Computational haemodynamics in two idealised cerebral wide-necked aneurysms after stent placement

Endovascular stents are being commonly used to treat cerebral wide-necked aneurysms recently. The effect of a stent placed in the parent artery is not only to protect the parent artery from occlusion, due to extension of coils and thrombosis, but also to act as flow diverter to vary the haemodynamics in the aneurysm. In this article, two idealised cerebral wide-necked aneurysms were created, one was sidewall aneurysm with curved parent vessel and the other was terminal aneurysm with the bifurcated parent vessel. The plexiglass models of the two aneurysms were 'treated' with commercial porous intravascular stents. The stented physical models were scanned by Micro-CT and the numerical models of the two idealised cerebral wide-necked aneurysms after stent placement were constructed from the scanned image files. The pulsatile flow of non-Newtonian fluid inside the models was simulated by using computational fluid dynamics package. From the simulated flow dynamics, various haemodynamic characteristics such as velocity contours, wall shear stress and oscillatory shear index (OSI) were computed. The velocity of the jet entering the sacs reduced after stent was deployed across the necks of both sidewall and terminal aneurysms; the wall shear stress on the distal neck of sidewall aneurysm reduced, the wall shear stress on the dome of the terminal aneurysm increased and the OSI on the dome of the terminal aneurysm reduced. Therefore, stent placement not only promotes thrombus formation in both aneurysm models but also reduces the regrowth risk of the sidewall aneurysm and the rupture risk of the terminal aneurysm.     

Computational haemodynamics in two idealised cerebral wide-necked aneurysms after stent placement

Endovascular stents are being commonly used to treat cerebral wide-necked aneurysms recently. The effect of a stent placed in the parent artery is not only to protect the parent artery from occlusion, due to extension of coils and thrombosis, but also to act as flow diverter to vary the haemodynamics in the aneurysm. In this article, two idealised cerebral wide-necked aneurysms were created, one was sidewall aneurysm with curved parent vessel and the other was terminal aneurysm with the bifurcated parent vessel. The plexiglass models of the two aneurysms were ‘treated’ with commercial porous intravascular stents. The stented physical models were scanned by Micro-CT and the numerical models of the two idealised cerebral wide-necked aneurysms after stent placement were constructed from the scanned image files. The pulsatile flow of non-Newtonian fluid inside the models was simulated by using computational fluid dynamics package. From the simulated flow dynamics, various haemodynamic characteristics such as velocity contours, wall shear stress and oscillatory shear index (OSI) were computed. The velocity of the jet entering the sacs reduced after stent was deployed across the necks of both sidewall and terminal aneurysms; the wall shear stress on the distal neck of sidewall aneurysm reduced, the wall shear stress on the dome of the terminal aneurysm increased and the OSI on the dome of the terminal aneurysm reduced. Therefore, stent placement not only promotes thrombus formation in both aneurysm models but also reduces the regrowth risk of the sidewall aneurysm and the rupture risk of the terminal aneurysm.     

Influence of inlet boundary conditions on the local haemodynamics of intracranial aneurysms

Haemodynamics is believed to play an important role in the initiation, growth and rupture of intracranial aneurysms. In this context, computational haemodynamics has been extensively used in an effort to establish correlations between flow variables and clinical outcome. It is common practice in the application of Dirichlet boundary conditions at domain inlets to specify transient velocities as either a flat (plug) profile or a spatially developed profile based on Womersley's analytical solution. This paper provides comparative haemodynamics measures for three typical cerebral aneurysms.

Three dimentional rotational angiography images of aneurysms at three common locations, viz. basilar artery tip, internal carotid artery and middle cerebral artery were obtained. The computational tools being developed in the European project @neurIST were used to reconstruct the fluid domains and solve the unsteady Navier–Stokes equations, using in turn Womersley and plug-flow inlet velocity profiles. The effects of these assumptions were analysed and compared in terms of relevant haemodynamic variables within the aneurismal sac. For the aneurysm at the basilar tip geometries with different extensions of the afferent vasculature were considered to study the plausibility of a fully-developed axial flow at the inlet boundaries.

The study shows that assumptions made on the velocity profile while specifying inlet boundary conditions have little influence on the local haemodynamics in the aneurysm, provided that a sufficient extension of the afferent vasculature is considered and that geometry is the primary determinant of the flow field within the aneurismal sac. For real geometries the Womersley profile is at best an unnecessary over-complication, and may even be worse than the plug profile in some anatomical locations (e.g. basilar confluence).     

Stability of pulsatile blood flow at the ostium of cerebral aneurysms

The strength and direction of blood flow into and within a cerebral aneurysm are important issues in developing effective interventional strategies to stabilize the aneurysm. We tested the hypothesis that there are significant major hemodynamic features that are common to many aneurysm flows of the type studied here. This was investigated by performing computational fluid dynamic simulations of flow near 7 cerebral aneurysms using geometrical data obtained from clinical CT scans. Our numerical simulations of flow across the ostium plane of an aneurysm show that in many cases there is relatively stable flow structure that is maintained over the phase of the pulsatile flow cycle. The two main features of this flow are (1) quasi-permanent regions of flow influx and efflux across the ostium plane exist, separated by a “virtual boundary”, and (2) a helical vortex flow pattern within the aneurismal sac with swirl in two orthogonal cross-sectional planes. These numerical observations are consistent with in vitro experimental data from ultrasound color-Doppler velocimetry and other numerical and experimental studies. The observed flow patterns are found to occur in different types of aneurysms (bifurcation and sidewall), and can persist even after flow parameters are perturbed beyond the normal range of physiological flow conditions. These results suggest that in many cases, major aspects of the behavior of aneurismal hemodynamics for important classes of aneurysms can be learned from an analysis of steady, non-pulsatile flow, which is simpler and faster to simulate than time-dependent, pulsatile flow. An understanding of this fluid dynamical behavior may also prove useful in the design of stents, coils, and various other endovascular flow diverting devices.     

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

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

Biomechanical behaviour of cerebral aneurysm and its relation with the formation of intraluminal thrombus: a patient-specific modelling study

Cerebral aneurysm is an irreversible dilatation causing intracranial haemorrhage with severe complications. It is assumed that the biomechanical factor plays a significant role in the development of cerebral aneurysm. However, reports on the correlations between the formation of intraluminal thrombus and the flow pattern, wall shear stress (WSS) distribution of the cerebral aneurysm as well as wall compliance are still limited. In this research, patient-specific numerical simulation was carried out for three cerebral aneurysms based on magnetic resonance imaging (MRI) data-sets. The interaction between pulsatile blood and aneurysm wall was taken into account. The biomechanical behaviour of cerebral aneurysm and its relation with the formation of intraluminal thrombus was studied systematically. The results of the numerical simulation indicated that the region of low blood flow velocity and the region of swirling recirculation were nearly coincident with each other. Besides, there was a significant correlation between the slow swirling flow and the location of thrombus deposition. Excessively low WSS was also found to have strong association with the regions of thrombus formation. Moreover, the relationship between cerebral aneurysm compliance and thrombus deposition was discovered. The patient-specific modelling study based on fluid–structure interaction) may provide a basis for future investigation on the prediction of thrombus formation in cerebral aneurysm.     

A Patient-Specific Computational Fluid Dynamic Model of Middle Cerebral Artery Aneurysm Before and One Year After Surgery

Computational fluid dynamics (CFD) has been widely used for studying intracranial aneurysm hemodynamics, while its use for guiding clinical strategy is still in development. In this study, CFD simulations helped inform treatment decision for a middle cerebral artery (MCA) aneurysm case was investigated. A patient with a 10.4 × 9.8 mm aneurysm attached with a small aneurysm at the edge of the trifurcation in the left MCA was included in this study. For removing the MCA aneurysm, two scenarios were considered: Plan-A involved clipping the small aneurysm and Plan-B involved clipping the whole aneurysm. A suitable treatment plan was decided by comparing the clinical measurements and CFD analysis between these two plans. One-year after the surgery, the CFD analysis was conducted again on the post-operative aneurysm model to verify the selected surgical plan in terms of morphometric and hemodynamic properties changes in the aneurysm. Based on the CFD simulation and clinical experience, surgical Plan-A was adopted. One-year after the surgery, both the hemodynamic and morphological properties improved in the post-operative aneurysm model, indicating the recovery of the patient. The patient-specific aneurysm CFD analysis can help to determine a better surgical plan for patients with special cerebral aneurysms. This study showed how CFD analysis can be used to aid clinical diagnosis and treatment.     

犬囊状动脉瘤模型的制作

本文报道用“静脉囊镶嵌技术·制成犬的囊状动脉瘤模型。18个模型(6个单侧型,6个分叉型,6个末梢型)造型后2周经IA DSA检查。本模型在分型、血流动力学改变方面与人类囊状脑动脉瘤类似。不同类型的动脉瘤模型既有相同的血流动力学特征,又有各自的特点,这与动脉瘤与载瘤动脉的角度有关。我们认为该模型可应用于研究动脉瘤的血流动力学与血管内栓塞治疗。     

Blood flow dynamics in saccular aneurysm models of the basilar artery

Blood flow dynamics under physiologically realistic pulsatile conditions plays an important role in the growth, rupture, and surgical treatment of intracranial aneurysms. The temporal and spatial variations of wall pressure and wall shear stress in the aneurysm are hypothesized to be correlated with its continuous expansion and eventual rupture. In addition, the assessment of the velocity field in the aneurysm dome and neck is important for the correct placement of endovascular coils. This paper describes the flow dynamics in two representative models of a terminal aneurysm of the basilar artery under Newtonian and non-Newtonian fluid assumptions, and compares their hemodynamics with that of a healthy basilar artery. Virtual aneurysm models are investigated numerically, with geometric features defined by beta = 0 deg and beta = 23.2 deg, where beta is the tilt angle of the aneurysm dome with respect to the basilar artery. The intra-aneurysmal pulsatile flow shows complex ring vortex structures for beta = 0 deg and single recirculation regions for beta = 23.2 deg during both systole and diastole. The pressure and shear stress on the aneurysm wall exhibit large temporal and spatial variations for both models. When compared to a non-Newtonian fluid, the symmetric aneurysm model (beta = 0 deg) exhibits a more unstable Newtonian flow dynamics, although with a lower peak wall shear stress than the asymmetric model (beta = 23.2 deg). The non-Newtonian fluid assumption yields more stable flows than a Newtonian fluid, for the same inlet flow rate. Both fluid modeling assumptions, however, lead to asymmetric oscillatory flows inside the aneurysm dome.     

Mathematical models of the flow in the basilar artery

The flow in the basilar artery arises from the merging of the flows from the two vertebral arteries. This study deals with the question whether a parabolic (Poiseuille) profile will have been established before the basilar artery divides into both posterior cerebral arteries. The inlet length (that is, the downstream distance needed for the flow to become approximately equal to the limiting Poiseuille flow) and velocity profiles have been computed from two- and three-dimensional mathematical models in which flow pulsatility and vessel wall distensibility have been neglected and the complex geometry of the junction has been taken into account in a simplified form. The results show that the flow at the end of the basilar artery is far from being parabolic and that an asymmetry in the entrance flow will be carried along towards the end of the basilar artery, thus affecting flows in the circle of Willis.     

Residence times and basins of attraction for a realistic right internal carotid artery with two aneurysms

We are presenting computational fluid dynamics simulation results for the flow in an anatomically accurate right internal carotid artery, exhibiting two saccular aneurysms close to each other. Our study focuses on the investigation of passage times for blood cells through the two-aneurysm malformation. We construct residence time maps that exhibit strong non-uniformity, linked to the entry of fluid in only the first, only the second, or in both aneurysms. An entrance index is computed, showing qualitatively the regions at an arterial section upstream of the aneurysms, where cells following one of these scenarios emanate. The significance of the residence time profiles and entry scenarios obtained is discussed with respect to thrombosis and pharmacokinetics. Preliminary evidence that the inflow-outflow patterns of the two aneurysms may be leading to particularly complex flow and to chaotic mixing is discussed.     

Slowness of blood flow and resultant thrombus formation in cerebral aneurysms

It is not yet fully understood what causes cerebral aneurysms to rupture. Although no definitive conclusion has been reached, it is considered that there are haemodynamic, biochemical and physiological factors contributing to rupture. Numerical techniques seem promising for investigation of this multi-physical phenomenon. In fact, recent intensive numerical studies with computational fluid dynamics have revealed detailed haemodynamic features of the flow in cerebral aneurysms such as velocity, pressure and wall shear stress distributions. It is, therefore, expected that biochemical and physiological aspects of aneurysmal rupture will also be actively investigated using numerical approaches. Considering this background, the authors have been working on modelling of thrombus formation in cerebral aneurysms caused by stagnant blood flow, because many studies have suggested that slow blood flow and resulting low wall shear stress are connected with rupture. Firstly, in this review paper, slowness of the intra-aneurysmal flow is reviewed with an energy balance theory, and secondly, thrombus formation in cerebral bifurcation aneurysms is discussed from the viewpoint of numerical modelling. A computational result obtained by application of the authors’ platelet aggregation–adhesion model is also provided.     

Posterior Cerebral Artery Angle and the Rupture of Basilar Tip Aneurysms

Since the initial publication of the International Study of Unruptured Intracranial Aneurysms (ISUIA), management of unruptured intracranial aneurysms has been mainly based on the size of the aneurysm. The contribution of morphological characteristics to treatment decisions of unruptured aneurysms has not been well studied in a systematic and location specific manner. We present a large sample of basilar artery tip aneurysms (BTA) that were assessed using a diverse array of morphological variables to determine the parameters associated with ruptured aneurysms. Demographic and clinical risk factors of aneurysm rupture were obtained from chart review. CT angiograms (CTA) were evaluated with Slicer, an open source visualization and image analysis software, to generate 3-D models of the aneurysms and surrounding vascular architecture. Morphological parameters examined in each model included aneurysm volume, aspect ratio, size ratio, aneurysm angle, basilar vessel angle, basilar flow angle, and vessel to vessel angles. Univariate and multivariate analyses were performed to determine statistical significance. From 2008–2013, 54 patients with BTA aneurysms were evaluated in a single institution, and CTAs from 33 patients (15 ruptured, 18 unruptured) were available and analyzed. Aneurysms that underwent reoperation, that were associated with arteriovenous malformations, or that lacked preoperative CTA were excluded. Multivariate logistic regression revealed that a larger angle between the posterior cerebral arteries (P1-P1 angle, p = 0.037) was most strongly associated with aneurysm rupture after adjusting for other morphological variables. In this location specific study of BTA aneurysms, the larger the angle formed between posterior cerebral arteries was found to be a new morphological parameter significantly associated with ruptured BTA aneurysms. This is a physically intuitive parameter that can be measured easily and readily applied in the clinical setting.     

Reproducibility of haemodynamical simulations in a subject-specific stented aneurysm model--a report on the Virtual Intracranial Stenting Challenge 2007

This paper presents the results of the Virtual Intracranial Stenting Challenge (VISC) 2007, an international initiative whose aim was to establish the reproducibility of state-of-the-art haemodynamical simulation techniques in subject-specific stented models of intracranial aneurysms (IAs). IAs are pathological dilatations of the cerebral artery walls, which are associated with high mortality and morbidity rates due to subarachnoid haemorrhage following rupture. The deployment of a stent as flow diverter has recently been indicated as a promising treatment option, which has the potential to protect the aneurysm by reducing the action of haemodynamical forces and facilitating aneurysm thrombosis. The direct assessment of changes in aneurysm haemodynamics after stent deployment is hampered by limitations in existing imaging techniques and currently requires resorting to numerical simulations. Numerical simulations also have the potential to assist in the personalized selection of an optimal stent design prior to intervention. However, from the current literature it is difficult to assess the level of technological advancement and the reproducibility of haemodynamical predictions in stented patient-specific models. The VISC 2007 initiative engaged in the development of a multicentre-controlled benchmark to analyse differences induced by diverse grid generation and computational fluid dynamics (CFD) technologies. The challenge also represented an opportunity to provide a survey of available technologies currently adopted by international teams from both academic and industrial institutions for constructing computational models of stented aneurysms. The results demonstrate the ability of current strategies in consistently quantifying the performance of three commercial intracranial stents, and contribute to reinforce the confidence in haemodynamical simulation, thus taking a step forward towards the introduction of simulation tools to support diagnostics and interventional planning.     

Image-based modeling of hemodynamics in coronary artery aneurysms caused by Kawasaki disease

Kawasaki Disease (KD) is the leading cause of acquired pediatric heart disease. A subset of KD patients develops aneurysms in the coronary arteries, leading to increased risk of thrombosis and myocardial infarction. Currently, there are limited clinical data to guide the management of these patients, and the hemodynamic effects of these aneurysms are unknown. We applied patient-specific modeling to systematically quantify hemodynamics and wall shear stress in coronary arteries with aneurysms caused by KD. We modeled the hemodynamics in the aneurysms using anatomic data obtained by multi-detector computed tomography (CT) in a 10-year-old male subject who suffered KD at age 3?years. The altered hemodynamics were compared to that of a reconstructed normal coronary anatomy using our subject as the model. Computer simulations using a robust finite element framework were used to quantify time-varying shear stresses and particle trajectories in the coronary arteries. We accounted for the cardiac contractility and the microcirculation using physiologic downstream boundary conditions. The presence of aneurysms in the proximal coronary artery leads to flow recirculation, reduced wall shear stress within the aneurysm, and high wall shear stress gradients at the neck of the aneurysm. The wall shear stress in the KD subject (2.95-3.81 dynes/sq cm) was an order of magnitude lower than the normal control model (17.10-27.15 dynes/sq cm). Particle residence times were significantly higher, taking 5 cardiac cycles to fully clear from the aneurysmal regions in the KD subject compared to only 1.3 cardiac cycles from the corresponding regions of the normal model. In this novel quantitative study of hemodynamics in coronary aneurysms caused by KD, we documented markedly abnormal flow patterns that are associated with increased risk of thrombosis. This methodology has the potential to provide further insights into the effects of aneurysms in KD and to help risk stratify patients for appropriate medical and surgical interventions.     

Contribution of the vertebral artery to cerebral circulation in the rat snake Elaphe obsoleta

Blood supplying the brain in vertebrates is carried primarily by the carotid vasculature. In most mammals, cerebral blood flow is supplemented by the vertebral arteries, which anastomose with the carotids at the base of the brain. In other tetrapods, cerebral blood is generally believed to be supplied exclusively by the carotid vasculature, and the vertebral arteries are usually described as disappearing into the dorsal musculature between the heart and head. There have been several reports of a vertebral artery connection with the cephalic vasculature in snakes. We measured regional blood flows using fluorescently labeled microspheres and demonstrated that the vertebral artery contributes a small but significant fraction of cerebral blood flow (∼13% of total) in the rat snake Elaphe obsoleta. Vascular casts of the anterior vessels revealed that the vertebral artery connection is indirect, through multiple anastomoses with the inferior spinal artery, which connects with the carotid vasculature near the base of the skull. Using digital subtraction angiography, fluoroscopy, and direct observations of flow in isolated vessels, we confirmed that blood in the inferior spinal artery flows craniad from a point anterior to the vertebral artery connections. Such collateral blood supply could potentially contribute to the maintenance of cerebral circulation during circumstances when craniad blood flow is compromised, e.g., during the gravitational stress of climbing. J. Morphol. 238:39–51, 1998. © 1998 Wiley-Liss, Inc.     

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.     

Continuous monitoring of absolute cerebral blood flow by near-infrared spectroscopy during global and focal temporary vessel occlusion

Treatment of intracranial aneurysms by surgical clipping carries a risk of intraoperative ischemia, caused mainly by prolonged temporary occlusion of cerebral arteries. The objective of this study was to develop a near-infrared spectroscopy (NIRS) technique for continuous monitoring of cerebral blood flow (CBF) during surgery. With this approach, cerebral hemodynamics prior to clipping are measured by a bolus-tracking method that uses indocyanine green as an intravascular contrast agent. The baseline hemodynamic measurements are then used to convert the continuous Hb difference (HbD) signal (HbD = oxyhemoglobin - deoxyhemoglobin) acquired during vessel occlusion to units of CBF. To validate the approach, HbD signal changes, along with the corresponding CBF changes, were measured in pigs following occlusion of the common carotid arteries or a middle cerebral artery. For both occlusion models, the predicted CBF change derived from the HbD signal strongly correlated with the measured change in CBF. Linear regression of the predicted and measured CBF changes resulted in a slope of 0.962 (R(2) = 0.909) following carotid occlusion and 0.939 (R(2) = 0.907) following middle cerebral artery occlusion. These results suggest that calibrating the HbD signal by baseline hemodynamic measurements provides a clinically feasible method of monitoring CBF changes during neurosurgery.     

Tandem aneurysms of an internal mammary-aortocoronary bypass graft

Graft aneurysms following aortocoronary surgery are a rare occurrence in clinical practice. Reported cases have mostly involved saphenous vein grafts. Here we report the rare finding of a tandem aneurysm of an internal mammary artery graft which was incidentally detected 17 years following bypass surgery. (Neth Heart J 2009;17:300–2.)     

Wall shear stress at the initiation site of cerebral aneurysms

Hemodynamics are believed to play an important role in the initiation of cerebral aneurysms. In particular, studies have focused on wall shear stress (WSS), which is a key regulator of vascular biology and pathology. In line with the observation that aneurysms predominantly occur at regions of high WSS, such as bifurcation apices or outer walls of vascular bends, correlations have been found between the aneurysm initiation site and high WSS. The aim of our study was to analyze the WSS field at an aneurysm initiation site that was neither a bifurcation apex nor the outer wall of a vascular bend. Ten cases with aneurysms on the A1 segment of the anterior cerebral artery were analyzed and compared with ten controls. Aneurysms were virtually removed from the vascular models of the cases to mimic the pre-aneurysm geometry. Computational fluid dynamics (CFD) simulations were created to assess the magnitude, gradient, multidirectionality, and pulsatility of the WSS. To aid the inter-subject comparison of hemodynamic variables, we mapped the branch surfaces onto a two-dimensional parametric space. This approach made it possible to view the whole branch at once for qualitative evaluation. It also allowed us to empirically define a patch for quantitative analysis, which was consistent among subjects and encapsulated the aneurysm initiation sites in our dataset. To test the sensitivity of our results, CFD simulations were repeated with a second independent observer virtually removing the aneurysms and with a 20 % higher flow rate at the inlet. We found that branches harboring aneurysms were characterized by high WSS and high WSS gradients. Among all assessed variables, the aneurysm initiation site most consistently coincided with peaks of temporal variation in the WSS magnitude.