Flow instability and wall shear stress variation in intracranial aneurysms

Understanding development of jugular bulb stenosis in vein of galen malformations: identifying metrics of complex flow dynamics in the cerebral venous vasculature of infants

Introduction: Computational fluid dynamics (CFD) assess biological systems based on specific boundary conditions. We propose modeling more advanced hemodynamic metrics, such as core line length (CL) and critical points which characterize complexity of flow in the context of cerebral vasculature, and specifically cerebral veins during the physiologically evolving early neonatal state of vein of Galen malformations (VOGM). CFD has not been applied to the study of arteriovenous shunting in Vein of Galen Malformations but could help illustrate the pathophysiology of this malformation. Methods: Three neonatal patients with VOGM at Boston Children's Hospital met inclusion criteria for this study. Structural MRI data was segmented to generate a mesh of the VOGM and venous outflow. Boundary condition flow velocity was derived from PC-MR sequences with arterial and venous dual velocity encoding. The mesh and boundary conditions were applied to model the cerebral venous flow. We computed flow variables including mean wall shear stress (WSSmean), mean OSI, CL, and the mean number of critical points (nCrPointsmean) for each patient specific model. A critical point is defined as the location where the shear stress vector field is zero (stationary point) and can be used to describe complexity of flow. Results: The division of flow into the left and right venous outflow was comparable between PC-MR and CFD modeling. A high complexity recirculating flow pattern observed on PC-MR was also identified on CFD modeling. Regions of similar WSSmean and OSImean (<1.3 fold) in the left and right venous outflow channels of a single patient have several-fold magnitude difference in higher order hemodynamic metrics (> 3.3 fold CL, > 1.7 fold nCrPointsmean). Specifically, the side which developed JBS in each model had greater nCrPointsmean compared to the jugular bulb with no stenosis (VOGM1: 4.49 vs. 2.53, VOGM2: 1.94 vs. 0, VOGM3: 1 vs. 0). Biologically, these regions had subsequently divergent development, with increased complexity of flow associating with venous stenosis. Discussion: Advanced metrics of flow complexity identified in computational models may reflect observed flow phenomena not fully characterized by primary or secondary hemodynamic parameters. These advanced metrics may indicate physiological states that impact development of jugular bulb stenosis in VOGM.

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.

High-fidelity fluid structure interaction simulations of turbulent-like aneurysm flows reveals high-frequency narrowband wall vibrations: A stimulus of mechanobiological relevance?

Recent high-fidelity/resolution computational fluid dynamics simulations of intracranial aneurysm hemodynamics have revealed turbulent-like flows. We hypothesized that the associated high-frequency pressure fluctuations could promote aneurysm wall vibrations. We performed fully coupled high-fidelity transient fluid structure interaction simulations between the blood flow and compliant aneurysm sac wall taking 5,000 time steps per second using a 3D patient-specific model previously shown to harbour turbulent-like flow. Our results show that the flow velocity contained fluctuations with a smooth and continuously decaying energy up to ∼160Hz, and fluctuating pressures with characteristic frequency peaks at approximately 30, 130 and 210Hz. There was a strong two-way coupling between the pressure and the wall deformation, for which the frequency spectrum showed similar characteristics, but with a narrow band peak at ∼120Hz with large regional differences in amplitude up to 80μm. The physics of the flow is broadly consistent with clinical reports of turbulent-like flows, while the physics of the wall is consistent with reports of spectral peaks in aneurysm patients. As many aneurysms are known to harbour turbulent-like flows, wall vibrations could be a widespread phenomenon. Finally, since aneurysms are vascular pathologies by definition and many/most aneurysms do not have endothelial cells but still display a focal remodeling, we hypothesize that vibrations and stresses within the wall itself might play a role in the mechanobiological processes of vessel wall pathology.

Medical Image-Based Computational Fluid Dynamics and Fluid-Structure Interaction Analysis in Vascular Diseases

Hemodynamic factors, induced by pulsatile blood flow, play a crucial role in vascular health and diseases, such as the initiation and progression of atherosclerosis. Computational fluid dynamics, finite element analysis, and fluid-structure interaction simulations have been widely used to quantify detailed hemodynamic forces based on vascular images commonly obtained from computed tomography angiography, magnetic resonance imaging, ultrasound, and optical coherence tomography. In this review, we focus on methods for obtaining accurate hemodynamic factors that regulate the structure and function of vascular endothelial and smooth muscle cells. We describe the multiple steps and recent advances in a typical patient-specific simulation pipeline, including medical imaging, image processing, spatial discretization to generate computational mesh, setting up boundary conditions and solver parameters, visualization and extraction of hemodynamic factors, and statistical analysis. These steps have not been standardized and thus have unavoidable uncertainties that should be thoroughly evaluated. We also discuss the recent development of combining patient-specific models with machine-learning methods to obtain hemodynamic factors faster and cheaper than conventional methods. These critical advances widen the use of biomechanical simulation tools in the research and potential personalized care of vascular diseases.

Vertigo: Could this Symptom Indicate the Existence of an Unruptured Intracranial Aneurysm?

Background:Unruptured intracranial aneurysms (UIAs) can be presented with various symptoms, including atypical headaches and cranial nerve deficits. Vertigo is often referred in the literature as a coexisting symptom. Our aim was to investigate the importance of vertigo in the UIA symptomatology and present a possible explanation for its existence. Methods:We conducted a retrospective observational multicenter study concerning patients with surgically treated intracranial aneurysms. During a period of 10 years, 1 085 patients with cerebral aneurysms underwent surgery. There were 812 patients with ruptured intracranial aneurysms (RIA) and 273 with UIA. The medical records for each of the 273 patients were analyzed. Results: After the implementation of exclusion criteria, 89 (32.6%) of UIA patients were selected in the study, from which 71 (79.8%) were females and 18 (20.2%) males. The mean age was 56.9 (± 12.876) years old. Vertigo existed in 72 (80.9%), headache in 41 (46.1%) and visual symptoms in 21 (23.6%) patients. No significant correlation (p >0.05) was demonstrated between gender, age or aneurysm location in correlation with vertigo, headache or visual symptoms, apart from a negative significant correlation between age and vertigo (p=0.031). Conclusion:Vertigo is an alarming symptom that could indicate the existence of an UIA. The pathophysiological mechanism could be explained by the formation of an aneurysmal vortex that projects into the parent artery, leading to disturbances in the laminar flow and formation of an irregular/turbulent flow, which potentially affects the cerebral autoregulation and by consequence, the central processing of movement.

Morphological factors affecting vortex core instability on 4D flow MRI of unruptured cerebral aneurysms

OBJECTIVE

The spatiotemporal instability of intra-aneurysmal vortex flow may be associated with unruptured cerebral aneurysm rupture. We identified morphological factors that affect intra-aneurysmal vortex core patterns classified based on the instability on four-dimensional (4D) flow magnetic resonance imaging (MRI) and determined cutoff values for the factors to discriminate unstable core patterns.

METHODS

We classified vortex core patterns of 40 unruptured aneurysms on 4D flow MRI into stable, stable with a flapping tip, continuously deforming wave-or-coil-like, and non-visualized. We statistically compared nine morphological parameters among aneurysm groups with individual patterns.

RESULTS

The vortex cores were stable (n = 16) (group A), stable with a flapping tip (n = 15) (group B), wave-or-coil-like (n = 7) (group C), and non-visualized (n = 2) (group D). Since there were no statistically significant differences between groups A and B, we compared the difference between the groups A and B and the other groups. Multivariate logistic regression analyses found that size ratio (SR) was an only independently significant parameter (p < 0.05). The receiver-operating characteristic analysis between groups A and B and group C and between groups A and B and groups C and D revealed that the area under the curve value for SR was the highest (0.829 [95% CI, 0.642-1.0]; 0.867 [95% CI, 0.715-1.0], respectively) among morphological factors; the cutoff value for SR was 1.72 (specificity 0.714, sensitivity 0.756; specificity 0.806, sensitivity 0.778, respectively).

CONCLUSION

SR was an independent morphological factor contributing to vortex core instability based on the vortex core patterns on 4D flow MRI.Abbreviations: CFD: computational fluid dynamics; 3D: three-dimensional; 4D: four-dimensional; MRI: magnetic resonance imaging; MRA: magnetic resonance angiography; ICA: internal carotid artery; AR: aspect ratio; SR: size ratio; CI: confidence interval; AUC: area under the curve; ROC: receiver-operating characteristic.

On the prevalence of flow instabilities from high-fidelity computational fluid dynamics of intracranial bifurcation aneurysms

High-fidelity computational fluid dynamics (HF-CFD) has revealed the potential for high-frequency flow instabilities (aka "turbulent-like" flow) in intracranial aneurysms, consistent with classic in vivo and in vitro reports of bruits and/or wall vibrations. However, HF-CFD has typically been performed on limited numbers of cases, often with unphysiological inflow conditions or focused on sidewall-type aneurysms where flow instabilities may be inherently less prevalent. Here we report HF-CFD of 50 bifurcation aneurysm cases from the open-source Aneurisk model repository. These were meshed using quadratic finite elements having an average effective spatial resolution of 0.065 mm, and solved under physiologically-pulsatile flow conditions using a well-validated, minimally-dissipative solver with 20,000 time-steps per cardiac cycle Flow instability was quantified using the recently introduced spectral power index (SPI), which quantifies, from 0 to 1, the power associated with velocity fluctuations above those of the driving inflow waveform. Of the 50 cases, nearly half showed regions within the sac having SPI up to 0.5, often with non-negligible power into the 100's of Hz, and roughly 1/3 had sac-averaged SPI > 0.1. High SPI did not significantly predict rupture status in this cohort. Proper orthogonal decomposition of cases with highest SPI_avg revealed time-varying energetics consistent with transient turbulence. Our reported prevalence of high-frequency flow instabilities in HF-CFD modelling of aneurysms suggests that care must be taken to avoid routinely overlooking them if we are to understand the highly dynamic mechanical forces to which some aneurysm walls may be exposed, and their prevalence in vivo.

Numerical study on the energy cascade of pulsatile Newtonian and power-law flow models in an ICA bifurcation

The complex physics and biology underlying intracranial hemodynamics are yet to be fully revealed. A fully resolved direct numerical simulation (DNS) study has been performed to identify the intrinsic flow dynamics in an idealized carotid bifurcation model. To shed the light on the significance of considering blood shear-thinning properties, the power-law model is compared to the commonly used Newtonian viscosity hypothesis. We scrutinize the kinetic energy cascade (KEC) rates in the Fourier domain and the vortex structure of both fluid models and examine the impact of the power-law viscosity model. The flow intrinsically contains coherent structures which has frequencies corresponding to the boundary frequency, which could be associated with the regulation of endothelial cells. From the proposed comparative study, it is found that KEC rates and the vortex-identification are significantly influenced by the shear-thinning blood properties. Conclusively, from the obtained results, it is found that neglecting the non-Newtonian behavior could lead to underestimation of the hemodynamic parameters at low Reynolds number and overestimation of the hemodynamic parameters by increasing the Reynolds number. In addition, we provide physical insight and discussion onto the hemodynamics associated with endothelial dysfunction which plays significant role in the pathogenesis of intracranial aneurysms.

Dynamic modes of inflow jet in brain aneurysms

The transition of the inflow jet to turbulence is crucial in understanding the pathology of brain aneurysms. Previous works Le et al. (2010, 2013) have shown evidence for a highly dynamic inflow jet in the ostium of brain aneurysms. While it is highly desired to investigate this inflow jet dynamics in clinical practice, the constraints on spatial and temporal resolutions of in vivo data do not allow a detailed analysis of this transition. In this work, Dynamic Mode Decomposition (DMD) is used to identify the most energetic modes of the inflow jet in patient-specific models of internal carotid aneurysms via the utilization of high-resolution simulation data. It is hypothesized that dynamic modes are not solely controlled by the blood flow waveform at the parent artery. They are also dependent on jet-wall interaction phenomena. DMD analysis shows that the spatial extent of low- frequency modes corresponds well to the most energetic areas of the inflow jet. The high-frequency modes are short-lived and correspond to the flow separation at the proximal neck and the jet's impingement onto the aneurysmal wall. Low-frequency modes can be reconstructed at relatively low spatial and temporal resolutions comparable to ones of in vivo data. The current results suggest that DMD can be practically useful in analyzing blood flow patterns of brain aneurysms with in vivo data.

Amplified Flow Imaging (aFlow): A Novel MRI-Based Tool to Unravel the Coupled Dynamics Between the Human Brain and Cerebrovasculature

With each heartbeat, periodic variations in arterial blood pressure are transmitted along the vasculature, resulting in localized deformations of the arterial wall and its surrounding tissue. Quantification of such motions may help understand various cerebrovascular conditions, yet it has proven technically challenging thus far. We introduce a new image processing algorithm called amplified Flow (aFlow) which allows to study the coupled brain-blood flow motion by combining the amplification of cine and 4D flow MRI. By incorporating a modal analysis technique known as dynamic mode decomposition into the algorithm, aFlow is able to capture the characteristics of transient events present in the brain and arterial wall deformation. Validating aFlow, we tested it on phantom simulations mimicking arterial walls motion and observed that aFlow displays almost twice higher SNR than its predecessor amplified MRI (aMRI). We then applied aFlow to 4D flow and cine MRI datasets of 5 healthy subjects, finding high correlations between blood flow velocity and tissue deformation in selected brain regions, with correlation values r = 0.61 , 0.59, 0.52 for the pons, frontal and occipital lobe ( ). Finally, we explored the potential diagnostic applicability of aFlow by studying intracranial aneurysm dynamics, which seems to be indicative of rupture risk. In two patients, aFlow successfully visualized the imperceptible aneurysm wall motion, additionally quantifying the increase in the high frequency wall displacement after a one-year follow-up period (20%, 76%). These preliminary data suggest that aFlow may provide a novel imaging biomarker for the assessment of aneurysms evolution, with important potential diagnostic implications.

Effect of bifurcation in the hemodynamic changes and rupture risk of small intracranial aneurysm

The role of bifurcations is prominent in the intracranial aneurysm (IA) evaluation, and there are many contradictions and complexities in the rupture risk of small IA. Therefore, in the present study, the effect of bifurcation on the manner of hemodynamic changes and the rupture risk of the small middle cerebral artery (MCA) aneurysm is investigated. 3D anatomical models of the MCAs of 21 healthy subjects, 19 patients/IA/bifurcation, and 19 patients/IA were generated, and the models were analyzed by the computational fluid dynamic (CFD) analysis. The presence of bifurcation in the pathway of the blood flow in the parent artery of healthy subjects has reduced the maximum velocity, flow rate, and wall shear stress (WSS) by 25.8%, 38.6%, and 11.1%, respectively. The bifurcation decreased the maximum velocity and flow rate in the neck and sac of the aneurysm by 1.65~2.1 times, respectively. It increased the maximum WSS, and phase lag between the WSS graph of healthy subjects and patients by 12.8%~13.9% and 10.2%~40.4%, respectively. The effect of bifurcation on the Womersley number change in the aneurysm was insignificant, and the blood flow was in the laminar flow condition in all samples. The results also showed bifurcation increased the phase lag between the flow rate and pressure gradient graphs up to approximately 1.5 times. The rupture prediction index for patients/IA/bifurcation and patients/IA was 62.1%(CV = 4.1) and 51.8%(CV = 4.4), respectively. Thus, in equal conditions, the presence of bifurcation increased the probability of the rupture of the aneurysm by 19.9%.

A Eulerian method to analyze wall shear stress fixed points and manifolds in cardiovascular flows

Based upon dynamical systems theory, a fixed point of a vector field such as the wall shear stress (WSS) at the luminal surface of a vessel is a point where the vector field vanishes. Unstable/stable manifolds identify contraction/expansion regions linking fixed points. The significance of such WSS topological features lies in their strong link with "disturbed" flow features like flow stagnation, separation and reversal, deemed responsible for vascular dysfunction initiation and progression. Here, we present a Eulerian method to analyze WSS topological skeleton through the identification and classification of WSS fixed points and manifolds in complex vascular geometries. The method rests on the volume contraction theory and analyzes the WSS topological skeleton through the WSS vector field divergence and Poincar[Formula: see text] index. The method is here applied to computational hemodynamics models of carotid bifurcation and intracranial aneurysm. An in-depth analysis of the time dependence of the WSS topological skeleton along the cardiac cycle is provided, enriching the information obtained from cycle-average WSS. Among the main findings, it emerges that on the carotid bifurcation, instantaneous WSS fixed points co-localize with cycle-average WSS fixed points for a fraction of the cardiac cycle ranging from 0 to [Formula: see text]; a persistent instantaneous WSS fixed point confined on the aneurysm dome does not co-localize with the cycle-average low-WSS region. In conclusion, the here presented approach shows the potential to speed up studies on the physiological significance of WSS topological skeleton in cardiovascular flows, ultimately increasing the chance of finding mechanistic explanations to clinical observations.

High-frequency wall vibrations in a cerebral patient-specific aneurysm model

The presence of high-frequency velocity fluctuations in aneurysms have been confirmed by in-vivo measurements and by several numerical simulation studies. Only a few studies have located and recorded wall vibrations in in-vitro experiments using physiological patient models. In this study, we investigated the wall fluctuations produced by a flowing perfusion fluid in a true-to-scale elastic model of a cerebral fusiform aneurysm using a laser Doppler vibrometer (LDV). The model was obtained from patient data. The experimental setup reproduced physiologically relevant conditions using a compliant perfusion system, physiological flow parameters, unsteady flow and a non-Newtonian fluid. Three geometrically identical models with different wall elasticities were used for measurements. The influence of five different flow rates was considered. Wall vibrations were predominantly found at frequencies in the range 40-60 Hz and 255-265 Hz. Their amplitude increased with increasing elasticity of the model, but the spectral peaks remained at about the same frequency. Varying the flow rate produced almost no changes in the frequency domain of the models. The frequency of the spectral peaks varied slightly between points at the lateral wall and at the bottom of the aneurysm. Indeed, embedding the model in a fluid during measurements produced higher and smoother amplitude fluctuations.

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.

Hemodynamic Differences Between Recurrent and Nonrecurrent Intracranial Aneurysms: Fluid Dynamics Simulations Based on MR Angiography

BACKGROUND AND PURPOSE

Although the role of wall shear stress (WSS) in the initiation, growth, and rupture of intracranial aneurysms has been well studied, its influence on aneurysm recurrence after endovascular treatment requires further investigation. We aimed to compare WSS at necks of recurrent and nonrecurrent aneurysms.

METHODS

Nine recurrent coil-embolized aneurysms were identified and matched with nine nonrecurrent aneurysms. Patient-specific vessel geometries reconstructed from follow-up 3-D time-of-flight magnetic resonance angiography were analyzed using computational fluid dynamics (CFD) simulations. Absolute WSS and the percentage of abnormally low and high WSS at the aneurysm neck compared to the near artery were measured.

RESULTS

The median percentage of abnormal WSS at the aneurysm neck was 49.3% for recurrent and 34.7% for nonrecurrent aneurysms (P = .011). The area under the receiver-operating-characteristic curve for distinguishing these aneurysms according to the percentage of abnormal WSS was .86 (95% CI .62 to .98). The optimal cut-off value of 45.1% resulted in a sensitivity and a specificity of 88.89% (95% CI 51.8% to 99.7%).

CONCLUSION

Our findings indicate that necks of recurrent aneurysms are exposed to abnormal WSS to a larger extent. Abnormal WSS may serve as a metric to distinguish them from nonrecurrent aneurysms with CFD simulations a priori.

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.

Expression profile analysis of differentially expressed genes in ruptured intracranial aneurysms: In search of biomarkers

Intracranial aneurysms (IAs) result from the bulging of arterial walls secondary to several factors such as flow, vessel morphology, and genetics. Subarachnoid hemorrhage occurs when such walls rupture, leading to high disability and mortality. Despite numerous investigations pertaining to the relationship between geometric characteristics and IA rupture, only a few have obtained consistent results. This study aimed to further identify the potential genes associated with the pathogenesis of IAs, which may provide novel molecular biomarkers. We downloaded and reanalyzed six datasets, which were divided into four groups. IA walls and blood samples were screened for differentially expressed genes (DEGs); then, functional and pathway enrichment analyses were conducted. In total, 158 common DEGs were identified from Groups 1-3 and 396 genes (187 upregulated and 209 downregulated genes) were differentially expressed in Group 4. The functional analysis revealed that the DEGs were mainly associated with the major histocompatibility complex class II protein complex and antigen processing and presentation. Finally, we identified nine key genes, both in aneurysm tissue samples and blood samples, of which three were mostly associated with the progression and rupture of IAs. Bioinformatics was used to analyze the datasets of the ruptured IAs and identify potential biomarkers, which may provide information for the early detection and treatment of IAs.

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.

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.

Flow instability detected in ruptured versus unruptured cerebral aneurysms at the internal carotid artery

Flow instability has emerged as a new hemodynamic metric hypothesized to have potential value in assessing the rupture risk of cerebral aneurysms. However, diverse findings have been reported in the literature. In the present study, high-resolution hemodynamic simulations were performed retrospectively on 35 aneurysms (10 ruptured & 25 unruptured) located at the internal carotid artery (ICA). Simulated hemodynamic parameters were statistically compared between the ruptured and unruptured aneurysms, with emphasis on examining the correlation of flow instability with the status of aneurysm rupture. Pronounced flow instability was detected in 20% (2 out of 10) of the ruptured aneurysms, whereas in 44% (11 out of 25) of the unruptured aneurysms. Statistically, the flow instability metric (quantified by the temporally and spatially averaged fluctuating kinetic energy over the aneurysm sac) did not differ significantly between the ruptured and unruptured aneurysms. In contrast, low wall shear stress area (LSA) and pressure loss coefficient (PLC) exhibited significant correlations with the status of aneurysm rupture. In conclusion, the present study suggests that the presence of flow instability may not correlate closely with the status of aneurysm rupture, at least for ICA aneurysms. On the other hand, the retrospective nature of the study and the small sample size may have to some extent compromised the reliability of the conclusion, and therefore large-scale prospective studies would be needed to further address the issue.

Computational Fluid Dynamics and Additive Manufacturing to Diagnose and Treat Cardiovascular Disease

Noninvasive engineering models are now being used for diagnosing and planning the treatment of cardiovascular disease. Techniques in computational modeling and additive manufacturing have matured concurrently, and results from simulations can inform and enable the design and optimization of therapeutic devices and treatment strategies. The emerging synergy between large-scale simulations and 3D printing is having a two-fold benefit: first, 3D printing can be used to validate the complex simulations, and second, the flow models can be used to improve treatment planning for cardiovascular disease. In this review, we summarize and discuss recent methods and findings for leveraging advances in both additive manufacturing and patient-specific computational modeling, with an emphasis on new directions in these fields and remaining open questions.

Non-Newtonian versus numerical rheology: Practical impact of shear-thinning on the prediction of stable and unstable flows in intracranial aneurysms

Computational fluid dynamics (CFD) shows promise for informing treatment planning and rupture risk assessment for intracranial aneurysms. Much attention has been paid to the impact on predicted hemodynamics of various modelling assumptions and uncertainties, including the need for modelling the non-Newtonian, shear-thinning rheology of blood, with equivocal results. Our study clarifies this issue by contextualizing the impact of rheology model against the recently demonstrated impact of CFD solution strategy on the prediction of aneurysm flow instabilities. Three aneurysm cases were considered, spanning a range of stable to unstable flows. Simulations were performed using a high-resolution/accuracy solution strategy with Newtonian and modified-Cross rheology models and compared against results from a so-called normal-resolution strategy. Time-averaged and instantaneous wall shear stress (WSS) distributions, as well as frequency content of flow instabilities and dome-averaged WSS metrics, were minimally affected by the rheology model, whereas numerical solution strategy had a demonstrably more marked impact when the rheology model was fixed. We show that point-wise normalization of non-Newtonian by Newtonian WSS values tended to artificially amplify small differences in WSS of questionable physiological relevance in already-low WSS regions, which might help to explain the disparity of opinions in the aneurysm CFD literature regarding the impact of non-Newtonian rheology. Toward the goal of more patient-specific aneurysm CFD, we conclude that attention seems better spent on solution strategy and other likely "first-order" effects (eg, lumen segmentation and choice of flow rates), as opposed to "second-order" effects such as rheology.

Exploring potential association between flow instability and rupture in patients with matched-pairs of ruptured-unruptured intracranial aneurysms

Background

Patients with multiple intracranial aneurysms present a great challenge to the neurosurgeon, particularly when presenting with subarachnoid hemorrhage. Misjudgment may result in disastrous postoperative rebleeding from the untreated but true-ruptured lesion.

Methods

In this study, computational fluid dynamic simulations of two matched-pairs of ruptured–unruptured cerebral aneurysms were performed to investigate the potential association between flow instability and aneurysm rupture. Two pairs of cerebral aneurysms from two patients were located in the middle cerebral artery and the anterior communicating artery respectively.

Results

Our results demonstrated highly disturbed states of the blood flows in the ruptured aneurysms of the two patients with multiple aneurysms, which are characterized by remarked velocity and wall shear stress (WSS) fluctuations at late systole. The ruptured aneurysms exhibit obviously temporal intra-cycle WSS fluctuations rather than the unruptured aneurysms of the same patient. Cycle-to-cycle fluctuations are further observed in the ruptured aneurysms when the flow turns to decelerate.

Conclusions

The obvious differences observed between matched-pairs of ruptured–unruptured aneurysms imply that flow instability may be a potential source correlating to aneurysm rupture.

Vortex Analysis of Intra-Aneurismal Flow in Cerebral Aneurysms

This study aims to develop an alternative vortex analysis method by measuring structure ofIntracranial aneurysm (IA) flow vortexes across the cardiac cycle, to quantify temporal stability of aneurismal flow. Hemodynamics were modeled in “patient-specific” geometries, using computational fluid dynamics (CFD) simulations. Modified versions of known λ₂ and Q-criterion methods identified vortex regions; then regions were segmented out using the classical marching cube algorithm. Temporal stability was measured by the degree of vortex overlap (DVO) at each step of a cardiac cycle against a cycle-averaged vortex and by the change in number of cores over the cycle. No statistical differences exist in DVO or number of vortex cores between 5 terminal IAs and 5 sidewall IAs. No strong correlation exists between vortex core characteristics and geometric or hemodynamic characteristics of IAs. Statistical independence suggests this proposed method may provide novel IA information. However, threshold values used to determine the vortex core regions and resolution of velocity data influenced analysis outcomes and have to be addressed in future studies. In conclusions, preliminary results show that the proposed methodology may help give novel insight toward aneurismal flow characteristic and help in future risk assessment given more developments.

Multiscale modeling and simulation of brain blood flow

The aim of this work is to present an overview of recent advances in multi-scale modeling of brain blood flow. In particular, we present some approaches that enable the in silico study of multi-scale and multi-physics phenomena in the cerebral vasculature. We discuss the formulation of continuum and atomistic modeling approaches, present a consistent framework for their concurrent coupling, and list some of the challenges that one needs to overcome in achieving a seamless and scalable integration of heterogeneous numerical solvers. The effectiveness of the proposed framework is demonstrated in a realistic case involving modeling the thrombus formation process taking place on the wall of a patient-specific cerebral aneurysm. This highlights the ability of multi-scale algorithms to resolve important biophysical processes that span several spatial and temporal scales, potentially yielding new insight into the key aspects of brain blood flow in health and disease. Finally, we discuss open questions in multi-scale modeling and emerging topics of future research.

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.

Influence of Parent Artery Segmentation and Boundary Conditions on Hemodynamic Characteristics of Intracranial Aneurysms

PURPOSE

The purpose of this study is to explore the influence of segmentation of the upstream and downstream parent artery and hemodynamic boundary conditions (BCs) on the evaluated hemodynamic factors for the computational fluid dynamics (CFD) analysis of intracranial aneurysms.

MATERIALS AND METHODS

Three dimensional patient-specific aneurysm models were analyzed by applying various combinations of inlet and outlet BCs. Hemodynamic factors such as velocity pattern, streamline, wall shear stress, and oscillatory shear index at the systolic time were visualized and compared among the different cases.

RESULTS

Hemodynamic factors were significantly affected by the inlet BCs while there was little influence of the outlet BCs. When the inlet length was relatively short, different inlet BCs showed different hemodynamic factors and the calculated hemodynamic factors were also dependent on the inlet length. However, when the inlet length (L) was long enough (L>20D, where D is the diameter of inlet section), the hemodynamic factors became similar regardless of the inlet BCs and lengths. The error due to different inlet BCs was negligible. The effect of the outlet length on the hemodynamic factors was similar to that of the inlet length.

CONCLUSION

Simulated hemodynamic factors are highly sensitive to inlet BCs and upstream parent artery segmentation. The results of this work can provide an insight into how to build models and to apply BCs for more accurate estimation of hemodynamic factors from CFD simulations of intracranial aneurysms.

FABRICATION OF 3D MILI-SCALE CHANNELS FOR HEMODYNAMIC STUDIES

3D mili-scale channel representing simplified anatomical models of blood vessels were constructed in polidimethylsiloxane (PDMS). The objective was to obtain a sequential method to fabricate transparent PDMS models from a mold produced by rapid prototyping. For this purpose, two types of casting methods were compared, a known lost-wax casting method and a casting method using sucrose. The channels fabricated by both casting methods were analyzed by Optical Microscopy, Scanning Electron Microscopy (SEM), and Energy Dispersive X-ray Spectroscopy (EDS). The lost-wax method is not ideal since the channels become contaminated during the removal process. The models produced with the lost-sucrose casting method exhibit much better optical characteristics. These models are transparent with no visible contamination, since the removing process is done by dissolution at room temperature rather than melting. They allow for good optical access for flow visualization and measurement of the velocity field by micro-Particle Image Velocimetry (μPIV). The channels fabricated by the lost-sucrose casting method were shown to be suitable for future hemodynamic studies using optical techniques.

The 'Sphere': A Dedicated Bifurcation Aneurysm Flow-Diverter Device

We present flow-based results from the early stage design cycle, based on computational modeling, of a prototype flow-diverter device, known as the 'Sphere', intended to treat bifurcation aneurysms of the cerebral vasculature. The device is available in a range of diameters and geometries and is constructed from a single loop of NITINOL^® wire. The 'Sphere' reduces aneurysm inflow by means of a high-density, patterned, elliptical surface that partially occludes the aneurysm neck. The device is secured in the healthy parent vessel by two armatures in the shape of open loops, resulting in negligible disruption of parent or daughter vessel flow. The device is virtually deployed in six anatomically accurate bifurcation aneurysms: three located at the Basilar tip and three located at the terminus bifurcation of the Internal Carotid artery (at the meeting of the middle cerebral and anterior cerebral arteries). Both steady state and transient flow simulations reveal that the device presents with a range of aneurysm inflow reductions, with mean flow reductions falling in the range of 30.6-71.8% across the different geometries. A significant difference is noted between steady state and transient simulations in one geometry, where a zone of flow recirculation is not captured in the steady state simulation. Across all six aneurysms, the device reduces the WSS magnitude within the aneurysm sac, resulting in a hemodynamic environment closer to that of a healthy vessel. We conclude from extensive CFD analysis that the 'Sphere' device offers very significant levels of flow reduction in a number of anatomically accurate aneurysm sizes and locations, with many advantages compared to current clinical cylindrical flow-diverter designs. Analysis of the device's mechanical properties and deployability will follow in future publications.

Mind the gap: impact of computational fluid dynamics solution strategy on prediction of intracranial aneurysm hemodynamics and rupture status indicators

BACKGROUND AND PURPOSE

Computational fluid dynamics has become a popular tool for studying intracranial aneurysm hemodynamics, demonstrating success for retrospectively discriminating rupture status; however, recent highly refined simulations suggest potential deficiencies in solution strategies normally used in the aneurysm computational fluid dynamics literature. The purpose of the present study was to determine the impact of this gap.

MATERIALS AND METHODS

Pulsatile flow in 12 realistic MCA aneurysms was simulated by using both high-resolution and normal-resolution strategies. Velocity fields were compared at selected instants via domain-averaged error. We also compared wall shear stress fields and various reduced hemodynamic indices: cycle-averaged mean and maximum wall shear stress, oscillatory shear index, low shear area, viscous dissipation ratio, and kinetic energy ratio.

RESULTS

Instantaneous differences in flow and wall shear stress patterns were appreciable, especially for bifurcation aneurysms. Linear regressions revealed strong correlations (R(2) > 0.9) between high-resolution and normal-resolution solutions for all indices except kinetic energy ratio (R(2) = 0.25) and oscillatory shear index (R(2) = 0.23); however, for most indices, the slopes were significantly <1, reflecting a pronounced underestimation by the normal-resolution simulations. Some high-resolution simulations were highly unstable, with fluctuating wall shear stresses reflected by the poor oscillatory shear index correlation.

CONCLUSIONS

Typical computational fluid dynamics solution strategies may ultimately be adequate for augmenting rupture risk assessment on the basis of certain highly reduced indices; however, they cannot be relied on for predicting the magnitude and character of the complex biomechanical stimuli to which the aneurysm wall may be exposed. This impact of the computational fluid dynamics solution strategy is likely greater than that for other modeling assumptions or uncertainties.

Mucin covalently bonded to microfibers improves the patency of vascular grafts

Due to high incidence of vascular bypass procedures, an unmet need for suitable vessel replacements exists, especially for small-diameter (<6 mm) vascular grafts. Here, we developed a novel, bilayered, synthetic vascular graft of 1-mm diameter that consisted of a microfibrous luminal layer and a nanofibrous outer layer, which was tailored to possess the same mechanical property as native arteries. We then chemically modified the scaffold with mucin, a glycoprotein lubricant on the surface of epithelial tissues, by either passive adsorption or covalent bonding using the di-amino-poly(ethylene glycol) linker to microfibers. Under static and physiological flow conditions, conjugated mucin was more stable than adsorbed mucin on the surfaces. Mucin could slightly inhibit blood clotting, and mucin coating suppressed platelet adhesion on microfibrous scaffolds. In the rat common carotid artery anastomosis model, grafts with conjugated mucin, but not adsorbed mucin, exhibited excellent patency and higher cell infiltration into the graft walls. Mucin, which can be easily obtained from autologous sources, offers a novel method for improving the hemocompatibility and surface lubrication of vascular grafts and many other implants.

Exploring high frequency temporal fluctuations in the terminal aneurysm of the basilar bifurcation

Cerebral aneurysms are a common cause of death and disability. Of all the cardiovascular diseases, aneurysms are perhaps the most strongly linked with the local fluid mechanic environment. Aside from early in vivo clinical work that hinted at the possibility of high-frequency intra-aneurysmal velocity oscillations, flow in cerebral aneurysms is most often assumed to be laminar. This work investigates, through the use of numerical simulations, the potential for disturbed flow to exist in the terminal aneurysm of the basilar bifurcation. The nature of the disturbed flow is explored using a series of four idealized basilar tip models, and the results supported by four patient specific terminal basilar tip aneurysms. All four idealized models demonstrated instability in the inflow jet through high frequency fluctuations in the velocity and the pressure at approximately 120 Hz. The instability arises through a breakdown of the inflow jet, which begins to oscillate upon entering the aneurysm. The wall shear stress undergoes similar high-frequency oscillations in both magnitude and direction. The neck and dome regions of the aneurysm present 180 deg changes in the direction of the wall shear stress, due to the formation of small recirculation zones near the shear layer of the jet (at the frequency of the inflow jet oscillation) and the oscillation of the impingement zone on the dome of the aneurysm, respectively. Similar results were observed in the patient-specific models, which showed high frequency fluctuations at approximately 112 Hz in two of the four models and oscillations in the magnitude and direction of the wall shear stress. These results demonstrate that there is potential for disturbed laminar unsteady flow in the terminal aneurysm of the basilar bifurcation. The instabilities appear similar to the first instability mode of a free round jet.

Shear-thinning effects of hemodynamics in patient-specific cerebral aneurysms

Two different generalized Newtonian mathematical models for blood flow, derived for the same experimental data, are compared, together with the Newtonian model, in three different anatomically realistic geometries of saccular cerebral aneurysms obtained from rotational CTA. The geometries differ in size of the aneurysm and the existence or not of side branches within the aneurysm. Results show that the differences between the two generalized Newtonian mathematical models are smaller than the differences between these and the Newtonian solution, in both steady and unsteady simulations.

Quantitative comparison of the dynamic flow waveform changes in 12 ruptured and 29 unruptured ICA-ophthalmic artery aneurysms

Introduction

Studies have reported a correlation between blood flow dynamics in the cardiac cycle and vascular diseases, but research to analyze the dynamic changes of flow in cerebral aneurysms is limited. This quantitative study investigates the temporal changes in flow during a cardiac cycle (flow waveform) in different regions of aneurysms and their association with aneurysm rupture.

Methods

Twelve ruptured and 29 unruptured aneurysms from the internal carotid artery–ophthalmic artery segment were studied. Patient-specific aneurysm data were implemented to simulate blood flow. The temporal flow changes at different regions of the aneurysm were recorded to compare the flow waveforms.

Results

In more than 60 % of the cases, peak flow in the aneurysm sac occurred after peak flow in the artery. Flow rate varied among cases and no correlation with rupture, aneurysm flow rate, and aneurysm size was found. Higher pulsatility within aneurysm sacs was found when comparing with the parent artery (P < 0.001). Pulsatility was high throughout ruptured aneurysms, but increased from neck to dome in unruptured ones (P = 0.021). Significant changes between inflow and outflow flow profile were found in unruptured aneurysms (P = 0.023), but not in ruptured aneurysms.

Conclusion

Quantitative analysis which considers temporal blood flow changes appears to provide additional information which is not apparent from aneurysmal flow at a single time point (i.e., peak of systole). By considering the flow waveform throughout the cardiac cycle, statistically significant differences were found between ruptured and unruptured cases — for flow profile, pulsatility and timing of peak flow.

Rheology of human blood plasma: viscoelastic versus Newtonian behavior

We investigate the rheological characteristics of human blood plasma in shear and elongational flows. While we can confirm a Newtonian behavior in shear flow within experimental resolution, we find a viscoelastic behavior of blood plasma in the pure extensional flow of a capillary breakup rheometer. The influence of the viscoelasticity of blood plasma on capillary blood flow is tested in a microfluidic device with a contraction-expansion geometry. Differential pressure measurements revealed that the plasma has a pronounced flow resistance compared to that of pure water. Supplementary measurements indicate that the viscoelasticity of the plasma might even lead to viscoelastic instabilities under certain conditions. Our findings show that the viscoelastic properties of plasma should not be ignored in future studies on blood flow.

Sensitivity to outflow boundary conditions and level of geometry description for a cerebral aneurysm

Mathematical models, namely the flow boundary conditions, as well as the detail of the bounding geometry, can highly influence the computed flow field. In this work, an anatomically realistic portion of cerebral vasculature with a saccular aneurysm, and its geometric idealisation, are considered. The importance of the geometric description, namely including the side branches or modelling them as holes in the main vessel, is studied. Several approaches to prescribe the outflow boundary conditions at the side branches are analysed, including the traction-free condition, zero velocity (hence neglecting the side-branch), and the coupling with simple zero-dimensional and one-dimensional models. Results of the effects of outflow boundary modelling choice on computed haemodynamic parameters are used to identify appropriateness of the models based on the physical interpretation. Estimated range of error-bars associated to outflow boundary model choice and the level of geometric details are presented for patient-specific computational haemodynamics, and can serve as invitation for future studies. The zero-dimensional and one-dimensional models are shown to provide good representations of the side branches in the case of the clipped geometry.

The Murine Angiotensin II-Induced Abdominal Aortic Aneurysm Model: Rupture Risk and Inflammatory Progression Patterns

An abdominal aortic aneurysm (AAA) is an enlargement of the greatest artery in the body defined as an increase in diameter of 1.5-fold. AAAs are common in the elderly population and thousands die each year from their complications. The most commonly used mouse model to study the pathogenesis of AAA is the angiotensin II (Ang II) infusion method delivered via osmotic mini-pump for 28 days. Here, we studied the site-specificity and onset of aortic rupture, characterized three-dimensional (3D) images and flow patterns in developing AAAs by ultrasound imaging, and examined macrophage infiltration in the Ang II model using 65 apolipoprotein E-deficient mice. Aortic rupture occurred in 16 mice (25%) and was nearly as prevalent at the aortic arch (44%) as it was in the suprarenal region (56%) and was most common within the first 7 days after Ang II infusion (12 of 16; 75%). Longitudinal ultrasound screening was found to correlate nicely with histological analysis and AAA volume renderings showed a significant relationship with AAA severity index. Aortic dissection preceded altered flow patterns and macrophage infiltration was a prominent characteristic of developing AAAs. Targeting the inflammatory component of AAA disease with novel therapeutics will hopefully lead to new strategies to attenuate aneurysm growth and aortic rupture.