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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
 
AJNR Am J Neuroradiol. Author manuscript; available in PMC 2011 April 5.
Published in final edited form as:
PMCID: PMC3070915
NIHMSID: NIHMS284033

Association of Hemodynamic Characteristics and Cerebral Aneurysm Rupture

Abstract

Background and purpose

Hemodynamic factors are thought to play an important role in the initiation, growth and rupture of cerebral aneurysms. This report describes a study of the associations between qualitative intra-aneurysmal hemodynamics and the rupture of cerebral aneurysms.

Methods

210 consecutive aneurysms were analyzed using patient-specific CFD simulations under pulsatile flow conditions. The aneurysms were classified into categories depending on the complexity and stability of the flow pattern, size of the impingement region, and inflow concentration by two blinded observers. A statistical analysis was then performed with respect to history of previous rupture. Inter-observer variability analysis was performed.

Results

Ruptured aneurysms were more likely to have complex flow patterns (83%, p<0.001), stable flow patterns (75%, p=0.0018), 66% concentrated inflow (66%, p=<0.0001), and small impingement regions (76%, p=0.0006) compared to unruptured aneurysms. Inter-observer variability analyses indicate that all the classifications performed are in very good agreement, i.e. well within the 95% confidence interval.

Conclusions

A qualitative hemodynamic analysis of cerebral aneurysms using image based patient-specific geometries has shown that concentrated inflow jets, small impingement regions, complex flow patterns, and unstable flow patterns are correlated with a clinical history of prior aneurysm rupture. These qualitative measures provide a starting point for more sophisticated quantitative analysis aimed at assigning aneurysm risk of future rupture. These analyses highlight the potential for CFD to play an important role in the clinical determination of aneurysm risks.

Introduction

Although unruptured cerebral aneurysms carry a relatively low risk of rupture1, 2, preventive interventions are commonly considered because of the poor prognosis of intracranial hemorrhage. Current treatments of intracranial aneurysms carry a small but significant risk that can exceed the natural risk of aneurysm rupture2, 3 making the development of methods to better define the rupture risk of cerebral aneurysms very valuable for clinicians. Current risk assessment is mainly based on aneurysm size, i.e. larger aneurysms are more likely to rupture than smaller aneurysms4,5. However, small aneurysms do rupture, thus aneurysm size alone may not be enough for a reliable stratification of aneurysm rupture risk. Hemodynamics is commonly thought to play an important role in the mechanisms of aneurysm development, progression and rupture69. It is reasonable to assume that rupture risk assessment can be improved by incorporating hemodynamic information. Several researchers have considered a number of geometric measures such as aspect ratio and shape descriptors as surrogates for hemodynamic information1013. These parameters may be useful for improving risk evaluation, but they are difficult to connect to the underlying mechanisms. Others have focused on extracting hemodynamic information from computational fluid dynamics (CFD) models 1416. So far, these studies have been limited to small numbers of aneurysms, which has prevented the establishment of statistical associations between hemodynamic characteristics and aneurysm rupture. The purpose of this study was to statistically confirm previous trends relating qualitative hemodynamic characteristics and aneurysm rupture using image-based CFD analysis17.

Methods

Patients and Aneurysms

A total of 210 intracranial aneurysms in 128 consecutive patients referred to the Interventional Neuroradiology Service and imaged by conventional catheter angiograms and 3D rotational angiography (3DRA) were included in this study. Patients’ ages ranged from 28 to 88 years of age with a mean age of 54 years. Females (males) accounted for 68% (32%) of the patients. The patients’ medical and radiological records were reviewed and evaluated for evidence of aneurysmal intracranial hemorrhage. In patients with multiple aneurysms, the clinical and radiological information were considered and a judgment of the most likely source of hemorrhage was made. The other co-incident aneurysms were classified as unruptured. Dissecting aneurysms or aneurysms with inconclusive clinical information or with evidence of vasospasm were excluded. In addition to the symptoms associated with the intracranial hemorrhage in patients with ruptured aneurysms, a relatively small number of patients (10%) presented with a variety of symptoms. These symptoms included: aphasia (3 patients), bilateral peripheral weakness (1 patient), cranial nerve III palsy (4 patients), right neck pain (1 patient), right side weakness (2 patients), brain arteriovenous malformations (BAVMs – 2 patients) and seizure disorder (1 patient). The aneurysms were distributed in various locations: 53 in the internal carotid artery (ICA), 39 in the middle cerebral artery (MCA), 52 in the posterior communicating artery (Pcom), 28 in the anterior communicating artery (ACom), 4 in the anterior cerebral artery (ACA), 26 in the basilar artery (BA), 2 in the superior cerebellar artery (SCA), 1 in the posterior cerebral artery (PCA) and 5 in the vertebral artery (VA). A total of 176 (83%) aneurysms were located in the anterior circulation while 34 (17%) in the posterior circulation. The distribution of aneurysms among morphological categories was as follows: 67 bifurcation aneurysms, 69 terminal aneurysms, 59 lateral aneurysms, 12 bilateral Acom aneurysms, and 3 fusiform aneurysms.

Image Data

All catheter angiograms were performed by standard transfemoral catheterizations of the cerebral blood vessels. Digital subtraction angiography imaging was done on a Philips Integris biplane unit (Philips Health Care, Best, The Netherlands). Rotational angiograms were performed during a six second contrast injection for a total of 24 cc of contrast agent and a 180 degree rotation imaging at 15 frames per second over 8 seconds for acquisition of 120 projection images. Bilateral 3DRA images were acquired for aneurysms in the Acom artery accepting blood from both A1 segments of the ACAs. The projection images were transferred to the Philips Integris Workstation and reconstructed into 3D voxel data using standard proprietary software (Philips XtraVision).

Vascular and Hemodynamics Modeling

Patient-specific models of the cerebral aneurysms were constructed using a previously developed methodology18, 19. Briefly, 3D images are filtered to reduce noise and segmented using a seeded region growing algorithm to reconstruct the arterial network topology followed by an iso-surface deformable model to recover the vascular geometry. The vascular models are then smoothed and vessel branches are truncated perpendicularly to their axes. Unstructured grids composed of tetrahedral elements are then generated for numerical simulations with a minimum uniform resolution between 0.02 cm and 0.01 cm. The resulting grids contained between 1 to 5 million elements.

Blood flows were approximated by the unsteady 3D Navier-Stokes equations for an incompressible Newtonian fluid and vessel walls were assumed rigid. Since patient-specific blood flow information was not available, typical physiologic flow boundary conditions were derived from phase-contrast magnetic resonance measurements of flow rates in normal subjects20. The measured flow waveforms were scaled with the areas of the inlet boundaries in order to achieve a mean wall shear stress (WSS) of 15 dyne/cm2 at the inlets, which were located in the internal carotid artery, vertebral artery or basilar artery for all models. Fully developed velocity profiles were prescribed at the inlets using the Womersley solution21. The governing equations were numerically solved using in house developed software based on an implicit pressure-projection algorithm22, 23. All numerical simulations were performed using 100 timesteps per cardiac cycle for a total of two cycles. All analyses and visualizations were done for the second cycle.

Data Analysis

The computed blood flow fields were visualized using a variety of techniques, including: a) iso-velocity surfaces to depict the aneurysm inflow stream, b) streamlines to depict the intra-aneurysmal flow structures, c) velocity magnitudes on cut-planes to depict the inflow jets and velocity profiles at the neck, and d) shaded surfaces to depict the distribution of WSS magnitudes. The hemodynamic visualizations were analyzed to classify blood flows according the following characteristics:

  1. Flow complexity. Simple (S): flow patterns consisting on a single recirculation zone or vortex structure within the aneurysm. Complex (C): flow patterns exhibiting flow divisions or separations within the aneurysm sac and containing more than one recirculation zone or vortex structure.
  2. Flow stability. Stable (S): flows patterns that persist (do not move or change) during the cardiac cycle. Unstable (U): flow patterns where the flow divisions and/or vortex structures move or are created or destroyed during the cardiac cycle.
  3. Inflow concentration. Concentrated (C): inflow streams or jets that penetrate relatively deep into the aneurysm sac and are thin or narrow in the main flow direction. Diffuse (D): inflow streams that are thick compared to the aneurysm neck and flow jets that disperse quickly once they penetrate into the aneurysm sac.
  4. Flow impingement. The flow impingement zone is the region of the aneurysm where the inflow stream is seen to impact the aneurysm wall and change its direction and/or disperse. Typically this region has an associated region of elevated WSS. Small impingement (S): if the area of the impingement region is small compared to the area of the aneurysm (less than 50%). Large impingement (L): if the area of impingement is large compared to the area of the aneurysm (more than 50%).

Two observers blinded to the clinical history of the patients independently evaluated and classified the aneurysms into the categories described above. The degree of agreement between the two observers was quantified using the Kappa test24. In cases where the observers disagreed, the models were re-examined by both observers and a consensus was reached. The data was then analyzed to look for associations between the hemodynamic characteristics and the clinical history of aneurysm rupture. Statistical analysis was performed using 2×2 contingency tables and two-tailed p-values were calculated using the Chi Square (Pearsons uncorrected) test24. Associations were considered statistically significant if the p-values were below 0.05 (95% confidence).

Results

Numerical simulations were performed on the 210 patient-specific aneurysm geometries under pulsatile flows. Visualizations of the unsteady flow fields were composed into cine-loops and used to classify the aneurysms into the hemodynamic categories described earlier. Examples of aneurysms with simple and complex flow patterns are shown in Figure 1. Examples of aneurysms with stable and unstable flow patterns are shown in Figure 2. Examples of aneurysms with large and small impingement regions are shown in Figure 3. Examples of aneurysms with diffuse and concentrated inflow streams are shown in Figure 4.

Figure 1
Examples of aneurysms with simple (top) and complex (bottom) flow patterns. From left to right the visualizations show iso-velocity surfaces, velocity magnitudes on a cut plane, streamlines and WSS distribution, all at peak systole.
Figure 2
Examples of aneurysms with stable (top) and unstable (bottom) flow patterns. Visualizations at peak systole (top row of each panel) and end diastole (bottom row of each panel) are shown using (from left to right) iso-velocity surfaces, velocity magnitudes ...
Figure 3
Examples of aneurysms with large (top) and small (bottom) impingement regions. From left to right the visualizations show iso-velocity surfaces, velocity magnitudes on a cut plane, streamlines and WSS distribution, all at peak systole.
Figure 4
Examples of aneurysms with diffuse (top) and concentrated (bottom) inflows. From left to right the visualizations show iso-velocity surfaces, velocity magnitudes on a cut plane, streamlines and WSS distribution, all at peak systole.

The number of aneurysms classified into each category by each observer were counted and used to assess the degree of agreement of the hemodynamic classification. The results are presented in Table 1. This table shows for each hemodynamic characteristic, the agreement-disagreement table, the number of aneurysms that were classified by both observers into the same categories (agreements), the number of agreements expected by chance (random), the Kappa value (κ), and the 95% confidence interval (CI). The agreement-disagreement tables list the number of aneurysms that were classified into the same category by both observers, and the number of aneurysms classified into one category by observer 1 and into another by observer 2. The Kappa values obtained indicate that all the classifications performed by both observers were in very good agreement, i.e. well within the 95% confidence interval.

Table 1
Inter-observer variability analysis of hemodynamics characterization.

The number of ruptured and unruptured aneurysms in each category was then counted. These numbers along with the results of the statistical analyses using contingency tables are presented in Table 2. This table also lists the Chi square (χ2) values, two-tailed p-values (p) and odds ratios (OR) computed from the 2×2 contingency tables. The odd ratios indicate that ruptured aneurysms are 4.701 times more likely to have complex flow patterns, 2.733 times more likely to have unstable flow patterns, 3.975 more likely to have concentrated inflows, and 3.005 more likely to have small impingement regions. The corresponding p-values show that these associations reached a strong statistical significance, well above the 95% confidence level. On the other hand, unruptured aneurysms are more likely to have diffuse inflows, but they are roughly equally likely to have simple or complex, stable or unstable flow patterns and large or small impingement regions. In addition, it was found that the average size (maximum dome diameter) of the ruptured aneurysm group (9.3mm) was larger than the average size of the unruptured aneurysm group (6.5mm). This difference was statistically significant according to the Student’s t-test with a 95% confidence.

Table 2
Statistical analyses of the associations between hemodynamic categories and aneurysm rupture.

Discussion

The pathophysiology of cerebral aneurysms is complex and poorly understood. Current theories implicate genetic factors, perianeurysmal environment, and vascular wall biology in combination with the hemodynamic environment as the determinants of which aneurysms will progress and ultimately rupture7. Although intravascular hemodynamics is widely considered important in the process, there is no consensus on which variables are most important. Great controversy exists whether regions of low or high flow are the most critical in promoting the events responsible for rupture. Presence of a low flow environment could potentially lead to changes in the arterial wall that would weaken its structural integrity through mechanisms related to wall inflammation. Low flows lead to regions of low WSS which can be detrimental to the wall endothelium. In particular, stagnant blood flow promotes thrombus formation which when adjacent to the aneurysm wall can lead to the release of substances that promote inflammation in the aneurysm wall2527. Inflammation can be associated with structural degradation through the release of numerous types of destructive enzymes28, 29. High intravascular blood flow causes an elevation of WSS. At high levels of WSS the endothelium releases nitrous oxide that leads to remodeling of the arterial wall in a system which seeks to maintain the WSS within acceptable range3032. At excessive levels of WSS, the endothelium becomes dysfunctional and can be destroyed33. Determining which hemodynamics variables are most closely correlated to clinical progression and rupture may help us determine the relative influence of these mechanisms. This knowledge may help in further improvements in our treatment paradigms for cerebral aneurysm.

Cebral et al.17 reported a series of 62 aneurysms in which CFD analysis was performed on patient-specific models and CFD findings were correlated with clinical history of prior rupture. They found unruptured aneurysms more commonly had simple stable flow patterns, large impingement regions, and large jet sizes while ruptured aneurysms had disturbed flow patterns, small impingement regions, and narrow jets. Of these characteristics only impingement size reached statistical significance possibly due to the small sample size. The current study focuses on confirming the previous trends observed. Our study incorporates a number of improvements and extensions to previously reported analyses. First, the sample was large enough to achieve statistically significant results. Secondly, the aneurysm population included aneurysms in the anterior communicating complex, which had been previously excluded because not all avenues of flow had been properly imaged and therefore did not allow for proper CFD modeling. Thirdly, the classification of intra-aneurysmal flow patterns has been simplified by considering flow complexity and flow stability separately. These two characteristics now have become dichotomous variables, which makes both the aneurysm classification and subsequent statistical analysis simpler and more robust. Finally, the current study includes an inter-observer variability analysis showing a high degree of agreement between observers classifying aneurysms into the proposed hemodynamic categories.

The statistical analysis indicates that the qualitative hemodynamic characteristics considered are strongly correlated with aneurysm rupture. Namely, that ruptured aneurysms are more likely to have complex and unstable flows, concentrated inflows and small impingement regions. While the majority of unruptured aneurysms had diffuse inflows, many of them had complex flows, unstable flows and/or small impingement regions. From the mechanistic perspective, the result seem to point to regions of concentrated more rapid flow as correlating with rupture rather implicating the presence of a low flow environment. However, the simplified qualitative analysis performed in this study does not specifically seek to examine the probably complex interrelationship between low and high flow hemodynamic variables. This would require a more sophisticated quantitative multivariate analysis before any strong conclusions should be drawn.

It is not surprising that both categories of aneurysms are found in the unruptured group since this analysis is an examination of only a single point in time without a complete knowledge of each aneurysm’s final outcome. Many unruptured aneurysms may progress overtime and become ruptured. Therefore, many of the unruptured aneurysms with complex and unstable flows, concentrated inflows and small impingement regions may join the ruptured category leaving a predominance of aneurysms with simpler, less concentrated flows. A longitudinal study of these aneurysms would be necessary to confirm this. If confirmed these CFD characterizations could potentially improve our ability to assign risk to an individual aneurysm and thereby improve the judgments made on the need for treatment of asymptomatic unruptured aneurysms.

The current study suffers from a number of limitations that should be considered when interpreting the results. Similarly to previous studies focusing on geometrical characteristics of cerebral aneurysms (which are the basis of current rupture risk assessment), in the current study a retrospective analysis of a population including both unruptured and ruptured aneurysms was performed. This does not allow us to confirm whether unruptured aneurysms in the high risk categories (those more likely to occur in ruptured aneurysms) will indeed rupture. However, recent case studies of cerebral aneurysms imaged just before their rupture are in very good agreement with the predictions of our current study34, 35. In addition, this study relies on an assumption that the aneurysm anatomy is little changed by the event of rupture; however, an aneurysm may undergo a variety of structural changes during and immediately after a hemorrhage. For example, a portion of the aneurysm may be filled with thrombus or a new daughter sac may form. Small changes in the geometry can have significant effects on intra-aneurysmal patterns. Therefore, it may be necessary to conduct prospective natural history studies of CFD-analyzed unruptured aneurysms to evaluate conclusively the association of a predetermined hemodynamic factor to risk of aneurysmal rupture.

As in most CFD analyses a number of assumptions and approximations were made during the modeling process. These include: blood was modeled as a Newtonian fluid, vessel wall compliance was neglected, physiologic flow conditions were not patient-specific but derived from flow measurements in the cerebral arteries of normal subjects, and the vascular geometries were approximated from 3D images with limited resolution. Previous sensitivity analyses using a small number of aneurysm models suggested that the most important factor for a realistic representation of the in vivo hemodynamics is the vascular geometry18, 36. Using different flow conditions37, non-Newtonian viscosity models, or compliant models38 did not substantially affect the qualitative hemodynamic characteristics. In the current study, careful attention was paid to the reconstruction of vascular models from the 3D rotational angiography images. Images that failed to properly depict the parent vessel because of incomplete filling or images that were too noisy due to low contrast dose were discarded. The entire portion of the proximal parent artery visible in the images was included in the models in order to properly capture the secondary and swirling flows created by the curving geometry of the parent vessel. Despite all these limitations and approximations, it has been shown that these CFD models are capable of realistically representing the in vivo intra-aneurysmal hemodynamic patterns observed with conventional angiography39.

Over the last decade, great progress has been made in image-based CFD modeling of blood flows. Simulation software has become more accessible and easier to use. However, these techniques are still challenging and models must be constructed carefully. The choice of boundary conditions, mesh and time resolution, segmentation methods and parameters, location of vessel truncation, inclusion of side arterial branches, etc. can affect the quantitative hemodynamic results. For this reason, before attempting the quantification of hemodynamic variables, we proposed a qualitative characterization of aneurysmal flows based on observations of gross flow features and investigated possible relationships with aneurysm rupture. The current study showed that these qualitative characteristics are indeed related to aneurysm rupture, and thus justifies the search for quantitative variables that objectively describe these hemodynamic categories. Perhaps some of the gross hemodynamic characteristics could be determined using simplified models in an efficient manner, for instance using steady flows, truncated models, coarse computational grids, etc. This could allow quick computarized clinical evaluation of cerebral aneurysms and could potentially improve current patient management.

Conclusions

A qualitative hemodynamic analysis of cerebral aneurysms using image based patient-specific geometries has shown that concentrated inflow jets, small impingement regions, complex flow patterns, and unstable flow patterns are correlated with a clinical history of prior aneurysm rupture. These qualitative measures provide a starting point for more sophisticated quantitative analysis aimed at assigning aneurysm risk of future rupture. These analyses highlight the potential for CFD to play an important role in the clinical determination of aneurysm risks.

Acknowledgements

We thank Philips Medical Systems and the National Institutes of Health (grant # R01NS059063) for financial support.

References

1. Kassell NF, Torner JC, Haley ECJ, Jane JA, Adams HP, Kongable GL. The international cooperative study on the timing of aneurysm surgery. Part 1: Overall management results. J Neurosurg. 1990;73:18–36. [PubMed]
2. Wiebers DO, Whisnant JP, Huston Jr, Meissner I, Brown RDJ, Piepgras DG, Forbes GS, Thielen K, Nichols D, O'Fallon WM, Peacock J, Jaeger L, Kassell N, Kongable-Beckman GL, Torner JC. International study of unruptured intracranial aneurysms investigators. Unruptured intracranial aneurysms: Natural history, clinical outcome, and risks of surgical and endovascular treatment. Lancet. 2003;362:103–110. [PubMed]
3. Tomasello F, D'Avella D, Salpietro FM, Longo M. Asymptomatic aneurysms. Literature meta-analysis and indications for treatment. Journal of Neurosurgical Science. 1998;42:47–51. [PubMed]
4. Nishioka H, Torner JC, Graf CJ, Kassell NF, Sahs AL, Goettler LC. Cooperative study of intracranial aneurysms and subarachnoid hemorrhage: A long-term prognostic study. Ii. Ruptured intracranial aneurysms managed conservatively. Arch Neurol. 1984;41:1142–1146. [PubMed]
5. White PM, Wardlaw JM. Unruptured intracranial aneurysms. J Neuroradiol. 2003;30:336–350. [PubMed]
6. Stehbens WE. Pathology of the cerebral blood vessels. St. Louis, Misoury: CV Mosby; 1972. Intracranial aneurysms; pp. 351–470.
7. Sforza D, Putman CM, Cebral JR. Hemodynamics of cerebral aneurysms. Ann Rev Fluid Mechanics. 2009;41:91–107. [PMC free article] [PubMed]
8. Kayembe KNT, Sasahara M, Hazama F. Cerebral aneurysms and variations of the circle of willis. Stroke. 1984;15:846–850. [PubMed]
9. Nixon AM, Gunel M, Sumpio BE. The critical role of hemodynamics in the development of cerebral vascular disease. J Neurosurg. 2009 (PMID: 19943737) - in press. [PubMed]
10. Ujiie H, Tamano Y, Sasaki K, Hori T. Is the aspect ratio a reliable index for predicting the rupture of a saccular aneurysm ? Neurosurgery. 2001;48:495–503. [PubMed]
11. Raghavan ML, Ma B, Harabaugh RE. Quantified aneurysm shape and rupture risk. Journal of Neurosurgery. 2005;102:355–362. [PubMed]
12. Ma B, harbaugh RE, Raghavan ML. Three-dimensional geometrical characterization of cerebral aneurysms. ABME. 2004;32:264–273. [PubMed]
13. Millan D, Dempere-Marco L, Pozo JM, Cebral JR, Frangi AF. Morphological characterization of intracranial aneurysms using 3-d moment invariants. IEEE Trans on Medical Imaging. 2007;26:1270–1282. [PubMed]
14. Shojima M, Oshima M, Takagi K, Torii R, Hayakawa M, Katada K, Morita A, Kirino T. Magnitude and role of wall shear stress on cerebral aneurysm: Computational fluid dynamic study of 20 middle cerebral artery aneurysms. Stroke. 2004;35:2500–2505. [PubMed]
15. Steinman DA, Milner JS, Norley CJ, Lownie SP, Holdworth DW. Image-based computational simulation of flow dynamics in a giant intracranial aneurysm. AJNR American Journal of Neuroradiology. 2003;24:559–566. [PubMed]
16. Jou LD, Quick CM, Young WL, Lawton MT, Higashida R, Martin A, Saloner D. Computational approach to quantifying hemodynamic forces in giant cerebral aneurysms. AJNR American Journal of Neuroradiology. 2003;24:1804–1810. [PubMed]
17. Cebral JR, Castro MA, Burgess JE, Pergolizzi R, Sheridan MJ, Putman CM. Characterization of cerebral aneurysm for assessing risk of rupture using patient-specific computational hemodynamics models. AJNR American Journal of Neuroradiology. 2005;26:2550–2559. [PubMed]
18. Cebral JR, Castro MA, Appanaboyina S, Putman CM, Millan D, Frangi AF. Efficient pipeline for image-based patient-specific analysis of cerebral aneurysm hemodynamics: Technique and sensitivity. IEEE Transactions in Medical Imaging. 2005;24:457–467. [PubMed]
19. Castro MA, Putman CM, Cebral JR. Patient-specific computational modeling of cerebral aneurysms with multiple avenues of flow from 3d rotational angiography images. Academic Radiology. 2006;13:811–821. [PubMed]
20. Cebral JR, Castro MA, Putman CM, Alperin N. Flow-area relationship in internal carotid and vertebral arteries. Physiol Meas. 2008;29:585–594. [PMC free article] [PubMed]
21. Taylor CA, Hughes TJR, Zarins CK. Finite element modeling of blood flow in arteries. CMAME. 1998;158:155–196.
22. Löhner R. Applied cfd techniques. John Wiley & Sons; 2001.
23. Mut F, Aubry R, Löhner R, Cebral JR. Fast numerical solutions in patient-specific simulations of arterial models. Comm Num Meth Eng. 2009
24. Pezzullo JC. 2010 http://www.Statpages.Org/
25. Griffith TM. Modulation of blood flow and tissue perfusion by endothelium-derived relaxing factor. Exp Physiolo. 1994;779:873–913. [PubMed]
26. Moncada S, Plamer RMJ, Higgs EA. Nitric oxide: Physiology, pathology and pharmacology. Pharmacol Rev. 1991;43:109–142. [PubMed]
27. Moritake K, Handa H, Hayashi K, Sato M. Experimental studies on intracranial aneurysms (a preliminary report): Some biomechanical considerations on the wall structures of intracranial aneurysms and experimentally produced aneurysms. No shinkei Sheka. 1973;1:115–123.
28. Crawford T. Some observations of the pathogenesis and natural history of intracranial aneurysms. J Neurol Neurosurg Psychiatry. 1959;22:259–266. [PMC free article] [PubMed]
29. Crompton M. Mechanism of growth and rupture in cerebral berry aneurysms. Br Med J. 1966;1:1138–1142. [PMC free article] [PubMed]
30. Sho E, Sho M, Singh TM, Xu C, Zarins C, Masuda H. Bloodflow decrease induces apoptosis of endothelial cells in previously dilated arteries resulting from chromic high blood flow. Arteriosclerosis, Thrombosis & Vasc Biology. 2001;21:1139–1145. [PubMed]
31. Hara A, Yoshimi N, Mori H. Evidence for apoptosis in human intracranial aneurysms. Neurol Res. 1998;20:127–130. [PubMed]
32. Fukuda S, Hashimoto N, Naritomi H, Nagata I, Nozaki K, Kondo S, Kurino M, Kikuchi H. Prevention of rat cerebral aneurysm formation by inhibition of nitric oxide synthase. Circulation. 2000;101:2532–2538. [PubMed]
33. Nakatani H, Hashimoto N, Kang Y, Yamazoe N, Kikuchi H, Yamaguchi S, Niimi H. Cerebral blood flow patterns at major vessel bifurcations and aneurysms in rats. J Neurosurg. 1991;74:258–262. [PubMed]
34. Cebral JR, Hendrickson S, Putman CM. Hemodynamics in a lethal basilar artery aneurysm just before its rupture. AJNR American Journal of Neuroradiology. 2009;30:95–98. [PMC free article] [PubMed]
35. Sforza D, Putman CM, Scrivano E, Lylyk P, Cebral JR. Blood flow characteristics in a terminal basilar tip aneurysm prior to its fatal rupture. AJNR American Journal of Neuroradiology. 2010 in press. [PMC free article] [PubMed]
36. Castro MA, Putman CM, Cebral JR. Computational fluid dynamics modeling of intracranial aneurysms: Effects of parent artery segmentation on intra-aneurysmal hemodynamcis. AJNR American Journal of Neuroradiology. 2006;27:1703–1709. [PubMed]
37. Castro MA, Putman CM, Cebral JR. Patient-specific computational fluid dynamics modeling of anterior communicating artery aneurysms: A study of the sensitivity of intra-aneurysmal flow patterns to flow conditions in the carotid arteries. AJNR American Journal of Neuroradiology. 2006;27:2061–2068. [PubMed]
38. Dempere-Marco L, Oubel E, Castro MA, Putman CM, Frangi AF, Cebral JR. Estimation of wall motion in intracranial aneurysms and its effects on hemodynamic patterns. LNCS. 2006;4191:438–445.
39. Cebral JR, Pergolizzi R, Putman CM. Computational fluid dynamcis modeling of intracranial aneurysms: Qualitatively comparison with cerebral angiography. Acad Radiol. 2007;14:804–813. [PubMed]