Hemodynamic Considerations in Peripheral Vascular and Cerebrovascular Disease

1 Hemodynamic Considerations in Peripheral Vascular and Cerebrovascular Disease



Joseph F. Polak, MD, MPH , Stefan A. Carter, MD, MSC, FRCP(C) , John S. Pellerito, MD, FACR, FSRU, FAIUM


The circulatory system is extremely complex in both structure and function. Blood flow is influenced by many factors, including cardiac function; elasticity of the vessel walls (compliance); the tone of vascular smooth muscle; and the various patterns, dimensions, and interconnections of millions of small branching vessels. Some of these factors can be measured and described in reasonably simple terms, but many others cannot be described succinctly because they are difficult to quantify and generally are not well understood.


With these limitations in mind, this chapter presents the basic principles of the dynamics of blood circulation, some of the many factors that influence blood flow, and the hemodynamic consequences of occlusive disease. These considerations are helpful in understanding the normal physiology of blood circulation and the abnormalities that can occur in the presence of vascular obstruction.



Physiologic Factors Governing Blood Flow and Its Characteristics



Energy and Pressure


For blood flow to occur between any two points in the circulatory system, there must be a difference in the energy level between these two points. Usually, the difference in energy level is reflected by a difference in blood pressure, and the circulatory system generally consists of a high-pressure, high-energy arterial reservoir and a venous pool of low pressure and energy. These reservoirs are connected by a system of distributing vessels (smaller arteries) and by the resistance vessels of the microcirculation, which consist of arterioles and to a lesser extent the capillaries (Figure 1-1).


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FIGURE 1-1 This diagram is a simplified representation of the relative differences in pressure, effective resistance, and overall vessel cross-luminal area at the different levels of the circulation.


During blood flow, energy is continuously lost because of the friction between the layers of flowing blood. Both pressure and energy levels therefore decrease from the arterial to the venous ends. The energy necessary for blood flow is continuously restored by the pumping action of the heart during systole, stored in the elastic wall of the aorta and large arteries, and released during diastole. The generated arterial pressure forces blood to move from the arterial system into the venous system and maintains the arterial pressure and the energy difference needed for flow to occur.


The high arterial energy level is a result of the large volume of blood in the arterial reservoir. The function of the heart and blood vessels is normally regulated to maintain volume and pressure in the arteries within the limits required for smooth function. This is achieved by maintaining a balance between the amounts of blood that enter and leave the arterial reservoir. The amount that enters the arteries during a cardiac cycle is the stroke volume. The amount that leaves depends on the arterial pressure and on the total peripheral resistance, which is controlled in turn by the amount of vasoconstriction in the microcirculation.


Under normal conditions, blood flow to all the body tissues is adjusted according to the tissues’ particular needs at a given time. This adjustment is accomplished by local alterations in the level of vasoconstriction of the arterioles within the organs supplied. Maintenance of normal volume and pressure in the arteries thus allows for both adjustment of blood flow to all parts of the body and regulation of cardiac output (which equals the sum of blood flow to all the vascular beds).



Forms of Energy in the Blood and its Dissipation During Flow


This section considers the forms in which energy exists in the circulation and the important factors that govern the dissipation of energy during flow, including friction, resistance, and the influence of laminar and turbulent flow. In addition to reviewing Bernoulli’s equation and Poiseuille’s law, an equation that summarizes the basic relationships between flow, pressure, and resistance, this chapter also reviews the effects of connecting vascular resistances in parallel and in series.



Forms of Energy



Potential and Kinetic Energy


The main form of energy present in flowing blood is the pressure distending the vessels (a form of potential energy), which is created by the pumping action of the heart. However, some of the energy of the blood is kinetic; namely, the ability of flowing blood to do work as a result of its velocity. Usually, the kinetic energy component is small compared with the pressure energy, and under normal resting conditions, it is equivalent to only a few millimeters of mercury or less. The kinetic energy of blood is proportional to its density (which is stable in normal circumstances) and to the square of its velocity. In essence, over relatively straight arterial segments, this balance of kinetic (blood flow) and potential (blood pressure) energy is maintained. The equation that summarizes this relationship is Bernoulli’s equation (Figure 1-2). If the artery lumen increases, kinetic energy is converted back into pressure (potential energy) when velocity is decreased. Conversely, if the artery lumen narrows, the potential energy is converted into kinetic energy. Therefore, within certain limits, important increases in kinetic energy occur in the systemic circulation when blood flow is high (e.g., during exercise) and in mildly stenotic lesions where luminal narrowing leads to increases in blood flow velocities. The effects of gravity due to differences in height of the blood vessel are normally neglected over short arterial segments.


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FIGURE 1-2 This diagram represents the complementary changes in potential and kinetic energy taking place at an idealized stenosis. Bernoulli’s equation indicates that as velocity increases, the potential energy (pressure) of blood decreases. This idealized representation is not to scale and neglects viscous and inertial forces.



Energy Differences Related to Differences in the Levels of Body Parts


There is also variation in the energy of the blood associated with differences in the levels of body parts. For example, the pressure in the vessels in the dependent parts of the body, such as the lower portions of the legs, increases by an amount that depends on the weight of the column of blood resting on the blood in the legs. This hydrostatic pressure increases the transmural pressure and the distention of the vessels. Gravitational potential energy (potential for doing work related to the effect of gravity on a free-falling body), however, is reduced in the dependent parts of the body by the same amount as the increase resulting from hydrostatic pressure. Therefore, differences in the level of the body parts usually do not lead to changes in the driving pressure along the vascular tree unless the column of blood is interrupted, as may be the case when the venous valves close. Changes in energy and pressure associated with differences in level are important under certain conditions, such as with changes in posture or when the venous pump is activated because of muscular action during walking.



Dissipation of Energy



During Laminar Flow


In most vessels, blood moves in concentric layers, or laminae; hence the flow is said to be laminar. Each infinitesimal layer flows with a different velocity. In theory, a thin layer of blood is held stationary next to the vessel wall at zero velocity because of an adhesive force between the blood and the inner surface of the vessel. The next layer flows with a certain velocity, but its movement is delayed by the stationary layer because of friction between the layers, generated by the viscous properties of the fluid. The second layer, in turn, delays the next layer, which flows at a greater velocity. The layers in the middle of the vessel flow with the highest velocity, and the basic physics underlying this effect are such that the mean velocity averaged across the vessel is half of the maximal velocity measured in the center. Because the rate of change of velocity is greatest near the walls and decreases toward the center of the vessel, a velocity profile in the shape of a parabola exists along the vessel diameter, and this type of blood flow is typically referred to as laminar flow (Figure 1-3).


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FIGURE 1-3 Blood flow velocity profiles across a normal arterial lumen. A, Parabolic profile of laminar flow. B, Flattened profile with a central core of relatively uniform velocity encountered in the proximal portion (inlet length) of arterial branches or with turbulent flow.


Loss of energy during blood flow occurs because of friction, and the amount of friction and energy loss is determined in large part by the dimensions of the vessels. In a small-diameter vessel, especially in the microcirculation, even the layers in the middle of the lumen are relatively close to the wall and are thus delayed considerably, resulting in a significant opposition or resistance to flow in that vessel segment. In large vessels, by contrast, a large central core of blood is far from the walls, and the frictional energy losses are less important. As indicated later, friction and energy losses increase if laminar flow is disturbed.



Poiseuille’s Law and Equation

In a cylindric-tube model, the mean linear velocity of laminar flow is directly proportional to the energy difference between the ends of the tube and the square of the radius and is inversely proportional to the length of the tube and the viscosity of the fluid. In the circulatory system, however, volume flow is of more interest than velocity. Volume flow is proportional to the fourth power of the vessel radius, because it is equal to the product of the mean linear velocity and the cross-sectional area of the tube. These important considerations are helpful in understanding Poiseuille’s law, as expressed in Poiseuille’s equation:



image    (1-1)



where Q is the volume flow; P1 and P2 are the pressures at the proximal and distal ends of the tube, respectively; r and L are the radius and length of the tube, respectively; and η is the viscosity of the fluid.


Because volume flow is proportional to the fourth power of the radius, even small changes in radius can result in large changes in volume flow. For example, a decrease in radius of 10% would decrease volume flow in a tube model by about 35%, and a decrease of 50% would lead to a 95% decrease in volume flow. Because the length of the vessels and the viscosity of blood do not change much in the cardiovascular system, alterations in volume blood flow occur mainly as a result of changes in the radius of the vessels and in the difference in the pressure energy level available for flow.


Poiseuille’s equation can be rewritten, therefore, as follows:



image    (1-2)




image    (1-3)




image    (1-4)



The resistance term (R) depends on the viscous properties of the blood and on the dimensions of the vessels. Although these parameters cannot be measured in a complex system, the pressure difference (P1 − P2) and the volume flow (Q) can be measured, and the resistance can thus be calculated. Because resistance is equal to the pressure difference divided by the volume flow (the pressure difference per unit flow), it can be thought of as the pressure difference needed to produce one unit of flow and, therefore, can be considered as an index of the difficulty in forcing blood through the vessels.



Vessel Interconnection and Energy Dissipation

Poiseuille’s law applies with precision only to constant laminar flow of a simple fluid (such as water) in a rigid tube of a uniform bore. In the blood circulation, these conditions are not met. Instead, the resistance is influenced by the presence of numerous interconnected vessels with a combined effect similar to that observed in electrical resistances. In the case of vessels in series, the overall resistance is equal to the sum of the resistances of the individual vessels, whereas in the case of parallel vessels, the reciprocal of the total resistance equals the sum of the reciprocals of the individual vessel resistances. Thus, the contribution of any single vessel to the total resistance of a vascular bed, or the effect of a change in the dimension of a vessel, depends on the presence and relative size of the other vessels linked in series or in parallel.


Deviations from the conditions to which Poiseuille’s law applies also occur in relation to changes in blood viscosity, which is affected by hematocrit, temperature, vessel diameter, and rate of blood flow.



During Nonlaminar Flow


Various degrees of deviation from orderly laminar flow occur in the circulation under both normal and abnormal conditions. Minor factors responsible for these deviations include changes in blood flow velocity during the cardiac cycle as a result of acceleration during systole and deceleration in diastole and alterations of the lines of flow due to small changes in the diameter of the vessel. Alterations in the blood flow profiles occur at curves (Figure 1-4), at bifurcations, in branches that take off at various angles, and at stenotic lesions. Once altered, the laminar (parabolic) velocity profile is often not reestablished for a considerable distance. Instead, the velocity distributions can remain skewed after curves and branches or flattened within and just distal to stenotic lesions (plug flow) (see Figure 1-3, B).


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FIGURE 1-4 Alteration in the velocity distribution of red cells in a curving arterial segment. The velocity distribution becomes asymmetric as red cells enter a curve. A laminar pattern is reestablished downstream over a distance that is mostly dependent on the velocity of blood and the diameter of the artery.


In certain circumstance, laminar flow can evolve into a blood flow pattern that is mixed: a flow profile that has both forward and backward flow velocity components across the diameter of the artery. The transition zone where the lamina reach zero velocity is then referred to as the site of boundary layer separation. This phenomenon can occur at branch points and is classically described at the carotid artery bifurcation (Figure 1-5). Another situation is distal to stenotic lesions.


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FIGURE 1-5 This representation of the carotid artery bifurcation displays the principal alterations that take place in a normal bifurcation. The flow profile in the distal common carotid artery (CCA) starts to deviate from a laminar pattern to one favoring the internal carotid artery (ICA). As the red cells enter the carotid sinus, a zone of boundary layer separation (where the effective velocity is zero) forms. To one side, blood flow is reversed, whereas blood continues forward on the other side. Blood flow reestablishes itself toward a laminar one more distally in the ICA. For purposes of illustration, the actual effects of the external carotid artery (ECA) on blood flow are neglected.


At the carotid bifurcation, the blood flow profile in the distal common carotid artery tends to diverge toward the internal carotid artery and then to evolve a zone of boundary layer separation in the proximal internal carotid artery (see Figure 1-5).


Laminar flow may be altered or become disturbed or fully turbulent, even in a uniform tube. The factors that affect the development of turbulence are expressed by the dimensionless Reynolds number (Re):



image    (1-5)



where v is the velocity, ρ is the density of the fluid, r is the radius of the tube, and η is the viscosity of the fluid. Because the density (ρ) and viscosity (η) of the blood are relatively constant at 1.04 to 1.05 g/cm3 and 0.03 to 0.05 poise (g/[cm sec]), respectively, the development of turbulence depends mainly on the size of the vessel and on the velocity of blood flow. In a tube model, laminar flow tends to be present if the Reynolds number is less than 2000, is considered in transition between 2000 and 4000, and is absent as turbulence is established at values above 4000. However, in the circulatory system, disturbances and various degrees of turbulence are likely to occur at lower values because of body movements, the pulsatile nature of blood flow, changes in vessel dimensions, roughness of the endothelial surface, and other factors. Turbulence develops more readily in large vessels under conditions of high flow and can be detected clinically by the finding of bruits or thrills. This would typically be seen in dialysis access fistulas. Bruits may sometimes be heard over the ascending aorta during systolic acceleration in normal individuals at rest and are frequently heard in states of high cardiac output and blood flow, even in more distal arteries, such as the femoral artery.1 Distortion of laminar flow velocity profiles can be assessed using Doppler ultrasound, and such assessments can be applied for diagnostic purposes. For example, in arteries with severe stenosis, pronounced turbulence is a diagnostic feature observed in the poststenotic zone. This is typically associated with soft tissue vibrations in the range of 100 to 300 Hz.2


Turbulence occurs because a jet of blood with high velocity and high kinetic energy suddenly encounters a normal-diameter lumen or a lumen of increased diameter (because of poststenotic dilatation), where both the velocity and energy level are lower than in the stenotic region. During turbulent flow, the loss of pressure energy between two points in a vessel is greater than that which would be expected from the factors in Poiseuille’s equation and Bernoulli’s equation (see Figure 1-2), and the parabolic velocity profile is flattened (see Figure 1-3, B).



Pulsatile Pressure and Flow Changes in the Arterial System


With each heartbeat, a stroke volume of blood is ejected into the arterial system, resulting in a pressure wave that travels throughout the arterial tree. The speed of propagation, amplitude (strength), and shape of the pressure wave change as it traverses the arterial system. The velocity of the pulse wave is strongly influenced by the varying characteristics of the vessel wall it traverses, and the shape is affected by reflected waves. The velocity and, in some parts of the circulation, the direction of flow, also vary with each heartbeat.


Correct interpretation of noninvasive tests based on recordings of arterial pressure and velocity, as well as pressure and velocity waveforms, requires knowledge of the factors that influence these variables. This section considers these factors as they occur in various portions of the circulatory system.



Pressure Changes From Cardiac Activity


As indicated previously, the pumping action of the heart maintains a high volume of blood in the arterial end of the circulation and thus provides the high pressure difference between the arterial and venous ends necessary to maintain blood flow. Because of the intermittent pumping action of the heart, pressure and flow vary in a pulsatile manner. During the rapid phase of ventricular ejection, the volume of blood at the arterial end increases, raising the pressure to a systolic peak. During the latter part of systole, when cardiac ejection decreases, the outflow through the peripheral resistance vessels exceeds the volume being ejected by the heart, and the pressure begins to decline. This decline continues throughout diastole as blood continues to flow from the arteries into the microcirculation. Part of the work of the heart leads directly to forward flow, but a large portion of the energy of each cardiac contraction results in distention of the arteries that serve as reservoirs for storing the blood volume and the energy supplied to the system (Figure 1-6). This storage of energy and blood volume helps maintain blood flow to the tissues during diastole.


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FIGURE 1-6 This simple representation of the circulatory system shows the principal elements of the circulatory system. Wave reflection can take place within the muscular arteries as well as in the larger elastic artery. The effective location of the principal reflection sites varies with age, migrating more centrally with aging.



Arterial Pressure Wave


The pulsatile variations in blood volume and energy occurring with each cardiac cycle are manifested as a pressure wave that can be detected throughout the arterial system. The amplitude and shape of the arterial pressure wave depend on a complex interplay of factors, which include the stroke volume and time course of ventricular ejection, the peripheral resistance, and the stiffness of the arterial walls.


In general, an increase in any of these factors results in an increase in the pulse amplitude (i.e., pulse pressure, difference between systolic and diastolic pressures) and frequently in a concomitant increase in systolic pressure. For example, increased stiffness of the arteries with age tends to increase both the systolic and pulse pressures through an increase in the magnitude of reflected pressure waves from natural branch points in the arterial system.


The arterial pressure wave is propagated from the heart distally along the arterial tree. The speed of propagation, or pulse wave velocity, increases with stiffness of the arterial walls (the elastic modulus of the material of which the walls are composed) and with the ratio of the wall thickness to diameter. In the mammalian circulation, arteries become progressively stiffer from the aorta toward the periphery. Therefore, the speed of propagation of the wave increases as it moves peripherally. Also, the gradual increase in stiffness tends to increase wave reflection (discussed later) and in young people has a protective effect by decreasing central aortic pressures. With aging, the degree of stiffening increases to such a degree that the reflected waves return earlier and have a detrimental effect by increasing the pulse and systolic pressures in the aorta.3–5

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Mar 5, 2016 | Posted by in ULTRASONOGRAPHY | Comments Off on Hemodynamic Considerations in Peripheral Vascular and Cerebrovascular Disease
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