Computational modelling of emboli travel trajectories in cerebral arteries: influence of microembolic particle size and density

Ischaemic stroke is responsible for up to 80 % of stroke cases. Prevention of the reoccurrence of ischaemic attack or stroke for patients who survived the first symptoms is the major treatment target. Accurate diagnosis of the emboli source for a specific infarction lesion is very important for a better treatment for the patient. However, due to the complex blood flow patterns in the cerebral arterial network, little is known so far of the embolic particle flow trajectory and its behaviour in such a complex flow field. The present study aims to study the trajectories of embolic particles released from carotid arteries and basilar artery in a cerebral arterial network and the influence of particle size, mass and release location to the particle distributions, by computational modelling. The cerebral arterial network model, which includes major arteries in the circle of Willis and several generations of branches from them, was generated from MRI images. Particles with diameters of 200, 500 and 800  $\upmu \hbox {m}$ and densities of 800, 1,030 and 1,300 $\hbox {kg/m}^{3}$ were released in the vessel’s central and near-wall regions. A fully coupled scheme of particle and blood flow in a computational fluid dynamics software ANASYS CFX 13 was used in the simulations. The results show that heavy particles (density large than blood or a diameter larger than 500  $\upmu \hbox {m}$ ) normally have small travel speeds in arteries; larger or lighter embolic particles are more likely to travel to large branches in cerebral arteries. In certain cases, all large particles go to the middle cerebral arteries; large particles with higher travel speeds in large arteries are likely to travel at more complex and tortuous trajectories; emboli raised from the basilar artery will only exit the model from branches of basilar artery and posterior cerebral arteries. A modified Circle of Willis configuration can have significant influence on particle distributions. The local branch patterns of internal carotid artery to middle cerebral artery and anterior communicating artery can have large impact on such distributions.     

The variability of the circle of Willis: univariate and bivariate analysis

The results are presented of a statistical analysis of the variability of the circle of Willis using univariate and bivariate methods. For this purpose 100 circles of Willis were available. From each circle 19 indexes of arterial size were determined, the basilar artery was measured in two places. Half the circumference was measured. This data yielded no evidence of differences between left- and right-sided vessels in the sample. An important source of variation is the general size of all vessels considered. When the data are cleared from this general size variation, correlation coefficients reveal interesting relations between the vessels. The posterior communicating arteries are strongly related to the ipsilateral carotid artery, whereas a strong inverse relationship exists with the basilar artery and the precommunicating part of the ipsilateral posterior cerebral artery. These relationships can be understood from the expected patterns of the blood flow in these vessels. Similar relationships can be found in the anterior part of the circle of Willis and in the vertebro-basilar junction. In a different manner, based on previous haemodynamic studies, the relation between blood flow and vessel size within the circle of Willis can be demonstrated by relating the ratios of the sizes of afferent and efferent arteries to the sizes of the posterior communicating arteries, an "intuitive" model. The supposed correlations of the outcome of this "intuitive" model with the size of the communicating arteries appeared to by highly significant. It is concluded that the variations of the circle of Willis are related to the individual variations of the blood flow in this arterial network.     

One-dimensional and three-dimensional models of cerebrovascular flow

The Circle of Willis is a ring-like structure of blood vessels found beneath the hypothalamus at the base of the brain. Its main function is to distribute oxygen-rich arterial blood to the cerebral mass. One-dimensional (1D) and three-dimensional (3D) computational fluid dynamics (CFD) models of the Circle of Willis have been created to provide a simulation tool which can potentially be used to identify at-risk cerebral arterial geometries and conditions and replicate clinical scenarios, such as occlusions in afferent arteries and absent circulus vessels. Both models capture cerebral haemodynamic autoregulation using a proportional-integral (PI) controller to modify efferent artery resistances to maintain optimal efferent flow rates for a given circle geometry and afferent blood pressure. The models can be used to identify at-risk cerebral arterial geometries and conditions prior to surgery or other clinical procedures. The 1D model is particularly relevant in this instance, with its fast solution time suitable for real-time clinical decisions. Results show the excellent correlation between models for the transient efferent flux profile. The assumption of strictly Poiseuille flow in the 1D model allows more flow through the geometrically extreme communicating arteries than the 3D model. This discrepancy was overcome by increasing the resistance to flow in the anterior communicating artery in the 1D model to better match the resistance seen in the 3D results.     

基于集中参数模型的脑血管疾病数值模拟

脑血管疾病的血流动力研究一直是和脑血管疾病的预防和诊断密切相关的,由于脑部血流循环是一个四端输入的网络,其复杂性导致它的血液动力学规律和体循环有着本质的差别,讨论脑循环这模型和临床应用有着重要的意义,本文使用集中参数模型来模拟三种常见的脑血管疾病;脑动脉硬化,脑梗塞,锁骨下动脉盗血,考察其对相应脑血管的压力和流量的影响,结果显示脑部血液循环的代偿功能在发病情况下的重要作用,本文通过分析数值模拟结果,对不同疾病的血液动力学特征进行研究,给脑血管疾病的临床诊断提供血液动力学方面的参考。     

Numerical simulations of the blood flow in the patient-specific arterial cerebral circle region

The Cerebral Circle Region, also known as the Circle of Willis (CoW), is a loop of arteries that form arterial connections between supply arteries to distribute blood throughout the cerebral mass. Among the population, only 25% to 50% have a complete system of arteries forming the CoW. 3D time-varying simulations for three different patient-specific artery anatomies of CoW were performed in order to gain a better insight into the phenomena existing in the cerebral blood flow. The models reconstructed on the basis of computer tomography images start from the aorta and include the largest arteries that supply the CoW and the arteries of CoW. Velocity values measured during the ultrasound examination have been compared with the results of simulations. It is shown that the flow in the right anterior artery in some cases may be supplied from the left internal carotid artery via the anterior communicating artery. The investigations conducted show that the computational fluid dynamic tool, which provides high resolution in both time and space domains, can be used to support physicians in diagnosing patients of different ages and various anatomical arterial structures.     

Pathway of nerves with vasoactive intestinal polypeptide-like immunoreactivity to the major cerebral arteries of the rat

Summary The pathway of nerves with vasoactive intestinal polypeptide(VIP)-like immunoreactivity to the major cerebral arteries was studied in rats by means of the indirect immunofluorescent method. The fibers are densely distributed in the ethmoidal nerves and in the adventitia of both the external and internal ethmoidal arteries. Section of both ethmoidal nerves and external ethmoidal arteries before they enter the cranial cavity induced a marked reduction of VIP-like immunoreactive fibers in the walls of the vessels of the circle of Willis and its major branches. However, section of the external ethmoidal artery alone did not result in visible changes of the nerves around major cerebral arteries. The present study suggests that VIP-like immunoreactive fibers surrounding major cerebral arteries of the rat arise from fibers in the ethmoidal nerve showing immunoreactivity to VIP.     

Thalamic arterial pattern: an endocast and scanning electron microscopic study in normotensive male rats

Rat cerebral vasculature serves as a model for study of the pathophysiology of stroke in humans. Human thalamic arteries show a high incidence of stroke. The objective is to describe the thalamic arterial vascular pattern in normotensive male rats as the initial step for quantitative histochemical studies of enzyme activities in the walls of these vessels. Intracardiac injections of methyl methacrylate monomer provide detailed vascular endocasts. The thalamic vascular bed defined by in situ dissection, serial reconstruction, and light and scanning electron microscopy of endocasts contained four groups of vessel: ventral medial thalamic arteries, thalamic branches from the posterior cerebral artery, and ventral lateral and ventral anterior thalamic arteries. Thalamic vessels are muscular arterioles that, after three to four bipinnate branches, feed into a continuous capillary bed (no loops). The parent vessels and their subsequent branches have been evaluated in terms of their mean internal diameters, mean interbranch intervals, and branch angles. The arterial patterns to rat and human thalami are very similar, with the exception of the anterior choroidal artery which is missing in the rat. The branches supplying the thalamus in both the rat and human are closely associated with the circle of Willis; however, the constituent parts of the circle in rat vary from the pattern in human brain. The rat thalamic arteries show morphological features similar to those seen in the stroke-prone ganglionic arteries in the human basal ganglia.     

The variability of the circulus arteriosus (Willisii): order or anarchy?

The variation of the circulus arteriosus is studied using multivariate methods. The data which form the basis of this study are 19 measurements of half the circumference of the arteries that form the circle of Willis and its afferent and efferent branches; 100 circles of Willis were measured for this purpose. Since the number of variables per individual is large, multivariate statistical techniques are the most appropriate method to gain insight in the relations of vessel sizes that exist within the circle of Willis. So a principal component analysis was performed on the data. The results clearly show a number of relations between vessel sizes. In general, inverse relationships were found of vessels that have (at least partially) an identical irrigation area: both internal carotid arteries and the ipsilateral posterior communicating artery show an intimate relationship and are together inversely related to the basilar artery and the precommunicating part of the posterior cerebral artery. Inverse relationships are also found for both vertebral arteries and both precommunicating parts of the anterior cerebral arteries. The homonymous efferent arteries appear to be closely related and show an independent variation. Together the first six principal components explain 69% of the variance. These results support a haemodynamical hypothesis on the explanation of the variability of the circle of Willis. Moreover, the differential growth in the head-neck region during the first two decades of life is postulated to be the origin of a part of the variation.     

Lumped parameter and feedback control models of the auto-regulatory response in the Circle of Willis

The Circle of Willis (CoW) is a ring-like structure of blood vessels found beneath the hypothalamus at the base of the brain. Its main function is to distribute oxygen-rich arterial blood to the cerebral mass. A 1-dimensional model of the CoW has been created to simulate a series of possible clinical scenarios such as occlusions in afferent arteries, absent or string-like circulus vessels, or arterial infarctions. The model captures cerebral haemodynamic auto-regulation by using a proportional-integral-derivative (PID) controller to modify efferent resistances and maintain optimal efferent flowrates for a given circle geometry and afferent blood pressure. Results match limited clinical data and results obtained in prior studies to within 6%. In addition, a set of boundary conditions and geometry is presented for which the auto-regulated system cannot provide the necessary efferent flowrates and perfusion, representing a condition with increased risk of stroke and highlighting the importance of modelling the haemodynamics of the CoW. The system model created is computationally simple so it can be used to identify at-risk cerebral arterial geometries and conditions prior to surgery or other clinical procedures.     

Lumped Parameter and Feedback Control Models of the Auto-regulatory Response in the Circle of Willis

The Circle of Willis (CoW) is a ring-like structure of blood vessels found beneath the hypothalamus at the base of the brain. Its main function is to distribute oxygen-rich arterial blood to the cerebral mass. A 1-dimensional model of the CoW has been created to simulate a series of possible clinical scenarios such as occlusions in afferent arteries, absent or string-like circulus vessels, or arterial infarctions. The model captures cerebral haemodynamic auto-regulation by using a proportional-integral-derivative (PID) controller to modify efferent resistances and maintain optimal efferent flowrates for a given circle geometry and afferent blood pressure. Results match limited clinical data and results obtained in prior studies to within 6%. In addition, a set of boundary conditions and geometry is presented for which the auto-regulated system cannot provide the necessary efferent flowrates and perfusion, representing a condition with increased risk of stroke and highlighting the importance of modelling the haemodynamics of the CoW. The system model created is computationally simple so it can be used to identify at-risk cerebral arterial geometries and conditions prior to surgery or other clinical procedures.     

Hemodynamic role of the circle of Willis in stenoses of internal carotid arteries. An analytical solution of a linear model

A mathematical model of blood flow through the circle of Willis was developed, within a linear framework. Comprehensive analytical solutions, including a remarkably small number of parameters, were derived in the cases of obstructive lesions of extracranial carotid arteries. The influence of these lesions and the role of anterior and posterior communicating arteries on the blood pressure at the entry of the cerebral territories were quantified and analyzed emphasizing that the responses of the system of Willis to obstructive carotid lesions are extremely varied, depending on the communicating artery anatomy. Comparison with numerical results obtained by using a non-linear model showed no physiologically significant differences. Such a model might be an essential tool for an accurate assessment of the cerebral hemodynamics in carotid diseases.     

On the subclavian steal syndrome in vitro studies.

An elastic model of the arterial system has been used in which a specially designed pumping unit simulated the heart action. Physiological pressures and normal geometry, size, and flow distribution together with the normal cardiac output and use of prosthetic heart valves are the features of the system. Atherosclerosis was simulated by introducing blockages of known cross-section at specific sites of predilection. It has been shown that, for some specific occlusion magnitude in the left or right subclavian, or in the brachycephalic arteries, the stagnant no blood flow condition will appear in the left vertebral, or the right vertebral, or right common carotid, or the right internal carotid arteries. For larger occlusions the blood flow in these arteries reverses its direction, i.e., the "steal syndrome" appears. It is shown that besides the known single steal syndrome there exists also a double steal syndrome, i.e., blood reverses its flow direction simultaneously in two arteries, both on the right side of the arterial system. This blood is taken from the circle of Willis, which at the same time is significantly supplemented by the increased blood flow through the other arteries leading into the circle of Willis.     

Three-dimensional hemodynamics analysis of the circle of Willis in the patient-specific nonintegral arterial structures

The hemodynamic alteration in the cerebral circulation caused by the geometric variations in the cerebral circulation arterial network of the circle of Wills (CoW) can lead to fatal ischemic attacks in the brain. The geometric variations due to impairment in the arterial network result in incomplete cerebral arterial structure of CoW and inadequate blood supply to the brain. Therefore, it is of great importance to understand the hemodynamics of the CoW, for efficiently and precisely evaluating the status of blood supply to the brain. In this paper, three-dimensional computational fluid dynamics of the main CoW vasculature coupled with zero-dimensional lumped parameter model boundary condition for the CoW outflow boundaries is developed for analysis of the blood flow distribution in the incomplete CoW cerebral arterial structures. The geometric models in our study cover the arterial segments from the aorta to the cerebral arteries, which can allow us to take into account the innate patient-specific resistance of the arterial trees. Numerical simulations of the governing fluid mechanics are performed to determine the CoW arterial structural hemodynamics, for illustrating the redistribution of the blood flow in CoW due to the structural variations. We have evaluated our coupling methodology in five patient-specific cases that were diagnosed with the absence of efferent vessels or impairment in the connective arteries in their CoWs. The velocity profiles calculated by our approach in the segments of the patient-specific arterial structures are found to be very close to the Doppler ultrasound measurements. The accuracy and consistency of our hemodynamic results have been improved (to \(16.1 \pm 18.5\) %) compared to that of the pure-resistance boundary conditions (of 43.5 \(\pm \) 28 %). Based on our grouping of the five cases according to the occurrence of unilateral occlusion in vertebral arteries, the inter-comparison has shown that (i) the flow reduction in posterior cerebral arteries is the consequence of the unilateral vertebral arterial occlusion, and (ii) the flow rate in the anterior cerebral arteries is correlated with the posterior structural variations. This study shows that our coupling approach is capable of providing comprehensive information of the hemodynamic alterations in the pathological CoW arterial structures. The information generated by our methodology can enable evaluation of both the functional and structural status of the clinically significant symptoms, for assisting the treatment decision-making.     

Anatomy of the arteries of the head in the domestic fowl

The anatomy of the cephalic arterial system in the fowl was studied in 24 specimens by means of latex-injected preparations and by dissection. Branches of the external carotid artery supply the extracranial regions. The vertebral arteries unite with the occipitals and have no major communications with the encephalic system. Blood can reach the brain directly from the internal carotid artery and indirectly by way of the extensive cerebral-extracranial anastomoses; especially prominent are those to the palatine and sphenomaxillary arteries from the maxillary and facial branches of the external carotid artery. A large external ophthalmic artery supplies the temporal rete and eye musculature, and an internal ophthalmic artery links the rete and the cerebral vessels. The circle of Willis is incomplete both anteriorly and posteriorly; the anterior cerebral arteries do not unite and the basilar artery is generally asymmetrical in origin. The basilar artery tapers caudally and is continued as the ventral spinal artery.     

High-Resolution Postcontrast Time-of-Flight MR Angiography of Intracranial Perforators at 7.0 Tesla

Background and Purpose

Different studies already demonstrated the benefits of 7T for precontrast TOF-MRA in the visualization of intracranial small vessels. The aim of this study was to assess the performance of high-resolution 7T TOF-MRA after the administration of a gadolinium-based contrast agent in visualizing intracranial perforating arteries.

Materials and Methods

Ten consecutive patients (7 male; mean age, 50.4 ± 9.9 years) who received TOF-MRA at 7T after contrast administration were retrospectively included in this study. Intracranial perforating arteries, branching from the parent arteries of the circle of Willis, were identified on all TOF-MRA images. Provided a TOF-MRA before contrast administration was present, a direct comparison between pre- and postcontrast TOF-MRA was made.

Results

It was possible to visualize intracranial perforating arteries branching off from the entire circle of Willis, and their proximal branches. The posterior cerebral artery (P1 and proximal segment of P2) appeared to have the largest number of visible perforating branches (mean of 5.1 in each patient, with a range of 2–7). The basilar artery and middle cerebral artery (M1 and proximal segment M2) followed with a mean number of 5.0 and 3.5 visible perforating branches (range of 1–9 and 1–8, respectively). Venous contamination in the postcontrast scans sometimes made it difficult to discern the arterial or venous nature of a vessel.

Conclusion

High-resolution postcontrast TOF-MRA at 7T was able to visualize multiple intracranial perforators branching off from various parts of the circle of Willis and proximal intracranial arteries. Although confirmation in a larger study is needed, the administration of a contrast agent for high-resolution TOF-MRA at 7T seems to enable a better visualization of the distal segment of certain intracranial perforators.     

Migraine with Aura Is Associated with an Incomplete Circle of Willis: Results of a Prospective Observational Study

Objective

To compare the prevalence of an incomplete circle of Willis in patients with migraine with aura, migraine without aura, and control subjects, and correlate circle of Willis variations with alterations in cerebral perfusion.

Methods

Migraine with aura, migraine without aura, and control subjects were prospectively enrolled in a 1∶1∶1 ratio. Magnetic resonance angiography was performed to examine circle of Willis anatomy and arterial spin labeled perfusion magnetic resonance imaging to measure cerebral blood flow. A standardized template rating system was used to categorize circle of Willis variants. The primary pre-specified outcome measure was the frequency of an incomplete circle of Willis. The association between circle of Willis variations and cerebral blood flow was also analyzed.

Results

170 subjects were enrolled (56 migraine with aura, 61 migraine without aura, 53 controls). An incomplete circle of Willis was significantly more common in the migraine with aura compared to control group (73% vs. 51%, p = 0.02), with a similar trend for the migraine without aura group (67% vs. 51%, p = 0.08). Using a quantitative score of the burden of circle of Willis variants, migraine with aura subjects had a higher burden of variants than controls (p = 0.02). Compared to those with a complete circle, subjects with an incomplete circle had greater asymmetry in hemispheric cerebral blood flow (p = 0.05). Specific posterior cerebral artery variants were associated with greater asymmetries of blood flow in the posterior cerebral artery territory.

Conclusions

An incomplete circle of Willis is more common in migraine with aura subjects than controls, and is associated with alterations in cerebral blood flow.     

The serpentine mitral valve and cerebral embolism

Valvular strands, well-delineated filiform masses, attached to cardiac valve edges are associated with cerebral embolism and stroke. Strokes, caused by emboli from valvular strands, tend to occur among younger persons. In this case report a valvular strand, giving a peculiar serpentine appearance to the mitral valve is described. This mitral valvular strand was the only explanation for an episode of cerebral embolism, presenting with a transient right sided hemiparesis. It is proposed that a randomized study involving combined treatment with aspirin and clopidogrel is warranted in young patients with valvular strands, presenting with a first episode of cerebral embolism.     

Distribution of serotonin-like immunoreactive nerves in major cerebral arteries of rabbit: an immunohistochemical study

We studied the distribution pattern of serotonin-like immunoreactive nerve fibers in the major cerebral vessels of rabbit by an indirect immunofluorescence technique using whole-mount stretch preparations. The density of serotonin-like immunoreactive nerve fibers was greater in vessels of the posterior part of the circle of Willis compared with that in the anterior part. This is in contrast to most of the observations reported previously regarding adrenergic, cholinergic, and peptidergic innervation of the circle of Willis.     

Randomized trial of therapy with platelet antiaggregants for threatened stroke. 2: Observations on the pathogenesis and natural history of threatened stroke.

Transient cerebral ischemia and stroke may occur despite previous occlusion of the artery supplying the appropriate part of the brain. After occlusion of the internal carotid artery, emboli may pass from the "stump" of the occluded artery to later produce transient cerebral ischemia or a stroke. Transient cerebral ischemia and stroke are due to a variety of conditions, some of which are strongly correlated with platelet thromboembolism, while others have little primary relation to thrombosis. The impact of this on therapeutic considerations is obvious. Thromboembolism related to myxomatous degeneration of the mitral valve (mitral valve prolapse) is a factor to consider in determining the cause of a stroke in a younger person. The prognosis for the different varieties of threatened stroke is incompletely known. When due to arteriosclerosis of the large cerebral arteries, transient cerebral ischemia and minor strokes pose a cumulative threat for a major stroke or death of 13% in the first year, 22% in the second year and 30% in the third year.     

Blood vessel size of circulus arteriosus cerebri (circle of Willis): a statistical research on 100 human subjects

The brain weight of 100 fresh cadavers of Italian subjects (60 males and 40 females), aged between 17 and 84 years, was obtained and the corrected circumference of the following blood vessels was measured: basilar artery, internal carotid arteries, anterior and posterior cerebral arteries, and anterior and posterior communicating arteries. The cerebral 'potential flow' was expressed in each case by adding the circumference of the basilar artery to that of the internal carotid arteries. Moreover, the sides and the perimeter of the circle of Willis as well as the length of the basilar artery were calculated. The statistical analysis of the obtained data yielded the following main results: (1) the brain weight decreases with aging, is lower in females than in males and and is statistically correlated neither with the circumferences of the considered arteries and the 'potential flow' nor with the perimeter of the arterial polygon (circle of Willis); (2) the arteries of the left side appear to be larger than those of the right one; (3) no significant difference exists in the circumference and length of the arteries between males and females; (4) the increase of the perimeter of the arterial polygon is achieved by means of a harmonious increase of all its sides; (5) the anterior and posterior communicating arteries have an anarchic pattern, because of the relatively frequent anomalies and the lack of a correlation between their circumference and that of the vessel of origin or of outlet.