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

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 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

#### **Figure 3.**

*(Left panel) Red, thin areas on aneurysm wall are more often associated with low WSS. (A1) Right ICA aneurysm. (A2) Intraoperative microscopical view. (A3) CFD analysis. (Right panel) Yellow, atherosclerotic areas on aneurysm wall are more often associated with low WSS, high pressure, diverging WSS vectors, direct impact of streamlines with high-velocity flow (labeled with "1" in the figure). (B1) Anterior communicating artery aneurysm. (B2) Intraoperative endoscopic view. (B3) CFD analysis.*

surprisingly, the authors found that the high WSS and high-velocity flow were associated with the appearance of inflammatory changes in the aneurysm wall, while low flow areas were associated with degenerative changes in the aneurysm wall and loss of smooth muscle and pericytes. This finding is quite different from the previous studies, which did not correlate hemodynamics and histological characteristics. The correlation of histological changes and hemodynamics avoids the risk of error in comparing ruptured and unruptured aneurysms. There will most likely be a difference between an aneurysm that never ruptures and an aneurysm whose rupture is imminent. However it is not known which aneurysms we are analyzing.

In a less elaborative way, CFD modeling can be correlated simply with the perioperative findings during surgery (**Figures 2E**, **F and 3**). The wall of many aneurysms can be heterogenous including thin red areas, calcifications, and the thick yellow atherosclerotic wall part. In one such study, red, thin aneurysm wall areas were more often associated with low WSS (**Figure 3A1–3**) [44]. A total of 39 areas were identified and directly visually inspected on the aneurysms walls. The study showed that red, thin aneurysm wall areas were more often associated with low WSS, high pressure, parallel WSS vectors, and curved streamlines (75%) [40]. On the other hand, the association of low WSS with high pressure, diverging WSS vectors, direct impact of streamlines, and high-velocity flow more frequently matched with yellow, atherosclerotic aneurysm walls (79%) (**Figure 3B1–3**). Although routinely used imaging techniques can provide information about morphology and anatomical relationships of the aneurysm with the surrounding structures, there is currently no way to predict the thickness of the aneurysm wall. CFD can potentially provide this kind of information, which would be valuable not only to assess rupture risk but also to improve the surgical strategy during clipping or coiling. The authors of this study hypothesize that direct, high-velocity impact of blood flow on a specific area of the aneurysm could trigger a remodeling of the wall, ultimately leading to a reactive thickening.

In our recent project, we evaluated histological changes in ruptured and unruptured intracranial aneurysms. According to our preliminary data on the first 30 samples of individuals with ruptured and unruptured IA together with some control samples from similar locations of the cadaver's Willis's circle, the wall was

**29**

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

sclerotic wall, etc.) by a neurosurgeon.

quite complicated to be applied in clinical practice.

ing of atherosclerosis and degenerative changes in the vascular wall.

**3.4 Hemodynamics and the risk of intracranial aneurysm rupture**

The degeneration of the aneurysm wall progresses from the neck toward the dome. Aneurysm rupture usually occurs at the apex, which is also often a low shear stress region. According to a large meta-analysis by Zhou et al., the low shear stress (0–1.5 Pa) in the aneurysm sac is a characteristic of ruptured aneurysms [28]. It

limitations:

damaged by scarring, with the disappearance of the tunica intima and the internal elastic membrane, in patients with both ruptured and unruptured aneurysms (**Figure 2G**–**I**). In the classification according to Frösen et al., categories A to C were demonstrated for unruptured IA, i.e., minor to moderate structural changes, such as fibrosis and disorganization of SMC (**Figure 2H**). However, the wall of ruptured aneurysms was thin, hypocellular, and fibrotized, often with the presence of an organized thrombus (**Figure 2I**). In the classification according to Frösen, it

corresponded to categories C and D, i.e., a significantly damaged wall.

The correlation of vessel wall biology in intracranial aneurysms also has

1.Resection of only a part of the aneurysm sac. The entire aneurysm cannot be taken for histological evaluation. Due to the need to close at least the neck, but often also significant parts of the dome with an aneurysm clip, it is often possible to remove only the apex bag, even for larger aneurysms. Often small aneurysms are all hidden within a clip. On the other hand, large aneurysms often have a wall that is altered by atherosclerosis, weakened or calcified, and thus requires the application of, for example, several parallel clips and often a minimal residue of free sac to allow for sampling. A possible, at least partial, solution is the correlation of hemodynamics with the perioperative description of the aneurysm wall character (thinned wall, calcification, thickened athero-

2. 3D orientation of the histological sample against angiographic imaging. The problem is the orientation of the cut bag in 3D space or 3D neuroradiological mapping. The hemodynamic parameters are processed in a 3D image based on CTA or 3D DSA. However, after cutting off the tip of the bag, it is necessary to orient the specimen and mark it properly so that the histology of the vessel wall with hemodynamic results can be ideally correlated. So far, a methodological study has been published to address this topic. However, it is currently

Another disease that is also used to investigate the relationship between atherosclerosis and hemodynamics is the carotid plaque in the bifurcation of the common carotid artery (**Figure 4**) [45]. This model is more advantageous for several reasons. It can be removed completely without disturbing its structure and then prepared for histological examination in one piece. Due to the size of the plaque and a simple orientation in the 3D geometry of the carotid arteries, the spatial correlation of the plaque model relative to the 3D image of hemodynamic calculations is simple. Also mathematical calculations on the carotid arteries are significantly simpler due to the relatively flat shape of the vessels and the larger cross-sectional size of the arteries, which are thus less affected by minor inequalities and errors given by the neuroradiological images. Therefore, the histological studies of carotid plaques in correlation with hemodynamic characteristics in the common carotid bifurcation can be performed with fewer approximations and thus can contribute to the understand*Hemodynamics in Ruptured Intracranial Aneurysms DOI: http://dx.doi.org/10.5772/intechopen.88695*

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

surprisingly, the authors found that the high WSS and high-velocity flow were associated with the appearance of inflammatory changes in the aneurysm wall, while low flow areas were associated with degenerative changes in the aneurysm wall and loss of smooth muscle and pericytes. This finding is quite different from the previous studies, which did not correlate hemodynamics and histological characteristics. The correlation of histological changes and hemodynamics avoids the risk of error in comparing ruptured and unruptured aneurysms. There will most likely be a difference between an aneurysm that never ruptures and an aneurysm whose rupture

*(Left panel) Red, thin areas on aneurysm wall are more often associated with low WSS. (A1) Right ICA aneurysm. (A2) Intraoperative microscopical view. (A3) CFD analysis. (Right panel) Yellow, atherosclerotic areas on aneurysm wall are more often associated with low WSS, high pressure, diverging WSS vectors, direct impact of streamlines with high-velocity flow (labeled with "1" in the figure). (B1) Anterior communicating* 

*artery aneurysm. (B2) Intraoperative endoscopic view. (B3) CFD analysis.*

In a less elaborative way, CFD modeling can be correlated simply with the perioperative findings during surgery (**Figures 2E**, **F and 3**). The wall of many aneurysms can be heterogenous including thin red areas, calcifications, and the thick yellow atherosclerotic wall part. In one such study, red, thin aneurysm wall areas were more often associated with low WSS (**Figure 3A1–3**) [44]. A total of 39 areas were identified and directly visually inspected on the aneurysms walls. The study showed that red, thin aneurysm wall areas were more often associated with low WSS, high pressure, parallel WSS vectors, and curved streamlines (75%) [40]. On the other hand, the association of low WSS with high pressure, diverging WSS vectors, direct impact of streamlines, and high-velocity flow more frequently matched with yellow, atherosclerotic aneurysm walls (79%) (**Figure 3B1–3**). Although routinely used imaging techniques can provide information about morphology and anatomical relationships of the aneurysm with the surrounding structures, there is currently no way to predict the thickness of the aneurysm wall. CFD can potentially provide this kind of information, which would be valuable not only to assess rupture risk but also to improve the surgical strategy during clipping or coiling. The authors of this study hypothesize that direct, high-velocity impact of blood flow on a specific area of the aneurysm could

is imminent. However it is not known which aneurysms we are analyzing.

trigger a remodeling of the wall, ultimately leading to a reactive thickening. In our recent project, we evaluated histological changes in ruptured and unruptured intracranial aneurysms. According to our preliminary data on the first 30 samples of individuals with ruptured and unruptured IA together with some control samples from similar locations of the cadaver's Willis's circle, the wall was

**28**

**Figure 3.**

damaged by scarring, with the disappearance of the tunica intima and the internal elastic membrane, in patients with both ruptured and unruptured aneurysms (**Figure 2G**–**I**). In the classification according to Frösen et al., categories A to C were demonstrated for unruptured IA, i.e., minor to moderate structural changes, such as fibrosis and disorganization of SMC (**Figure 2H**). However, the wall of ruptured aneurysms was thin, hypocellular, and fibrotized, often with the presence of an organized thrombus (**Figure 2I**). In the classification according to Frösen, it corresponded to categories C and D, i.e., a significantly damaged wall.

The correlation of vessel wall biology in intracranial aneurysms also has limitations:


Another disease that is also used to investigate the relationship between atherosclerosis and hemodynamics is the carotid plaque in the bifurcation of the common carotid artery (**Figure 4**) [45]. This model is more advantageous for several reasons. It can be removed completely without disturbing its structure and then prepared for histological examination in one piece. Due to the size of the plaque and a simple orientation in the 3D geometry of the carotid arteries, the spatial correlation of the plaque model relative to the 3D image of hemodynamic calculations is simple. Also mathematical calculations on the carotid arteries are significantly simpler due to the relatively flat shape of the vessels and the larger cross-sectional size of the arteries, which are thus less affected by minor inequalities and errors given by the neuroradiological images. Therefore, the histological studies of carotid plaques in correlation with hemodynamic characteristics in the common carotid bifurcation can be performed with fewer approximations and thus can contribute to the understanding of atherosclerosis and degenerative changes in the vascular wall.

#### **3.4 Hemodynamics and the risk of intracranial aneurysm rupture**

The degeneration of the aneurysm wall progresses from the neck toward the dome. Aneurysm rupture usually occurs at the apex, which is also often a low shear stress region. According to a large meta-analysis by Zhou et al., the low shear stress (0–1.5 Pa) in the aneurysm sac is a characteristic of ruptured aneurysms [28]. It

**Figure 4.** *CFD in a model of carotid stenosis. WSS (A) and streamlines (B).*

is assumed that wall shear stress of approximately 2.0 N/m<sup>2</sup> (Pa) is most suitable for maintaining the integrity of the vessel wall. A shear stress of less than 1.5 N/m2 results in endothelial cell apoptosis [46]. Takao et al. found that the minimum WSS value for ruptured aneurysms was half that of ruptured aneurysms [26]. Thus, low WSS may be an indicator of an increased risk of intracranial aneurysm rupture. Furthermore, several authors have demonstrated that in ruptured aneurysms, the low WSS region is greater than in unruptured aneurysms [21, 25, 47]. Similar results were found in our study (Sejkorová et al., in preparation), in which we have shown that the area of low wall shear stress (LSA) grows over time in those aneurysms that eventually ruptured. The nature of the flow and its properties are influenced by the shape of the sac. Inside the narrow neck aneurysms, there may be a slow flow with recirculations, resulting in low shear stress leading to increased vascular degeneration. Hemodynamic changes within the aneurysm lead to the production of biological signals in endothelial cells and may result in microscopic changes in the vessel wall [48]. Nitric oxide is a key mediator of low WSS and shear stress oscillation. The low shear stress further promotes the expression of adhesion molecules such as VCAM-1 and ICAM-1. These promote adhesion of leukocytes leading to inflammation and vascular changes. Therefore low WSS seems to be associated with degeneration of cerebral aneurysm vessel wall resulting in rupture. But the situation is probably more complex as in another study in a large number of aneurysms, the authors found that ruptured aneurysms were characterized by concentrated blood stream and a higher shear stress compared to unruptured ones [29].

#### **3.5 Limitations of mathematical modeling of IA**

Mathematical modeling performed in IA extends our knowledge on the pathophysiology of their initiation, growth, development, and rupture [13, 49]. At the same time, it is necessary to note that CFD modeling is usually based on many approximations and carries several limitations. In most studies, individual patient data are not available. This is particularly difficult to obtain in patients with ruptured aneurysms that require acute treatment, and there is usually no time for additional diagnostic examinations (TCD or PC-MR). The method that can partially reduce the disadvantage of missing individual data is to relate values

**31**

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

Newtonian fluid.

universally applicable results.

**4. Final remarks and future directions**

in the aneurysm to the parent artery. Such value normalization reduces the impact of missing input data. Another limitation is that CFD represents mathematical models that are currently not able to describe all aspects of the biology of the cerebral aneurysms and cerebral blood vessels, their histology, atherosclerotic changes, pulsations, etc. Also during modeling, blood vessels are simplified as rigid tubes. The rheological properties of blood are simplified as incompressible

Another aspect associated with limitations in CFD modeling is the use of different mathematical modeling algorithms among various groups working on CFD. This has been clearly shown in the CFD rupture challenge—phase I and phase II [50, 51]. In the rupture challenge, two MCA aneurysms, one ruptured and one unruptured IA, were evaluated using CFD analysis, and the status of the aneurysm was supposed to be identified by the research groups. In the second phase, several research groups were supposed to describe the hemodynamic parameters in one IA. The vast differences among the research groups confirmed the fact that various algorithms may lead to significant differences in the hemodynamic analysis [52]. In future it will be necessary to somehow unify the methodology in order to get more

Another disadvantage of CFD modeling is the relatively complicated protocol with the need to include sophisticated and laborious calculations requiring supercomputers. Nonetheless, technological advances in imaging may provide hemodynamic modeling during regular MRI examinations [53]. If MRI allows precise evaluation of hemodynamic parameters in the future, it can be used even during

The rationale for studying hemodynamics of IA is the increasing detection of UIA with the need to decide whether to treat or watch the aneurysm. Studying and modeling hemodynamics within an aneurysm provides more information on the pathophysiology of IA. We can evaluate the hemodynamic parameter at one time point or follow the aneurysm with CFD assessments over time [40, 54]. The method has been mostly developed by endovascular surgeons with the goal to assess the effect of various treatment modalities, such as flow diverters, stents, scarification of the parent vessel, etc. The neurosurgeons would mostly need information on aneurysm hemodynamics with respect to the rupture risk in the assessment of UIA [40]. The neurosurgeons themselves may provide unique information on aneurysm wall quality: direction visualization of the aneurysm sac under the operating microscope (calcifications, wall weakening, atherosclerotic changes, thrombosis), identification of the site of rupture, aneurysm sac harvesting after clipping, etc. The aneurysm sac wall may then be assessed histologically. Some pilot studies have already been published [43]. Despite an increasing number of CFD studies, there are, to date, still no conclusions with respect

initial MRI evaluation and during follow-ups without radiation burden.

to hemodynamics and growth or rupture that would be universally accepted. From a clinical point of view, the CFD data need to be clinically useful and relevant, such as in a study that points out the relationship between the hemodynamic factors and the risk of endovascular treatment failure in patients treated for a basilar apex aneurysm [55]. The CFD parameters more often mentioned with respect to clinical use are WSS and character of flow. Many studies show that aneurysms with low WSS and complex flow tend to be associated with a higher risk of rupture [27, 28]. Further developments are still required in CFD research before it may be considered clinically relevant in providing useful information on UIA and

its assessment, with respect to the risk of rupture.

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

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

is assumed that wall shear stress of approximately 2.0 N/m<sup>2</sup>

*CFD in a model of carotid stenosis. WSS (A) and streamlines (B).*

stream and a higher shear stress compared to unruptured ones [29].

Mathematical modeling performed in IA extends our knowledge on the pathophysiology of their initiation, growth, development, and rupture [13, 49]. At the same time, it is necessary to note that CFD modeling is usually based on many approximations and carries several limitations. In most studies, individual patient data are not available. This is particularly difficult to obtain in patients with ruptured aneurysms that require acute treatment, and there is usually no time for additional diagnostic examinations (TCD or PC-MR). The method that can partially reduce the disadvantage of missing individual data is to relate values

**3.5 Limitations of mathematical modeling of IA**

for maintaining the integrity of the vessel wall. A shear stress of less than 1.5 N/m2 results in endothelial cell apoptosis [46]. Takao et al. found that the minimum WSS value for ruptured aneurysms was half that of ruptured aneurysms [26]. Thus, low WSS may be an indicator of an increased risk of intracranial aneurysm rupture. Furthermore, several authors have demonstrated that in ruptured aneurysms, the low WSS region is greater than in unruptured aneurysms [21, 25, 47]. Similar results were found in our study (Sejkorová et al., in preparation), in which we have shown that the area of low wall shear stress (LSA) grows over time in those aneurysms that eventually ruptured. The nature of the flow and its properties are influenced by the shape of the sac. Inside the narrow neck aneurysms, there may be a slow flow with recirculations, resulting in low shear stress leading to increased vascular degeneration. Hemodynamic changes within the aneurysm lead to the production of biological signals in endothelial cells and may result in microscopic changes in the vessel wall [48]. Nitric oxide is a key mediator of low WSS and shear stress oscillation. The low shear stress further promotes the expression of adhesion molecules such as VCAM-1 and ICAM-1. These promote adhesion of leukocytes leading to inflammation and vascular changes. Therefore low WSS seems to be associated with degeneration of cerebral aneurysm vessel wall resulting in rupture. But the situation is probably more complex as in another study in a large number of aneurysms, the authors found that ruptured aneurysms were characterized by concentrated blood

(Pa) is most suitable

**30**

**Figure 4.**

in the aneurysm to the parent artery. Such value normalization reduces the impact of missing input data. Another limitation is that CFD represents mathematical models that are currently not able to describe all aspects of the biology of the cerebral aneurysms and cerebral blood vessels, their histology, atherosclerotic changes, pulsations, etc. Also during modeling, blood vessels are simplified as rigid tubes. The rheological properties of blood are simplified as incompressible Newtonian fluid.

Another aspect associated with limitations in CFD modeling is the use of different mathematical modeling algorithms among various groups working on CFD. This has been clearly shown in the CFD rupture challenge—phase I and phase II [50, 51]. In the rupture challenge, two MCA aneurysms, one ruptured and one unruptured IA, were evaluated using CFD analysis, and the status of the aneurysm was supposed to be identified by the research groups. In the second phase, several research groups were supposed to describe the hemodynamic parameters in one IA. The vast differences among the research groups confirmed the fact that various algorithms may lead to significant differences in the hemodynamic analysis [52]. In future it will be necessary to somehow unify the methodology in order to get more universally applicable results.

Another disadvantage of CFD modeling is the relatively complicated protocol with the need to include sophisticated and laborious calculations requiring supercomputers. Nonetheless, technological advances in imaging may provide hemodynamic modeling during regular MRI examinations [53]. If MRI allows precise evaluation of hemodynamic parameters in the future, it can be used even during initial MRI evaluation and during follow-ups without radiation burden.
