A CFD Approach to Quantifying the Hemodynamic Forces in Giant Cerebral Aneurysms

Anna Hoppe, Brian Walsh

Department of Biomedical Engineering, University of Iowa, Iowa City, IA

Dr. Ching-Long LinDepartment of Mechanical Engineering, University of Iowa, Iowa City, IA

Abstract:

Background and Purpose: The therapeutic treatment options available for patients presenting with giant (> 25 mm in diameter) basilar aneurysms are limited. However, a method commonly performed by neurosurgeons on patients presenting with such a condition is proximal feeding artery occlusion. It is hoped that by blocking a proximal feeding artery, the resultant hemodynamic forces within the aneurysm sac will decreased, as will the likelihood of subarachnoid hemorrhage. However, there is no quantitative validation that this method actually decreases the resulting hemodynamic forces and, thus, represents a viable treatment option for patients with giant intracranial aneurysms. Therefore, this CFD simulation was developed in an effort to assess the effect that proximal feeding artery occlusion has on the hemodynamic conditions within an aneurysm. This simulation was designed to be similar to one performed by Jou et. al.4

Methodology: A CFD approach was used to calculate the velocity field, wall shear stress, and pressure distribution for a model of a giant intracranial aneurysm located in the Circle of Willis. This model was generated from data obtained from a patient-specific MR image and was subsequently meshed in Gambit. The velocity fields, wall shear stress, and pressure distributions were determined both before and after simulated occlusion of each inlet artery (three in total) in Fluent. Additionally, this geometry was modified using Magics software to create a healthy aneurysm geometry from which baseline (or control) velocity, wall shear stress, and pressure distributions were determined.

Results and Conclusion: The velocity field, wall shear stress, and pressure distributions were determined for each of the five cases. It was inconclusive whether or not blocking a proximal feeding artery represented a viable therapeutic treatment for patients presenting with giant intracranial aneurysms. Specifically, it was found that there was a strong geometry dependence on blood flow patterns within an aneurysm; therefore, it is likely that sacrificing a proximal feeding artery only succeeds in mitigating hemodynamic forces in limited, patient-specific cases. Additional numerical simulations using data from long-term follow-up studies are required in order to determine if changes in vascular anatomy can be correlated to calculated hemodynamic forces in the same vascular region. A similar conclusion was drawn by Jou and colleagues.4

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Introduction:

Intracranial cerebral aneurysms are localized dilatations within the neurological vasculature. There are many types of aneurysms; however, the most common aneurysm in the cerebral vasculature is the saccular aneurysm. This type of aneurysm is asymmetric and possesses a relatively spherical shape that protrudes from the parent vessel. Saccular aneurysms have a prevalence between 2% - 6.5%.3 The most common location for these aneurysms in the human body is the anterior communicating artery; in fact, 25-38% of intracranial aneurysms occur at this site.7 While many such aneurysms present no symptoms and allow the patient to live a normal healthy life, giant cerebral aneurysms (> 25 mm in diameter) have numerous symptoms including: headaches, nausea, and even blindness (if the aneurysm grows large enough to put pressure on the optic nerve).7

Rupture of intracranial aneurysms is rare (approximately 0.1% per year), however when rupture occurs the effects can be catastrophic.5 As it turns out, approximately fifty percent of subarachnoid hemorrhages result in death, while the other fifty percent generally result in severe disability.6 Furthermore, giant cerebral aneurysms often cause degeneration of the extracellular matrix, as well as the degeneration of intimal and medial endothelial cells.7 In turn, this can lead to the death of smooth muscle cells and result in the thinning of the blood vessel wall, which increases the risk of rupture for this type of aneurysm.7

The Circle of Willis is a particularly important structure in the cerebral vasculature because it is a “fail safe”, ensuring a constant flow of blood to the brain. More specifically, it has a circular geometry with numerous redundancies so that, in the event of an occlusion, blood can be redirected to the areas that would otherwise suffer from decreased circulation and damage due to lack of blood flow.2 However, these redundancies lead to more complex flow patterns as there is increased blood flow recirculation.2

The hemodynamics of the human circulatory system is an active research area. In recent years computational fluid dynamics, or CFD, has become a powerful tool, aiding researchers in their understanding of the complex fluid mechanics of the human circulatory system.2 CFD analysis is also being used in combination with various imaging modalities (such as MR imaging).2 In addition, MRI and ultrasound images can be used to obtain quantitative data which can be used as validation for experimental CFD simulations.

In healthy neurological vasculature, flow velocities range from 0.10 m/s or less (observed in some parts of the Basilar artery) to almost 1 m/s (observed in parts of the middle cerebral artery).2  In contrast, physiologically normal wall shear stresses can vary from approximately 2 Pa (in the internal carotid artery) to approximately 20 Pa (in the middle cerebral and anterior cerebral arteries).3  In addition, research has shown that in areas of vessel bifurcation and curvature, hemodynamic flow characteristics (such as wall shear stress) become more exaggerated and are characterized by higher maximum and lower minimum values.1  

Many CFD and experimental studies have been performed in an attempt to better quantify the hemodynamics of intracranial aneurysms. These studies have shown various characteristic flow patterns for cerebral aneurysms, ranging from simple and steady to patterns which have a high degree of turbulence.2 These studies have also shown that the flow patterns that develop within an aneurysm are heavily influenced by its specific geometry.2 However, geometry is not the only factor influencing these flow patterns. The inflow and outflow characteristics can also have a significant effect on the resulting blood flow.2 For example, when parent vessels flow directly into an aneurysm they can be classified as inflow jets.2 Blood flow

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through these jets becomes turbulent at a Reynolds number of approximately 600, as opposed to a Reynolds number of 2300 (which is characteristic of transitional flow, flow becomes fully turbulent at a Reynolds number of 4000).2 These inflow jets can also cause localized areas of high wall shear stress, which can lead to increased risk of aneurysm rupture.2

There are several treatment options for patients presenting with small intracranial aneurysms. The most invasive therapeutic technique is a neurosurgical clip.3 This technique is characterized by the neurosurgeon cutting the diseased vessel out and inserting a graft.3 Another common treatment modality is a coil embolization technique and requires neurosurgeons to fill the aneurysm with embolization coils. Usually composed of platinum, these coils slow entering blood to the point at which natural blood clotting is induced.3 In contrast, one of the only treatment options for patients presenting with giant intracranial aneurysms is proximal artery occlusion. This particular method is characterized by the occlusion of a proximal feeding artery. It is hoped that by blocking a proximal feeding artery, the resultant hemodynamic forces within the aneurysm sac will decreased, as will the likelihood of subarachnoid hemorrhage. However, there is no quantitative validation that this method actually decreases the resulting hemodynamic forces and, thus, represents a viable treatment option for patients with giant intracranial aneurysms. Therefore, this experimental CFD simulation was developed in an effort to assess the effect that proximal feeding artery occlusion has on the hemodynamic conditions within an aneurysm. This simulation was designed to be similar to one performed by Jou et. al.4

Materials and Methods:

In order to perform the experimental CFD simulation an MRI scan was obtained of a patient possessing an intracranial aneurysm (located in the Circle of Willis), courtesy of Dr. Raghavan. More specifically, the obtained MRI image data was in the .STL file format. The .STL file was subsequently meshed using Gambit to create a volumetric mesh. The software Magics (courtesy of Dr. Lin) was then used to cut each inlet, particularly to ensure each was normal to the direction of flow. This was done to minimize turbulence at the entrance of the aneurysm. The modified inlet and outlet vessels are shown as Figure A1 in the Appendix. Magics was also used to “clip” the aneurysm off of the associated vasculature to recreate a healthy artery geometry. This healthy geometry was later used as a control for the CFD simulation. Then, after the mesh was created, it was loaded into Fluent for evaluation and analysis. Figure A2 in the Appendix shows a schematic of the diseased geometry mesh.

In order to obtain acceptable simulation results that converged, a few assumptions had to be made. First, it was assumed that the aneurysm had rigid walls. In human physiology, artery walls are actually elastic.2 However, aneurysms have less elastin than healthy blood vessels, which results in aneurysm walls that are approximately twice as stiff as a normal blood vessels.4 Therefore, this assumption is valid for aneurysm models. Second, the blood in this study was assumed to be a Newtonian Fluid (or the blood’s stress and strain rate were assumed to be proportional). As it turns out, this assumption is acceptable for most regions within the human circulatory system (except for regions where the blood is characterized by a small strain rate).2 Studies have shown that the assumption of a Newtonian fluid in large arteries is valid.2 Therefore, blood was modeled as a Newtonian fluid in this simulation, possessing a density of 1.056 g/cc and a viscosity of .0035 poise.2

Once the mesh was loaded into Fluent and the fluid properties had been created each of the three inlets were set to velocity inlets and given an inlet velocity of 0.6 m/s, or the average

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velocity observed during systole.1 Using this particular velocity value was chosen because it will yield the greatest hemodynamic forces within the aneurysm, which have the most clinical significance.1 Subsequently, five individual cases were run: a case employing the diseased geometry with no proximal feeding arteries occluded, three cases of the diseased geometry with each of the three proximal feeding arteries occluded, and the healthy geometry control case with no feeding arteries occluded.

A transient time, k-omega model was used because the calculated theoretical Reynolds number was 7241(see Equation 3 and the associated computations in the Appendix). In order to keep this CFD simulation as similar to the study done by Jou and colleages (which inspired this project), a SIMPLE scheme was used.4 Additionally the momentum, turbulent kinetic energy, and specific dissipation rate were set to be solved using second order upwind schemes.4 Pressure was left as the default of standard and gradient was set to least-cells-square-based.4

Results:

Subsequent to obtaining the geometry of the intracranial saccular aneurysm from Professor Raghavan, a healthy artery geometry was created by taking the obtained geometry and cutting out the diseased aneurysm sac in order to recreate the natural artery physiology. This was done using Professor Lin’s Magics Software. For a control simulation, using a physiologically normal artery geometry from the same location (the cerebral Circle of Willis) obtained from MR imaging of a healthy patient would have been preferred. However, such data was not available and could not be obtained. Nevertheless, great care was taken in finding and smoothing (or completely eliminating) any hard edges that were generated as a result of the geometry modifications performed in Magics.

Next, the healthy geometry was loaded into Gambit, where any remaining hard edges were removed, and the geometry was meshed. The healthy artery mesh was then imported to Fluent where a CFD simulation was run until solution convergence was reached (the specifics regarding the Fluent settings used during this simulation are discussed in the Methodology section). Because a control simulation was needed in order to establish baseline velocity vector, wall shear stress, and pressure magnitudes in a healthy artery, no proximal feeding arteries were blocked in this simulation (additionally, blocking proximal feeding arteries in a physiologically normal environment possesses no clinical significance). Subsequently, the velocity vector magnitudes were obtained by loading the case and data files generated from this particular simulation into the software Tecplot and viewing the velocity vectors as projected onto a y-plane cutting through the middle of the healthy artery geometry. The resulting velocity vector distribution is shown as Figure 1(in cm/s).

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Figure 1: The velocity vectors associated with the CFD simulation run on the healthy artery with no proximal feeding arteries blocked.

Then the case and data files obtained from the healthy artery simulation were re-loaded into Fluent. The contours of wall shear stress were plotted. This was done because the wall shear stress distribution within a vessel has clinical significance, as it is linked to the progression of atherosclerosis and aneurysm disease development.2 The corresponding wall shear stress contours are shown as Figure 2.

Figure 2: The wall shear stress distribution associated with the CFD simulation run on the healthy artery with no proximal feeding arteries blocked.

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Finally, the pressure contours were plotted for the healthy aneurysm simulation. Like the distribution of wall shear stress, the pressure distribution within a vessel has important diagnostic ramifications; particularly, it is linked to aneurysm growth and development.2

Figure 3: The pressure distribution associated with the CFD simulation run on the healthy artery with no proximal feeding arteries blocked.

Next the geometry of the intracranial saccular aneurysm (or the diseased geometry) was loaded into Gambit where it was meshed. The cerebral aneurysm mesh was then imported to Fluent where a CFD simulation was run until solution convergence was reached (the specifics regarding the Fluent settings used during this simulation are discussed in the Methodology section). This was done because another control simulation was needed in order to establish velocity vector, wall shear stress, and pressure magnitudes in a diseased artery manifesting a saccular aneurysm; because of this, no proximal feeding arteries were blocked in this simulation. Then, as done with the healthy artery simulation, the velocity vector magnitudes specific to this simulation were obtained by loading the corresponding case and data files into the software Tecplot and viewing the velocity vectors as projected onto a y-plane cutting through the middle of the diseased artery geometry. The resulting velocity vector distribution (throughout the entire diseased geometry) is shown as Figure 4 (in cm/s).

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Figure 4: The velocity vectors associated with the CFD simulation run on the same artery

possessing a saccular aneurysm with no proximal feeding arteries blocked.

Subsequently the case and data files were reloaded into Fluent and the contours of wall shear stress were plotted. The resulting wall shear stress distribution is shown as Figure 5.

Figure 5: The wall shear stress distribution associated with the CFD simulation run on the same artery possessing a saccular aneurysm with no proximal feeding arteries blocked.

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Also the pressure contours, specific to the diseased artery geometry with no blocked proximal feeding arteries, was plotted in Fluent. The corresponding pressure contours are shown as Figure 6.

Figure 6: The pressure distribution associated with the CFD simulation run on the same artery possessing a saccular aneurysm with no proximal feeding arteries blocked.

In an effort to provide quantitative validation for proximal artery occlusion as a therapeutic treatment for patients presenting with giant cerebral aneurysms, each feeding artery of the diseased geometry was blocked in succession and the resulting velocity vector, wall shear stress, and pressure magnitudes were determined. This particular set of experimental simulations was modeled after a similar experiment performed by Jou and colleagues.4 More specifically, in this study the large proximal feeding artery was blocked first.

Similar to the healthy and unoccluded diseased simulations, the velocity vector magnitudes for this particular simulation (occluded large inlet) were obtained by loading the corresponding case and data files into the software Tecplot and viewing the velocity vectors as projected onto a y-plane cutting through the middle of the occluded diseased artery geometry. The resulting velocity vector distribution is shown as Figure 7 (in cm/s).

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Figure 7: The velocity vectors associated with the CFD simulation run on the same artery possessing a saccular aneurysm with the large proximal feeding artery blocked.

Subsequently the case and data files, associated with the simulation in which the large feeding artery was occluded, were reloaded into Fluent and the contours of wall shear stress were plotted. The resulting wall shear stress distribution is shown as Figure 8.

Figure 8: The wall shear stress distribution associated with the CFD simulation run on the same artery possessing a saccular aneurysm with the large proximal feeding artery blocked.

Also the pressure contours, specific to the diseased artery geometry possessing an occlusion in the large proximal feeding artery, was plotted in Fluent. The corresponding pressure contours are shown as Figure 9.

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Figure 9: The pressure distribution associated with the CFD simulation run on the same artery possessing a saccular aneurysm with the large proximal feeding artery blocked.

After running the case corresponding to the simulated occlusion of the large proximal feeding artery, the medium proximal feeding artery was occluded. Again, the velocity vector magnitudes for this particular simulation (occluded medium inlet) were obtained by loading the corresponding case and data files into the software Tecplot and viewing the velocity vectors as projected onto a y-plane cutting through the middle of the occluded diseased artery geometry. The resulting velocity vector distribution is shown as Figure 10 (in cm/s).

Figure 10: The velocity vectors associated with the CFD simulation run on the same artery possessing a saccular aneurysm with the medium proximal feeding artery blocked.

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Next the case and data files, associated with the simulation in which the medium feeding artery was occluded, were reloaded into Fluent and the contours of wall shear stress were plotted. The resulting wall shear stress distribution is shown as Figure 11.

Figure 11: The wall shear stress distribution associated with the CFD simulation run on the same artery possessing a saccular aneurysm with the medium proximal feeding artery blocked.

Also the pressure contours, specific to the diseased artery geometry possessing an occlusion in the medium proximal feeding artery, was plotted in Fluent. The corresponding pressure contours are shown as Figure 12.

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Figure 12: The pressure distribution associated with the CFD simulation run on the same artery possessing a saccular aneurysm with the medium proximal feeding artery blocked.

After running the case corresponding to the simulated occlusion of the medium proximal feeding artery, the small proximal feeding artery was occluded. Again, the velocity vector magnitudes for this particular simulation (occluded small inlet) were obtained by loading the corresponding case and data files into the software Tecplot and viewing the velocity vectors as projected onto a y-plane cutting through the middle of the occluded diseased artery geometry. The resulting velocity vector distribution is shown as Figure 13 (in cm/s).

Figure 13: The velocity vectors associated with the CFD simulation run on the same artery possessing a saccular aneurysm with the small proximal feeding artery blocked.

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Next the case and data files, associated with the simulation in which the small feeding artery was occluded, were reloaded into Fluent and the contours of wall shear stress were plotted. The resulting wall shear stress distribution is shown as Figure 14.

Figure 14: The wall shear stress distribution associated with the CFD simulation run on the same artery possessing a saccular aneurysm with the small proximal feeding artery blocked.

Also the pressure contours, specific to the diseased artery geometry possessing an occlusion in the small proximal feeding artery, was plotted in Fluent. The corresponding pressure contours are shown as Figure 15.

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Figure 15: The pressure distribution associated with the CFD simulation run on the same artery possessing a saccular aneurysm with the small proximal feeding artery blocked.

Figure 16 depicts the velocity and pressure magnitude results obtained by Jou and Colleagues.4 In Figure 16 (A), note the highly asymmetric flow secondary to the near occlusion of the lower right proximal feeding artery. Also note the large region of slow, recirculating flow in the aneurysm sac. In Figure 16 (B), note that the pressure distribution throughout the entire diseased geometry has no regions of pronounced pressure increases. More specifically, there is a smooth decrease from the inlet to outlet vessels.

Figure 16 (A): The calculated velocity field (in m/s) obtained by Jou and colleagues in a similar experimental simulation.4

Figure 16 (B): The calculated pressure distribution (ranging from 0 to 150 Pa) obtained by Jou and colleagues in a similar experimental simulation.4

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Similarly, Figure 17 depicts the wall shear stress results obtained by Jou and Colleagues.4 In this Figure note the low wall shear stress calculated in the lumen of the aneurysm sac (blue region). Regions of increased wall shear stress are calculated in curved or branching regions of the diseased geometry used by Jou et. al. (green and yellow regions).

Figure 17: The calculated wall shear stress distribution (ranging from 0 to 5 Pa) obtained by Jou and colleagues in a similar experimental simulation.4

Conclusions:

The purpose of this set of experimental CFD simulations was to quantify the validity of using the method of proximal feeding artery occlusion as a therapeutic treatment for patients presenting with giant cerebral aneurysms. Currently neurosurgeons employ the method of proximal artery occlusion because existing treatment modalities remain insufficient for giant intracranial aneurysms. The hope is that by blocking an aneurysm’s feeding artery the hemodynamic forces within the aneurysm sac will be lessened and the probability of subarachnoid hemorrhaging will be mitigated. However, there is no quantitative data to support this belief (aside from the data obtained by Jou and colleagues2). In addition, this study was performed in order to determine if the results from a similar set of CFD simulations, run by Jou and colleagues, could be replicated.4

In order to simplify this study (particularly to limit the computation time and complexity), several assumptions were made. First, the arterial wall was assumed to be rigid. This assumption results in an overestimation of wall shear stress, which is only significant at peak systole.2 However since an aneurysm is approximately twice as stiff as normal vessels, due to a lack of elastin, employing the rigid wall assumption for these experimental models is valid.4

Second, the blood in this study was assumed to be a Newtonian Fluid (or the blood’s stress and strain rate were assumed to be proportional). As it turns out, this assumption is acceptable for most regions within the human circulatory system (except for regions where the blood is characterized by a small strain rate).4 Studies have shown that the assumption of a Newtonian fluid in large arteries is valid.4 Additional research regarding the strain rate of blood within large aneurysms, where recirculation is common, must be completed to wholly determine the

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appropriateness of this assumption for this study. However, in light of having no research invalidating this assumption, it was deemed acceptable in both this study and that performed by Jou et. al.4 Additionally this study assumed steady, rather than pulsatile, flow. Because the inlet velocities were set as the velocity characteristic of peak systole, all of the hemodynamic forces studied (velocity, wall shear stress, and pressure) were computed as their maximum value within the cardiac cycle.4 These maximum values possess the most clinical significance.4 Finally, it should be mentioned that since the diseased aneurysm geometry used in this experimental CFD simulation was located in the cerebral Circle of Willis, it possesses no clear inlet and outlet vessels in human physiology. However, the geometry used in this study was under the complete discretion of Professor Raghavan; it was his best judgment that the inlet and outlet vessels (specified previously for this study) were sufficient.

As evidenced by Figure 4, increased velocity was calculated as exiting from the small distal outlet artery in the diseased model geometry possessing no proximal artery occlusions. This corresponds to a similar trend seen by Jou et. al. and depicted in Figure 16 (A). In Jou’s study, increased velocity was observed in both small distal outlet vessels; however, the velocity magnitudes were, approximately, a factor of ten larger than those observed in this study. The most probable explanation for this discrepancy is the fact that two completely different aneurysm geometries were used in the two studies. From the continuity equation, given as Equation 1 in the Appendix, it can be seen that velocity is related to geometry. Therefore, such a discrepancy is not only likely; rather, it is expected. Nevertheless, it follows from the continuity equation (Equation 1 of the Appendix) that as the lumen diameter of a vessel decreases, the associated velocity within that vessel will increase. Thus, the observance of high velocity in the small, distal outlet vessel is warranted. Employing similar logic, the observance of slow, recirculating blood in the aneurysm sac is also expected. This particular phenomenon is also seen in Figure 16 (A), the velocity field calculated by Jou and colleagues. As before, the velocity magnitudes in this region, as calculated by Jou’s team, were approximately a factor of ten larger than those observed in this study. Again, the most likely explanation for this discrepancy is the multitude of differences existing between the model geometries used for each study.

Comparing Figures 7, 10, and 13 it can be seen that regardless of which proximal feeding artery is blocked the velocity distribution pattern remains largely unchanged. More specifically, a large region of recirculating blood flow is evident within the aneurysm sac in all of the cases; in addition, a high velocity region is present in the small, distal outlet artery in all cases. Also when the large proximal feeding artery is blocked, the largest velocity magnitude observed in the aneurysm sac is 56% slower than that observed in the unoccluded diseased case. Similarly, when the medium proximal feeding artery is blocked, the largest velocity magnitude observed in the aneurysm sac is 36% slower than that observed in the unoccluded diseased case. In contrast, when the small proximal feeding artery is blocked, the largest velocity magnitude observed in the aneurysm sac is only 10% slower than that observed in the unoccluded diseased case. In contrast, in the healthy artery geometry no regions of extremely slow recirculating flow are seen (shown in Figure 1) as they are observed in the diseased cases. Nevertheless, relatively high velocity magnitudes do still exit the small distal outlet vessel, similar to all of the previously discussed cases. Therefore it can be concluded that, considering velocity distribution alone, blocking the large proximal feeding artery has the most promise as an effective treatment modality for patients presenting with large intracranial aneurysms as it results in the largest decrease in velocity within the aneurysm sac. Blocking the medium feeding artery shows some promise as a possible therapeutic treatment; however, blocking the small feeding artery appears

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to do little in reducing the hemodynamic velocity and thus, shows little promise as an effective treatment modality. Still, the pressure and wall shear stress distributions need to be analyzed in order to determine which proximal feeding artery (if any) should be blocked. It should also be mentioned that a trade-off exists with respect to velocity. Certainly, reducing the velocity (and, ultimately, the resulting hemodynamic forces) is desired; however blood has a tendency to clot when moving slowly, which leads to thrombus formation. These thrombi may then embolize to distal sites (such as a foot) which can lead to ischemic conditions (or a lack of oxygen). Such conditions possess negative clinical implications.2

As evidenced by Figure 5, the diseased model geometry possessing no proximal artery occlusions has a wall shear stress distribution (within the aneurysm sac) between 0 – 4.39 Pa. When the small proximal feeding artery was occluded, the wall shear stress distribution decreased to between 0 – 3.66 Pa (a decrease of approximately 16.6%), as shown in Figure 8. Similarly, when the medium proximal feeding artery was occluded, the wall shear stress distribution decreased to between 0 – 2.06 Pa (a decrease of approximately 53.1%), as shown as Figure 11. Additionally, when the large proximal feeding artery was occluded, the wall shear stress distribution decreased even more to between 0 – 1.14 Pa (a decrease of approximately 74.0%), as shown as Figure 14. It should also be noted that the wall shear stress distribution of the healthy artery geometry is between 0 – 7.09 Pa, as depicted by Figure 2. Therefore, blocking the small proximal feeding artery appears to have little effect on the wall shear stress distribution within the aneurysm sac. In contrast, blocking both the medium and large feeding arteries result in clinically significant decreases in wall shear stress within the aneurysm sac. However, the implications of reduced wall shear stress on the probability of subarachnoid hemorrhaging are unknown.2 Initially, it was believed by researchers that regions of high wall shear stress resulted in atypical vessel wall weakening and the corresponding outward ballooning of the wall.2 Now, this concept has been disputed.2 According to Jou et. al., high wall shear stresses within an aneurysm sac result in damage to the associated endothelial cell lining.4 Thus, low wall shear stress is a preferred characteristic of an effective treatment modality. Using this particular criterion, blocking either a medium or large proximal feeding artery possesses the most promise as an effective treatment modality for patients presenting with giant intracranial aneurysms (blocking the large proximal feeding artery shows the most promise).

Additionally, it should be noted that the uniform wall shear stress distributions shown in Figures 8, 11, 14 differ from the wall shear stress distribution calculated by Jou and colleagues as shown in Figure 17.4 This wall shear stress distribution is relatively non-uniform, with regions of high wall shear stress near curved or bifurcated regions in the model geometry. The reason for this discrepancy is most likely due to the geometry differences between the model geometries used in each simulation. This is because wall shear stress is proportional to velocity and velocity is highly dependent upon geometry.2

As evidenced by Figure 6, the diseased model geometry possessing no proximal artery occlusions has a uniform pressure distribution (within the aneurysm sac) of approximately 959 Pa. When the small proximal feeding artery was occluded, the pressure distribution decreased to between 202 – 927 Pa (a decrease of approximately 3.3%), as shown in Figure 9. Similarly, when the medium proximal feeding artery was occluded, the pressure distribution decreased to between -7.71 – 233 Pa (a decrease of approximately 75.7%), as shown as Figure 12. Additionally, when the large proximal feeding artery was occluded, the pressure distribution decreased even more to between -5.23 – 116 Pa (a decrease of approximately 87.9%), as shown as Figure 15. Therefore, blocking the small proximal feeding artery appears to have little effect

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on the pressure distribution within the aneurysm sac. In contrast, blocking either the medium or large feeding arteries result in clinically significant decreases in the pressure distribution within the aneurysm sac. Jou and colleagues found that the pressure distribution in the case of the occluded proximal feeding artery was also relatively uniform, as depicted in Figure 16 (B). A small region of increased pressure was seen along one aneurysm wall at the impinging site. However, it is not clear in Jou’s published results if a general increase in pressure distribution is seen when the proximal feeding artery is occluded, as no results from a baseline, or from an unoccluded diseased model, are presented or discussed.4 It should also be noted that as evidenced from the range in pressure magnitudes calculated by Jou et al and given in Figure 16 (B), the pressure magnitudes calculated for each simulated case in this study are approximately several hundred Pascals higher than those calculated by Jou and colleagues.4 The most probable explanation for this discrepancy is because of the differences that exist between the geometries used for each study. Through the Bernoulli equation (given as Equation 2 in the Appendix), pressure is indirectly coupled to geometry. In fact, at the bulged cross-section of the aneurysm pressure will increase due to the Bernoulli effect (as a result of an associated velocity decrease).2 This particular phenomenon is observed in this experimental simulation. More specifically, the pressure difference within the aneurysm sac associated with the healthy geometry model is approximately 866 Pa. In contrast, the pressure distribution within the aneurysm sac of the diseased model geometry possessing no proximal artery occlusions is approximately 959 Pa, which is a 9.7% pressure increase.

Based on the presented findings, it is inconclusive whether or not blocking a proximal feeding artery represents a viable therapeutic treatment for patients presenting with giant intracranial aneurysms. Because of the high dependence of geometry on blood flow patterns within an aneurysm, it is likely that sacrificing a proximal feeding artery only succeeds in mitigating hemodynamic forces in limited, patient-specific cases. However, qualifying this statement would require additional numerical simulations employing data from long-term follow-up studies in which changes in vascular anatomy could be correlated with calculated hemodynamic forces in the same vascular region. It should be noted that a similar conclusion was reached by Jou et. al.4 In addition, as with the simulation performed by Jou and Colleagues, this study laid the groundwork for predicting the role hemodynamic forces play in aneurysm growth. Additionally, this study laid groundwork needed to determine the quantitative effect of interventional procedures taken on feeding arteries by neurosurgeons in order to prevent subarachnoid hemorrhaging.

Recommendations for future experiments in this research area include: First, run additional numerical simulations using data from long-term follow-up studies in order to determine if changes in vascular anatomy can be correlated to calculated hemodynamic forces in the same vascular region. Second, include the effect of pulsatile flow in the new numerical simulation in an effort to more closely mimic the actual human circulatory system and third, use a geometrical model with clearly defined inlet and outlet vessels. Most importantly a variety of aneurysm geometries should be used as computational models in new simulations to ascertain the scope of proximal artery occlusion as a therapeutic treatment for patients presenting with giant intracranial aneurysms.

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Appendix

Figure A1: Schematic of the diseased model geometry used in this experimental simulation, with velocity inlet and outflow outlet arteries specified (the healthy model geometry possessed the same

number of nodes on each inlet and outlet artery)

Figure A2: Schematic of the diseased model geometry mesh used in this experimental simulation

A1 V 1=A2 V 2

Equation 1: The Continuity Equation, as specified by Chandran et. al. in the textbook, Biofluid Mechanics: The Human Circulation2

p+ρV 2

2+ρgz=H

Equation 2: The Bernoulli Equation, as specified by Chandran et. al. in the textbook, Biofluid Mechanics: The Human Circulation2

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ℜ= ρVdμ

=(1.056

g

cm3 )(.6 ms )(.004 cm)

.0035 Poise≈ 7241

Equation 3: Reynolds Number Equation (and computations) as specified by Chandran et. al. in the textbook, Biofluid Mechanics: The Human Circulation2

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Works Cited

[1] Cebral JR, Putman CM, Alley MT, et al. Hemodynamics in Normal Cerebral Arteries: Qualitative Comparison of 4D Phase-Contrast Magnetic Resonance and Image-Based Computational Fluid Dynamics. J Eng Math. 2009;64:367-378.

[2] Chandran, K.B. et al. (2006). Biofluid Mechanics: The Human Circulation. CRC. Print.

[3] Chien A, Castro MA, Tateshima S, et al. Quantitative Hemodynamic Analysis of Brain Aneurysms at Different Locations. Am J Neuroradiol. 2009;30:1507-1512.

[4] Jou, L., et al. Computational Approach to Quantifying Hemodynamic Forces in Giant Cerebral Aneurysms. Am J Neuroradiol. 2003;24:1804-1810.

[5] Lall RR, Eddleman CS, Bendok BR, et al. Unruptured Intracranial Aneurysms and the Assessment of Rupture Risk Based on Anatomical and Morphological Factors: Sifting Through the Sands of Data. Neurosurg Focus. 2009;26:E2.

[6] Lysack JT, Coakley A. Asymptomatic Unruptured Intracranial Aneurysms: Approach to Screening and Treatment. Can Fam Physician. 2008;54:1535-1538.

[7] Park JH, Park SK, Kim TH, et al. Anterior Communicating Artery Aneurysm Related to Visual Symptoms. J Korean Neurosurg Soc. 2009;46:232-238.

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