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Dynamics of blood flow in stenotic vascular lesions
Fundamentals of clinical
Dynamics
cardiology
of Masd
Simon Rodbard, M.D., Duurte, C&if.
flew
waseuIQc
brief statement of normal arterial dynamics will serve as the basis for an analysis of the dynamics of stenotic vascular lesions. caliber
A normal artery serves as a conduit for several times the normal resting flow, with only minimal losses of pressure due to friction (Fig. 1). The volume flowing through a normal artery is determined nearly entirely by the degree of openness, i.e., conductance (rate of flow/drop in pressure, i.e., the inverse of resistance) of the peripheral vessels.* When conductance increases, as in the hyperemia of exercise, the pulsations of the vessel walls are enhanced, as revealed by palpation of the arteries, or by oscillometry.2 Since flow is laminar, vibrations are not produced and no bruit is heard. Variations in the viscosity of the blood introduce no significant increase in losses of energy in such large vessels, although viscosity may affect flow through the arteriolar, venular, and capillary segments. Stenosis
Narrowed vessels are the sites of drops in pressure, vibrations, and the stimulation of processeswhich tend to eliminate these dynamic factors. Arteries may be narro\ved l)y intravasc-ular plaques or collarlike narrowings, 1,).
impingement of ligaments or spurs which abut on the vessel wall (Hardin), or even by excessive force applied against the vessel by a stethoscope bell (Fig. 2). Transitory stenosis by means of compression of arteries by a sphygmomanometer cuff is utilized clinically in the measurement of the blood pressure. Efect of peripheral vascular conductance. The extent of the disturbance produced at an arterial narrowing varies with the vascular conductance of the tissues which the vessel supplies (Table I). When the flow of blood through the tissue is minimal, as in resting organs, a slight stenosis introduces no significant impedance to the rate of flow to the tissues, the drop in pressure at the orifice is negligible, and murmurs are absent. Autoregulation. A persistent rise or fall in arterial perfusion pressure triggers intrinsic mechanisms in muscle, brain, kidney, and other tissue@ which adjust the peripheral vascular conductance so that the rate of blood flow remains unaffected (autoregulation). Thus, the fall in perfusion pressure introduced by a partial narrowing of an artery is associated with an increase in the conductance ot the tissue, with the result that the rate of delivery of blood remains unaffected. Such autoregulatory mechanisms can rounteract the effects of slight to moderate stenosis on the rate of blood flow to resting
This study was aided by tirant No. HE 08721 from the National Heart Institute, Received for publication June 2. 1966. *IXrector of Cardiology and Cardiac Research. City of Hope Medical Center. Professor of Medicine, University of Soutllern California School of Medicine.
698
ldawws
Ph.D.*
A
Normal
in stewtic
United
States
Duarte. Calif Los Angele:.
Public and Calif.
Healtll
Servicr.
,ksociate
Clinical
Volume
Nwnbcr
72 5
Dynamics
of blood jlow in stenotic vasculur lesions
699
THE NORMAL ARTERY CAN CONDUCT SEVERAL TIMES THE RESTING FLOW WITHOUT SIGNIFICANT ENERGY LOSSES
FLOW RATE IS DETERMINED
8Y PERIPHERAL VASCULAR CONDUCTANCE
Fig. 1. Laminar flow in a large vessel. Flow through a vessel of normal caliber results in minimal losses of energy. No murmurs are produced. The rate of flow in such a system is determined by the conductance of the peripheral vessels and not by the characteristics of the vessel itself.
VESSEL NARROWING MAY RESULT FROM
Fig. 2. Vascular narrowing may result from intrinsic pathology of the vessel (upper two drawings), or as a result of deformation from without, by ligaments or pressure from a stethoscope (ZGWW two drawings).
vessels, even though the pressure in the arterial segment beyond the narrowing is less than normal. An increase in activity of the tissue opens the vascular beds more widely, and the pressure in the distal segment falls. Efect of the narrowing. A narrowing impedes flow, and a drop in pressure across
Fig. 3. Effect of a stenosis on the distribution of hydraulic energy (above) in a vessel (b&w). At the upstream segment, most of the energy is evident as pressure (black), a smaller amount is in the kinetic energy of velocity (da&d lines), and a small amount has already been converted to heat (stip$ed area) by friction, especially due to vortex formation. At the orifice (shown in drawing of vessel) the velocity increases sharply at the expense of pressure, and a significant portion is lost as heat. Beyond the orifice the pressure rises, although not to the prestenosis level, and velocity approaches normal values. The amount of energy converted to heat increases progressively.
the orifice becomes evident. Flow through a stenotic orifice varies with the square root of the difference between the proximal and distal pressures,’ and with the orifice area. The rate of flow does not keep pace with the drop in pressure. Thus, a doubling of the drop in pressure across an orifice increases the rate of flow by only 40 per cent ( 4 200 per cent = 140 per cent). When the vascular bed opens widely and the rate of flow increases greatly, as after muscular exercise (Fig. 3), the stenosis becomes the limiting factor in the delivery of blood to the active tissues. The drop in pressure at the orifice and the velocity of the stream increase, and vibrations are generated. However, as Ejrups has shown, the oscillations of the poststenotic artery decrease. This effect, considered by some workers to be due to arterial spasm, can be accounted for entirely on the basis of the decrease in the oscillations in pressure in the poststenotic arterial segment2 associated with the increased peripheral vascular conductance of exercise.g In moderate narrowing of an arterial orifice, the drop in pressure across the stenosis is of greater magnitude, the duration of the resulting murmur increases,
Pressure drop, velocity, and muiwws Degree of
___
narrowing Resting
tissue
I
At-live
tissue
I
None Slight Moderate Severe Complete
0 0 0 Systolic
Very
active tissue
1
0 0 Systolic Systolic and diastolic
0 Systolic Systolic and diastolic Systolic and diastolic ischemic symptoms (fatigue, pain)
Ischemia (murmurs are due to collaterals)
and the intensity and pitch exhibit crescendos as the aortic pressure risesin systole. During the falling arterial pressure of diastole, the murmur decreasesin intensity and pitch.‘O In severe stenosis, a systolic murmur may be present even when the tissue is at rest. With the increased conductance of exercise the murmur is prolonged and extends into diastole. When the blood flow is inadequate to wash away the end products of metabolism, localized pain or fatigue and other ischemic disturbances become manifest. With complete obstruction of an artery, pulsations are absent beyond the narrowing, and the murmur is no longer heard. Collaterals. The marked difference in pressure at the junction of normal and ischemic tissues serves to increase flow through existing intercommunicating vessels and to stimulate the development of new vessels. These enlarge gradually, in accord with the flow through them. These collaterals announce their inadequacy in the form of localized murmurs. When these collateral vessels are of suficient size to deliver an adequate rate of blood flow so that the drop in arterial pressure is eliminated, the stenosed artery will decrease in size, as discussed below, and one of the new vessels will become the primary vessel of the tissue. Ij’enous hums. The laws that adjust vascular adequacy to the rate of flow operate in the veins as well as in the arteries. An inadequacy of the venous collecting
networks and of the major venous channels is manifested in increases in pressure gradients, flow velocity, and the production of vibrations.ll “Venous hums” are not uncommon in children during the rapid growth phase, and when the general increase in metabolic activity enhances the volume of the venous return. The disproportion between vascular caliber and rate of blood flow is especially evident when the child is in the upright position; the drop in pressure from the veins draining the head to the subatmospheric pressure in the thorax may collapse the veins at the clavicle sufficiently so that murmurs and hums are heard over these vessels.13 Light pressure over the veins at the clavicle or placement of the subject in a reclining position reduces the drop in pressure and eliminates the venous hum, thereby readily differentiating the hum from arterial bruits originating in the adjacent arteries. The high right atria1 pressure of right heart failure also distends the veins and inhibits the hum. Venous hums are also heard at other sites at which the venous network is inadequate. For example, hums may be heard over the abdomen when the hepatic blood flow is deviated through subcutaneous collaterals. A similar dynamic pattern is heard during the period of rapid gestational growth of the uterus and its contents. The hums are enhanced with the drop in pressure during the inspiratory fall in pressure in the thorax and superior vena cave. The murmurs may diminish
Volume Number
72 5
Dynamics
with the reduction in the drop in pressure as the thoracic pressure rises during expiration. The growth of anastomotic venous channels eliminates the drop in pressure and the bruit. Flow through anastomoses. When arteries which supply different vascular beds are connected by anastomoses, the rate of flow through each of the arteries is affected by the relative conductance of the two beds,r3 and by the size of the anastomoses. When one of the vascular beds opens widely, the increased rate of runoff through it lowers the pressure in its main supplying artery. The higher blood pressure in the anastomosing artery will then flow into the vascular bed which has the higher conductance, and the tissue of lower conductance may receive an inadequate supply of blood. Thus, in a limb with a partially stenotic arteria1 supply, opening of the cutaneous vessels by the application of heat to the skin deviates blood from the muscles, which are thereby rendered even more ischemic. Attention has been called recently to the ischemic symptomatology which results when a narrowing at the root of the subclavian artery limits the rate of the flow of blood to the arm (Fig. 4). During rest, no effects may be noted. However, the marked increase in vascular conductance produced in the muscles during exercise of the arm can drain off some of the blood from the circle of Willis, Exercise of the arm may thus precipitate an episode of cerebral ischemia, an effect known as ’ ‘su bclavian steal. ’ ‘14 Effects of this type which are more generally appreciated include the deviation of aortic blood through a ductus arteriosus and thence through the high conductance of the pulmonary vascular bed (Table II). Coarctation of the aorta beyond the ductus increases the deviation and leads to ischemia of the vessels of the lower limbs. When the blood pressure in the two arms differs by more than a few millimeters of mercury, palpation may establish a significant asynchrony of the pressure waves at the radial or brachial arteries. The indirect measurement of blood pressure in the two arms, or of the delay in the transmission of the arterial pressure wave quantifies the severity of such an obstruc-
of blood jlow in stenotic vascular lesions
701
At Rest
Fig. 4. Steal syndrome. At rest (upper left), flow through the aorta (horizonbl arrow) is distributed among the subclavian (left) and carotid arteries. The carotid (u@er) vessel and vertebral arteries supply the brain through the circle of Willis. In the drawing at right, a severe stenosis is shown in the subclavian artery. When exercise opens the vessels of the arm, some of the blood moving toward the head is deviated across the circle of Willis to the vertebral artery and runs off into the high conductance of the vessels of the arm. If the blood flow to the brain is compromised, symptoms of cerebral ischemia will ensue.
Table II. “Steal”
syndromes
Stenosis
1. Subclavian + arm exercise -~2. Femoral arterial + heating of skin --------Leg 3. Coarctation of aorta + ductus arteriosus
Ischemia
-Cerebral muscles *Lower
extremities
tion. We have observed a number of patients with marked differences in pressure, timing, and duration of the arterial Korotkoff sounds in the two arms. However, the presence of such murmurs and other evidence of stenosis of the arteries to an arm is not necessarily associated with cerebral ischemia or the imminence of a cerebrovascular occlusion. The gradual modifications in vascular caliber which are induced by hydrodynamic forces may account for the benign course of this ahnormality in some patients.
Hydrodynamic vascular caliber
forces
and
The occasional tendencies for the progression of a localized stenosis,15-17the proliferation of collateral vessels, and the development of poststenotic dilatations have been attributed to the operation of hydrodynamic forces. The effects of the pressures on the walls of the vessels have excited the continuing interest of physiologists, pathologists, and clinicians. In earlier analyses, this laboratory had discussed the possibility that, at drops in pressure and increased velocities, the ingrowth of the vascular lining with a resultant progression of the stenotic tendency is facilitated. This thesis has subsequently been restated by others. 18*lgHowever, although the pressures in all of the arteries of the body are approximately equal, the calibers of these arteries vary enormously, from that of the aorta to that of the small arteries. The concept that changes in pressure affect vascular caliber is, therefore, without basis. The caliber of most blood vessels varies directly with the size and activity of the vascular bed being supplied.20 This correlation, as well as the tendency to progression of stenosis and poststenotic dilatation, have recently been shown to result from the interaction of the stream with the wall (hydrodynamic drag).21.23 As a laminar stream moves through a blood vessel, the central (axial) fluid moves with relatively high velocity. Adjacent enclosing sleeves of fluid move at progressively lesser velocities. The sleeve of fluid adjacent to the wall (boundary layer) moves at minimal velocities, but exerts a shearing force (hydrodynamic drag) on the endothelial cells (Fig. 5). When peripheral vascular conductance increases, the velocity of all of the lamina increases; the drag of the boundary layer, which acts on the endothelium, also increases. It is known that an increase in the rate of flow through a vessel is associated with an immediate increase in its caliber.23 This effect. can be attributed to the increased drag on the endothelium, which apparently stimulates a localized dilation of the smooth muscle of the vessel \vall. If 11~~inc.reased flow is persistent, the
vcsscl
\\,ill
lwd
to
Iw
rcorg;knizd
Fig. 5. The role of hydrodynamic drag in the determination of vascular caliber. In the upper drawing, the first arrow indicates a normal drag acting on an endothelial cell. With increased drag, shearing stress is applied to the endothelial cell, which causes the vessel to widen acutely. This decreases the velocity of the stream and reduces drag to normal values. If the increased drag is persistent, the lumen of the vessel is reorganized around a larger lumen. The force of drag is indicated by the horizontal arrows. In the lower drawing, a reduced rate of flow results in a subnormal drag force (skort arrow at left). The lumen of the vessel is decreased, thereby increasing the velocity and the drag force to normal values. The vessel is then reorganized around the reduced lumen.
around the larger lumen. Conversely, a reduction in peripheral vascular conductance reduces the velocity and drag of the stream, and endothelial-medial re1ationshipP reduce the vascular lumen. If the reduced drag persists, subendothelial proliferations and general vascular reorganization take place around a reduced lumen (Fig. 5). A change in the drag forces on the wall thus can be considered to activate feedback mechanisms which return the drag forces to “normal” values. This mechanism of normal vascular growth and atrophy can thus account for the fine adjustment of the caliber of the vessel with the blood flow through the tissues it supplies. Depending on local circumstances, the foregoing blind mechanical forces may also operate to induce progressive enlargement or progressive stenosis, either of which can threaten the integrity of the tissue or even of the individual. Poststenotic diltrtat,ion. At a narrowing, flow generates high velocities which destroy laminarit), and produce vortices and turbulence in the docvnstrcani vascular segmcnl. In ;I region 0I s~~cliIionlaniinar llo\v.
Dynamics of blood jlow in stenolic vascular lesions
703
drag increases out of proportion to the
laminar. Thus, a murmur is the announce-
volume of blood flowing through the vessel. Poststenotic dilatation can thus be attributed to the chronically increased drag beyond a region of narrowing. Progressive narrowing. Hydrodynamic patterns can induce a progression of the stenotic process at the point of greatest narrowing in a stenosis. This effect may be attributed to the hydrodynamic conditions at the downstream end (nozzle) of a narrowing. Fluid is accelerated as it passes through the nozzle of a narrowing, gaining momentum in accord with the increase in velocity. At the downstream tip of the nozzle, the high momentum of the stream lines continues to move them inward toward the central axis of the stream, thereby separating the stream from the vessel wall. The interaction of stream and wall and the hydrodynamic drag on the endothelium are minimal at such a site of separation. As mentioned above, subendothelial proliferation appears at sites of reduced drag. The tip of a stenotic nozzle is, therefore, a locus of increased rate of growth and thus of progressive stenosis. At some sites, as at a ductus arteriosus or a ventricular septal defect, such an ingrowth with a consequent closure of the connection may prove to be beneficial. In other sites, this stenotic tendency may threaten limb and even life itself.
ment that the caliber of a vessel or valve is inadequate to provide for laminar flow. With further increases in peripheral vascular conductance and rate of flow, the murmur increases in intensity, pitch, and duration. Cross flow is minimal in an anastomosis between two parallel arteries which deliver blood to separate vascular beds of equal conductance. If a stenosis is present in one of the arterial roots, blood will shunt from the normal vessel to the vascular bed of the narrowed vessel. If the stenosis is severe, the deviation of blood will be marked and the tissues normally supplied by the normal vessel will become ischemic (steal syndrome). The interaction (hydrodynamic drag) of the stream with the vessel wall determines vascular caliber. Laminar streams interact normally with the wall. The separation of the stream lines from the wall at the downstream lip of a stenotic orifice produces a locus at which stream-wall interaction is minimal, with the result that the narrowing becomes progressively marked. In the poststenotic segment, turbulence increases the interaction of stream and wall, and stimulates a localized enlargement (poststenotic dilatation).
Summary A normal artery can serve as a conduit for many times the resting flow without significant loss of energy or production of murmurs. In such vessels, the rate of flow is determined primarily by the peripheral vascular conductance (rate of flow/drop in pressure) rather than by the characteristics of the artery. In a system of vessels connected in series, the rate of flow is limited by the segment of lowest conductance. Thus, when the conductance of the peripheral vascular bed is low, a partially stenotic lesion has no effect on the rate of flow. When an arteriovenous fistula or an increase in metabolic activity markedly increases the delivery through an arterial narrowing, the stenotic segment becomes the limiting factor, and a systolic bruit indicates that the stream is no longer
REFERENCES 1. Rodbard, S. : Evidence that vascular conductance is regulated at the capillary, in Hypertension 13:160-177, a monograph of the American Heart Association, Proceedings of the Council for High Blood Pressure Research, 1965. 2. Rodbard, S., and Jannotta, F.: An analysis of oscillometric pulsations, Circulation 7:922, 1953. 3. Hardin, C. A.: Vertebral artery insuficiency produced by cervical osteoarthritic spurs, Arch. Surg. 90:629, 1965. 4. Bay&s, W. M. : On the local reaction of arterial wall to change of internal pressure, J. Physiol. (London) 28:220, 1902. 5. Johnson, P. C., editor: Autoregulation of blood flow, Circulation lies. 15 (Suppl. 1):1964 (American Heart Association Monograph No. 8). 6. Rodbard, S.: Autoregulation in encapsulated, passive, soft-walled vessels, AM. HEART J. 65:648, 1963. 7. Rodbard, S.: Physics of blood flow. Chapter II, Sections 2-8, pp. 31-61, in Abramson, D. I., editor: Blood vessels and lymphatics, New York, 1962, Academic Press.
8.
9.
10.
11.
12.
13.
14.
Ejrup, B.: ‘l’oiioscillography~ after exercise: NW method for early diagnosis of organic arterial disease leading to intermittent claudication and for differential diagnosis of organic and functional arterial diseases with special ty-pe of apparatus adapted to purpose, Acta Med. Scandinav. 130 (Suppl. 211) :l-285, 1948. Rodbard, S.: A hydrodynamic basis for “exercise hyperemia” in a passive model of the peripheral circulation, Physiologist 7:238, 1964. Pinto, I. J., and Rodbard, S.: A study of the acoustic findings in patent ductus arteriosus, Cardiologia 28:1, 19.56. Allen, N., and Mustian, V.: Origin and significance of vascular murmurs of the head and neck, Medicine 41:227, 1962. Rodbard, S. : The production and physical qualities of sound in the cardiovascular system, in Segal, B., editor: The theory and practice of auscultation, Philadelphia, 1963, F. A. Davis Co., pp. 26-35. Rodbard, S., Zaas, R., and Cook, W.: A study of hydraulics in simulated patent ductus arteriosus, Circulation Res. 3:613, 1955. Pate], A., and Toole, J. A.: Subclavian steal syndrome-Reversal of cephalic blood flow, Medicine 44:289, 1965.
15.
Rodbard, by
16.
17.
18.
19.
20.
21.
22.
23.
How,
S.:
\‘ascular modifications induced J. 51:926, 1956. S. : Physical factors in the progression vascular lesions, Circulation 17:410,
.‘!a~
&ART
Rodbard, of stenotic 1958. Rodbard, S., and Harasawa, M.: Stenosis in a deformable tube inhibited by outlet pressure, AM. HEART J. 57~544, 1959. Texon, M., Imparato, A. M., and Helpern, M.: The role of vascular dynamics in the development of atherosclerosis, J.A.M.A. 194:1226, 1965. Texan, M.: In Brest, I\. pi., and Moyer, J. H., editors: Atherosclerotic vascular disease, New York, Appleton-Century-Crofts. In press. Thoma, R.: Untersuchungen iiber die Histogenese und Histomechanik des Gefasssystems, Stuttgart, 1893, Enke. Rodbard, S., Ikeda, K., and Montes, M.: Mechanism of post-stenotic dilatation, (Abstract) Circulation 28:791, 1963. Rodbard, S., Ikeda, Ii., and Montes, M.: An analysis of mechanisms of post-stenotic dilatation. Submitted for,,publication. Schretzenmayr, A. : Irber Kreislauf regulatorische Vorgange an der grossen Arterien bei der Muskelarbeit, Pfltigers Arch ges. Physiol. 236:93, 193.5.
Dynamics
cardiology
of Masd
Simon Rodbard, M.D., Duurte, C&if.
flew
waseuIQc
brief statement of normal arterial dynamics will serve as the basis for an analysis of the dynamics of stenotic vascular lesions. caliber
A normal artery serves as a conduit for several times the normal resting flow, with only minimal losses of pressure due to friction (Fig. 1). The volume flowing through a normal artery is determined nearly entirely by the degree of openness, i.e., conductance (rate of flow/drop in pressure, i.e., the inverse of resistance) of the peripheral vessels.* When conductance increases, as in the hyperemia of exercise, the pulsations of the vessel walls are enhanced, as revealed by palpation of the arteries, or by oscillometry.2 Since flow is laminar, vibrations are not produced and no bruit is heard. Variations in the viscosity of the blood introduce no significant increase in losses of energy in such large vessels, although viscosity may affect flow through the arteriolar, venular, and capillary segments. Stenosis
Narrowed vessels are the sites of drops in pressure, vibrations, and the stimulation of processeswhich tend to eliminate these dynamic factors. Arteries may be narro\ved l)y intravasc-ular plaques or collarlike narrowings, 1,).
impingement of ligaments or spurs which abut on the vessel wall (Hardin), or even by excessive force applied against the vessel by a stethoscope bell (Fig. 2). Transitory stenosis by means of compression of arteries by a sphygmomanometer cuff is utilized clinically in the measurement of the blood pressure. Efect of peripheral vascular conductance. The extent of the disturbance produced at an arterial narrowing varies with the vascular conductance of the tissues which the vessel supplies (Table I). When the flow of blood through the tissue is minimal, as in resting organs, a slight stenosis introduces no significant impedance to the rate of flow to the tissues, the drop in pressure at the orifice is negligible, and murmurs are absent. Autoregulation. A persistent rise or fall in arterial perfusion pressure triggers intrinsic mechanisms in muscle, brain, kidney, and other tissue@ which adjust the peripheral vascular conductance so that the rate of blood flow remains unaffected (autoregulation). Thus, the fall in perfusion pressure introduced by a partial narrowing of an artery is associated with an increase in the conductance ot the tissue, with the result that the rate of delivery of blood remains unaffected. Such autoregulatory mechanisms can rounteract the effects of slight to moderate stenosis on the rate of blood flow to resting
This study was aided by tirant No. HE 08721 from the National Heart Institute, Received for publication June 2. 1966. *IXrector of Cardiology and Cardiac Research. City of Hope Medical Center. Professor of Medicine, University of Soutllern California School of Medicine.
698
ldawws
Ph.D.*
A
Normal
in stewtic
United
States
Duarte. Calif Los Angele:.
Public and Calif.
Healtll
Servicr.
,ksociate
Clinical
Volume
Nwnbcr
72 5
Dynamics
of blood jlow in stenotic vasculur lesions
699
THE NORMAL ARTERY CAN CONDUCT SEVERAL TIMES THE RESTING FLOW WITHOUT SIGNIFICANT ENERGY LOSSES
FLOW RATE IS DETERMINED
8Y PERIPHERAL VASCULAR CONDUCTANCE
Fig. 1. Laminar flow in a large vessel. Flow through a vessel of normal caliber results in minimal losses of energy. No murmurs are produced. The rate of flow in such a system is determined by the conductance of the peripheral vessels and not by the characteristics of the vessel itself.
VESSEL NARROWING MAY RESULT FROM
Fig. 2. Vascular narrowing may result from intrinsic pathology of the vessel (upper two drawings), or as a result of deformation from without, by ligaments or pressure from a stethoscope (ZGWW two drawings).
vessels, even though the pressure in the arterial segment beyond the narrowing is less than normal. An increase in activity of the tissue opens the vascular beds more widely, and the pressure in the distal segment falls. Efect of the narrowing. A narrowing impedes flow, and a drop in pressure across
Fig. 3. Effect of a stenosis on the distribution of hydraulic energy (above) in a vessel (b&w). At the upstream segment, most of the energy is evident as pressure (black), a smaller amount is in the kinetic energy of velocity (da&d lines), and a small amount has already been converted to heat (stip$ed area) by friction, especially due to vortex formation. At the orifice (shown in drawing of vessel) the velocity increases sharply at the expense of pressure, and a significant portion is lost as heat. Beyond the orifice the pressure rises, although not to the prestenosis level, and velocity approaches normal values. The amount of energy converted to heat increases progressively.
the orifice becomes evident. Flow through a stenotic orifice varies with the square root of the difference between the proximal and distal pressures,’ and with the orifice area. The rate of flow does not keep pace with the drop in pressure. Thus, a doubling of the drop in pressure across an orifice increases the rate of flow by only 40 per cent ( 4 200 per cent = 140 per cent). When the vascular bed opens widely and the rate of flow increases greatly, as after muscular exercise (Fig. 3), the stenosis becomes the limiting factor in the delivery of blood to the active tissues. The drop in pressure at the orifice and the velocity of the stream increase, and vibrations are generated. However, as Ejrups has shown, the oscillations of the poststenotic artery decrease. This effect, considered by some workers to be due to arterial spasm, can be accounted for entirely on the basis of the decrease in the oscillations in pressure in the poststenotic arterial segment2 associated with the increased peripheral vascular conductance of exercise.g In moderate narrowing of an arterial orifice, the drop in pressure across the stenosis is of greater magnitude, the duration of the resulting murmur increases,
Pressure drop, velocity, and muiwws Degree of
___
narrowing Resting
tissue
I
At-live
tissue
I
None Slight Moderate Severe Complete
0 0 0 Systolic
Very
active tissue
1
0 0 Systolic Systolic and diastolic
0 Systolic Systolic and diastolic Systolic and diastolic ischemic symptoms (fatigue, pain)
Ischemia (murmurs are due to collaterals)
and the intensity and pitch exhibit crescendos as the aortic pressure risesin systole. During the falling arterial pressure of diastole, the murmur decreasesin intensity and pitch.‘O In severe stenosis, a systolic murmur may be present even when the tissue is at rest. With the increased conductance of exercise the murmur is prolonged and extends into diastole. When the blood flow is inadequate to wash away the end products of metabolism, localized pain or fatigue and other ischemic disturbances become manifest. With complete obstruction of an artery, pulsations are absent beyond the narrowing, and the murmur is no longer heard. Collaterals. The marked difference in pressure at the junction of normal and ischemic tissues serves to increase flow through existing intercommunicating vessels and to stimulate the development of new vessels. These enlarge gradually, in accord with the flow through them. These collaterals announce their inadequacy in the form of localized murmurs. When these collateral vessels are of suficient size to deliver an adequate rate of blood flow so that the drop in arterial pressure is eliminated, the stenosed artery will decrease in size, as discussed below, and one of the new vessels will become the primary vessel of the tissue. Ij’enous hums. The laws that adjust vascular adequacy to the rate of flow operate in the veins as well as in the arteries. An inadequacy of the venous collecting
networks and of the major venous channels is manifested in increases in pressure gradients, flow velocity, and the production of vibrations.ll “Venous hums” are not uncommon in children during the rapid growth phase, and when the general increase in metabolic activity enhances the volume of the venous return. The disproportion between vascular caliber and rate of blood flow is especially evident when the child is in the upright position; the drop in pressure from the veins draining the head to the subatmospheric pressure in the thorax may collapse the veins at the clavicle sufficiently so that murmurs and hums are heard over these vessels.13 Light pressure over the veins at the clavicle or placement of the subject in a reclining position reduces the drop in pressure and eliminates the venous hum, thereby readily differentiating the hum from arterial bruits originating in the adjacent arteries. The high right atria1 pressure of right heart failure also distends the veins and inhibits the hum. Venous hums are also heard at other sites at which the venous network is inadequate. For example, hums may be heard over the abdomen when the hepatic blood flow is deviated through subcutaneous collaterals. A similar dynamic pattern is heard during the period of rapid gestational growth of the uterus and its contents. The hums are enhanced with the drop in pressure during the inspiratory fall in pressure in the thorax and superior vena cave. The murmurs may diminish
Volume Number
72 5
Dynamics
with the reduction in the drop in pressure as the thoracic pressure rises during expiration. The growth of anastomotic venous channels eliminates the drop in pressure and the bruit. Flow through anastomoses. When arteries which supply different vascular beds are connected by anastomoses, the rate of flow through each of the arteries is affected by the relative conductance of the two beds,r3 and by the size of the anastomoses. When one of the vascular beds opens widely, the increased rate of runoff through it lowers the pressure in its main supplying artery. The higher blood pressure in the anastomosing artery will then flow into the vascular bed which has the higher conductance, and the tissue of lower conductance may receive an inadequate supply of blood. Thus, in a limb with a partially stenotic arteria1 supply, opening of the cutaneous vessels by the application of heat to the skin deviates blood from the muscles, which are thereby rendered even more ischemic. Attention has been called recently to the ischemic symptomatology which results when a narrowing at the root of the subclavian artery limits the rate of the flow of blood to the arm (Fig. 4). During rest, no effects may be noted. However, the marked increase in vascular conductance produced in the muscles during exercise of the arm can drain off some of the blood from the circle of Willis, Exercise of the arm may thus precipitate an episode of cerebral ischemia, an effect known as ’ ‘su bclavian steal. ’ ‘14 Effects of this type which are more generally appreciated include the deviation of aortic blood through a ductus arteriosus and thence through the high conductance of the pulmonary vascular bed (Table II). Coarctation of the aorta beyond the ductus increases the deviation and leads to ischemia of the vessels of the lower limbs. When the blood pressure in the two arms differs by more than a few millimeters of mercury, palpation may establish a significant asynchrony of the pressure waves at the radial or brachial arteries. The indirect measurement of blood pressure in the two arms, or of the delay in the transmission of the arterial pressure wave quantifies the severity of such an obstruc-
of blood jlow in stenotic vascular lesions
701
At Rest
Fig. 4. Steal syndrome. At rest (upper left), flow through the aorta (horizonbl arrow) is distributed among the subclavian (left) and carotid arteries. The carotid (u@er) vessel and vertebral arteries supply the brain through the circle of Willis. In the drawing at right, a severe stenosis is shown in the subclavian artery. When exercise opens the vessels of the arm, some of the blood moving toward the head is deviated across the circle of Willis to the vertebral artery and runs off into the high conductance of the vessels of the arm. If the blood flow to the brain is compromised, symptoms of cerebral ischemia will ensue.
Table II. “Steal”
syndromes
Stenosis
1. Subclavian + arm exercise -~2. Femoral arterial + heating of skin --------Leg 3. Coarctation of aorta + ductus arteriosus
Ischemia
-Cerebral muscles *Lower
extremities
tion. We have observed a number of patients with marked differences in pressure, timing, and duration of the arterial Korotkoff sounds in the two arms. However, the presence of such murmurs and other evidence of stenosis of the arteries to an arm is not necessarily associated with cerebral ischemia or the imminence of a cerebrovascular occlusion. The gradual modifications in vascular caliber which are induced by hydrodynamic forces may account for the benign course of this ahnormality in some patients.
Hydrodynamic vascular caliber
forces
and
The occasional tendencies for the progression of a localized stenosis,15-17the proliferation of collateral vessels, and the development of poststenotic dilatations have been attributed to the operation of hydrodynamic forces. The effects of the pressures on the walls of the vessels have excited the continuing interest of physiologists, pathologists, and clinicians. In earlier analyses, this laboratory had discussed the possibility that, at drops in pressure and increased velocities, the ingrowth of the vascular lining with a resultant progression of the stenotic tendency is facilitated. This thesis has subsequently been restated by others. 18*lgHowever, although the pressures in all of the arteries of the body are approximately equal, the calibers of these arteries vary enormously, from that of the aorta to that of the small arteries. The concept that changes in pressure affect vascular caliber is, therefore, without basis. The caliber of most blood vessels varies directly with the size and activity of the vascular bed being supplied.20 This correlation, as well as the tendency to progression of stenosis and poststenotic dilatation, have recently been shown to result from the interaction of the stream with the wall (hydrodynamic drag).21.23 As a laminar stream moves through a blood vessel, the central (axial) fluid moves with relatively high velocity. Adjacent enclosing sleeves of fluid move at progressively lesser velocities. The sleeve of fluid adjacent to the wall (boundary layer) moves at minimal velocities, but exerts a shearing force (hydrodynamic drag) on the endothelial cells (Fig. 5). When peripheral vascular conductance increases, the velocity of all of the lamina increases; the drag of the boundary layer, which acts on the endothelium, also increases. It is known that an increase in the rate of flow through a vessel is associated with an immediate increase in its caliber.23 This effect. can be attributed to the increased drag on the endothelium, which apparently stimulates a localized dilation of the smooth muscle of the vessel \vall. If 11~~inc.reased flow is persistent, the
vcsscl
\\,ill
lwd
to
Iw
rcorg;knizd
Fig. 5. The role of hydrodynamic drag in the determination of vascular caliber. In the upper drawing, the first arrow indicates a normal drag acting on an endothelial cell. With increased drag, shearing stress is applied to the endothelial cell, which causes the vessel to widen acutely. This decreases the velocity of the stream and reduces drag to normal values. If the increased drag is persistent, the lumen of the vessel is reorganized around a larger lumen. The force of drag is indicated by the horizontal arrows. In the lower drawing, a reduced rate of flow results in a subnormal drag force (skort arrow at left). The lumen of the vessel is decreased, thereby increasing the velocity and the drag force to normal values. The vessel is then reorganized around the reduced lumen.
around the larger lumen. Conversely, a reduction in peripheral vascular conductance reduces the velocity and drag of the stream, and endothelial-medial re1ationshipP reduce the vascular lumen. If the reduced drag persists, subendothelial proliferations and general vascular reorganization take place around a reduced lumen (Fig. 5). A change in the drag forces on the wall thus can be considered to activate feedback mechanisms which return the drag forces to “normal” values. This mechanism of normal vascular growth and atrophy can thus account for the fine adjustment of the caliber of the vessel with the blood flow through the tissues it supplies. Depending on local circumstances, the foregoing blind mechanical forces may also operate to induce progressive enlargement or progressive stenosis, either of which can threaten the integrity of the tissue or even of the individual. Poststenotic diltrtat,ion. At a narrowing, flow generates high velocities which destroy laminarit), and produce vortices and turbulence in the docvnstrcani vascular segmcnl. In ;I region 0I s~~cliIionlaniinar llo\v.
Dynamics of blood jlow in stenolic vascular lesions
703
drag increases out of proportion to the
laminar. Thus, a murmur is the announce-
volume of blood flowing through the vessel. Poststenotic dilatation can thus be attributed to the chronically increased drag beyond a region of narrowing. Progressive narrowing. Hydrodynamic patterns can induce a progression of the stenotic process at the point of greatest narrowing in a stenosis. This effect may be attributed to the hydrodynamic conditions at the downstream end (nozzle) of a narrowing. Fluid is accelerated as it passes through the nozzle of a narrowing, gaining momentum in accord with the increase in velocity. At the downstream tip of the nozzle, the high momentum of the stream lines continues to move them inward toward the central axis of the stream, thereby separating the stream from the vessel wall. The interaction of stream and wall and the hydrodynamic drag on the endothelium are minimal at such a site of separation. As mentioned above, subendothelial proliferation appears at sites of reduced drag. The tip of a stenotic nozzle is, therefore, a locus of increased rate of growth and thus of progressive stenosis. At some sites, as at a ductus arteriosus or a ventricular septal defect, such an ingrowth with a consequent closure of the connection may prove to be beneficial. In other sites, this stenotic tendency may threaten limb and even life itself.
ment that the caliber of a vessel or valve is inadequate to provide for laminar flow. With further increases in peripheral vascular conductance and rate of flow, the murmur increases in intensity, pitch, and duration. Cross flow is minimal in an anastomosis between two parallel arteries which deliver blood to separate vascular beds of equal conductance. If a stenosis is present in one of the arterial roots, blood will shunt from the normal vessel to the vascular bed of the narrowed vessel. If the stenosis is severe, the deviation of blood will be marked and the tissues normally supplied by the normal vessel will become ischemic (steal syndrome). The interaction (hydrodynamic drag) of the stream with the vessel wall determines vascular caliber. Laminar streams interact normally with the wall. The separation of the stream lines from the wall at the downstream lip of a stenotic orifice produces a locus at which stream-wall interaction is minimal, with the result that the narrowing becomes progressively marked. In the poststenotic segment, turbulence increases the interaction of stream and wall, and stimulates a localized enlargement (poststenotic dilatation).
Summary A normal artery can serve as a conduit for many times the resting flow without significant loss of energy or production of murmurs. In such vessels, the rate of flow is determined primarily by the peripheral vascular conductance (rate of flow/drop in pressure) rather than by the characteristics of the artery. In a system of vessels connected in series, the rate of flow is limited by the segment of lowest conductance. Thus, when the conductance of the peripheral vascular bed is low, a partially stenotic lesion has no effect on the rate of flow. When an arteriovenous fistula or an increase in metabolic activity markedly increases the delivery through an arterial narrowing, the stenotic segment becomes the limiting factor, and a systolic bruit indicates that the stream is no longer
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&ART
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