(Stroke. 1996;27:2086-2094.)
© 1996 American Heart Association, Inc.
Articles |
Hemodynamic Study of the Anterior Communicating Artery
the Department of Neurosurgery, Neurological Institute, Tokyo Women's Medical College (Japan) (H.U., H.Y., K.T.); Fachhochschule Munich (Germany) (D.W.L., M.G.); and the Department of Mechanical Engineering, Shibaura Institute of Technology, Tokyo, Japan (R.Y.).
Correspondence to Dr H. Ujiie, Department of Neurosurgery, Neurological Institute, Tokyo Women's Medical College, 8-1 Kawada-cho, Shinjuku-ku, 162 Tokyo, Japan.
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Abstract |
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Background and Purpose The anterior communicating artery (ACoA) is a site of predilection for intracranial saccular aneurysms causing subarachnoid hemorrhage. ACoA aneurysms are frequently associated with an asymmetrical circle of Willis. In such cases, the ACoA is probably exposed to high hemodynamic stress caused by a considerable shunt flow across the ACoA to the distal segment of the contralateral anterior cerebral artery (ACA). In the present study, the flow pattern and flow-induced shear stress in the ACoA complex that may initiate aneurysmal lesions were studied under steady and pulsatile flow conditions.
Methods Flow visualization was studied with dye injection and birefringent flow visualization in symmetrical and asymmetrical models of various sizes of ACoA. The distribution of wall shear stress was measured using an electrochemical method based on a diffusion-controlled reaction of ferricyanide ion to ferrocyanide ion at a platinum electrode embedded in the wall of the ACoA model.
Results With equal flow rate (Reynolds number 150 to 600), vortical flow was formed in the mouth of the ACoA, and no cross flow through the ACoA was observed. The wall shear stress on the mid-wall of the ACoA was almost zero. However, as soon as the flow rate became unequal, a cross flow through the ACoA was observed. The stagnation point also appeared at the medial junction of the ACoA and ACA. The wall shear stress increased to a very high level at the wall of the ACoA and around the stagnation point.
Conclusions Geometric changes from the symmetrical to the asymmetrical ACoA develop higher shear stress on the ACoA than critical values and the stagnation point at the ACoA junction. A combination of these hemodynamic factors is considered to play an important role in initiation of aneurysm.
Key Words: hemodynamics • aneurysm • cerebral arteries
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The ACoA is a recognized site of predilection for the development of saccular intracranial aneurysms. The geometry and function of the ACoA differs from vessels in the circle of Willis. The ACoA serves as a collateral channel between the bilateral ACAs so that its flow is determined by the pressure difference between the internal carotid arteries. Unequal pressure at the proximal segment of the ACA (A1) affects the flow in the ACoA. It has been reported that asymmetry of the proximal segment of the ACA is associated with a high incidence of ACoA aneurysms.1 2 3 4 5 Experimentally, Hashimoto et al6 induced ACoA aneurysms in hypertensive rats by unilaterally ligating the common carotid artery with concomitant dietary supplementation with r-aminopropionitrile. This suggests a causative relationship between increased flow in the ACoA and aneurysm formation. While hemodynamically generated forces resulting from the impingement of the central streams at the apex of intracranial bifurcations could be an important factor contributing to aneurysm initiation,7 8 9 the question why aneurysms develop on some bifurcations and not others is not explained by this mechanism only. Aneurysm formation seems to correlate more often with so-called "hemodynamic stress" in the ACoA than at other sites. However, the flow patterns in the ACoA are complex, and their potential influence on the development of aneurysms has not been fully investigated. To address this question, we examined flow characteristics and measured flow-induced shear stress using symmetrical and asymmetrical ACoA models and analyzed the relationship between the geometric change in the ACoA complex and hemodynamic stress.
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Materials and Methods |
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Visualization Study
Flow characteristics were examined in symmetrical or asymmetrical afferent tubes (A1), symmetrical efferent tubes (A2), and various sizes of communicating canals (ACoA) using glass models of the ACoA (Fig 1
). The internal diameter of the A1s varied from 6 mm to 2 mm and the caliber of ACoA from 5 mm to 2 mm; the caliber of A2s was 4 mm. The glass models were true to scale but were slightly larger than physiological models. This did not change the flow because the flow parameters remained the same in the model as under physiological conditions, using the same Reynolds number. Flow visualization was studied with dye injection and streaming birefringence.
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Dye injection was performed under steady flow conditions. Perfusion pressure was generated by an elevated container filled with tap water as perfusate. All flow conduits were connected to individual stopcocks and volume flow gauges, thus allowing exact calibration of the flow ratios of the asymmetrical outlets and inlets. Three reservoirs containing red, blue, and green aqueous dye solutions were connected to injection cannulas mounted in the inlets of the models.
Streaming birefringence studies were made under steady and pulsatile flow conditions. The birefringent technique provides additional information because it allows an overview of the whole flow field, in contrast to other methods in which only single-stream paths can be observed. Fig 2 shows the birefringent experimental setup. The photoelastic apparatus consisted of a light box with sodium vapor bulbs and normal light bulbs, a polarizer, an analyzer, and two 
/4 filters. We used linear polarized light that allowed simultaneous observation of the isocline and isochromates. We used an aqueous vanadium pentoxide solution with micelles in a concentration of 1%. This has a viscosity slightly higher than water. The fluid consists of small micelles with a diameter of 1 to 2 µm and length of about 6 µm. In a standing fluid, the particles, owing to their Brownian molecular motion, are in ideal statistical disorder. The fluid is optically isotropic. When the solution is set in motion, the longitudinal axes of the particles are aligned in the direction of the flow and the flow becomes optically anisotropic. Each different shear rate within a velocity profile creates a different orientation of the particles. Therefore, flow produces a distinct pattern of bright and dark zones that are a function of local shear stress in the moving fluid. The colored, white, and black lines, however, give only one integral effect over the whole tube diameter. This method can be used as a qualitative method to localize flow separation, reattachment points, recirculation zones, and flow disturbances in three-dimensional models. In two-dimensional models, this method also can be used quantitatively. The optical principles of streaming birefringence have been discussed in detail by Liepsch10 11 12 and Merzkirch.13
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We studied flow behavior at different Reynolds numbers ranging from 150 to 600. These values are realistic for the circle of Willis and coincide with the diastolic and systolic phases, respectively.8 14 15 The Reynolds number is a nondimensional number used to characterize flow in geometrically similar situations because it allows study of flow conditions comparable with those in the circulation by use of models. The nondimensional Reynolds number (Re) is calculated as Re=UD/
, where U (meters per second) is the mean velocity over the cross section of the tube, D (meters) is the diameter of the tube, and (square meters per second) is the kinematic viscosity of the fluid. Pulsatile flow was obtained by superposition of a sinusoidal wave generated by a piston pump on the steady flow. The characteristic quantity for pulsatile flow is the Strouhal number (St): St=fD/U, where f is the frequency, D is the diameter over the cross section of the tube, and U is the mean velocity. The Strouhal number represents the ratio of local to convective acceleration. Assuming a physiological pulse rate of 60 to 90 beats per minute, mean flow velocity of 0.3 to 0.5 m/s, and diameter of 2 to 3 mm for the circle of Willis, a physiological Strouhal number of approximately 0.01 or smaller is calculated. Flow with such small Strouhal numbers is normally called a quasi-steady flow. We performed the pulsatile flow studies with pulse cycles of 10 and 30 seconds,13 thus the flow in the experiments duplicates physiological flow because the Reynolds number and the Womersley parameter are equal. The Womersley parameter is calculated as 
=(
/2.Re.St)1/2.
Measurement of Wall Shear Stress
The configuration of the ACoA model used for the measurement is shown in Fig 3. The internal diameter was 24 mm for the inlet tube, 18 mm for the outlet tube, and 6 mm for the communicating tube (ACoA). Wall shear stress was measured with the electrochemical method. The measurement positions are also shown in Fig 3. Approximately 150 test platinum electrodes (diameter, 0.5 mm) were embedded at the common median plane with an acrylic cement. The electrode series Ai is along the inferior wall of both afferent tubes (A1s) and the ACoA. Bi is along the median wall of both efferent tubes (A2s) and the ACoA. Ei and Fi are along the lateral wall of the bilateral afferent and efferent tubes (A1s and A2s). These test electrodes were carefully polished with sandpaper and emery paper before each experiment. For measurement of the wall shear stress, an electrolytic solution composed of 0.01 mol/L potassium ferricyanide, 0.01 mol/L potassium ferrocyanide, and 1.0 mol/L potassium hydroxide as a supporting electrolyte was used as the working fluid. The characteristics of this fluid are approximately the same as those of distilled water (ie, density of 1.044 g/cm3, kinematic viscosity of 0.839.10-6 m2/s at a temperature of 303°K). Measurement of wall shear stress is based on the fact that the shear stress is proportional to the cube of electric current i flowing between each test electrode and the counter electrode.16 17
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Flow Visualization Study
The flow rate in the efferent tube was closely adjusted to be equal in both A2s in all experiments. With an equal flow rate in both A1s of the symmetrical ACoA model, a center-flow stream path impinged on the ACoA-A2 junction and reflected into the orifice of the ACoA and distally into A2 with periodic wave flow. Equal vortices were formed in the mouth of the ACoA, and no cross flow through the ACoA was observed (Fig 4
, left). However, as soon as the flow rate ratio became unequal, a cross flow through the ACoA was observed. The stagnation point, functioning as the flow divider point, moved to the ACoA side with an increase of shunt flow through the ACoA (Fig 4, right). The flow separation area was observed around the A1-A2 junction. Flow regurgitated into the contralateral A1 through the ACoA in the model with a large asymmetrical flow (Fig 5).
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With birefringent studies it was possible to measure the length of the disturbed flow area and to visualize flow separation and stagnation points. Fig 6 shows the symmetrical ACoA model. The flow divider point at the ACoA-A2 junction was demonstrated during acceleration (Reynolds number 
600) and deceleration (Reynolds number 150) phases. A so-called "dead flow zone" in the middle of the ACoA, observed during the deceleration phase, diminished in the acceleration phase because of very unstable flow in the ACoA. A disturbed laminar flow developed during the acceleration phase in both A2s. In the asymmetrical A1 model (Fig 7), the shunt flow developed into jet flow because of high velocity. This appears as a bright band. The jet flow developed into fully disturbed laminar flow in the contralateral A2, which recovered to normal parabolic flow (isochrome center line) at the periphery. This finding was much more clearly demonstrated during the acceleration stage. The stagnation point at the ACoA-A2 junction can be clearly observed with increased shunt flow. This diminished during the acceleration stage because the flow refluxed at the divider, developing small vortices (shown in bright color), thus leading to highly complex patterns of flow in this area. High-velocity flow developed around the bilateral A1-A2 junction and in the ACoA during the acceleration phase, then decreased during the deceleration phase. However, these characteristic flow patterns in asymmetrical ACoA models were abolished by increasing the caliber of the ACoA (Fig 8). When the flow through the ACoA decreased in velocity, because of the increased caliber the jet flow did not develop, and the streamline in the ACoA complex resembled that of the normal bifurcation.
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Measurement of Wall Shear Stress
The experiments were performed under steady flow conditions with symmetrical and asymmetrical flow rates and an average Reynolds number of 400 in both parent tubes. The resistances of both peripheries were maintained equal to keep the same flow rate in the peripheries.
Symmetrical Flow (Ql/Qr=1.01)
Fig 9 shows the distribution of wall shear stress in the ACoA model. With symmetrical flow, the wall shear stress was symmetrical. The stagnation points at the corner of the bilateral ACoA-A2 junction (B3, B4) and dead flow area in the middle of the ACoA (A21, B0) showed minimum shear stress. As the main flow divided at the bifurcation and refluxed into the orifice of the ACoA (going mainly into the A2), the shear stress increased sharply close to these points because of the high shear rate near the wall (B5-B7). In the orifice of the ACoA, the shear stress rose slightly (A16-A18 and A22-A24) because of the formation of small vortices derived from reflected flow. At the lateral walls of both A2s, the shear stress increased more than expected (E12-E14 and F12-F14) and then decreased after passing the junction (E15-E17 and F15-F17). This difference is related to the taper of the A1-A2 junction (the cross-sectional area of 45%) and the secondary flow. The shear rate increased because of acceleration of flow in the tapered and curved A1-A2 junction and then decreased because the flow detached just downstream of this junction. The flow separation zone at the lateral corner was replaced by secondary flow. Therefore, no negative shear stress was found.
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Asymmetrical Flow (Ql/Qr=1.15, 1.55)
Figs 10 and 11 show the distribution of wall shear stress at the asymmetrical flow rates of 1.15 and 1.55 in the parent conduits (Ql/Qr) using the same ACoA model. With the asymmetrical flow rate, the wall shear stress on the ACoA (A19, B1, B2) increased with the shunt flow rate, creating an increasing wall shear rate along the wall of the ACoA-A1 junction. This characteristic pattern of wall shear stress is caused by the jet flow in the ACoA at the smallest cross-sectional area of the ACoA. This jet flow diverged at the entrance of the ACoA-A1 junction, creating the vortices shown in the visualization study. The maximum shear stress was 36 Pa for a flow rate ratio of Ql/Qr=1.15 and 72 Pa for a flow rate ratio of Ql/Qr=1.55 at each flow rate.
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With an unequal flow rate, the medial wall of the ACoA-A2 junction functioned as the flow divider point, where the shear stress is almost zero and the dynamic pressure is at a maximum. The stagnation point was more medial at the flow rate of 1.55 than at 1.15. These experimental data imply that the stagnation point on the ACoA-A2 junction moves according to an increasing flow rate through the ACoA itself. The stagnation point at the contralateral side cannot be seen clearly because of the development of flow separation and vortices created by divergence of flow from the ACoA and the main stream from the A1.
The shear stresses at the lateral wall of A1-A2 (walls E and F) showed almost the same pattern as that of the symmetrical flow rate; however, the low shear stress area was much more clearly demonstrated at the right A1-A2 junction.
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Discussion |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionReferencesIntroduction References |
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We investigated flow patterns and flow-induced shear stress in an ACoA model and identified the differences in flow characteristics between the symmetrical and asymmetrical ACoAs. There are three main conclusions from the study: (1) With equal flow rate in the symmetrical ACoA model, the main stream passes from A1 into A2. There is no cross flow in the ACoA, but there is a small recirculation zone in the orifice of the ACoA. The flow field of the A1-A2 junction is almost the same as that found in a curved tube in which secondary flow develops at the lateral corner. The wall shear stress increases around the stagnation point and decreases in the secondary flow area. (2) In the asymmetrical ACoA model, flow through the ACoA was induced by and increased in relation to asymmetry. In this case, the corner of the ACoA-A2 junction functioned as a flow divider so that a stagnation point appeared at the point where the main flow impinged on the ACoA-A2 junction. The wall shear stress on the ACoA and close to the stagnation point markedly increased. The jet flow from the ACoA enters the contralateral A1, creating complex vortices and flow separation at the entrance of the A1. (3) In the asymmetrical ACoA model with the enlarged ACoA, there was no jet flow, and the flow passed smoothly into the bilateral A2s.
Flow patterns and flow-induced shear stress are mainly governed by arterial geometry under physiological conditions18 because the viscosity of blood and the elasticity of the arterial wall are not critically different in each individual. The characteristic geometry and function of the ACoA influence the flow in several ways compared with the other intracranial arteries. The ACoA serves as a collateral channel between the bilateral ACAs and completes the circle of Willis.19 The circle of Willis is the most important pressure-equalizing and distribution system for the arteries supplying the brain. Therefore, any unequal pressure in the proximal segment or peripheral resistance of the ACAs can define the flow in the ACoA; the flow direction in the ACoA is not always defined one way. In adults, the proximal segment of the ACA frequently shows a convex downward curvature and is interconnected above the optic chiasm by the short and narrow ACoA. Beyond the ACoA, the distal segment of the ACA passes forward and upward, making a curve of almost 90°.20 21 Inequality of the proximal segments of the ACA has been reported to occur in 7% to 46% of selected cases.20 These figures are characteristic in adults. Lazorthes and coworkers22 examined the circle of Willis in 100 fetuses and neonates and stated that the asymmetry of the circle of Willis seen in adults may be considered to be the result of lifelong hemodynamic factors, such as compression of the carotid and vertebral arteries by movement of the head and neck and arteriosclerotic changes. Thus, the geometry of the ACA, including the ACoA, is very complicated and changes according to physiological factors and aging.
The geometry of our experimental models was almost identical to that found in human adults. We focused on the differences in the flow behavior between the symmetrical ACA and asymmetrical ACA models to clarify hemodynamic factors that may initiate aneurysm.
ACoA aneurysms have commonly been found where there is inequality of the proximal segment of the ACAs.1 2 3 4 5 Experimentally, Hashimoto et al6 reported that aneurysms of the ACoA in hypertensive rats were induced by ligation of the unilateral common carotid artery and feeding of r-aminopropionitrile. They suggested that exposure to high hemodynamic stress due to a large shunt of blood across the ACoA forming the bifurcation is related with aneurysm formation. Although intracranial aneurysms are considered to result from the interplay between structural change and the hemodynamic stress, the question of what kind of hemodynamic stress initiates aneurysms has not been fully explored. If high flow alone contributes to the formation of aneurysms, it might be expected that the occurrence of aneurysms must be related to large intracranial arteries. However, the most common sites for intracranial aneurysms are the PCoA and the ACoA.23 It is therefore likely that there are other factors that contribute to the formation of aneurysms rather than simply increased flow.
Our experiments showed that a change in diameter or pressure in the unilateral A1 created a cross flow in the ACoA. A geometric change in the A1s caused important hemodynamic changes to the ACoA complex: a curved artery, such as a normal A1-A2 with no cross flow through the ACoA, developed into a bifurcated artery in which an enlarged A1 supplied bilateral A2s through the ACoA. In the latter case, the main flow in the A1 impinged on the corner of the ACoA-A2 junction and passed into the bilateral A2s. A stagnation point clearly appeared at the ACoA-A2 junction and moved on the wall from the A2 side to the ACoA side, correlating with the increase of shunt flow. Rapid changes in the direction of flow between the two ACAs and the various rates of flow volume in the ACoA shown in this experiment can all occur under physiological conditions. When flow passed into the narrow ACoA, remarkably high shear stresses were created on the wall of the ACoA and the area very close to the stagnation point, correlating with asymmetrical flow rate. Because the mean wall shear stress in arteries is 1.0 to 2.0 Pa, the shear stress found in our experiment was almost 5 to 10 times larger. An asymmetrical flow rate such as Ql/Qr=1.15 is considered to cause shear stresses of 10.0 to 20.0 Pa at the ACoA and 17.5 to 35.0 Pa very near the stagnation point. For the asymmetrical flow rate of Ql/Qr=1.55, 34.0 to 68.0 Pa of wall shear stress on the ACoA and 35.0 to 70.0 Pa on the area around the stagnation point were estimated. Fry24 claimed that exposure of the endothelial surface to a time-averaged wall shear stress of approximately 38.0 Pa would result in serious deterioration of the endothelial surface. This means that the likelihood of injury to the intima of the ACoA and junction area would be high if the ACoA caliber failed to dilate with increased shear rate. Another important result of our experiments was that the stagnation point at the ACoA-A2 junction changed its position with asymmetry of flow rate in the A1s. Therefore, the main stream may directly impinge on the injured intima caused by high shear stress, and repetition of this mechanism may ultimately increase the risk of aneurysm formation.
A slight enlargement of the ACoA attenuated the high shear rate considerably. An acute dilatation of the ACoA was observed in clinical cases such as unilateral carotid artery compression.19 25 Recently, increases in blood flow velocities have been demonstrated to provoke an increase in vessel caliber through endothelial mediation. This is regulated by continuous release of EDRF.26 27 EDRF is also a potent inhibitor of platelet adhesion.28 In this way, EDRF reduces the wall shear stress by vasodilation and possibly by decreasing focal blood viscosity. Shear stress also influences endothelial cell structure and function.29 30 Thus, shear stress–induced endothelial mediation might also be responsible for the progressive remodeling of the cerebral vascular network during the high flow conditions, and wall shear stress in the entire arterial tree is controlled at an approximately constant level.31 The same observation applies to cerebral circulation. Rossitti and Loefgren32 have shown, on the basis of a study of cerebral angiograms, that the cerebral vascular network obeys the principle of minimum work and establishes strict functional relationships between volumetric flow, flow velocity, and vessel radius.
Physiologically, the ACoA is considered to change its own size according to the flow rate.19 It has been suggested that in long-term adaptation to flow change, any intensification of further high flow rate on the ACoA beyond the limitation will lead to excess monolayer permeability, remodeling of the extracellular matrix, and finally profound vascular damage. This mechanism should help to increase the chance of aneurysmal formation at the ACoA if the ACoA itself fails to avoid increased shear stress. The efficacy of vasodilatation in the ACoA might be limited compared with other intracranial arteries because the ACoA is the only cerebral artery that evolves from an arterial plexus in the deep interhemispheric fissure in the early stage and shows a lot of anomalies such as duplication, fenestration, and plexus formation.20 33
In conclusion, there is a definite correlation between geometric changes of the ACoA and changes in flow behavior. A newly developed stagnation point at the flow divider between the A2 and the ACoA and high shear stress on the wall of the ACoA are characteristic features in the asymmetrical ACoA model. Furthermore, the position of the stagnation point and the values of shear stress are influenced by the extent of flow rate. So-called "hemodynamic stress" derived from the asymmetrical ACoA developed at the medial wall of the ACoA-A2 junction at the side with increased flow, and it can produce the synergistic effect of a moving stagnation point and high shear injury due to increased shunt flow to the arterial endothelium.
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Selected Abbreviations and Acronyms |
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Acknowledgments |
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This study was supported in part by Ernst und Berta Grimmke-Stiftung, Munich, Germany (Dr Ujiie). Thanks are due to Joyce McLean for editorial assistance in preparing the manuscript.
Received March 18, 1996; revision received July 1, 1996; accepted July 29, 1996.
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References |
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Kayembe KNT, Sasahara M, Hazama F. Cerebral aneurysms and variations in the circle of Willis. Stroke. 1984;15:846-850.
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Roach MR, Scott S, Ferguson GG. The hemodynamic importance of the geometry of bifurcations in the circle of Willis (Glass model studies). Stroke. 1972;3:255-267.
8. Ferguson GG. Physiological factors in the initiation, growth, and rupture of human intracranial saccular aneurysms. J Neurosurg. 1972;37:666-677.[Medline] [Order article via Infotrieve]
9. Stehbens WE. Flow in glass models of arterial bifurcations and berry aneurysms at low Reynolds numbers. Q J Exp Physiol. 1975;60:181-192.
10. Liepsch DW. Untersuchungen der Stromungsverhaltnisse in Verzweigungen von Rohren kleiner Durchmesser bei Stromtrennung. Technical University Munich und VDI Berichte 232: 423-441, 1975. Thesis.
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16. Mizushina T. The electrochemical method in transport phenomena. Adv Heart Transf. 1971;7:87-161.
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20. Huber P. Cerebral Angiography. Stuttgart, Germany: Georg Thieme Verlag; 1982:79-93.
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Editorial Comment
Section of Neurosurgery, University of Chicago Medical Center, Chicago, Ill
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Introduction |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionReferencesIntroduction References |
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The etiology and pathogenesis of the typical saccular intracranial arterial aneurysm is probably multifactorial. It is most likely that the critical event is acquired degeneration of the internal elastic lamina secondary to abnormal hemodynamic stresses at arterial bifurcations. The thinner tunica media, absence of external elastic lamina, and possibly decreased soft-tissue support of the muscular cerebral arteries of the circle of Willis could account for the increased incidence of aneurysms compared with systemic arteries. Defects in the tunica media occur commonly and are not necessarily associated with aneurysms. The occurrence of aneurysms in families suggests an underlying genetic predisposition or possibly common environmental factors. Therefore, aneurysms probably develop in susceptible individuals when there is increased hemodynamic stress.1
An association of inequality in the sizes of the precommunicating segments of the ACAs with ACoA aneurysms has been known for some time and has been attributed to hemodynamic stress.2 Ujiie and colleagues have conducted elegant studies of hemodynamic stresses in models of the ACoA complex that support this theory. Although any therapeutic significance seems remote, and it is unlikely that models will be able to reproduce pulsatile flow through compliant tubes resembling intracranial arteries, these studies are a step forward. It would be interesting to apply similar methods to models of other bifurcations to determine how hemodynamic stress acts on these and why there is not such a strong association with aneurysms, such as with the variability in the size of the PCoA.
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Selected Abbreviations and Acronyms |
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References |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionReferencesIntroduction References |
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1R. Stehbens WE. Etiology of intracranial berry aneurysms. J Neurosurg.. 1989;70:823-831.[Medline] [Order article via Infotrieve]
2R. Yasargil MG, Smith RD, Young PH, Teddy PJ. Microneurosurgery, II: Clinical Considerations, Surgery of the Intracranial Aneurysms and Results. Stuttgart, Germany: Georg Thieme; 1984.
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