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  1. 1. DEPARTMENT OF BIOMEDICAL ENGINEERING, THE UNIVERSITY OF IOWA CFD Analysis of Intracranial Aneurysms 51:155 Cardiovascular Fluid Dynamics James Arter, Austin Ramme & Brian Walsh 12/4/2009
  2. 2. December 4th, 2009 51:155 Cardiovascular Fluid Mechanics James Arter, Austin Ramme & Brian Walsh 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 migraine with aura since the age of 3; otherwise, the review A. Our Patients of systems is noncontributory. Physical examination Patient 1: Mrs. X is a 50 year old woman who presents to reveals a healthy male. Medical imaging studies show an her family physician complaining of a three day history of intracranial aneurysm of the anterior communicating artery recurrent stabbing headaches directly behind her eyes. She with an aneurysm height to neck ratio of 2.6. Mr. Y also reports photophobia, nausea, and vomiting associated understands the tragic consequences of aneurysm rupture with the headaches. On further questioning, Mrs. X reveals and wants to better understand his rupture risk in order to that she is a long-term victim of spousal abuse. In fact, the make an informed decision about his treatment plan. onset of symptoms aligns with the most recent incident where her partner stuck her with a closed fist. Her past B. Intracranial Aneurysms medical history is significant for a "small aneurysm in her Intracranial aneurysms are pathologic dilations of the head" that had been incidentally identified several years vasculature within the skull that have prevalence between back. It had been described as "nothing to worry about." 2-6.5% in the general population. They have also been She reveals a family history of three relatives that died called saccular aneurysms due to their stereotypical from a ruptured "brain aneurysm." On physical spherical shape that offshoots from a parent vessel. They examination, the patient appears anxious but not in acute have been reported in a variety of locations within the distress. She is oriented to person, time, and place, but cerebral vasculature including the middle cerebral artery, there exists a complete loss of peripheral visual fields. The internal carotid artery, basilar artery, and the anterior remainder of the exam is noncontributory with the communicating artery1. Aneurysms of the anterior exception of several contusions consistent with the communicating artery are most common and account for described assault. Medical imaging studies reveal an 25-38% of all intracranial aneurysms2. The anterior intracranial aneurysm of the anterior communicating artery communicating artery is a small artery that connects the left with an aneurysm height to neck ratio of 4.0 that appears to and right anterior cerebral arteries and lies in close be impinging on the optic chiasm. On comparison to past proximity to the optic nerves. Regardless of location, medical imaging studies, the aneurysm had significantly rupture of any intracerebral aneurysm will inevitably lead enlarged since the last investigation. Mrs. X desires to to subarachnoid hemorrhage whereby half of patients die know why the previous "small aneurysm" now requires and the other half become severely disabled3. such urgent attention. Most patients with intracranial aneurysms are Patient 2: Mr. Y is a 35 year old man that presents to the asymptomatic, and in most cases they will live normal lives neurology clinic after being referred from his family without complications3. However, some patients may physician for an incidental finding of intracranial aneurysm experience symptoms prior to rupture depending on the during workup for an occupational injury. Mr. Y is size, location, and orientation of the aneurysm. The completely asymptomatic. He has a family history that is anterior communicating artery belongs to the anterior positive for unruptured "brain aneurysm." He reports circulation of the cerebrum and is in close proximity to the 2|P a ge
  3. 3. December 4th, 2009 51:155 Cardiovascular Fluid Mechanics James Arter, Austin Ramme & Brian Walsh optic nerves and optic chiasm. If an aneurysm is present, it B. Normal Cerebral Hemodynamics can cause visual symptoms due to compression of the optic Many studies have been performed to quantify human nerves such as visual field loss and visual dimness2. cerebral hemodynamic properties such as wall shear stress, Compression of surrounding structures can cause stabbing velocity profiles, and pressure. Customized computational cluster headaches that are often felt behind the eyes and are fluid dynamics (CFD) models, MR imaging, and ultrasound associated nausea and vomiting4. have been demonstrated as methods of estimating in vivo values. One of the most important anatomical structures in Histologically, degeneration of the vascular extracellular cerebral hemodynamics is the Circle of Willis. The Circle matrix and degeneration of the intimal and medial of Willis creates redundancies within the cerebral endothelial cells are indicative of cerebral aneurysms5. circulation such that if part of the circulation becomes Elevated levels of elastase and matrix mellanoproteinases occluded, blood flow from other contributing vessels can have been observed in patients with cerebral aneurysms and maintain blood flow and prevent major damage. As long as they are believed to be partly responsible for extracellular the Circle of Willis can maintain blood pressure at fifty matrix degeneration in vascular remodeling. They have percent of normal, no infarction or death of tissue will also been shown to induce smooth muscle cell apoptosis, occur in an area where a blockage exists1. These which leads to arterial wall thinning. It is theorized that redundancies often introduce some turbulent flow. Flow smooth muscle cell apoptosis and the degradation of the rates and especially wall shear stresses vary greatly elastin and collagen fibers of the vascular extracellular depending on location and specific patient vascular matrix are the primary components of arterial wall geometries. Flow rates vary from less than 10 cm/s in weakening. some parts of the basilar artery to nearly 100 cm/s in parts of the middle cerebral artery1. While wall shear stresses The exact mechanism of aneurysm initiation and vary from approximately 20 dynes/cm2 in the internal progression is a debated topic, but many agree they result carotid artery to approximately 200 dynes/cm2 in the from mechanical weakening over time5. A specific inciting middle cerebral and anterior cerebral arteries. It had been event has not been identified, but an association between found that areas of increased and decreased wall shear aneurysm initiation and anatomic variation or pathologic stress can be observed in regions of high arterial curvature feature has been established. Regions of increased blood and near bifurcations. Arteries with higher degrees of flow (e.g. arteriovenous malformations) or regions of curvature tend to exhibit higher wall shear stresses6. increased wall shear stress (e.g. arterial bifurcations) have been shown to have increased rates of aneurysm C. Intracranial Aneurysm Hemodynamics development. Some animal models have shown that Numerous computational and experimental studies of increased flow and hypertension are required for aneurysm intracranial aneurysm hemodynamics have been conducted development. The progressive weakening of the arterial using patient-specific vasculature geometry. The results of wall in aneurysm development has been correlated with 3D CFD studies reveal flow patterns that range from those endothelium-dependent nitric oxide (NO), which has been that are simple and stable to those that are complex and shown to be released in response to elevated levels of wall unstable. The simple flow patterns observed shear stress. Controversy exists as to the exact mechanism, consists largely of a single recirculation or vortex region but it is believed that aneurysm progression is the result of within the aneurysm. The complex intra-aneurysmal a NO induced passive yield to blood pressure forces hemodynamics may contain more than one recirculation coupled with reactive healing of the wall. The combination region, and have been shown to be highly dependent on the of elevated forces and wall remodeling can lead to an patient-specific vascular geometry. Furthermore, intra- increasing aneurysm diameter and thinning vessel wall. aneurysmal hemodynamics does not only depend on the Each aneurysm has two possible outcomes: progression in aneurysm shape and size, but also on the inlet and outlet size until rupture or maintenance of size. 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 3|P a ge
  4. 4. December 4th, 2009 51:155 Cardiovascular Fluid Mechanics James Arter, Austin Ramme & Brian Walsh have been shown to directly impact on the aneurysm, Increased use of medical imaging has led to an increasing producing local regions of elevated wall shear stress number of incidental discoveries of unruptured intracranial (WSS)5. In order to allow for in vivo hemodynamic aneurysms, with some studies reporting prevalence as high measurements, 3D phase contrast MR imaging has been as 6.5% in the general population7. Most often these used to view velocity and inflow hemodynamics in and incidental findings never cause a problem for the patient, around aneurysms. The results of these studies correlate but the devastating consequences of aneurysm rupture have well with most high wall shear stress theories in that the made surgical intervention a debated topic. Patients and highest wall shear stresses were found in the inlet flow physicians must weigh the benefits and risks of the region. While both CFD and phase contrast MRI treatment plan for each patient. Conservative management techniques have revealed a great deal of insight into intra- is considered the gold standard of treatment for aneurysmal hemodynamics, neither technique is practical asymptomatic patients with intracranial aneurysms less for clinical use at this time due to the significant amount of than 7 mm in size3. Treatment of intracranial aneurysm has computational power required7. been shown to have an 11.5% chance of adverse outcome with a 2.1% of chance of death during the intervention7. D. Treatment Methods for Intracranial Aneurysms Endovascular coiling has been shown to have better patient Presently, intracranial aneurysms can be treated with outcomes than surgical clipping, but both carry an inherent endovascular or surgical techniques. In 1937, Walter risk2. A patient-specific evaluation of rupture risk often Dandy performed the first surgical treatment of an guides the management of these patients. aneurysm using a vascular clip designed by Harvey Cushing. Surgical clipping involves a craniotomy to expose E. Rupture Risk Assessment the aneurysm, and the placement of a surgical clip to close Intracranial aneurysms are not uncommon in the general the neck of the aneurysm. Advances in neurosurgical population, and for the most part will never cause a techniques have allowed for the treatment of most cerebral problem for most patients. The risk of anterior circulation aneurysms, and surgical clipping remains the best way to intracranial aneurysm rupture, like that of our patients, has eliminate cerebral aneurysms. Surgical treatment remained been estimated to be between 0-0.1% per year, a seemingly the predominant treatment for nearly four decades until the small number7. However, the severe consequences (i.e. development of the detachable coil (shown on the cover severe disability or death) of rupture have motivated page) by Gglielmi in the late 1980s. Initially, endovascular research into factors that may increase the risk of aneurysm treatment was used only in patients who were thought to be rupture. Unfortunately, aneurysm rupture risk research has poor candidates for surgical treatment. In the past decade, been limited to two specific patient populations: patients however, endovascular treatment has become more that are unruptured and probably won't rupture and patients widespread due to new developments in endovascular that have already ruptured7. A human investigation of techniques. Endovascular coiling is a much less invasive patients following the natural history of aneurysm rupture treatment involving percutaneous access and insertion of is blatantly unethical. With this limitation, several factors platinum coils into the anuerysm via a catheter. When have been linked to rupture risk using retrospective reviews placed in the aneurysm, the coils induce thrombogenesis of patient medical records. Some of these relationships that, when successful, will eliminate the aneurysm. In include: certain cases, stents are inserted as a scaffold for the coils.  Symptomatic aneurysms are 4-5 times more likely to While endovascular coiling is a cost effective, minimally rupture than asymptomatic aneurysms3. invasive treatment, there exists a major complication of  Intracranial aneurysms found in the posterior aneurysm reoccurrence and subsequent bleeding. Treatment circulation are 2-3 times more likely to rupture than selection depends greatly on the clinical condition of the those found in the anterior circulation3, 7. patient, the morphology and location of the aneurysm, and  An aneurysm that is greater than 5 mm is 2-3 times less likely to rupture than an aneurysm that is less than institutional expertise8. 5 mm in size3, 7. 4|P a ge
  5. 5. December 4th, 2009 51:155 Cardiovascular Fluid Mechanics James Arter, Austin Ramme & Brian Walsh  Aneurysms showing evidence of surface irregularities a clear presentation of height to neck ratio and it's effect on and daughter sacks are at an increased risk of rupture7. wall shear stress and flow patterns in the parent vessel and  Aneurysms originating from parent arteries with larger aneurysm. The goal of this study is to relate the height to diameters also tend to rupture at relatively larger neck ratio with wall shear stress values and changes seen in sizes1. the fluid dynamics of the aneurysm. Our second patient One relationship that has been shown to be clinically useful exhibits a height to neck ratio that is not included on the and statistically significant is the aneurysm height to neck risk scale presented earlier. Another goal is to compare the ratio7. It has been postulated that intracranial aneurysms results using that height to neck ratio to the other values with a height to neck ratio less than 1.4 are at low risk of that appear on the risk scale. We hypothesize that as height rupture, those with a ratio from 1.6-2.2 have a borderline to neck ratio increases, we will also see an increase in wall risk of rupture, and those with a ratio greater than 3.0 have shear stress. We all also hypothesize that as the height to a high risk of rupture. These risk statistics have been neck ratio increases, changes in fluid flow patterns will established based on patient outcomes. become more apparent. F. Hemodynamic Modeling II. Materials & Methods Advancements in medical imaging modalities have allowed A. Overview for patient-specific reconstruction of aneurysm and The principles of fluid dynamics can be applied to our vascular geometries for CFD analysis. Numerous evaluation of anterior communicating artery aneurysms. computational and experimental studies have revealed a We have developed five fluid dynamics finite element wide variety of complex intra-aneurysmal flow patterns models to simulate how changes in an aneurysm's geometry that are strongly specific to the patient-specific geometries, affect vascular fluid dynamics and the wall shear stresses in and thus may not correlate well with idealized models. the aneurysm. The first model simulates flow in the normal Furthermore, fluid-structure interaction algorithms have anterior communicating artery, while the remaining models been implemented to incorporate wall compliance into simulate flow in saccular aneurysms with varying height to CFD models. These models reveal that fluid-structure neck ratios. In this section, we discuss the simplifying interactions produce alterations in wall shear stress and assumptions and initial conditions used in the model. We velocity magnitudes, but have minimal affect on flow also discuss the model's geometry, theoretical calculations, patterns5. Despite potential discrepancies in results, and the methods used to generate and simulate the five idealized and two dimensional geometries are frequently different situations. used for initial CFD studies due to their predictability and minimal computational requirements. B. Governing Assumptions & Initial Conditions To determine the hemodynamic characteristics associated G. Goals of This Study with anterior communicating artery aneurysms of varying Both of our patient's exhibited the most common type of aspect ratio, idealized two dimensional models were intracranial aneurysm, an aneurysm of the anterior utilized. For each model, flow was assumed to be steady, communicating artery; however, the presentations of the laminar, and fully developed in segment of the anterior two cases are drastically different. The first patient communicating artery upstream of the aneurysm. When definitely exhibits many of the risk factors associated with viewed instantaneously, flow in the human circulation is aneurysm rupture including a very high height to neck considered pulsatile; however, when the flow is averaged ratio. The second patient has very few risk factors over time, it can be considered steady. In addition, laminar associated with his incidentally found aneurysm and has an flow can be considered a valid assumption as there is no intermediate height to neck ratio. In both cases, how do we experimental evidence to suggest that sustained turbulent best inform the patient of the situation so that they can flow exists in the human circulation9. While the make an informed decision in regards to their treatment assumptions of steady, laminar flow are generally satisfied plan? We've discussed many of the factors related to in circulation, fully developed flow does not exist in aneurysm growth and rupture. However, we have not seen circulation. Frequent branching, curvature, and tapering of 5|P a ge
  6. 6. December 4th, 2009 51:155 Cardiovascular Fluid Mechanics James Arter, Austin Ramme & Brian Walsh blood vessels do not permit flow to become fully developed cm, inlet velocity of 30 cm/s, and blood viscosity and this assumption is invalid for circulatory flow. Blood coefficient of 0.035 P. Assuming the aneurysm to be a thin was also assumed to behave as a Newtonian fluid. While walled, spherical vessel theoretical wall stresses within the blood exhibits non-Newtonian behavior at low shear rates, aneurysm can be approximated using Laplace’s Equation, blood has been shown to behave as a Newtonian fluid in where ������ is the circumferential wall stress [N/m2], t is the relatively large blood vessels, where shear rates in excess wall thickness [m], and R is the radius [m]9. of 50 sec-1 exist9. Two dimensional, idealized vessel and ������ = p×R (4) ������ aneurysm geometries were also assumed to minimize Thus the wall stress will increase directly with aneurysm computational requirements. diameter; assuming pressure and wall thickness remain constant. However, due to conservation of mass, wall The initial conditions for our models were taken from thinning occurs with increasing diameter, and thus this quantitative hemodynamic studies performed by Chien, et calculation cannot be performed due to the variability in al.1 and Chandran, et al9. Using computational models wall thickness. reconstructed from 3D rotational angiographic images taken from six patients with aneurysms of the anterior D. Model Geometry communicating artery, Chien, et al. found the average To realistically develop a two-dimensional model of parent vessel diameter to be 2.1 mm, with an average saccular aneurysms of the anterior communicating artery, aneurysm neck diameter of 3.5 mm. The study also found average dimensions for that vessel were identified. The the average blood flow velocity through the anterior anterior communicating artery has been described as communicating artery to be 30 cm/s. Furthermore, the having an average diameter(d) of 2.1 mm with an average intrinsic blood properties density and viscosity were aneurysm neck length(n) of 3.5 mm1. To establish fully assumed to be 1.06 g/cc and 0.035 Poise, respectively9. developed flow prior to entering the aneurysm, the aforementioned theoretical calculations were used to C. Theoretical Calculations determine an entrance of length (s1, s2) of 2.4 cm which As a means of comparison and for the purposes of was applied before and after the aneurysm. The length(l) experimental setup, theoretical calculations were performed of our theoretical vessel was then equal to twice the to establish values for entrance length, Reynold's number entrance length plus the aneurysm neck length. Our study for the normal vessel, and expected wall shear stress in the investigates four different aneurysms of the anterior normal vessel. Reynold's number can be calculated using communicating artery with a normal anterior equation 19: communicating artery for comparison purposes. The ρ × ������ × ������ ������������ = (1) aneurysm height(h) was the only variable that was varied µ The Reynold's number was calculated to be 190.08 using a between the cases, and this was based on the height to neck blood density of 1.056 g/cm3, velocity of 30 cm/sec, ratio described earlier. The normal case had a height of diameter of 0.21 cm, and blood viscosity coefficient of zero, while the four aneurysm cases were given heights of 0.035 P. The theoretical entrance can be calculated using 3.5 mm, 7.0 mm, 9.1mm, and 14 mm to represent height to equation 29: neck ratios of 1.0, 2.0, 2.6, and 4.0, respectively. Figure 1 ������������ = .06 × ������ × ������������ (2) demonstrates a "generic" aneurysm with the variables The theoretical entrance length was calculated to be assigned. 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: −d × ∆������ 4 × µ ×Q ������ = 4 ×L = π ×R 3 (3) The theoretical maximum wall shear stress in the normal vessel was calculated to be 40 Pa using a diameter of 0.21 6|P a ge
  7. 7. December 4th, 2009 51:155 Cardiovascular Fluid Mechanics James Arter, Austin Ramme & Brian Walsh 6 5 Maximum WSS (Pa) 4 y = 0.1877ln(x) + 5.1683 3 R² = 0.9977 2 1 Figure 1: A generic 2D aneurysm displaying variables for our four aneurysms and normal case where h = aneurysm height, 0 d = vessel diameter, l = length of vessel, s1 = length of 0 1 2 3 4 5 segment one, s2 = length of segment 2, and n = aneurysm neck Height to Neck Ratio 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. Figure 2: Plot of maximum wall shear stress versus height The height (h) was varied between each of the cases as to neck ratio of each aneurysm case. A logarithmic follows: h = 0 cm for the normal case, h = 0.35 cm for the 1.0 trendline was fit to the data points with a correlation height to neck ratio, h = 0.70 cm for the 2.0 height to neck coefficient of .9977. 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. When the various aneurysm cases were included into the simulations, many changes related to the fluid dynamics E. Computer Simulations were noted. Uniformly across the aneurysms, the Using Gambit, the five 2D planar geometries, previously maximum wall shear stress occurred at 2.75 cm discussed, were created to study the effects of varying downstream of the vessel inlet, which corresponds to the height to neck ratio on intra-aneurysm hemodynamics. For distal aspect of the aneurysm neck, labeled Point A in each model created, three meshes of varying densities were Appendix Figure A-4. The maximum wall shear stress was created in GAMBIT and imported into FLUENT for CFD shown to increase with increasing height to neck ratio as analysis. The initial conditions were applied in FLUENT shown in Figure 2. The maximum wall shear stress for the and a convergence study was performed for each case to aneurysms ranged between 5.25 Pa and 5.63 Pa. When ensure appropriate mesh density. For each simulation, the plotted against aspect ratio, maximum WSS exhibited a solutions were iterated until the residual for each governing logarithmic response, as shown in Figure 2. equation fell below 1E-6. From the convergence study, mesh densities of 4000, 6883, 6863, 7000, and 6790 While elevated wall shear stresses were observed at the elements were selected for the normal, 1.0 ratio, 2.0 ratio, distal aspect of the aneurysm neck, the wall shear stress in 2.6 ratio, and 4.0 ratio cases, respectively. The wall shear the aneurysm dome significantly dropped in each of the stresses, velocity magnitudes, flow profiles, and pressures aneurysm cases. Larger height to neck ratios were were then analyzed for each of the five selected meshes. observed to have larger regions of low wall shear stress as depicted in an overlap diagram in Appendix Figure A-1. It III. Results was also noted that the vessel wall opposing the aneurysm The simulation of the anterior communicating artery exhibited a drop in wall shear stress of approximately 0.5 without aneurysm showed a maximum wall shear stress of Pa in all four cases. Figure 3 shows a typical wall shear approximately 3.0 Pa, a maximum axial velocity of 0.4 m/s, stress versus position plot for our aneurysm cases; the and full developed flow being reached at 2.2cm vessel wall including the aneurysm is represented in red downstream (Appendix Figure A-5). A steady pressure and the opposing wall is represented in black. drop was also observed along the length of the vessel. Our simulations revealed that the pressure within the aneurysm ranged from 80 mmHg to 90 mmHg for the 7|P a ge
  8. 8. December 4th, 2009 51:155 Cardiovascular Fluid Mechanics James Arter, Austin Ramme & Brian Walsh examined height to neck ratios, as demonstrated in Appendix Figure A-2. For each of the aneurysm Each simulated aneurysm also demonstrated a single simulations, a maximum axial velocity of 40 cm/s was recirculation zone as shown in Figure 4. Increasing height found at the center of the artery and axial velocity to neck ratio affected the velocity magnitudes within the decreased as the position became closer to the wall. The recirculation zone with larger height to neck ratios addition of an aneurysm caused a skewing of the velocity corresponding to larger velocity magnitudes within the profile as demonstrated in Appendix Figure A-3. The recirculation zone. The velocity within the aneurysm amount of skew was observed to increase as the height to ranged from 0-0.1 m/s. Appendix Table A-1 summarizes neck ratio increased. the results of our simulation. 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. 8|P a ge
  9. 9. December 4th, 2009 51:155 Cardiovascular Fluid Mechanics James Arter, Austin Ramme & Brian Walsh 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. IV. Discussion correspond with the pressure found within the parent artery Due to the asymmetric nature of saccular aneurysms, a 2D at the origin of the aneurysm. axisymmetric simulation was not applicable. Thus, a 2D planar model was used in Fluent for our simulations. The The normal anterior communicating artery reached fully theoretical calculations were based on the assumption that developed flow and had a velocity profile corresponding to the cross-sections of the arteries were circular, which was this. The maximum axial velocity reached in all not the case in Fluent. Thus, our theoretical wall shear simulations was uniformly 40 cm/s; however, the presence stress did not match well with the theoretical values for the of the aneurysm resulted in a skewed flow profile with an normal anterior communicating artery case. However, the increased amount of skew towards the aneurysm theoretical entrance length for the normal case did corresponding to an increasing height to neck ratio. The reasonably match, within a 10% margin of, that found in skew is likely caused by increased flow into the aneurysm the simulation. This confirmed that fully developed flow caused by the low intra-aneurysmal pressures observed. should be reached in our aneurysm simulations. Furthermore, it was observed that the skewing of the flow profile induced a WSS drop in the opposing arterial wall, as The normal anterior communicating artery simulation was shown by the black line in Figure 3. A detailed view of the performed as a means of comparison for the aneurysm velocity vector profile, shown in Figure A-3, reveals that cases. All simulations exhibited a pressure drop over the the increase in flow into the aneurysm minimizes flow at length of the artery, which would be expected. However, the opposing arterial wall, thus inducing low WSS. This is an interesting finding was that the pressure within the significant in that low arterial WSS has attributed to the aneurysm was uniform and did not vary based on the height formation of arteriosclerosis, which is the leading cause of to neck ratio of the aneurysm (Figure A-2). It appeared to death in the United States9. 9|P a ge
  10. 10. December 4th, 2009 51:155 Cardiovascular Fluid Mechanics James Arter, Austin Ramme & Brian Walsh As aforementioned, the maximum wall shear stress was Another common trait found in each of the aneurysm cases consistently located at the distal aspect of the neck of the was the prevalence of a single recirculation zone found aneurysm. Our results correspond well with published CFD entirely within the aneurysm, as shown in Figure 4. The experiments, which have shown that focal elevations in velocity magnitudes found within the aneurysm were WSS are largely confined to the downstream lip of an significantly smaller (<15%) than those found within the aneurysm5. The velocity vector profiles shown in Figure 4 parent vessel. The largest intra-aneurysmal velocities were reveal increased flow in that region putting additional force found at the start of the recirculation zone located at the on the vessel wall. As previously mentioned, the minimum downstream region of the aneurysm inlet. These velocities wall shear stress in the aneurysm cases was found to be in were consistent between each aneurysm case ranging the dome of the aneurysm where values close to 0 Pa were between 4.45 and 5.55cm/s, and no direct correlation was recorded. The flow patterns exhibited in these regions were observed between aspect ratio and maximum intra- close to stagnant, which resulted in low forces applied to aneurysmal velocity. Minimal intra-aneurysmal velocities the aneurysm dome and thus low wall shear stresses. were found at the center of the aneurysm, where the recirculation flow diminished. Minimal intra-aneurysmal Our results do not support the high WSS theory of velocities ranged between 0.0398 and 0.0791 cm/s with aneurysm progression and rupture as the dome is the most lower aspect ratios correlating to larger velocities. This is common site of rupture and our results show this to be a significant in that low flow velocities induce low WSS, location of low WSS. Furthermore, angiographically which are associated with thrombus and lesion formation, documented cases of aneurysm growth generally show as mentioned previously. This indicates that there may exist progression of the dome with rare changes in the neck an association between aneurysm height to neck ratio and region5. This observation is further reinforced by the low thrombus formation, however, further studies will be WSS and minimal velocity magnitudes found within the required to confirm this. dome region, shown in Figures 4 and A-1. Figure A-1, in particular, displays an increase in the region of low WSS In the normal artery simulation, a uniform WSS of 3Pa was and stagnant flow with increasing aneurysm aspect ratio. It observed across the vessel. However, this was not the case has been shown that, due to the stagnant blood flow, in the in the aneurysm as demonstrated in Figures 2 and 3. Figure aneurysm dome, thrombus deposition and growth can 2 demonstrates the maximum wall shear stress exhibited by occur. This can be particularly dangerous as pseudo flow the normal case and the four aneurysm cases. A patterns similar to that of non-diseased vessels may form, logarithmic trend line best fit the data with a correlation which may appear normal when viewed with radiographic coefficient of 0.998. It should be noted that the normal angiography when, in fact, the vessel wall is highly artery had a maximum wall shear stress that was 42.9- weakened and distended9. 44.4% lower than that of the aneurysm cases. The maximum wall shear stress in our simulation was on the As previously discussed, this study was a simplification of same order of magnitude as reported in at least one other reality; however, this simplification allowed our study1. The height to neck ratio of 4.0, exhibited the largest investigation to focus on how varying the aneurysm height wall shear stress; however, there was minimal differences to neck ratio affected the fluid dynamics of the anterior in maximum wall shear stresses between the aneurysms communicating artery. In the future, additional factors with a maximum of 3% variability. Despite these results, a could be investigated including varying the neck width as general trend of increasing height to neck ratio did exist. opposed to the aneurysm height. Pulsatile flow patterns, The special case of a height to neck ratio of 2.6 was found curved vascular geometries, material properties of the to have a maximum wall shear stress that was the same as vessels, and aneurysms located at vascular junctions would the height to neck ratio of 2.0. Based on this observation, a also be of interest. Extending our analysis to 3D patient- ratio of 2.6 could be classified as intermediate risk if only specific geometries could also allow for patient-specific the wall shear stress values were considered. risk assessment. 10 | P a g e
  11. 11. December 4th, 2009 51:155 Cardiovascular Fluid Mechanics James Arter, Austin Ramme & Brian Walsh V. Conclusions which may have caused a recent increase in size and The maximum wall shear stress at the aneurysm neck was sequela of symptoms. Immediate intervention is necessary noted to slightly increase with increasing height to neck to avoid a tragic outcome. Either surgical clipping or ratios. While an increasing pattern of wall shear stress does endovascular coiling of the aneurysm would be suitable, correspond with the increasing rupture risk based on height but this decision would be left to a medical professional. to neck ratios, our study does not indicate a significant Studies have shown that surgical intervention will likely increase in wall shear stress strictly based on the increasing resolve her symptoms2,4. height to neck ratio. It would be difficult to argue that increased risk was solely caused by height to neck ratio, but Mr. Y appears to have a benign case of intracranial it would be reasonable to suggest an association between an aneurysm that is common in the general population. His increase in wall shear stress (due to large height to neck family history of unruptured aneurysm and lack of ratio) and rupture risk. symptoms argues against the necessity of an immediate treatment plan. The results of our study show that his However, this study has shown that large height to neck height to neck ratio would have a similar maximum wall ratios exhibit more exaggerated effects than lower height to shear stress to that of the intermediate risk group based on neck ratios. This was directly seen in the velocity height to neck ratios. Unless, Mr. Y is experiencing magnitudes within the recirculation zone of the aneurysm extreme anxiety related to the aneurysm, it would be and the amount of the aneurysm wall exhibiting decreased plausible to simply follow-up with him on a regular basis to wall shear stress values. This study has also shown that ensure that the aneurysm is not increasing in size through regardless of height to neck ratio, the presence of a saccular MR imaging. Again, the determination of aneurysm aneurysm will cause skewing of the axial velocity profile rupture risk and treatment method should left to a medical and a decrease in the wall shear stress in the wall opposite professional. 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, 11 | P a g e
  12. 12. December 4th, 2009 51:155 Cardiovascular Fluid Mechanics James Arter, Austin Ramme & Brian Walsh VI. References 1. Chien A, Castro MA, Tateshima S, et al. Quantitative 6. Cebral JR, Putman CM, Alley MT, et al. Hemodynamics in hemodynamic analysis of brain aneurysms at different normal cerebral arteries: Qualitative comparison of 4D phase- locations. AJNR Am J Neuroradiol. 2009;30:1507-1512. contrast magnetic resonance and image-based computational fluid dynamics. J Eng Math. 2009;64:367-378. 2. Park JH, Park SK, Kim TH, et al. Anterior communicating artery aneurysm related to visual symptoms. J Korean 7. Lall RR, Eddleman CS, Bendok BR, et al. Unruptured Neurosurg Soc. 2009;46:232-238. intracranial aneurysms and the assessment of rupture risk based on anatomical and morphological factors: Sifting 3. Lysack JT, Coakley A. Asymptomatic unruptured through the sands of data. Neurosurg Focus. 2009;26:E2. intracranial aneurysms: Approach to screening and treatment. Can Fam Physician. 2008;54:1535-1538. 8. Qureshi AI, Janardhan V, Hanel RA, et al. Comparison of endovascular and surgical treatments for intracranial 4. Gentile S, Fontanella M, Giudice RL, et al. Resolution of aneurysms: An evidence-based review. Lancet Neurol. cluster headache after closure of an anterior communicating 2007;6:816-825. artery aneurysm: The role of pericarotid sympathetic fibres. Clin Neurol Neurosurg. 2006;108:195-198. 9. Chandran KB, Yoganathan AP, Rittgers SE. Biofluid Mechanics: The Human Circulation. 2007. 5. Sforza DM, Putman CM, Cebral JR. Hemodynamics of cerebral aneurysms. Annu Rev Fluid Mech. 2009;41:91-107. 12 | P a g e
  13. 13. December 4th, 2009 51:155 Cardiovascular Fluid Mechanics James Arter, Austin Ramme & Brian Walsh VII. Appendix Table A-1: This table summarizes the most pertinent results from our study including velocity, wall shear stress (WSS), and pressure values. Intra- Maximum Intra- Minimum Intra- Maximum Minimum aneurysmal Case Aneurysmal Velocity Aneurysmal Velocity WSS (Pa) WSS (Pa) Pressure Magnitude (m/s) Magnitude (m/s) (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 Height to Neck Ratio 2.0 4.45E-02 4.1E-04 5.3 0 90 Height to Neck Ratio 2.6 4.45E-02 3.98E-04 5.3 0 90 Height to Neck Ratio 4.0 5.55E-02 4.07E-04 5.63 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. 13 | P a g e
  14. 14. December 4th, 2009 51:155 Cardiovascular Fluid Mechanics James Arter, Austin Ramme & Brian Walsh 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. 14 | P a g e
  15. 15. December 4th, 2009 51:155 Cardiovascular Fluid Mechanics James Arter, Austin Ramme & Brian Walsh 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. 15 | P a g e