Can temporal fluctuation in spatial wall shear stress gradient initiate a cerebral aneurysm? A proposed novel hemodynamic index, the gradient oscillatory number (GON)

Turbulent blood flow in a cerebral artery with an aneurysm

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

Identifying hemodynamic factors associated with the rupture of anterior communicating artery aneurysms based on global modeling of blood flow in the cerebral artery network

Anterior communicating artery (ACoA) aneurysms are more prone to rupture compared to aneurysms present in other cerebral arteries. We hypothesize that systemic blood flow in the cerebral artery network plays an important role in shaping intra-aneurysmal hemodynamic environment thereby affecting the rupture risk of ACoA aneurysms. The majority of existing numerical studies in this field employed local modeling methods where the physical boundaries of a model are confined to the aneurysm region, which, though having the benefit of reducing computational cost, may compromise the physiological fidelity of numerical results due to insufficient account of systemic cerebral arterial hemodynamics. In the present study, we firstly carried out numerical experiments to address the difference between the outcomes of local and global modeling methods, demonstrating that local modeling confined to the aneurysm region results in inaccurate predictions of hemodynamic parameters compared with global modeling of the ACoA aneurysm as part of the cerebral artery network. Motivated by this finding, we built global hemodynamic models for 40 ACoA aneurysms (including 20 ruptured and 20 unruptured ones) based on medical image data. Statistical analysis of the computed hemodynamic data revealed that maximum wall shear stress (WSS), minimum WSS divergence, and maximum WSS gradient differed significantly between the ruptured and unruptured ACoA aneurysms. Optimal threshold values of high/low WSS metrics were determined through a series of statistical tests. In the meantime, some morphological parameters of aneurysms, such as large nonsphericity index, aspect ratio, and bottleneck factor, were found to be associated closely with aneurysm rupture. Furthermore, multivariate logistic regression analyses were performed to derive models combining hemodynamic and morphological parameters for discriminating the rupture status of aneurysms. The capability of the models in rupture status discrimination was high, with the area under the receiver operating characteristic curve reaching up to 0.9. The findings of the study suggest that global modeling of the cerebral artery network is essential for reliable quantification of hemodynamics in ACoA aneurysms, disturbed WSS and irregular aneurysm morphology are associated closely with aneurysm rupture, and multivariate models integrating hemodynamic and morphological parameters have high potential for assessing the rupture risk of ACoA aneurysms.

Hemodynamic characteristics and mechanism for intracranial aneurysms initiation with the circle of Willis anomaly

Clinically, circle of Willis (CoW) is prone to anomaly and is also the predominant incidence site of intracranial aneurysms (IAs). This study aims to investigate the hemodynamic characteristics of CoW anomaly, and ascertain the mechanism of IAs initiation from the perspective of hemodynamics. Thus, the flow of IAs and pre-IAs were analyzed for one type of cerebral artery anomaly, that is, anterior cerebral artery A1 segment (ACA-A1) unilateral absence. Three patient geometrical models with IAs were selected from Emory University Open Source Data Center. IAs were virtually removed from the geometrical models to simulate the pre-IAs geometry. For calculation methods, a one-dimensional (1-D) solver and a three-dimensional (3-D) solver were combined to obtain the hemodynamic characteristics. The numerical simulation revealed that the average flow of Anterior Communicating Artery (ACoA) is almost zero when CoW is complete. In contrast, ACoA flow increases significantly in the case of ACA-A1 unilateral absence. For per-IAs geometry, the jet flow is found at the bifurcation between contralateral ACA-A1 and ACoA, which exhibits characteristics of high Wall Shear Stress (WSS) and high wall pressure in the impact region. It triggers the initiation of IAs from the perspective of hemodynamics. The vascular anomaly that leads to jet flow should be considered as a risk factor for IAs initiation.

A Fluid-Solid-Growth Solver for Cardiovascular Modeling

We implement full, three-dimensional constrained mixture theory for vascular growth and remodeling into a finite element fluid-structure interaction (FSI) solver. The resulting "fluid-solid-growth" (FSG) solver allows long term, patient-specific predictions of changing hemodynamics, vessel wall morphology, tissue composition, and material properties. This extension from short term (FSI) to long term (FSG) simulations increases clinical relevance by enabling mechanobioloigcally-dependent studies of disease progression in complex domains.

Common mechanisms of physiological and pathological rupture events in biology: novel insights into mammalian ovulation and beyond

Ovulation is a cyclical biological rupture event fundamental to fertilisation and endocrine function. During this process, the somatic support cells that surround the germ cell undergo a remodelling process that culminates in breakdown of the follicle wall and release of a mature egg. Ovulation is driven by known proteolytic and inflammatory pathways as well as structural alterations to the follicle vasculature and the fluid-filled antral cavity. Ovulation is one of several types of systematic remodelling that occur in the human body that can be described as rupture. Although ovulation is a physiological form of rupture, other types of rupture occur in the human body which can be pathological, physiological, or both. In this review, we use intracranial aneurysms and chorioamniotic membrane rupture as examples of rupture events that are pathological or both pathological and physiological, respectively, and compare these to the rupture process central to ovulation. Specifically, we compared existing transcriptomic profiles, immune cell functions, vascular modifications, and biomechanical forces to identify common processes that are conserved between rupture events. In our transcriptomic analysis, we found 12 differentially expressed genes in common among two different ovulation data sets and one intracranial aneurysm data set. We also found three genes that were differentially expressed in common for both ovulation data sets and one chorioamniotic membrane rupture data set. Combining analysis of all three data sets identified two genes (Angptl4 and Pfkfb4) that were upregulated across rupture systems. Some of the identified genes, such as Rgs2, Adam8, and Lox, have been characterised in multiple rupture contexts, including ovulation. Others, such as Glul, Baz1a, and Ddx3x, have not yet been characterised in the context of ovulation and warrant further investigation as potential novel regulators. We also identified overlapping functions of mast cells, macrophages, and T cells in the process of rupture. Each of these rupture systems share local vasoconstriction around the rupture site, smooth muscle contractions away from the site of rupture, and fluid shear forces that initially increase and then decrease to predispose one specific region to rupture. Experimental techniques developed to study these structural and biomechanical changes that underlie rupture, such as patient-derived microfluidic models and spatiotemporal transcriptomic analyses, have not yet been comprehensively translated to the study of ovulation. Review of the existing knowledge, transcriptomic data, and experimental techniques from studies of rupture in other biological systems yields a better understanding of the physiology of ovulation and identifies avenues for novel studies of ovulation with techniques and targets from the study of vascular biology and parturition.

Geometric influence of anterior cerebral artery rotation on the formation of anterior communicating artery aneurysm

OBJECTIVE

Several particular morphological factors that contribute to the hemodynamics of the anterior communicating artery (ACoA) have been documented, but no study has investigated the role of the degree of anterior cerebral artery (ACA) rotation on the presence of ACoA aneurysms (ACoAAs).

METHODS

A retrospective study of an institutional aneurysm database was performed; patients with ruptured or nonruptured ACoAAs were selected. Two sex- and age-matched control groups were identified: control Group A (nonaneurysms) and control Group B (middle cerebral artery aneurysms). Measurements of ACA rotation degree were obtained by using a three-dimensional imaging tool.

RESULTS

From 2015 to 2020, 315 patients were identified: 105 in the ACoAA group, 105 in control Group A, and 105 in control Group B. The average age at the time of presentation was 64 years, and 52.4% were female. The ACA rotation degree of the ACoAA group was significantly higher than that of control Group A (p <0.01). The A1 ratio and the A1A2 ratio of the ACoAA group were greater than those of control Group A (p <0.01 and p <0.01, respectively). The ACA rotation degree correlated insignificantly with aneurysm size in ACoAA patients (p=0.78). The ACA rotation degree in the ACoAA group was also insignificantly different from that in control B (p=0.11).

CONCLUSIONS

The degree of ACA rotation was greater in the ACoAA group than in the nonaneurysm group, and it may serve as an imaging marker for ACoAA.

High hemodynamic stresses induce aneurysms at internal carotid artery bends

To investigate the role of hemodynamic stresses in initiating cerebral aneurysms at bends of internal carotid artery (ICA). Sixty-one patients with 68 aneurysms at ICA bends were retrospectively enrolled as the experiment group. Among the 61 patients, 30 normal ICAs without aneurysms were chosen as the control. All patients had 3-dimensional angiography and CFD analysis. The bending angle was significantly (P < .0001) smaller in the experiment than control group (131.2º ± 14.9º vs 150.3º ± 9.5º). The dynamic pressure, shear stress, vorticity magnitude and strain rate were the least at direct flow impinging center where the total pressure was very high. The dynamic stress, shear stress, strain rate and gradients of total pressure except for gradient 1 were significantly (P < .05) greater at the aneurysm site than at all the other sites. The total pressure at the aneurysm site was greater (P < .05) than at 1 lateral location and at the distal area but smaller (P < .05) than at the proximal area. The dynamic pressure, shear stress, strain rate and gradient of total pressure at the aneurysm site were significantly (P < .001) greater than on the aneurysm dome. The hemodynamic stresses were all significantly (P < .01) greater at the aneurysm site in the experiment group than at the site corresponding to the aneurysm in the control group. Aneurysms at the ICA bends are caused by direct flow impingement and increased hemodynamic stresses, and smaller arterial bending angles result in abnormally enhanced hemodynamic stresses to initiate an aneurysm near the flow impingement area.

Reinforcement learning for patient-specific optimal stenting of intracranial aneurysms

Developing new capabilities to predict the risk of intracranial aneurysm rupture and to improve treatment outcomes in the follow-up of endovascular repair is of tremendous medical and societal interest, both to support decision-making and assessment of treatment options by medical doctors, and to improve the life quality and expectancy of patients. This study aims at identifying and characterizing novel flow-deviator stent devices through a high-fidelity computational framework that combines state-of-the-art numerical methods to accurately describe the mechanical exchanges between the blood flow, the aneurysm, and the flow-deviator and deep reinforcement learning algorithms to identify a new stent concepts enabling patient-specific treatment via accurate adjustment of the functional parameters in the implanted state.

Aneurysm wall enhancement, hemodynamics, and morphology of intracranial fusiform aneurysms

Background and objective

Intracranial fusiform aneurysms (IFAs) are considered to have a complex pathophysiology process and poor natural history. The purpose of this study was to investigate the pathophysiological mechanisms of IFAs based on the characteristics of aneurysm wall enhancement (AWE), hemodynamics, and morphology.

Methods

A total of 21 patients with 21 IFAs (seven fusiform types, seven dolichoectatic types, and seven transitional types) were included in this study. Morphological parameters of IFAs were measured from the vascular model, including the maximum diameter (Dmax), maximum length (Lmax), and centerline curvature and torsion of fusiform aneurysms. The three-dimensional (3D) distribution of AWE in IFAs was obtained based on high-resolution magnetic resonance imaging (HR-MRI). Hemodynamic parameters including time-averaged wall shear stress (TAWSS), oscillatory shear index (OSI), gradient oscillatory number (GON), and relative residence time (RRT) were extracted by computational fluid dynamics (CFD) analysis of the vascular model, and the relationship between these parameters and AWE was investigated.

Results

The results showed that Dmax (p = 0.007), Lmax (p = 0.022), enhancement area (p = 0.002), and proportion of enhancement area (p = 0.006) were significantly different among three IFA types, and the transitional type had the largest Dmax, Lmax, and enhancement area. Compared with the non-enhanced regions of IFAs, the enhanced regions had lower TAWSS but higher OSI, GON, and RRT (p &lt; 0.001). Furthermore, Spearman’s correlation analysis showed that AWE was negatively correlated with TAWSS, but positively correlated with OSI, GON, and RRT.

Conclusion

There were significant differences in AWE distributions and morphological features among the three IFA types. Additionally, AWE was positively associated with the aneurysm size, OSI, GON, and RRT, while negatively correlated with TAWSS. However, the underlying pathological mechanism of the three fusiform aneurysm types needs to be further studied.

Hemodynamic indicators of the formation of tandem intracranial aneurysm based on a vascular restoration algorithm

Background

Hemodynamic factors are believed to be closely related to IA growth. However, the underlying pathophysiological mechanism that induces the growth sequence in tandem intracranial aneurysms (IAs) remains unclear.

Methods and results

This study involved five patients with tandem IAs. Aneurysm models were reconstructed based on image datasets. A novel vascular restoration algorithm was proposed to generate the hypothetical geometry of the healthy parent vessel before each IA formation in the concatenated structure. Detailed hemodynamic patterns and morphological features were revealed under various growth sequences of tandem IAs to investigate the flow-driven mechanism of IA growth. Potential hemodynamic indicators of IA formation were proposed.

Results

The patient cases were divided into two groups based on the size difference of tandem IAs. In the group with a similar size of tandem IAs, the position of the vortex core was associated with the site of the secondary aneurysm, while in the group with a significant size difference of the IAs, the position with the maximum curvature of the parent vessel plays a significant role in aneurysm formation.

Conclusions

This study preliminarily revealed key hemodynamic and morphological indicators that determine the formation of tandem IAs. The proposed vascular restoration algorithm that provided the pre-aneurysm vasculature might be useful in investigating the flow-driven mechanism of IA growth, thus contributing to the risk evaluation of secondary aneurysm formation.

Patient-specific modeling of hemodynamic characteristics associated with the formation of visceral artery aneurysms at uncommon locations

Objective

Hemodynamic characteristics play critical roles in aneurysm initiation and growth. This study aims to explore the effect of common hemodynamic parameters on the formation of visceral artery aneurysms (VAAs), especially those from the pancreaticoduodenal arteries or other uncommon locations, using real patients' models.

Methods

Three-dimension vessel models of 14 VAAs from 13 patients were selected and constructed from computed tomography angiography (CTA) images. Aneurysms were manually removed to perform computational fluid dynamics (CFD) simulations of the models before aneurysm formation. Flow field characteristics were obtained and compared at the aneurysm forming and para-aneurysm areas. Aneurysm forming models were categorized into high-wall-shear stress (WSS) and low-WSS groups according to WSS value at aneurysm forming versus para-aneurysm areas.

Results

Computational fluid dynamics analysis revealed that the high WSS group had significantly higher WSSmax (P = 0.038), higher time average WSS (TAWSS) (P = 0.011), higher WSS gradient (WSSG) (p = 0.036), as well as lower oscillatory shear index (OSI) (P = 0.022) compared to the low WSS group. Significant higher WSSmax (P = 0.003), TAWSS (P = 0.003), WSSG (P = 0.041) and lower OSI (P = 0.021) was observed at the aneurysm forming site compared to both upstream and downstream areas.

Conclusion

Both local increase and decrease of WSS and WSS gradient were observed for the visceral artery aneurysm forming area. Computational fluid dynamics analysis could shed light on the pathogenesis of visceral artery aneurysms at uncommon vessel locations.

Computational fluid dynamic analysis of the initiation of cerebral aneurysms

OBJECTIVE

Relationships between aneurysm initiation and hemodynamic factors remain unclear since de novo aneurysms are rarely observed. Most previous computational fluid dynamics (CFD) studies have used artificially reproduced vessel geometries before aneurysm initiation for analysis. In this study, the authors investigated the hemodynamic factors related to aneurysm initiation by using angiographic images in patients with cerebral aneurysms taken before and after an aneurysm formation.

METHODS

The authors identified 10 cases of de novo aneurysms in patients who underwent follow-up examinations for existing cerebral aneurysms located at a different vessel. The authors then reconstructed the vessel geometry from the images that were taken before aneurysm initiation. In addition, 34 arterial locations without aneurysms were selected as control cases. Hemodynamic parameters acting on the arterial walls were calculated by CFD analysis.

RESULTS

In all de novo cases, the aneurysmal initiation area corresponded to the highest wall shear stress divergence (WSSD point), which indicated that there was a strong tensile force on the arterial wall at the initiation area. The other previously reported parameters did not show such correlations. Additionally, the pressure loss coefficient (PLc) was statistically significantly higher in the de novo cases (p < 0.01). The blood flow impact on the bifurcation apex, or the secondary flow accompanied by vortices, resulted in high tensile forces and high total pressure loss acting on the vessel wall.

CONCLUSIONS

Aneurysm initiation may be more likely in an area where both tensile forces acting on the vessel wall and total pressure loss are large.

Blood flow analysis with computational fluid dynamics and 4D-flow MRI for vascular diseases

Both computational fluid dynamics (CFD) and time-resolved, three-dimensional, phase-contrast, magnetic resonance imaging (4D-flow MRI) enable visualization of time-varying blood flow structures and quantification of blood flow in vascular diseases. However, they are totally different. CFD is a method to calculate blood flow by solving the governing equations of fluid mechanics, so the obtained flow field is somewhat virtual. On the other hand, 4D-flow MRI measures blood flow in vivo, thus the flow is real. Recently, with the development and enhancement of computers, medical imaging techniques, and related software, blood flow analysis has become more accessible to clinicians and its usefulness in vascular diseases has been demonstrated. In this review, we have outlined the methods and characteristics of CFD and 4D-flow MRI, respectively. We have discussed the differences in the characteristics between both methods; reviewed the milestones achieved by blood flow analysis in various vascular diseases; and discussed the usefulness, challenges, and limitations of blood flow analysis. We have discussed the difficulties and limitations of current blood flow analysis. We have also discussed our views on future directions.

Reallocation of cutaneous and global blood circulation during sauna bathing through a closed-loop model

OBJECTIVE

Sauna bathing (SB) is an important strategy in cardiovascular protection, but there is no mathematical explanation for the reallocation of blood circulation during heat-induced superficial vasodilation. We sought to reveal such reallocation via a simulated hemodynamic model.

METHODS

A closed-loop cardiovascular model with a series of electrical parameters was constructed. The body surface was divided into seven blocks and each block was modeled by a lumped resistance. These resistances were adjusted to increase skin blood flow (SBF), with the aim of reflecting heat-induced vasodilation during SB. Finally, the blood pressure was compared before and after SB, and the blood flow inside the aorta and visceral arteries were also analyzed.

RESULTS

With increasing SBF in this model, the systolic, diastolic, and mean blood pressure in the arterial trunk decreased by 13-29, 18-36, and 19-37 mmHg, respectively. Despite the increase in the peak and mean blood flow in the arterial trunk, the diastolic blood flow reversal in the thoracic and abdominal aortas increased significantly. Nevertheless, the blood supply to the heart, liver, stomach, spleen, kidney, and intestine decreased by at least 25%. Moreover, the pulmonary blood flow increased significantly.

CONCLUSION

Simulated heat-induced cutaneous vasodilation in this model lowers blood pressure, induces visceral ischemia, and promotes pulmonary circulation, suggesting that the present closed-loop model may be able to describe the effect of sauna bathing on blood circulation. However, the increase of retrograde flow in the aortas found in this model deserves further examination.

Cerebral aneurysms at major arterial bifurcations are associated with the arterial branch forming a smaller angle with the parent artery

Currently, the relationship of bifurcation morphology and aneurysm presence at the major cerebral bifurcations is not clear. This study was to investigate cerebral arterial bifurcation morphology and accompanied hemodynamic stresses associated with cerebral aneurysm presence at major cerebral arterial bifurcations. Cerebral angiographic data of major cerebral artery bifurcations of 554 anterior cerebral arteries, 582 internal carotid arteries, 793 middle cerebral arteries and 195 basilar arteries were used for measurement of arterial diameter, lateral and bifurcation angles and aneurysm deviation. Hemodynamic stresses were analyzed using computational fluid dynamic simulation. Significantly (P < 0.001) more aneurysms deviated toward the smaller branch and the smaller lateral angle than towards the larger branch and larger lateral angle at all four major bifurcations. At the flow direct impinging center, the total pressure was the greatest while the dynamic pressure, wall shear stress (WSS), vorticity and strain rate were the least. Peak 1 and Peak 2 were located on the branch forming a smaller and larger angle with the parent artery, respectively. The dynamic pressure (175.4 ± 18.6 vs. 89.9 ± 7.6 Pa), WSS (28.9 ± 7.4 vs. 15.7 ± 5.3 Pa), vorticity (9874.6 ± 973.4 vs. 7237.8 ± 372.7 1/S), strain rate (9873.1 ± 625.6 vs. 7648.3 ± 472.5 1/S) and distance (1.9 ± 0.8 vs. 1.3 ± 0.3 mm) between the peak site and direct flow impinging center were significantly greater at Peak 1 than at Peak 2 (P < 0.05 or P < 0.01). Moreover, aneurysms deviation and Peak 1 were always on the same side. In conclusion, the branch forming a smaller angle with the parent artery is associated with abnormally enhanced hemodynamic stresses to initiate an aneurysm at the bifurcation apex.

Fluid Flow and Structural Numerical Analysis of a Cerebral Aneurysm Model

Intracranial aneurysms (IA) are dilations of the cerebral arteries and, in most cases, have no symptoms. However, it is a very serious pathology, with a high mortality rate after rupture. Several studies have been focused only on the hemodynamics of the flow within the IA. However, besides the effect of the flow, the development and rupture of the IA are also associated with a combination of other factors such as the wall mechanical behavior. Thus, the objective of this work was to analyze, in addition to the flow behavior, the biomechanical behavior of the aneurysm wall. For this, CFD simulations were performed for different Reynolds numbers (1, 100, 500 and 1000) and for two different rheological models (Newtonian and Carreau). Subsequently, the pressure values of the fluid simulations were exported to the structural simulations in order to qualitatively observe the deformations, strains, normal stresses and shear stress generated in the channel wall. For the structural simulations, a hyperelastic constitutive model (5-parameter Mooney–Rivlin) was used. The results show that with the increase in the Reynolds number (Re), the recirculation phenomenon is more pronounced, which is not seen for Re = 1. The higher the Re, the higher the strain, displacement, normal and shear stresses values.

Morphometry of cerebral arterial bifurcations harbouring aneurysms: a case-control study

Background

Conclusions from studies evaluating vessel dimensions and their deviations from values resulting from the principle of minimum work (PMW) on the formation of intracranial aneurysms (IAs) are still inconclusive. Our study aimed to perform a morphometric analysis of cerebral arterial bifurcations harbouring aneurysms.

Methods

The study comprised 147 patients with basilar artery (BA) and middle cerebral artery (MCA) aneurysms and 106 patients constituting the control group. The following morphometric parameters were evaluated: the radii of vessels forming the bifurcation, the junction exponent, the values of the bifurcation angles (Φ₁ and Φ₂ angles between the parent vessel trunk axis and the larger or smaller branches, respectively; α angle, the total bifurcation angle) and the difference between the predicted optimal and observed branch angles.

Results

The analysed parameters for internal carotid artery (ICA) bifurcations were not significantly different among the groups. The MCA and BA bifurcation angles and the radii of the parent MCA and BA vessels with aneurysms were significantly higher than those of the control group. The differences between the predicted optimal and observed branch angles were significantly higher for BA and MCA bifurcations with aneurysms compared to the control group. The mean junction exponent for bifurcations in the circle of Willis (i.e., ICA and BA bifurcations, respectively) and MCA bifurcations with aneurysms was significantly lower than the theoretical optimum and did not significantly differ among the groups. In a multilevel multivariate logistic regression analysis, the branch angles and the radius from the parent vessel were significant independent predictors of the presence of an IA. The ROC analysis indicated that the α angle was the best performer in discriminating between aneurysmal and nonaneurysmal bifurcations.

Conclusions

The dimensions of the arteries forming the circle of Willis do not follow the PMW. Deviation from the energetically optimum geometry for bifurcations beyond the circle of Willis (particularly, a larger radius of the parent artery and a wider total bifurcation angle) may lead to the formation of IAs. Further studies are warranted to investigate the significance of vessel dimensions and the bifurcation angle on the magnitude of shear stress in the walls of arterial bifurcations.

Hemodynamic risk factors for the development of carotid stenosis in patients with unilateral carotid stenosis

BACKGROUND

It is difficult to predict the development of carotid stenosis by means of the known risk factors. Using a computational fluid dynamics analysis, we examined the hemodynamic risks for carotid stenosis, focusing on wall shear stress (WSS) disturbances.

METHODS

In 59 cases of unilateral carotid stenosis, the plaque was removed from the original three-dimensional computed tomography angiographic images, and the vessel shape before stenosis was artificially reproduced. A multivariate regression analysis was performed to determine the associations between the degree of area stenosis and hemodynamic and morphological factors after adjustment for six known risk factors.

RESULTS

Metrics for WSS disturbances were higher at and distal to a bifurcation in the carotid arteries after plaque removal compared with the normal carotid arteries, and metrics for WSS magnitudes were lower. In the plaque-removed arteries, the degree of stenosis was significantly negatively correlated with the ratio of stenotic to distal values of metrics for WSS disturbances and the diameter ratio of the external to common carotid artery, and positively correlated with the ratio of proximal to stenotic values of metrics for WSS magnitudes.

CONCLUSIONS

Rapid increases in WSS from the common carotid artery toward the bifurcation, rapid decreases in WSS disturbance from the bifurcation toward the internal carotid artery, and lower diameter ratio of the external to common carotid artery are more likely than other risk factors to cause future severe stenosis. In patients with these hemodynamic risks, underlying diseases should be controlled more strictly with imaging examinations at shorter intervals.

Wall shear stress gradient is independently associated with middle cerebral artery aneurysm development: a case-control CFD patient-specific study based on 77 patients

Background

Previously published computational fluid dynamics (CFD) studies regarding intracranial aneurysm (IA) formation present conflicting results. Our study analysed the involvement of the combination of high wall shear stress (WSS) and a positive WSS gradient (WSSG) in IA formation.

Methods

We designed a case-control study with a selection of 38 patients with an unruptured middle cerebral artery (MCA) aneurysm and 39 non-aneurysmal controls to determine the involvement of WSS, oscillatory shear index (OSI), the WSSG and its absolute value (absWSSG) in aneurysm formation based on patient-specific CFD simulations using velocity profiles obtained from transcranial colour-coded sonography.

Results

Among the analysed parameters, only the WSSG had significantly higher values compared to the controls (11.05 vs − 14.76 [Pa/mm], P = 0.020). The WSS, absWSSG and OSI values were not significantly different between the analysed groups. Logistic regression analysis identified WSS and WSSG as significant co-predictors for MCA aneurysm formation, but only the WSSG turned out to be a significant independent prognosticator (OR: 1.009; 95% CI: 1.001–1.017; P = 0.025). Significantly more patients (23/38) in the case group had haemodynamic regions of high WSS combined with a positive WSSG near the bifurcation apex, while in the control group, high WSS was usually accompanied by a negative WSSG (14/39). From the analysis of the ROC curve for WSSG, the area under the curve (AUC) was 0.654, with the optimal cut-off value −0.37 Pa/mm. The largest AUC was recognised for combined WSS and WSSG (AUC = 0.671). Our data confirmed that aneurysms tend to form near the bifurcation apices in regions of high WSS values accompanied by positive WSSG.

Conclusions

The development of IAs is determined by an independent effect of haemodynamic factors. High WSS impacts MCA aneurysm formation, while a positive WSSG mainly promotes this process.

Non-Newtonian Blood Modeling in Intracranial Aneurysm Hemodynamics: Impact on the Wall Shear Stress and Oscillatory Shear Index Metrics for Ruptured and Unruptured Cases

When simulating blood flow in intracranial aneurysms (IAs), the Newtonian model seems to be ubiquitous. However, analyzing the results from the few studies on this subject, the doubt remains on whether it is necessary to use non-Newtonian models in computational fluid dynamics (CFD) simulations of cerebral vascular flows. The objective of this study is to investigate whether different rheology models would influence the hemodynamic parameters related to the wall shear stress (WSS) for ruptured and unruptured IA cases, especially because ruptured aneurysms normally have morphological features, such as lobular regions and blebs, that could trigger non-Newtonian phenomena in the blood flow due to low shear rates. Using CFD in an open-source framework, we simulated four ruptured and four unruptured patient-specific aneurysms to assess the influence of the blood modeling on the main hemodynamic variables associated with aneurysm formation, growth, and rupture. Results for WSS and oscillatory shear index (OSI) and their metrics were obtained using Casson and Carreau-Yasuda non-Newtonian models and were compared with those obtained using the Newtonian model. We found that all differences between non-Newtonian and the Newtonian models were consistent among all cases irrespective of their rupture status. We further found that the WSS at peak systole is overestimated by more than 50% by using the non-Newtonian models, but its metrics based on time and surface averaged values are less affected-the maximum relative difference among the cases is 7% for the Casson model. On the other hand, the surface-averaged OSI is underestimated by more than 30% by the non-Newtonian models. These results suggest that it is recommended to investigate different blood rheology models in IAs simulations when specific parameters to characterize the flow are needed, such as peak-systole WSS and OSI.

Hemodynamic Force as a Potential Regulator of Inflammation-Mediated Focal Growth of Saccular Aneurysms in a Rat Model

Past studies have elucidated the crucial role of macrophage-mediated inflammation in the growth of intracranial aneurysms (IAs), but the contributions of hemodynamics are unclear. Considering the size of the arteries, we induced de novo aneurysms at the bifurcations created by end-to-side anastomoses with the bilateral common carotid arteries in rats. Sequential morphological data of induced aneurysms were acquired by magnetic resonance angiography. Computational fluid dynamics analyses and macrophage imaging by ferumoxytol were performed. Using this model, we found that de novo saccular aneurysms with a median size of 3.2 mm were induced in 20/45 (44%) of animals. These aneurysms mimicked human IAs both in morphology and pathology. We detected the focal growth of induced aneurysms between the 10th and 17th day after the anastomosis. The regional maps of hemodynamic parameters demonstrated the area exposed to low wall shear stress (WSS) and high oscillatory shear index (OSI) colocalized with the regions of growth. WSS values were significantly lower in the growing regions than in ones without growth. Macrophage imaging showed colocalization of macrophage infiltration with the growing regions. This experimental model demonstrates the potential contribution of low WSS and high OSI to the macrophage-mediated growth of saccular aneurysms.

Aortic arch aneurysm repair - Unsteady hemodynamics and perfusion at different heart rates

The aortic arch aneurysm is a complex disease that requires branching of one or more aortic arch vessels and can be fatal if left untreated. In this in vitro study, we examine the effect of the treatment approach on the unsteady hemodynamics and blood perfusion to the upper vessel's in models of an aortic arch aneurysm, and of the three common repair approaches: open-chest surgical repair, chimney, and hybrid approach. A particle image velocimetry method was used to quantify the unsteady hemodynamics in the four models simulated in a mock circulatory loop, to evaluate unsteady hemodynamic parameters and measure perfusion to the brain and the upper body. According to the findings, in terms of perfusion to the brain and upper body, the surgery model has the highest flow rate comparing to the other models in most heart-rate conditions. It also shows oscillatory parameters in the upper vessels which in normal arteries are correlated with a better arterial function. Between the two endovascular procedures, the hybrid model exhibits slightly better hemodynamic characteristics than the chimney model, with lower shear stresses and more oscillatory flow and WSS in the upper vessels. The hybrid model had lower perfusion flow rates to upper vessels during rest conditions (90BPM). However, unlike the other models, perfusion in the hybrid model increased with heart rate, thus at 135 BPM, it results in flow rate to upper vessels similar to that of the chimney model. The results of this study may shed light on future endograft' design and placement techniques.

Evaluation of magnetic resonance angiography as a possible alternative to rotational angiography or computed tomography angiography for assessing cerebrovascular computational fluid dynamics

The aim of this study was to conduct a flow experiment using a cerebrovascular phantom and investigate whether magnetic resonance angiography (MRA) could replace three-dimensional rotational angiography (RA) and computed tomography angiography (CTA) to construct vascular models for computational fluid dynamics (CFD). We performed MRA and 3D cine phase-contrast (PC) MR imaging with a silicone cerebrovascular phantom of an internal carotid artery-posterior communicating artery aneurysm with blood-mimicking fluid, and controlled flow with a flowmeter. We also obtained RA and CTA data for the phantom. Four analysts constructed vascular models based on the three different modalities. These 12 constructed models used flow information based on 3D cine PC MR imaging for CFD. We compared RA-, CTA-, MRA-based CFD results using the micro-CT-based CFD result as the criterion standard to investigate whether MRA-based CFD was not inferior to RA- or CTA-based CFD. We also analyzed the inter-analyst variability. Wall shear stress (WSS) distributions and streamlines of RA- or MRA-based CFD and those of micro-CT-based CFD were similar, but the vascular models and WSS values were different. Accuracy in measurements of blood vessel diameter, cross-sectional maximum velocity, and spatially averaged WSS was the highest for RA-based CFD, followed by MRA-based and CTA-based CFD using micro-CT-based CFD result as the reference. Except maximum velocity from CTA, all other parameters had good inter-analyst agreement using different modalities. The results demonstrated that non-invasive MRA can be used for cerebrovascular CFD models with good inter-analyst agreements.

Haemodynamics in a patient-specific intracranial aneurysm according to experimental and numerical approaches: A comparison of PIV, CFD and PC-MRI

BACKGROUND

The haemodynamics determined by different approaches for studying fluid dynamics - i.e. computational fluid dynamics (CFD), particle image velocimetry (PIV), and phase-contrast magnetic resonance imaging (PC-MRI) - have rarely been thoroughly compared; nor have the factors that affect accuracy and precision in each method. As each method has its own advantages and limitations, this knowledge is important for future studies to be able to achieve valid analyses of fluid flows.

OBJECTIVE

To gauge the capacity of these methods for analysing aneurysmal flows, we compared the haemodynamic behaviours determined by each method within a patient-specific aneurysm model.

METHODS

An in vitro silicone aneurysm model was fabricated for PIV and PC-MRI, and an in silico aneurysm model with the same geometry was reconstructed for CFD. With the same fluid model prepared numerically and physically, CFD, PIV and PC-MRI were performed to study aneurysmal haemodynamics.

RESULTS

2D velocity vectors and magnitudes show good agreement between PIV and CFD, and 3D flow patterns show good similarity between PC-MRI and CFD.

CONCLUSIONS

These findings give confidence to future haemodynamic studies using CFD technology. For the first time, the morphological inconsistency between the PCMRI model and others is found to affect the measurement of local flow patterns.

Numerical Analysis of Bifurcation Angles and Branch Patterns in Intracranial Aneurysm Formation

BACKGROUND

Hemodynamic factors, especially wall shear stress (WSS), are generally thought to play an important role in intracranial aneurysm (IA) formation. IAs frequently occur at bifurcation apices, where the vessels are exposed to the impact of WSS.

OBJECTIVE

To elucidate the relationship between bifurcation geometry and WSS for IA formation.

METHODS

Twenty-one bifurcation models varying in branch angles and branch diameters were made with 3-dimensional computer-aided design software. In all models, the value of maximum WSS (WSSMAX), the area of high WSS (AREA), and the magnitude of wall shear force over AREA ($| {{{\vec{F}}_w}} |$) were investigated by the steady-flow simulation of computational fluid dynamics.

RESULTS

On the basis of statistical analysis, WSSMAX tended to be high when the bifurcation angle and/or branch diameter was small. AREA and $| {{{\vec{F}}_w}} |$ significantly increase as the bifurcation and/or the branch angle became larger.

CONCLUSION

The magnitude of WSS strongly correlated with bifurcation geometry. In addition to high WSS, AREA and $| {{{\vec{F}}_w}} |$ were thought to affect IA formation. Observed bifurcation geometry may predict IA formation. Large branch angles and small branch may increase the risk of IA formation.

Influence of Relative Residence Time on Side-Wall Aneurysm Inception

BACKGROUND

Relative residence time (RRT) is a marker of disturbed blood flow, marked by low magnitude and high oscillatory wall shear stress (WSS). The relation between solute residence time in proximity to the vascular endothelium and the atherosclerotic process is well appreciated in the literature.

OBJECTIVE

To assess the influence of RRT on side-wall aneurysm inception to better understand the role of atherosclerosis in aneurysm formation.

METHODS

Fourteen side-wall internal carotid artery aneurysms from the Aneurisk repository which met criteria for parent vessel reconstruction were reconstructed with Vascular Modeling Toolkit. Computational fluid dynamics analysis was carried out in Fluent. RRT was calculated in MATLAB (The MathWorks Inc, Natick, Massachusetts). We analyzed the results for correlations, defined as presence or absence of local elevations in RRT in specific regions of vasculature.

RESULTS

RRT was concluded to be negatively correlated with aneurysm inception in this study of side-wall internal carotid artery aneurysms, with 12/14 cases yielding the absence of local RRT elevations within or in close proximity of the removed ostium. Subsequent analysis of WSS showed that 11 of 14 aneurysms were formed in an atheroprotective environment, with only 1 of 14 formed in an atherogenic environment. Two models were found to be of indeterminate environment.

CONCLUSION

Atherogenesis and atherosclerosis have long been thought to be a major inciting factor responsible for the formation of aneurysms in the cerebral vasculature. We propose that inception of side-wall aneurysms occurs in hemodynamic environments that promote an atheroprotective endothelial phenotype and that the atheroprotective phenotype is therefore aneurysmogenic.

Numerical Investigation of Turbulence in Abdominal Aortic Aneurysms

Computational fluid dynamics (CFD) is a powerful method to investigate aneurysms. The primary focus of most investigations has been to compute various hemodynamic parameters to assess the risk posed by an aneurysm. Despite the occurrence of transitional flow in aneurysms, turbulence has not received much attention. In this article, we investigate turbulence in the context of abdominal aortic aneurysms (AAA). Since the clinical practice is to diagnose an AAA on the basis of its size, hypothetical axisymmetric geometries of various sizes are constructed. In general, just after the peak systole, a vortex ring is shed from the expansion region of an AAA. As the ring advects downstream, an azimuthal instability sets in and grows in amplitude thereby destabilizing the ring. The eventual breakdown of the vortex ring into smaller vortices leads to turbulent fluctuations. A residence time study is also done to identify blood recirculation zones, as a recirculation region can lead to degradation of the arterial wall. In some of the geometries simulated, the enhanced local mixing due to turbulence does not allow a recirculation zone to form, whereas in other geometries, turbulence had no effect on them. The location and consequence of a recirculation zone suggest that it could develop into an intraluminal thrombus (ILT). Finally, the possible impact of turbulence on the oscillatory shear index (OSI), a hemodynamic parameter, is explored. To conclude, this study highlights how a small change in the geometric aspects of an AAA can lead to a vastly different flow field.

Near-Wall Flow in Cerebral Aneurysms

The region where the vascular lumen meets the surrounding endothelium cell layer, hence the interface region between haemodynamics and cell tissue, is of primary importance in the physiological functions of the cardiovascular system. The functions include mass transport to/from the blood and tissue, and signalling via mechanotransduction, which are primary functions of the cardiovascular system and abnormalities in these functions are known to affect disease formation and vascular remodelling. This region is denoted by the near-wall region in the present work, and we outline simple yet effective numerical recipes to analyse the near-wall flow field. Computational haemodynamics solutions are presented for six patient specific cerebral aneurysms, at three instances in the cardiac cycle: peak systole, end systole (taken as dicrotic notch) and end diastole. A sensitivity study, based on Newtonian and non-Newtonian rheological models, and different flow rate profiles, is effected for a selection of aneurysm cases. The near-wall flow field is described by the wall shear stress (WSS) and the divergence of wall shear stress (WSSdiv), as descriptors of tangential and normal velocity components, respectively, as well as the wall shear stress critical points. Relations between near-wall and free-stream flow fields are discussed.

A non-dimensional parameter for classification of the flow in intracranial aneurysms. II. Patient-specific geometries

A simple parameter, called the Aneurysm number (An) which is defined as the ratio of transport to vortex time scales, has been shown to classify the flow mode in simplified aneurysm geometries. Our objective is to test the hypothesis that An can classify the flow in patient-specific intracranial aneurysms (IA). Therefore, the definition of this parameter is extended to anatomic geometries by using hydraulic diameter and the length of expansion area in the approximate direction of the flow. The hypothesis is tested using image-based flow simulations in five sidewall and four bifurcation geometries, i.e., if An ≲ 1 (shorter transport time scale), then the fluid is transported across the neck before the vortex could be formed, creating a quasi-stationary shear layer (cavity mode). By contrast, if An ≳ 1 (shorter vortex time scale), a vortex is formed. The results show that if An switches from An ≲ 1 to An ≳ 1, then the flow mode switches from the cavity mode to the vortex mode. However, if An does not switch, then the IAs stay in the same mode. It is also shown that IAs in the cavity mode have significantly lower An, temporal fluctuations of wall shear stress and oscillatory shear index (OSI) compared to the vortex mode (p < 0.01). In addition, OSI correlates with An in each flow mode and with pulsatility index in each IA. This suggests An to be a viable hemodynamic parameter which can be easily calculated without the need for detailed flow measurements/ simulations.

A new hypothesis on the role of vessel topology in cerebral aneurysm initiation

Aneurysm pathogenesis is thought to be strongly linked with hemodynamical effects. According to our current knowledge, the formation process is initiated by locally disturbed flow conditions. The aim of the current work is to provide a numerical investigation on the role of the flow field at the stage of the initiation, before the aneurysm formation. Digitally reconstructed pre-aneurysmal geometries are used to examine correlations of the flow patterns to the location and direction of the aneurysms formed later. We argue that a very specific rotational flow pattern is present in all the investigated cases marking the location of the later aneurysm and that these flow patterns provide the mechanical load on the wall that can lead to a destructive remodelling in the vessel wall. Furthermore, these patterns induce elevated vessel surface related variables (e.g. wall shear stress (WSS), wall shear stress gradient (WSSG) and oscillatory shear index (OSI)), in agreement with the previous findings. We emphasise that the analysis of the flow patterns provides a deeper insight and a more robust numerical methodology compared to the sole examination of the aforementioned surface quantities.

Relationship between hemodynamic parameters and cerebral aneurysm initiation

Research on the relationship between cerebralaneurysm initiation and hemodynamic parameters, but several open questions remain on initiation and growth mechanisms of cerebral aneurysms. If factors contributing to initiation were identified, it would be possible to predict the initiation of aneurysms. The purpose of this study is to investigate the relationship between cerebral aneurysm initiation and hemodynamic factors. Blood flow simulations in aneurysms of three patients were performed using computational fluid dynamics (CFD) based on the cerebral blood vessel geometry before aneurysm initiation. We evaluated pressure, wall shear stress (WSS), wall shear stress gradient (WSSG), oscillatory shear index (OSI) and gradient oscillatory number (GON) since these factors are known to be associated with aneurysmal initiation. We also focused on the wall shear stress divergence (WSSD) in particular on the direction of WSS. Our results indicated that only high WSSD regions corresponded to the initiation regions, and the value of WSSD was remarkably high. Stretching force to the vessel wall may be related to the initiation of cerebral aneurysms.

Synergistic Integration of Laboratory and Numerical Approaches in Studies of the Biomechanics of Diseased Red Blood Cells

In red blood cell (RBC) disorders, such as sickle cell disease, hereditary spherocytosis, and diabetes, alterations to the size and shape of RBCs due to either mutations of RBC proteins or changes to the extracellular environment, lead to compromised cell deformability, impaired cell stability, and increased propensity to aggregate. Numerous laboratory approaches have been implemented to elucidate the pathogenesis of RBC disorders. Concurrently, computational RBC models have been developed to simulate the dynamics of RBCs under physiological and pathological conditions. In this work, we review recent laboratory and computational studies of disordered RBCs. Distinguished from previous reviews, we emphasize how experimental techniques and computational modeling can be synergically integrated to improve the understanding of the pathophysiology of hematological disorders.

Fluid shear stress combined with shear stress spatial gradients regulates vascular endothelial morphology

High shear stress (SS) causes local changes around arterial bifurcations, which are common sites for cerebral aneurysms. High SS and SS spatial gradient (SSG) are thought to play important roles in the pathology of cerebral aneurysms. However, whether SS and SSG independently affect the function and morphology of vascular endothelial cells (ECs) exposed to fluid flow remains unclear. This study evaluated the morphology of ECs exposed to various SS and SSG combinations. Confluent ECs were exposed to a SS of 2-60 Pa and a uniform SSG of 0, 5, 10, or 15 Pa mm^-1 for 24 h. Although ECs exposed to lower levels of SS/SSG were not oriented or elongated in the direction of flow, they began to exhibit orientation, elongation, and development of actin stress fibers under the conditions of SS with a SSG when the SS exceeded a threshold value depending on the magnitude of SSG. Using a simplified computational model, we found that the presence of a SSG affects the strain field in ECs, resulting in a morphological response. SS combined with a SSG can alter the localization of SS mechano-sensing proteins along the strain field as a result of shear flow. Our results suggest that the magnitude of the relationship between SS and SSG plays an important role in regulating morphological changes in ECs in response to fluid flow by regulating EC polarity.

Hemodynamic vascular biomarkers for initiation of paraclinoid internal carotid artery aneurysms using patient-specific computational fluid dynamic simulation based on magnetic resonance imaging

PURPOSE

We performed computational fluid dynamics (CFD) for patients with and without paraclinoid internal carotid artery (ICA) aneurysms to evaluate the distribution of vascular biomarkers at the aneurysm initiation sites of the paraclinoid ICA.

METHODS

This study included 35 patients who were followed up for aneurysms using 3D time of flight (TOF) magnetic resonance angiography (MRA) and 3D cine phase-contrast MR imaging. Fifteen affected ICAs were included in group A with the 15 unaffected contralateral ICAs in group B. Thirty-three out of 40 paraclinoid ICAs free of aneurysms and arteriosclerotic lesions were included in group C. We deleted the aneurysms in group A based on the 3D TOF MRA dataset. We performed CFD based on MR data set and obtained wall shear stress (WSS), its derivatives, and streamlines. We qualitatively evaluated their distributions at and near the intracranial aneurysm initiation site among three groups. We also calculated and compared the normalized highest (nh-) WSS and nh-spatial WSS gradient (SWSSG) around the paraclinoid ICA among three groups.

RESULTS

High WSS and SWSSG distribution were observed at and near the aneurysm initiation site in group A. High WSS and SWSSG were also observed at similar locations in group B and group C. However, nh-WSS and nh-SWSSG were significantly higher in group A than in group C, and nh-SWSSG was significantly higher in group A than in group B.

CONCLUSION

Our findings indicated that nh-WSS and nh-SWSSG were good biomarkers for aneurysm initiation in the paraclinoid ICA.

Hemodynamic impingement and the initiation of intracranial side-wall aneurysms

Objective The natural history intracranial aneurysms (IA) remains poorly understood despite significant morbidity and mortality associated with IA rupture. Hemodynamic impingement resulting in elevations in wall shear stress and wall shear stress gradient (WSSG) has been shown to induce aneurysmal remodeling at arterial bifurcations. We investigate the hemodynamic environment specific to side-wall pre-aneurysmal vasculature. We hypothesize that fluid impingement and secondary flow patterns play a role in side-wall aneurysm initiation. Methods Eight side-wall internal carotid artery aneurysms from the Aneurisk repository were identified. Pre-aneurysmal vasculature was algorithmically reconstructed. Blood flow was simulated with computational fluid dynamic simulations. An indicator of isolated fluid impingement energy was developed by insetting the vessel surface and calculating the impinging component of the fluid dynamic pressure. Results Isolated fluid impingement was found to be elevated in the area of aneurysm initiation in 8/8 cases. The underlying fluid flow for each area of initiation was found to harbor secondary flow patterns known as Dean's vortices, the result of changes in momentum imparted by bends in the internal carotid artery (ICA). Conclusion Isolated fluid impingement and secondary flow patterns may play a major role in the initiation of side-wall aneurysm initiation. We are unable to determine if this role is through direct or indirect mechanisms but hypothesize that elevations in isolated fluid impingement mark areas of cerebral vasculature that are at risk for aneurysm initiation. Thus, this indicator provides vascular locations to focus future study of side-wall aneurysm initiation.

Stagnation and complex flow in ruptured cerebral aneurysms: a possible association with hemostatic pattern

OBJECT

Histopathological examination has revealed that ruptured cerebral aneurysms have different hemostatic patterns depending on the location of the clot formation. In this study, the authors investigated whether the hemostatic patterns had specific hemodynamic features using computational fluid dynamics (CFD) analysis.

METHODS

Twenty-six ruptured middle cerebral artery aneurysms were evaluated by 3D CT angiography and harvested at the time of clipping. The hemostatic patterns at the rupture points were assessed by means of histopathological examination, and morphological parameters were obtained. Transient analysis was performed, and wall shear stress–related hemodynamic parameters and invariant Q (vortex core region) were calculated. The morphological and hemodynamic parameters were compared among the hemostatic patterns.

RESULTS

Hematoxylin and eosin staining of the aneurysm wall showed 13 inside-pattern, 9 outside-pattern, and 4 other-pattern aneurysms. Three of the 26 aneurysms were excluded from further analysis, because their geometry models could not be generated due to low vascular CT values. Mann-Whitney U-tests showed that lower dome volume (0.04 cm3 vs 0.12 cm3, p = 0.014), gradient oscillatory number (0.0234 vs 0.0289, p = 0.023), invariant Q (−0.801 10−2/sec2 vs −0.124 10−2/sec2, p = 0.045) and higher aneurysm formation indicator (0.986 vs 0.963, p = 0.041) were significantly related to inside-pattern aneurysms when compared with outside-pattern aneurysms.

CONCLUSIONS

Inside-pattern aneurysms may have simpler flow patterns and less flow stagnation than outside-pattern aneurysms. CFD may be useful to characterize the hemostatic pattern of ruptured cerebral aneurysms.

Pulsatility Index as a Diagnostic Parameter of Reciprocating Wall Shear Stress Parameters in Physiological Pulsating Waveforms

Arterial wall shear stress (WSS) parameters are widely used for prediction of the initiation and development of atherosclerosis and arterial pathologies. Traditional clinical evaluation of arterial condition relies on correlations of WSS parameters with average flow rate (Q) and heart rate (HR) measurements. We show that for pulsating flow waveforms in a straight tube with flow reversals that lead to significant reciprocating WSS, the measurements of HR and Q are not sufficient for prediction of WSS parameters. Therefore, we suggest adding a third quantity—known as the pulsatility index (PI)—which is defined as the peak-to-peak flow rate amplitude normalized by Q. We examine several pulsating flow waveforms with and without flow reversals using a simulation of a Womersley model in a straight rigid tube and validate the simulations through experimental study using particle image velocimetry (PIV). The results indicate that clinically relevant WSS parameters such as the percentage of negative WSS (P[%]), oscillating shear index (OSI) and the ratio of minimum to maximum shear stress rates (min/max), are better predicted when the PI is used in conjunction with HR and Q. Therefore, we propose to use PI as an additional and essential diagnostic quantity for improved predictability of the reciprocating WSS.

Association of Hemodynamic Factors With Intracranial Aneurysm Formation and Rupture: Systematic Review and Meta-analysis

BACKGROUND

Recent evidence suggests a link between the magnitude and distribution of hemodynamic factors and the formation and rupture of intracranial aneurysms. However, there are many conflicting results.

OBJECTIVE

To quantify the effect of hemodynamic factors on aneurysm formation and their association with ruptured aneurysms.

METHODS

We performed a systematic review and meta-analysis through October 2014. Analysis of the effects of hemodynamic factors on aneurysm formation was performed by pooling the results of studies that compared geometrical models of intracranial aneurysms and "preaneurysm" models where the aneurysm was artificially removed. Furthermore, we calculated pooled standardized mean differences between ruptured and unruptured aneurysms to quantify the association of hemodynamic factors with ruptured aneurysms. Standard PRISMA guidelines were followed.

RESULTS

The hemodynamic factors that showed high positive correlations with location of aneurysm formation were high wall shear stress (WSS) and high gradient oscillatory number, with pooled proportions of 78.8% and 85.7%, respectively. Positive correlations were largely seen in bifurcation aneurysms, whereas negative correlations were seen in sidewall aneurysms. Mean and normalized WSS were significantly lower and low shear area significantly higher in ruptured aneurysms.

CONCLUSION

Pooled analyses of computational fluid dynamics models suggest that an increase in WSS and gradient oscillatory number may contribute to aneurysm formation, whereas low WSS is associated with ruptured aneurysms. The location of the aneurysm at the bifurcation or sidewall may influence the correlation of these hemodynamic factors.

Characterizations and Correlations of Wall Shear Stress in Aneurysmal Flow

Wall shear stress (WSS) is one of the most studied hemodynamic parameters, used in correlating blood flow to various diseases. The pulsatile nature of blood flow, along with the complex geometries of diseased arteries, produces complicated temporal and spatial WSS patterns. Moreover, WSS is a vector, which further complicates its quantification and interpretation. The goal of this study is to investigate WSS magnitude, angle, and vector changes in space and time in complex blood flow. Abdominal aortic aneurysm (AAA) was chosen as a setting to explore WSS quantification. Patient-specific computational fluid dynamics (CFD) simulations were performed in six AAAs. New WSS parameters are introduced, and the pointwise correlation among these, and more traditional WSS parameters, was explored. WSS magnitude had positive correlation with spatial/temporal gradients of WSS magnitude. This motivated the definition of relative WSS gradients. WSS vectorial gradients were highly correlated with magnitude gradients. A mix WSS spatial gradient and a mix WSS temporal gradient are proposed to equally account for variations in the WSS angle and magnitude in single measures. The important role that WSS plays in regulating near wall transport, and the high correlation among some of the WSS parameters motivates further attention in revisiting the traditional approaches used in WSS characterizations.

Transitional flow in aneurysms and the computation of haemodynamic parameters

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

Optimization of strut placement in flow diverter stents for four different aneurysm configurations

A modern technique for the treatment of cerebral aneurysms involves insertion of a flow diverter stent. Flow stagnation, produced by the fine mesh structure of the diverter, is thought to promote blood clotting in an aneurysm. However, apart from its effect on flow reduction, the insertion of the metal device poses the risk of occlusion of a parent artery. One strategy for avoiding the risk of arterial occlusion is the use of a device with a higher porosity. To aid the development of optimal stents in the view point of flow reduction maintaining a high porosity, we used lattice Boltzmann flow simulations and simulated annealing optimization to investigate the optimal placement of stent struts. We constructed four idealized aneurysm geometries that resulted in four different inflow characteristics and employed a stent model with 36 unconnected struts corresponding to the porosity of 80%. Assuming intracranial flow, steady flow simulation with Reynolds number of 200 was applied for each aneurysm. Optimization of strut position was performed to minimize the average velocity in an aneurysm while maintaining the porosity. As the results of optimization, we obtained nonuniformed structure as optimized stent for each aneurysm geometry. And all optimized stents were characterized by denser struts in the inflow area. The variety of inflow patterns that resulted from differing aneurysm geometries led to unique strut placements for each aneurysm type.

Proximal stenosis may induce initiation of cerebral aneurysms by increasing wall shear stress and wall shear stress gradient

Hemodynamic parameters, such as wall shear stress (WSS), WSS gradient (WSSG), aneurysm formation indicator (AFI), or gradient oscillatory number (GON), have been proposed to be linked to initiation of cerebral aneurysms. However, how such conditions occur in humans is unclear. We encountered a rare and interesting case to address this issue. A patient had a newly formed aneurysm with proximal stenosis, which was confirmed by serial imagings. We made two pre-aneurysm models: one with stenosis and the other without stenosis. We performed computational fluid dynamics simulations for these models. Owing to jet flow caused by the stenosis, the maximum WSS and WSSG on the aneurysm initiation site were approximately doubled and tripled, respectively. However, the oscillatory shear index (OSI), AFI, and GON did not change substantially by the stenosis. Computer simulations using artificial vascular models with different degrees of proximal stenosis at different distances demonstrated that oscillatory shear index, AFI, and GON did not change substantially by the stenosis. These results showed that proximal stenosis caused high WSS and high WSSG at the aneurysm initiation site, possibly leading to aneurysm initiation. Proximal stenosis may be a potential factor to induce initiation of one class of cerebral aneurysms by increasing WSS and WSSG.