameter waveforms provides important information about cardiovascular and circulatory health. These can be used to derive clinical indices of atherosclerosis, vascular aging, and hemodynamic status. To derive clinical insight from carotid waveforms, it is essential to understand the relationship of the observed variability in morphology with the underlying hemodynamic status and cardiovascular properties. For this purpose, using a one-dimensional modeling approach, we have developed and validated a virtual population that is able to realistically simulate carotid waveforms of healthy subjects aged between 10 and 80 years old.Clinical Relevance-Our virtual population of carotid waveforms can support the interpretation of US patient data. It can be used, e.g., to investigate how waveform morphology and derived indices relate to individual arterial and cardiac properties.

Evaluation of Plaque Vulnerability via Combination of Hemodynamic Analysis and Simultaneous Non-Contrast Angiography and Intraplaque Hemorrhage (SNAP) Sequence for Carotid Intraplaque Hemorrhage

The purpose of this study was to assess the vulnerability of plaque using a combination of simultaneous non-contrast angiography, intraplaque hemorrhage (SNAP) sequence, and local hemodynamic analysis in an intraplaque hemorrhage (IPH), and to evaluate the association between morphological and hemodynamic factors and IPH by comparing the IPH (presence of IPH) and non-IPH (plaque with absence of IPH) groups. In total, 27 IPH patients and 27 non-IPH patients were involved in this study, and baseline characteristics were collected. For morphological factors, diameters, and areas of the internal carotid artery (ICA), external carotid artery, and common carotid artery were measured, and bifurcation angle (α) and ICA angle (β) were also measured for comparison between the IPH group and non-IPH group. For hemodynamic factors, time-averaged wall shear stress (WSS), minimum WSS, maximum WSS, and oscillatory shear index were calculated using computational fluid dynamics (CFD) simulations. For the qualitative analysis, cross-sectional images with analyzed WSS and SNAP sequences were combined to precisely assess local hemodynamics. Bifurcation angle (α) was significantly different between the IPH and non-IPH groups (39.47 degrees vs. 47.60 degrees, p = 0.041). Significantly higher time-averaged WSS, minimum WSS, and maximum WSS were observed in the IPH group compared to the non-IPH group. In the IPH group, when using the combined analysis with SNAP sequences and WSS, the WSS of the region with IPH was significantly higher than the region without IPH (2.32 vs. 1.21 Pa, p = 0.005). A smaller bifurcation angle (α) and higher time-averaged WSS, minimum WSS, and maximum WSS were associated with IPH. The combined analysis of SNAP sequences and WSS might help to evaluate the risk of carotid IPH.

Quantitative analysis of flow vortices: differentiation of unruptured and ruptured medium-sized middle cerebral artery aneurysms

BACKGROUND

Surgical intervention for unruptured intracranial aneurysms (IAs) carries inherent health risks. The analysis of "patient-specific" IA geometric and computational fluid dynamics (CFD) simulated wall shear stress (WSS) data has been investigated to differentiate IAs at high and low risk of rupture to help clinical decision making. Yet, outcomes vary among studies, suggesting that novel analysis could improve rupture characterization. The authors describe a CFD analytic method to assess spatiotemporal characteristics of swirling flow vortices within IAs to improve characterization.

METHODS

CFD simulations were performed for 47 subjects harboring one medium-sized (4-10 mm) middle cerebral artery (MCA) aneurysm with available 3D digital subtraction angiography data. Alongside conventional indices, quantified IA flow vortex spatiotemporal characteristics were applied during statistical characterization. Statistical supervised machine learning using a support vector machine (SVM) method was run with cross-validation (100 iterations) to assess flow vortex-based metrics' strength toward rupture characterization.

RESULTS

Relying solely on vortex indices for statistical characterization underperformed compared with established geometric characteristics (total accuracy of 0.77 vs 0.80) yet showed improvements over wall shear stress models (0.74). However, the application of vortex spatiotemporal characteristics into the combined geometric and wall shear stress parameters augmented model strength for assessing the rupture status of middle cerebral artery aneurysms (0.85).

CONCLUSIONS

This preliminary study suggests that the spatiotemporal characteristics of flow vortices within MCA aneurysms are of value to improve the differentiation of ruptured aneurysms from unruptured ones.

Integrating multi-fidelity blood flow data with reduced-order data assimilation

High-fidelity patient-specific modeling of cardiovascular flows and hemodynamics is challenging. Direct blood flow measurement inside the body with in-vivo measurement modalities such as 4D flow magnetic resonance imaging (4D flow MRI) suffer from low resolution and acquisition noise. In-vitro experimental modeling and patient-specific computational fluid dynamics (CFD) models are subject to uncertainty in patient-specific boundary conditions and model parameters. Furthermore, collecting blood flow data in the near-wall region (e.g., wall shear stress) with experimental measurement modalities poses additional challenges. In this study, a computationally efficient data assimilation method called reduced-order modeling Kalman filter (ROM-KF) was proposed, which combined a sequential Kalman filter with reduced-order modeling using a linear model provided by dynamic mode decomposition (DMD). The goal of ROM-KF was to overcome low resolution and noise in experimental and uncertainty in CFD modeling of cardiovascular flows. The accuracy of the method was assessed with 1D Womersley flow, 2D idealized aneurysm, and 3D patient-specific cerebral aneurysm models. Synthetic experimental data were used to enable direct quantification of errors using benchmark datasets. The accuracy of ROM-KF in reconstructing near-wall hemodynamics was assessed by applying the method to problems where near-wall blood flow data were missing in the experimental dataset. The ROM-KF method provided blood flow data that were more accurate than the computational and synthetic experimental datasets and improved near-wall hemodynamics quantification.

Quantitative Assessment of Changes in Hemodynamics After Obliteration of Large Intracranial Carotid Aneurysms Using Computational Fluid Dynamics

Background: It was speculated that the alteration of the geometry of the artery might lead to hemodynamic changes of distal arteries. This study was to investigate the hemodynamic changes of distal arterial trees, and to identify the factors accounting for hyperperfusion after the obliteration of large intracranial aneurysms.

Methods: We retrospectively reviewed data of 12 patients with intracranial carotid aneurysms. Parametric models with intracranial carotid aneurysm were created. Patient-specific geometries were generated by three-dimensional rotational angiography. To mimic the arterial geometries after complete obliteration of the aneurysms, the aneurysms were virtually removed. The Navier–Stokes equations were solved using ANSYS CFX 14. The average wall shear stress, pressure and flow velocity were measured.

Results: Pressure ratio values were significantly higher in A1 segments, M1 segments, and M2 + M3 segments after obliteration of the aneurysms (p = 0.048 in A1 segments, p = 0.017 in M1 segments, p = 0.001 in M2 + M3 segments). Velocity ratio values were significantly higher in M1 segments and M2 + M3 segments after obliteration of the aneurysms (p = 0.047 in M1 segments, p = 0.046 in M2 + M3 segments). The percentage of pressure ratio increase after obliteration of aneurysms was significantly correlated with aneurysmal angle (r = 0.739, p = 0.006 for M2 + M3).

Conclusions: The pressure and flow velocity of distal arterial trees became higher after obliteration of aneurysms. The angle between the aneurysm and the parent artery was the factor accounting for pressure increase after treatment.

In vitro performance of echoPIV for assessment of laminar flow profiles in a carotid artery stent

Purpose: Detailed blood flow studies may contribute to improvements in carotid artery stenting. High-frame-rate contrast-enhanced ultrasound followed by particle image velocimetry (PIV), also called echoPIV, is a technique to study blood flow patterns in detail. The performance of echoPIV in presence of a stent has not yet been studied extensively. We compared the performance of echoPIV in stented and nonstented regions in an in vitro flow setup.

Approach: A carotid artery stent was deployed in a vessel-mimicking phantom. High-frame-rate contrast-enhanced ultrasound images were acquired with various settings. Signal intensities of the contrast agent, velocity values, and flow profiles were calculated.

Results: The results showed decreased signal intensities and correlation coefficients inside the stent, however, PIV analysis in the stent still resulted in plausible flow vectors.

Conclusions: Velocity values and laminar flow profiles can be measured in vitro in stented arteries using echoPIV.

Computed Poststenotic Flow Instabilities Correlate Phenotypically With Vibrations Measured Using Laser Doppler Vibrometry: Perspectives for a Promising In Vivo Device for Early Detection of Moderate and Severe Carotid Stenosis

Early detection of asymptomatic carotid stenosis is crucial for treatment planning in the prevention of ischemic stroke. Auscultation, the current first-line screening methodology, comes with severe limitations that create urge for novel and robust techniques. Laser Doppler vibrometer (LDV) is a promising tool for inferring carotid stenosis by measuring stenosis-induced vibrations. The goal of the current study was to evaluate the feasibility of LDV for carotid stenosis detection. LDV measurements on a carotid phantom were used to validate our previously verified high-resolution computational fluid dynamics methodology, which was used to evaluate the impact of flowrate, flow split, and stenosis severity on the poststenotic intensity of flow instabilities (IFI). We evaluated sensitivity, specificity, and accuracy of using IFI for stenoses detection. Linear regression analyses showed that computationally derived pressure fluctuations correlated (R2 = 0.98) with LDV measurements of stenosis-induced vibrations. The flowrate of stenosed vessels correlated (R2 = 0.90) with the presence of poststenotic instabilities. Receiver operating characteristic analyses of power spectra revealed that the most relevant frequency bands for the detection of moderate (56-76%) and severe (86-96%) stenoses were 80-200 Hz and 0-40 Hz, respectively. Moderate stenosis was identified with sensitivity and specificity of 90%; values decreased to 70% for severe stenosis. The use of LDV as screening tool for asymptomatic stenosis can potentially provide improved accuracy of current screening methodologies for early detection. The applicability of this promising device for mass screening is currently being evaluated clinically.

How patient specific are patient-specific computational models of cerebral aneurysms? An overview of sources of error and variability

Computational modeling of cerebral aneurysms, derived from clinical 3D angiography, has become widespread over the past 15 years. While such "image-based" or "patient-specific" models have shown promise for the assessment of rupture risk, much debate remains about their reliability in light of necessary modeling assumptions and incomplete or uncertain model input parameters derived from the clinic. The aims of this review were to walk through the various steps of this so-called patient-specific modeling pipeline and to highlight evidence supporting those steps that we can or cannot rely on. The relative importance of the different sources of error and variability on hemodynamic predictions is summarized, with recommendations to standardize for those that can be avoided and to pay closer attention those to that cannot.

A review on the reliability of hemodynamic modeling in intracranial aneurysms: why computational fluid dynamics alone cannot solve the equation

Computational blood flow modeling in intracranial aneurysms (IAs) has enormous potential for the assessment of highly resolved hemodynamics and derived wall stresses. This results in an improved knowledge in important research fields, such as rupture risk assessment and treatment optimization. However, due to the requirement of assumptions and simplifications, its applicability in a clinical context remains limited.This review article focuses on the main aspects along the interdisciplinary modeling chain and highlights the circumstance that computational fluid dynamics (CFD) simulations are embedded in a multiprocess workflow. These aspects include imaging-related steps, the setup of realistic hemodynamic simulations, and the analysis of multidimensional computational results. To condense the broad knowledge, specific recommendations are provided at the end of each subsection.Overall, various individual substudies exist in the literature that have evaluated relevant technical aspects. In this regard, the importance of precise vessel segmentations for the simulation outcome is emphasized. Furthermore, the accuracy of the computational model strongly depends on the specific research question. Additionally, standardization in the context of flow analysis is required to enable an objective comparison of research findings and to avoid confusion within the medical community. Finally, uncertainty quantification and validation studies should always accompany numerical investigations.In conclusion, this review aims for an improved awareness among physicians regarding potential sources of error in hemodynamic modeling for IAs. Although CFD is a powerful methodology, it cannot provide reliable information, if pre- and postsimulation steps are inaccurately carried out. From this, future studies can be critically evaluated and real benefits can be differentiated from results that have been acquired based on technically inaccurate procedures.

Velocity Pulsatility and Arterial Distensibility Along the Internal Carotid Artery

Background Attenuation of velocity pulsatility along the internal carotid artery (ICA) is deemed necessary to protect the microvasculature of the brain. The role of the carotid siphon within the whole ICA trajectory in pulsatility attenuation is still poorly understood. This study aims to assess arterial variances in velocity pulsatility and distensibility over the whole ICA trajectory, including effects of age and sex. Methods and Results We assessed arterial velocity pulsatility and distensibility using flow-sensitized 2-dimensional phase-contrast 3.0 Tesla magnetic resonance imaging in 118 healthy participants. Velocity pulsatility index (vPI=(V_max-V_min)/V_mean) and arterial distensibility defined as area pulsatility index (A_max-A_min)/A_mean) were calculated at C1, C3, and C7 segments of the ICA. vPI increased between C1 and C3 (0.85±0.13 versus 0.93±0.13, P<0.001 for averaged right+left ICA) and decreased between C3 and C7 (0.93±0.13 versus 0.84±0.13, P<0.001) with overall no effect (C1-C7). Conversely, the area pulsatility index decreased between C1 and C3 (0.18±0.06 versus 0.14±0.04, P<0.001) and increased between C3 and C7 (0.14±0.04 versus 0.31±0.09, P<0.001). vPI in men is higher than in women and increases with age (P<0.015). vPI over the carotid siphon declined with age but remained stable over the whole ICA trajectory. Conclusions Along the whole ICA trajectory, vPI increased from extracranial C1 up to the carotid siphon C3 with overall no effect on vPI between extracranial C1 and intracranial C7 segments. This suggests that the bony carotid canal locally limits the arterial distensibility of the ICA, increasing the vPI at C3 which is consequently decreased again over the carotid siphon. In addition, vPI in men is higher and increases with age.

How patient-specific do internal carotid artery inflow rates need to be for computational fluid dynamics of cerebral aneurysms?

BACKGROUND

Computational fluid dynamics (CFD) has become a popular tool for studying 'patient-specific' blood flow dynamics in cerebral aneurysms; however, rarely are the inflow boundary conditions patient-specific. We aimed to test the impact of widespread reliance on generalized inflow rates.

METHODS

Internal carotid artery (ICA) flow rates were measured via 2D cine phase-contrast MRI for 24 patients scheduled for endovascular therapy of an ICA aneurysm. CFD models were constructed from 3D rotational angiography, and pulsatile inflow rates imposed as measured by MRI or estimated using an average older-adult ICA flow waveform shape scaled by a cycle-average flow rate (Q_avg) derived from the patient's ICA cross-sectional area via an assumed inlet velocity.

RESULTS

There was good overall qualitative agreement in the magnitudes and spatial distributions of time-averaged wall shear stress (TAWSS), oscillatory shear index (OSI), and spectral power index (SPI) using generalized versus patient-specific inflows. Sac-averaged quantities showed moderate to good correlations: R²=0.54 (TAWSS), 0.80 (OSI), and 0.68 (SPI). Using patient-specific Q_avg to scale the generalized waveform shape resulted in near-perfect agreement for TAWSS, and reduced bias, but not scatter, for SPI. Patient-specific waveform had an impact only on OSI correlations, which improved to R²=0.93.

CONCLUSIONS

Aneurysm CFD demonstrates the ability to stratify cases by nominal hemodynamic 'risk' factors when employing an age- and vascular-territory-specific recipe for generalized inflow rates. Q_avg has a greater influence than waveform shape, suggesting some improvement could be achieved by including measurement of patient-specific Q_avg into aneurysm imaging protocols.

Data-Driven Pulsatile Blood Flow Physics with Dynamic Mode Decomposition

Dynamic mode decomposition (DMD) is a purely data-driven and equation-free technique for reduced-order modeling of dynamical systems and fluid flow. DMD finds a best fit linear reduced-order model that represents any given spatiotemporal data. In DMD, each mode evolves with a fixed frequency and therefore DMD modes represent physically meaningful structures that are ranked based on their dynamics. The application of DMD to patient-specific cardiovascular flow data is challenging. First, the input flow rate is unsteady and pulsatile. Second, the flow topology can change significantly in different phases of the cardiac cycle. Finally, blood flow in patient-specific diseased arteries is complex and often chaotic. The objective of this study was to overcome these challenges using our proposed multistage dynamic mode decomposition with control (mDMDc) method and use this technique to study patient-specific blood flow physics. The inlet flow rate was considered as the controller input to the systems. Blood flow data were divided into different stages based on the inlet flow waveform and DMD with control was applied to each stage. The system was augmented to consider both velocity and wall shear stress (WSS) vector data, and therefore study the interaction between the coherent structures in velocity and near-wall coherent structures in WSS. First, it was shown that DMD modes can exactly represent the analytical Womersley solution for incompressible pulsatile flow in tubes. Next, our method was applied to image-based coronary artery stenosis and cerebral aneurysm models where complex blood flow patterns are anticipated. The flow patterns were studied using the mDMDc modes and the reconstruction errors were reported. Our augmented mDMDc framework could capture coherent structures in velocity and WSS with a fewer number of modes compared to the traditional DMD approach and demonstrated a close connection between the velocity and WSS modes.

A framework for automated and objective modification of tubular structures: Application to the internal carotid artery

Patient-specific medical image-based computational fluid dynamics has been widely used to reveal fundamental insight into mechanisms of cardiovascular disease, for instance, correlating morphology to adverse vascular remodeling. However, segmentation of medical images is laborious, error-prone, and a bottleneck in the development of large databases that are needed to capture the natural variability in morphology. Instead, idealized models, where morphological features are parameterized, have been used to investigate the correlation with flow features, but at the cost of limited understanding of the complexity of cardiovascular flows. To combine the advantages of both approaches, we developed a tool that preserves the patient-specificness inherent in medical images while allowing for parametric alteration of the morphology. In our open-source framework morphMan we convert the segmented surface to a Voronoi diagram, modify the diagram to change the morphological features of interest, and then convert back to a new surface. In this paper, we present algorithms for modifying bifurcation angles, location of branches, cross-sectional area, vessel curvature, shape of bends, and surface roughness. We show qualitative and quantitative validation of the algorithms, performing with an accuracy exceeding 97% in general, and proof-of-concept on combining the tool with computational fluid dynamics. By combining morphMan with appropriate clinical measurements, one could explore the morphological parameter space and resulting hemodynamic response using only a handful of segmented surfaces, effectively minimizing the main bottleneck in image-based computational fluid dynamics.

Inter-patient variations in flow boundary conditions at middle cerebral artery from 7T PC-MRI and influence on Computational Fluid Dynamics of intracranial aneurysms

BACKGROUND

Computational fluid dynamics(CFD) of intracranial aneurysms requires flow boundary conditions(BCs) as inputs. Patient-specific BCs are usually unavailable and substituted by literature-derived generic BCs. Therefore, we investigated inter-patient BC variations and their influence on middle cerebral artery aneurysmal hemodynamics.

METHOD

We retrospectively collected CT angiography and 7-T Phase-Contrast(PC)-MRI data from eight middle-cerebral-artery bifurcation aneurysms to reconstruct the geometry and measure the arterial flowrates, respectively. The coefficient of variation(CoV) was calculated for the inlet flowrate and the pulsatility index(PI). The outflow split estimated by Murray's law was compared with PC-MRI measurements. For each aneurysm, we performed seven simulations: "baseline" using PC-MRI-derived BCs and the other six with changing BCs to explore the influence of BC variations on hemodynamics.

RESULTS

From PC-MRI, the inlet flowrate was 1.94 ± 0.71 cm³/s(CoV = 36%) and PI was 0.37 ± 0.13(CoV = 34%). The outflow split estimated by Murray's law deviated by 15.3% compared to PC-MRI. Comparing to "baseline" models, ±36% variations in inlet flowrate caused -61% to +89% changes in time-averaged wall shear stress(WSS), -37% to +32% in normalized WSS(NWSS; by parent-artery), and -42% to +126% in oscillatory shear index(OSI). The ±34% variations in PI caused, -46% to +67% in OSI. Applying ±15% variations in outflow split led to inflow jet deflection and -41% to +52% changes in WSS, -41% to +47% in NWSS, and -44% to +144% in OSI.

CONCLUSION

Inflow rate and outflow split have a drastic impact on hemodynamics of intracranial aneurysms. Inlet waveform has a negligible impact on WSS and NWSS but major impact on OSI. CFD-based models need to consider such sensitivity.

Association between aneurysm hemodynamics and wall enhancement on 3D vessel wall MRI

OBJECTIVE

Aneurysm wall enhancement (AWE) on 3D vessel wall MRI (VWMRI) has been suggested as an imaging biomarker for intracranial aneurysms (IAs) at higher risk of rupture. While computational fluid dynamics (CFD) studies have been used to investigate the association between hemodynamic forces and rupture status of IAs, the role of hemodynamic forces in unruptured IAs with AWE is poorly understood. The authors investigated the role and implications of abnormal hemodynamics related to aneurysm pathophysiology in patients with AWE in unruptured IAs.

METHODS

Twenty-five patients who had undergone digital subtraction angiography (DSA) and VWMRI studies from September 2016 to September 2017 were included, resulting in 22 patients with 25 IAs, 9 with and 16 without AWE. High-resolution CFD models of hemodynamics were created from DSA images. Univariate and multivariate analyses were performed to investigate the association between AWE and conventional morphological and hemodynamic parameters. Normalized MRI signal intensity was quantified and quantitatively associated with wall shear stresses (WSSs) for the entire aneurysm sac, and in regions of low, intermediate, and high WSS.

RESULTS

The AWE group had lower WSS (p < 0.01) and sac-averaged velocity (p < 0.01) and larger aneurysm size (p < 0.001) and size ratio (p = 0.0251) than the non-AWE group. From multivariate analysis of both hemodynamic and morphological factors, only low WSS was found to be independently associated with AWE. Sac-averaged normalized MRI signal intensity correlated with WSS and was significantly different in regions of low WSS compared to regions of intermediate (p = 0.018) and high (p < 0.001) WSS.

CONCLUSIONS

The presence of AWE was associated with morphological and hemodynamic factors related to rupture risk. Low WSS was found to be an independent predictor of AWE. Our findings support the hypothesis that low WSS in IAs with AWE may indicate a growth and remodeling process that may predispose such aneurysms to rupture; however, a causality between the two cannot be established.

Population-specific modelling of between/within-subject flow variability in the carotid arteries of the elderly

Computational fluid dynamics models are increasingly proposed for assisting the diagnosis and management of vascular diseases. Ideally, patient-specific flow measurements are used to impose flow boundary conditions. When patient-specific flow measurements are unavailable, mean values of flow measurements across small cohorts are used as normative values. In reality, both the between-subjects and within-subject flow variabilities are large. Consequently, neither one-shot flow measurements nor mean values across a cohort are truly indicative of the flow regime in a given person. We develop models for both the between-subjects and within-subject variability of internal carotid flow. A log-linear mixed effects model is combined with a Gaussian process to model the between-subjects flow variability, while a lumped parameter model of cerebral autoregulation is used to model the within-subject flow variability in response to heart rate and blood pressure changes. The model parameters are identified from carotid ultrasound measurements in a cohort of 103 elderly volunteers. We use the models to study intracranial aneurysm flow in 54 subjects under rest and exercise and conclude that OSI, a common wall shear-stress derived quantity in vascular CFD studies, may be too sensitive to flow fluctuations to be a reliable biomarker.

4D-CT angiography versus 3D-rotational angiography as the imaging modality for computational fluid dynamics of cerebral aneurysms

Background and purpose

Computational fluid dynamics (CFD) can provide valuable information regarding intracranial hemodynamics. Patient-specific models can be segmented from various imaging modalities, which may influence the geometric output and thus hemodynamic results. This study aims to compare CFD results from aneurysm models segmented from three-dimensional rotational angiography (3D-RA) versus novel four-dimensional CT angiography (4D-CTA).

Methods

Fourteen patients with 16 cerebral aneurysms underwent novel 4D-CTA followed by 3D-RA. Endoluminal geometries were segmented from each modality using an identical workflow, blinded to the other modality, to produce 28 'original' models. Each was then minimally edited a second time to match length of branches, producing 28 additional 'matched' models. CFD simulations were performed using estimated flow rates for 'original' models (representing real-world experience) and patient-specific flow rates from 4D-CTA for 'matched' models (to control for influence of modality alone).

Results

Overall, geometric and hemodynamic results were consistent between models segmented from 3D-RA and 4D-CTA, with correlations improving after matching to control for operator-introduced variability. Despite smaller 4D-CTA parent artery diameters (3.49±0.97 mm vs 3.78±0.92 mm for 3D-RA; p=0.005) and sac volumes (157 (37–750 mm3) vs 173 (53–770 mm3) for 3D-RA; p=0.0002), sac averages of time-averaged wall shear stress (TAWSS), oscillatory shear (OSI), and high frequency fluctuations (measured by spectral power index, SPI) were well correlated between 3D-RA and 4D-CTA 'matched' control models (TAWSS, R2=0.91; OSI, R2=0.79; SPI, R2=0.90).

Conclusions

Our study shows that CFD performed using 4D-CTA models produces reliable geometric and hemodynamic information in the intracranial circulation. 4D-CTA may be considered as a follow-up imaging tool for hemodynamic assessment of cerebral aneurysms.

Blood flow rate and wall shear stress in seven major cephalic arteries of humans

Blood flow rate ( Q ˙ ) in relation to arterial lumen radius (r_i ) is commonly modelled according to theoretical equations and paradigms, including Murray's Law ( Q ˙ ∝ r i 3 ) and da Vinci's Rule ( Q ˙ ∝ r i 2 ). Wall shear stress (τ) is independent of r_i with Murray's Law (τ ∝  r i 0 ) and decreases with da Vinci's Rule (τ ∝  r i - 1 ). These paradigms are tested empirically with a meta-analysis of the relationships between Q ˙ and r_i in seven major arteries of the human cephalic circulation from 19 imaging studies in which both variables were presented. The analysis shows that Q ˙ ∝ r i 2.16 and τ ∝  r i - 1.02 , more consistent with da Vinci's Rule than Murray's Law. This meta-analysis provides standard values for Q ˙ , r_i and τ in the human cephalic arteries that may be a useful baseline in future investigations. On average, the paired internal carotid arteries supply 75%, and the vertebral arteries supply 25%, of total brain blood flow. The internal carotid arteries contribute blood entirely to the anterior and middle cerebral arteries and also partly to the posterior cerebral arteries via the posterior communicating arteries of the circle of Willis. On average, the internal carotid arteries provide 88% of the blood flow to the cerebrum and the vertebral arteries only 12%.

Automated and objective removal of bifurcation aneurysms: Incremental improvements, and validation against healthy controls

Abnormal hemodynamic stresses are thought to correlate with aneurysm initiation, growth, and rupture. We have previously investigated the role of wall shear stress (WSS) and WSS gradients (WSSG) in search for a mechanistic link to formation of sidewall aneurysms using an automated and objective tool for aneurysm removal and arterial reconstruction in combination with computational fluid dynamics (CFD). However, we warned against the use of the tool for bifurcation type aneurysms because of a potential unrealistic reconstruction of the apex. We hypothesized that inclusion of additional morphological features from the surrounding vasculature could overcome these constraints. We extended the previously published method for removal and reconstruction of the bifurcation vasculature based on diverging and converging points of the parent and daughter artery centerlines, to also include two new centerlines between the daughter vessels, one of them passed through the bifurcation center. Validation was performed by comparing the efficacy of the two algorithms, using ten healthy models of the internal carotid artery terminus as ground truth. Qualitative results showed that the bifurcation apexes became smoother relative to the original algorithm; more consistent with the reference models. This was reflected quantitatively by a reduced maximum distance between the reference and reconstructed surfaces, although not statistically significant. Furthermore, the modified algorithm also quantitatively improved CFD derived WSS and WSSG, especially the latter. In conclusion, the modified algorithm does not perfectly reconstruct the bifurcation apex, but provides an incremental improvement, especially important for the derived hemodynamic metrics of interest in vascular pathobiology.

Wall Shear Stress and T1 Contrast Ratio Are Associated With Embolic Signals During Carotid Exposure in Endarterectomy

Supplemental Digital Content is available in the text.

Background and Purpose—

The frictional force because of blood flow may dislodge masses present on the surface of a plaque. Such frictional force is calculated as wall shear stress (WSS) using computational fluid dynamics. The aims of the present study were to determine whether, in addition to carotid plaque intensity on T1-weighted magnetic resonance (MR) imaging, WSS calculated using computational fluid dynamics analysis for carotid arteries is associated with development of an embolism during exposure of carotid arteries during carotid endarterectomy.

Methods—

One hundred patients with internal carotid artery stenosis (≥70%) underwent carotid plaque imaging with MR, and 54 patients with a vulnerable plaque (intraplaque hemorrhage or lipid/necrotic core) displayed as a high-intensity lesion underwent additional cervical 3-dimensional MR angiography. The maximum value of WSS within the most severe stenotic segment of the internal carotid artery was calculated using MR angiography. Transcranial Doppler monitoring of microembolic signals (MES) in the ipsilateral middle cerebral artery was performed during carotid endarterectomy.

Results—

Although none of the 46 patients with a nonvulnerable carotid plaque had MES during exposure of carotid arteries, 24 of the 54 patients with a vulnerable carotid plaque (44%) had MES. Logistic regression analysis showed that higher plaque intensity (P=0.0107) and higher WSS (P=0.0029) were significantly associated with the development of MES. When both cutoff points of plaque intensity and WSS in the receiver operating characteristic curves for predicting development of MES were combined, specificity (from 63% to 93%) and positive predictive value (from 66% to 90%) became greater than those for plaque intensity alone.

Conclusions—

In addition to carotid plaque intensity on T1-weighted MR imaging, WSS calculated using computational fluid dynamics analysis for carotid arteries is associated with development of an embolism during exposure of carotid arteries during carotid endarterectomy.

Multivariate analysis of hemodynamic parameters on intracranial aneurysm initiation of the internal carotid artery

Although fluctuating hemodynamic wall stressors are known to impact intracranial aneurysms (IA) initiation, specificity of those stressors has not been evaluated. In this study, using human IA data, we investigated: (1) specificity of stressors in regions with and without IA eventual IA formation; and (2) how combinations of multiple stressors could improve IA formation prediction. 3D computational vasculatures were constructed based on angiographic images of 18 subjects having multiple closely-spaced IAs in the internal carotid artery. Two models were created: Model A with all IAs computationally removed, Model B which kept keep one IA. Computational fluid dynamics (CFD) simulated flow within models. Based on simulated flow fields, wall shear stress and its gradient (WSS, WSSG), oscillatory shear index (OSI), gradient oscillatory number (GON), aneurysm formation index (AFI), and mean number of swirling flow vortices (MV) were analysed. Multivariate logistic regression determined the accuracy of different combinations of those above-mentioned stressors. Overall, we found that combining hemodynamic stressors improves IA formation prediction over individual indices. Both Model A and Model B's parsimonious model was MV+WSS+GON: AUROC 0.88 and 0.83, respectively. Future studies are planned to understand biological meanings induced by fluctuating stressors.

Correlation of flow complexity parameter with aneurysm rupture status

Ruptured aneurysms are known to have complex flow patterns and concentrated inflow jet, but a quantifiable measure for the degree of flow complexity in patient-specific geometries has not been established. Previously, we proposed a flow complexity parameter that provides a quantitative description of the complexity of flow patterns through calculated curvature and torsion of the flow field. The purpose of the current study was to provide an analytic solution of the flow complexity parameter and assess a possible correlation with the rupture status of cerebral aneurysms by analyzing the parameter on five ruptured and five unruptured aneurysms from anterior communicating artery. We analyzed the flow complexity parameter in jet and non-jet regions in order to measure the concentration of the jet flow and the complexity of the non-jet flow. We found that on average, in a ruptured case the jet region is significantly less complex (4.5 times) than the jet region in an unruptured case, while the non-jet region is significantly more complex (3.5 times) than the non-jet region in an unruptured case. We also found a strong positive correlation of the non-jet complexity with dome volume in ruptured cases, but no correlation of jet complexity with dome volume. These findings suggest that a ruptured aneurysm has more than 4 times more concentrated inflow jet and more than 3 times more complex flow patterns in non-jet region than an unruptured aneurysm. This newly implemented kinematic parameter provides a measurable degree of complexity of flow patterns in cerebral aneurysms that can better assess aneurysm rupture risk.

Segment-specific associations between local haemodynamic and imaging markers of early atherosclerosis at the carotid artery: an in vivo human study

Low and oscillatory wall shear stress (WSS) has long been hypothesized as a risk factor for atherosclerosis; however, evidence has been inferred primarily from model and post-mortem studies, or clinical studies of patients with already-developed plaques. This study aimed to identify associations between local haemodynamic and imaging markers of early atherosclerosis. Comprehensive magnetic resonance imaging allowed quantification of contrast enhancement (CE) (a marker of endothelial dysfunction) and vessel wall thickness at two distinct segments: the internal carotid artery bulb and the common carotid artery (CCA). Strict criteria were applied to a large dataset to exclude inward remodelling, resulting in 41 cases for which personalized computational fluid dynamic simulations were performed. After controlling for cardiovascular risk factors, bulb wall thickening was found to be weakly, but not significantly, associated with oscillatory WSS. CE at the bulb was significantly associated with low WSS (p < 0.001) and low flow helicity (p < 0.05). No significant associations were found for the CCA segment. Local haemodynamics at the bulb were significantly correlated with blood flow rates and heart rates, but not carotid bifurcation geometry (flare and curvature). Therefore low, but not oscillatory, WSS is an early independent marker of atherosclerotic changes preceding intimal thickening at the carotid bulb.

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

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.

Influence of aging-induced flow waveform variation on hemodynamics in aneurysms present at the internal carotid artery: A computational model-based study

The variation of blood flow waveform in the internal carotid artery (ICA) with age is a well-documented hemodynamic phenomenon, but little is known about how such variation affects the characteristics of blood flow in aneurysms present in the region. In the study, hemodynamic simulations were conducted for 26 ICA aneurysms, with flow waveforms measured in the ICAs of young and older adults being used respectively to set the inflow boundary conditions. Obtained results showed that replacing the young-adult flow waveform with the older-adult one led to little changes (<10%) in simulated time-averaged wall shear stress (WSS), transient maximum WSS, relative residence time and trans-aneurysm pressure loss coefficient, but resulted in a marked increase (32.36 ± 17.24%) in oscillatory shear index (OSI). Frequency-domain wave analysis revealed that the progressive enhancement of low-frequency harmonics dominated the observed flow waveform variation with age and was a major factor contributing to the increase in OSI. Cross-sectional comparisons among the aneurysms further revealed that the degree of increase in OSI correlated positively with some specific morphological features of aneurysm, such as aspect ratio and size ratio. In summary, the study demonstrates that the variation in flow waveform with age augments the oscillation of WSS in ICA aneurysms, which underlies the importance of setting patient-specific boundary conditions in hemodynamic studies on cerebral aneurysms, especially those involving long-term patient follow-up or cross-sectional comparison among patients of different ages.

Quantification of near-wall hemodynamic risk factors in large-scale cerebral arterial trees

Detailed hemodynamic analysis of blood flow in pathological segments close to aneurysm and stenosis has provided physicians with invaluable information about the local flow patterns leading to vascular disease. However, these diseases have both local and global effects on the circulation of the blood within the cerebral tree. The aim of this paper is to demonstrate the importance of extending subject-specific hemodynamic simulations to the entire cerebral arterial tree with hundreds of bifurcations and vessels, as well as evaluate hemodynamic risk factors and waveform shape characteristics throughout the cerebral arterial trees. Angioarchitecture and in vivo blood flow measurement were acquired from healthy subjects and in cases with symptomatic intracranial aneurysm and stenosis. A global map of cerebral arterial blood flow distribution revealed regions of low to high hemodynamic risk that may significantly contribute to the development of intracranial aneurysms or atherosclerosis. Comparison of pre-intervention and post-intervention of pathological cases further shows large angular phase shift (~33.8°), and an augmentation of the peak-diastolic velocity. Hemodynamic indexes of waveform analysis revealed on average a 16.35% reduction in the pulsatility index after treatment from lesion site to downstream distal vessels. The lesion regions not only affect blood flow streamlines of the proximal sites but also generate pulse wave shift and disturbed flow in downstream vessels. This network effect necessitates the use of large-scale simulation to visualize both local and global effects of pathological lesions.

A data-driven approach for addressing the lack of flow waveform data in studies of cerebral arterial flow in older adults

OBJECTIVE

Blood flow waveforms-essential data for hemodynamic modeling-are often in practice unavailable to researchers. The objectives of this work were to assess the variability among the waveforms for a clinically relevant older population, and develop data-based methods for addressing the missing waveform data for hemodynamic studies.

APPROACH

We analyzed 272 flow waveforms from the internal carotid arteries of older patients (73  ±  13 yr) with moderate cardiovascular disease, and used these data to develop methods to guide new approaches for hemodynamic studies.

MAIN RESULTS

Profound variations in waveform parameters were found within the aged population that were not seen in published data for young subjects. Common features in the aged population relative to the young included a larger systole-to-diastole flow rate ratio, increased flow during late systole, and absence of a dicrotic notch. Eight waveforms were identified that collectively represent the range of waveforms in the older population. A relationship between waveform shape and flow rate was obtained that, in conjunction with equations relating flow rate to diameter, can be used to provide individualized waveforms for patient-specific geometries. The dependence of flow rate on diameter was statistically different between male and female patients.

SIGNIFICANCE

It was shown that a single archetypal waveform cannot well-represent the diverse waveforms found within an aged population, although this approach is frequently used in studies of flow in the cerebral vasculature. Motivated by these results, we provided a set of eight waveforms that can be used to assess the hemodynamic uncertainty associated with the lack of patient-specific waveform data. We also provided a methodology for generating individualized waveforms when patient gender, age, and cardiovascular disease state are known. These data-driven approaches can be used to devise more relevant in vitro or in silico intra-cranial hemodynamic studies for older patients.

Better Than Nothing: A Rational Approach for Minimizing the Impact of Outflow Strategy on Cerebrovascular Simulations

BACKGROUND AND PURPOSE

Computational fluid dynamics simulations of neurovascular diseases are impacted by various modeling assumptions and uncertainties, including outlet boundary conditions. Many studies of intracranial aneurysms, for example, assume zero pressure at all outlets, often the default ("do-nothing") strategy, with no physiological basis. Others divide outflow according to the outlet diameters cubed, nominally based on the more physiological Murray's law but still susceptible to subjective choices about the segmented model extent. Here we demonstrate the limitations and impact of these outflow strategies, against a novel "splitting" method introduced here.

MATERIALS AND METHODS

With our method, the segmented lumen is split into its constituent bifurcations, where flow divisions are estimated locally using a power law. Together these provide the global outflow rate boundary conditions. The impact of outflow strategy on flow rates was tested for 70 cases of MCA aneurysm with 0D simulations. The impact on hemodynamic indices used for rupture status assessment was tested for 10 cases with 3D simulations.

RESULTS

Differences in flow rates among the various strategies were up to 70%, with a non-negligible impact on average and oscillatory wall shear stresses in some cases. Murray-law and splitting methods gave flow rates closest to physiological values reported in the literature; however, only the splitting method was insensitive to arbitrary truncation of the model extent.

CONCLUSIONS

Cerebrovascular simulations can depend strongly on the outflow strategy. The default zero-pressure method should be avoided in favor of Murray-law or splitting methods, the latter being released as an open-source tool to encourage the standardization of outflow strategies.

Rupture prediction of intracranial aneurysms: a nationwide matched case-control study of hemodynamics at the time of diagnosis

The authors used computer simulation to investigate the hemodynamics in 36 unruptured aneurysms on the first day the lesions were discovered; 12 of them later ruptured. Knowledge about any differences in hemodynamics at this early stage improves predictions about which patients will get a subarachnoid hemorrhage-a dangerous bleeding in the brain-and helps decide which patients should be treated in advance to avoid the bleeding.

A model of blood supply to the brain via the carotid arteries: Effects of obstructive vs. sclerotic changes

The carotid artery is one of the major supply routes of blood to the brain and a common site of vascular disease. Obstructive and sclerotic disorders within the carotid artery impact local blood flow patterns as well as overall impedance and blood supply to the brain. A lumped parameter model and an experimental in-vitro flow loop were used to study the effects of local stenosis and stiffness in the carotid artery based on a family of phantoms with different degrees of stenosis and compliance. The model also allows independent examination of the effects of downstream resistance and compliance. Mild to moderate stenosis was found to lead to minimal (∼1%) reduction in blood supply to the brain. Reduction in mean internal carotid artery (ICA) flow was statistically significant (p< 0.01) only above 70% stenosis. On the other hand, a three-fold increase in stiffness of the carotid artery, as might occur in aging, was found to lead to a modest yet statistically significant reduction (p< 0.01) in mean ICA flow. Effects of changing downstream resistance and compliance were examined. For a given pressure waveform, reduction in downstream compliance led to altered waveform shape and reduction in peak systolic flow rates where the mean flow rates were not altered. Increased downstream resistance resulted in drastic reduction in mean flow rates.