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Experimental results to the deposition hypothesis of atherosclerosis
THROMBOSIS RESEARCH Printed in the United States
vol.
8, PP~ 553-566, 1976 Pergamon Press, Inc.
EXPERIMENTAL RESULTS TO THE DEPOSITION HYPOTHESIS OF ATHEROSCLEROSIS H. Mtiller-Mohnssen Institute of Biology - GSF, De artment of Physiology D-8042 NeuherbergPMunich, Germany
(Received 8.12.1975; in reT,-ised form 10.3.1976. Accepted by Editor $3.Witte)
ABSTRACT A simplified model of a main predilection site of coronary atherosclerosis was perfused by suspensions of either erythrocytes (RBC) or thrombocytes (platelets) in order to prove the deposition hypothesis of atherosclerosis from a hydrodynamic point of view. The results show that RBC and platelets can be concentrated separately at particular regions of the wall by means of hydrodynamic mechanisms alone. In the same way, they can additionally be deposited, provided the particles are adherent. The sites where deposits occur are hydrodynamically characterized by the appearance of stagnation flow, i.e. of velocity components which are directed towards the wall and perpendicular to it while at the same time the velocity components parallel to the wall (wall shearing force) are small. These regions correspond to the location of atheromas and thrombosis within that branching of coronary artery which has a geometry similar to that of the model used in the experiments described. Therefore, these experiments suggest that hydrodynamic forces are involved in the mechanism of the first settlement of a wall-adherent thrombosis in unaltered living arteries. INTRODUCTION At flow velocities comparable to those found in muscular arteries the flow in tubes is undisturbed, i.e. parallel to the axis, if the tubes are straight, unbranched and have constant diameters. Predilection sites of atherosclerosis and thrombosis are characterized by the geometrical complexity of the vessel configuration and, consequently by a localized flow disturbance. Within these sites, atheromas and thrombosis are localized at
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certain parts of the vessel-cross section which are defined by their correlation to the specific geometrical parameters (center and radius of a curvature, intersection point and angle of a branching). Many observations support the view that hydrodynamic forces induce the pathogenic mechanism of atherosclerosis, but it has not yet been proven, whether a cause and effect relation exists, partly because of the difficulty in observing the pathological process from its very beginning in vivo. To answer the question, whether hydrodynamic forces participate in forming microthrombi, i.e. in the atherosclerogenetic mechanism supposed by the deposition (incrustation)hypothesis, experiments were designed to determine:
1. What are the hydrodynamic forces at the predilection sites? 2. Can hydrodynamic forces produce localized deposits of erythrocytes (RBC) and thrombocytes (platelets) at the inner surface of the arterial wall? METHOD The experiments were performed in geometrically simplified glass-models of the first septal branch from the anterior descendent coronary artery, because: 1. This is the site of the first appearance of atherosclerosis in man (1,2). 2. Branthings are the main predilection sites in general. 3. In branched flow the critical Reynolds number (Re rit) is observed to attain extremely low values and may, there Ei ore, be reached in living arteries. The glass-tubes were T-shaped with a main tube of 3 mm diam (300 mm length, branching in the center) and a side tube of 1.5 mm diam (100 mm length). The angle is comparable to the course angle of the real arterial branching, the diameters correspond to the diameters of the respective arteries as determined from stereoscopic arteriograms at post mortem. These models were mounted as a part of the flow apparatus in the following positions: 1. With the branching plane (connecting the axis of both tubes) horizontal; this position was used in most of the hydrodynamic measurements. 2. With the main tube vertical, to eliminate the effect of gravity on the deposition of RBC and platelets at the wall of the main tube. Flow apparatus. A 10 1 reservoir is mounted above the branching section of the model. By a flow-over, the level Of the liquid within the reservoir is held constant, ensuring the constancy of the hydrostatic pressure necessary to produce a steady inflow to the model. In addition, to obtain nearly constant input flow-rate Q. (ml s-I) into the main tube of the model, a high flow resistance was put between reservoir and model. The resistance to flow was adjusted such that the influence of the small resistance fluctuations on Qo caused by the flow disturbance within the model could be neglected. These experiments were, therefore, performed at "constant" Qo. All the average flow rates, Qor in the main tube upstream from the branching, Qll in the main tube downstream the branching and Q2, in the
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side tube were adjusted by valves. Qo, Ql, Q2 were each monitored by floating flow-meters, inserted a distance of at least 300 mm from the branching; in the same regions the average hydrostatic pressure was measured by Statham elements. 1500 mm downstream from the branching, the liquid flowed out freely and was collected separately from each branch. Ql and Q2 was measured again by the rising rate of the liquid level in the collecting vessels. From here the liquid was pumped back to the reservoir. Because the hydrodynamical situation differs from crosssection to cross-section, the hydrodynamic events were investigated "morphologically". This was done only for the main tube since the pathological alterations appear mostly in the main artery. After macroscopic observation of the flow phenomena by means of conventional techniques (dye-injection, polarisation-optical examination using a birefringent fluid, laser-doppler anemometry), microscopic techniques were used to examine the paths of single tluid particles (streamlines). Streamlines were recorded using a fluid of the same refractive index as glass (94% Dimethyl-sulfoxid, 6% water ) labelled with spherical polystyrol particles of collodial size ( 5 Urn diam, 105 particles/ml) ; these microspheres are assumed to produce only negligibly small alterations of flow. To make the movement of the fluid visible, the sample was illuminated perpendicular to the axis of a microscope (dark-field illumination) by a series of 10 laser pulses of 10 IJ.Sduration each, separated by 1 + 1000 IJ.S(3). By means of a special optical arrangement, a thin slice of the sample was illuminated. Every particle moving in the plane of this slice writes a dashed line on a photographic film with the length of the intervals between the dashes proportional to the velocity and the shape of the curve describing the path of the particle. The ratio of dashes to flashes per series allows an estimation of the average angle between the path and the illuminated plane. Therefore, not only the velocity profiles but also the real path of a particle can be derived from these photographs. The components composing the physical system were exchanged step by step for those involved in a living system. (In separate experiments not described here, the tube wall was replaced by elastic and also by porous walls to prove the infiltration hypothesis. A pulsating flow will be used instead of a stationary, if the branched flow under stationary inflow conditions will be better known as it is the case now).In the present experiments model particles are replaced by RBC and platelets, DMSO and water by electrolyte solutions, serum etc.. The paths of single RBC and platelets (streaklines) and the deposition of these particles at the wall were investigated by the laser technique, but also by conventional dark-field microscopy. Suspensions: 1. Human RBC (2% Hct) in isosmotic NaCl-solution, 5% human plasma added. 2. Same as 1 but 1 g% Polyvinylprolidone added, to make the RBC adhaesive. 3. ADP-excited bovine platelets with the same solvent as mentioned above. The preparation of isolated platelets will be described elsewhere
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et al, to be published). RESULTS
Preliminary
hydrodynamic
experiments
In the first experiments, the flow of the main tube in the plane of branching was investigated (3). The average velocity in the influx tube (Qo) is kept constant at 80 mm/s (Re, = 88). The volume flow in the side-branch (Qz) was increased stepwise and consequently the flow in the main tube (Ql) downstream of the branching was diminished. The dashed lines in Fig. 1 show the paths of the fluid during 10 ms illumination. If the flow in the side-branch is stopped, the flow is parallel to the axis - except for negligible small disturbances in the orifice region - with the maximum velocity at the axis: the velocity profile is a rotation-symmetric paraboloid. When the flow in the side-branch is started, only the fluid from near the wall with the lowest kinetic energy, flows into the side-branch. Whereas the faster main stream deviates from the
FIGURE
1
Streamlines of flow in a branched tube at Re = 88 of inflow. Re-numbers of branch flow increases from theotop (zero) to bottom, thus the Re-number of the down-stream part of the main tube decreases as indicated at the right. (Experiment of KRATZER, KINDER).
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axis-parallel flow the least, the higher the kinetic energy. Therefore, the line of maximum velocity is deviated from the tube axis more the higher the volume flow in the side-branch and almost touches the main tube wall tangentially in the region downstream the mouth of the side-branch. Near the edge of the orifice, where the flow is divided, a region can be found where streamlines are directed toward the wall and perpendicular to it. From this "first stagnation point" some part of the fluid moves downstream the main tube and some part moves back into the side branch.(A stagnation point separates two areas where, in the flow near the wall, the velocity components parallel to the tube axis are opposite in sign). Most of the back flow glides to both sides in a curve, tangentially along the Wall of the main tube and reaches the mouth of the side branch laterally. These parts of back-flow leave the plane of branching and cannot be seen in Fig. 1. A fast flow is found downstream to the mouth of the sidebranch, a Slow flow in the opposite half part of the same crosssection. Hence the velocity profile downstream of the branching becomes asymmetrical and contains a point of inflection. In this region, the shearing forces overcome the viscosity which is responsible for inner cohesion of the fluid: the flow disrupts. The main flow separates from the wall for a short distance, forming a water jet which surrounds a dead water region at Rel= 10. Here a circulating flow is driven indirectly by the main stream via shearing forces. In the axial-parallel flow of the main tube, upstream and far downstream to the point of branching, as well as in the water jet close downstream to the mouth of branching, the fluid moves down the pressure gradient supplied in the experiment (primary flow). In the dead water a circulatory flow arise which is not driven directly by the main pressure gradient but indirectly by the primary flow via shearing forces being effective in the boundary layer between the dead. waterregion and the jet (secondary flow). The velocity profile within the dead water (Fig. 5 inset) taken in the plane of branching clearly demonstrates the mechanism of inducing and maintaining a dead water circulation. Within the dead water the velocity is highest at its boundary with the water jet and decreases with increasing distance from this boundary towards the center of the circulatory flow (Fig. 5 inset). At the opposite, i.e. the wall side border of the dead water the velocity of the outermost layer of the fluid, touching the wall, is zero and increases with increasing distance from the wall towards the circulation center. At the jet side border of the dead water the velocity gradient behaves inversily compared to the velocity gradient at the wall, indicating that the dead water circulation is driven on by the jet and is slowed down by the wall. Since the dead water can be approximated by a separated volume of fluid, the driving force induces a back flow in the region opposite to its point of onset, this is at the wall. The mechanism of dead water circulation has been sometimes illustrated by the rotation of a ball in a ball bearing. At higher degrees of disturbance than for separation of flow from the wall, regular oscillations of 10 f 100 cycles per sec-
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ond and a wavelength of 3 + 5 mm arise in the interface between the dead water and the jet (comparable to the generation of oscillations in a flute, where a flow is divided at an acute edge). The oscillations change over into irregular turbulences at still ; the ncn-stationary higher disturbance (the flute is"overblown" flow phenomena as oscillations and turbulence are not demonstra(wallted in Fig. 1). The start of each degree of flow-alteration not depend on a critseparation, oscillation and turbulence)does ical Reynolds number, but on a critical difference between the Reynolds numbers upstream(Reo) and downstream (Rel) of the branching: (Re, - Rel)crit = (Re2)crit is nearly constant in the range of Re, 100 + 1400. Close upstream from the region where the primary flow reattaches itselfto the wall, streamlines, which come from the interface between the circulating dead water and the jet, are directed perpendicularly towards the wall. In this "second stagnation point" the flow is divided and diverges into opposite directions (point of divergency). Outer streamlines of the jet belonging to the interface between the jet and the dead water are directed downstream, whereas the accelerated dead water drifts towards the wall where the overwhelming part is forced to move backward (upstream) along the wall. During the back flow, the velocity of circulation decreases until it reaches the region where the primary flow separates from the wall (point of convergency). Here it is turned into main flow direction and accelerated again. Erythrocyte
deposition
In a second series of experiments the same model was perfused by suspension of human RBC (Suspension 1, see 4,s) at Re,'90. Fig. 2 shows the distribution of RBC in the region adjacent to the wall, opposite to the orifice. If the flow in the sidebranch is interrupted, - the main flow thus parallel to the axis - an RBC-free layer of a 100 urn thickness is established at the wall probably due to a process known as "radial-migration". At 10~ volume flows in the side branch the thickness of the RBC-free layer is increased in the regjon of low velocity opposite to the orifice. If at higher degrees of flow disturbance the dead water region is developed, the RBC-free layer vanishes at first in the region of the stagnation point. At higher velocities of the circulation flow, the broadened RBCfree layer is over more than half the length of the dead water region, replaced by RBC-rich fluid, which is flowing back from the stagnation point. The zone with decreased thickness of RBCfree layer is clearly separated from the region, close downstream to the point of divergency, where the thickness of RBCfree layer is still enlarged. 10 s after onset of flow in the side-branch, the new distribution reaches stationary values, If the RBC are not adhesive, the increase of concentration at the wall is reversible - that is, the normal RBC-distribution is restored if the flow in the side-branch is interrupted and this way, the hydrodynamic disturbance is eliminated. But if the RBC are made adhesive (Suspension 2) they stick to the wall in the stagnation region, where they aggre-
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gate forming leaflets of irregular thickness (2 t 20 urn diam) covering a defined area of the wall surface. These RBC depositions can only be removed by increasing the flow-velocity (Reo290) as a result of higher shearing forces at the wall (see under "The hydrodynamic situation in the regions of deposition").
FIGURE 2 Distribution of RBC in a dead-water region of a branched flow at different degrees of flow disturbance. Suspension 1 (human RBC, 2% Hct) is used as fluid; same model and same experimental procedure as in Fig. 1. Only the section of the main tube opposite to the orifice, indicated in the inset, is shown. The vertical bars indicate location and size of the side branch (bright field illumination, RBC-depleted regions of fluid appear bright). a) Rel = Re, (Q2=0); flow is parallel to the axis. The white band parallel to the wall shows that the RBC-free layer is of constant thickness. c) Beginning of dead water circulation; the thickness of RBC-free layer is increased in the region where the flow separates from the wall (negative values of VA, see Fig. 5) and decreases in th$ stagnation region (positive values of VI) c - e) Back-flow carries RBC along the wall surface from the stagnation point into the stagnation region (v, >O) of the dead water. At Rel = 71, the border between the region where the RBC-free layer is broadened and where it disappears, becomes clearly visible. (Experiment of BALDAUF).
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FIGURE 3 RBC-deposition produced by stagnation flow within the dead water analog to Fig. 2 (Suspension 2). The picture was taken after diminishing Q2; This way the disturbance of flow is reduced to the stage where only broadening of RBC-free layer occurs (experiment BALDAUF). The main result of this experiment is, that the hydrodynamically induced RBC-deposition is localized in the region of the second stagnation point, which corresponds to the predilection site of thromboses and atheromas. At the first stagnation point no deposits were observed. Thrombocyte-deposition In another series of experiments (6) a thrombocyte suspension was used as fluid. If the inflow Re-number is the same as in the RBC-experiment described above (Re,= 901, the platelet concentration increases in the stagnation region of the dead water - just like the RBC - concentration at the same hydrodynamic condition - but desposition at the wall occurs only at much higher velocities of the stagnation flow. Deposition starts, therefore, in the stagnation region at the edge of the orifice where the velocity of stagnation flow is 40 mm/s compared to 2.5 mm/s of the stagnant flow of the dead water. The process starts with the deposition of single platelets 30 t 40 s after the onset of the flow disturbation. By apposition of other platelets, mainly at the lee-side of platelets already adhered, the deposition grows and this predominantly in the back flow direction thus forming streaks which follow the streamlines near the TaTall.After another 60 S, the growth of deposition is termina.ted 'Fig. 4). (Because these streamlines are spiral, they cannot be observed in the plane of branching: they were made visible by illuminating slices of the fluid which touch the inner surface of the wall tangentially). The hydrodanamic The distribution
situation
in the regions
of the hydrodynamic
of deposition
force components
at the
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FIGURE 4 Thrombocyte deposition in the region of first stagnation point at the wall of a branched tube (dark field illumination; the streak shaped depositions occur bright. See text for further explanation; experiment QnLDAUF et al 1. wall within the dead water region can be derived approximately from the velocity-field visualized by photographs as in Fig. 1. This was done as an example for the RBC deposition at the second stagnation region (Fig. 5). In terms of velocity gradients (v), the stagnation point is characterized by a maximum component towards the wall and perpendicular to it (vl solid line). The stagnation point separates two regions in which the direction of the parallel components is opposite (v/j dashed line). In both regions, the parallel components increase with the distance from the stagnating point, reaching a limited value which is, of course, much smaller in the dead water region than in the primary flow downstream from the stagnation point. The perpendicular component decreases during back flow, attaining negative values where the rotating fluid deviates from the wall. The point of sign reversal is located near the middle between the points of convergency and divergency. The region where the vi is positive, we call the stagnation region.(The region where vl is negative may be called as region of negative stagnation). The total forces which act on the wall are difficult to measure directly by measurement of pressure but they can be derived qualitatively from complementary experiments, where the wall of the branched tube is interrupted parallel to the line connecting the points of divergency and convergency by a narrow slit of 0.1 mm height and 5 mm depth. Under the same hydrodynamic condition as valid for Fig. 1 at Rel= 10 and Fig. 5, i.e. at fully developed dead water circulation, the fluid enters the slit where velocity components towards the wall are positive and leaves it where they are negative. Thus the fluid within the slit is included in the dead water circulation (see dashed lines in Fig. 5,b)The vI and v,, valid for each part of the
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Correlation between the localization of RBC-deposition and stagnation region (schematically)
a
b
FIGURE 5
Below: streamlines at Re- 80 of inflow and Re= 10 of outflow in the plane of branching (arrows indicate flow direction). Stagnation points 1 and 2 are recognizable by a streamline directed towards the wall and perpendicular to it. First stagnation point is at the edge of the orifice where the flow is divided: second stagnation point is identical with the divergency point (streamlines indicated by dashes can only be observed at tubes with porous walls). Diagramm above: distribution of hydrodynamic forces (proportional to v, ordinate) at the wall opposite to the orifice of the side branch. The dead water region is marked by the appearance of flow components perpendicular to the wall vl (con(dashed line) which tinuous line) and parallel components v are negative with respect to the main s44 earn direction. (The forces near the wall can be derived from the changes of the velocity components vI and v/i as a function of the distance from the wall; v/i represents also the wall shearing force). vI reaches maximum positive values at the point of divergency (stagnation point), maximum negative values at the convergency point (region of negative stagnation); see text for explanation of the inset and of the indication of RBC-Deposition.
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non-perforated wall were estimated from the angle under which the streamline intersects the wall and from the velocity at the point of intersection. The results of this experiment correspond to the diagram of Fig. 5,a.Analogous results are valid for the first stagnation region which is equal to the predilection-sites of the platelet deposition. DISCUSSION A
physical
hypothesis
of deposition
The localizations where depositions occur are characterized by the appearance of stagnation flow, i.e. by strong velocity components perpendicular to and towards the wall, which overcome the radial migration while in the same region the parallel components (wall shearing forces) attain low values. The basic physical mechanism of such hydrodynamically induced depositions thus seems to be sus risingly simple. In undisturbed flow, the wall is covered by a particle-free layer of fluid of (in Fig. 5 lower diagram indicated by a constant distance a dotted area from the wall). In a stagnation region, however, particle-rich fluid from the interior of the tube moves towards the wall and replaces the particle-free layer (in Fig. 5 indicated by a region where the dotted area touches the wall). In the first stagnation region, moreover, the particle concentration in the vicinity of the wall may also exceed that in the tube center. Where velocity components appear which are directed perpendicularly towards the wall, while at the same time the components parallel to the axis become small, interaction (mechanical, electrical etc.) of particles with the wall is enhanced. Provided the wall surface interacts more strongly with the particles than with the fluid, the movement of particles along the wall is more retarded than that of the surrounding fluid. Consequently the inflow of particles into the stagnation region becomes larger than the outflow and the particle concentration increases. If the particles are adherent, a deposition at the wall results. It should be mentioned that the region where the particle free layer is broadened (increased distance of the dotted area from the wall in Fig. 5,b) corresponds to the region of "negative stagnation flow". A flow containing V, of negative values probably increase the radial migration; the mechanism of this could not clearly be identified and shall not be discussed here. For the sake of simplification, only the events in the plane of branching were taken into consideration. Within planes parallel to the main tube axis and perpendicular to the plane of branching, regions of slow back-flow and positive values of vi can be observed, especially in the vicinity of the mouth of the side branch. Correlations between the mOVertEnt of platelets against the wall and the growth of platelet deposits analogous to those as described for RBC in the setond stagnation region are valid also for the events in this plane. Deposits of RBC tend to form flat layers of irregularly aggregated cells, whereas platelets almost form streak-shaped deposits. lo-fold velocities of stagnation flow and 6-fold
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times of growing are necessary for deposition of thrombocytes. are already carried At the same velocities, RBC-depositions away. These differences in morphological characteristics, hydrodynamic condition and in the duration of growth show, that - in spite of the same basic mechanism - different mechanisms are involved in the process of deposition for different particles. In contrast to deposits in branchings and curvatures of a river, where sedimentation is an important mechanism, gravity forces can be ruled out for the formation of deposits in arteries (4). Here the vl and the interaction may play a more dominant role as this is also the case for deposits of lightweight particles which at the wall of technical pipes (as for instance in the waste water canalization) occur in nearly the same region as the sediment-deposits do. The main aspects of the deposit-mechanism will now be discussed by using the following tentative formula D=
K f (VI, v//)
-A
(D) describes the enhancement of RBC-concentration over the Hct Of the original suspension in a definite fluid volume adjacent to the wall. (A) accounts for the decrease of RBC-concentration due to "radial migration" which will be effective in the same volume if vI=O. K means characteristic properties of the particle and the wall which have still to be identi1 stands for the unknown function of~e~hdS~~tel~ct,"=l-;!l~t:oV~'b~~~een v and v/i with respect to D, About the detailed structure of f'(v,, v/j) very little is known but some general statements can-be made. Provided that v '> 0 means towards the wall (VI and v/i are threshold values of these components) the following conditions are valid:
To- get positive values of D, vi has to exceed a certain-threshold to overcome the influence of term A. A more complete formula has to consider the absolute values of the velocity components. Especially the absolute value of v/i influences the the sign of D and by it the formation of deposits. A threshv/ has to be assumed with the property of obtainold value ing positive b values only for v/j < V-1 . Further information we expect from experiments under th e clear conditions of a symmetric stagnation flow because the distribution of in every plane is identical to those in the inv"~s,"2~aZ/d plane . In preliminary experiments the flow is directed perpendicularly towards a glass cover-plate. Circular RBC-depositions are formed, the center of which is identical with the stagnation point. The growth of depositions can be observed continuously during the experiments. Whether or not a particle is deposited at the wall by hydrodynamic forces depends on K, an empirical constant which is necessary to be introduced in describing the correlation between deposition and the hydrodynamic situation. The physical
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meaning of K is rather complex and cannot yet be defined exactly. Physical quantities involved in K are mainly: 1. surface properties of the particle and of the wall which determine the surface interaction; the mode of interaction (mechaby surnically by roughness or viscosity, electro-adsorption face charges of opposite sign etc.) is to be identified by further investigations; 2. properties of the particle (volume, shape, density) which are necessary for the moving fluid to bring the particles into immediate contact with the wall. The pathway of a particle (streak-line) differs from the pathway of the fluid (streamline) when the particle density differs from that of the fluid. If a critical STOKE's number is reached, the particles can actually reach the tube wall. In case of curved streamlines, as in a stagnation region of a dead water for instance, this is caused by the inertia of heavier particles which forces them to move in straighter lines than the streamlines. By impact on the wall the particles lose most of their kinetic energy and provided the v/i are too small to compensate the retardation, deposits may be formed. Our observations correspond qualitatively to the results of other authors who investigated the hydrodynamically induced deposition of corpuscular blood elements under still more simplified flow conditions. PETCHEK and WEISS (7) used axially symmetric stagnation point flow of fresh heparinized blood from a dog's carotid artery flowing against a glass wall. Comparison of their results with those described here yield qualitative agreement with regard to the hydrodynamic conditions that induce deposition. Disagreement occurs only in some details of interpretation of the results. The authors' opinion for instance, that streaklines do not touch the surface of the wall, but a "turbulent diffussion" is held responsible for deposition, does not agree with our observations. FORSTROM, VOSS and BLACKSHEAR (8) investigated the phenomena connected with the deposition of RBC from a cylindrical COUETTE flow. The inner surface of the flow is bounded by a porous wall. A secondary flow can thus be induced by a pressure gradient perpendicular to the wall. The deposition rate of particles increases with increasing flow velocity U perpendicular to the wall (corresponding to our V,) and decreases the higher 1. the velocity gradient S in the COUETTE flow (corresponding to the of our experiment) and the greater 2. the "repulsive efZY~ of the wall, dependent on S. In spite of these experiments are quite different from those described here, they yield, all in all, comparable conclusions. Only the author's statement that flow separation at the wall is a necessary condition for hydrodynamically induced deposition of platelets in medium and large arteries, contradicts to our observation of platelet deposition at the first stagnation point. CONCLUSION The deposits observed in these experiments attain a thickness of maximum 100 pm. Consequently, under the condition in living
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arteries the physical mechanism of deposition described in this paper may lead, at the most, to the formation of microthrombi and, because of this, to the initiation of atherosclerotic alterations, provided the process really starts with a thrombosis in accordance with the deposition hypothesis. Arterial thrombi, which produce the clinical and morphological symptoms of infarction on the other hand grow more rapid and cover, as a rule, a comparatively large part of the cross section or even lead to a total occlusion of the vessel. A rapid growth of such large arterial thrombi cannot be explained by the physical mechanism of deposition alone: an additional amplification of deposit growth has to be assumed for living arteries to explain the formation of occluding thrombosis in early stages of atherosclerosis. Further investigations with suspensions containing also other components of the coagulation system will show, whether or not and under which conditions a small deposit, as described in this paper, may overcome a certain threshold to activate the coagulation system thus inducing an amplification of deposit growth. ACKNOWLEDGEMENT I am greatly indepted to Dr. Armin Tippe and to Dr. June Mason for helpful discussion of the manuscript. REFERENCES 1.
2.
3.
4.
5. 6.
7. 8.
SCHIMERT, G., SCHIMMLER, W., SCHWALB, H. and EBERL.,J.: Die Coronarerkrankungen. In: Handb. inn.Med. 1X/3, 732, Springer Verlag, Berlin-Gottingen-Heidelberg, 1960. MULLER-MOHNSSEN, H.: Die Stromungsverhaltnisse in den Coronararterien und ihre,Bedeutung fiirdie Manifestierung der Coronarsklerose. In: Bad Oeynhausener Gesprgche iiber "Probleme der Coronardurchblutung" 2, 179, 1957. KINDER, J., KRATZER, M.: Geschwindigkeitsmessung im Inneren komplizierter Strijmungenmit Lichtschnittverfahren. Biomed. Technik 20, 11, 1975. BALDAUF, W., KRATZER, M., MULLER-MOHNSSEN, H.: Deposition of erythrocytes in models of arterial branchings perfused by pure erythrocyte suspensions. PfliigersArch.Ges.Physiol. 347 Suppl., R 11, 1974. BALDAUF, W.: Das Verhalten von Erythrozyten-Suspensionen in Verzweigungsstrdmungen. In preparation. BALDAUF, W., WURZINGER, L.J., SCHMID-SCHGNBEIN, H.: Hemodynamically induced blood platelet deposits in branched, curved, and constricted glass tubes. PfliigersArch.Ges. Physiol. 355 Suppl., R 38, 1975. PETSCHEK, H.E., WEISS, R.F.: Hydrodynamic problems in blood coagulation. AIAA paper No. 70 - 143, 1, 1970. FORSTROM, R.J., VOSS, G.O., BLACKSHEAR, P.L., JR.: Fluid dynamics of particle (platelet) deposition for filtering walls: Relationship to atherosclerosis. J. Fluid Engineering (Transact. ASME) 111, 168, 1974.
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EXPERIMENTAL RESULTS TO THE DEPOSITION HYPOTHESIS OF ATHEROSCLEROSIS H. Mtiller-Mohnssen Institute of Biology - GSF, De artment of Physiology D-8042 NeuherbergPMunich, Germany
(Received 8.12.1975; in reT,-ised form 10.3.1976. Accepted by Editor $3.Witte)
ABSTRACT A simplified model of a main predilection site of coronary atherosclerosis was perfused by suspensions of either erythrocytes (RBC) or thrombocytes (platelets) in order to prove the deposition hypothesis of atherosclerosis from a hydrodynamic point of view. The results show that RBC and platelets can be concentrated separately at particular regions of the wall by means of hydrodynamic mechanisms alone. In the same way, they can additionally be deposited, provided the particles are adherent. The sites where deposits occur are hydrodynamically characterized by the appearance of stagnation flow, i.e. of velocity components which are directed towards the wall and perpendicular to it while at the same time the velocity components parallel to the wall (wall shearing force) are small. These regions correspond to the location of atheromas and thrombosis within that branching of coronary artery which has a geometry similar to that of the model used in the experiments described. Therefore, these experiments suggest that hydrodynamic forces are involved in the mechanism of the first settlement of a wall-adherent thrombosis in unaltered living arteries. INTRODUCTION At flow velocities comparable to those found in muscular arteries the flow in tubes is undisturbed, i.e. parallel to the axis, if the tubes are straight, unbranched and have constant diameters. Predilection sites of atherosclerosis and thrombosis are characterized by the geometrical complexity of the vessel configuration and, consequently by a localized flow disturbance. Within these sites, atheromas and thrombosis are localized at
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certain parts of the vessel-cross section which are defined by their correlation to the specific geometrical parameters (center and radius of a curvature, intersection point and angle of a branching). Many observations support the view that hydrodynamic forces induce the pathogenic mechanism of atherosclerosis, but it has not yet been proven, whether a cause and effect relation exists, partly because of the difficulty in observing the pathological process from its very beginning in vivo. To answer the question, whether hydrodynamic forces participate in forming microthrombi, i.e. in the atherosclerogenetic mechanism supposed by the deposition (incrustation)hypothesis, experiments were designed to determine:
1. What are the hydrodynamic forces at the predilection sites? 2. Can hydrodynamic forces produce localized deposits of erythrocytes (RBC) and thrombocytes (platelets) at the inner surface of the arterial wall? METHOD The experiments were performed in geometrically simplified glass-models of the first septal branch from the anterior descendent coronary artery, because: 1. This is the site of the first appearance of atherosclerosis in man (1,2). 2. Branthings are the main predilection sites in general. 3. In branched flow the critical Reynolds number (Re rit) is observed to attain extremely low values and may, there Ei ore, be reached in living arteries. The glass-tubes were T-shaped with a main tube of 3 mm diam (300 mm length, branching in the center) and a side tube of 1.5 mm diam (100 mm length). The angle is comparable to the course angle of the real arterial branching, the diameters correspond to the diameters of the respective arteries as determined from stereoscopic arteriograms at post mortem. These models were mounted as a part of the flow apparatus in the following positions: 1. With the branching plane (connecting the axis of both tubes) horizontal; this position was used in most of the hydrodynamic measurements. 2. With the main tube vertical, to eliminate the effect of gravity on the deposition of RBC and platelets at the wall of the main tube. Flow apparatus. A 10 1 reservoir is mounted above the branching section of the model. By a flow-over, the level Of the liquid within the reservoir is held constant, ensuring the constancy of the hydrostatic pressure necessary to produce a steady inflow to the model. In addition, to obtain nearly constant input flow-rate Q. (ml s-I) into the main tube of the model, a high flow resistance was put between reservoir and model. The resistance to flow was adjusted such that the influence of the small resistance fluctuations on Qo caused by the flow disturbance within the model could be neglected. These experiments were, therefore, performed at "constant" Qo. All the average flow rates, Qor in the main tube upstream from the branching, Qll in the main tube downstream the branching and Q2, in the
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side tube were adjusted by valves. Qo, Ql, Q2 were each monitored by floating flow-meters, inserted a distance of at least 300 mm from the branching; in the same regions the average hydrostatic pressure was measured by Statham elements. 1500 mm downstream from the branching, the liquid flowed out freely and was collected separately from each branch. Ql and Q2 was measured again by the rising rate of the liquid level in the collecting vessels. From here the liquid was pumped back to the reservoir. Because the hydrodynamical situation differs from crosssection to cross-section, the hydrodynamic events were investigated "morphologically". This was done only for the main tube since the pathological alterations appear mostly in the main artery. After macroscopic observation of the flow phenomena by means of conventional techniques (dye-injection, polarisation-optical examination using a birefringent fluid, laser-doppler anemometry), microscopic techniques were used to examine the paths of single tluid particles (streamlines). Streamlines were recorded using a fluid of the same refractive index as glass (94% Dimethyl-sulfoxid, 6% water ) labelled with spherical polystyrol particles of collodial size ( 5 Urn diam, 105 particles/ml) ; these microspheres are assumed to produce only negligibly small alterations of flow. To make the movement of the fluid visible, the sample was illuminated perpendicular to the axis of a microscope (dark-field illumination) by a series of 10 laser pulses of 10 IJ.Sduration each, separated by 1 + 1000 IJ.S(3). By means of a special optical arrangement, a thin slice of the sample was illuminated. Every particle moving in the plane of this slice writes a dashed line on a photographic film with the length of the intervals between the dashes proportional to the velocity and the shape of the curve describing the path of the particle. The ratio of dashes to flashes per series allows an estimation of the average angle between the path and the illuminated plane. Therefore, not only the velocity profiles but also the real path of a particle can be derived from these photographs. The components composing the physical system were exchanged step by step for those involved in a living system. (In separate experiments not described here, the tube wall was replaced by elastic and also by porous walls to prove the infiltration hypothesis. A pulsating flow will be used instead of a stationary, if the branched flow under stationary inflow conditions will be better known as it is the case now).In the present experiments model particles are replaced by RBC and platelets, DMSO and water by electrolyte solutions, serum etc.. The paths of single RBC and platelets (streaklines) and the deposition of these particles at the wall were investigated by the laser technique, but also by conventional dark-field microscopy. Suspensions: 1. Human RBC (2% Hct) in isosmotic NaCl-solution, 5% human plasma added. 2. Same as 1 but 1 g% Polyvinylprolidone added, to make the RBC adhaesive. 3. ADP-excited bovine platelets with the same solvent as mentioned above. The preparation of isolated platelets will be described elsewhere
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et al, to be published). RESULTS
Preliminary
hydrodynamic
experiments
In the first experiments, the flow of the main tube in the plane of branching was investigated (3). The average velocity in the influx tube (Qo) is kept constant at 80 mm/s (Re, = 88). The volume flow in the side-branch (Qz) was increased stepwise and consequently the flow in the main tube (Ql) downstream of the branching was diminished. The dashed lines in Fig. 1 show the paths of the fluid during 10 ms illumination. If the flow in the side-branch is stopped, the flow is parallel to the axis - except for negligible small disturbances in the orifice region - with the maximum velocity at the axis: the velocity profile is a rotation-symmetric paraboloid. When the flow in the side-branch is started, only the fluid from near the wall with the lowest kinetic energy, flows into the side-branch. Whereas the faster main stream deviates from the
FIGURE
1
Streamlines of flow in a branched tube at Re = 88 of inflow. Re-numbers of branch flow increases from theotop (zero) to bottom, thus the Re-number of the down-stream part of the main tube decreases as indicated at the right. (Experiment of KRATZER, KINDER).
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axis-parallel flow the least, the higher the kinetic energy. Therefore, the line of maximum velocity is deviated from the tube axis more the higher the volume flow in the side-branch and almost touches the main tube wall tangentially in the region downstream the mouth of the side-branch. Near the edge of the orifice, where the flow is divided, a region can be found where streamlines are directed toward the wall and perpendicular to it. From this "first stagnation point" some part of the fluid moves downstream the main tube and some part moves back into the side branch.(A stagnation point separates two areas where, in the flow near the wall, the velocity components parallel to the tube axis are opposite in sign). Most of the back flow glides to both sides in a curve, tangentially along the Wall of the main tube and reaches the mouth of the side branch laterally. These parts of back-flow leave the plane of branching and cannot be seen in Fig. 1. A fast flow is found downstream to the mouth of the sidebranch, a Slow flow in the opposite half part of the same crosssection. Hence the velocity profile downstream of the branching becomes asymmetrical and contains a point of inflection. In this region, the shearing forces overcome the viscosity which is responsible for inner cohesion of the fluid: the flow disrupts. The main flow separates from the wall for a short distance, forming a water jet which surrounds a dead water region at Rel= 10. Here a circulating flow is driven indirectly by the main stream via shearing forces. In the axial-parallel flow of the main tube, upstream and far downstream to the point of branching, as well as in the water jet close downstream to the mouth of branching, the fluid moves down the pressure gradient supplied in the experiment (primary flow). In the dead water a circulatory flow arise which is not driven directly by the main pressure gradient but indirectly by the primary flow via shearing forces being effective in the boundary layer between the dead. waterregion and the jet (secondary flow). The velocity profile within the dead water (Fig. 5 inset) taken in the plane of branching clearly demonstrates the mechanism of inducing and maintaining a dead water circulation. Within the dead water the velocity is highest at its boundary with the water jet and decreases with increasing distance from this boundary towards the center of the circulatory flow (Fig. 5 inset). At the opposite, i.e. the wall side border of the dead water the velocity of the outermost layer of the fluid, touching the wall, is zero and increases with increasing distance from the wall towards the circulation center. At the jet side border of the dead water the velocity gradient behaves inversily compared to the velocity gradient at the wall, indicating that the dead water circulation is driven on by the jet and is slowed down by the wall. Since the dead water can be approximated by a separated volume of fluid, the driving force induces a back flow in the region opposite to its point of onset, this is at the wall. The mechanism of dead water circulation has been sometimes illustrated by the rotation of a ball in a ball bearing. At higher degrees of disturbance than for separation of flow from the wall, regular oscillations of 10 f 100 cycles per sec-
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ond and a wavelength of 3 + 5 mm arise in the interface between the dead water and the jet (comparable to the generation of oscillations in a flute, where a flow is divided at an acute edge). The oscillations change over into irregular turbulences at still ; the ncn-stationary higher disturbance (the flute is"overblown" flow phenomena as oscillations and turbulence are not demonstra(wallted in Fig. 1). The start of each degree of flow-alteration not depend on a critseparation, oscillation and turbulence)does ical Reynolds number, but on a critical difference between the Reynolds numbers upstream(Reo) and downstream (Rel) of the branching: (Re, - Rel)crit = (Re2)crit is nearly constant in the range of Re, 100 + 1400. Close upstream from the region where the primary flow reattaches itselfto the wall, streamlines, which come from the interface between the circulating dead water and the jet, are directed perpendicularly towards the wall. In this "second stagnation point" the flow is divided and diverges into opposite directions (point of divergency). Outer streamlines of the jet belonging to the interface between the jet and the dead water are directed downstream, whereas the accelerated dead water drifts towards the wall where the overwhelming part is forced to move backward (upstream) along the wall. During the back flow, the velocity of circulation decreases until it reaches the region where the primary flow separates from the wall (point of convergency). Here it is turned into main flow direction and accelerated again. Erythrocyte
deposition
In a second series of experiments the same model was perfused by suspension of human RBC (Suspension 1, see 4,s) at Re,'90. Fig. 2 shows the distribution of RBC in the region adjacent to the wall, opposite to the orifice. If the flow in the sidebranch is interrupted, - the main flow thus parallel to the axis - an RBC-free layer of a 100 urn thickness is established at the wall probably due to a process known as "radial-migration". At 10~ volume flows in the side branch the thickness of the RBC-free layer is increased in the regjon of low velocity opposite to the orifice. If at higher degrees of flow disturbance the dead water region is developed, the RBC-free layer vanishes at first in the region of the stagnation point. At higher velocities of the circulation flow, the broadened RBCfree layer is over more than half the length of the dead water region, replaced by RBC-rich fluid, which is flowing back from the stagnation point. The zone with decreased thickness of RBCfree layer is clearly separated from the region, close downstream to the point of divergency, where the thickness of RBCfree layer is still enlarged. 10 s after onset of flow in the side-branch, the new distribution reaches stationary values, If the RBC are not adhesive, the increase of concentration at the wall is reversible - that is, the normal RBC-distribution is restored if the flow in the side-branch is interrupted and this way, the hydrodynamic disturbance is eliminated. But if the RBC are made adhesive (Suspension 2) they stick to the wall in the stagnation region, where they aggre-
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gate forming leaflets of irregular thickness (2 t 20 urn diam) covering a defined area of the wall surface. These RBC depositions can only be removed by increasing the flow-velocity (Reo290) as a result of higher shearing forces at the wall (see under "The hydrodynamic situation in the regions of deposition").
FIGURE 2 Distribution of RBC in a dead-water region of a branched flow at different degrees of flow disturbance. Suspension 1 (human RBC, 2% Hct) is used as fluid; same model and same experimental procedure as in Fig. 1. Only the section of the main tube opposite to the orifice, indicated in the inset, is shown. The vertical bars indicate location and size of the side branch (bright field illumination, RBC-depleted regions of fluid appear bright). a) Rel = Re, (Q2=0); flow is parallel to the axis. The white band parallel to the wall shows that the RBC-free layer is of constant thickness. c) Beginning of dead water circulation; the thickness of RBC-free layer is increased in the region where the flow separates from the wall (negative values of VA, see Fig. 5) and decreases in th$ stagnation region (positive values of VI) c - e) Back-flow carries RBC along the wall surface from the stagnation point into the stagnation region (v, >O) of the dead water. At Rel = 71, the border between the region where the RBC-free layer is broadened and where it disappears, becomes clearly visible. (Experiment of BALDAUF).
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FIGURE 3 RBC-deposition produced by stagnation flow within the dead water analog to Fig. 2 (Suspension 2). The picture was taken after diminishing Q2; This way the disturbance of flow is reduced to the stage where only broadening of RBC-free layer occurs (experiment BALDAUF). The main result of this experiment is, that the hydrodynamically induced RBC-deposition is localized in the region of the second stagnation point, which corresponds to the predilection site of thromboses and atheromas. At the first stagnation point no deposits were observed. Thrombocyte-deposition In another series of experiments (6) a thrombocyte suspension was used as fluid. If the inflow Re-number is the same as in the RBC-experiment described above (Re,= 901, the platelet concentration increases in the stagnation region of the dead water - just like the RBC - concentration at the same hydrodynamic condition - but desposition at the wall occurs only at much higher velocities of the stagnation flow. Deposition starts, therefore, in the stagnation region at the edge of the orifice where the velocity of stagnation flow is 40 mm/s compared to 2.5 mm/s of the stagnant flow of the dead water. The process starts with the deposition of single platelets 30 t 40 s after the onset of the flow disturbation. By apposition of other platelets, mainly at the lee-side of platelets already adhered, the deposition grows and this predominantly in the back flow direction thus forming streaks which follow the streamlines near the TaTall.After another 60 S, the growth of deposition is termina.ted 'Fig. 4). (Because these streamlines are spiral, they cannot be observed in the plane of branching: they were made visible by illuminating slices of the fluid which touch the inner surface of the wall tangentially). The hydrodanamic The distribution
situation
in the regions
of the hydrodynamic
of deposition
force components
at the
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FIGURE 4 Thrombocyte deposition in the region of first stagnation point at the wall of a branched tube (dark field illumination; the streak shaped depositions occur bright. See text for further explanation; experiment QnLDAUF et al 1. wall within the dead water region can be derived approximately from the velocity-field visualized by photographs as in Fig. 1. This was done as an example for the RBC deposition at the second stagnation region (Fig. 5). In terms of velocity gradients (v), the stagnation point is characterized by a maximum component towards the wall and perpendicular to it (vl solid line). The stagnation point separates two regions in which the direction of the parallel components is opposite (v/j dashed line). In both regions, the parallel components increase with the distance from the stagnating point, reaching a limited value which is, of course, much smaller in the dead water region than in the primary flow downstream from the stagnation point. The perpendicular component decreases during back flow, attaining negative values where the rotating fluid deviates from the wall. The point of sign reversal is located near the middle between the points of convergency and divergency. The region where the vi is positive, we call the stagnation region.(The region where vl is negative may be called as region of negative stagnation). The total forces which act on the wall are difficult to measure directly by measurement of pressure but they can be derived qualitatively from complementary experiments, where the wall of the branched tube is interrupted parallel to the line connecting the points of divergency and convergency by a narrow slit of 0.1 mm height and 5 mm depth. Under the same hydrodynamic condition as valid for Fig. 1 at Rel= 10 and Fig. 5, i.e. at fully developed dead water circulation, the fluid enters the slit where velocity components towards the wall are positive and leaves it where they are negative. Thus the fluid within the slit is included in the dead water circulation (see dashed lines in Fig. 5,b)The vI and v,, valid for each part of the
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Correlation between the localization of RBC-deposition and stagnation region (schematically)
a
b
FIGURE 5
Below: streamlines at Re- 80 of inflow and Re= 10 of outflow in the plane of branching (arrows indicate flow direction). Stagnation points 1 and 2 are recognizable by a streamline directed towards the wall and perpendicular to it. First stagnation point is at the edge of the orifice where the flow is divided: second stagnation point is identical with the divergency point (streamlines indicated by dashes can only be observed at tubes with porous walls). Diagramm above: distribution of hydrodynamic forces (proportional to v, ordinate) at the wall opposite to the orifice of the side branch. The dead water region is marked by the appearance of flow components perpendicular to the wall vl (con(dashed line) which tinuous line) and parallel components v are negative with respect to the main s44 earn direction. (The forces near the wall can be derived from the changes of the velocity components vI and v/i as a function of the distance from the wall; v/i represents also the wall shearing force). vI reaches maximum positive values at the point of divergency (stagnation point), maximum negative values at the convergency point (region of negative stagnation); see text for explanation of the inset and of the indication of RBC-Deposition.
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non-perforated wall were estimated from the angle under which the streamline intersects the wall and from the velocity at the point of intersection. The results of this experiment correspond to the diagram of Fig. 5,a.Analogous results are valid for the first stagnation region which is equal to the predilection-sites of the platelet deposition. DISCUSSION A
physical
hypothesis
of deposition
The localizations where depositions occur are characterized by the appearance of stagnation flow, i.e. by strong velocity components perpendicular to and towards the wall, which overcome the radial migration while in the same region the parallel components (wall shearing forces) attain low values. The basic physical mechanism of such hydrodynamically induced depositions thus seems to be sus risingly simple. In undisturbed flow, the wall is covered by a particle-free layer of fluid of (in Fig. 5 lower diagram indicated by a constant distance a dotted area from the wall). In a stagnation region, however, particle-rich fluid from the interior of the tube moves towards the wall and replaces the particle-free layer (in Fig. 5 indicated by a region where the dotted area touches the wall). In the first stagnation region, moreover, the particle concentration in the vicinity of the wall may also exceed that in the tube center. Where velocity components appear which are directed perpendicularly towards the wall, while at the same time the components parallel to the axis become small, interaction (mechanical, electrical etc.) of particles with the wall is enhanced. Provided the wall surface interacts more strongly with the particles than with the fluid, the movement of particles along the wall is more retarded than that of the surrounding fluid. Consequently the inflow of particles into the stagnation region becomes larger than the outflow and the particle concentration increases. If the particles are adherent, a deposition at the wall results. It should be mentioned that the region where the particle free layer is broadened (increased distance of the dotted area from the wall in Fig. 5,b) corresponds to the region of "negative stagnation flow". A flow containing V, of negative values probably increase the radial migration; the mechanism of this could not clearly be identified and shall not be discussed here. For the sake of simplification, only the events in the plane of branching were taken into consideration. Within planes parallel to the main tube axis and perpendicular to the plane of branching, regions of slow back-flow and positive values of vi can be observed, especially in the vicinity of the mouth of the side branch. Correlations between the mOVertEnt of platelets against the wall and the growth of platelet deposits analogous to those as described for RBC in the setond stagnation region are valid also for the events in this plane. Deposits of RBC tend to form flat layers of irregularly aggregated cells, whereas platelets almost form streak-shaped deposits. lo-fold velocities of stagnation flow and 6-fold
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times of growing are necessary for deposition of thrombocytes. are already carried At the same velocities, RBC-depositions away. These differences in morphological characteristics, hydrodynamic condition and in the duration of growth show, that - in spite of the same basic mechanism - different mechanisms are involved in the process of deposition for different particles. In contrast to deposits in branchings and curvatures of a river, where sedimentation is an important mechanism, gravity forces can be ruled out for the formation of deposits in arteries (4). Here the vl and the interaction may play a more dominant role as this is also the case for deposits of lightweight particles which at the wall of technical pipes (as for instance in the waste water canalization) occur in nearly the same region as the sediment-deposits do. The main aspects of the deposit-mechanism will now be discussed by using the following tentative formula D=
K f (VI, v//)
-A
(D) describes the enhancement of RBC-concentration over the Hct Of the original suspension in a definite fluid volume adjacent to the wall. (A) accounts for the decrease of RBC-concentration due to "radial migration" which will be effective in the same volume if vI=O. K means characteristic properties of the particle and the wall which have still to be identi1 stands for the unknown function of~e~hdS~~tel~ct,"=l-;!l~t:oV~'b~~~een v and v/i with respect to D, About the detailed structure of f'(v,, v/j) very little is known but some general statements can-be made. Provided that v '> 0 means towards the wall (VI and v/i are threshold values of these components) the following conditions are valid:
To- get positive values of D, vi has to exceed a certain-threshold to overcome the influence of term A. A more complete formula has to consider the absolute values of the velocity components. Especially the absolute value of v/i influences the the sign of D and by it the formation of deposits. A threshv/ has to be assumed with the property of obtainold value ing positive b values only for v/j < V-1 . Further information we expect from experiments under th e clear conditions of a symmetric stagnation flow because the distribution of in every plane is identical to those in the inv"~s,"2~aZ/d plane . In preliminary experiments the flow is directed perpendicularly towards a glass cover-plate. Circular RBC-depositions are formed, the center of which is identical with the stagnation point. The growth of depositions can be observed continuously during the experiments. Whether or not a particle is deposited at the wall by hydrodynamic forces depends on K, an empirical constant which is necessary to be introduced in describing the correlation between deposition and the hydrodynamic situation. The physical
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meaning of K is rather complex and cannot yet be defined exactly. Physical quantities involved in K are mainly: 1. surface properties of the particle and of the wall which determine the surface interaction; the mode of interaction (mechaby surnically by roughness or viscosity, electro-adsorption face charges of opposite sign etc.) is to be identified by further investigations; 2. properties of the particle (volume, shape, density) which are necessary for the moving fluid to bring the particles into immediate contact with the wall. The pathway of a particle (streak-line) differs from the pathway of the fluid (streamline) when the particle density differs from that of the fluid. If a critical STOKE's number is reached, the particles can actually reach the tube wall. In case of curved streamlines, as in a stagnation region of a dead water for instance, this is caused by the inertia of heavier particles which forces them to move in straighter lines than the streamlines. By impact on the wall the particles lose most of their kinetic energy and provided the v/i are too small to compensate the retardation, deposits may be formed. Our observations correspond qualitatively to the results of other authors who investigated the hydrodynamically induced deposition of corpuscular blood elements under still more simplified flow conditions. PETCHEK and WEISS (7) used axially symmetric stagnation point flow of fresh heparinized blood from a dog's carotid artery flowing against a glass wall. Comparison of their results with those described here yield qualitative agreement with regard to the hydrodynamic conditions that induce deposition. Disagreement occurs only in some details of interpretation of the results. The authors' opinion for instance, that streaklines do not touch the surface of the wall, but a "turbulent diffussion" is held responsible for deposition, does not agree with our observations. FORSTROM, VOSS and BLACKSHEAR (8) investigated the phenomena connected with the deposition of RBC from a cylindrical COUETTE flow. The inner surface of the flow is bounded by a porous wall. A secondary flow can thus be induced by a pressure gradient perpendicular to the wall. The deposition rate of particles increases with increasing flow velocity U perpendicular to the wall (corresponding to our V,) and decreases the higher 1. the velocity gradient S in the COUETTE flow (corresponding to the of our experiment) and the greater 2. the "repulsive efZY~ of the wall, dependent on S. In spite of these experiments are quite different from those described here, they yield, all in all, comparable conclusions. Only the author's statement that flow separation at the wall is a necessary condition for hydrodynamically induced deposition of platelets in medium and large arteries, contradicts to our observation of platelet deposition at the first stagnation point. CONCLUSION The deposits observed in these experiments attain a thickness of maximum 100 pm. Consequently, under the condition in living
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arteries the physical mechanism of deposition described in this paper may lead, at the most, to the formation of microthrombi and, because of this, to the initiation of atherosclerotic alterations, provided the process really starts with a thrombosis in accordance with the deposition hypothesis. Arterial thrombi, which produce the clinical and morphological symptoms of infarction on the other hand grow more rapid and cover, as a rule, a comparatively large part of the cross section or even lead to a total occlusion of the vessel. A rapid growth of such large arterial thrombi cannot be explained by the physical mechanism of deposition alone: an additional amplification of deposit growth has to be assumed for living arteries to explain the formation of occluding thrombosis in early stages of atherosclerosis. Further investigations with suspensions containing also other components of the coagulation system will show, whether or not and under which conditions a small deposit, as described in this paper, may overcome a certain threshold to activate the coagulation system thus inducing an amplification of deposit growth. ACKNOWLEDGEMENT I am greatly indepted to Dr. Armin Tippe and to Dr. June Mason for helpful discussion of the manuscript. REFERENCES 1.
2.
3.
4.
5. 6.
7. 8.
SCHIMERT, G., SCHIMMLER, W., SCHWALB, H. and EBERL.,J.: Die Coronarerkrankungen. In: Handb. inn.Med. 1X/3, 732, Springer Verlag, Berlin-Gottingen-Heidelberg, 1960. MULLER-MOHNSSEN, H.: Die Stromungsverhaltnisse in den Coronararterien und ihre,Bedeutung fiirdie Manifestierung der Coronarsklerose. In: Bad Oeynhausener Gesprgche iiber "Probleme der Coronardurchblutung" 2, 179, 1957. KINDER, J., KRATZER, M.: Geschwindigkeitsmessung im Inneren komplizierter Strijmungenmit Lichtschnittverfahren. Biomed. Technik 20, 11, 1975. BALDAUF, W., KRATZER, M., MULLER-MOHNSSEN, H.: Deposition of erythrocytes in models of arterial branchings perfused by pure erythrocyte suspensions. PfliigersArch.Ges.Physiol. 347 Suppl., R 11, 1974. BALDAUF, W.: Das Verhalten von Erythrozyten-Suspensionen in Verzweigungsstrdmungen. In preparation. BALDAUF, W., WURZINGER, L.J., SCHMID-SCHGNBEIN, H.: Hemodynamically induced blood platelet deposits in branched, curved, and constricted glass tubes. PfliigersArch.Ges. Physiol. 355 Suppl., R 38, 1975. PETSCHEK, H.E., WEISS, R.F.: Hydrodynamic problems in blood coagulation. AIAA paper No. 70 - 143, 1, 1970. FORSTROM, R.J., VOSS, G.O., BLACKSHEAR, P.L., JR.: Fluid dynamics of particle (platelet) deposition for filtering walls: Relationship to atherosclerosis. J. Fluid Engineering (Transact. ASME) 111, 168, 1974.