2D CFD simulation of intracranial aneurysm


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2D CFD simulation of intracranial aneurysm

  1. 1. 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 g e    
  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 Many studies have been performed to quantify human can cause visual symptoms due to compression of the optic cerebral hemodynamic properties such as wall shear stress, nerves such as visual field loss and visual dimness2. velocity profiles, and pressure. Customized computational Compression of surrounding structures can cause stabbing fluid dynamics (CFD) models, MR imaging, and ultrasound cluster headaches that are often felt behind the eyes and are have been demonstrated as methods of estimating in vivo associated nausea and vomiting4. values. One of the most important anatomical structures in cerebral hemodynamics is the Circle of Willis. The Circle Histologically, degeneration of the vascular extracellular of Willis creates redundancies within the cerebral matrix and degeneration of the intimal and medial circulation such that if part of the circulation becomes endothelial cells are indicative of cerebral aneurysms5. occluded, blood flow from other contributing vessels can Elevated levels of elastase and matrix mellanoproteinases maintain blood flow and prevent major damage. As long as have been observed in patients with cerebral aneurysms and the Circle of Willis can maintain blood pressure at fifty they are believed to be partly responsible for extracellular percent of normal, no infarction or death of tissue will matrix degeneration in vascular remodeling. They have occur in an area where a blockage exists1. These also been shown to induce smooth muscle cell apoptosis, redundancies often introduce some turbulent flow. Flow which leads to arterial wall thinning. It is theorized that rates and especially wall shear stresses vary greatly smooth muscle cell apoptosis and the degradation of the depending on location and specific patient vascular elastin and collagen fibers of the vascular extracellular geometries. Flow rates vary from less than 10 cm/s in matrix are the primary components of arterial wall some parts of the basilar artery to nearly 100 cm/s in parts weakening. of the middle cerebral artery1. While wall shear stresses vary from approximately 20 dynes/cm2 in the internal The exact mechanism of aneurysm initiation and carotid artery to approximately 200 dynes/cm2 in the progression is a debated topic, but many agree they result middle cerebral and anterior cerebral arteries. It had been from mechanical weakening over time5. A specific inciting found that areas of increased and decreased wall shear event has not been identified, but an association between stress can be observed in regions of high arterial curvature aneurysm initiation and anatomic variation or pathologic and near bifurcations. Arteries with higher degrees of feature has been established. Regions of increased blood curvature tend to exhibit higher wall shear stresses6. flow (e.g. arteriovenous malformations) or regions of increased wall shear stress (e.g. arterial bifurcations) have C. Intracranial Aneurysm Hemodynamics been shown to have increased rates of aneurysm Numerous computational and experimental studies of development. Some animal models have shown that intracranial aneurysm hemodynamics have been conducted increased flow and hypertension are required for aneurysm using patient-specific vasculature geometry. The results of development. The progressive weakening of the arterial 3D CFD studies reveal flow patterns that range from those wall in aneurysm development has been correlated with that are simple and stable to those that are complex and endothelium-dependent nitric oxide (NO), which has been unstable. The simple flow patterns observed shown to be released in response to elevated levels of wall consists largely of a single recirculation or vortex region shear stress. Controversy exists as to the exact mechanism, within the aneurysm. The complex intra-aneurysmal but it is believed that aneurysm progression is the result of hemodynamics may contain more than one recirculation a NO induced passive yield to blood pressure forces region, and have been shown to be highly dependent on the coupled with reactive healing of the wall. The combination patient-specific vascular geometry. Furthermore, intra- of elevated forces and wall remodeling can lead to an aneurysmal hemodynamics does not only depend on the increasing aneurysm diameter and thinning vessel wall. aneurysm shape and size, but also on the inlet and outlet Each aneurysm has two possible outcomes: progression in flow patterns found in the parent vessel(s). For example, size until rupture or maintenance of size. concentrated inflow jets are found to exist when a parent vessel flows directly into the aneurysm. These inflow jets B. Normal Cerebral Hemodynamics have been shown to directly impact on the aneurysm,   3 | P a g e    
  4. 4. December 4th, 2009 51:155 Cardiovascular Fluid Mechanics James Arter, Austin Ramme & Brian Walsh  producing local regions of elevated wall shear stress aneurysms, with some studies reporting prevalence as high (WSS)5. In order to allow for in vivo hemodynamic as 6.5% in the general population7. Most often these measurements, 3D phase contrast MR imaging has been incidental findings never cause a problem for the patient, used to view velocity and inflow hemodynamics in and but the devastating consequences of aneurysm rupture have around aneurysms. The results of these studies correlate made surgical intervention a debated topic. Patients and well with most high wall shear stress theories in that the physicians must weigh the benefits and risks of the highest wall shear stresses were found in the inlet flow treatment plan for each patient. Conservative management region. While both CFD and phase contrast MRI is considered the gold standard of treatment for techniques have revealed a great deal of insight into intra- asymptomatic patients with intracranial aneurysms less aneurysmal hemodynamics, neither technique is practical than 7 mm in size3. Treatment of intracranial aneurysm has for clinical use at this time due to the significant amount of been shown to have an 11.5% chance of adverse outcome computational power required7. with a 2.1% of chance of death during the intervention7. Endovascular coiling has been shown to have better patient D. Treatment Methods for Intracranial Aneurysms outcomes than surgical clipping, but both carry an inherent Presently, intracranial aneurysms can be treated with risk2. A patient-specific evaluation of rupture risk often endovascular or surgical techniques. In 1937, Walter guides the management of these patients. Dandy performed the first surgical treatment of an E. Rupture Risk Assessment aneurysm using a vascular clip designed by Harvey Intracranial aneurysms are not uncommon in the general Cushing. Surgical clipping involves a craniotomy to expose population, and for the most part will never cause a the aneurysm, and the placement of a surgical clip to close problem for most patients. The risk of anterior circulation the neck of the aneurysm. Advances in neurosurgical intracranial aneurysm rupture, like that of our patients, has techniques have allowed for the treatment of most cerebral been estimated to be between 0-0.1% per year, a seemingly aneurysms, and surgical clipping remains the best way to small number7. However, the severe consequences (i.e. eliminate cerebral aneurysms. Surgical treatment remained severe disability or death) of rupture have motivated the predominant treatment for nearly four decades until the research into factors that may increase the risk of aneurysm development of the detachable coil (shown on the cover rupture. Unfortunately, aneurysm rupture risk research has page) by Gglielmi in the late 1980s. Initially, endovascular been limited to two specific patient populations: patients treatment was used only in patients who were thought to be that are unruptured and probably won't rupture and patients poor candidates for surgical treatment. In the past decade, that have already ruptured7. A human investigation of however, endovascular treatment has become more patients following the natural history of aneurysm rupture widespread due to new developments in endovascular is blatantly unethical. With this limitation, several factors techniques. Endovascular coiling is a much less invasive have been linked to rupture risk using retrospective reviews treatment involving percutaneous access and insertion of of patient medical records. Some of these relationships platinum coils into the anuerysm via a catheter. When include: placed in the aneurysm, the coils induce thrombogenesis  Symptomatic aneurysms are 4-5 times more likely to that, when successful, will eliminate the aneurysm. In rupture than asymptomatic aneurysms3. certain cases, stents are inserted as a scaffold for the coils.  Intracranial aneurysms found in the posterior While endovascular coiling is a cost effective, minimally circulation are 2-3 times more likely to rupture than invasive treatment, there exists a major complication of those found in the anterior circulation3, 7. aneurysm reoccurrence and subsequent bleeding. Treatment  An aneurysm that is greater than 5 mm is 2-3 times selection depends greatly on the clinical condition of the less likely to rupture than an aneurysm that is less than 5 mm in size3, 7. patient, the morphology and location of the aneurysm, and  Aneurysms showing evidence of surface irregularities institutional expertise8. and daughter sacks are at an increased risk of rupture7.  Aneurysms originating from parent arteries with larger Increased use of medical imaging has led to an increasing diameters also tend to rupture at relatively larger number of incidental discoveries of unruptured intracranial sizes1.   4 | P a g e    
  5. 5. December 4th, 2009 51:155 Cardiovascular Fluid Mechanics James Arter, Austin Ramme & Brian Walsh  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 a clear presentation of height to neck ratio and it's effect on blood vessels do not permit flow to become fully developed wall shear stress and flow patterns in the parent vessel and and this assumption is invalid for circulatory flow. Blood aneurysm. The goal of this study is to relate the height to was also assumed to behave as a Newtonian fluid. While neck ratio with wall shear stress values and changes seen in blood exhibits non-Newtonian behavior at low shear rates, the fluid dynamics of the aneurysm. Our second patient blood has been shown to behave as a Newtonian fluid in   5 | P a g e    
  6. 6. December 4th, 2009 51:155 Cardiovascular Fluid Mechanics James Arter, Austin Ramme & Brian Walsh  relatively large blood vessels, where shear rates in excess where is the circumferential wall stress [N/m2], t is the of 50 sec-1 exist9. Two dimensional, idealized vessel and wall thickness [m], and R is the radius [m]9. R aneurysm geometries were also assumed to minimize   (4) computational requirements. Thus the wall stress will increase directly with aneurysm diameter; assuming pressure and wall thickness remain The initial conditions for our models were taken from constant. However, due to conservation of mass, wall quantitative hemodynamic studies performed by Chien, et thinning occurs with increasing diameter, and thus this al.1 and Chandran, et al9. Using computational models calculation cannot be performed due to the variability in reconstructed from 3D rotational angiographic images wall thickness. taken from six patients with aneurysms of the anterior communicating artery, Chien, et al. found the average D. Model Geometry parent vessel diameter to be 2.1 mm, with an average To realistically develop a two-dimensional model of aneurysm neck diameter of 3.5 mm. The study also found saccular aneurysms of the anterior communicating artery, the average blood flow velocity through the anterior average dimensions for that vessel were identified. The communicating artery to be 30 cm/s. Furthermore, the anterior communicating artery has been described as intrinsic blood properties density and viscosity were having an average diameter(d) of 2.1 mm with an average assumed to be 1.06 g/cc and 0.035 Poise, respectively9. aneurysm neck length(n) of 3.5 mm1. To establish fully developed flow prior to entering the aneurysm, the C. Theoretical Calculations aforementioned theoretical calculations were used to As a means of comparison and for the purposes of determine an entrance of length (s1, s2) of 2.4 cm which experimental setup, theoretical calculations were performed was applied before and after the aneurysm. The length(l) to establish values for entrance length, Reynold's number of our theoretical vessel was then equal to twice the for the normal vessel, and expected wall shear stress in the entrance length plus the aneurysm neck length. Our study normal vessel. Reynold's number can be calculated using investigates four different aneurysms of the anterior equation 19: communicating artery with a normal anterior ρ                  (1) communicating artery for comparison purposes. The µ The Reynold's number was calculated to be 190.08 using a aneurysm height(h) was the only variable that was varied blood density of 1.056 g/cm3, velocity of 30 cm/sec, between the cases, and this was based on the height to neck diameter of 0.21 cm, and blood viscosity coefficient of ratio described earlier. The normal case had a height of 0.035 P. The theoretical entrance can be calculated using zero, while the four aneurysm cases were given heights of equation 29: 3.5 mm, 7.0 mm, 9.1mm, and 14 mm to represent height to   .06   (2) neck ratios of 1.0, 2.0, 2.6, and 4.0, respectively. Figure 1 The theoretical entrance length was calculated to be demonstrates a "generic" aneurysm with the variables approximately 2.4 cm using the calculated Reynold's assigned. number and a diameter of 0.21 cm. The theoretical wall shear stress in fully developed flow was determined from using equation 39:    ∆    µ  Q           (3)   L π  R 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 Figure 1: A generic 2D aneurysm displaying variables for our walled, spherical vessel theoretical wall stresses within the four aneurysms and normal case where h = aneurysm height, aneurysm can be approximated using Laplace’s Equation, d = vessel diameter, l = length of vessel, s1 = length of segment one, s2 = length of segment 2, and n = aneurysm neck   6 | P a g e    
  7. 7. December 4th, 2009 51:155 Cardiovascular Fluid Mechanics James Arter, Austin Ramme & Brian Walsh  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 6 aneurysm ranged from 80 mmHg to 90 mmHg for the examined height to neck ratios, as demonstrated in 5 Maximum WSS (Pa) Appendix Figure A-2. For each of the aneurysm 4 simulations, a maximum axial velocity of 40 cm/s was 3 y = 0.1877ln(x) + 5.1683 found at the center of the artery and axial velocity R² = 0.9977 decreased as the position became closer to the wall. The 2 addition of an aneurysm caused a skewing of the velocity 1 profile as demonstrated in Appendix Figure A-3. The amount of skew was observed to increase as the height to 0 neck ratio increased. 0 1 2 3 4 5 Height  to  Neck Ratio Each simulated aneurysm also demonstrated a single recirculation zone as shown in Figure 4. Increasing height   7 | P a g e    
  8. 8. December 4th, 2009 51:155 Cardiovascular Fluid Mechanics James Arter, Austin Ramme & Brian Walsh  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.   8 | P a g e    
  9. 9. December 4th, 2009 51:155 Cardiovascular Fluid Mechanics James Arter, Austin Ramme & Brian Walsh  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.   9 | P a g e    
  10. 10. December 4th, 2009 51:155 Cardiovascular Fluid Mechanics James Arter, Austin Ramme & Brian Walsh  IV. Discussion velocity magnitudes found within the aneurysm were Due to the asymmetric nature of saccular aneurysms, a 2D significantly smaller (<15%) than those found within the axisymmetric simulation was not applicable. Thus, a 2D parent vessel. The largest intra-aneurysmal velocities were planar model was used in Fluent for our simulations. The found at the start of the recirculation zone located at the theoretical calculations were based on the assumption that downstream region of the aneurysm inlet. These velocities the cross-sections of the arteries were circular, which was were consistent between each aneurysm case ranging not the case in Fluent. Thus, our theoretical wall shear between 4.45 and 5.55cm/s, and no direct correlation was stress did not match well with the theoretical values for the observed between aspect ratio and maximum intra- normal anterior communicating artery case. However, the aneurysmal velocity. Minimal intra-aneurysmal velocities theoretical entrance length for the normal case did were found at the center of the aneurysm, where the reasonably match, within a 10% margin of, that found in recirculation flow diminished. Minimal intra-aneurysmal the simulation. This confirmed that fully developed flow velocities ranged between 0.0398 and 0.0791 cm/s with should be reached in our aneurysm simulations. lower aspect ratios correlating to larger velocities. This is significant in that low flow velocities induce low WSS, The normal anterior communicating artery simulation was which are associated with thrombus and lesion formation, performed as a means of comparison for the aneurysm as mentioned previously. This indicates that there may exist cases. All simulations exhibited a pressure drop over the an association between aneurysm height to neck ratio and length of the artery, which would be expected. However, thrombus formation, however, further studies will be an interesting finding was that the pressure within the required to confirm this. aneurysm was uniform and did not vary based on the height to neck ratio of the aneurysm (Figure A-2). It appeared to In the normal artery simulation, a uniform WSS of 3Pa was correspond with the pressure found within the parent artery observed across the vessel. However, this was not the case at the origin of the aneurysm. in the aneurysm as demonstrated in Figures 2 and 3. Figure 2 demonstrates the maximum wall shear stress exhibited by The normal anterior communicating artery reached fully the normal case and the four aneurysm cases. A developed flow and had a velocity profile corresponding to logarithmic trend line best fit the data with a correlation this. The maximum axial velocity reached in all coefficient of 0.998. It should be noted that the normal simulations was uniformly 40 cm/s; however, the presence artery had a maximum wall shear stress that was 42.9- of the aneurysm resulted in a skewed flow profile with an 44.4% lower than that of the aneurysm cases. The increased amount of skew towards the aneurysm maximum wall shear stress in our simulation was on the corresponding to an increasing height to neck ratio. The same order of magnitude as reported in at least one other skew is likely caused by increased flow into the aneurysm study1. The height to neck ratio of 4.0, exhibited the largest caused by the low intra-aneurysmal pressures observed. wall shear stress; however, there was minimal differences Furthermore, it was observed that the skewing of the flow in maximum wall shear stresses between the aneurysms profile induced a WSS drop in the opposing arterial wall, as with a maximum of 3% variability. Despite these results, a shown by the black line in Figure 3. A detailed view of the general trend of increasing height to neck ratio did exist. velocity vector profile, shown in Figure A-3, reveals that The special case of a height to neck ratio of 2.6 was found the increase in flow into the aneurysm minimizes flow at to have a maximum wall shear stress that was the same as the opposing arterial wall, thus inducing low WSS. This is the height to neck ratio of 2.0. Based on this observation, a significant in that low arterial WSS has attributed to the ratio of 2.6 could be classified as intermediate risk if only formation of arteriosclerosis, which is the leading cause of the wall shear stress values were considered. death in the United States9. 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   10 | P a g e    
  11. 11. December 4th, 2009 51:155 Cardiovascular Fluid Mechanics James Arter, Austin Ramme & Brian Walsh  WSS are largely confined to the downstream lip of an correspond with the increasing rupture risk based on height aneurysm5. The velocity vector profiles shown in Figure 4 to neck ratios, our study does not indicate a significant reveal increased flow in that region putting additional force increase in wall shear stress strictly based on the increasing on the vessel wall. As previously mentioned, the minimum height to neck ratio. It would be difficult to argue that wall shear stress in the aneurysm cases was found to be in increased risk was solely caused by height to neck ratio, but the dome of the aneurysm where values close to 0 Pa were it would be reasonable to suggest an association between an recorded. The flow patterns exhibited in these regions were increase in wall shear stress (due to large height to neck close to stagnant, which resulted in low forces applied to ratio) and rupture risk. the aneurysm dome and thus low wall shear stresses. However, this study has shown that large height to neck Our results do not support the high WSS theory of ratios exhibit more exaggerated effects than lower height to aneurysm progression and rupture as the dome is the most neck ratios. This was directly seen in the velocity common site of rupture and our results show this to be a magnitudes within the recirculation zone of the aneurysm location of low WSS. Furthermore, angiographically and the amount of the aneurysm wall exhibiting decreased documented cases of aneurysm growth generally show wall shear stress values. This study has also shown that progression of the dome with rare changes in the neck regardless of height to neck ratio, the presence of a saccular region5. This observation is further reinforced by the low aneurysm will cause skewing of the axial velocity profile WSS and minimal velocity magnitudes found within the and a decrease in the wall shear stress in the wall opposite dome region, shown in Figures 4 and A-1. Figure A-1, in the aneurysm. particular, displays an increase in the region of low WSS and stagnant flow with increasing aneurysm aspect ratio. It Return to Our Patients: has been shown that, due to the stagnant blood flow, in the Our results do not give a clear answer to the questions aneurysm dome, thrombus deposition and growth can posed by our patients. Based on our discussion of risk occur. This can be particularly dangerous as pseudo flow factors for rupture, Mrs. X is at significant risk for patterns similar to that of non-diseased vessels may form, aneurysm rupture due to her family history, past medical which may appear normal when viewed with radiographic history, aneurysm height to neck ratio, and recent angiography when, in fact, the vessel wall is highly appearance of symptoms correlated with traumatic insult. weakened and distended9. It would be reasonable to explain that her aneurysm had likely slowly increased in size over time. The direct blow As previously discussed, this study was a simplification of to her head may have further weakened the aneurysm wall, reality; however, this simplification allowed our which may have caused a recent increase in size and investigation to focus on how varying the aneurysm height sequela of symptoms. Immediate intervention is necessary to neck ratio affected the fluid dynamics of the anterior to avoid a tragic outcome. Either surgical clipping or communicating artery. In the future, additional factors endovascular coiling of the aneurysm would be suitable, could be investigated including varying the neck width as but this decision would be left to a medical professional. opposed to the aneurysm height. Pulsatile flow patterns, Studies have shown that surgical intervention will likely curved vascular geometries, material properties of the resolve her symptoms2,4. vessels, and aneurysms located at vascular junctions would also be of interest. Extending our analysis to 3D patient- Mr. Y appears to have a benign case of intracranial specific geometries could also allow for patient-specific aneurysm that is common in the general population. His risk assessment. family history of unruptured aneurysm and lack of symptoms argues against the necessity of an immediate V. Conclusions treatment plan. The results of our study show that his The maximum wall shear stress at the aneurysm neck was height to neck ratio would have a similar maximum wall noted to slightly increase with increasing height to neck shear stress to that of the intermediate risk group based on ratios. While an increasing pattern of wall shear stress does height to neck ratios. Unless, Mr. Y is experiencing   11 | P a g e    
  12. 12. December 4th, 2009 51:155 Cardiovascular Fluid Mechanics James Arter, Austin Ramme & Brian Walsh  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.             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    
  16. 16. December 4th, 2009 51:155 Cardiovascular Fluid Mechanics James Arter, Austin Ramme & Brian Walsh  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   16 | P a g e