2D CFD simulation of intracranial aneurysm

THE UNIVERSITY OF IOWA

CFD Analysis of Intracranial Aneurysms

51:155 Cardiovascular Fluid Dynamics

James Arter, Austin Ramme & Brian Walsh 12/4/2009

December 4th, 2009 51:155 Cardiovascular Fluid Mechanics James Arter, Austin Ramme & Brian Walsh

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Abstract Intracranial aneurysms are pathologic dilations of the vasculature within the skull that have prevalence between 2-6.5% in the general population. The severe consequences (i.e. severe disability or death) of aneurysm rupture have motivated research into factors that may increase the risk of aneurysm rupture. The goal of this study is to relate aneurysm height to neck ratio with wall shear stress values and changes seen in the fluid dynamics of an intracranial aneurysm. We have developed five fluid dynamics finite element models to simulate how changes in an aneurysm's geometry affect vascular fluid dynamics and the wall shear stresses in the aneurysm. Our simulations indicate an increasing pattern of wall shear stress does correspond with the increasing height to neck ratios. It would be difficult to argue that increased risk of rupture was solely caused by height to neck ratio increases, but it would be reasonable to suggest an association between an increase in wall shear stress (due to large height to neck ratio) and rupture risk. I. Introduction A. Our Patients Patient 1: Mrs. X is a 50 year old woman who presents to her family physician complaining of a three day history of recurrent stabbing headaches directly behind her eyes. She also reports photophobia, nausea, and vomiting associated with the headaches. On further questioning, Mrs. X reveals that she is a long-term victim of spousal abuse. In fact, the onset of symptoms aligns with the most recent incident where her partner stuck her with a closed fist. Her past medical history is significant for a "small aneurysm in her head" that had been incidentally identified several years back. It had been described as "nothing to worry about." She reveals a family history of three relatives that died from a ruptured "brain aneurysm." On physical examination, the patient appears anxious but not in acute distress. She is oriented to person, time, and place, but there exists a complete loss of peripheral visual fields. The remainder of the exam is noncontributory with the exception of several contusions consistent with the described assault. Medical imaging studies reveal an intracranial aneurysm of the anterior communicating artery with an aneurysm height to neck ratio of 4.0 that appears to be impinging on the optic chiasm. On comparison to past medical imaging studies, the aneurysm had significantly enlarged since the last investigation. Mrs. X desires to know why the previous "small aneurysm" now requires such urgent attention. Patient 2: Mr. Y is a 35 year old man that presents to the neurology clinic after being referred from his family physician for an incidental finding of intracranial aneurysm during workup for an occupational injury. Mr. Y is completely asymptomatic. He has a family history that is positive for unruptured "brain aneurysm." He reports

migraine with aura since the age of 3; otherwise, the review of systems is noncontributory. Physical examination reveals a healthy male. Medical imaging studies show an intracranial aneurysm of the anterior communicating artery with an aneurysm height to neck ratio of 2.6. Mr. Y understands the tragic consequences of aneurysm rupture and wants to better understand his rupture risk in order to make an informed decision about his treatment plan. B. Intracranial Aneurysms Intracranial aneurysms are pathologic dilations of the vasculature within the skull that have prevalence between 2-6.5% in the general population. They have also been called saccular aneurysms due to their stereotypical spherical shape that offshoots from a parent vessel. They have been reported in a variety of locations within the cerebral vasculature including the middle cerebral artery, internal carotid artery, basilar artery, and the anterior communicating artery1. Aneurysms of the anterior communicating artery are most common and account for 25-38% of all intracranial aneurysms2. The anterior communicating artery is a small artery that connects the left and right anterior cerebral arteries and lies in close proximity to the optic nerves. Regardless of location, rupture of any intracerebral aneurysm will inevitably lead to subarachnoid hemorrhage whereby half of patients die and the other half become severely disabled3. Most patients with intracranial aneurysms are asymptomatic, and in most cases they will live normal lives without complications3. However, some patients may experience symptoms prior to rupture depending on the size, location, and orientation of the aneurysm. The anterior communicating artery belongs to the anterior circulation of the cerebrum and is in close proximity to the


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optic nerves and optic chiasm. If an aneurysm is present, it can cause visual symptoms due to compression of the optic nerves such as visual field loss and visual dimness2. Compression of surrounding structures can cause stabbing cluster headaches that are often felt behind the eyes and are associated nausea and vomiting4. Histologically, degeneration of the vascular extracellular matrix and degeneration of the intimal and medial endothelial cells are indicative of cerebral aneurysms5. Elevated levels of elastase and matrix mellanoproteinases have been observed in patients with cerebral aneurysms and they are believed to be partly responsible for extracellular matrix degeneration in vascular remodeling. They have also been shown to induce smooth muscle cell apoptosis, which leads to arterial wall thinning. It is theorized that smooth muscle cell apoptosis and the degradation of the elastin and collagen fibers of the vascular extracellular matrix are the primary components of arterial wall weakening. The exact mechanism of aneurysm initiation and progression is a debated topic, but many agree they result from mechanical weakening over time5. A specific inciting event has not been identified, but an association between aneurysm initiation and anatomic variation or pathologic feature has been established. Regions of increased blood flow (e.g. arteriovenous malformations) or regions of increased wall shear stress (e.g. arterial bifurcations) have been shown to have increased rates of aneurysm development. Some animal models have shown that increased flow and hypertension are required for aneurysm development. The progressive weakening of the arterial wall in aneurysm development has been correlated with endothelium-dependent nitric oxide (NO), which has been shown to be released in response to elevated levels of wall shear stress. Controversy exists as to the exact mechanism, but it is believed that aneurysm progression is the result of a NO induced passive yield to blood pressure forces coupled with reactive healing of the wall. The combination of elevated forces and wall remodeling can lead to an increasing aneurysm diameter and thinning vessel wall. Each aneurysm has two possible outcomes: progression in size until rupture or maintenance of size. B. Normal Cerebral Hemodynamics

Many studies have been performed to quantify human cerebral hemodynamic properties such as wall shear stress, velocity profiles, and pressure. Customized computational fluid dynamics (CFD) models, MR imaging, and ultrasound have been demonstrated as methods of estimating in vivo values. One of the most important anatomical structures in cerebral hemodynamics is the Circle of Willis. The Circle of Willis creates redundancies within the cerebral circulation such that if part of the circulation becomes occluded, blood flow from other contributing vessels can maintain blood flow and prevent major damage. As long as the Circle of Willis can maintain blood pressure at fifty percent of normal, no infarction or death of tissue will occur in an area where a blockage exists1. These redundancies often introduce some turbulent flow. Flow rates and especially wall shear stresses vary greatly depending on location and specific patient vascular geometries. Flow rates vary from less than 10 cm/s in some parts of the basilar artery to nearly 100 cm/s in parts of the middle cerebral artery1. While wall shear stresses vary from approximately 20 dynes/cm2 in the internal carotid artery to approximately 200 dynes/cm2 in the middle cerebral and anterior cerebral arteries. It had been found that areas of increased and decreased wall shear stress can be observed in regions of high arterial curvature and near bifurcations. Arteries with higher degrees of curvature tend to exhibit higher wall shear stresses6. C. Intracranial Aneurysm Hemodynamics Numerous computational and experimental studies of intracranial aneurysm hemodynamics have been conducted using patient-specific vasculature geometry. The results of 3D CFD studies reveal flow patterns that range from those that are simple and stable to those that are complex and unstable. The simple flow patterns observed consists largely of a single recirculation or vortex region within the aneurysm. The complex intra-aneurysmal hemodynamics may contain more than one recirculation region, and have been shown to be highly dependent on the patient-specific vascular geometry. Furthermore, intra-aneurysmal hemodynamics does not only depend on the aneurysm shape and size, but also on the inlet and outlet flow patterns found in the parent vessel(s). For example, concentrated inflow jets are found to exist when a parent vessel flows directly into the aneurysm. These inflow jets have been shown to directly impact on the aneurysm,


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producing local regions of elevated wall shear stress (WSS)5. In order to allow for in vivo hemodynamic measurements, 3D phase contrast MR imaging has been used to view velocity and inflow hemodynamics in and around aneurysms. The results of these studies correlate well with most high wall shear stress theories in that the highest wall shear stresses were found in the inlet flow region. While both CFD and phase contrast MRI techniques have revealed a great deal of insight into intra-aneurysmal hemodynamics, neither technique is practical for clinical use at this time due to the significant amount of computational power required7.

D. Treatment Methods for Intracranial Aneurysms Presently, intracranial aneurysms can be treated with endovascular or surgical techniques. In 1937, Walter Dandy performed the first surgical treatment of an aneurysm using a vascular clip designed by Harvey Cushing. Surgical clipping involves a craniotomy to expose the aneurysm, and the placement of a surgical clip to close the neck of the aneurysm. Advances in neurosurgical techniques have allowed for the treatment of most cerebral aneurysms, and surgical clipping remains the best way to eliminate cerebral aneurysms. Surgical treatment remained the predominant treatment for nearly four decades until the development of the detachable coil (shown on the cover page) by Gglielmi in the late 1980s. Initially, endovascular treatment was used only in patients who were thought to be poor candidates for surgical treatment. In the past decade, however, endovascular treatment has become more widespread due to new developments in endovascular techniques. Endovascular coiling is a much less invasive treatment involving percutaneous access and insertion of platinum coils into the anuerysm via a catheter. When placed in the aneurysm, the coils induce thrombogenesis that, when successful, will eliminate the aneurysm. In certain cases, stents are inserted as a scaffold for the coils. While endovascular coiling is a cost effective, minimally invasive treatment, there exists a major complication of aneurysm reoccurrence and subsequent bleeding. Treatment selection depends greatly on the clinical condition of the patient, the morphology and location of the aneurysm, and institutional expertise8. Increased use of medical imaging has led to an increasing number of incidental discoveries of unruptured intracranial

aneurysms, with some studies reporting prevalence as high as 6.5% in the general population7. Most often these incidental findings never cause a problem for the patient, but the devastating consequences of aneurysm rupture have made surgical intervention a debated topic. Patients and physicians must weigh the benefits and risks of the treatment plan for each patient. Conservative management is considered the gold standard of treatment for asymptomatic patients with intracranial aneurysms less than 7 mm in size3. Treatment of intracranial aneurysm has been shown to have an 11.5% chance of adverse outcome with a 2.1% of chance of death during the intervention7. Endovascular coiling has been shown to have better patient outcomes than surgical clipping, but both carry an inherent risk2. A patient-specific evaluation of rupture risk often guides the management of these patients. E. Rupture Risk Assessment Intracranial aneurysms are not uncommon in the general population, and for the most part will never cause a problem for most patients. The risk of anterior circulation intracranial aneurysm rupture, like that of our patients, has been estimated to be between 0-0.1% per year, a seemingly small number7. However, the severe consequences (i.e. severe disability or death) of rupture have motivated research into factors that may increase the risk of aneurysm rupture. Unfortunately, aneurysm rupture risk research has been limited to two specific patient populations: patients that are unruptured and probably won't rupture and patients that have already ruptured7. A human investigation of patients following the natural history of aneurysm rupture is blatantly unethical. With this limitation, several factors have been linked to rupture risk using retrospective reviews of patient medical records. Some of these relationships include:

Symptomatic aneurysms are 4-5 times more likely to rupture than asymptomatic aneurysms3.

Intracranial aneurysms found in the posterior circulation are 2-3 times more likely to rupture than those found in the anterior circulation3, 7.

An aneurysm that is greater than 5 mm is 2-3 times less likely to rupture than an aneurysm that is less than 5 mm in size3, 7.

Aneurysms showing evidence of surface irregularities and daughter sacks are at an increased risk of rupture7.

Aneurysms originating from parent arteries with larger diameters also tend to rupture at relatively larger sizes1.


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One relationship that has been shown to be clinically useful and statistically significant is the aneurysm height to neck ratio7. It has been postulated that intracranial aneurysms with a height to neck ratio less than 1.4 are at low risk of rupture, those with a ratio from 1.6-2.2 have a borderline risk of rupture, and those with a ratio greater than 3.0 have a high risk of rupture. These risk statistics have been established based on patient outcomes. F. Hemodynamic Modeling Advancements in medical imaging modalities have allowed for patient-specific reconstruction of aneurysm and vascular geometries for CFD analysis. Numerous computational and experimental studies have revealed a wide variety of complex intra-aneurysmal flow patterns that are strongly specific to the patient-specific geometries, and thus may not correlate well with idealized models. Furthermore, fluid-structure interaction algorithms have been implemented to incorporate wall compliance into CFD models. These models reveal that fluid-structure interactions produce alterations in wall shear stress and velocity magnitudes, but have minimal affect on flow patterns5. Despite potential discrepancies in results, idealized and two dimensional geometries are frequently used for initial CFD studies due to their predictability and minimal computational requirements. G. Goals of This Study Both of our patient's exhibited the most common type of intracranial aneurysm, an aneurysm of the anterior communicating artery; however, the presentations of the two cases are drastically different. The first patient definitely exhibits many of the risk factors associated with aneurysm rupture including a very high height to neck ratio. The second patient has very few risk factors associated with his incidentally found aneurysm and has an intermediate height to neck ratio. In both cases, how do we best inform the patient of the situation so that they can make an informed decision in regards to their treatment plan? We've discussed many of the factors related to aneurysm growth and rupture. However, we have not seen a clear presentation of height to neck ratio and it's effect on wall shear stress and flow patterns in the parent vessel and aneurysm. The goal of this study is to relate the height to neck ratio with wall shear stress values and changes seen in the fluid dynamics of the aneurysm. Our second patient

exhibits a height to neck ratio that is not included on the risk scale presented earlier. Another goal is to compare the results using that height to neck ratio to the other values that appear on the risk scale. We hypothesize that as height to neck ratio increases, we will also see an increase in wall shear stress. We all also hypothesize that as the height to neck ratio increases, changes in fluid flow patterns will become more apparent. II. Materials & Methods A. Overview The principles of fluid dynamics can be applied to our evaluation of anterior communicating artery aneurysms. We have developed five fluid dynamics finite element models to simulate how changes in an aneurysm's geometry affect vascular fluid dynamics and the wall shear stresses in the aneurysm. The first model simulates flow in the normal anterior communicating artery, while the remaining models simulate flow in saccular aneurysms with varying height to neck ratios. In this section, we discuss the simplifying assumptions and initial conditions used in the model. We also discuss the model's geometry, theoretical calculations, and the methods used to generate and simulate the five different situations. B. Governing Assumptions & Initial Conditions To determine the hemodynamic characteristics associated with anterior communicating artery aneurysms of varying aspect ratio, idealized two dimensional models were utilized. For each model, flow was assumed to be steady, laminar, and fully developed in segment of the anterior communicating artery upstream of the aneurysm. When viewed instantaneously, flow in the human circulation is considered pulsatile; however, when the flow is averaged over time, it can be considered steady. In addition, laminar flow can be considered a valid assumption as there is no experimental evidence to suggest that sustained turbulent flow exists in the human circulation9. While the assumptions of steady, laminar flow are generally satisfied in circulation, fully developed flow does not exist in circulation. Frequent branching, curvature, and tapering of blood vessels do not permit flow to become fully developed and this assumption is invalid for circulatory flow. Blood was also assumed to behave as a Newtonian fluid. While blood exhibits non-Newtonian behavior at low shear rates, blood has been shown to behave as a Newtonian fluid in


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relatively large blood vessels, where shear rates in excess of 50 sec-1 exist9. Two dimensional, idealized vessel and aneurysm geometries were also assumed to minimize computational requirements. The initial conditions for our models were taken from quantitative hemodynamic studies performed by Chien, et al.1 and Chandran, et al9. Using computational models reconstructed from 3D rotational angiographic images taken from six patients with aneurysms of the anterior communicating artery, Chien, et al. found the average parent vessel diameter to be 2.1 mm, with an average aneurysm neck diameter of 3.5 mm. The study also found the average blood flow velocity through the anterior communicating artery to be 30 cm/s. Furthermore, the intrinsic blood properties density and viscosity were assumed to be 1.06 g/cc and 0.035 Poise, respectively9. C. Theoretical Calculations As a means of comparison and for the purposes of experimental setup, theoretical calculations were performed to establish values for entrance length, Reynold's number for the normal vessel, and expected wall shear stress in the normal vessel. Reynold's number can be calculated using equation 19:

ρ

µ (1)

The Reynold's number was calculated to be 190.08 using a blood density of 1.056 g/cm3, velocity of 30 cm/sec, diameter of 0.21 cm, and blood viscosity coefficient of 0.035 P. The theoretical entrance can be calculated using equation 29:

.06 (2) The theoretical entrance length was calculated to be approximately 2.4 cm using the calculated Reynold's number and a diameter of 0.21 cm. The theoretical wall shear stress in fully developed flow was determined from using equation 39:

∆

L

µ Q

π R (3)

The theoretical maximum wall shear stress in the normal vessel was calculated to be 40 Pa using a diameter of 0.21 cm, inlet velocity of 30 cm/s, and blood viscosity coefficient of 0.035 P. Assuming the aneurysm to be a thin walled, spherical vessel theoretical wall stresses within the aneurysm can be approximated using Laplace’s Equation,

where is the circumferential wall stress [N/m2], t is the wall thickness [m], and R is the radius [m]9.

R (4)

Thus the wall stress will increase directly with aneurysm diameter; assuming pressure and wall thickness remain constant. However, due to conservation of mass, wall thinning occurs with increasing diameter, and thus this calculation cannot be performed due to the variability in wall thickness. D. Model Geometry To realistically develop a two-dimensional model of saccular aneurysms of the anterior communicating artery, average dimensions for that vessel were identified. The anterior communicating artery has been described as having an average diameter(d) of 2.1 mm with an average aneurysm neck length(n) of 3.5 mm1. To establish fully developed flow prior to entering the aneurysm, the aforementioned theoretical calculations were used to determine an entrance of length (s1, s2) of 2.4 cm which was applied before and after the aneurysm. The length(l) of our theoretical vessel was then equal to twice the entrance length plus the aneurysm neck length. Our study investigates four different aneurysms of the anterior communicating artery with a normal anterior communicating artery for comparison purposes. The aneurysm height(h) was the only variable that was varied between the cases, and this was based on the height to neck ratio described earlier. The normal case had a height of zero, while the four aneurysm cases were given heights of 3.5 mm, 7.0 mm, 9.1mm, and 14 mm to represent height to neck ratios of 1.0, 2.0, 2.6, and 4.0, respectively. Figure 1 demonstrates a "generic" aneurysm with the variables assigned.

Figure 1: A generic 2D aneurysm displaying variables for our four aneurysms and normal case where h = aneurysm height, d = vessel diameter, l = length of vessel, s1 = length of segment one, s2 = length of segment 2, and n = aneurysm neck


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length. For all cases, the following values were used: d = 2.1 mm, s1 = 2.4 cm, s2 = 2.4 cm, n = 3.5 mm, and l = 5.15 cm. The height (h) was varied between each of the cases as follows: h = 0 cm for the normal case, h = 0.35 cm for the 1.0 height to neck ratio, h = 0.70 cm for the 2.0 height to neck ratio, h = 0.91 cm for the 2.6 height to neck ratio, and h = 1.4 cm for the 4.0 height to neck ratio. E. Computer Simulations Using Gambit, the five 2D planar geometries, previously discussed, were created to study the effects of varying height to neck ratio on intra-aneurysm hemodynamics. For each model created, three meshes of varying densities were created in GAMBIT and imported into FLUENT for CFD analysis. The initial conditions were applied in FLUENT and a convergence study was performed for each case to ensure appropriate mesh density. For each simulation, the solutions were iterated until the residual for each governing equation fell below 1E-6. From the convergence study, mesh densities of 4000, 6883, 6863, 7000, and 6790 elements were selected for the normal, 1.0 ratio, 2.0 ratio, 2.6 ratio, and 4.0 ratio cases, respectively. The wall shear stresses, velocity magnitudes, flow profiles, and pressures were then analyzed for each of the five selected meshes. III. Results The simulation of the anterior communicating artery without aneurysm showed a maximum wall shear stress of approximately 3.0 Pa, a maximum axial velocity of 0.4 m/s, and full developed flow being reached at 2.2cm downstream (Appendix Figure A-5). A steady pressure drop was also observed along the length of the vessel.

Figure 2: Plot of maximum wall shear stress versus height to neck ratio of each aneurysm case. A logarithmic trendline was fit to the data points with a correlation coefficient of .9977. When the various aneurysm cases were included into the simulations, many changes related to the fluid dynamics were noted. Uniformly across the aneurysms, the maximum wall shear stress occurred at 2.75 cm downstream of the vessel inlet, which corresponds to the distal aspect of the aneurysm neck, labeled Point A in Appendix Figure A-4. The maximum wall shear stress was shown to increase with increasing height to neck ratio as shown in Figure 2. The maximum wall shear stress for the aneurysms ranged between 5.25 Pa and 5.63 Pa. When plotted against aspect ratio, maximum WSS exhibited a logarithmic response, as shown in Figure 2. While elevated wall shear stresses were observed at the distal aspect of the aneurysm neck, the wall shear stress in the aneurysm dome significantly dropped in each of the aneurysm cases. Larger height to neck ratios were observed to have larger regions of low wall shear stress as depicted in an overlap diagram in Appendix Figure A-1. It was also noted that the vessel wall opposing the aneurysm exhibited a drop in wall shear stress of approximately 0.5 Pa in all four cases. Figure 3 shows a typical wall shear stress versus position plot for our aneurysm cases; the vessel wall including the aneurysm is represented in red and the opposing wall is represented in black. Our simulations revealed that the pressure within the aneurysm ranged from 80 mmHg to 90 mmHg for the examined height to neck ratios, as demonstrated in Appendix Figure A-2. For each of the aneurysm simulations, a maximum axial velocity of 40 cm/s was found at the center of the artery and axial velocity decreased as the position became closer to the wall. The addition of an aneurysm caused a skewing of the velocity profile as demonstrated in Appendix Figure A-3. The amount of skew was observed to increase as the height to neck ratio increased. Each simulated aneurysm also demonstrated a single recirculation zone as shown in Figure 4. Increasing height

y = 0.1877ln(x) + 5.1683R² = 0.9977

0

1

2

3

4

5

6

0 1 2 3 4 5

Maxim

um W

SS (Pa)

Height to Neck Ratio


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to neck ratio affected the velocity magnitudes within the recirculation zone with larger height to neck ratios corresponding to larger velocity magnitudes within the recirculation zone. The velocity within the aneurysm ranged from 0-0.1 m/s. Appendix Table A-1 summarizes the results of our simulation.


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Figure 3: Plot of wall shear stress vs. position along longitudinal axis of the vessel. The vessel wall including the aneurysm is shown in red, while the opposing vessel wall is shown in black. The peak wall shear stress corresponds to the neck of the aneurysm. A drop in wall shear stress is also shown at the vessel wall opposing the aneurysm.

Figure 4: Vector diagram showing flow velocity magnitudes (m/s) and vectors for anterior communicating aneurysm of height to neck ratio of 4.0. A large, single recirculation zone is observed within the aneurysm with minimal velocity magnitudes found in the dome region, and larger inlet flows found at the neck.


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IV. Discussion Due to the asymmetric nature of saccular aneurysms, a 2D axisymmetric simulation was not applicable. Thus, a 2D planar model was used in Fluent for our simulations. The theoretical calculations were based on the assumption that the cross-sections of the arteries were circular, which was not the case in Fluent. Thus, our theoretical wall shear stress did not match well with the theoretical values for the normal anterior communicating artery case. However, the theoretical entrance length for the normal case did reasonably match, within a 10% margin of, that found in the simulation. This confirmed that fully developed flow should be reached in our aneurysm simulations. The normal anterior communicating artery simulation was performed as a means of comparison for the aneurysm cases. All simulations exhibited a pressure drop over the length of the artery, which would be expected. However, an interesting finding was that the pressure within the aneurysm was uniform and did not vary based on the height to neck ratio of the aneurysm (Figure A-2). It appeared to correspond with the pressure found within the parent artery at the origin of the aneurysm. The normal anterior communicating artery reached fully developed flow and had a velocity profile corresponding to this. The maximum axial velocity reached in all simulations was uniformly 40 cm/s; however, the presence of the aneurysm resulted in a skewed flow profile with an increased amount of skew towards the aneurysm corresponding to an increasing height to neck ratio. The skew is likely caused by increased flow into the aneurysm caused by the low intra-aneurysmal pressures observed. Furthermore, it was observed that the skewing of the flow profile induced a WSS drop in the opposing arterial wall, as shown by the black line in Figure 3. A detailed view of the velocity vector profile, shown in Figure A-3, reveals that the increase in flow into the aneurysm minimizes flow at the opposing arterial wall, thus inducing low WSS. This is significant in that low arterial WSS has attributed to the formation of arteriosclerosis, which is the leading cause of death in the United States9. Another common trait found in each of the aneurysm cases was the prevalence of a single recirculation zone found entirely within the aneurysm, as shown in Figure 4. The

velocity magnitudes found within the aneurysm were significantly smaller (<15%) than those found within the parent vessel. The largest intra-aneurysmal velocities were found at the start of the recirculation zone located at the downstream region of the aneurysm inlet. These velocities were consistent between each aneurysm case ranging between 4.45 and 5.55cm/s, and no direct correlation was observed between aspect ratio and maximum intra-aneurysmal velocity. Minimal intra-aneurysmal velocities were found at the center of the aneurysm, where the recirculation flow diminished. Minimal intra-aneurysmal velocities ranged between 0.0398 and 0.0791 cm/s with lower aspect ratios correlating to larger velocities. This is significant in that low flow velocities induce low WSS, which are associated with thrombus and lesion formation, as mentioned previously. This indicates that there may exist an association between aneurysm height to neck ratio and thrombus formation, however, further studies will be required to confirm this. In the normal artery simulation, a uniform WSS of 3Pa was observed across the vessel. However, this was not the case in the aneurysm as demonstrated in Figures 2 and 3. Figure 2 demonstrates the maximum wall shear stress exhibited by the normal case and the four aneurysm cases. A logarithmic trend line best fit the data with a correlation coefficient of 0.998. It should be noted that the normal artery had a maximum wall shear stress that was 42.9-44.4% lower than that of the aneurysm cases. The maximum wall shear stress in our simulation was on the same order of magnitude as reported in at least one other study1. The height to neck ratio of 4.0, exhibited the largest wall shear stress; however, there was minimal differences in maximum wall shear stresses between the aneurysms with a maximum of 3% variability. Despite these results, a general trend of increasing height to neck ratio did exist. The special case of a height to neck ratio of 2.6 was found to have a maximum wall shear stress that was the same as the height to neck ratio of 2.0. Based on this observation, a ratio of 2.6 could be classified as intermediate risk if only the wall shear stress values were considered. As aforementioned, the maximum wall shear stress was consistently located at the distal aspect of the neck of the aneurysm. Our results correspond well with published CFD experiments, which have shown that focal elevations in


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WSS are largely confined to the downstream lip of an aneurysm5. The velocity vector profiles shown in Figure 4 reveal increased flow in that region putting additional force on the vessel wall. As previously mentioned, the minimum wall shear stress in the aneurysm cases was found to be in the dome of the aneurysm where values close to 0 Pa were recorded. The flow patterns exhibited in these regions were close to stagnant, which resulted in low forces applied to the aneurysm dome and thus low wall shear stresses. Our results do not support the high WSS theory of aneurysm progression and rupture as the dome is the most common site of rupture and our results show this to be a location of low WSS. Furthermore, angiographically documented cases of aneurysm growth generally show progression of the dome with rare changes in the neck region5. This observation is further reinforced by the low WSS and minimal velocity magnitudes found within the dome region, shown in Figures 4 and A-1. Figure A-1, in particular, displays an increase in the region of low WSS and stagnant flow with increasing aneurysm aspect ratio. It has been shown that, due to the stagnant blood flow, in the aneurysm dome, thrombus deposition and growth can occur. This can be particularly dangerous as pseudo flow patterns similar to that of non-diseased vessels may form, which may appear normal when viewed with radiographic angiography when, in fact, the vessel wall is highly weakened and distended9.

As previously discussed, this study was a simplification of reality; however, this simplification allowed our investigation to focus on how varying the aneurysm height to neck ratio affected the fluid dynamics of the anterior communicating artery. In the future, additional factors could be investigated including varying the neck width as opposed to the aneurysm height. Pulsatile flow patterns, curved vascular geometries, material properties of the vessels, and aneurysms located at vascular junctions would also be of interest. Extending our analysis to 3D patient-specific geometries could also allow for patient-specific risk assessment. V. Conclusions The maximum wall shear stress at the aneurysm neck was noted to slightly increase with increasing height to neck ratios. While an increasing pattern of wall shear stress does

correspond with the increasing rupture risk based on height to neck ratios, our study does not indicate a significant increase in wall shear stress strictly based on the increasing height to neck ratio. It would be difficult to argue that increased risk was solely caused by height to neck ratio, but it would be reasonable to suggest an association between an increase in wall shear stress (due to large height to neck ratio) and rupture risk. However, this study has shown that large height to neck ratios exhibit more exaggerated effects than lower height to neck ratios. This was directly seen in the velocity magnitudes within the recirculation zone of the aneurysm and the amount of the aneurysm wall exhibiting decreased wall shear stress values. This study has also shown that regardless of height to neck ratio, the presence of a saccular aneurysm will cause skewing of the axial velocity profile and a decrease in the wall shear stress in the wall opposite the aneurysm. Return to Our Patients: Our results do not give a clear answer to the questions posed by our patients. Based on our discussion of risk factors for rupture, Mrs. X is at significant risk for aneurysm rupture due to her family history, past medical history, aneurysm height to neck ratio, and recent appearance of symptoms correlated with traumatic insult. It would be reasonable to explain that her aneurysm had likely slowly increased in size over time. The direct blow to her head may have further weakened the aneurysm wall, which may have caused a recent increase in size and sequela of symptoms. Immediate intervention is necessary to avoid a tragic outcome. Either surgical clipping or endovascular coiling of the aneurysm would be suitable, but this decision would be left to a medical professional. Studies have shown that surgical intervention will likely resolve her symptoms2,4. Mr. Y appears to have a benign case of intracranial aneurysm that is common in the general population. His family history of unruptured aneurysm and lack of symptoms argues against the necessity of an immediate treatment plan. The results of our study show that his height to neck ratio would have a similar maximum wall shear stress to that of the intermediate risk group based on height to neck ratios. Unless, Mr. Y is experiencing


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extreme anxiety related to the aneurysm, it would be plausible to simply follow-up with him on a regular basis to ensure that the aneurysm is not increasing in size through MR imaging. Again, the determination of aneurysm rupture risk and treatment method should left to a medical professional.

VI. References

1. Chien A, Castro MA, Tateshima S, et al. Quantitative hemodynamic analysis of brain aneurysms at different locations. AJNR Am J

Neuroradiol. 2009;30:1507‐1512.

2. Park JH, Park SK, Kim TH, et al. Anterior communicating artery aneurysm related to visual symptoms. J Korean Neurosurg Soc.

2009;46:232‐238.

3. Lysack JT, Coakley A. Asymptomatic unruptured intracranial aneurysms: Approach to screening and treatment. Can Fam Physician.

2008;54:1535‐1538.

4. Gentile S, Fontanella M, Giudice RL, et al. Resolution of cluster headache after closure of an anterior communicating artery

aneurysm: The role of pericarotid sympathetic fibres. Clin Neurol Neurosurg. 2006;108:195‐198.

5. Sforza DM, Putman CM, Cebral JR. Hemodynamics of cerebral aneurysms. Annu Rev Fluid Mech. 2009;41:91‐107.

6. 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.

7. 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.

8. Qureshi AI, Janardhan V, Hanel RA, et al. Comparison of endovascular and surgical treatments for intracranial aneurysms: An

evidence‐based review. Lancet Neurol. 2007;6:816‐825.

9. Chandran KB, Yoganathan AP, Rittgers SE. Biofluid Mechanics: The Human Circulation. 2007.


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VII. Appendix Table A-1: This table summarizes the most pertinent results from our study including velocity, wall shear stress (WSS), and pressure values.

Case Maximum Intra-

Aneurysmal Velocity Magnitude (m/s)

Minimum Intra-Aneurysmal Velocity

Magnitude (m/s)

Maximum WSS (Pa)

Minimum WSS (Pa)

Intra-aneurysmal

Pressure (mmHg)

Normal n/a n/a 3 n/a

Height to Neck Ratio 1.0 4.48E-02 7.91E-04 5.25 0 80




Figure A-1: Plots of WSS vs. longitudinal position along vessels with anuerysm of aspect ratios 1, 2, 2.6, and 4 are shown. A schematic of the aneurysm has been incorporated to visualize location of WSS fluctuations. An increasing region of low WSS within the aneurysm dome are observed with increasing aneurysm aspect ratio. Elevated regions of WSS are also seen at the downstream lip of the aneurysm neck.


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Figure A-2: Static pressure profile for aneurysm of aspect ratio 4. Intra-aneurysmal pressures were consistently observed between 80 and 90 mmHg, and are greatly dependent upon inlet pressure of the parent artery.

Figure A-3: Velocity vectors colored by magnitude for an of aneurysm aspect ratio of 4. A skewing of the parent vessel flow profile is observed toward the aneurysm, and velocity flows of 1.33m/s are observed at the inlet to the aneurysm.


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Figure A-4: Vector diagram showing wall shear stress (Pa) for the anterior communicating artery aneurysm of height to neck ratio of 4.0. Point A displays an elevation in wall shear stress of 5.63Pa at the downstream area of the neck.

Figure A-5: Velocity magnitudes and fully developed flow profile for non-diseased anterior communicating artery observed 2.2cm downstream of inlet. Maximum velocity magnitudes of 4.48 m/s are observed at the vessel center with decreasing velocity magnitude observed with increases radial distance, indicative of fully developed flow.


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Feedback:

This is a very nice report. Employing specific patient cases adds a nice touch to the report on the motivation for the study. You have presented detailed flow conditions within the aneurysm based on the height to neck ratio. There are similar studies presented in the literature and it would have been worthwhile comparing your results with previous publications qualitatively.

Presentation:

+ Understood the clinical problem very well

+ Had a clear hypothesis and framed a well posed problem

+/‐ Study methods were thorough although only steady flow modeling

Problem identification, hypotheses and goals clearly stated. Overall a nice presentation and each member

had a good grasp of the material.

Grade:

Report: 50/50

Presentation: 46.5

Total: 96.5

2D CFD simulation of intracranial aneurysm

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Transcript of 2D CFD simulation of intracranial aneurysm