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Disturbance of blood flow as a factor of thrombus formation
THROMBOSIS RESEARCH Printed in the United
Suppl. II, Vol. 8, 1.976 Pergamon Press, Inc.
States
SECTION
DISTURBANCE
OF BLOOD Takehiko
Department
FLOW
Azuma
VII
AS A FACTOR and
Takayoshi
Shinshu of Physiology, School, Matsumoto,
OF THROMIXJS
FORMATION
Fukushima
University Japan
Medical
ABSTRACT A model study was undertaken to investigate disturbances of blood flow through stenotic blood vessels. Both axisymmetric and nonsymmetric models, having different diameter ratios of constriction, were used. A sudden decrease in the critical Reynolds number took place as the degree of axisymmetric constriction increased. Two symmetrical standing eddies were noticed within the separated region behind a hemispherical bulge projecting into the boundary layer. Increase in Reynolds number resulted in the formation of secondary flow, the horse-shoe vortex. A striking feature of a pulsatile laminar flow through a circular cylinder was the appearance of reverse flow near the wall at the end of the decelerating phase. The presence of axisymmetric constriction caused pulsatile disturbances. Pulsation seemed to facilitate not only the production of vortices but also the backward spread of turbulence. INTRODUCTION -
Atherogenesis and thrombus formation have been supposed to be intimately related with local hydrodynamic factors resulted from disturbances in blood stream. Early investigators of atherosclerosis suggested mechanical irritation of the arterial wall as a causal factor. The importance of mechanical effects is consistent with the observations that atherosclerosis occurs predominantly at specific sites within the arterial system (1, 2). In some of the models that have been proposed sites of atherosclerotic predilection are correlated directly with anticipated regions of local turbulence (3). Some investigators contended that flow separation is regarded as the primary hemodynamic factor associated with atherosclerotic lesion development (4). Whether atheromatous lesions tend to develop predominantly in regions of high wall shear or in regions of low wall shear has been a subject of controversy between Fry (1) and Caro et al. (2). The present model study was undertaken to investigate disturbances of blood flow produced by axisymmetric and 375
376
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nonsymmetric constriction of blood vessel lumen METHOD Three kinds of straight cylindrical tubes made of glass or metacrylate resion, were used instead of normal and morbid blood vessels. A cylindrical circular tube with no distortion of lumen was used as a substitute for normal vessels. Tubes with an axisymmetric constriction of varying degrees were utilized as the models of stenotic blood vessels. Tubes with a hemispherical bulge projecting inwards in varying degrees were used to model blood vessels with a large mural thrombus. Water was substituted for blood. The apparatus used to study flow conditions in the blood vessel models is shown schematically in FIG.l. The rate of steady flow was controlled by a stopcock at the end of the tube system consisted of metacrylate pipes of the same size joined The together end to end. blood vessel models were insterted between two of these Sinusoidal oscilpipes. lations were superimposed upon a steady flow by means of a piston pump connected to FIG. 1 Patterns of flow the end. Apparatus layout were observed by the following four method: (A) the condensed milk mehtod, (B) the dyefilament method, (C) the aluminium dust method, and (D) the hydrogen bubble method. Patterns of flow visualized by one of these four methods were photographed by a motor-driven camera (Nikon F-2), using an intense light projected through a narrow slit. RESULTS AND DISCUSSION I. Experiments with steady flow. An axial streamline was straight at a very low Reynolds number. The streaamline began to oscillate with increasing Reynolds number. Up to an intermediate range of flow rate, the oscillation was damped out a short distance downstream. Increasing the Reynolds number amplified the oscillation to form turbulence. In the constricted tubes the onset of the oscillation and transition to turbulence were observable at much lower Reynolds numbers than in the tube with no constriction. The critical Reynolds number was 3300 in the latter tube. It decreased steeply a0m to 580 as the constriction ratio (constriction diameter/tube diameter) reduced from 1 to 0.6. FIG. 2 demonstrates velocity profiles in front of and behind a constriction visualized by the hydrogen bubble method. At the upstram side of the constriction, the profile could be regarded as parabolic. On passing through the constriction, the profile became distorted and a considerable increase in axial velocity made the profile long and slender (FIG. 2A). An elevation of Reynolds number resulted in remarkable flattening of velocity profiles past the constriction (FIG. 2B). With increasing Reynolds number, clearly noticeable vortices began to form at some distance downstream from the constriction (FIG. 2c). Each vortex became larger and, in a little while, it was broken down into turbulence (Fig. 2D). Even at Reynolds numbers far below the critical value, a region of flow separation consisting of a large elipsoidal standing vortex was clearly seen just behind the constriction. In the separated region near the wall, the flow direction will actually be reversed from the main stream direction,
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thereby leading to a complete reversal in the direction of the shearing stresses on the internal This reversal surface of the tube. may be related to the development of endothelial lesions. The flow was still laminar both outside and inside the separated region. The circumstance is shown schematically in the upper half of FIG. 3. An eddying wake inside the separated region spread downstream as the Reynolds number increased. At the critical Reynolds number vortices were formed due to the concentration of vorticity at the distal end of The vortices thus the wake. produced were shed downstream in succession and broken down to form turbulence. In the proximal section of the separated region, however, the motion of the liquid was extremely retarded (the lower half of FIG. 3). This retardation might have something to do with the mechanism of thrombus formation. Examinations were also made on changes in flow pattern produced by a hemispherical bulge projectin FIG. 2 into the boundary layer. No Velocity profiles in front appreciable separation of stream of and behind a constriction. occurred at a low Reynolds number. The stream impinged upon the base of the bulge spread over its whole surface, and then converged again to a thin stream. intermediate Reynolds number, the stream separated from the surface of the bulge. metrical standing eddies were noticed within the separated region behind separatidn point concentrated turbulence vortices the obstacle. Further increase in Reynolds number resulted in the FIG. 3 formation of secondary Separation of flow past a constriction. flow, so that the flow Upper half: laminar flow, lower half: pattern behind the bulge laminar-to-tubulent transition. became very complicated. A streamline near the wall turned round downward directly before the obstacle. Then it curled round on itself and formed a vortex tube which in turn passed round the front of the bulge in both directions and led to a vortex pair trailing downstream. This vortex tube,
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called the horse-shoe vortex, is a secondary flow ensued from a radial m Hemispherical pressure gradient generated by a bluff Bulging obstacle within the boundary layer. The complicated flow pattern is illustrated schematically in FIG. 4. The bulge and separated region are surrounded by a tube representing horse-shoe vortex. The stream next to the center line of the bottom wall stagnates just before the top of This stagthe horse-shoe vortex. 0 Horseshoe vortex nation point is the site of low shear 0 Separated region rate in the upstream side of the At this point, the stream obstacle. FIG. 4 is divided into two flows which pass around the front and side of the Schematical illustration vortex tube in both directions. Then of flow pattern around the divided streams are rolled inside a hemispherical bulge. the separated region, curled into the existing wake eddies, coiled up spirally, and passed downstream. II. Experiments with nonsteady flow. U cm/set The basic form of nonsteady flow is the pulsatile flow composed of a sinusoidal oscillatory flow superposed The upon a steady flow (FIG. 5). instantaneous spatial mean velocity averaged across the tube, U, may be given by ) wt u=Yi - fi COSWt, 5LO (degree) 0 90 180 270 360 60 where u is the spatial and temporal mean velocity averaged across the FIG. 5 tube over one cycle, 0 is the amplitude Velocity wave form of the of oscillatory component, and w is the pulsatile flow used in the angular frequency of oscillation. present study. Accordingly, instantaneous Reynolds number, Re, csn be written as Re = 2RU/v = ??e- Re cosut, where R is the tube radius, V is the kinematic viscosity of the fluid, and lieand ge represent the Reynolds numbers for steady and oscillatory flow components, respectively. Making use of the amplitude coefficient 6, which is given by 6 = i?e/Be= e/Y?, the above equation can be rewritten as Re=Ee ( I-Bcoswt ). Thus the similarity parameters required for characterizing a pulsatile flow are the following three dimensionless numbers: the Reynolds number for steady flow component, Re, the amplitude coefficient, 6, and the frequency parameter, cx., proposed by Womersley, which is defined as a== R2 w/v. Velocity profiels were strikingly flattened in an oscillatory flow through the circular tube with no constriction. Velocities at every moment at different radial positions were almost uniform over the whole cross section except in a thin layer next to the wall. A very steep velocity gradient was established within this boundary layer, the thickness of which is inversely proportional to the frequency parameter, ~1.
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Velocity profiles in a r/R pulsatile flow through the tube 1.0 <.: o\ ~;ri“_-~-~~~-~---~.~, o,fecelerating phase with no constriction were flatter yb \r L, OkO\. X, than those in the Poiseuille flow "1 0.5 "\ 'Olp a\90& X0 but much more parabolic than those 90 / ‘p g p b in the oscillatory flow. 2 0 -05 3 Normalized velocity profiles at 0 ;ddd 1 ” 2/o ij 10 j00 different stages in decelerating d d 10 JO 0.5 / /O / and accelerating phases are shown & /a /Q Radial positions are in FIG. 6. phase ---y,,/‘ ._..-.~o S./
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The A vortex layer was formed inside the back-flow stratum. the tube wall. wake vortex was put back toward the constriction and made round (FIG. 7A). Then the rounded vortex was shed downstream in the form of a vortex ring (FIG. A new vortex was formed near the constriction as the first vortex ring 7B). This new vortex developed gradually and was shed downpassed downstream. stream again in the form of vortex ring (FIG. 7C). After repeating this vortex shedding three or four times, the flow was restored to the original These findings suggest that disturbances will be liable to steady pattern. take place in nonsteady blood flow, especially when the shape of blood vessel lumen is distorted. Detailed results of the present investigation will be published elsewhere. This work was supported by research grants from the Japan Heart Foundation and the Japanease Ministry of Education. 1.
REFERENCES FRY, D.L. Certain chemorheologic considerations regarding the blood vascular interface with particular reference to coronary artery disease. Circulation. 40 (suppl. IY) , m-38, 1969.
2.
CARO, C.C., FITZ-GERALD, J.M. and SCHROTER, R.C. Atheroma and arterial wall shear : Observation, correlation, and proposal for a shear dependent mass transfer mechanism for atherogenesis. Proc. R. Sot. Lond. [Biol]. x7, 109, 1971.
3.
WESOLOWSKI, S.A., FRIES, C.C., SABINI, A.M. and SAWYER, P.N. Significance of turbulence in hemic systems and in the distribution of the atherosclerotic lesion. Surgery. z, 155, 1965.
4.
FOX, J.A. and HUGH, A.E. Localization of atheroma : Theory based on boundary layer separation. Br. Heart J. 28, 388, 1966.
Suppl. II, Vol. 8, 1.976 Pergamon Press, Inc.
States
SECTION
DISTURBANCE
OF BLOOD Takehiko
Department
FLOW
Azuma
VII
AS A FACTOR and
Takayoshi
Shinshu of Physiology, School, Matsumoto,
OF THROMIXJS
FORMATION
Fukushima
University Japan
Medical
ABSTRACT A model study was undertaken to investigate disturbances of blood flow through stenotic blood vessels. Both axisymmetric and nonsymmetric models, having different diameter ratios of constriction, were used. A sudden decrease in the critical Reynolds number took place as the degree of axisymmetric constriction increased. Two symmetrical standing eddies were noticed within the separated region behind a hemispherical bulge projecting into the boundary layer. Increase in Reynolds number resulted in the formation of secondary flow, the horse-shoe vortex. A striking feature of a pulsatile laminar flow through a circular cylinder was the appearance of reverse flow near the wall at the end of the decelerating phase. The presence of axisymmetric constriction caused pulsatile disturbances. Pulsation seemed to facilitate not only the production of vortices but also the backward spread of turbulence. INTRODUCTION -
Atherogenesis and thrombus formation have been supposed to be intimately related with local hydrodynamic factors resulted from disturbances in blood stream. Early investigators of atherosclerosis suggested mechanical irritation of the arterial wall as a causal factor. The importance of mechanical effects is consistent with the observations that atherosclerosis occurs predominantly at specific sites within the arterial system (1, 2). In some of the models that have been proposed sites of atherosclerotic predilection are correlated directly with anticipated regions of local turbulence (3). Some investigators contended that flow separation is regarded as the primary hemodynamic factor associated with atherosclerotic lesion development (4). Whether atheromatous lesions tend to develop predominantly in regions of high wall shear or in regions of low wall shear has been a subject of controversy between Fry (1) and Caro et al. (2). The present model study was undertaken to investigate disturbances of blood flow produced by axisymmetric and 375
376
AZUMA
AND
FIJKVSHIMA
Suppl.
II
nonsymmetric constriction of blood vessel lumen METHOD Three kinds of straight cylindrical tubes made of glass or metacrylate resion, were used instead of normal and morbid blood vessels. A cylindrical circular tube with no distortion of lumen was used as a substitute for normal vessels. Tubes with an axisymmetric constriction of varying degrees were utilized as the models of stenotic blood vessels. Tubes with a hemispherical bulge projecting inwards in varying degrees were used to model blood vessels with a large mural thrombus. Water was substituted for blood. The apparatus used to study flow conditions in the blood vessel models is shown schematically in FIG.l. The rate of steady flow was controlled by a stopcock at the end of the tube system consisted of metacrylate pipes of the same size joined The together end to end. blood vessel models were insterted between two of these Sinusoidal oscilpipes. lations were superimposed upon a steady flow by means of a piston pump connected to FIG. 1 Patterns of flow the end. Apparatus layout were observed by the following four method: (A) the condensed milk mehtod, (B) the dyefilament method, (C) the aluminium dust method, and (D) the hydrogen bubble method. Patterns of flow visualized by one of these four methods were photographed by a motor-driven camera (Nikon F-2), using an intense light projected through a narrow slit. RESULTS AND DISCUSSION I. Experiments with steady flow. An axial streamline was straight at a very low Reynolds number. The streaamline began to oscillate with increasing Reynolds number. Up to an intermediate range of flow rate, the oscillation was damped out a short distance downstream. Increasing the Reynolds number amplified the oscillation to form turbulence. In the constricted tubes the onset of the oscillation and transition to turbulence were observable at much lower Reynolds numbers than in the tube with no constriction. The critical Reynolds number was 3300 in the latter tube. It decreased steeply a0m to 580 as the constriction ratio (constriction diameter/tube diameter) reduced from 1 to 0.6. FIG. 2 demonstrates velocity profiles in front of and behind a constriction visualized by the hydrogen bubble method. At the upstram side of the constriction, the profile could be regarded as parabolic. On passing through the constriction, the profile became distorted and a considerable increase in axial velocity made the profile long and slender (FIG. 2A). An elevation of Reynolds number resulted in remarkable flattening of velocity profiles past the constriction (FIG. 2B). With increasing Reynolds number, clearly noticeable vortices began to form at some distance downstream from the constriction (FIG. 2c). Each vortex became larger and, in a little while, it was broken down into turbulence (Fig. 2D). Even at Reynolds numbers far below the critical value, a region of flow separation consisting of a large elipsoidal standing vortex was clearly seen just behind the constriction. In the separated region near the wall, the flow direction will actually be reversed from the main stream direction,
Suppl.
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BLOOD
FLOW
Bc THROMBUS
FORMATION
377
thereby leading to a complete reversal in the direction of the shearing stresses on the internal This reversal surface of the tube. may be related to the development of endothelial lesions. The flow was still laminar both outside and inside the separated region. The circumstance is shown schematically in the upper half of FIG. 3. An eddying wake inside the separated region spread downstream as the Reynolds number increased. At the critical Reynolds number vortices were formed due to the concentration of vorticity at the distal end of The vortices thus the wake. produced were shed downstream in succession and broken down to form turbulence. In the proximal section of the separated region, however, the motion of the liquid was extremely retarded (the lower half of FIG. 3). This retardation might have something to do with the mechanism of thrombus formation. Examinations were also made on changes in flow pattern produced by a hemispherical bulge projectin FIG. 2 into the boundary layer. No Velocity profiles in front appreciable separation of stream of and behind a constriction. occurred at a low Reynolds number. The stream impinged upon the base of the bulge spread over its whole surface, and then converged again to a thin stream. intermediate Reynolds number, the stream separated from the surface of the bulge. metrical standing eddies were noticed within the separated region behind separatidn point concentrated turbulence vortices the obstacle. Further increase in Reynolds number resulted in the FIG. 3 formation of secondary Separation of flow past a constriction. flow, so that the flow Upper half: laminar flow, lower half: pattern behind the bulge laminar-to-tubulent transition. became very complicated. A streamline near the wall turned round downward directly before the obstacle. Then it curled round on itself and formed a vortex tube which in turn passed round the front of the bulge in both directions and led to a vortex pair trailing downstream. This vortex tube,
378
AZUMA
AND
FUKUSHIMA
Suppl.
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called the horse-shoe vortex, is a secondary flow ensued from a radial m Hemispherical pressure gradient generated by a bluff Bulging obstacle within the boundary layer. The complicated flow pattern is illustrated schematically in FIG. 4. The bulge and separated region are surrounded by a tube representing horse-shoe vortex. The stream next to the center line of the bottom wall stagnates just before the top of This stagthe horse-shoe vortex. 0 Horseshoe vortex nation point is the site of low shear 0 Separated region rate in the upstream side of the At this point, the stream obstacle. FIG. 4 is divided into two flows which pass around the front and side of the Schematical illustration vortex tube in both directions. Then of flow pattern around the divided streams are rolled inside a hemispherical bulge. the separated region, curled into the existing wake eddies, coiled up spirally, and passed downstream. II. Experiments with nonsteady flow. U cm/set The basic form of nonsteady flow is the pulsatile flow composed of a sinusoidal oscillatory flow superposed The upon a steady flow (FIG. 5). instantaneous spatial mean velocity averaged across the tube, U, may be given by ) wt u=Yi - fi COSWt, 5LO (degree) 0 90 180 270 360 60 where u is the spatial and temporal mean velocity averaged across the FIG. 5 tube over one cycle, 0 is the amplitude Velocity wave form of the of oscillatory component, and w is the pulsatile flow used in the angular frequency of oscillation. present study. Accordingly, instantaneous Reynolds number, Re, csn be written as Re = 2RU/v = ??e- Re cosut, where R is the tube radius, V is the kinematic viscosity of the fluid, and lieand ge represent the Reynolds numbers for steady and oscillatory flow components, respectively. Making use of the amplitude coefficient 6, which is given by 6 = i?e/Be= e/Y?, the above equation can be rewritten as Re=Ee ( I-Bcoswt ). Thus the similarity parameters required for characterizing a pulsatile flow are the following three dimensionless numbers: the Reynolds number for steady flow component, Re, the amplitude coefficient, 6, and the frequency parameter, cx., proposed by Womersley, which is defined as a== R2 w/v. Velocity profiels were strikingly flattened in an oscillatory flow through the circular tube with no constriction. Velocities at every moment at different radial positions were almost uniform over the whole cross section except in a thin layer next to the wall. A very steep velocity gradient was established within this boundary layer, the thickness of which is inversely proportional to the frequency parameter, ~1.
Suppl.
II
BLOOD
FLOW
& THROMEKJS
FORMATION
379
Velocity profiles in a r/R pulsatile flow through the tube 1.0 <.: o\ ~;ri“_-~-~~~-~---~.~, o,fecelerating phase with no constriction were flatter yb \r L, OkO\. X, than those in the Poiseuille flow "1 0.5 "\ 'Olp a\90& X0 but much more parabolic than those 90 / ‘p g p b in the oscillatory flow. 2 0 -05 3 Normalized velocity profiles at 0 ;ddd 1 ” 2/o ij 10 j00 different stages in decelerating d d 10 JO 0.5 / /O / and accelerating phases are shown & /a /Q Radial positions are in FIG. 6. phase ---y,,/‘ ._..-.~o S./
380
AZUMA
AND
FUKUSHIMA
Suppl.
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The A vortex layer was formed inside the back-flow stratum. the tube wall. wake vortex was put back toward the constriction and made round (FIG. 7A). Then the rounded vortex was shed downstream in the form of a vortex ring (FIG. A new vortex was formed near the constriction as the first vortex ring 7B). This new vortex developed gradually and was shed downpassed downstream. stream again in the form of vortex ring (FIG. 7C). After repeating this vortex shedding three or four times, the flow was restored to the original These findings suggest that disturbances will be liable to steady pattern. take place in nonsteady blood flow, especially when the shape of blood vessel lumen is distorted. Detailed results of the present investigation will be published elsewhere. This work was supported by research grants from the Japan Heart Foundation and the Japanease Ministry of Education. 1.
REFERENCES FRY, D.L. Certain chemorheologic considerations regarding the blood vascular interface with particular reference to coronary artery disease. Circulation. 40 (suppl. IY) , m-38, 1969.
2.
CARO, C.C., FITZ-GERALD, J.M. and SCHROTER, R.C. Atheroma and arterial wall shear : Observation, correlation, and proposal for a shear dependent mass transfer mechanism for atherogenesis. Proc. R. Sot. Lond. [Biol]. x7, 109, 1971.
3.
WESOLOWSKI, S.A., FRIES, C.C., SABINI, A.M. and SAWYER, P.N. Significance of turbulence in hemic systems and in the distribution of the atherosclerotic lesion. Surgery. z, 155, 1965.
4.
FOX, J.A. and HUGH, A.E. Localization of atheroma : Theory based on boundary layer separation. Br. Heart J. 28, 388, 1966.