Hemodynamics - Hemodynamics Hemodynamics (Pressure, Flow,...

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Unformatted text preview: Hemodynamics Hemodynamics (Pressure, Flow, and Resistance) Hemodynamics can be defined as the physical factors that govern blood flow. These are the same physical factors that govern the flow of any fluid, and are based on a fundamental law of physics, namely Ohm's Law, which states that current (I) equals the voltage difference (DV) divided by resistance (R). In relating Ohm's Law to fluid flow, the voltage difference is the pressure difference (DP; sometimes called driving pressure, perfusion pressure, or pressure gradient), the resistance is the resistance to flow (R) offered by the blood vessel and its interactions with the flowing blood, and the current is the blood flow (F). This hemodynamic relationship can be summarized by: For the flow of blood in a blood vessel, the DP is the pressure difference between any two points along a given length of the vessel. When describing the flow of blood for an organ, the pressure difference is generally expressed as the difference between the arterial pressure (PA) and venous pressure (PV). For example, the blood flow for the kidney is determined by the renal artery pressure, renal vein pressure, and renal vascular resistance. The blood flow across a heart valve follows the same relationship as for a blood vessel; however, the pressure difference is the two pressures on either side of the valve. For example, the pressure difference across the aortic valve that drives flow across that valve during ventricular ejection is the intraventricular pressure (PIV) minus the aortic pressure (PAo). The resistance (R) is the resistance to flow that is related in large part to the size of the valve opening. Therefore, the relationship describing the flow across the aortic valve is: Under ideal laminar flow conditions, in which vascular resistance is independent of flow and pressure, the relationship between pressure, flow and resistance can be depicted as shown in the figure to the right. Because flow and resistance are reciprocally related, an increase in resistance decreases flow at any given DP. Also, at any given flow along a blood vessel or across a heart valve, an increase in resistance increases the DP. 1 Hemodynamics Changes in resistance are the primary means by which blood flow is regulated within organs because control mechanisms in the body generally maintain arterial and venous blood pressures within a narrow range. However, changes in perfusion pressure, when they occur, will affect flow. The above relationship also indicates that there is a linear and proportionate relationship between flow and perfusion pressure. This linear relationship, however, is not followed when pathological conditions lead to turbulent flow, because turbulence decreases the flow at any given perfusion pressure. Furthermore, the pulsatile nature of flow in large arteries also alters this relationship so that greater pressures are required for a given flow. In other words, pulsatility, like turbulence, increases resistance to flow. 2 Hemodynamics Resistance to Blood Flow Resistance to blood flow within a vascular network is determined by the size of individual vessels (length and diameter), the organization of the vascular network (series and parallel arrangements), physical characteristics of the blood (viscosity, laminar flow versus turbulent flow), and extravascular mechanical forces acting upon the vasculature. Of the above factors, changes in vessel diameter are most important quantitatively for regulating blood flow within an organ, as well as for regulating arterial pressure. Changes in vessel diameter, particularly in small arteries and arterioles, enable organs to adjust their own blood flow to meet the metabolic requirements of the tissue. Therefore, if an organ needs to adjust its blood flow (and therefore, oxygen delivery), cells surrounding these blood vessels release vasoactive substances that can either constrict or dilate the resistance vessels. The ability of an organ to regulate its own blood flow is termed local regulation of blood flow and is mediated by vasoconstrictor and vasodilator substances released by the tissue surrounding blood vessels (vasoactive metabolites) and by the vascular endothelium. There is also a mechanism intrinsic to the vascular smooth muscle (myogenic mechanism) that is involved in local blood flow regulation. In organs such as the heart and skeletal muscle, mechanical activity (contraction and relaxation) produces compressive forces that can effectively decrease vessel diameters and increase resistance to flow during muscle contraction (see extravascular compression). Besides local regulatory mechanisms, there are extrinsic mechanisms acting on the vasculature to regulate vessel diameter. One important extrinsic mechanism regulating vascular diameter operates through the autonomic innervation of blood vessels. In general, sympathetic adrenergic influences acting through vascular alphaadrenoceptors cause resistance vessels as well as veins to be partially constricted under basal conditions. This is termed "sympathetic vascular tone." Therefore, removal of sympathetic adrenergic influences (for example, by administration of an alphaadrenoceptor antagonist or by sympathectomy) leads to vasodilation and an increase in organ blood flow. A second type of extrinsic influence on the vasculature is circulating vasoactive hormones such as angiotensin II, epinephrine and norepinephrine, vasopressin (antidiuretic hormone, ADH), atrial natriuretic peptide (ANP), and endothelin. Both the neural and humoral factors, while affecting organ blood flow, primarily serve the function of regulating arterial pressure by altering systemic vascular resistance. 3 Hemodynamics Determinants of Resistance to Flow (Poiseuille's Equation) There are three primary factors that determine the resistance to blood flow within a single vessel: vessel diameter (or radius), vessel length, and viscosity of the blood. Of these three factors, the most important quantitatively and physiologically is vessel diameter. The reason for this is that vessel diameter changes because of contraction and relaxation of the vascular smooth muscle in the wall of the blood vessel. Furthermore, as described below, very small changes in vessel diameter lead to large changes in resistance. Vessel length does not change significantly and blood viscosity normally stays within a small range (except when hematocrit changes). Vessel resistance (R) is directly proportional to the length (L) of the vessel and the viscosity (h) of the blood, and inversely proportional to the radius to the fourth power (r4). Because changes in diameter and radius are directly proportional to each other (D = 2r; therefore D r), diameter can be substituted for radius in the following expression. Therefore, a vessel having twice the length of another vessel (and each having the same radius) will have twice the resistance to flow. Similarly, if the viscosity of the blood increases 2-fold, the resistance to flow will increase 2-fold. In contrast, an increase in radius will reduce resistance. Furthermore, the change in radius alters resistance to the fourth power of the change in radius. For example, a 2-fold increase in radius decreases resistance by 16-fold! Therefore, vessel resistance is exquisitely sensitive to changes in radius. The relationship between flow and vessel radius to the fourth power (assuming constant DP, L, hand laminar flow conditions) is illustrated in the figure to the right. This figure shows how very small decreases in radius dramatically reduces flow. Vessel length does not change appreciably in vivo and, therefore, can generally be considered as a constant. Blood viscosity normally does 4 Hemodynamics not change very much; however, it can be significantly altered by changes in hematocrit, temperature, and by low flow states. If the above expression for resistance is combined with the equation describing the relationship between flow, pressure and resistance (F=DP/R), then This relationship (Poiseuille's equation) was first described by the 19th century French physician Poiseuille. It is a description of how flow is related to perfusion pressure, radius, length, and viscosity. The full equation contains a constant of integration and pi, which are not included in the above proportionality. In the body, however, flow does not conform exactly to this relationship because this relationship assumes long, straight tubes (blood vessels), a Newtonian fluid (e.g., water, not blood which is non-Newtonian), and steady, laminar flow conditions. Nevertheless, the relationship clearly shows the dominant influence of vessel radius on resistance and flow and therefore serves as an important concept to understand how physiological (e.g., vascular tone) and pathological (e.g., vascular stenosis) changes in vessel radius affect pressure and flow, and how changes in heart valve orifice size (e.g., in valvular stenosis) affect flow and pressure gradients across heart valves. Although the above discussion is directed toward blood vessels, the factors that determine resistance across a heart valve are the same as described above except that length becomes insignificant because path of blood flow across a valve is extremely short compared to a blood vessel. Therefore, when resistance to flow is described for heart valves, the primary factors considered are radius and blood viscosity. 5 Hemodynamics Series and Parallel Vascular Networks The vascular anatomy of the entire body or for an individual organ is comprised of both in-series and in-parallel vascular components as shown to the right. Blood leaves the heart through the aorta from which it is distributed to major organs by large arteries, each of which originates from the aorta. Therefore, these major distributing arteries (e.g., carotid, brachial, superior mesenteric, renal, iliac) are inparallel with each other. This further means that the vascular networks of most individual organs are in-parallel with other organ networks. For example, the circulations of the head, arms, gastrointestinal systems, kidneys, and legs are all parallel circulations. There are some exceptions, notably the gastrointestinal and hepatic circulations, which are partly in-series because the venous drainage from the intestines become the hepatic portal vein which supplies most of the blood flow to the liver. Within an organ, the vessels comprising the microcirculation are arranged in-series and inparallel (see figure to right). A small artery is in-series with its two daughter branches (arterioles), and each of these arteriolar branches are inparallel to each other. The arterioles give rise to capillaries (in-series connection), which are in-parallel to each other. Therefore, each of the vascular segments depicted in the figure are in-series to each other, although within the segment there are parallel vessels. Furthermore, each vascular segment will have a segmental resistance value (Rx) that is determined by the length and radius of each of the vessels that comprise the segment of parallel vessels (see parallel resistance calculation). For an in-series resistance network, the total resistance (RT) equals the sum of the individual resistances. Therefore, for the vessels depicted in the figure, the total resistance is equal to the sum of the small artery (RA), arterioles (Ra), capillaries (Rc), venules (Rv), and vein (RV) resistances. RT = RA + Ra + Rc + Rv + RV The resistance of a each segment relative to the total resistance of all the segments will determine how changing the resistance of one segment will affect total resistance. To illustrate this principle, a relative resistance value can be assigned to each of the five 6 Hemodynamics resistance segments in this model. The relative resistances will be similar to what is observed in a typical vascular bed. Assume, RA = 20, Ra = 50, Rc = 20, Rv = 8, RV = 1 Therefore, RT = 20 + 50 +20 +6 + 4 = 100 Using this empirical model, we can see that doubling RV from 4 to 8 increases RT from 100 to 104, a 4% increase. In contrast, doubling Ra from 50 to 100 increases RT from 100 to 150, a 50% increase. If this were done for each of the segment, we would find that the arteriolar segment with the highest relative resistance (arterioles) has the greatest effect on total resistance. As a group, changes in diameter (and therefore resistance) of small arteries and arterioles have the greatest effect on vascular resistance because these two vessel segments comprise about 70% of the total resistance in most organs. The above analysis also explains why the radius of a large, distributing artery must be decreased by more than 50% to have a significant effect on organ blood flow. These large arteries comprise only about 1% of the total resistance. Therefore, unlike arterioles, small changes in their diameter have a relatively small affect on total resistance. They must undergo large reductions in diameter before resistance and flow are significantly reduced. This is referred to as a "critical" stenosis. This can be confusing because the Poiseuille's equation indicates that resistance to flow is inversely related to radius to the fourth power. Therefore, a 50% reduction in radius should increase resistance 16-fold (1500% increase); however, total resistance will only increase by about 16% because the large artery resistance is normally only about 1% of the total resistance. 7 Hemodynamics Parallel Resistance Calculations Assume that a small artery is giving rise to three smaller arterioles, each parallel to the other. The total resistance (Rx) for the three parallel arterioles comprising the segment would be: or solving for Rx, To illustrate this relationship empirically, assume that R1 = 5, R2 = 10 and R3 = 20. In this example, Rx = 2.86. This demonstrates two important principles regarding the parallel arrangement of blood vessels: 1. The total resistance of a network of parallel vessels is less than the resistance of the vessel having the lowest resistance. Therefore, a parallel arrangement of vessels greatly reduces resistance to blood flow. That is why capillaries, which have the highest resistance of individual vessels because of their small diameter, constitute only a small portion of the total vascular resistance of an organ or microvascular network. 2. When there are many parallel vessels, changing the resistance of a small number of these vessels will have little effect on total resistance for the segment. 8 Hemodynamics Laminar Flow Laminar flow is the normal condition for blood flow throughout most of the circulatory system. It is characterized by concentric layers of blood moving in parallel down the length of a blood vessel. The highest velocity (Vmax) is found in the center of the vessel. The lowest velocity (V=0) is found along the vessel wall. The flow profile is parabolic once laminar flow is fully developed. This occurs in long, straight blood vessels, under steady flow conditions. One practical implication of parabolic, laminar flow is that when flow velocity is measured using a Doppler flowmeter, the velocity value represents the average velocity of a cross-section of the vessel, not the maximal velocity found in the center of the flow stream. The orderly movement of adjacent layers of blood flow through a vessel helps to reduce energy losses in the flowing blood by minimizing viscous interactions between the adjacent layers of blood and the wall of the blood vessel. Disruption of laminar flow leads to turbulence and increased energy losses. 9 Hemodynamics Turbulent Flow Generally in the body, blood flow is laminar. However, under conditions of high flow, particularly in the ascending aorta, laminar flow can be disrupted and become turbulent. When this occurs, blood does not flow linearly and smoothly in adjacent layers, but instead the flow can be described as being chaotic. Turbulent flow also occurs in large arteries at branch points, in diseased and narrowed (stenotic) arteries (see figure below), and across stenotic heart valves. Turbulence increases the energy required to drive blood flow because turbulence increases the loss of energy in the form friction, which generates heat. When plotting a pressure-flow relationship (see figure to right), turbulence increases the perfusion pressure required to drive a given flow. Alternatively, at a given perfusion pressure, turbulence leads to a decrease in flow. Turbulence does not begin to occur until the velocity of flow becomes high enough that the flow lamina break apart. Therefore, as blood flow velocity increases in a blood vessel or across a heart valve, there is not a gradual increase in turbulence. Instead, turbulence occurs when a critical Reynolds number (Re) is exceeded. Reynolds number is a way to predict under idea conditions when turbulence will occur. The equation for Reynolds number is: 10 Hemodynamics Where v = mean velocity, D = vessel diameter, r = blood density, and h = blood viscosity As can be seen in this equation, Re increases as velocity increases and decreases as viscosity increases. Therefore, high velocities and low blood viscosity (as occurs with anemia due to reduced hematocrit) are more likely to cause turbulence. An increase in diameter without a change in velocity also increases Re and the likelihood of turbulence; however, the velocity in vessels ordinarily decreases disproportionately as diameter increases. The reason for this is that flow (F) equals the product of mean velocity (V) times cross-sectional area (A), and area is proportionate to radius squared; therefore, the velocity at constant flow is inversely related to radius (or diameter) squared. For example, if radius (or diameter) is doubled, the velocity decreases to onefourth its normal value, and Re decreases by one-half. Under ideal conditions (e.g., long, straight, smooth blood vessels), the critical Re is relatively high. However, in branching vessels, or in vessels with atherosclerotic plaques protruding into the lumen, the critical Re is much lower so that there can be turbulence even at normal physiological flow velocities. Turbulence generates sound waves (e.g., ejection murmurs, carotid bruits) that can be heard with a stethoscope. Because higher velocities enhance turbulence, murmurs intensify as flow increases. Elevated cardiac outputs, even across anatomically normal aortic valves, can cause physiological murmurs because of turbulence. This sometimes occurs in pregnant women who have elevated cardiac output and who may also have anemia, which decreases blood viscosity. Both factors increase the Reynolds number and increases the likelihood of turbulence. 11 Hemodynamics Critical Stenosis The term "stenosis" can refer to an abnormal narrowing of an artery, usually of a discrete segment. Stenosis can also refer to a reduced cross-sectional area of a heart valve when it opens. In the case of an artery, stenosis most commonly most commonly occurs in large distributing arteries such as coronary, renal, cerebral, iliac and femoral arteries. The narrowing commonly results from a chronic disease process atherosclerosis. Sometimes a vessel can become acutely stenotic due to focal vasospasm. But in general, stenosis results from chronic vascular disease. Stenosis increases the vascular resistance as described by Poiseuille's equation, which says that resistance is inversely related to the radius to the fourth power. Therefore, if the radius (or diameter) of a vascular segment is reduced by one-half, the resistance within that narrowed segment increases by 16-fold. If this vascular segment were being perfused in isolation, the flow would be decreased 16-fold if perfusion pressure is held constant. However, in vivo this degree of stenosis would have relatively little effect on flow because the vessel is coupled in-series with other resistance vessels (CLICK HERE for more information). If we consider the renal artery and kidney circulation, the renal artery contributes to only a small fraction (<1%) of the total renal vascular resistance. Therefore, the renal artery needs to be narrowed considerably before overall renal vascular resistance is increased enough to significantly decrease renal blood flow. This is also true for other organ circulations such as the heart, limbs and brain. The term "critical stenosis" refers to a critical narrowing of an artery (stenosis) that results in a significant reduction in maximal flow capacity in a distal vascular bed. A critical stenosis may or may not reduce resting flow depending on the organ's capacity to autoregulate its blood flow and the development of collateral blood flow, both of which serve to reduce the overall resistance in the smaller resistance vessels. Clinically, a critical stenosis typically is thought of in terms of a 60-75% reduction in the diameter of the large distributing artery. This explains why interventional measures such as balloon angioplasty, stent placement, or arterial bypass surgery are not usually conducted in patients until there is at least a 75% reduction in vessel diameter. 12 Hemodynamics Pressure Gradients In order for blood to flow through a vessel or across a heart valve, there must be a force propelling the blood. This force is the difference in blood pressure (i.e., pressure gradient) across the vessel length or across the valve (P1-P2 in the figure to the right). At any given pressure gradient (DP), the actual flow rate is determined by the resistance (R) to that flow. The factors determining the resistance are described by the Poiseuille relationship. The most important factor, quantitatively and functionally, is the radius of the vessel, or in the case of a heart valve, the orifice area of the opened valve. Resistance is inversely related to the fourth power of the radius (r4) of a blood vessel. For heart valves, it is not possible to use orifice radius because the opening is not circular. Therefore, in actual practice, the area of the valve orifice is used to compute resistance instead of radius, where area (A) is proportional to the square of the radius (r2), based upon the equation A = p r2. For a heart valve, therefore, the resistance to flow is inversely proportional to A2. The pressure gradient can be viewed as the force driving flow (F), where F = DP/R. This relationship is based upon Ohm's Law from physics in which current equals the voltage difference divided by the resistance (I= DV/R). Flow is decreased, for example, if there is a decrease in DP or an increase in R as shown in the figure below. In this example, DP is an independent variable while flow is the dependent variable. The pressure gradient can also be viewed as the pressure drop (i.e., energy loss) that results from a given flow and resistance (i.e., DP is the dependent variable), where DP=F R. In other words, DP is increased by either an increase in flow or resistance. For example, under laminar flow conditions, doubling the flow across a heart valve or along a length of blood vessel doubles the pressure drop across the valve or along the length of vessel. A normal valve, like a normal large artery, has a very small resistance to flow, and therefore the pressure gradient across the valve is 13 Hemodynamics very small. In contrast, in vascular or valvular stenosis the pressure gradient is increased because of the increased resistance to flow (e.g., by decreased vessel radius or valve cross-sectional area). Furthermore, as flow increases across the stenotic lesion (e.g., when cardiac output increases during exercise), the pressure gradient (DP) increases. Other factors such as turbulence can further enhance the pressure gradient for any given flow. Viscosity Viscosity is a property of fluid related to the internal friction of adjacent fluid layers sliding past one another (see laminar flow) as well as the friction generated between the fluid and the wall of the vessel. This internal friction contributes to the resistance to flow. The viscosity of plasma is about 1.8-times the viscosity of water (termed relative viscosity) at 37C and is related to the protein composition of the plasma. Whole blood has a relative viscosity of 3-4 depending upon hematocrit, temperature, and flow rate. The viscosity of whole blood is strongly influenced by three factors: hematocrit, temperature and flow as described below. 1. Hematocrit is an important determinant of the viscosity of blood. As hematocrit increases, there is a disproportionate increase in viscosity (see figure to right). For example, at a hematocrit of 40%, the relative viscosity is 4. At a hematocrit of 60%, the relative viscosity is about 8. Therefore, a 50% increase in hematocrit from a normal value increases blood viscosity by about 100%. Such changes in hematocrit and blood viscosity occur in a patients with polycythemia. 2. Temperature also has a significant effect on viscosity. As temperature decreases, viscosity increases. Viscosity increases approximate 2% for each C decrease in temperature. This effect has several implications. For example, when a person's hand is cooled by exposure to a cold environment, the increase in blood viscosity contributes to the decrease in blood flow (along with neural-mediated thermoregulatory mechanisms that constrict the vessels). The use of whole body hypothermia during certain surgical procedures also increases blood viscosity and therefore increases resistance to blood flow. 3. The flow rate of blood also affects viscosity. At very low flow states in the microcirculation, as occurs during circulatory shock, the blood viscosity can increase quite significantly. This occurs because at low flow states there are increased cell-tocell and protein-to-cell adhesive interactions that can cause erythrocytes to adhere to one another and increase the blood viscosity. 14 Hemodynamics Bernoulli's Principle and Energetics of Flowing Blood Because flowing blood has mass and velocity it has kinetic energy (KE). This KE is proportionate to the mean velocity squared (V2; from KE = mV2). Furthermore, as the blood flows inside a vessel, pressure is exerted against the walls of the vessel; this pressure represents the potential or pressure energy (PE). The total energy (E) of the blood flowing within the vessel, therefore, is the sum of the kinetic and potential energies (assuming no gravitational effects) as shown below. E = KE + PE (where KE V2) Therefore, E V2 + PE There are two important concepts that follow from this relationship. 1. Blood flow is driven by the difference in total energy between two points. Although pressure is normally considered as the driving force for blood flow, in reality it is the total energy that drives flow between two points (e.g., longitudinally along a blood vessel or across a heart valve). Throughout most of the cardiovascular system, KE is relatively low, so practically speaking, it is the pressure (PE) difference that drives flow. When KE is high, however, that energy added to the PE (i.e., the total energy, E) is really what drives the flow. To illustrate this, consider the flow across the aortic valve during cardiac systole. During the phase of reduced ejection, the intraventricular pressure falls slightly below the aortic pressure, nevertheless, flow continues to be ejected into the aorta. The reason for this is that the KE of the blood as it moves across the valve at a very high velocity ensures that the total energy in the the blood crossing the valve is higher than the total energy of the blood more distal in the aorta. 2. Kinetic energy and pressure energy can be interconverted so that total energy remains unchanged. This is the basis of Bernoulli's Principle. This principle can be illustrated by a blood vessel that is suddenly narrowed then returned to its normal diameter. In the narrowed region, the velocity increases as the diameter decreases (V 1/D2). If the diameter is reduced by one-half in the region of the stenosis, the velocity increases 4-fold. Because KE V2, the KE increases 16-fold. If the total energy is conserved, then the 16-fold increase in KE must result in a proportionate decrease in PE. Once past the narrowed segment, the KE and PE will revert back to their original values because the diameter is the same as before the narrowed segment. This simplistic model assumes that there is no loss of total 15 Hemodynamics energy along the length of the vessel. In fact, there will be some loss of total energy and pressure (as indicated in the figure) because of the high resistance in the narrowed region and because of turbulence that occurs distal to the narrowed region. To summarize this concept, blood flowing at higher velocities has a higher ratio of kinetic energy to potential (pressure) energy. An interesting, yet practical application of Bernoulli's Principle is found when blood pressure measurements are made from within the ascending aorta. As described above, during ventricular ejection, the velocity and hence kinetic energy of the flowing blood is very high. The instantaneous blood pressure that is measured within the aorta will be very different depending upon how the pressure is measured. As illustrated to the right, if a catheter has an end-port (E) sensor that is facing the flowing stream of blood, it will measure a pressure that is significantly higher than the pressure measured by a side-port (S) sensor on the same catheter. The reason for the discrepancy is that the end-port measures the total energy of the flowing blood. As the flow stream "hits" the end of the catheter, the kinetic energy (which is high) is converted to potential (or pressure) energy, and added to the potential energy to equal the total energy. The side-port will not be "hit" by the flowing stream so kinetic energy is not converted to potential energy. The side-port sensor, therefore, only measures the potential energy, which is the lateral pressure acting on the walls of the aorta. The difference between the two types of pressure measurements can range from a few mmHg to more than 20 mmHg depending upon the peak velocity of the flowing blood within the aorta. 16 Hemodynamics Velocity versus Flow The terms "velocity" and "flow" can sometimes be confused and thought of as being interchangeable, but they are not. Velocity is the distance an object (solid, liquid or gas) moves with respect to time (i.e., the distance traveled per unit of time). In the case of blood flowing in a vessel, velocity is often expressed in the units of cm/sec. In contrast, flow is the volume of a liquid or gas that is moving per unit of time. For blood flowing in a large vessel, flow is often expressed in the units of ml/min (cm3/min; 1 ml = 1cm3). The flow of blood in a vessel is related to velocity by the following equation: F = V A (F = flow, V = mean velocity, and A = cross-sectional area of the vessel) It is important to use the mean velocity of the moving blood because blood flowing in a vessel has a parabolic profile under laminar flow conditions. Therefore, the mean velocity will be a value less than the maximal centerline velocity in a vessel. The cross-sectional area of a vessel (A) equals pi (p) times the radius squared (r2), or A= r2. Therefore, the relationship between flow and velocity can be expressed as: F V r2 This relationship indicates that at a constant vessel radius, changes in flow are proportionate to changes in velocity, and visa versa. Another important relationship to be derived from above is that velocity, at constant flow, is inversely related to the radius squared (V 1 / r2 at constant flow). This relationship has important implications for turbulent flow and the Bernoulli effect. It is important not to draw the conclusion from the above relationship that flow is proportionate to radius squared. The relationship between flow and radius for a fluid flowing in a tube is much more complex and is described by Poiseuille's relationship. As a practical application of the above relationships, the use of hemodynamic data obtained from Doppler measurements must be carefully interpreted. Doppler techniques measure velocity of the flowing blood, not flow per se. If a Doppler measurement shows that velocity decreases (for example in a brachial artery) under two different conditions (e.g., before and after administration of a vasoactive drug), the only way to know for sure that the change in velocity represents a proportionate change in flow is to know that the intervention did not alter vessel diameter. In fact, a situation could occur in which velocity falls but flow is increased. This could occur if the vasoactive drug dilates the artery from which the velocity is be measured and at the same time slightly dilates vessels downstream. The dilated brachial artery would result in a fall in velocity within the brachial artery; however, the downstream vasodilation could cause total flow to increase because of the series relationship of the vasculature. Another example would be using a Doppler technique to measure velocity in a stenotic region of a peripheral artery. In this case, the velocity in the region of the stenosis will be very high, yet the flow will likely be reduce. 17 Hemodynamics Valsalva When a person forcefully expires against a closed glottis, changes occur in intrathoracic pressure that dramatically affect venous return, cardiac output, arterial pressure, and heart rate. This forced expiratory effort is called a Valsalva maneuver. Initially during a Valsalva, intrathoracic (intrapleural) pressure becomes very positive due to compression of the thoracic organs by the contracting rib cage. This increased external pressure on the heart and thoracic blood vessels compresses the vessels and cardiac chambers by decreasing the transmural pressure across their walls. Venous compression, and the accompanying large increase in right atrial pressure, impedes venous return into the thorax. This reduced venous return, and along with compression of the cardiac chambers, reduces cardiac filling and preload despite a large increase in intrachamber pressures. Reduced filling and preload leads to a fall in cardiac output by the Frank-Starling mechanism. At the same time, compression of the thoracic aorta transiently increases aortic pressure (phase I); however, aortic pressure begins to fall (phase II) after a few seconds because cardiac output falls. Changes in heart rate are reciprocal to the changes in aortic pressure due to the operation of the baroreceptor reflex. During phase I, heart rate decreases because aortic pressure is elevated; during phase II, heart rate increases as the aortic pressure falls. When the person starts to breathe normally again, aortic pressure briefly decreases as the external compression on the aorta is removed, and heart rate briefly increases reflexively (phase III). This is followed by an increase in aortic pressure (and reflex decrease in heart rate) as the cardiac output suddenly increases in response to a rapid increase in cardiac filling (phase IV). Aortic pressure also rises above normal because of a baroreceptor, sympathetic-mediated increase in systemic vascular resistance that occurred during the Valsava. Similar changes occur whenever a person conducts a force expiration against either a closed glottis or high pulmonary outflow resistance, or when the thoracic and abdominal muscles are strongly contracted. This can occur when a person strains while having a bowel movement. Similar changes can also occur when a person lifts a heavy weight while holding their breath. 18 ...
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This note was uploaded on 04/18/2008 for the course PHYS 1010 taught by Professor Thompson during the Fall '07 term at New York Medical College.

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