| | Flow patterns and distributions of fluid velocity and wall shear stress in the human internal carotid and middle cerebral arteriesReceived 1 September 2008; accepted 24 March 2009. published online 26 October 2009.
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Commentary
, 26 October 2009
Kern H. Guppy
World Neurosurgery
March 2010 (Vol. 73, Issue 3, Page e27)
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Abstract BackgroundThe aim of this study is to elucidate the relationship between the flow patterns and the preferred sites of the development of atherosclerotic lesions and cerebral aneurysms in the human ICA and MCA. MethodsFive isolated transparent arterial trees containing the ICA and MCA with a sufficient length of the carotid siphon were prepared from humans postmortem, and flow patterns and distributions of fluid velocity and wall shear stress in these vessels were studied in detail using flow visualization and high-speed cinemicrographic techniques. ResultsIn the carotid siphon that contained several acute bends, due to the impingement and deflection of the flow at the bends, a strong and complex helicoidal flow formed. As a result, the approaching velocity profile was flattened at the terminal bifurcation of the ICA, but it was sharpened at the first bifurcation of the MCA. Thus, at this latter bifurcation, fluid elements impinged on the vessel wall around the flow divider with much larger velocity than that at the preceding terminal bifurcation of the ICA. Throughout the entire arterial tree, atherosclerotic lesions were found almost exclusively in regions of low wall shear stress. ConclusionsThe carotid siphon provided a flattened approaching velocity profile at the terminal bifurcation of the ICA, making the hemodynamic stresses (pressure, tension, and shear stress) exerted on the vessel wall much lower than that at the bifurcation of the MCA where the approaching velocity profile was sharpened. This may account for the relatively low incidence of aneurysm formation at this site. Abbreviations: ACA, anterior cerebral artery, AComA, anterior communicating artery, ICA, internal carotid artery, LDL, low-density lipoproteins, MCA, middle cerebral artery, PCA, posterior cerebral artery, PComA, posterior communicating artery 1. Introduction  It has been shown that most cerebral aneurysms form in the region of the circle of Willis and its associated branches. Frequent sites of aneurysm formation are the regions of the internal carotid-PComA junction, the anterior communicating-anterior cerebral artery junction, and the MCA bifurcation [9], [10], [16], [27], [28], [41], [45]. The incidence of aneurysm formation at the terminal bifurcation of both the ICA and basilar artery was found to be somehow lower than that at the above 3 sites despite their much larger vessel diameters and branching angles, suggesting the complex nature of the pathogenesis of cerebral aneurysms in the circle of Willis [10], [16], [27]. It was also found that most of the aneurysms were localized around the flow divider of bifurcations and T junctions where defects of the media and degenerative changes of the internal elastic lamina of the vessel wall occurred [13], [38], [40]. Thus, some investigators believed that aneurysms arise from congenital defects of the media [3], [4], [15], [32]. Others believed that aneurysms originate from acquired [14], [42], [44] or both congenital and acquired [5], [8], [9], [13] defects of the media at some branching sites of cerebral arteries. In any case, hemodynamic factors are suspected to play a key role in the localization of saccular aneurysms. Thus, attempts were made to correlate flow patterns, velocity, and shear-rate distributions at sites where saccular aneurysms formed with the genesis and progression of the vascular disease [12], [34], [43]. However, except for the development of animal models of cerebral aneurysms [19], [20], [21], [22], [24], no further progress has been made on this topic. One of the reasons for this is that by the development of sophisticated diagnostic techniques such as CAT, PET, and NMR, the main thrust of research on cerebral circulation has shifted from the study of hemodynamics in cerebral vessels to the study of the regional and overall hemodynamics in brain tissues. However, such techniques cannot help elucidate the pathogenesis of cerebrovascular diseases. For that purpose, it is necessary to observe the flow in individual vessels at the level of individual corpuscles. Therefore, we have prepared transparent segments of human intracranial cerebral arteries containing the network of the circle of Willis and studied the flow patterns and distributions of fluid velocity and wall shear stress in various regions of the human internal carotid and middle cerebral arteries to correlate these with the preferred sites of the development of atherosclerotic lesions and the formation of saccular aneurysms. 2. Materials and methods 2.1. Preparation of transparent cerebral arterial trees Five fresh and intact human brains with the carotid siphon were obtained at autopsy in the Department of Pathology, Montreal General Hospital, from 3 male subjects aged 53, 70, and 77 years and 2 female subjects aged 26 and 71 years, in all of whom the primary cause of death was not cerebrovascular diseases. From these autopsy materials, 9 isolated transparent arterial trees containing the internal carotid and middle cerebral arteries with a sufficient length of the carotid siphon were prepared. As illustrated in Fig. 1, the ICA contains at least 5 curved segments (bends) within the arterial segment that encompasses from the origin of the artery at the neck to the terminal bifurcation where the ICA bifurcates into the middle and anterior cerebral arteries in vessels with normal anatomic structure [11]. The arterial trees harvested contained the portion of the carotid siphon just distal to the second bend (indicated by line A in Fig. 1) in 7 trees and distal to the first bend (indicated by line B in Fig. 1) in 2 trees. In this study, the carotid siphon was defined as the region between the site of cannulation and the branching site of the PComA. After isolating and rinsing the vessel with isotonic saline, the inflow vessel (the ICA) and all the outflow vessels were cannulated with short and thin-walled tightly fitting stainless steel pipes. All other smaller vessels including the ophthalmic artery were occluded at their branching points by ligating and coagulating them with a fulgurator. The vessel segment was then perfused with isotonic saline and mounted on a 3-dimensional aluminum supporting frame by fixing each cannula on the frame while keeping the physiological mean transmural pressure of approximately 100 mm Hg. The vessel was then rendered transparent by the method described by Karino and Motomiya [26]. 2.2. Experimental procedures The ICA and each of its branches were connected via a flexible plastic tube to a head tank and a collecting reservoir, respectively. The arterial tree was then placed in a glass chamber filled with the same liquid used to render the vessel transparent (methyl salicylate containing ethanol at 5% by volume), and the areas of interest on the arterial tree were transilluminated with a condensed parallel light from a tungsten-filament lamp or a mercury arc lamp. A dilute suspension of a mixture of 32-, 50-, 80-, 100-, 115-, 160-, and 230-μm-diameter polystyrene microspheres (density ρs = 1.06 g/cm3; Duke Scientific Corp, Palo Alto, Calif) in methyl salicylate (oil of wintergreen) containing ethanol at 5% by volume (density ρ = 1.16 g/cm3, viscosity μ = 0.026 g/cm s) was used as a substitute for blood. After filling the arterial tree and the entire flow system with the suspension, the fluid was subjected to a steady or pulsatile flow, which was obtained using a head tank system in combination with a sinusoidal oscillatory flow pump through the arterial tree, and the flow rate in the ICA and its branches were set to their desired values by adjusting the height of the head tank as well as each collecting reservoir. The behavior of individual suspended tracer microspheres flowing in various regions of the vessel was observed through a magnifying lens system attached to a cinecamera and photographed on black-and-white 16-mm cinefilm with a 16-mm high-speed cinecamera at a film speed of 2000 pictures per second. Flow experiments were carried out at a physiological range of flow rates in the ICA from 200 to 300 mL/min [17]. Most of the flow experiments were conducted in steady flow. Only one experiment was carried out in pulsatile flow (steady plus oscillatory flow) with an oscillatory frequency of 2 Hz and a displacement volume of 2 mL (Womersley number α = 6.57) to compare the results obtained in steady flow with those in pulsatile flow and determine whether the phenomena observed in steady flow also occur in pulsatile flow. After finishing the flow studies, the transparent arterial tree placed in a glass chamber filled with methyl salicylate containing ethanol at 5% by volume was photographed together with a ruler. 2.3. Analysis The developed 35-mm films were projected with a slide projector onto a glass screen and analyzed to obtain the inner diameter of the vessel. The developed 16-mm cinefilms were subsequently projected onto a drafting table, and the movements of individual tracer microspheres were analyzed on a frame-by-frame basis with the aid of a stop-motion 16-mm movie analyzer to obtain detailed flow patterns and distributions of fluid velocity and wall shear rate (shear stress). For each segment of interest chosen for filming, the representative geometric and flow conditions such as the vessel diameter, Do, mean volume flow rate, Qo, mean fluid velocity, U%, and Reynolds number, Reo ( = DoU%ρ/μ, where ρ and μ are the density and the viscosity of the flowing fluid, respectively) were evaluated in the main vessel proximal to the site of interest (branching or bending). Velocity distributions at various axial locations were obtained by plotting the axial components of particle translational velocities (calculated from tracings of the paths of tracer particles) against the radial distance from the vessel wall. Wall shear stress, τw = μGw, was calculated by multiplying the wall shear rate, Gw, obtained from the slope of the tangent drawn at the vessel wall on a best-fit curve of velocity vs radial distance at various axial locations by the viscosity of the fluid, μ. The locations of the points of flow separation and stagnation were determined from the movements of the smallest visible tracer microspheres (32-μm-diameter particles). 3. Results Fig. 2 shows the photographs of some of the transparent arterial trees taken at the end of the preparation. The transparent arterial trees lost the elasticity of natural living artery during the process of fixing, dehydrating, and rendering them transparent. However, the method ensured the preservation of the complex 3-dimensional configuration of the natural cerebral arteries that is most important in studying the flow patterns. Moreover, they became transparent without any optical distortion, even in the presence of atherosclerotic thickening of the vessel wall, although the areas of calcification remained as nontransparent dark spots as shown in Fig. 2B. Thus, it was possible to observe the wall thickening and the flow in both normal and diseased vessels from any direction without the errors that arise from optical distortion. The transparent arterial trees were used first to study the precise anatomic locations of atherosclerotic lesions and then the characteristics of the flow in some regions of interest such as the carotid siphon and the bifurcations of the internal carotid and the middle cerebral arteries. The results are described in detail below. 3.1. Preferred sites for the development of atherosclerotic lesions Atherosclerotic lesions were found in all specimens except for one that was obtained from a 26-year-old female subject. In the carotid siphon, atherosclerotic wall thickenings were found at the inner walls of the curved segments and some other parts randomly. In 5 vessels, calcified plaques were also found at the inner walls of the curved segments mainly and in some other regions between the site of cannulation and the site where the ICA went through the dura mater (distal to the fourth bend in Fig. 1). In the region where PComA branched off from the ICA, atherosclerotic wall thickenings were localized at the outer wall (hip) of the bifurcation on the side of the PComA and at the inner wall of the bend of the terminal ICA in one arterial tree prepared from a 70-year-old male subject (cf, Fig. 2, Fig. 3-B). At the terminal bifurcation of the ICA where the ICA bifurcated into the ACA and MCA, atherosclerotic wall thickenings were found almost exclusively along one or both of the outer walls (hip) of the bifurcation in 7 vessels. Among the 7 cases, very pronounced atherosclerotic wall thickenings were found in both the left and right ICAs harvested from a 70-year-old male subject (cf, Fig. 2D). No calcified plaque was found at this bifurcation in any arterial tree. At the bifurcation of the MCA, atherosclerotic wall thickenings were observed along the inner wall of the curved segment in the horizontal part of the MCA and along the outer walls (hips) of the first bifurcation. No calcified plaque was found in this region in any arterial tree. 3.2. Flow patterns, velocity profiles, and wall shear stresses obtained in steady flow 3.2.1. In the carotid siphon Formation of strong secondary flows and standing recirculation flows were observed in all the arterial trees. Fig. 3A shows an example of the flow patterns observed in steady flow in the arterial tree prepared from a 70-year-old male subject. As illustrated in the figure, flow separation occurred at the location S on the inner wall of the first bend in this figure. Then the region of separated flow was filled with thick-layered spiral secondary flows that were formed as a result of a strong sideways deflection of the fluid elements in the mainstream upon their impingement on the outer wall of the bend. Similar processes were repeated at the second and third bend, and a typical helicoidal flow consisting of strong secondary flows developed in the carotid siphon. At each bend, a part of the secondary flows moved backward along the inner wall distal to the apex of the bend, then suddenly changed its direction and rejoined the mainstream on the median plane of the bend after describing a single orbit. Thus, a region of slow reverse flow (recirculation zone) was formed along the inner wall of each of the curved segments distal to the point of flow separation. Pronounced atherosclerotic wall thickenings were found at such sites. Almost the same flow patterns were observed in all other 8 arterial trees. The distributions of fluid axial velocity (axial component of the fluid linear velocity) and wall shear stress on the common diametrical plane of the carotid siphon are shown in Fig. 3B. As it is evident from the figure, the velocity distribution was flattened at any cross section of the arterial segment, although in the proximal portion of each bend, it was slightly skewed toward the inner wall, thus facilitating flow separation and formation of a recirculation zone along the inner wall distal to the apex of the bend. It was also found that both mean and maximum velocities of the fluid and wall shear stresses at any cross section in the carotid siphon were much smaller than those in the distal ICA, the MCA, and the ACA due to a much larger diameter of the vessel and formation of a helicoidal flow in the carotid siphon. Atherosclerotic wall thickenings were localized in an alternating manner mainly at the inner wall of each bend with a maximum thickening occurring in regions of recirculation flows where fluid velocity and wall shear stress were low. Distal to the third bend, the helicoidal flow gradually faded away as going further down the arterial tree, and due to a gradual decrease in vessel diameter, fluid velocity increased as can be seen in Fig. 3B. 3.2.2. At the branching site of the PComA As shown in Fig. 3A, very strong spiral secondary flows newly formed in both the ICA and the PComA as the results of flow separation at the leading edge of the PComA and at the inner wall of the fifth bend, and a strong deflection of the main flow at the flow divider of the bifurcation and at the outer wall of the fifth bend of the ICA, which was located just distal to the branching site of the PComA (cf Fig. 1). Atherosclerotic wall thickenings were localized at the outer walls (opposite the flow divider) of the bifurcation occupied by slow secondary and recirculation flows. The approaching velocity profile (the distribution of fluid axial velocity just proximal to the bifurcation) observed in this particular vessel, which had a relatively large-diameter PComA, showed an asymmetric bipolar shape as shown in Fig. 3B, and the fluid elements located at the summit of the higher side pole in the velocity distribution and having high momentum energy impinged on the vessel wall around the flow divider where the PComA branched off. However, in other arterial trees having a small-diameter PComA, the approaching velocity profile showed either a flattened or a symmetric bipolar shape with a lower velocity at the summit of the velocity distribution compared with the case of the arterial trees having a large-diameter PComA. In such a vessel, the degree of flow disturbances created in the PComA was much lower. 3.2.3. At the terminal bifurcation of the ICA Fig. 4 shows an example of the flow patterns observed in the terminal bifurcation of the ICA prepared from a 71-year-old female subject. As illustrated in detail in the figure, the flow proximal to the terminal bifurcation of the ICA, where the ICA bifurcated into the MCA and ACA, was highly disturbed by the presence of a strong helicoidal flow, which was generated first within the carotid siphon and then reinforced at the last bend (the fifth bend) of the carotid siphon. Flow separation occurred at points S located on both the outer walls (hips) of the bifurcation, and the region of separated flow was filled with slow secondary flows that were formed by the deflection of the main flow at the flow divider of the bifurcation. A part of the secondary flows moved backward and formed a standing recirculation zone at the leading edge of the MCA. A mild atherosclerotic wall thickening was found at the outer wall (hip) of the bifurcation where wall shear stresses were low. 3.2.4. At the first bifurcation of the MCA Fig. 5 shows typical flow patterns observed in steady flow at the first bifurcation of the MCA, which corresponded to the distal portion of the arterial tree shown in Fig. 4 under the same flow conditions as those for the case of the terminal bifurcation of the ICA. As it is evident from the figure, the approaching flow proximal to the flow divider was stabilized as going down from the orifice of the MCA, and a laminar flow with streamlines almost parallel to the vessel wall developed proximal to the bifurcation of the MCA. The degree of stabilization of the secondary flows formed at the branching site of the MCA, and ACA depended on the Reynolds number in the parent vessel and the length of the vessel between the flow dividers of the terminal bifurcation of the ICA and the first bifurcation of the MCA. However, the flow was disturbed again at the branching site of the MCA. Flow separation occurred at points S located on both outer walls (hip) of the bifurcation, and the regions of the separated flow were filled with the secondary flows that were formed as a result of a strong deflection of the main flow at the flow divider. 3.2.5. At the distal ICA to MCA Fig. 6 shows 2 examples of the distributions of fluid axial velocity and wall shear stress in the arterial segments containing the terminal bifurcation of the ICA and the first bifurcation of the MCA prepared from a 71-year-old female subject (A), which is the same as those shown in Fig. 4, Fig. 5, and from a 53-year-old male subject (B). As shown in these figures, the velocity distribution proximal to the flow divider of the terminal bifurcation of the ICA was found to be either flattened or symmetric bipolar shape with a local minimum at the axis of the ICA. The absolute values of the velocities of fluid elements that impinged on the flow divider were 600 to 750 mm/s at a physiological range of Re of 500 to 800 evaluated in the parent artery in 4 arterial trees. The velocity distributions in the MCA and the ACA were skewed toward the inner wall of the bifurcation. The velocity distribution proximal to the flow divider of the MCA bifurcation was still not in a fully developed parabolic shape but flattened in the core region, and the summit of the velocity distribution was skewed toward the flow divider. Thus, the fluid elements having the highest velocity impinged on the vessel wall around the flow divider, exerting high fluid mechanical stresses (pressure, shear stress, and tension) there. The absolute values of the velocities of the fluid elements, which impinged on the flow divider, were 900 to 1300 mm/s at Re of 600 to 800 evaluated in the parent artery (MCA). As it is evident from the figure, the approaching velocity of fluid elements which impinged on the vessel wall around the flow divider of MCA bifurcation and exerted high fluid pressure, high wall shear stress, and high wall tension there was much greater than that at the terminal bifurcation of the ICA. The velocity profiles in the daughter vessels were skewed toward the inner walls of the bifurcation. Atherosclerotic wall thickenings were localized at the outer walls (hips) of the bifurcation where fluid velocity and wall shear stress were low. Similar flow patterns and velocity profiles were observed also in all other arterial trees regardless of the Reynolds number in the parent vessel and the flow rate ratios in the daughter vessels. 3.3. Flow patterns observed in pulsatile flow The phenomena occurring in pulsatile flow were qualitatively the same as those found in steady flow. However, both the secondary and recirculation flows that formed in the carotid siphon and at the terminal bifurcation of the ICA vanished when the main flow velocity attained a minimum in each cycle of pulsation. The degree of flow disturbance judged from the size and the velocity of the recirculation flows was higher in pulsatile than steady flow when compared at the same mean Reynolds number (hence, flow rate), and it appeared to be the highest just after the main flow velocity attained a maximum in each cycle of pulsation. 4. Discussion 4.1. Fluid velocity, wall shear stress, and preferred sites of atherogenesis It has been reported that the cavernous segment of the ICA is the site most susceptible to the development of atherosclerotic lesions in the human intracranial arteries, and most of the lesions develop along the inner walls of curved segments [7], [35], [37]. The results from our present study well agree with those presented by other investigators. However, in some advanced stages of atherosclerosis, wall thickenings and calcified plaques were also found randomly at sites other than the inner walls of the bends. In the carotid siphon, wall shear stresses were quite low even in regions other than the inner wall of bends because of the low mean fluid velocity and the presence of a strong helicoidal flow. This may explain the fact that wall thickenings and calcified plaques were found not only in the inner wall of curved segments but also in other regions of the carotid siphon in vessels suffering from advanced atherosclerosis. It was also shown in this study that in cerebral arteries, atherosclerotic lesions were formed almost exclusively along the inner wall of curved segments and at the outer wall (hip) of one or both daughter vessels at major bifurcations. These regions were the very places where flow was either slow (region of low wall shear stress) or disturbed with formation of slow secondary and recirculation flows. These findings are exactly the same as those obtained previously in a similar study carried out in our laboratory with human coronary arteries [2] and indicate that the major hemodynamic factors directly related to the localization of atherosclerotic lesions in the human arterial system are low fluid velocity and the resultant low shear stress acting on the vessel wall. 4.2. Anomaly of vascular structure, increased blood flow, and development of cerebral aneurysms Our main interest in the present anatomic and hemodynamic study of the ICA and MCA was the role of the carotid siphon in the localization of saccular aneurysms at some selected branching sites in these arteries. Cerebral aneurysms were found with very high probability in arteries pertaining to an arteriovenous malformation [1], [25], [29], [33], [39]. In such vessels, some aneurysms shrank in size or disappeared by only removing the malformation without any direct treatment of the aneurysm itself, suggesting that increased blood flow rate caused by the development of an arteriovenous malformation was responsible for the development of the aneurysm in these cases [25], [29]. However, as far as the terminal bifurcation of the ICA is concerned, aneurysm or infundibulum formation is very rare even though it is located proximally to the site of malformation and through which an excess volume of blood flows into the portion of the malformation. Apart from the cases of arteriovenous malformation, cerebral aneurysms are formed artificially even in normal arteries by varying only hemodynamic conditions. It has been shown that occlusion of one of the common carotid arteries results in the increase in flow rate and flow velocity in the contralateral internal carotid and the vertebral arteries [18], [49]. In experimental animals, this results in the formation of cerebral aneurysms. Hassler [24] showed in rabbits that aneurysmal bulging forms in the basilar and posterior cerebral arteries as a result of ligation of both the common and internal carotid arteries of one side and at the end of the basilar artery as a result of ligation of both carotid arteries. Hashimoto et al [20] showed that in rats and monkeys, aneurysms develop in both the ACA-AComA complex and the posterior half of the circle of Willis by ligation of unilateral common carotid artery, but only in the posterior half of the circle of Willis by ligation of bilateral carotid arteries. Similar phenomenon also occurs in humans who went through ligation of a carotid artery [6]. Important fact here is that formation of cerebral aneurysms was never found without carotid ligation even under the conditions of hypertension, which was induced artificially. These results suggest that altered hemodynamics, more specifically, a drastic increase in flow rate and fluid velocity in certain vessels created by ligation of the carotid artery was responsible for the development of cerebral aneurysms at some selected branching sites of the particular vessel. 4.3. Approaching velocity profile, hemodynamic stress, and development of cerebral aneurysms Although the importance of hemodynamic factors in the development of cerebral aneurysms has been pointed out by many investigators [6], [12], [20], [25], [44], it was not clear what is different from the hemodynamic point of view between the sites of high incidence of aneurysm formation and the sites of low incidence in the human circle of Wills in the absence of any anatomic abnormality such as arteriovenous malformations and occlusion of major arteries. In this study, the velocity profile just proximal to the branching site of the PComA was found to be bipolar-shaped on the lateral projection. When the diameter of the PComA was large enough and there was flow from the ICA to the PCA through it as it occurs under normal physiological conditions [36], the bipolar-shaped velocity profile became asymmetric with a higher side summit in the velocity profile appearing on the side of the PCA, and the fluid elements with high momentum energy impinged on the vessel wall around the flow divider of the bifurcation, exerting higher fluid pressure (dynamic pressure given by  ) and high wall shear stress there than the case where the PComA was small or totally missing. Kayembe et al [27] reported that all the aneurysms that he found at this site were located on the side where a thick PComA branched off. The particular hemodynamic conditions at this site described above may account for the high incidence of aneurysm formation as well as funnel-shaped dilatations observed by Stehbens [41] and infundibular widening of the PComA observed by Hassler and Saltzman [23]. At the terminal bifurcation of the ICA, the velocity distribution proximal to the flow divider was bipolar-shaped in all the vessels as observed perpendicular to the common median plane of the ICA, the MCA, and the ACA, and the fluid elements located in the central portion of the concaved velocity profile with low momentum energy impinged on the vessel wall around the flow divider. Thus, the fluid pressure and wall shear stress imposed on the vessel wall around the flow divider are considered to be much lower compared with the case where the fluid elements located at the summit of a parabolic velocity profile strikes the flow divider with high momentum energy. Our simple calculation based on the experimental data given in Fig. 7 shows that the dynamic pressure (given by  ) acting on the vessel wall around the flow divider is approximately 1.5 to 2 mm Hg if the approaching velocity profile is bipolar-shaped, which is less than half of the value (3.5-5 mm Hg) calculated for the case where the approaching velocity profile is in a parabolic shape. It is expected that the shear stresses and tensions acting on the vessel wall are also lower when the approaching velocity profile is in a bipolar-shape compared with the case of a parabolic shape. These may provide some explanations for why the incidence of aneurysm formation at this site is low despite the high flow rate and the large (obtuse) branching angle at the flow divider. The bipolar-shaped approaching velocity profile at the terminal bifurcation of the ICA and at the branching site of the PComA resulted from a strong helicoidal flow generated in the carotid siphon. If the ICAs run up straight from its origin at the neck to the terminal bifurcation without any bend, the approaching velocity profile at the terminal bifurcation of the ICA would be in a parabolic shape, and the incidence of aneurysm formation at this site would be much higher. It appears that the carotid siphon that contains 5 bends was designed as a braking system for blood flow to prevent the formation of aneurysms at the terminal bifurcation of the ICA. In contrast with the case of the terminal bifurcation of the ICA, the velocity profile proximal to the flow divider of the first bifurcation of the MCA was sharpened with the summit in the velocity profile skewing a little toward the flow divider, although the velocity profile was affected by the length of the MCA from its origin to the flow divider of the first bifurcation (M1 segment). The velocity of fluid elements located at the summit of the sharpened approaching velocity profile that impinged on the vessel wall around the flow divider of the first bifurcation of the MCA was 1.5 to 2 times larger than that found at the preceding terminal bifurcation of the ICA. Thus, the vessel wall around the flow divider of the first bifurcation of the MCA was exposed to fluid pressures and wall shear stresses much higher than those at the terminal bifurcation of the ICA. These differences in hemodynamic stresses may account for the difference in the incidence of the formation of saccular aneurysms between the terminal bifurcation of the ICA and the bifurcations of the MCA. 4.4. Possible role of impinging flow on the development of cerebral aneurysms It is considered that hypertension itself cannot initiate the formation of cerebral aneurysms [21], but it accelerates the development of aneurysms [30], [31]. Although the dynamic pressure acting on the vessel wall around the flow divider of arterial bifurcations and the outer wall of arterial bends is much smaller than the static pressure (the systemic blood pressure), it is acting incessantly throughout the whole life of men and women. Furthermore, the vessel wall at such sites is exposed to much higher wall shear stresses and wall tensions than other sites due to direct impingement of fluid elements with high momentum energy on the vessel wall. These could affect the function of endothelial cells as well as the transport of nutriment including cholesterol from flowing blood to the vessel wall via the endothelium. In connection with this, Wada and Karino [46], [47], [48] showed that in the arterial tree, due to the presence of a filtration flow of water at the vessel wall, concentration polarization of macromolecules, including LDLs that carry cholesterol, occurs at the luminal surface, resulting in concentration and depletion of LDLs in regions of low and high shear stresses, respectively. In regions of high wall shear stress, this may lead to thinning of the vessel wall due to malnutrition to the cells of the vessel wall, leading to the formation of an aneurysm in the long run. The results from this study suggest that the most important factor for the development of cerebral aneurysms is the magnitude of the approaching velocity of blood at bifurcations and bends, which determines the magnitude of fluid pressures, wall shear stresses, and wall tensions exerted on the vessel wall upon impingement on the vessel wall there and that affects the mass transport of nutriments including cholesterol necessary for the survival, growth, and proliferation of the cells forming the vessel wall. 5. Conclusion Throughout the entire ICA-MCA system, atherosclerotic lesions developed almost exclusively along the inner wall of curved segments and at the outer wall (hip) of one or both daughter vessels at major bifurcations where the flow was either slow or disturbed with formation of slow secondary and recirculation flows. The carotid siphon that contained several acute bends provided a flattened approaching velocity profile at the terminal bifurcation of the ICA, making the hemodynamic stresses (pressure, tension, and shear stress) exerted on the vessel wall much lower than that at the bifurcation of the MCA where the approaching velocity profile was sharpened. This may account for the relatively low incidence of aneurysm formation at this site. Acknowledgments A major part of this work was carried out while the authors were working at the McGill University Medical Clinic, Montreal General Hospital, Montreal, Canada, and it was supported by a grant HL-29502 from the National Heart, Lung and Blood Institute of the NIH (USA). Analysis of data and preparation of the manuscript were carried out at the Research Institute for Electronic Science, Hokkaido University, Sapporo, Japan. The authors thank the late Dr W.P. 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PII: S0090-3019(09)00286-9 doi:10.1016/j.surneu.2009.03.030 © 2010 Elsevier Inc. All rights reserved. | |
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