Types of the cerebral arterial circle (circle of Willis) in a Sri Lankan Population

Background  

The variations of the circle of Willis (CW) are clinically important as patients with effective collateral circulations have a lower risk of transient ischemic attack and stroke than those with ineffective collaterals. The aim of the present cadaveric study was to investigate the anatomical variations of the CW and to compare the frequency of prevalence of the different variations with previous autopsy studies as variations in the anatomy of the CW as a whole have not been studied in the Indian subcontinent.     

Are the distributions of variations of circle of Willis different in different populations? – Results of an anatomical study and review of literature

Background  

Previous studies have proposed correlation between variants of the cerebral arterial circle (also known as circle of Willis) and some cerebrovascular diseases. Differences in the incidence of these diseases in different populations have also been investigated. The study of variations in the anatomy of the cerebral arterial circle may partially explain differences in the incidence of some of the cerebrovascular diseases in different ethnic or racial groups.     

Characteristics of circle of Willis variations in the mongolian gerbil and a newly established ischemia-prone gerbil group

Mongolian gerbils (Meriones unguiculatus) have an incomplete circle of Willis (CoW), as a result of which approximately 30-40% of these animals develop focal cerebral ischemia after unilateral carotid occlusion (UCO). There are four types of patterns of the anterior and posterior communicating arteries (ACoAs and PCoAs, respectively) of the CoW and they determine the severity of the ischemic symptoms. We used 398 gerbils from five generations, including a selectively bred ischemia-prone group, to investigate post-UCO ischemic symptoms and possible correlations of ACoA and PCoA patterns between parents and their progeny. We observed that if the parents had complete ACoAs, their progeny also had complete ACoAs, and we found significant differences when the parents' ACoAs were incomplete: in 60.4% of offspring the type of ACoA was consistent with that of the mother and in 48.2% it was consistent with that of the father. The severity of the neurological symptoms after UCO was significantly related to the patterns of the ACoAs when PCoAs were absent. The proportion of UCO ischemia in gerbils with incomplete ACoAs was significantly higher than in those with complete ACoAs. After selectively breeding five generations, the proportion of UCO ischemia increased from 40% in the F1 animals to 75% in the F5 animals. Our results suggest that variations in the CoW are genetic and demonstrate that we successfully established an ischemia-prone group of gerbils.     

A 3D numerical study of the collateral capacity of the circle of Willis with anatomical variation in the posterior circulation

Background

The Circle of Willis (CoW) is the most important collateral pathway of the cerebral artery. The present study aims to investigate the collateral capacity of CoW with anatomical variation when unilateral internalcarotid artery (ICA) is occluded.

Methods

Basing on MRI data, we have reconstructed eight 3D models with variations in the posterior circulation of the CoW and set four different degrees of stenosis in the right ICA, namely 24%, 43%, 64% and 79%, respectively. Finally, a total of 40 models are performed with computational fluid dynamics simulations. All of the simulations share the same boundary condition with static pressure and the volume flow rate (VFR) are obtained to evaluate their collateral capacity.

Results

As for the middle cerebral artery (MCA) and the anterior cerebral artery (ACA), the transitional-type model possesses the best collateral capacity. But for the posterior cerebral artery (PCA), unilateral stenosis of ICA has the weakest influence on the unilateral posterior communicating artery (PCoA) absent model. We also find that the full fetal-type posterior circle of Willis is an utmost dangerous variation which must be paid more attention.

Conclusion

The results demonstrate that different models have different collateral capacities in coping stenosis of unilateral ICA and these differences can be reflected by different outlets. The study could be used as a reference for neurosurgeon in choosing the best treatment strategy.

     

Computational models of blood flow in the circle of Willis

A two-dimensional, steady state model of the circle of Willis has been developed. To simulate the peripheral resistance of the cerebrovascular tree, blocks of porous media were used. Their effective resistance was kept constant, disregarding the effects of arterial auto-regulation. The model was then used to simulate different common abnormalities of the circle of Willis while a range of varying boundary conditions was imposed to the right internal carotid artery (ICA). The total flux was tabulated and compared favourably with both clinical measurements and other models of the circle of Willis. Relevant fluid dynamics effects were also observed and analysed. The present model demonstrates that the use of CFD can produce physiological results if the appropriate boundary conditions are used. We can provide clinicians with a priority list of the severity of the flux reduction for the considered abnormalities for different degrees of stenosis of the right ICA. From this study it is apparent that the redistribution of blood via the circle of Willis is mainly driven by changes in the vascular resistance of the brain rather than in the local arterial geometry. The use of valid peripheral resistances allows for a more realistic model of the circle of Willis but also highlights the need for more accurate means to estimate the vascular resistance of a patient.     

A mathematical model of the flow in the circle of Willis

A mathematical model of the flow in the circle of Willis has been designed and the effects of (a) the large anatomical variation of the communicating arteries and (b) physiological changes of the resistances of the vertebral arteries have been studied. The influence of the posterior perforating arteries on the flow in the posterior communicating arteries has been investigated as well, with special attention being paid to the possible occurrence of a 'dead point'. In the model, the influence of diameters of the communicating arteries on the flow in the afferent vessels and the segments of the circle turns out to be considerable, especially in the range of the anatomical variation of the diameters. Within this range flow reductions due to an increased resistance of the vertebral artery will be compensated for by the system. Assuming that the values and ratios of the peripheral resistances are within the physiological range, a dead point is not to be expected in the flow in the posterior communicating arteries.     

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.     

A circle of Willis simulation using distensible vessels and pulsatile flow

The development of a one-dimensional numerical (finite-difference) model of the arterial network surrounding the circle of Willis is described based on the full Navier-Stokes and conservation of mass equations generalized for distensible vessels. The present model assumes an elastic wall defined by a logarithmic pressure-area relation obtained from the literature. The viscous term in the momentum equation is evaluated using the slope of a Karman-Pohlhausen velocity profile at the vessel boundary. The afferent vessels (two carotids and two vertebrals) are forced with a canine physiologic pressure signature corresponding to an aortic site. The network associated with each main efferent artery of the circle is represented by a single vessel containing an appropriate amount of resistance so that the mean flow through the system is distributed in accordance with the weight of brain irrigated by each vessel as determined from a steady flow model of the same network. This resistance is placed a quarter wave-length downstream from the heart to insure proper reflection from the terminations, where the quarter wavelength is determined using the frequency corresponding to the first minimum on an input impedance-frequency diagram obtained at the heart. Computer results are given as time histories of pressure and flow at any model nodal point starting from initial conditions of null flow and constant pressure throughout the model. Variations in these pressure and flow distributions caused by the introduction of pathologic situations into the model illustrate the efficacy of the simulation and of the circle in equalizing and redistributing flows in abnormal situations.     

Investigations of flow and pressure distributions in physical model of the circle of Willis

The paper presents the results of experiments concerning flow in the model of cerebral supplying arteries and the circle of Willis (CW). Vascular phantom was prepared on the basis of anatomical specimens. The most typical artery shapes and dimensions were considered. Pressure distribution in six characteristic points is provided, and so are the average flow rates in the anterior, middle and posterior section of the brain. Tests were run in the conditions replicating the physiological state (i.e. when the supplying arteries were fully patent) and in pathological conditions, in which the internal carotid and vertebral arteries were occluded on one or both sides. Thus obtained results were compared with the results of computer simulations based on linear and non-linear flow models. To estimate the non-linear resistance of vascular segment two phenomenological formulae were proposed. High degree of correlation between the values obtained from experiments and those registered in non-linear computer model proves usefulness of proposed formulae. It verifies the hypothesis that non-linearity of flow characteristics of the vessel segments to a great extent is caused by their tortuousity and small length in relation to diameter. Non-linear effects are particularly pronounced in conditions of pathological occlusion of supplying vessels.     

Analysis of flow and vascular resistance in a model of the circle of Willis

A very simple model of the flow in the circle of Willis is described in this paper. Disregarding pulsatility and vessel wall elasticity, fluxes in all segments of the circle of Willis and its afferent and efferent vessels are calculated by applying the Poiseuille-Hagen formula. Comparison with the fluxes calculated numerically from a more sophisticated mathematical model, including pulsatility, vessel wall elasticity and nonlinear effects, revealed only very slight differences. In short, fluxes in the afferent vessels and the segments of the circle of Willis are influenced by any change of resistance within the network, whereas the fluxes in the efferent segments are dominated by the efferent resistance distribution. However, a great advantage of the present simple model is that it offers the possibility of an analytical approach which yields both an easy sensitivity analysis of parameters and an insight into the mechanisms that govern the flow in a network like the circle of Willis. It can be concluded that these mechanisms are similar to the principles of the Wheatstone bridge, known from electrical circuit theory.     

Modelling pulse wave propagation in the rabbit systemic circulation to assess the effects of altered nitric oxide synthesis

Pulse wave propagation in the mature rabbit systemic circulation was simulated using the one-dimensional equations of blood flow in compliant vessels. A corrosion cast of the rabbit circulation was manufactured to obtain arterial lengths and diameters. Pulse wave speeds and inflow and outflow boundary conditions were derived from in vivo data. Numerical results captured the main features of in vivo pressure and velocity pulse waveforms in the aorta, brachiocephalic artery and central ear artery. This model was used to elucidate haemodynamic mechanisms underlying changes in peripheral pulse waveforms observed in vivo after administering drugs that alter nitric oxide synthesis in the endothelial cells lining blood vessels. According to our model, these changes can be explained by single or combined alterations of blood viscosity, peripheral resistance and compliance, and the elasticity of conduit arteries.     

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.     

1D simulation of blood flow characteristics in the circle of Willis using THINkS

One-dimensional (1D) simulation of the complete vascular network, so called THINkS (Total Human Intravascular Network Simulation) is developed to investigate changes of blood flow characteristics caused by the variation of CoW. THINkS contains 158 major veins, 85 major arteries, and 77 venous and 43 arterial junctions. THINkS is validated with available in vivo blood flow waveform data. The overall trends of flow rates in variations of the CoW, such as the missing anterior cerebral artery (missing-A1) or missing posterior cerebral artery (missing-P1), are confirmed by in vivo experimental data. It is demonstrated that the CoW has the ability to shunt blood flow to different areas in the brain. Flow rates in efferent arteries remain unaffected under the variation of CoW, while the flow rates in afferent vessels can be subject to substantial changes. The redistribution of blood flow can cause particular vessels to undergo extra flow rate and hemodynamic stresses.     

Application of the adductome approach to assess intertissue DNA damage variations in human lung and esophagus

Methods for determining the differential susceptibility of human organs to DNA damage have not yet been explored to any large extent due to technical constraints. The development of comprehensive analytical approaches by which to detect intertissue variations in DNA damage susceptibility may advance our understanding of the roles of DNA adducts in cancer etiology and as exposure biomarkers at least. A strategy designed for the detection and comparison of multiple DNA adducts from different tissue samples was applied to assess esophageal and peripherally- and centrally-located lung tissue DNA obtained from the same person. This adductome approach utilized LC/ESI-MS/MS analysis methods designed to detect the neutral loss of 2′-deoxyribose from positively ionized 2′-deoxynucleoside adducts transmitting the [M+H]⁺ > [M+H−116]⁺ transition over 374 transitions. In the final analyses, adductome maps were produced which facilitated the visualization of putative DNA adducts and their relative levels of occurrence and allowed for comprehensive comparisons between samples, including a calf thymus DNA negative control. The largest putative adducts were distributed similarly across the samples, however, differences in the relative amounts of putative adducts in lung and esophagus tissue were also revealed. The largest-occurring lung tissue DNA putative adducts were 90% similar (n = 50), while putative adducts in esophagus tissue DNA were shown to be 80 and 84% similar to central and peripheral lung tissue DNA respectively. Seven DNA adducts, N²-ethyl-2′-deoxyguanosine (N²-ethyl-dG), 1,N⁶-etheno-2′-deoxyadenosine (dA), -S- and -R-methyl-γ-hydroxy-1,N²-propano-2′-deoxyguanosine (1,N²-PdG₁, 1,N²-PdG₂), 3-(2′-deoxyribosyl)-5,6,7,8-tetrahydro-8-hydroxy-pyrimido[1,2-a]purine-(3H)-one (8-OH-PdG) and the two stereoisomers of 3-(2′-deoxyribosyl)-5,6,7,8-tetrahydro-6-hydroxypyrimido[1,2-a]purine-(3H)-one (6-OH-PdG) were unambiguously detected in all tissue DNA samples by comparison to authentic adduct standards and stable isotope dilution and their identities were matched to putative adducts detected in the adductome maps.     

Use of immunohistochemical stains to assess the variations in color of fat of the upper eyelid

Although there are many variations on the technique, most practitioners agree that removal of periorbital eyelid fat is an integral part of the blepharoplasty operation. The retrieval and excision of the medial fat of the upper eyelid is a step that, when overlooked, leaves the patient with an unsatisfactory appearance of puffiness in this area. The medial fat is characteristically white; the other fat compartments are yellow. The authors attempt to understand why these two juxtaposed fat pockets are of distinct different colors. Four consecutive patients underwent traditional upper blepharoplasty surgery. From each patient two separate fat specimens were identified as upper lateral and upper medial. These fat specimens were processed with hematoxylin and eosin and various immunohistochemical stains. A board-certified pathologist, who was blinded as to the anatomic site of the fat, evaluated them. The medial fat showed much larger fat lobules than the upper lateral fat. Contrasting this, the lateral fat had many more endothelial-lined blood vessels and much thicker fibrous septa than its medial neighbor. These findings were supported immunohistochemically by using CD34 (endothelial antibody) and factor XIIIa (dermal dendritic cell/ normal fibroblast antibody). The use of other immunostains using various antibodies did not distinguish any distinct histomorphology among the specimens. Although for the operating surgeon it is important to recognize the white color of the medial fat to aid in identification during surgery, one can only speculate as to what contributes to this difference in blood vessels and supporting fibrous septa. Most likely this is the result of anatomic, embryologic, and vascular bed differences.     

A field trial to assess the effects of rabbit grazing on spring barley

Spring barley is widely grown throughout the UK and significant yield loss can occur as a result of rabbit grazing. In a 3-yr trial, spring barley was grown in six enclosures following current agronomic procedures and was subjected to grazing by different population densities of rabbits. The annual yield loss at the end of the trial was 0.5% rabbit⁻¹ ha⁻¹. The yield loss per rabbit was calculated to be around 25 kg and the financial loss was calculated as £2.00 per rabbit at 1998 prices (approx. £80 tonne⁻¹). Models allowing farmers to predict the levels and costs of damage by rabbits to winter wheat and for silage have already been developed. The results from this trial enable farmers to extend their predictions to include spring barley. The implications for this are discussed.     

A conceptual framework to assess the effects of environmental change on ecosystem services

A new conceptual framework is presented for the assessment of the impacts of environmental change drivers on ecosystem service provision and the policy and management responses that would derive from the valuation of these impacts. The Framework for Ecosystem Service Provision (FESP), is based on an interpretation of the widely-used Drivers-Pressures-State-Impact-Response (DPSIR) framework. FESP differs from the DPSIR by offering clarity in the definitions of the various DPSIR components as well as introducing novel elements of relevance to the ecosystem service approach. The value of a common framework lies in making the comparison across competing services accessible and clear as well as highlighting the conflicts and trade-offs between not only multiple ecosystem services, but also multiple service beneficiaries. The framework is explicit, for example, in recognising as state variables not only the attributes of the Ecosystem Service Providers (ESPs), but also the attributes of the Ecosystem Service Beneficiaries (ESBs). That a service depends as much on the attributes of the people whose well-being benefits from the service as on the attributes of the biology providing the service is an important step in integrated social-ecological thinking. FESP also identifies the mechanisms of either mitigation or adaptation to the environmental change problem through the effect of these response strategies on specific pressure or state variables. In this way, FESP can contribute to the policies and strategies that are used to support conservation management. This paper describes the principles of FESP and presents some indicative examples of its practical implementation.