The anterior communicating complex is one the most common locations for aneurysm development. It receives blood from both carotid circulations and the effect of synchrony on the arrival of blood flow has not been previously studied. The objective of this study was to compare the asynchrony conditions of the A1 pulse and its effects on the haemodynamic conditions of anterior communicating artery (ACoA) aneurysms.
Materials and methodsFrom 2008 to 2017, 54 anterior communicating artery aneurysms treated at our centre were included in the study. Computational fluid dynamics (CFD) techniques were employed and simulations consisted of complete conditions of synchrony and introducing a delay of 0.2s in the non-dominant A1 artery. Time-averaged wall shear stress (TAWSS), low shear area (LSA), A1 diameter and ACoA angles were measured.
ResultsThe difference in the LSA in conditions of synchrony and asynchrony resulted in a broad range of positive and negative values. The symmetry index (p=0.04) and A1/A2 angle on the dominant artery (p=0.04) were associated with changes in LSA.
ConclusionsIn asynchrony, LSA increased in the absence of A1 asymmetry and low A1/A2 angles, potentially increasing the risk of aneurysm rupture in this location.
El complejo comunicante anterior es una de las localizaciones más frecuentes para el desarrollo de aneurismas; recibe sangre de ambas circulaciones carotídeas y el efecto de la sincronía en la llegada de sangre no ha sido estudiado previamente. El objetivo de este estudio es comparar las condiciones de asincronía del pulso de A1 y sus efectos en las condiciones hemodinámicas de los aneurismas de la arteria comunicante anterior (ACoA).
Materiales y mèc)todosDesde 2008 hasta 2017, 54 aneurismas de la ACoA tratados en nuestro centro se incluyeron en el estudio. Se emplearon tèc)cnicas de dinámica de fluidos computacional y las simulaciones consistieron en condiciones de completa sincronía y en la introducción de un retraso de 0,2s en la arteria A1 no dominante. Se realizaron mediciones del TAWSS, área de bajo cizallamiento (LSA), diámetros de A1 y ángulos de la AcoA.
ResultadosLa diferencia producida en el LSA en condiciones de sincronía y asincronía resultó en un amplio rango de valores positivos y negativos. El índice de simetría (p=0,04) y el ángulo A1/A2 en la arteria dominante (p=0,04) se relacionan con los cambios en el LSA.
ConclusionesEn asincronía, el LSA se incrementó en ausencia de asimetría A1 y ángulos A1/A2 menores, incrementando potencialmente el riesgo de rotura de aneurismas en esta localización.
Intracranial aneurysms are pathological dilatations of the cerebral arteries, the estimated prevalence of cerebral aneurysms in the general population has been reported as high as 7%.1 The rupture of an intracranial aneurysm produces severe intracranial haemorrhages, among the survivors who reach hospital care, 27% will die despite modern intensive and surgical measures.2
Anterior communicating complex aneurysms are one the most frequent locations for intracranial aneurysms. A prevalence of 3.6% is described in prospective autopsy studies,3 and anterior communicating artery (AcoA) aneurysms are responsible of about 39% of aneurysmal subarachnoid haemorrhage cases.4 Previous studies showed certain features that could contribute to the formation of aneurysms in this location such as the hypoplasia of the A1 segment and the angulation of the arteries.5,6 Also, certain common concepts in general aneurysm literature such as the relationship of the size and aspect ratio and rupture seems not to behave similarly in this location, for example, in a recent study, 86.9% of the ruptured anterior communicating aneurysms had a size lower than 5mm,7 and ruptured AcoA aneurysms with a size lower than 7mm are found two times more frequent compared with other locations in anterior cerebral circulation.8
Anterior communicating artery aneurysms receive blood from the carotid circulation, and is the first point in which both left and right circulations met after its early bifurcation in the aortic arch. Each carotid artery has its own geometry, including diameter, elongations, tortuosity and atherosclerotic changes,9 as a consequence, four pulsatile waves reach the brain in an asynchronous fashion,10 this phenomena is also documented from non-selective arteriography using aortic injections of contrast.11
We have not found previous studies analysing the implications of the asynchrony of the carotid pulse in the haemodynamics of the anterior communicating aneurysms. The objective of this study is to compare conditions of asynchrony in the pulse of the A1 artery and its effects in the haemodynamic environment of naturally occurred aneurysms using computational fluid dynamics.
Materials and methodsStudy populationFrom January 2008 to December 2017, 652 intracranial aneurysms were diagnosed by digital subtraction arteriography (DSA) in our centre, of these, 122 patients (18.71%) had anterior communicating aneurysms. For this study, patients with multiple aneurysms, A1 segment agenesis, suboptimal quality or absent CT angiography were excluded.
The study population of this retrospective study corresponds to 54 anterior complex circulations. The design of this study was approved by the Galician Clinical Research Ethics Committee. Informed written consent was obtained from patients still alive.
Computational fluid dynamics analysisModel geometryFor the treatment of the geometry, anterior communicating artery complex was selected, starting from the first segment of the A1 artery to at least 3mm of the A2 segment. 3D sequences were obtained from 3D computed tomography angiogram (CTA) of cerebral arteries with a voxel resolution of 0.4í0.4í0.6mm. Digital subtraction angiography studies were not considered because of their vessel selectivity requiring registration/fusion procedures from 2 internal carotid angiograms to obtain a model, unsuitable for this retrospective study.
Segmentation and generation of STL surfaces were performed using the software Slicer3D (Harvard Medical School, Boston, MA, USA). These surfaces were processed in Meshlab (Visual Computing Lab, Pisa, Italy) and FreeCAD (Juergen Riegel, Werner Mayer, Yorik van Havre, OpenSource, http://freecadweb.org/), to create meshes with ≈100,000 tetrahedral elements into the CFD software ANSYS Fluent 17.0 (Ansys, Canonsburg, PA, USA). A viscous layer of 0.1D (D=diameter of the vessel lumen), adjacent to the vessel walls, was created to capture the boundary layer effects.
Governing equations and numerical simulationThe CFD software was used to solve the Navier•Stokes and mass conservation equations under the assumption of laminar, incompressible, and non-Newtonian blood flow. The corresponding governing equations are given as:
where u↧ and p are the fluid velocity and the pressure, respectively ρ is the density (1060kg/m3), and α/4 is the dynamic viscosity of blood. Dynamic viscosity is modelled using a Carreau model.20 This is given as:where α/4 is the effective viscosity depending upon the shear rate γ˨tm), α/40 the viscosity at zero shear rate (0.056Pas), α/4∞ the viscosity at infinite shear rate (0.0035Pas), the time constant (3.313s) and n the power law index (0.3568).Boundary conditions
Transient pulsatile simulations averaged over several cardiac cycles were performed. Regarding the entrance boundary, the input condition was a sinusoidal profile with a peak speed of 0.5m/s and a minimum speed of 0.1m/s. The pulse length was 0.125s, and the period 0.5s. The output boundaries were defined as constant pressure outlets, with a pressure close to the mean arterial pressure of a normal individual (100mmHg). Dominancy was defined as the A1 artery with the largest diameter.
The experiment was conducted with 2 profiles in each case, introducing a delay of 0.2s (asynchrony condition) and a second profile assuming complete synchrony of both A1 inlets.
Output variablesThe wall shear stress (WSS) describes the viscous stress exerted by the blood on the walls of the artery. This magnitude is calculated as:
where ni is the normal vector to the surface and Ϣij the viscous stress tensor. The time-averaged magnitude corresponding to the wall shear stress (TAWSS) is calculated as follows:where T denotes the period of the cardiac cycle (assumed T=0.5s).
Time-averaged WSS and pressure were considered. Low shear area WSS (LSA), was defined as the percentage of the aneurysmal area with a WSS below 10% of the TAWSS measured in the parent artery (dominant A1) of each case.12
Geometric analysisThe geometry of the aneurysm, regarding its shape and size was measured from 3D reconstructions, the definitions of these variables are well described by previous studies.13
The diameter of the 4 vessels A1L, A1R, A2L and A2R were measured. Aneurysm lateralization was defined as the direction on the left-right axis of the height vector. A1 dominance was defined as the side of the largest of both A1 arteries (diameter measured in mm). Symmetry index was defined as the quotient between the non-dominant and the dominant A1 diameters independently from the side, in a scale from 0 to 1, where 1 corresponds to fully symmetric A1 arteries.
We also include in the analysis 3 angles, left A1/A2 angle, right A1/A2 angle and A1•A1 angle, methods of this measurements were described elsewhere.14
StatisticsAll output variables from case-by-case simulations were registered for statistical analysis. For these analyses, SPSS software version 20 for MacOS was used. The inferential analysis was made from nonparametric tests for paired samples when comparing among comparisons between synchronic and asynchrony conditions, and tests for independent samples when considering grouped nominal variables. A p-value less than 0.05 is assumed to be significant. Rupture event or status of the aneurysm was not assessed in the analysis because of the imbalance of the distribution in this variable, risk was assumed according to the WSS changes.
ResultsPopulation characteristicsFifty-four cases were analyzed in this study, 31 cases (57.4%) were male and 23 cases (42.7%) were female. The mean age at diagnosis was 56.14 years (SD=14.09). 45 cases presented as ruptured aneurysms with subarachnoid haemorrhage (83.3%) and 9 cases as unruptured aneurysms (16.7%). Considering only the subarachnoid haemorrhage cases (n=45), the distribution of Fisher's radiological grade was grade 2 in 10 cases (22.22%), grade 3 in 16 cases (35.56%) and grade 4 in 19 cases (42.22%). In SAH cases the clinical severity in the WFNS scale was grade 1 in 22 cases (48.89%), grade 2 in 9 cases (20%), grade 3 in 1 case (2.22%), grade 4 in 7 cases (15.56%) and grade 5 in 6 cases (13.33%). Baseline characteristics of the population are summarized in Table 1.
Baseline characteristics of the population.
| Variable | Value | Percentage |
|---|---|---|
| Gender (n=54) | ||
| Male | 31 | 57.4% |
| Female | 23 | 42.7% |
| Rupture status (n=54) | ||
| SAH cases | 45 | 83.3% |
| Incidental cases | 9 | 16.7% |
| Treatment in SAH cases (n=45)a | ||
| Endovascular treatment | 33 | 61.1% |
| Surgery | 10 | 18.52 |
| A1 dominance (n=54) | ||
| Left A1 dominant | 33 | 61.11% |
| Right A1 dominant | 21 | 38.89% |
| Aneurysm axis lateralization | ||
| Left lateralization | 14 | 25.93% |
| Right lateralization | 40 | 74.07% |
Measurements of the dimensions of the aneurysm were obtained, including height and neck and aspect ratio. We also measured the diameter of both A1 and A2 arteries, the right and left A1/A2 angles, and the A1•A1 angle. These measurements are summarized in Table 2. There is a tendency to lateralization of the aneurysm towards the side with the smaller A1/A2 angle, in left lateralization aneurysms the A1/A2 angles had an average of 101 and 74 degrees for the left and right sides respectively; and in right lateralization aneurysms, these angles were 79 and 82 degrees for the left and right sides, respectively.
Geometric characteristics of the arteries studied.
| Variable | Minimum | Maximum | Mean | SD |
|---|---|---|---|---|
| Aneurysm height (mm) | 2.60 | 14.30 | 6.54 | 3.01 |
| Aneurysm neck (mm) | 1.46 | 7.94 | 3.53 | 1.23 |
| Aspect ratio | 0.63 | 3.87 | 1.90 | 0.68 |
| Left A1 diameter (mm) | 0.9 | 2.9 | 1.76 | 0.47 |
| Right A1 diameter (mm) | 0.9 | 2.8 | 1.57 | 0.49 |
| Left A2 diameter (mm) | 0.8 | 2.4 | 1.58 | 0.34 |
| Right A2 diameter (mm) | 0.8 | 2.5 | 1.52 | 0.38 |
| Left A1•A2 angle (mm) | 18.90 | 159.60 | 86.98 | 34.37 |
| Right A1•A2 angle (mm) | 2.3 | 160.60 | 78.25 | 37.47 |
| A1•A1 angle (degrees) | 56.50 | 176.80 | 136.12 | 27.37 |
| Symmetry index | 0.39 | 0.94 | 0.67 | 0.15 |
A significant difference exists in TAWSS in asynchrony conditions. Mean TAWSS was 1.25Pa and 1.34Pa in asynchrony and synchrony conditions respectively (p=0.04, paired samples T-test), mean time-averaged pressure was 13,205Pa and 13,495Pa in asynchrony and synchrony conditions respectively (p=0.004). The difference produced in the LSA in synchronous and asynchronous conditions resulted in a broad range including positive and negative values (from ∧35.68 to 27.34), for this reason the population was grouped owing to this variable into “LSA increased in asynchrony” and “LSA decreased in asynchrony” groups. Table 3 shows a summary of the effect of different geometric variables over this phenomenon in a univariate analysis. In this analysis, the symmetry index and A1/A2 angle on the dominant artery were related to changes in LSA.
Univariate analysis of low shear area changes in relation to geometric characteristics.
| Variable | LSA increased (n=31) | LSA decreased (n=23) | p-value (Mann Whitney-U test) |
|---|---|---|---|
| Mean aneurysm height (mm) | 5.99 | 6.72 | 0.99 |
| Mean aneurysm neck (mm) | 3.57 | 3.43 | 0.55 |
| Mean aspect ratio | 1.72 | 2.01 | 0.28 |
| Mean A1•A1 angle (degrees) | 139.49 | 137.48 | 0.70 |
| Dominant side A1•A2 angle (degrees) | 63.12 | 91.14 | 0.04 |
| Mean symmetry index | 0.72 | 0.62 | 0.04 |
The effects of asynchrony on the pressure measured in the aneurysm were mainly negative with a mean of ∧289.68Pa (range of ∧4755.84 to 218.10Pa, SD=717.16Pa).
DiscussionAs a result of the anatomical configuration of the arterial system, four different pulse waves reach the Willis complex at different times. The first aortic branch comprises the brachiocephalic trunk that branches off into the right common carotid and subclavian arteries, while the left common carotid and subclavian arteries emerges independently from the aortic arch. This particular asymmetric configuration and other anatomical and pathological variabilities such as the existence of atherosclerotic plaques in the lumen of large vessels are determinants of cerebral pulse asynchrony.10
Geometry of the anterior communicating artery complexThe anterior communicating artery is a complex site due to its anatomical features. It receives flow from two independent circulations; it is also known that the diameters of both anterior cerebral arteries are usually different in patients with aneurysms, several previous studies have shown that this configuration is a risk factor for both the development and rupture of the aneurysm and increases the risk of complications of the treatment of aneurysms in this location.15•17
In our study, asymmetry is present in virtually all cases, a symmetry index of less than 0.80 is present in 72% of cases and an index lower than 0.5 is present in up to 20% of cases. We did not find statistical differences in ruptured and unruptured aneurysms in our series, although our sample of unruptured aneurysms is small.
Zhang et al.6 analysing 665 patients with aneurysms in various locations described that the A1/A2 angle is lower in individuals with aneurysms of anterior communicant artery, with an average of 106 degrees compared to 120 degrees in the group without aneurysms in this location. In our study, A1/A2 angle is smaller, approaching a mean of 82 degrees. The previously cited author also finds that there is a lateralization of the anterior communicating aneurysm to the side that offers a lower A1/A2 angle, this finding is comparable in our study.
Lin et al.18 analysing 79 anterior communicating artery aneurysms described lower dominant A1/A2 angles in patients with ruptured aneurysms in this location, other studies found the same results.19,20 In our study, we did not find a significant association with this variable, we must consider that in our series only nine unruptured aneurysms were analyzed.
Haemodynamic characteristics of aneurysms in conditions of synchrony and asynchronyHaemodynamic conditions play an indisputable role in the pathophysiology of the formation, growth and rupture of aneurysms. The most described variable is the wall shear stress (WSS), defined as the frictional force exerted by the flowing blood tangentially on the vessel lumen.21 This variable is usually diminished in ruptured aneurysms highlighting its potential role in the event of rupture.22 Low shear area is also described in most studies as a variable; LSA is defined as the percentage of the aneurysm wall with a WSS lower than the 10% of the WSS measured in the parent vessel for most authors.23
In our study, there is a significant direct influence of the asynchrony of the pulse in the A1 artery in the haemodynamic conditions of the aneurysm, including a reduction of the total pressure, and changes in the TAWSS that are reflected in two different groups: some aneurysms had an increase and some had a decrease in TAWSS, and in LSA in an inverse way. In the univariate analysis, we found greater symmetry indexes and lower A1/A2 angles in patients in whom asynchrony conditions induced an increase in LSA, potentially increasing the theoretical risk of bleeding.
The effect of the asynchronous pulse may produce a decrease in TAWSS when there is less or none A1 asymmetry, two significant flows that produce a complex interaction resulting in an additive effect in the TAWSS over the complete cardiac cycle. This effect is not achieved when there is a second asynchronous pulse, the result is the decrease of the TAWSS, and in consequence the increase of the LSA.
In the presence of lower A1/A2 angles in the dominant artery, more volume of blood is directed to A2 arteries bypassing the aneurysm, synchrony may play a role in stabilizing the intra-aneurysmal flow; if asynchrony is assumed, TAWSS could be decreased and in consequence, LSA increased. In higher A1/A2 angles, the blood influx to the aneurysm is greater, the second asynchronous pulse may therefore induce an increase in the TAWSS.
In addition to the geometric characteristics described previously as associated with an increased incidence of aneurysms in this location, asynchrony could play an important role in the formation and growth of aneurysms, it is therefore advisable to include this variable in further studies to address haemodynamics of this complex location.
We conclude from our findings that in cases of mild or no asymmetry and/or low A1/A2 angles, asynchrony of A1 arteries may potentially increase LSA, increasing the theoretical risk of aneurysm rupture. Two representative cases are illustrated in Figs. 1 and 2.
Low shear area (white) in anterior communicating aneurysms in synchrony and asynchrony conditions. Upper row: left figure shows a right A1 hypoplasia with a symmetry index of 0.39 in synchrony conditions, right figure shows the same in asynchrony conditions; LSA decreased from 50.93 to 26.40 considering asynchrony condition. Lower row: left figure shows a right dominant A1 segment, symmetry index is 0.9, right figure shows the same aneurysm in asynchrony conditions, LSA increased from 25.03 to 36.78.
Low shear area (white) in anterior communicating aneurysms in synchrony and asynchrony conditions. Upper row: left figure shows a dominant A1/A2 angle of 88.62 degrees in synchronic conditions, right figure shows the same aneurysm in asynchrony conditions; LSA decreased from 31.64 to 26.06. Lower row: left figure shows a dominant A1/A2 angle of 46.45 degrees in synchronic conditions, right figure shows the same aneurysm in asynchrony; LSA increased from 27.69 to 36.95.
For this theoretical study, we have considered various conditions as true, in real conditions they may not be absolutely certain. Limitations inherent to out method are the absence of a specific velocity profile for each patient, the absence of data on the physical characteristics of the arterial wall, the geometric changes produced in the aneurysm after rupture, among others. Although DSA is the gold standard for brain vessels studies, only CTA were included in this study. CTA is highly accessible and is performed in all cases in our centre. Moreover, compared with DSA, CTA allows to represent AcomA geometry in only one step, DSA studies from AcomA needs two vessel catheterizations (both ICA) and registration/fusion procedures making this unaffordable for retrospective studies. Although low WSS is the most frequently described condition in ruptured aneurysms, the discussion about the role of low WSS and high WSS in the pathophysiology of a brain aneurysm remains open. The interpretation of our results assume a relevant role of low WSS in aneurysm rupture; more research is warranted in the pathobiology of this phenomena.
ConclusionThe asynchrony of the flow in A1 arteries produces significant haemodynamic changes in anterior communicating artery aneurysms, low shear area is increased in the absence of A1 asymmetry and low A1/A2 angles, potentially increasing the risk of rupture of aneurysms in this location.
FundingThis work was partially supported by Xunta de Galicia • Plan I2C Grant ProgramPOS-A/2013/161, ED481B 2016/047-0, ED481D 2017/010).
The contents of this manuscript were not presented or published before.
Conflict of interestsThe authors declare no conflict of interests.
