A review of hemodynamic parameters in cerebral aneurysm

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A R T I C L E I N F O Keywords:

Cerebral aneurysm Hemodynamics Wall shear stress Oscillatory shear index Relative residence time

A B S T R A C T

A cerebral aneurysm is a localized dilation that weakens the wall of a blood vessel in the brain. This condition comes in the form of abnormal widening, ballooning or in the form of a bleb. Gaining an understanding of the initiation, growth, and rupture of cerebral aneurysm has played a critical role in finding treatments that prevent the possibility of mortality and morbidity. Cerebral aneurysm develops as a result of the thinning of artery wall, and it is often difficult to diagnose prior to its rupture that leads to several fatal diseases, including brain damage, hemorrhagic stroke, behavioral inconsistency, and eye movement disturbance. A computational fluid dynamic study of cerebral aneurysm employs blood flow simulation wherein hemodynamic parameters indicate the rupture status of a vessel. These hemodynamic parameters actually trigger the biological factors of blood flow in the brain vessels with aneurysm. This paper offers a review of these hemodynamic parameters, and it elucidates the correlation of these parameters with cerebral aneurysm. Specifically, this review highlights the hemodynamic parameters that are related to the formation, growth, and morphological features, namely, size and shape, of cerebral aneurysm.

1. Introduction

A cerebral aneurysm is a vascular malformation in the brain’s arterial circulation involving a weakened vessel wall that is more prone to rupture. The size of cerebral aneurysm ranges from less than 0.5 mm to more than 25 mm[1]. Most aneurysms are saccular, and they are correlated with a thin media of tunica or with its absence, as well as correlated with significantly segmented internal elastic lamina or with its absence. A few aneurysms are fusiform and mycotic. Most cerebral aneurysms are silent and can be discoverable through neuroimaging or incidentally through autopsy. More than 85% of cerebral aneurysms are located in the anterior circulation at a vessel’s bifurcation. The initiation and growth of cerebral aneurysms are related to the abnormal blood flow in the bifurcation point of an artery, high blood pressure, atherosclerotic lesions, trauma, and heredity[2].

Generally, aneurysm has a high prevalence, wherein 10 out of 100,000 persons are affected by subarachnoid hemorrhage annually [3]. Subarachnoid hemorrhage is usually inextricably linked with high morbidity and mortality[4]. The detection of cerebral aneurysms has increased with the enhancement of neuroradiological technologies, but efficient monitoring of risk of rupture has not yet improved[5].

In addition, preventive surgical and endovascular treatments for cerebral aneurysms are not risk-free. These treatments aim to precisely

identify the aneurysms that will never rupture, those that will rupture, and those that could be treated is desired. Research efforts were therefore devoted to the development of statistical models that were more accurately predicting the rupture risk of aneurysms[6]. The size and location of posterior circulation arteries in the brain are typical risk factors. In the last two decades, rupture risk prediction for cerebral aneurysm in brain arteries has improved as a result of understanding the hemodynamic factors[4,6].

Currently, hemodynamic factors have deepened the interest on the study of the dynamic blood flow’s effect on cerebral aneurysm in the clinical context. In recent technology, an advanced simulation software is used in the hemodynamic analysis of cerebral aneurysm. This review paper highlights and summarizes the significant geometrical factor and hemodynamic parameters involved in cerebral aneurysm’s initiation, growth and rupture.

2. Aneurysm size, shape, and rupture risk

Aneurysm geometry is used as a primary indicator in aneurysm treatment. Unlike the hemodynamic factors, aneurysm size and shape are stationary. A minor change between aneurysm size and shape has been shown to heavily affect intra-aneurysmal flow[7]. Thus, the size and shape are important in predicting the risk of aneurysm rupture.

https://doi.org/10.1016/j.inat.2020.100716

Received 17 November 2019; Received in revised form 18 February 2020; Accepted 16 March 2020

⁎Corresponding author.

E-mail addresses:[email protected](M.A.A. Sheikh),[email protected](A.S. Shuib), [email protected](M.H.H. Mohyi).

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Aneurysm size has been described to be related to the development of cerebral aneurysm, and it can be used to predict the risk of rupture [8–10]. Korja et al. [11] reported that among 118 patients whose median size of cerebral aneurysm is 4 mm (range: 2 to 25 mm), those with an aneurysm size of larger than 7 mm had an increased risk of lifetime subarachnoid hemorrhage.

Predicting the risk of rupture based on aneurysm shape alone is insufficient[12]. In 290 intracranial aneurysm cases, the saccular aneurysm shape was further was classified into lobulated, beehive, spherical, ellipse, and pear. Elliptical shape is associated high rupture risk, whereas the round shape tends to be correlated with unruptured aneurysm [13]. However, according to studies, it implied that aneurysm geometry has remained controversial, and clinical factors must be considered as well.

Kono et al.[14]analyzed the image data of 13 patients, 5 of them have posterior circulation aneurysm. The images were examined before and after the rupture, and the results showed that the ruptured aneurysms were not shrink.

Most large aneurysm in small vessels rupture compared with the small aneurysm in large vessels. For example, an internal carotid artery with 3 mm aneurysm has a minimum chance of rupturing compared with the anterior cerebral artery with 3 mm aneurysm[15].

Various geometric indications have been reported to enhance the rupture risk prediction based on aneurysm size[16,11,9]. The common geometrical factors are the aspect ratio (AR) and size ratio (SR) as shown inFig. 1 [17]. AR is defined as the aneurysm depth (h) divided by the maximum length of the neck width (w); these parameters are perpendicular to each other. SR is defined as the maximum distance of aneurysm (hmax) divided by the diameter of the parent artery (d).

The AR of an aneurysm is the index that is likely most frequently used[18–20]. AR is the proportion between aneurysm depth and neck width. It is the height perpendicular to the neck width divided by the maximum length of the neck width. Based on the geometry of 75 ruptured and 107 unruptured aneurysms, the mean ARs for ruptured and unruptured aneurysms and were 2.7 and 1.8, respectively[19]. Simi- larly, a difference AR exists between ruptured and unruptured aneurysm as predicted by Jiang and Strother[21]. The AR of nearly 80%

of ruptured aneurysms is higher than 1.6 and that of 90% unruptured aneurysms smaller than 1.6. In a similar study, the median AR values of 119 cases of ruptured aneurysm of the anterior communicating artery, internal carotid artery, and middle cerebral artery, ranged from 0.92 to 1.13[17].

SR is defined as the maximum distance of aneurysm divided by the diameter of the parent artery. SR is the most crucial factor to correlate with the rupture risk of aneurysm[22]. The SR is easy to measure, and it provides some essential information to help determine the treatment and growth of small aneurysm in patients and to predict the rupture risk

of small aneurysms. The SR of small aneurysms, (ie., smaller than 5 mm), is significantly associated with the rupture of cerebral aneurysm [12]. Kashiwazaki and Kuroda,[12]analyzed 1,034 aneurysm cases the SR of the ruptured aneurysms was significantly higher than that of the unruptured aneurysms, although the locations or the sizes of the aneurysms did not significantly differ. The median SR of 119 cases of ruptured aneurysm of the anterior communicating artery, internal carotid artery, and middle cerebral artery ranged from 2.04 to 3.90 [17].

3. Hemodynamic forces and parameters of cerebral aneurysm The biomechanical properties of blood flow are of great sig- nificance, and they arouse the growing interest on the hemodynamic parameters that lead to the initiation, growth, and rupture of cerebral aneurysm [23]. The hydrodynamic flow of blood through vessels is referred to as hemodynamics. Hemodynamic is the study of the movement and flow of blood in the human body and in all solid structures through which it flows[24].

Fig. 2shows the types of stress related to blood flow in a straight vessel. Three types of stress in the vessel wall are influenced by blood flow [25]. Shear stress is a tangential frictional force acting on the vessel wall, Specifically, it is a perpendicular force acting on the vascular wall. Normal stress is due to hydrostatic pressure, which is the force acting orthogonally on the vessel wall. Tensile stress is the force acting against the blood vessel wall and acts in the circumferential direction.

3.1. Wall shear stress (WSS)

For many years, researchers have examined the role of WSS in the initiation, growth, and rupture of cerebral aneurysm; WSS is a dynamic force induced by the movement of a viscous fluid along the surface of Fig. 1.(A) Aspect ratio. (B) Size ratio.

Fig. 2.Three types of stress: (i) shear stress, (ii) normal stress, and (iii) tensile stress.

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blood vessel wall[26]. Generally, WSS is considered a primary parameter in cerebral aneurysm hemodynamics. Several parameters were further derived to describe the characteristics of WSS[27–29]. WSS is a dynamic tensile force triggered by a viscous fluid that moves over a solid material’s surface [30]. It is a tangential frictional force in the vessel wall and induced by the blood flow. In the context of pulsatile flow, the WSS magnitude of each element within one cardiac cycle is calculated using the time-averaged WSS[22]. WSS is calculated using by the following equation:

=

WSS T1 wss dt

| |

T i

0 (1.1)

where,wssiis the instantaneous shear stress vector and T is the duration of one cardiac cycle. Time-averaged WSS is evaluated using the characteristics for an entire time cycle; which is measured in Pa with a normal value from 1.5 to 10 and is calculated based on the accurate time-averaged magnitude of each wall mesh point vector[31,32].

Blood vessel wall responds to WSS and to wall tension in order to regulate the normal physiological flow rate. The flow in a typical saccular aneurysm with bifurcation and in an aneurysm on sidewall is shown in theFig. 3 [33,34].Fig. 3A depicts the tangential WSS induced by the blood moving across the flow velocity. Jet flow impinges toward the dome due to the bifurcation and the sudden enlargement of surface area. The kinetic energy is converted into inertial force, and the flow is reversed.Fig. 3B shows that wall tension is the vertical force resulting from the jet flow impacting the neck of the aneurysm dome[34]. Using patient-specific computational simulation modeling, Isaksen et al.[35]

reported that aneurysm rupture occurs in the middle carotid artery when the wall tension overcomes the wall tissue intensity. These

researchers investigated the maximum wall tension in the aneurysm dome on the impingement area. At the peak systole point, the wall tension is considerably high near the bifurcation point of the aneurysm neck, and the maximum velocity is reached[27].

A high WSS occurs as the viscosity and velocity of blood flow increase[26,36–38]. WSS plays a crucial role in the pathophysiology of cerebral aneurysm[28,29,38]. The influence of WSS initiation on the development and rupture impact zone could be distinct. In the last decade, WSS has been investigated in most hemodynamic related research studies. Jou & Mawad,[39]reported that flow velocity and the consequent WSS intensified on the distal side of the neck as the parent vessel’s diameter increased. Furthermore, WSS increased with the increasing neck width.

3.2. WSS gradient (WSSG)

WSSG is described by Mohamied et al.[40]as the changes of the WSS vector magnitude in a flow direction in the streamwise distance [31]. The flow direction of the spatial derivative is measured using the WSSG[31,41]. Moreover, the temporal WSSG is used to estimate the rate of changes in WSS magnitude over one cardiac cycle[42,43].

The WSSG is used in cerebral aneurysms with complex geometries arising in vessels, and it is measured in Pa/mm. The equation for WSSG is as follows:

= + +

WSSG x y z

w w w

2 2 2

(1.2) where wis the WSS vector.

Fig. 3.(A) wall shear stress and (B) wall tension (The broken line arrows indicate the flow direction and solid arrow is the force).

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3.3. Oscillatory shear index (OSI)

OSI describes a strongly oscillating path during a pulse flow that is characterized by a nondimensional parameter, and it ranges from 0 to 0.5, wherein 0 represents a steady flow and 0.5 indicates intense oscillation[44]. OSI is often used to describe the disturbance of the flow field in the aneurysm wall[22]. Himburg et al.[45]reported that the combination of low WSS and high OSI reflects the residence time of blood near the aneurysm wall. There is no consensus yet as to whether the WSS or the OSI is a meaningful indicator. However, these indicators have been linked with the regions of artery wall remodeling.

OSI shows the magnitude of WSS changes and it illustrates the tangential oscillation of force as one cardiac cycle function. The equation for OSI is as follows:

=

OSI wss dt

wss dt 1

2 1

T i

0

0 (1.3)

wherewssiis the shear stress vector, and T is the duration of one cardiac cycle.

3.4. Transverse WSS (TWSS)

TWSS is the median perpendicular to the temporal mean WSS vector over one cardiac cycle of WSS elements that are assumed to be aligned with endothelial cells[36]. This parameter introduces the physiological assumption in the crossflow that can adversely affect endothelial cells and this approach is supported by a direct in vitro proof.

Longo et al.[46]described several hemodynamic parameters that are used to calculate the hemodynamic concentration of cerebral aneurysm, and TWSS is one of them. TWSS is calculated by using a time- averaged WSS component that is perpendicular to the mean flow direction.

The average WSS is used to calculate the TWSS, and the equation was defined using the components vertically induced by the mean flow direction[40].

= ×

TransWSS

T n dt

dt dt

1 ^T

w

T w T w 0

0

0 (1.4)

where wis the WSS vector andn represents the surface normal.

3.5. Aneurysm formation indicator (AFI)

AFI is used to detect the flow stagnation area[47]. During cardiac cycle, it calculates the direction of the WSS vector blood flow in the vessel wall. Moreover, it may correlate with the location of aneurysm formation and initiation[47]. The equation for AFI is as follows:

= = ×

× WSS WSS WSS WSS

AFI cos

| | | |

i av

i av (1.5)

whereWSSi is the WSS vector and WSSavis the time-averaged WSS vector.

Many complex blood flow models exist for various important hemodynamic parameters that were indicated to describe blood flow on a vessel wall; these parameters include high and low WSS distribution, tangential force acting on the arterial wall surface, aneurysm wall expansion, high proportion of aneurysm formation, turbulent activities, and vortex or core area indication[29,48–50].

3.6. Oscillation velocity index (OVI)

OVI is used to describe different flow pattern conditions of the vascular wall in one complete cardiac cycle. OVI is quantified using the local velocity magnitude and the variation in flow patterns in one cardiac cycle. The duration of the velocity field stabilizes when the OVI

for the entire cycle is 0; by contrast, considerably strong varying flow patterns occur when the OVI is 1[48]. The equation for OVI is as follows:

=

OVI v r t dt

v r t dt

1 ( , )

( , )

T T 0

0 (1.6)

where v is the velocity vector, and T is the duration of one cardiac cycle.

3.7. Gradient oscillatory number (GON)

For cerebral aneurysm initiation, GON is a potential hemodynamic indicator, which quantifies the distortion of the tangential force caused by the blood flow on the vascular wall operating under pulsatile flow; it is a nondimensional parameter varying from 0 to 1 depending on the degree of temporal fluctuations in the spatial WSSG vector within one cardiac cycle[26,49].

=

GON Gdt

1 G dt

| |

T T0

0 (1.7)

G is the spatial WSS gradient vector, and T is the duration of one cardiac cycle. GON is used to describe the different flow pattern conditions of the vascular wall over one completed cardiac cycle[51,48].

3.8. Relative residence time (RRT)

RRT could characterize the distribution of blood flow near the proximity of the intra-aneurysmal flow vortex. RRT is an essential hemodynamic parameter used to calculate the residence time of blood cell flow circulating near the aneurysm wall. Moreover, RRT could quantify the state of disturbed flow[22,52,53]. A long-term circulation of blood flow near the aneurysm wall could lead to aneurysm rupture in a brain vessel. In a recent paper, Jiang et al.[54]stated that RRT helped to quantify and to differentiate between the thin and thick aneurysm wall regions.

RRT was examined based on the low WSS and high OSI near the aneurysm wall[22]. The equation for RRT is:

= × ×

RRT OSI WSS

1

(1 2 ) (1.8)

WSS, OSI, RRT, TWSS, WSSG, GON, AFI, and OVI are the hemodynamic parameters directly related to the initiation, growth, and rupture of cerebral aneurysm. Performing a quantitative analysis, Xiang et al.[22]used 119 aneurysm cases of computational fluid dynamics (CFD) simulation and statistically examined the rupture status based on a threshold value. The threshold values of the WSS, OSI, RRT, and WSSG were used to determine the difference between ruptured and unruptured aneurysms.

Table 1 presents the summary of the three key hemodynamic parameters, namely, WSS, OSI, and RRT. WSS and OSI are considerably relevant in predicting the rupture risk of cerebral aneurysm in CFD simulation. Long RRT associated with aneurysm wall lesions, and the extension of RRT is known as the intra-aneurysmal vortex and flow expansion at bleb[55].

4. Interaction of hemodynamic forces in cerebral aneurysms and the natural histories

4.1. Aneurysm formation

The flow environment in blood vessels correlates with the initiation of cerebral aneurysms. In the endothelial layer of the inner vessel wall, a cell reaction occurs when the hemodynamic forces are acting on the vessel wall induced by WSS [26]. Vascular remodeling, through a

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distinct expression by the endothelial cells, occurs due to high WSS and due to the changes expressed by WSSG, and several investigations have demonstrated that the initiation of aneurysm is linked to the stimula- tion of blood flow [41,56–58]. In some people who display de novo aneurysm development in the area of proximal stenosis, the shear stress changed under the state of turbulent flow[59–61]. An aneurysm formation indicator was used to determine the possibility of aneurysmal development which is indicated by the minimum rate of the WSS regions as well as a revolving WSS vector [59,62]. However, some researchers did not establish the connection between this index and WSSG, particularly when the vessels are close to each other. For this reason, another parameter defines the fluctuations of WSS vector over one cardiac cycle process was put forward, namely, GON[63].

In animal models, hemodynamic forces in cerebral aneurysm development were extensively evaluated in order to examine the vascular reaction to threats of shear stress. Alfano et al.[64]reported that cerebral aneurysm frequently occurs around 10 primary bifurcation points located around the circle of Willis. In the hemodynamic impact zone, cerebral aneurysms are associated with the magnitude of WSS and with positive WSSG. Cerebral aneurysms occur more frequently in a cerebral bifurcation, which typically experiences higher hemodynamic stress and a strong acceleration of flow conditions. By contrast, Meng et al.

[3]and Sejkorova et al.[65]reported that three distinct zones and two sidewall locations are in correspond to the arterial bifurcation point near the area shown inFig. 4 [46]. whereas At an WSS of 2 Pa, favor- able WSSG scores were obtained at the apex of sector 1 in the flow

impingement zone, and the WSSG calculated with positive values of 1–10 Pa/mm tends to improve quickly. Both WSS and WSSG significantly increased in the region close to the cusp in sector 2 or in the acceleration zone. The WSSG decreased after its peak point, whereas the WSS maintained its elevated numbers level of approximately 13Pa.

In this region, the formation of aneurysm may trigger the combination of several damaging events, such as the thinning of matrix degradation media, an average reduction of the internal elastic lamina. The inlet of different vessels is defined by small WSSG and steadily decreasing WSS in sector 3 or in the flow deceleration zone. In sectors 4 and 5, the bifurcation point of the vessel wall aneurysm occurs under high WSS in large or small vessels. At the early stage, rupture may be associate with WSS, which reaches its maximum point and continues to decline at approximately 1.5N m/²after this phase[58,66,67].

4.2. Aneurysm growth

Despite the extensive research on the location of interaction among hemodynamic forces during aneurysmal development, the exact cause of aneurysmal development remains uncertain [23,38,68,69]. Two different models influenced by distinct processes have been illustrated:

the models of blood flow change as a consequence of the increase and decrease in WSS[26,44,70–74]. The lower WSS concept demonstrates that the damage in endothelial cells is caused by shear stress and that vascular remodeling occurs from due to pro-inflammatory changes, enhancing the development of cerebral aneurysm[29,75]. Due to the disproportion between the stress in cerebral aneurysm wall and the elevated blood flow, the vessel wall dilates locally[76,77]. By contrast, several studies supported the hypothesis of low shear stress[49,78–80].

Chubin et al.[81]analyzed four aneurysm geometries by using a multiphase model of blood validated with experimental data to predict the low WSS of white blood cells and the flow distribution.

Another case study involving a 57-year old woman showed the occurrence of two unruptured aneurysms in the middle carotid artery and one ruptured aneurysm in the anterior carotid artery; the unruptured aneurysm grew with high WSS grew in 7 months, whereas the ruptured aneurysm with low WSS and high OSI grew in 11 months[82].

Aneurysm size is one of the most essential rupture risk factors that promote aneurysmal growth as shown by various follow-up studies. An aneurysm of greater size has a higher risk of rupture before the growth of the aneurysm. Aneurysm development is likely to be an erratic and interminable process involving long and short periods of aneurysm wall stability, allowing aneurysm to grow or rupture temporarily. Conse- quently, in the imaging technique, the stability of aneurysm wall should related to the atherosclerotic lesions in intra-aneurysmal wall.

Sugiyama et al., (2016)[53] RRT The age-of-fluid concept was used to calculate the residence time of blood near the aneurysm wall. Maximum RRT was found inside the atherosclerotic aneurysm but not non-atherosclerotic aneurysm.

Xiang et al., (2011)[22] WSS, OSI, and RRT A threshold value of the hemodynamic parameters was used to differentiate between the ruptured and unruptured aneurysms.

Fig. 4.Graphical model of an arterial bifurcation showing the three distinct sectors of the impact zone and the two sidewall sectors of the arterial bifurcation points.

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not be interpreted following the growth of the aneurysm. After growth, the median time of aneurysm development is 25–30 months as reported in different studies, and the commonly predicted risk factors were the size of aneurysm, hypertension, history of subarachnoid hemorrhage, dome or neck ratio, and the location of posterior circulation[8,10,83].

The growth of cerebral aneurysms and the hemodynamic forces are linked to the detected changes in endothelial cells and vessel wall under low WSS and to the higher chance of aneurysm development[38]. For instance, inflammatory cell infiltration through the endothelial layer is caused by nitrous oxides, and therefore it enhances the durability known as low WSS impact[37,84]. Moreover, researchers found that aneurysmal growth may occur in the bifurcation point with the high and low WSS, and in an inflow point with high OSI[69,85].

5. Conclusion

The principle of the hemodynamic parameters involved in the initiation, growth, and rupture of cerebral aneurysm could be understood in terms of blood vessel morphology and hemodynamics. Aneurysm size and shape have been identified as key indicators in predicting the risk of rupture in cerebral aneurysm. Hemodynamic forces are theoretically related to the development of cerebral aneurysms. WSS has been identified as a key parameter that links pressure with the vasodilation and constriction of blood vessels. Aneurysms occur at the bifurcation points in the vasculature with a sustained abnormally high and low WSS. Other hemodynamic parameters derived from WSS are WSSG, OSI, TWSS, AFI, OVI, GON, and RRT. The WSS, OSI, and RRT were widely investigated compared with the rest of the parameters in order to identify the risk of rupture. Future studies must correlate hemodynamic parameters with rupture risk based on solid clinical evidence.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors acknowledge the financial support provided by Taylor's University Malaysia through Taylor's University Flagship Research Programme (TUFR) and Taylor's Research Excellence Scholarship.

Appendix A. Supplementary data

Supplementary data to this article can be found online athttps://

doi.org/10.1016/j.inat.2020.100716.

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