**3. Computational fluid dynamics (CFD) of intracranial aneurysms**

The actual process of modeling hemodynamic parameters consists of several steps. Creating a 3D model is done by manual or semiautomatic segmentation (**Figure 1**). Angiographic examinations (3D angiography, CT angiography, or MR angiography) are used as the source data. Each radiological method has its own limitations (calcifications, flow artifacts, etc.). Several studies have tried to assess the relationship between different imaging examinations [14, 15]. In one such study, the authors compared the results of CFD obtained from CTA or DSA [14]. In conclusion, the authors state that, despite the quantitative differences in the individual hemodynamic parameters between the CTA and the DSA segmented group, the basic flow characteristics of both groups were identical.

In the next step, a calculation is performed using the Navier-Stokes equations, which describe the flow of incompressible fluid with constant viscosity. The use of the numerical solution of the Navier-Stokes equations calculates with assumption of blood having laminar flow. Possible influences of phenomena not captured by this model are further investigated, such as the influence of turbulent flow or viscosity change depending on the shear stress [16–19].

#### **Figure 1.**

*The process of obtaining patient-specific geometry from the CT or MR scan with high resolution includes accurate voxel segmentation of the vessel, generating surface mesh, and finally smoothing, generating volumetric mesh, and prescribing inlets and outlets with possible shortening and elongating of the outputs.*

These calculations characterize the flow, i.e., they provide information about fluid velocity and pressure on the vessel wall and the quantities derived there from such a stress tensor. Due to the uncertainty in the description of the area, as well as the specified boundary conditions, the inconsistency of these variables may be significant, but certain global-derived quantities—wall shear stress and oscillatory shear index (OSI)—are identical for a certain variation in the accuracy of numerical solutions [20]. WSS is defined as the pressure that acts in parallel with the blood vessel lumen. The OSI then describes the difference between the WSS vector and the blood flow during the cardiac cycle. When interpreting the data, we always need to bear in mind the approximations and assumptions during the process of CFD modeling.

The development of intracranial aneurysm can be divided into three phases: initiation, growth, and stabilization. Only a small percentage of aneurysms are unstable, progressing, and eventually resulting in rupture. The growth, shape change, and rupture of the aneurysm are the situations that we try to understand by mathematical modeling and to estimate the risk of these critical phases of development.

#### **3.1 CFD in ruptured vs. unruptured intracranial aneurysms**

One way to determine the risk of intracranial aneurysms is to compare the hemodynamic characteristics between ruptured and unruptured aneurysms. We can either compare non-specific aneurysms based on the status of rupture or only compare ruptured and unruptured aneurysms either at specific locations (MCA, PCom, etc.) or the so-called "mirror" aneurysms (right and left PCom or MCA aneurysms) [21, 22].

To date, several studies have been conducted to compare ruptured and unruptured aneurysms [22, 23]. Some of them were performed on a large number of aneurysms; others were focused on a small number of aneurysms at a specific location [22, 24–26]. The aim of these studies was to find differences between morphological and hemodynamic parameters, which would distinguish both groups. The characteristics of ruptured aneurysms could then help to identify the risky ones.

In one of the largest studies on 119 aneurysms, the authors found differences in 4 morphological and 6 hemodynamic parameters between ruptured and unruptured intracranial aneurysms [27]. The multivariate logistic regression analysis revealed that the morphological factor of size ratio and two hemodynamic factors, WSS and OSI, were independent factors of rupture risk. In 2017, a meta-analysis was published which, based on 1257 aneurysms from 22 studies, evaluated differences in hemodynamic parameters between ruptured and unruptured aneurysms. It showed that in ruptured aneurysms, WSS is significantly lower than in unruptured ones [28]. The same result was shown on 106 ACM aneurysms [22]. Alternatively, the largest ever study comparing ruptured and unruptured aneurysms has shown that wall shear stress is higher than those in unruptured aneurysms [29].

Previous results must therefore be given careful consideration as many factors have a significant influence on WSS. The meta-analysis itself shows, for example, the difference in WSS in aneurysms at different locations (the lowest is in the aneurysms of the apex of the basilar artery). One way to eliminate the influence of different localizations is to compare either the so-called mirror aneurysms (right and left IA MCA or PCom) or aneurysms of one localization in general (ACom, ICA, MCA, PCom, etc.).

Another important factor affecting IA hemodynamics is their size [13, 30]. We compared hemodynamic factors in small and large aneurysms based on the largest diameter of 10 mm (small <10 mm, large >10 mm) as this is commonly used to

**25**

apex of the aneurysm sac.

*Hemodynamics in Ruptured Intracranial Aneurysms DOI: http://dx.doi.org/10.5772/intechopen.88695*

the surface of the aneurysm sac [31].

**3.2 CFD in ruptured intracranial aneurysms**

differentiate between small and large aneurysms in clinical practice (publication in preparation). We have found that size significantly influences the WSS within the aneurysm, independent of its rupture status. WSS in small aneurysms was significantly smaller. The only similar study used a volume of the sac to differentiate small and large aneurysms [30]. However, in clinical practice, the volume of the sac is not assessed on a regular basis, and its use is less practical in clinics. Nonetheless the results of both studies emphasize the importance of aneurysm size assessment with respect to evaluation of hemodynamic factors; generally it is necessary to compare hemodynamic parameters in equally sized aneurysms. One possible way to circumvent this effect is to use the so-called WSS statistical maps to convert the results to

Specific limitations of studies comparing ruptured and unruptured aneurysms result from the fact that we already assess the condition given by rupture, not the aneurysm at risk, before rupture. Therefore, altered morphology of the aneurysm after rupture can lead to erroneous results or misinterpretations [32]. Another limitation in these studies is that we usually do not possess the individual boundary

The study of hemodynamics in ruptured aneurysms provides a chance to link the hemodynamic parameters with rupture (**Figure 2A**–**D**). Most studies have focused on the aneurysm sac as a whole. However, the aneurysm sac in ruptured aneurysms may be divided into the site of the rupture and the surrounding part of the sac. In these rare cases when we are able to differentiate those two parts of the aneurysm sac, we can combine our knowledge with local hemodynamic parameters. There are two types of studies in which the authors were able to identify the point of rupture. Firstly, there are surgical series when the neurosurgeon perioperatively identifies the site of rupture (perioperative rupture, apparent wall rupture during inspection of the sac usually before clip deployment, etc.) [33, 34]. Secondly, there are mostly case reports when the rupture in the angiographic room occurs, and the leakage of blood from the sac is thus identifiable during the interventional procedure [35, 36].

The site of rupture may show specific hemodynamic features (**Figure 2D**). So far there have been few studies with altogether a low number of patients (around 40 in total). The results are rather contradictory as it is apparent from the table; thus, it is difficult to make any straightforward general conclusions (**Table 1**). It seems that the site of rupture is associated either with concentrated jet flow and high WSS (**Figure 2D**) or, on the other hand, a slow flow and low WSS. Both types of flow can lead to degeneration of the blood vessel wall but via a different mechanism [13]. Whereas low WSS and high OSI may lead to the activation of inflammatory cells and impairment of vessel wall structure, high WSS leads to the activation of cells in the vessel wall, leading to the growth of aneurysm sacs and rupture in small sacs or blebs. Reaching a certain size of the aneurysm sac during its growth leads to slowing the flow and recirculations, resulting in WSS decrease. In the IA itself, the highest WSS is usually around the neck and it decreases toward the apex. The low WSS can lead to degradation of the internal structure of the vessel wall and a further increase in the size of the sac. Most ruptures take place just in the

The disadvantage of all studies evaluating local hemodynamic parameters relative to the rupture site is the same as in all studies evaluating ruptured aneurysms. As mentioned above ruptured aneurysms may have a different shape after rupture, which can influence the results of hemodynamic modeling parameters as compared to the pre-rupture situation [32, 37]. Studies in which a hemodynamic analysis was

conditions for each aneurysm and need to use literature-based information.

*Hemodynamics in Ruptured Intracranial Aneurysms DOI: http://dx.doi.org/10.5772/intechopen.88695*

*New Insight into Cerebrovascular Diseases - An Updated Comprehensive Review*

**3.1 CFD in ruptured vs. unruptured intracranial aneurysms**

These calculations characterize the flow, i.e., they provide information about fluid velocity and pressure on the vessel wall and the quantities derived there from such a stress tensor. Due to the uncertainty in the description of the area, as well as the specified boundary conditions, the inconsistency of these variables may be significant, but certain global-derived quantities—wall shear stress and oscillatory shear index (OSI)—are identical for a certain variation in the accuracy of numerical solutions [20]. WSS is defined as the pressure that acts in parallel with the blood vessel lumen. The OSI then describes the difference between the WSS vector and the blood flow during the cardiac cycle. When interpreting the data, we always need to bear in mind the approximations and assumptions during the process of CFD

The development of intracranial aneurysm can be divided into three phases: initiation, growth, and stabilization. Only a small percentage of aneurysms are unstable, progressing, and eventually resulting in rupture. The growth, shape change, and rupture of the aneurysm are the situations that we try to understand by mathematical modeling and to estimate the risk of these critical phases of

One way to determine the risk of intracranial aneurysms is to compare the hemodynamic characteristics between ruptured and unruptured aneurysms. We can either compare non-specific aneurysms based on the status of rupture or only compare ruptured and unruptured aneurysms either at specific locations (MCA, PCom, etc.) or the so-called "mirror" aneurysms (right and left PCom or MCA

To date, several studies have been conducted to compare ruptured and unruptured aneurysms [22, 23]. Some of them were performed on a large number of aneurysms; others were focused on a small number of aneurysms at a specific location [22, 24–26]. The aim of these studies was to find differences between morphological and hemodynamic parameters, which would distinguish both groups. The characteristics of ruptured aneurysms could then help to identify the risky ones. In one of the largest studies on 119 aneurysms, the authors found differences in 4 morphological and 6 hemodynamic parameters between ruptured and unruptured intracranial aneurysms [27]. The multivariate logistic regression analysis revealed that the morphological factor of size ratio and two hemodynamic factors, WSS and OSI, were independent factors of rupture risk. In 2017, a meta-analysis was published which, based on 1257 aneurysms from 22 studies, evaluated differences in hemodynamic parameters between ruptured and unruptured aneurysms. It showed that in ruptured aneurysms, WSS is significantly lower than in unruptured ones [28]. The same result was shown on 106 ACM aneurysms [22]. Alternatively, the largest ever study comparing ruptured and unruptured aneurysms has shown

that wall shear stress is higher than those in unruptured aneurysms [29].

Previous results must therefore be given careful consideration as many factors have a significant influence on WSS. The meta-analysis itself shows, for example, the difference in WSS in aneurysms at different locations (the lowest is in the aneurysms of the apex of the basilar artery). One way to eliminate the influence of different localizations is to compare either the so-called mirror aneurysms (right and left IA MCA or PCom) or aneurysms of one localization in general (ACom,

Another important factor affecting IA hemodynamics is their size [13, 30]. We compared hemodynamic factors in small and large aneurysms based on the largest diameter of 10 mm (small <10 mm, large >10 mm) as this is commonly used to

**24**

ICA, MCA, PCom, etc.).

modeling.

development.

aneurysms) [21, 22].

differentiate between small and large aneurysms in clinical practice (publication in preparation). We have found that size significantly influences the WSS within the aneurysm, independent of its rupture status. WSS in small aneurysms was significantly smaller. The only similar study used a volume of the sac to differentiate small and large aneurysms [30]. However, in clinical practice, the volume of the sac is not assessed on a regular basis, and its use is less practical in clinics. Nonetheless the results of both studies emphasize the importance of aneurysm size assessment with respect to evaluation of hemodynamic factors; generally it is necessary to compare hemodynamic parameters in equally sized aneurysms. One possible way to circumvent this effect is to use the so-called WSS statistical maps to convert the results to the surface of the aneurysm sac [31].

Specific limitations of studies comparing ruptured and unruptured aneurysms result from the fact that we already assess the condition given by rupture, not the aneurysm at risk, before rupture. Therefore, altered morphology of the aneurysm after rupture can lead to erroneous results or misinterpretations [32]. Another limitation in these studies is that we usually do not possess the individual boundary conditions for each aneurysm and need to use literature-based information.

#### **3.2 CFD in ruptured intracranial aneurysms**

The study of hemodynamics in ruptured aneurysms provides a chance to link the hemodynamic parameters with rupture (**Figure 2A**–**D**). Most studies have focused on the aneurysm sac as a whole. However, the aneurysm sac in ruptured aneurysms may be divided into the site of the rupture and the surrounding part of the sac. In these rare cases when we are able to differentiate those two parts of the aneurysm sac, we can combine our knowledge with local hemodynamic parameters. There are two types of studies in which the authors were able to identify the point of rupture. Firstly, there are surgical series when the neurosurgeon perioperatively identifies the site of rupture (perioperative rupture, apparent wall rupture during inspection of the sac usually before clip deployment, etc.) [33, 34]. Secondly, there are mostly case reports when the rupture in the angiographic room occurs, and the leakage of blood from the sac is thus identifiable during the interventional procedure [35, 36].

The site of rupture may show specific hemodynamic features (**Figure 2D**). So far there have been few studies with altogether a low number of patients (around 40 in total). The results are rather contradictory as it is apparent from the table; thus, it is difficult to make any straightforward general conclusions (**Table 1**).

It seems that the site of rupture is associated either with concentrated jet flow and high WSS (**Figure 2D**) or, on the other hand, a slow flow and low WSS. Both types of flow can lead to degeneration of the blood vessel wall but via a different mechanism [13]. Whereas low WSS and high OSI may lead to the activation of inflammatory cells and impairment of vessel wall structure, high WSS leads to the activation of cells in the vessel wall, leading to the growth of aneurysm sacs and rupture in small sacs or blebs. Reaching a certain size of the aneurysm sac during its growth leads to slowing the flow and recirculations, resulting in WSS decrease. In the IA itself, the highest WSS is usually around the neck and it decreases toward the apex. The low WSS can lead to degradation of the internal structure of the vessel wall and a further increase in the size of the sac. Most ruptures take place just in the apex of the aneurysm sac.

The disadvantage of all studies evaluating local hemodynamic parameters relative to the rupture site is the same as in all studies evaluating ruptured aneurysms. As mentioned above ruptured aneurysms may have a different shape after rupture, which can influence the results of hemodynamic modeling parameters as compared to the pre-rupture situation [32, 37]. Studies in which a hemodynamic analysis was

#### **Figure 2.**

*(A–C) Development of WSS over time in an IA that eventually ruptured. The WSS gradually decreased between the years 2007 and 2011. (D) A ruptured ACom aneurysm. The point of rupture (\*) was confirmed during surgery. It was associated with increased WSS. (E) A perioperative image showing a ruptured MCA aneurysm. The point of rupture is in the weak part of the aneurysm wall. (F) A perioperative image showing an unruptured MCA aneurysm with heterogenous wall, an atherosclerotic part with a thrombus inside (black asterisk) and a red thin wall (white asterisk). (G) A histological image showing in detail the vessel wall of the Willis's circle without an aneurysm: the structure consists of the tunica intima with endothelial cells, which is separated from the tunica media by the internal elastic lamina (IEL), the tunica media with linear layer of smooth muscle cells, and the tunica adventitia, the outermost layer, which comprise mainly of collagen. (H) An UIA: moderate structural changes of the vessel wall, mainly fibrosis across the vessel wall without layers and the internal elastic lamina. (I) A ruptured IA: severe structural changes of the vessel wall. The wall is thinner, without tunica intima, and linear layer of smooth muscle cells, with the presence of organized thrombus (Masson trichrome staining in all three histological images).*

performed shortly before rupture avoid this limitation and may be helpful [35, 38]. These studies are rare, but their results are important, as they provide a hemodynamic characteristic within an extremely vulnerable aneurysm (which will soon rupture). Zhang et al. described three cases of large carotid aneurysms just before their rupture (2–5 days before SAK from aneurysm) and compared them with the same large eight unruptured ones [35]. They found that all ruptured aneurysms had an irregular shape and a higher aspect ratio (AR), and the WSS was lower than in the parent artery, as opposed to ruptured aneurysms. Additionally, in another study where the hemodynamic study of the basilar artery apex was performed 2 hours before the aneurysm rupture, the authors also found that in this aneurysm, WSS was lower than the parent artery [38]. However, the actual rupture site was associated with high WSS at the point of the blood jet into the sac. We found a similar flow characteristic in our case report where the site of rupture correlated with concentrated jet flow accompanied with high WSS and high normal pressure [39].

Understanding the changes in hemodynamics in ruptured aneurysms over time before the moment of rupture is of great importance; such studies are obviously quite

**27**

*Hemodynamics in Ruptured Intracranial Aneurysms DOI: http://dx.doi.org/10.5772/intechopen.88695*

**cases**

*CFD studies evaluating hemodynamic parameters at the known site of rupture.*

**Author, year No. of** 

Omodaka et al., 2012 [56]

Fukazawa et al., 2015 [34]

**Table 1.**

active treatment of monitored UIA.

**aneurysms**

rare [32, 40]. Our own study showed that a secondary aneurysm, a frequent rupture site, was observed in the aneurysm that subsequently ruptured (**Figure 2A**-**C**) [40]. WSS was reduced and the flow was slow at the rupture point. Over time, the area of low WSS increases in aneurysms that rupture (Sejkorová et al., in preparation). Such studies are vital for identifying the hemodynamic factors associated with the increased risk of rupture and may possibly be used in the future as an indicator for the

**Identification of rupture**

Kono et al., 2012 [33] 1 3DRA Low WSS at diastole and high pressure

Hodis et al., 2013 [36] 1 2DA Jet flow, elevated WSS, and pressure at

Cebral et al., 2015 [57] 9 3DRA and CT High WSS Hejčl et al., 2017 [39] 1 Periop finding Jet flow and high WSS Wang et al., 2018 [58] 1 Periop finding Low WSS and high OSI Suzuki et al. 2019 [59] 7 Periop finding Max pressure areas, then decreased

6 Periop finding Low WSS and high OSI

12 Periop finding Low WSS and slow flow

**Hemodynamics at the site of rupture**

at systole

systole

WSS

**3.3 Correlating hemodynamics with the histology of the wall of intracranial** 

prior to the event, the unruptured one could be ruptured in a few hours.

Frösen et al. classified four types of histological wall structures of aneurysms, based on disorganization of the vessel wall structure, myointimal hyperplasia or hypocellularity of the vessel wall, smooth muscle cell (SMC) proliferation, and the presence of organized thrombus [42]. The ruptured aneurysm wall is more often characterized by being disorganized, thinner, hypocellular, with an organized thrombus present (**Figure 2I**). Different types of wall structures can be found within one aneurysm sac. One of the first studies to correlate hemodynamic parameters with the pattern of the vessel wall has recently been published [43]. Quite

One of the shortcomings of mathematical modeling is that we still know little about the relationship between hemodynamics and its influence of the biology of the vessel wall [41]. Understanding the balance between the flow and the biology of the aneurysm wall is the key factor in the life cycle intracranial aneurysms. The aneurysm wall ruptures when there is an imbalance between the aneurysm wall thickness and hemodynamic forces; both reciprocities are influenced. Modeling the relationship between histological changes and hemodynamic parameters is a logical way of research development (**Figure 2E**–**I**). The correlation of histological changes with mathematical models can help to verify the accuracy of mathematical models of hemodynamics, to improve understanding of the acquired data, and to transfer this methodology closer to practice in clinical neurosurgery. The correlation of histological changes and hemodynamics avoids errors related to CFD parameter evaluation in relation to, for example, aneurysm rupture; while the ruptured one was not ruptured *Hemodynamics in Ruptured Intracranial Aneurysms DOI: http://dx.doi.org/10.5772/intechopen.88695*


#### **Table 1.**

*New Insight into Cerebrovascular Diseases - An Updated Comprehensive Review*

performed shortly before rupture avoid this limitation and may be helpful [35, 38]. These studies are rare, but their results are important, as they provide a hemodynamic characteristic within an extremely vulnerable aneurysm (which will soon rupture). Zhang et al. described three cases of large carotid aneurysms just before their rupture (2–5 days before SAK from aneurysm) and compared them with the same large eight unruptured ones [35]. They found that all ruptured aneurysms had an irregular shape and a higher aspect ratio (AR), and the WSS was lower than in the parent artery, as opposed to ruptured aneurysms. Additionally, in another study where the hemodynamic study of the basilar artery apex was performed 2 hours before the aneurysm rupture, the authors also found that in this aneurysm, WSS was lower than the parent artery [38]. However, the actual rupture site was associated with high WSS at the point of the blood jet into the sac. We found a similar flow characteristic in our case report where the site of rupture correlated with concentrated jet flow accompanied with high WSS and high normal pressure [39]. Understanding the changes in hemodynamics in ruptured aneurysms over time before the moment of rupture is of great importance; such studies are obviously quite

*(Masson trichrome staining in all three histological images).*

*(A–C) Development of WSS over time in an IA that eventually ruptured. The WSS gradually decreased between the years 2007 and 2011. (D) A ruptured ACom aneurysm. The point of rupture (\*) was confirmed during surgery. It was associated with increased WSS. (E) A perioperative image showing a ruptured MCA aneurysm. The point of rupture is in the weak part of the aneurysm wall. (F) A perioperative image showing an unruptured MCA aneurysm with heterogenous wall, an atherosclerotic part with a thrombus inside (black asterisk) and a red thin wall (white asterisk). (G) A histological image showing in detail the vessel wall of the Willis's circle without an aneurysm: the structure consists of the tunica intima with endothelial cells, which is separated from the tunica media by the internal elastic lamina (IEL), the tunica media with linear layer of smooth muscle cells, and the tunica adventitia, the outermost layer, which comprise mainly of collagen. (H) An UIA: moderate structural changes of the vessel wall, mainly fibrosis across the vessel wall without layers and the internal elastic lamina. (I) A ruptured IA: severe structural changes of the vessel wall. The wall is thinner, without tunica intima, and linear layer of smooth muscle cells, with the presence of organized thrombus* 

**26**

**Figure 2.**

*CFD studies evaluating hemodynamic parameters at the known site of rupture.*

rare [32, 40]. Our own study showed that a secondary aneurysm, a frequent rupture site, was observed in the aneurysm that subsequently ruptured (**Figure 2A**-**C**) [40]. WSS was reduced and the flow was slow at the rupture point. Over time, the area of low WSS increases in aneurysms that rupture (Sejkorová et al., in preparation). Such studies are vital for identifying the hemodynamic factors associated with the increased risk of rupture and may possibly be used in the future as an indicator for the active treatment of monitored UIA.
