Introduction

The anterior communicating artery (AcomA) is recognized as the predilection site for intracranial aneurysms, accounting for > 25% of all intracranial aneurysm populations [1, 2]. The AcomA also carries higher risk of rupture than other locations in the anterior circulation. The complexity of the geometry in the AcomA determines the diversity in flow conditions, which makes AcomA aneurysms the most complex within the anterior circulation [3].

Despite the large number of animal experiments and clinical studies, the pathogenesis of intracranial aneurysm formation is still unclear. A growing number of studies based on numeral simulation of computational fluid dynamics (CFD) techniques have demonstrated that hemodynamics are essential to understanding AcomA aneurysm formation [4, 5]. Wall shear stress (WSS) is a flow-induced stress acting on the endothelial surface and can be described as the frictional force of viscous blood [3, 6]. WSS is recognized as a critical determinant of vessel diameter and is implicated in vascular remodeling [7]. In recent years, an increasing number of studies have demonstrated that WSS is closely related to determining aneurysm initiation, growth, and rupture [4, 5, 8,9,10]. Although WSS is widely reported in the process, there is no agreement on whether or not regions of low or high flow are most critical in promoting the events responsible for aneurysm formation. The growing number of such proposals has been controversial. Indeed, the accurate criterion for low or high levels of WSS related to AcomA aneurysm formation is unclear.

In this study, we identified which hemodynamic parameters independently characterized the formation of AcomA aneurysms using multivariate logistic regression and determined the WSS threshold in the parent artery using two-piecewise linear regression models to better illustrate the correlation between the magnitude of WSS and AcomA aneurysm formation. We also sought more simplified and convenient alternative techniques to detect WSS as a screening tool for evaluating the risk of aneurysm formation in primary care facilities and community hospitals in China and many developing countries because of the relatively low resource intensity.

Materials and methods

Study population

Approval for this study was obtained from the local Institutional Review Board of the participating centers. The study included consecutive patients who were diagnosed with single AcomA aneurysms, and participants without intracranial aneurysms served as the control population. All patients were admitted to the hospital with a suspected intracranial aneurysm detected by magnetic resonance angiography (MRA) or computed tomography angiography (CTA) examination and underwent digital subtraction angiography (DSA) after admission. The exclusion criteria were as per the study conducted by Kaspera et al [11].

Eighty-one consecutive patients with single, unruptured AcomA aneurysms and 118 participants without intracranial aneurysms were included in this cross-sectional study at Southern Medical University Zhujiang Hospital and the First Affiliated Hospital of Zhengzhou University from January 2014 to May 2017.

Evaluation of morphologic and hemodynamic characteristics (Fig. 1)

Three-dimensional-DSA was performed in all patients after admission. Specific geometrical patterns were reconstructed from 3D-DSA images to confirm the morphologic structure. Morphologic parameters, such as a dominant A1 and the angle between the A1 and A2 segments of the anterior cerebral artery (ACA), were defined and measured, as described in a previous study [12].

Fig. 1
figure 1

An ultrasound-based TCCD technique and reconstructed 3D-DSA image showing the measurements in ACA. a, b Doppler measurements in right ACA (white arrow, blue blood flow signal). c, d 2D-DSA and reconstructed 3D-DSA images for measuring morphologic parameters of ACA aneurysm

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Transcranial color-coded duplex (TCCD) was performed with a Philips EPIQ5 ultrasound system (Philips; Washington, USA), which includes a 2.0-MHz real-time imaging transducer and a 2.0-MHz pulsed Doppler transducer. The maximum in situ Doppler energy output intensity was 89 mW/cm2 spatial peak time average intensity (ISTPA.3). TCCD was performed by the same examiner. The ACA was imaged using a transtemporal window with the patient in the supine position [13]. The mean blood flow velocity (Vm) was measured for the bilateral distal end of each A1 segment of the ACA [14]. An ultrasound probe was placed as close as possible to the distal end of each A1 segment, and the lateral and paramedian frontal bone windows were used for accurate detection, according to the procedure described by Stolz et al [15]. Each TCCD examination was performed with the sample volume being placed within the color flow image of the examined artery.

In the case of aplasia of the A1 segment, these measurements were applied only to the dominant A1 segment. If the A1 segments were symmetric, the parameters were measured at the ipsilateral A1 in aneurysm cases and at the side with faster blood flow velocity in cases without aneurysms.

The internal diameter (ID) of the distal end of the ACA was measured between the leading edge of the echo produced by the intima-lumen interfaces of the near and far walls of the A1 segments at the R (IDR) and T (IDT) waves of the electrocardiogram, representing the minimum and maximum diameters, respectively [14]. Images of the interfaces between the lumen and intima were captured over five cardiac cycles and stored.

Blood viscosity (η) was measured in vitro at 37°C using a cone-plate viscometer and recorded at a shear rate of 200 s-1.

Systolic blood pressure (SBP) and diastolic blood pressure (DBP) were measured on the right arm using a calibrated, fully automated device (Omron HEM-705-CP; Tokyo, Japan) after the participant had rested for at least 5 min on at least two occasions. According to the formula of Wiggers, the average of the second and third of three readings was computed. The mean blood pressure (MBP) was computed as DBP + one-third of the differential pressure.

Hemodynamic parameter calculations

The vessel wall is assumed to be rigid, with blood as a Newtonian fluid. Mean WSS is calculated by the Poiseuille law according to the following formulas [14]: WSSm = 4 × η × Vm/ID (dyne/cm2), where Vm is expressed in centimeters per second and ID in centimeters and η in mPa·s.

Mean circumferential wall tension (CWTm) is calculated by the Laplace law according to the following formula [16]: CWT = MBP × (ID/2) (dyne/cm2), where MBPs are expressed in dynes/cm2 and mean ID in diameters in cm.

Sometimes an accidental rise in the WSS of the parent artery can occur as part of normal daily blood pressure variance. If a significantly higher WSS was detected while the blood pressure was raised, we suggested repeating the measurement after the participant had rested for at least 5-10 min.

Note: CWT is tensile stress divided by wall thickness. CWT acts perpendicularly to the arterial wall and results from the dilating effect of blood pressure on the vessel [17].

Statistic analysis

Continuous variables were expressed as mean ± standard deviation (normal distribution) or median (quartile) (skewed distribution). Categorical variables were expressed in frequency or as a percentage. The t test (normal) or one-way ANOVA, Mann-Whitney (skewed distribution) or Kruskal-Wallis H test and chi-square tests (categorical variables) were used to determine any statistical difference between the means and proportions of the WSS groups. p < 0.05 (two-sided) was considered statistically significant. Multiple WSS models were used to evaluate the associations between exposure (WSS) and outcome (AcomA aneurysm formation). Both non-adjusted and multivariate adjusted models were used. A two-piecewise linear regression model was used to examine the threshold effect of the WSS on the AcomA aneurysm formation according to the smoothing plot. The threshold level of WSS at which the relationship between the AcomA aneurysm formation and WSS level began to change and became notable was determined using a recurrence method. The inflection point was moved along a pre-defined interval and detected the inflection point that gave the maximum model likelihood.

All analyses were performed with R (R Foundation for Statistical Computing, Vienna, Austria) and EmpowerStats (X&Y Solutions, Inc., Boston, MA, USA).

Results

Baseline characteristics of participants

The baseline characteristics of participants are shown in Table 1. The statistical results showed that there was a statistically significant difference in aneurysm morphology, coronary artery disease (CAD) and dominant A1 among the categorical variable (quartile) groups of WSS.

Table 1 Baseline characteristics of participants
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Univariate analysis for each parameter variable

The results of univariate analysis are shown in Table 2, demonstrating that the WSS (p < 0.0001), the angle between the A1 and A2 segments of ACA (p < 0.001), hypertension (grade II) (p = 0.007), fasting blood glucose (FBG; > 6.0 mmol/L) (p = 0.005), and dominant A1 (p < 0.001) were significant parameters.

Table 2 The results of univariate analysis
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Multivariate Analyses

We chose WSS for the highlighted parameter in univariate analysis as a candidate variable for multivariate analyses, which were significantly correlated with AcomA aneurysm formation.

Non-adjusted and adjusted models are shown in Table 3. In the crude model, WSS correlated with AcomA aneurysm formation (HR = 1.39, 95% CI: 1.20 to 1.60, p < 0.0001). In the minimally adjusted model (adjusted age, gender), the effect size also had a significant correlation (HR = 1.43, 95% CI: 1.23 to 1.67, p < 0.0001). After adjusting other covariates, we still identified the significance in the fully adjusted model (HR = 1.87, 95% CI: 1.36 to 2.56, p < 0.0001). For the purpose of the sensitivity analysis, we also handled WSS as a categorical variable (quartile), and the same trend was observed as well (p for trend was 0.0009).

Table 3 The results of multivariable analysis
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The results of the two-piecewise linear regression model

WSS ranging between 7.8 and 12.3 dyne/cm2 showed a significant correlation between WSS and the formation of AcomA aneurysms (HR 2.0, 95% CI: 1.3-2.8, p < 0.001). The risk of AcomA aneurysm formation increased one-fold for each additional unit of WSS (Table 4, Fig. 2).

Table 4 The results of the two-piecewise linear regression model
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Fig. 2
figure 2

The illustrated curved line relation between WSS and AcomA aneurysm formation. The area between two dotted lines is expressed as a 95% CI. Each point shows the magnitude of the WSS and is connected to form a continuous line. The magnitude of the WSS is not correlated with AcomA aneurysm formation when it is ≤ 7.8 dyne/cm2 or > 12.3 dyne/cm2. Conversely, the magnitude of the WSS ranged between 7.8 and 12.3 dyne/cm2 and showed a significant correlation with the formation of AcomA aneurysms. The risk of AcomA aneurysm formation increases as the WSS increases

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Discussion

Our study showed that the WSS (p < 0.0001), the angle between the A1 and A2 segments of the ACA (p < 0.001), hypertension (grade II) (p = 0.007), FBG (> 6.0 mmol/L) (p = 0.005), and dominant A1 (p < 0.001) were significant parameters in the formation of AcomA aneurysms. We found that the magnitude of the WSS ranged between 7.8 and 12.3 dyne/cm2 and had a significant association with AcomA aneurysm formation (HR 2.0, 95% CI: 1.3-2.8, p < 0.001), consistent with the two-piecewise linear regression model. The probability of AcomA aneurysm formation increased one-fold for each additional unit of WSS.

An accurate criterion is essential for implementation of the diagnosis and therapeutic challenges in the management of intracranial aneurysms. Among the criteria of clinic and geometric morphology, local hemodynamics are the main predictors of intracranial aneurysm formation and rupture. Increasing publications involving CFD are in favor of a high WSS with intracranial aneurysm growth and low WSS producing rupture [4, 5, 8,9,10, 18, 19], albeit a growing number of such proposals are still controversial. Other researchers have presented different views with opposite results [20,21,22]. Shojima et al [21] suggested that in contrast to the pathogenic effect of a high WSS in the initiating phase, a low WSS may facilitate aneurysm growth. We partially approved these points. Herein we propose that this controversy is probably related to the absence of accepted standards for the threshold of high or low WSS. What thresholds of high or low WSS separately vary in aneurysm development remains unclear and thus may result in divergent and controversial findings. It is also important to note that some studies have calculated the magnitude of WSS in ruptured and unruptured aneurysms [3, 5, 23]; however, the magnitude of WSS reported varies, and the threshold of high or low WSS has rarely been reported. In addition, multivariable analysis is usually taken into consideration for controversial high versus low WSS parameters [9, 10, 24]. Few researchers have studied the threshold effect of the WSS on AcomA aneurysm formation further using the two-piecewise linear regression model. We identified the threshold of WSS in the parent artery affecting AcomA aneurysm formation using a two-piecewise linear regression model ranging from 7.8 to 12.3 dyne/cm2, which is partially inconsistent with high or low WSS theory, as suggested by Meng [4] and Can et al [8]. Notably, some studies have reported that WSS values in the range of 4-15 dyn/cm2 are considered normal on the basis of endothelial cells [6]. Malek et al [6] demonstrated that arterial-level shear stress (> 15 dyne/cm2) induces endothelial quiescence and an atheroprotective gene expression profile, while low shear stress (< 4 dyne/cm2) stimulates an atherogenic phenotype; however, this normal range of WSS distinguishes the atherosclerosis-related endothelial function and phenotype rather than intracranial aneurysm-related vascular remodeling. Regardless of the differences in WSS values, the result is application using different techniques to measure flow at different locations in the arterial network [25, 26]. It also has been reported that the normal mean WSS levels range from 9.5 to 15.0 dyn/cm2 in the common carotid artery using high-resolution echo Doppler or ultrasound share rate estimation [25, 27, 28]. Gnasso et al [27] reported the mean WSS as 12.1 ± 3.1 dyn/cm2, and Samijo et al [28] reported the mean WSS as 12.4 ± 2.0 dyn/cm2 in normal populations. The findings of Gnasso et al [27] and Samijo et al [28] agreed with our criterion derived from the threshold effect of the WSS in the parent artery using two-piecewise linear regression models, suggesting that WSS ranged between 7.8 and 12.3 dyne/cm2, and independently characterized the AcomA aneurysm formation.

WSS can be evaluated noninvasively and reliably using an ultrasound-based technique, which is a common approach in vivo [13,14,15, 29, 30]. As a widely used alternative to direct measurement of near-wall velocities, Doppler studies estimate WSS from an assumed velocity profile, which has been assumed to exhibit a parabolic (i.e., Poiseuille) profile. It has been demonstrated that a Poiseuille parabolic model of velocity distribution across the arterial lumen provides a useful estimate of WSS [31]; however, some researchers have proposed that the departure from an ideal Poiseuille may lead to errors in calculating WSS [32]. At present, few studies have demonstrated the deviation involved in estimating WSS via the Poiseuille law. The Sui et al study [31], based on MRA, reported that the Poiseuille approach led to a slightly (~10%) higher WSS value compared with a 3D paraboloid-fitting method because of the neglect of diameter variations during the cardiac cycle. A more thorough study conducted by Mynard et al [32] detailed how the assumptions would affect the results, including cylindrical geometry, steady flow, and Newtonian flow. They analyzed errors in the estimation of WSS by the maximum Doppler velocity and pointed out an important consequence of velocity profile skewing; specifically, WSS is likely to vary circumferentially around the vessel wall, being higher near regions of high velocity. In vivo blood flow is pulsatile and non-Newtonian. Because the vessel is not a cylindrical structure and the vessel walls are not rigid, even a relatively axisymmetric and nearly fully developed profile could be associated with substantial circumferential variation in WSS, probably resulting in deviations. Mynard et al [32] also found that there was no significant difference in percent variations between axisymmetric (type I), skewed (type II), and crescent (type III) cases. Nevertheless, cycle-averaged WSS varies circumferentially by ± 60% about the circumferential mean. Because these assumptions in the Poiseuille law are not generally met in the arterial circulation, the estimation of WSS using these expressions is only approximate. Even though it was different from the WSS measured with the CFD technique, the result is still an objective indicator of the WSS in the ACA.

Furthermore, it has been proposed that the disturbing variables, like blood viscosity, velocity, arterial inner diameter, hematocrit, and atherosclerosis, may be associated with the WSS values [6, 27, 33,34,35,36,37,38]. Physiologically, WSS reflects a hemodynamic force that resides within the vascular endothelial surface [3, 6]. WSS is a direct product of complicated hemodynamic blood flow. Box et al [36] have documented that a decrease in flow and an increase in inner diameter result in a corresponding decrease in WSS, whereas a decrease in blood viscosity will reduce WSS [6, 27]. Other researchers have focused on the correlation between the presence of atherosclerosis and the WSS and found that atherosclerotic plaque deposition accelerates the arterial wall remodeling during progression of atherosclerosis, causing arteries to harden and narrow and increasing the tortuosity of the vasculature [6]. Atherosclerosis is prone to result in a smaller arterial inner diameter, thus forcing an increase in blood flow velocity in the elderly. Therefore, it is reasonable to find that a high WSS calculated according to Poiseuille’s law would increase. Box et al [37] propose a whole-blood viscosity modeling in which the viscosity is dependent on the hematocrit. They also demonstrated that flow and arterial inner diameter changes have a significant influence on WSS values, which is the same for blood viscosity, but to a lesser extent. Nevertheless, WSS depends more heavily on hematocrit when low plasma viscosity exists. This is also supported by previous studies in which the relationship between blood viscosity and hematocrit is well approximated by an exponential function [38].

In our study, WSS was calculated according to the Poiseuille law and equation. Although the Poiseuille law and the resulting Hagen Poiseuille formula are based on specific assumptions regarding blood flow, it is still an appealing and fascinating method due to its simplicity and is utilized by several techniques in clinical practice. One of the advantages of our method described before is that the input data used to calculate WSS (Vm and ID) are being routinely recorded and reproduced during ultrasonography. It should be noted that this model provides a useful estimation of WSS and has been confirmed in a growing number of new studies [13,14,15, 29, 30]. It is a simple and accessible method and can be widely applied in primary care facilities and community hospitals in many developing countries because of the relatively low resource intensity.

Because the WSS of the parent artery is closely related to aneurysm formation, it is very important for predicting aneurysm formation with the assistance of screening and monitoring WSS. If the threshold of the WSS associated with a high risk of aneurysm formation is established, patients who have the WSS of the parent artery in this particular range can be monitored judiciously. Early intervention is of utmost importance in such situations to curtail adverse consequences.

Our study had some limitations. First, blood flow in vivo is pulsatile, non-Newtonian, and not in a cylindrical structure, the walls of which are not rigid. The major drawback of this approach is the assumption of a linear velocity distribution and the fact that only the central peak velocity is used to measure the WSS. Thus, hemodynamic parameters calculated by the Poiseuille law according to the formula are just an approximate value. Second, procedural-related factors may also affect the accuracy of the results. Third, we only measured the WSS of the parent artery rather than that in the AcomA aneurysm itself. The direct WSS in the AcomA aneurysm could not be detected using our clinical method.

Conclusions

WSS ranged between 7.8 and 12.3 dyne/cm2 and was found to be one of the reliable hemodynamic parameters in the formation of AcomA aneurysms. The probability of AcomA aneurysm formation increases one-fold for each additional unit of WSS. An ultrasound-based TCCD technique is a simple and accessible noninvasive method for detecting WSS in vivo and thus can be applied as a screening tool for evaluating the probability of aneurysm formation in primary care facilities and community hospitals because of the relatively low resource intensity.