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DOI: 10.1055/s-0045-1814149
Predicting Atherosclerosis in Unruptured MCA Aneurysm with Computational Fluid Dynamics (CFD) Study
Authors
Abstract
Background
Computational fluid dynamics (CFD) is being evaluated as a potential tool in diagnosing aneurysm hemodynamics. We have undertaken this study to evaluate the use of CFD as a tool to predict the atherosclerotic changes in unruptured middle cerebral artery (MCA) bifurcation aneurysm. In our study, we have compared the CFD images with intraoperative microscopic images of the MCA aneurysm. The purpose of our study was to find correlation between the CFD findings for the atherosclerotic changes in MCA bifurcation aneurysms. In aneurysms with atherosclerotic changes, there is risk of shower of emboli during the manipulation or placing of the clip because it can break the unstable local plaque resulting in distal arterial occlusion.
Aims
To find the correlation between CFD studies and the atherosclerotic changes occurring in the MCA bifurcation aneurysm.
Materials and Methods
A retrospective review of all intraoperative video recordings of patients with unruptured MCA bifurcation aneurysm from September 2014 to May 2017 at our hospital, Banbuntane Hotokukai Hospital, Fujita University, Nagoya, Aichi, Japan, was done. This is a single-center based study. Videos having atherosclerotic changes were selected. MCA bifurcation aneurysms with atherosclerotic changes were analyzed with CFD. We studied wall pressure, magnitude, and vectors of wall shear stress and streamline (flow pattern). The CFD findings were correlated with intraoperative findings. All the patients who were selected for this study had undergone open surgery.
Results
We found that there was decreased wall pressure in the areas of atherosclerotic changes. Low shear stress magnitude was seen in the atherosclerotic segment and there was divergent pattern of the shear stress vectors predicting the thick-walled segment with decreased flow velocity. Here, we have discussed four cases showing moderately decreased wall pressure in atherosclerotic segment and decreased wall shear stress magnitude in all these cases. Limitations of the study: This is a very small cohort study to establish any statistically significant correlation between the CFD findings and to predict atherosclerosis in MCA aneurysm. Hence, there is need of large multicentric cohort studies to establish the correlation and the statistical significance of the CFD findings in atherosclerosis.
Introduction
Computational fluid dynamics (CFD), a branch of fluid mechanics in mechanical engineering, has been in use in aerodynamics, hydrodynamics of vehicles, and many other fields.[1] It uses numerical analysis and algorithms to analyze and solve problems that involve fluid flows. Its use in biomedical engineering has progressed only in the last decade. Many simulations have been used to study carotid and intracranial cerebrovascular diseases. We were interested in its utilization, specifically in cerebral aneurysms. Advancement in the CFD technology has enabled the hemodynamic simulation of realistic aneurysm geometries with accuracy and reliability.[2] CFD has yielded advanced knowledge regarding the role of hemodynamics in the pathophysiology of intracranial aneurysms.[3] [4] Consideration of the hemodynamic characteristics has been included in the guidelines for the management of intracranial aneurysms to predict the chances of rupture in cases of unruptured aneurysms, in addition to the size, location of the aneurysm, patient's age, and health status.[5] [6] [7] CFD is being evaluated as a potential tool in studying aneurysm hemodynamics and predicting the atherosclerotic changes in intracranial aneurysms, which is important for predicting the potential risk of surgical management. In this study, we have compared the CFD images with intraoperative microscopic images of the aneurysm to establish any correlation, so that it can be used as a tool to predict the atherosclerotic changes in unruptured aneurysms. Fluid-induced wall shear stress (WSS) is a dynamic frictional force induced by a viscous fluid moving across a surface of solid material. Previous studies have demonstrated that WSS has a strong biological influence on vessels by impinging on various endothelial functions rather than a direct mechanical influence.[8] [9] [10] [11] [12] [13] [14] [15] WSS appears to be closely related to the development of various vascular diseases, such as atherosclerosis and cerebral aneurysms.[16] [17] [18] [19] [20] [21] High WSS is related to the formation of cerebral aneurysms. Conversely, low oscillating WSS is regarded as a risk factor in the development of atherosclerotic lesions in healthy arteries.
Materials and Methods
We retrospectively reviewed all intraoperative video recordings of patients with unruptured middle cerebral artery (MCA) bifurcation aneurysms from September 2014 to May 2017 at our hospital, Banbuntane Hotokukai Hospital, Fujita University, Nagoya, Aichi, Japan. Both male and female patients were included in our study ([Table 1]). This is a single-center based study. We selected the videos having atherosclerotic changes. MCA bifurcation aneurysms with atherosclerotic changes were analyzed with CFD images. Wall pressure, both magnitude and vectors of WSS along with streamline (flow pattern) was studied. The CFD findings were correlated with intraoperative findings.
Abbreviation: MCA, middle cerebral artery.
A multidetector computed tomography (CT) (Activion-16, Toshiba Medical Systems, Tokyo, Japan) was utilized in a Real-Prep scan mode with a contrast agent (Iomeron, iodine concentration 350 mg/mL, Eizai Pharmaceutical, Tokyo, Japan) injected at 3 mL/s by 100 mL from the forearm antecubital vein. Imaging conditions gave a field of view of 16 cm, a matrix of 512 × 512 pixels, a thickness of 0.5 mm, a scanning time of 8 seconds, and a total number of 201 images. Original volume data was reconstructed into a matrix of 1024 × 1024 pixels and a thickness of 0.3 mm using a workstation (Ziostation-2, Ziosoft-AMIN, Tokyo, Japan). A vascular geometry was abstracted by setting a threshold of 90 to 100 HU (Hounsfield unit). A compressed vessel was analyzed by a specialized CFD package (hemoscope-v1.4, EBM, Japan), which was composed of three modules, vessel, VCFD, and analysis. The vessel module gives the above vascular geometry and allowed us to segment vessels of interest individually. The vascular segmentation was made by placing a centerline and defining edge planes normal to the centerline at the inlet and outlet of each vessel. Specifically, the input vascular geometry was segmented including a proximal neurovascular compression (NVC) region (NVCp), NVC site (NVCs), and distal NVC region (NVCd). The VCFD module defined a flow inlet and outlet at the vertebral artery intracranial proximal end and basilar artery distal end, respectively. After segmentation and labeling, the vascular surface geometry was filled with unstructured cells whose shape was mainly composed of hexahedrons, and their size were approximately 0.25 mm in far-wall, and 0.125 (width) and 0.05 (height) mm in near-wall regions. The inlet and outlet vessels were extended by 5 and 10 times greater than their diameters, respectively. The diameter denotes the median of equivalent circle diameter as being scan measured along with a centerline at each segmented vessel. The blood flow was computed on a three-dimensional (3D) unsteady fashion using a finite volume method. The fluid blood was assumed to be incompressible and Newtonian fluid with a density of ρ = 1050 kg/m3 and a viscosity of μ = 0.004 Pas, and the nature of flow was allowed to have transient behaviors. Flow rates of inlet and outlet vessels were calculated using the following equations:


Here, Q, τ, μ, and D denoted flow rate, WSS, fluid viscosity, and vascular diameter, respectively. The equation is a well-known theoretical basis of a fully developed laminar pipe flow. Herein, the WSS was set to be τ = 1.5 Pa.[22] After calculating total inflow at an inlet vessel, the amount of inflow were distributed at each outlet vessel according to [Eq. (1)], and the specified boundary condition of inlet and outlet vessels, respectively. In order to reproduce a pulsatile flow rate Qt , the following was utilized,


Here, Qn is a flow rate normalized by a mean flow rate and a cardiac cycle as obtained from an open literature.[23] A pulsatile pressure waveform was set to be a physiological waveform with an average of 100 mm Hg.[24]
The analysis module visualized time-averaged flow velocity (FV-Avg), streamline (SL), time-averaged wall pressure (WP-Avg), WSS direction (WSSv), WSS magnitude (WSSm) and pressure loss (PL). At the site of NVCp, NVCs, and NVCd, time-averaged WSSm (WSSm-Avg), peal systolic WSSm (WSSm-Sys), end-diastolic WSSm (WSSm-Dia), and time-averaged PL (PL-Avg) were analyzed. WSSm was detailed in 3D time series. The cycle variation of WSSv and WSSm (WSSv-Var and WSSm-Var) was detailed in 3D. A characteristic flow pattern in a compressed vessel in the vicinity of NVC was analyzed in a surgical view and comparatively evaluated with an intraoperative observation and 3D fusion images accordingly.
Results
We found that there was decreased shear stress magnitude, divergent shear stress vectors, and decreased flow velocity in the aneurysm wall with atherosclerotic changes in 9 out of 20 cases (45%). We have discussed four cases here ([Figs. 1] [2] [3] [4]) showing moderately decreased wall pressure in the atherosclerotic segment and decreased WSSm in all the cases. We found that there were divergent WSS vectors (WSS-V) at the atherosclerotic site of the aneurysm, which predicted that the wall segment was thick at that area. There was decreased flow velocity at the thickened atherosclerotic site as the blood could not reach the apex of the dome of the aneurysmal sac.








Discussion
CFD, which was earlier a purely engineering tool, has come into practice in biomedical engineering with its usefulness in studying the flow dynamics in a vessel noninvasively. CFD helps in calculating the velocity of blood flowing in the aneurysmal sac, the pressure in the aneurysmal sac, and the WSS. It provides detailed visual and comprehensive information along with the ability to know the pressure, WSS, streamlines, and vectors at various points in the aneurysm.[25] However, it has some disadvantages. There is difficulty in interpreting the results, as the software is available only at few centers, and there is insufficient resolution when using low-resolution magnetic resonance imaging (MRI) or CT. Numerical errors can occur during the test leading to incorrect conclusions and wrong management. Cooperation between the surgeon and the biomedical engineer is also difficult at times. Overcoming the limitations with simplification of software and the analyses will help in the wider use of this modality.
There has been an ongoing debate regarding whether low WSS or high WSS contributes to aneurysm formation.[26] The high WSS correlates with type 1 aneurysm formation, that is, small and transparent aneurysms, whereas low WSS contributed to type 2 aneurysm formation, that is, thick-walled atherosclerotic type.[26] However, the mean flow velocity and the exchange rate were smaller in the atherosclerotic aneurysms than in the other nonatherosclerotic aneurysms.[27] To decide the role of surgery in the atherosclerotic aneurysm, we need to consider the risk of shower of emboli during the manipulation or placing the clip because it can break the unstable local plaque resulting in distal arterial occlusion.[28] No previous studies have focused on the incidence or the exact data regarding atherosclerotic aneurysm. They only reported that, atherosclerotic type of aneurysm was related with poor outcome after the surgery and was 7.8 times higher as compared with the patients who had nonatherosclerotic aneurysm.[28] MRI-based fluid dynamic studies have been done to study the rupture predictors of aneurysmal bleb but concerns have been raised regarding its accuracy as compared to CFD, though MRI-based studies are less invasive.[29] [30]
Oscillatory shear index (OSI) was not recorded in our study as the software was not programmed for this. However, studies done by other authors concluded that in unruptured cases both OSI and WSS was decreased.[31] These findings are in close correlation with the results of our study.
Conclusion
CFD as a diagnostic tool is noninvasive and helps in assessing the hemodynamic parameters in the aneurysmal sac. This can be used as a potential tool for the preoperative prediction of the atherosclerosis in unruptured MCA bifurcation aneurysm. Multicentric trials involving a larger cohort of the population are needed before drawing any definite conclusions. Improvement of the software in a clinician-friendly manner in interpreting the results will help further.
Conflict of Interest
None declared.
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References
- 1 Tu J, Yeoh GH, Liu C. Computational Fluid Dynamics: A Practical Approach. 2nd ed.. Oxford: Elsevier; 2013: 1-29
- 2 Karmonik C, Yen C, Grossman RG, Klucznik R, Benndorf G. Intra-aneurysmal flow patterns and wall shear stresses calculated with computational flow dynamics in an anterior communicating artery aneurysm depend on knowledge of patient-specific inflow rates. Acta Neurochir (Wien) 2009; 151 (05) 479-485 , discussion 485
- 3 Cebral JR, Mut F, Weir J, Putman C. Quantitative characterization of the hemodynamic environment in ruptured and unruptured brain aneurysms. AJNR Am J Neuroradiol 2011; 32 (01) 145-151
- 4 Xiang J, Natarajan SK, Tremmel M. et al. Hemodynamic-morphologic discriminants for intracranial aneurysm rupture. Stroke 2011; 42 (01) 144-152
- 5 Wiebers DO, Whisnant JP, Huston III J. et al; International Study of Unruptured Intracranial Aneurysms Investigators. Unruptured intracranial aneurysms: natural history, clinical outcome, and risks of surgical and endovascular treatment. Lancet 2003; 362 (9378): 103-110
- 6 Morita A, Kirino T, Hashi K. et al; UCAS Japan Investigators. The natural course of unruptured cerebral aneurysms in a Japanese cohort. N Engl J Med 2012; 366 (26) 2474-2482
- 7 Connolly Jr ES, Rabinstein AA, Carhuapoma JR. et al; American Heart Association Stroke Council, Council on Cardiovascular Radiology and Intervention, Council on Cardiovascular Nursing, Council on Cardiovascular Surgery and Anesthesia, Council on Clinical Cardiology. Guidelines for the management of aneurysmal subarachnoid hemorrhage: a guideline for healthcare professionals from the American Heart Association/American Stroke Association. Stroke 2012; 43 (06) 1711-1737
- 8 Guzman RJ, Abe K, Zarins CK. Flow-induced arterial enlargement is inhibited by suppression of nitric oxide synthase activity in vivo. Surgery 1997; 122 (02) 273-279 , discussion 279–280
- 9 Kamiya A, Ando J, Shibata M, Masuda H. Roles of fluid shear stress in physiological regulation of vascular structure and function. Biorheology 1988; 25 (1-2): 271-278
- 10 Lüscher TF, Tanner FC. Endothelial regulation of vascular tone and growth. Am J Hypertens 1993; 6 (7 Pt 2): 283S-293S
- 11 Stamler JS. Redox signaling: nitrosylation and related target interactions of nitric oxide. Cell 1994; 78 (06) 931-936
- 12 Palumbo R, Gaetano C, Melillo G, Toschi E, Remuzzi A, Capogrossi MC. Shear stress downregulation of platelet-derived growth factor receptor-beta and matrix metalloprotease-2 is associated with inhibition of smooth muscle cell invasion and migration. Circulation 2000; 102 (02) 225-230
- 13 Song RH, Kocharyan HK, Fortunato JE, Glagov S, Bassiouny HS. Increased flow and shear stress enhance in vivo transforming growth factor-beta1 after experimental arterial injury. Arterioscler Thromb Vasc Biol 2000; 20 (04) 923-930
- 14 Tuttle JL, Nachreiner RD, Bhuller AS. et al. Shear level influences resistance artery remodeling: wall dimensions, cell density, and eNOS expression. Am J Physiol Heart Circ Physiol 2001; 281 (03) H1380-H1389
- 15 Ueba H, Kawakami M, Yaginuma T. Shear stress as an inhibitor of vascular smooth muscle cell proliferation. Role of transforming growth factor-beta 1 and tissue-type plasminogen activator. Arterioscler Thromb Vasc Biol 1997; 17 (08) 1512-1516
- 16 Kuhlencordt PJ, Gyurko R, Han F. et al. Accelerated atherosclerosis, aortic aneurysm formation, and ischemic heart disease in apolipoprotein E/endothelial nitric oxide synthase double-knockout mice. Circulation 2001; 104 (04) 448-454
- 17 Fukuda S, Hashimoto N, Naritomi H. et al. Prevention of rat cerebral aneurysm formation by inhibition of nitric oxide synthase. Circulation 2000; 101 (21) 2532-2538
- 18 Kondo S, Hashimoto N, Kikuchi H, Hazama F, Nagata I, Kataoka H. Cerebral aneurysms arising at nonbranching sites. An experimental Study. Stroke 1997; 28 (02) 398-403 , discussion 403–404
- 19 Moore Jr JE, Xu C, Glagov S, Zarins CK, Ku DN. Fluid wall shear stress measurements in a model of the human abdominal aorta: oscillatory behavior and relationship to atherosclerosis. Atherosclerosis 1994; 110 (02) 225-240
- 20 Pedersen EM, Agerbaek M, Kristensen IB, Yoganathan AP. Wall shear stress and early atherosclerotic lesions in the abdominal aorta in young adults. Eur J Vasc Endovasc Surg 1997; 13 (05) 443-451
- 21 Pedersen EM, Oyre S, Agerbaek M. et al. Distribution of early atherosclerotic lesions in the human abdominal aorta correlates with wall shear stresses measured in vivo. Eur J Vasc Endovasc Surg 1999; 18 (04) 328-333
- 22 Zarins CK, Zatina MA, Giddens DP, Ku DN, Glagov S. Shear stress regulation of artery lumen diameter in experimental atherogenesis. J Vasc Surg 1987; 5 (03) 413-420
- 23 Ford MD, Alperin N, Lee SH, Holdsworth DW, Steinman DA. Characterization of volumetric flow rate waveforms in the normal internal carotid and vertebral arteries. Physiol Meas 2005; 26 (04) 477-488
- 24 Reymond P, Merenda F, Perren F, Rüfenacht D, Stergiopulos N. Validation of a one-dimensional model of the systemic arterial tree. Am J Physiol Heart Circ Physiol 2009; 297 (01) H208-H222
- 25 Talari S, Kato Y, Shang H. et al. Comparison of computational fluid dynamics findings with intraoperative microscopy findings in unruptured intracranial aneurysms- an initial analysis. Asian J Neurosurg 2016; 11 (04) 356-360
- 26 Meng H, Tutino VM, Xiang J, Siddiqui A. High WSS or low WSS? Complex interactions of hemodynamics with intracranial aneurysm initiation, growth, and rupture: toward a unifying hypothesis. AJNR Am J Neuroradiol 2014; 35 (07) 1254-1262
- 27 Sugiyama SI, Endo H, Niizuma K. et al. Computational hemodynamic analysis for the diagnosis of atherosclerotic changes in intracranial aneurysms: a proof-of-concept study using 3 cases harboring atherosclerotic and nonatherosclerotic aneurysms simultaneously. Comput Math Methods Med 2016; 2016: 2386031
- 28 Sakarunchai I, Kato Y, Yamada Y, Inamasu J. Ischemic event and risk factors of embolic stroke in atherosclerotic cerebral aneurysm patients treated with a new clipping technique. J Stroke Cerebrovasc Dis 2015; 24 (11) 2497-2507
- 29 Isoda H, Ohkura Y, Kosugi T. et al. Comparison of hemodynamics of intracranial aneurysms between MR fluid dynamics using 3D cine phase-contrast MRI and MR-based computational fluid dynamics. Neuroradiology 2010; 52 (10) 913-920
- 30 Isoda H, Ohkura Y, Kosugi T. et al. In vivo hemodynamic analysis of intracranial aneurysms obtained by magnetic resonance fluid dynamics (MRFD) based on time-resolved three-dimensional phase-contrast MRI. Neuroradiology 2010; 52 (10) 921-928
- 31 Kawaguchi T, Nishimura S, Kanamori M. et al. Distinctive flow pattern of wall shear stress and oscillatory shear index: similarity and dissimilarity in ruptured and unruptured cerebral aneurysm blebs. J Neurosurg 2012; 117 (04) 774-780
Address for correspondence
Publication History
Article published online:
22 December 2025
© 2025. Asian Congress of Neurological Surgeons. This is an open access article published by Thieme under the terms of the Creative Commons Attribution-NonDerivative-NonCommercial License, permitting copying and reproduction so long as the original work is given appropriate credit. Contents may not be used for commercial purposes, or adapted, remixed, transformed or built upon. (https://creativecommons.org/licenses/by-nc-nd/4.0/)
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References
- 1 Tu J, Yeoh GH, Liu C. Computational Fluid Dynamics: A Practical Approach. 2nd ed.. Oxford: Elsevier; 2013: 1-29
- 2 Karmonik C, Yen C, Grossman RG, Klucznik R, Benndorf G. Intra-aneurysmal flow patterns and wall shear stresses calculated with computational flow dynamics in an anterior communicating artery aneurysm depend on knowledge of patient-specific inflow rates. Acta Neurochir (Wien) 2009; 151 (05) 479-485 , discussion 485
- 3 Cebral JR, Mut F, Weir J, Putman C. Quantitative characterization of the hemodynamic environment in ruptured and unruptured brain aneurysms. AJNR Am J Neuroradiol 2011; 32 (01) 145-151
- 4 Xiang J, Natarajan SK, Tremmel M. et al. Hemodynamic-morphologic discriminants for intracranial aneurysm rupture. Stroke 2011; 42 (01) 144-152
- 5 Wiebers DO, Whisnant JP, Huston III J. et al; International Study of Unruptured Intracranial Aneurysms Investigators. Unruptured intracranial aneurysms: natural history, clinical outcome, and risks of surgical and endovascular treatment. Lancet 2003; 362 (9378): 103-110
- 6 Morita A, Kirino T, Hashi K. et al; UCAS Japan Investigators. The natural course of unruptured cerebral aneurysms in a Japanese cohort. N Engl J Med 2012; 366 (26) 2474-2482
- 7 Connolly Jr ES, Rabinstein AA, Carhuapoma JR. et al; American Heart Association Stroke Council, Council on Cardiovascular Radiology and Intervention, Council on Cardiovascular Nursing, Council on Cardiovascular Surgery and Anesthesia, Council on Clinical Cardiology. Guidelines for the management of aneurysmal subarachnoid hemorrhage: a guideline for healthcare professionals from the American Heart Association/American Stroke Association. Stroke 2012; 43 (06) 1711-1737
- 8 Guzman RJ, Abe K, Zarins CK. Flow-induced arterial enlargement is inhibited by suppression of nitric oxide synthase activity in vivo. Surgery 1997; 122 (02) 273-279 , discussion 279–280
- 9 Kamiya A, Ando J, Shibata M, Masuda H. Roles of fluid shear stress in physiological regulation of vascular structure and function. Biorheology 1988; 25 (1-2): 271-278
- 10 Lüscher TF, Tanner FC. Endothelial regulation of vascular tone and growth. Am J Hypertens 1993; 6 (7 Pt 2): 283S-293S
- 11 Stamler JS. Redox signaling: nitrosylation and related target interactions of nitric oxide. Cell 1994; 78 (06) 931-936
- 12 Palumbo R, Gaetano C, Melillo G, Toschi E, Remuzzi A, Capogrossi MC. Shear stress downregulation of platelet-derived growth factor receptor-beta and matrix metalloprotease-2 is associated with inhibition of smooth muscle cell invasion and migration. Circulation 2000; 102 (02) 225-230
- 13 Song RH, Kocharyan HK, Fortunato JE, Glagov S, Bassiouny HS. Increased flow and shear stress enhance in vivo transforming growth factor-beta1 after experimental arterial injury. Arterioscler Thromb Vasc Biol 2000; 20 (04) 923-930
- 14 Tuttle JL, Nachreiner RD, Bhuller AS. et al. Shear level influences resistance artery remodeling: wall dimensions, cell density, and eNOS expression. Am J Physiol Heart Circ Physiol 2001; 281 (03) H1380-H1389
- 15 Ueba H, Kawakami M, Yaginuma T. Shear stress as an inhibitor of vascular smooth muscle cell proliferation. Role of transforming growth factor-beta 1 and tissue-type plasminogen activator. Arterioscler Thromb Vasc Biol 1997; 17 (08) 1512-1516
- 16 Kuhlencordt PJ, Gyurko R, Han F. et al. Accelerated atherosclerosis, aortic aneurysm formation, and ischemic heart disease in apolipoprotein E/endothelial nitric oxide synthase double-knockout mice. Circulation 2001; 104 (04) 448-454
- 17 Fukuda S, Hashimoto N, Naritomi H. et al. Prevention of rat cerebral aneurysm formation by inhibition of nitric oxide synthase. Circulation 2000; 101 (21) 2532-2538
- 18 Kondo S, Hashimoto N, Kikuchi H, Hazama F, Nagata I, Kataoka H. Cerebral aneurysms arising at nonbranching sites. An experimental Study. Stroke 1997; 28 (02) 398-403 , discussion 403–404
- 19 Moore Jr JE, Xu C, Glagov S, Zarins CK, Ku DN. Fluid wall shear stress measurements in a model of the human abdominal aorta: oscillatory behavior and relationship to atherosclerosis. Atherosclerosis 1994; 110 (02) 225-240
- 20 Pedersen EM, Agerbaek M, Kristensen IB, Yoganathan AP. Wall shear stress and early atherosclerotic lesions in the abdominal aorta in young adults. Eur J Vasc Endovasc Surg 1997; 13 (05) 443-451
- 21 Pedersen EM, Oyre S, Agerbaek M. et al. Distribution of early atherosclerotic lesions in the human abdominal aorta correlates with wall shear stresses measured in vivo. Eur J Vasc Endovasc Surg 1999; 18 (04) 328-333
- 22 Zarins CK, Zatina MA, Giddens DP, Ku DN, Glagov S. Shear stress regulation of artery lumen diameter in experimental atherogenesis. J Vasc Surg 1987; 5 (03) 413-420
- 23 Ford MD, Alperin N, Lee SH, Holdsworth DW, Steinman DA. Characterization of volumetric flow rate waveforms in the normal internal carotid and vertebral arteries. Physiol Meas 2005; 26 (04) 477-488
- 24 Reymond P, Merenda F, Perren F, Rüfenacht D, Stergiopulos N. Validation of a one-dimensional model of the systemic arterial tree. Am J Physiol Heart Circ Physiol 2009; 297 (01) H208-H222
- 25 Talari S, Kato Y, Shang H. et al. Comparison of computational fluid dynamics findings with intraoperative microscopy findings in unruptured intracranial aneurysms- an initial analysis. Asian J Neurosurg 2016; 11 (04) 356-360
- 26 Meng H, Tutino VM, Xiang J, Siddiqui A. High WSS or low WSS? Complex interactions of hemodynamics with intracranial aneurysm initiation, growth, and rupture: toward a unifying hypothesis. AJNR Am J Neuroradiol 2014; 35 (07) 1254-1262
- 27 Sugiyama SI, Endo H, Niizuma K. et al. Computational hemodynamic analysis for the diagnosis of atherosclerotic changes in intracranial aneurysms: a proof-of-concept study using 3 cases harboring atherosclerotic and nonatherosclerotic aneurysms simultaneously. Comput Math Methods Med 2016; 2016: 2386031
- 28 Sakarunchai I, Kato Y, Yamada Y, Inamasu J. Ischemic event and risk factors of embolic stroke in atherosclerotic cerebral aneurysm patients treated with a new clipping technique. J Stroke Cerebrovasc Dis 2015; 24 (11) 2497-2507
- 29 Isoda H, Ohkura Y, Kosugi T. et al. Comparison of hemodynamics of intracranial aneurysms between MR fluid dynamics using 3D cine phase-contrast MRI and MR-based computational fluid dynamics. Neuroradiology 2010; 52 (10) 913-920
- 30 Isoda H, Ohkura Y, Kosugi T. et al. In vivo hemodynamic analysis of intracranial aneurysms obtained by magnetic resonance fluid dynamics (MRFD) based on time-resolved three-dimensional phase-contrast MRI. Neuroradiology 2010; 52 (10) 921-928
- 31 Kawaguchi T, Nishimura S, Kanamori M. et al. Distinctive flow pattern of wall shear stress and oscillatory shear index: similarity and dissimilarity in ruptured and unruptured cerebral aneurysm blebs. J Neurosurg 2012; 117 (04) 774-780












