Circulation Research SPECIAL ARTICLE. The Cardiac and Vascular Factors That Determine Systemic Blood Flow

Transcription

1 Circulation Research An Official Journal of the American Heart Association SPECIAL ARTICLE The Cardiac and Vascular Factors That Determine Systemic Blood Flow JUNE 1979 VOL. 44 NO. 6 MATTHEW N. LEVY THE CARDIOVASCULAR system is a closed circuit. At any given moment, the rate at which blood returns to the heart from the venous system (venous return) may differ considerably from the rate at which the heart pumps it out into the arterial system (cardiac output). Under steady state conditions, however, cardiac output (CO) and venous return (VR) are virtually equal. Therefore, it probably is better not to distinguish between CO and VR under such conditions, but simply to consider the total blood flow (OJ around the circuit. There has been a tendency on the part of some investigators to explain steady state changes in CO in response to certain conditions (e.g., blood loss, exercise, vasoactdve drugs) by invoking changes in VR. Such an explanation is meaningless, however. These conditions affect Q. for reasons that merit analysis, and such changes in Q are, of course, attended by equal changes in CO and VR at equilibrium. However, to explain the steady state change in CO on the basis of a change in VR is a patent example of circular reasoning; it is tantamount to explaining a change in Q on the basis of a change in Q. This paper will deal with the cardiac and vascular factors that determine the rate of blood flow around the circulatory system, principally under steady state conditions. The following are some of the salient questions to be addressed: What are the factors responsible for the equality of VR and CO at equilibrium? Is there one group of factors that influences the heart to pump a certain level of CO, and are these then the same factors responsible for the VR? Or is a separate group of factors responsible for the VR? Specifically, is the right atrial pressure an important determinant of the VR, by virtue of its being one of two critical factors in a hypothetical From the Division of Investigative Medicine, Mt Sinai Hospital, and Case Western Reserve University, Cleveland, Ohio. Supported by U.S. Public Health Service Grant HL Address for reprints: Matthew N. Levy, M.D., Chief, Investigative Medicine, Mt. Sinai Hospital, 1800 East 105th Street, Cleveland, Ohio "gradient for venous return"? Or is the level of the right atrial pressure simply the result, not the cause, of a change in VR? Does the level of the right atrial pressure have opposite effects on CO and VR? Coupling of the Heart and Circulation In the early investigations of the control of CO, such as those of Frank (1895) and of Starling and his collaborators (Patterson et al., 1914), the heart was studied after it had been separated from the vascular system. Such isolated heart preparations permitted rigorous control of the experimental variables, and many basic mechanisms were elucidated. However, it became increasingly evident that the vascular system interacts with the heart, and that the control of CO is influenced substantially by the characteristics of the blood vessels and of the blood itself (i.e., its volume and viscosity). Much of the work on the role of the vascular system in the control of CO was done by Guyton and his associates (Guyton, 1955; Guyton et al., 1955, 1957, 1973). To analyze the functional coupling between the heart and the blood vessels, a model will be used in which the cardiovascular system has been reduced to its simplest components. As shown in Figure 1, the model consists of a pump, an elastic arterial system, a peripheral resistance (R), and an elastic venous system. The advantage of the simplified model is the relative ease of analysis of the interactions among the components, thereby permitting the elucidation of certain basic principles. For many purposes (e.g., when there are substantial blood volume shifts between the pulmonary and systemic circuits), the model is much too simple and potentially misleading. For such purposes, more complicated models must be used, such as those developed by Grodins and his coworkers (Grodins, 1959; Grodins et al., 1960), Sagawa (1972), and Guyton et al. (1973). The model of the cardiovascular system shown in Figure 1 may be subdivided arbitrarily into car-

2 740 CIRCULATION RESEARCH VOL. 44, No. 6, JUNE 1979 bottom half of the loop represent the vascular activity. A preliminary version of this block diagram has been presented previously by Fennoso et al. (1964), and a more detailed version has been developed by Grodins and his coworkers (Grodins, 1959; GrodinsetaL, 1960). Vein Artery FIGURE 1 Simplified model of the systemic circulation. The coupling between the heart and the vascular system consists of the right atrium (RA) and the aortic origin (AO). Other abbreviations: R, systemic resistance; P w central venous pressure; Pra, right atrial pressure; and Pa, arterial pressure. diac find vascular components. There are two sites of coupling between these components; (1) the right atrium serves to connect the terminal veins to the input side of the pump, and (2) the aortic origin serves to connect the output side of the pump to the upstream end of the vascular system. From the functional viewpoint, the pressures in the aorta (P a ) and in the right atrium (Pr.) and central veins (P v ) are the mechanical feedback signals that coordinate the activities of these two principal components of the cardiovascular system. In the model, the pressures in the right atrium and large veins are considered to be equal; i.e., P ~ Pv. The cardiac contraction tends to establish the prevailing levels of P, and P v, which in turn are important determinants of the rate of blood flow through the vascular system. Concomitantly, the characteristics of the vascular system tend also to determine the levels of P«and P v, which in turn critically affect the quantity of blood to be pumped by the heart. Of course, in the real cardiovascular system, there are many ways in which the cardiac and vascular components may interact with one another, other than simply by virtue of the prevailing levels of P a and P v. Such important reflex and humoral mechanisms will be neglected in this discussion, and only the mechanical factors will be considered. The influence of the modulating factors has been described in detail in the monograph by Guyton et al. (1973). The block diagram shown in Figure 2 will help to outline the manner in which the two principal subunits of the simplified model of the cardiovascular system interact mechanically with each other. The blocks in the diagram constitute a feedback loop. The block in the top half of the loop represents the cardiac behavior, whereas the two blocks in the The Cardiac Component Skeletal muscle contraction, including that of the respiratory muscles, may play a small role in propelling blood around the circulatory system. However, for all practical purposes, the heart must be considered to be the energy source responsible for pumping the total blood flow (Q) around the body, regardless of whether that flow be denoted as CO orvr. Preload, afterload, cardiac contractility, and heart rate usually are considered to be the factors that determine the output of the heart. P ra and right ventricular dimensions are the determinants of right ventricular preload. Similarly, P a and left ventricular dimensions are the determinants of left ventricular afterload. Hence, in the "cardiac function" block (A) in Figure 2, P«and P v are shown as two critical inputs that tend to determine Q. The response surface displayed in Figure 3 shows the influence of these two factors on Q (Hemdon and Sagawa, 1969). In general, Q varies directly with P v and inversely with P a. Changes in either heart rate or myocardial contractility result in a shift to a new response surface. The Vascular Component When a fluid is pumped through a system of tubes, the hydraulic equivalent of Ohm's law is: Q. = (Pi - P 2 )/R, (1) where Q is the flow, R is the total resistance, and (Pi - P2) is the pressure gradient across that resistance. If the hydraulic system under consideration were p. Q =f(p.,p.,hr,cont) CARDIAC (A) A P. C» AP, = " C. VASCULAR (C) P.-P. P.-P, = QR VASCULAR (B) FIGURE 2 Block diagram of the feedback loop involved in the coupling of the cardiac and vascular portions of the circulatory system. Abbreviations: 0, systemic flow; Pa, arterial pressure; P a venous pressure; HR, heart rate; Cont, cardiac contractility; R, systemic resistance; Co, arterial capacitance; and C w venous capacitance. 6

3 CARDIAC OUTPUT REGULATION/Levy 741 t OOO 20O FIGURE 3 Response surface, showing the change in aortic flow in an anesthetized dog as a function of the mean arterial pressure (MAP) and mean right atrial pressure (MRAP) (from Herndon and Sagawa, 1969, with permission). VJ 300 taken to be the systemic vascular system, the pressure gradient would be the arteriovenous pressure gradient, P. - P v. Substituting (P. - P v ) for (Pi - P 2 ) in Equation 1 and rearranging, we obtain P. -Pv (2) From this equation, it is apparent that the magnitude of the arteriovenous pressure gradient at equilibrium is determined by the peripheral vascular resistance, R, and by the quantity of blood per minute being pumped by the heart, Q. An increase in Q would evoke a proportionate increase in the gradient, and a decrease in Q would elicit a proportionate reduction in the gradient. Assuming a constant R for the present purpose, and given that the energy source for the flow is derived from the pumping action of the heart, we may consider Q to be the independent variable (i.e., the input, or stimulus) in this relationship, and (P, P v ) to be the dependent variable (i.e., the output, or response). Therefore, in block B of Figure 2, Q is shown as the input variable to the block, and (P. P v ) is shown as the output variable. The selection of the dependent and independent variables is often arbitrary. For example, the energy of cardiac contraction is involved in the development of pressure as well as flow. Therefore, for other purposes, the opposite assignment of dependent and independent variables might have been made. The problem of the optimal assignment of variables is discussed in greater detail below. The actual level of each of the two terms, P a and P v, of the pressure gradient that occurs with a given change in Q (Equation 2) is determined by the elastic characteristics of the systemic circulation and by the blood volume. The arterial capacitance, C a, is defined as dv«/dp«, where V«and P«are the blood volume and pressure, respectively, on the arterial side of the circuit. Similarly, the venous capacitance, Cv, is defined as dv v /dp v, where V v and P v are the venous volume and pressure, respectively. In our model (Fig. 1), let C«and Cv both be constant, i.e., independent of both pressure and volume. Under such conditions, it is also true that C. = AV./AP., and C v = AV V /AP V. In the model under consideration (Fig. 1), let the changes in blood volume take place only in the systemic arteries and veins. Given a constant total blood volume, AV - -AV. (3) Hence, any increment in V. is accompanied by an equal decrement in V v, or vice versa. But AV, C«AP«, and AV V = Cv AP V. Substituting these values in Equation 3 and rearranging, we obtain AP./APv = -Cv/C (4) A simple example will illustrate how, with a

4 742 CIRCULATION RESEARCH VOL. 44, No. 6, JUNE 1979 specific ratio of C v /C«, a given change in (P. P v ) will produce specific changes in P, and P v. For the schema in Figure 1, let R = 20 mm Hg min/liter, let C V :C«= 19:1, and let C v and C a remain constant, regardless of the levels of pressure and volume. These values for R and the Cv:C, ratio are close to the mean values for normal, resting adults. Consider the system at first to be static; i.e., Q = 0. At equilibrium, the pressures throughout the system all will be equal. Guyton et al. (1973) have termed this static pressure the "mean systemic pressure," P. This pressure depends on the total blood volume and on the overall capacitance of the systemic vascular system. Under normal conditions, Pros is about 7 mm Hg (Guyton, 1955; Guyton et al, 1957, 1973). For our model, therefore, let Pm, = 7 mm Hg. Also, because pressures are equal throughout the system, P«P v = 7 mm Hg. A graph can be constructed relating P«and P v to Q (Fig. 4). Note that point a on this graph has the coordinates (0, 7) and represents the value of Pm,. Consider next that the heart in this previously static system begins to pump blood at a constant rate of 1 liter/min. The equilibrium value for (P. P v ) may be computed from Equation 2: P. - P v = 20 mm Hg. (5) This computation is represented by block B in Figure 2. Clearly, the operation of the pump produces the flow of 1 liter/min throughout the systemic circulation. At equilibrium, VR and CO will both equal 1 liter/min. This flow through the resistance of 20 mm Hg-min/liter is responsible for the pressure gradient of 20 mm Hg. Stated in another way, Q is the independent variable for this process, and (P, Pv) is the dependent variable. The individual values for P. and P v depend not only on this gradient but also on P m and the ratio of C v :C a. In our example, Pm, - 7 mm Hg, and C v / C a = 19, as stated above. Therefore, from Equation 4: AP./APv (6) Let AP a = P. - P m, and let AP V = P v - P m. With reference to Figure 4, AP. and AP V represent the deviations of P«and P v, respectively, from P m, for any given level of Q. By substitution of these values for AP«and AP V into Equation 6: P (P - (7) By solving simultaneous Equations 5 and 7, it is found that P, = 26 and P v = 6. Note that the process by which the individual values for P, and P v are derived from the value for the arteriovenous pressure gradient is represented by block C in Figure 2. Note also that the points with coordinates (Q 1, P a = 26) and (Q =» 1, P v = 6) appear as points b and c, respectively, in Figure 4. Finally, let the heart begin to pump blood at a constant rate of 5 liters/min. By the same analytical P. 80 irnhg p, mmhg y 20 - b/ > ft P.»p. (p a-p.) Pm. 1 1 ^ ^ (l/min) FIGURE 4 The values of arterial pressure (P a ) and central venous pressure (P u ) as functions of the systemic flow (0) in the model depicted in Figure 1, where R 20 and CJC a 19. Point a denotes the value of the mean systemic pressure (Pms), i.e., the common value for P a and P v when 0 = 0. Points b and c denote the values of P a and P o when 0 1, and points d and e, the values of P a and P v when 0 = 5. The deviations ofp a and P v from P*, are denoted by AP O and AP D, respectively. Note that the scales for P a and P u are not the same. process, P a - P v = 100 mm Hg (block B, Fig. 2), and P, and P v = 102 and 2 mm Hg, respectively (block C, Fig. 2). Note that points d and e in Figure 4 have the coordinates (Q = 5, P. = 102) and (Q =» 5, P v = 2), respectively. The Closed Circulatory Loop The heart and blood vessels operate in the circulatory system as an integral unit, and the function of either component is affected by the other. The heart provides virtually all of the energy for the circulation of the blood through the vascular system. It therefore is responsible for total Q around the circuit, whether that flow be called "cardiac output" or "venous return." The magnitude of Q is determined by a variety of factors, including P. and P v (block A, Fig. 2). P, and P v, in turn, are determined not only by the operation of the heart itself but, also, by certain critical characteristics of the vascular bed. Q and R determine the arteriovenous pressure gradient (block B), and the total blood volume and vascular capacitances determine the actual levels of P. and P v (block C). Thus P, and P v are determinants of Q by virtue of their influences on the heart, and Q

5 CARDIAC OUTPUT REGULATION/Lei/y 743 is a determinant of P. and P v by virtue of its interaction with the vasculature. The equilibrium values of Q., P«, and P v constitute the solution of the simultaneous equations represented by the three blocks in Figure 2. The value of P, which depends in part on the blood volume, is a boundary condition for the equation represented by block C. Interrelations between CO and P,, A complicated, three-dimensional graph (Fig. 3) is necessary to depict the simultaneous influences of P. and P v on the pumping capabilities of the heart (block A, Fig. 2). The functions represented by blocks B and C in Figure 2 could be represented by other response surfaces. For a given set of conditions, the equilibrium values for P«, P v, and Q. would be represented graphically by the point of intersection of these three response surfaces. Sagawa (1973) has shown that the equilibrium value also may be represented by the intersection of the three-dimensional response surface for CO (Fig. 3) with a curve in space that represents the vascular components of the system. Guyton and his coworkers (Guyton, 1955; Guyton et al., 1973) have developed a simpler graphical analysis, in which the interrelations are plotted between just two of these variables, P v and Q. Two separate sets of relationships have been delineated, as shown in Figure 5. Curve A has been called a "cardiac output curve," and curve B a "venous return curve." Unfortunately, these designations tend to be ambiguous because they each represent the flow around a closed circuit, and, except for transient influences, any factor that affects CO has an equal effect on VR, and vice versa. For this reason, and for others to be cited below, I suggest substituting the terms "cardiac function curve" and "vascular function curve" for curves A and B, respectively, in Figure 5. These terms stress the applicability of the respective curves to the cardiac and vascular components of the cardiovascular system. The cardiac function curve represents the Frank- Starling mechanism. This curve (or, more precisely, the response surface as shown in Figure 3) describes the behavior of the heart specifically and is independent of the nature of the vascular system. Indeed, the original studies by Starling and his collaborators were done on isolated heart-lung preparations (Patterson et al., 1914); the systemic circulation was eliminated. The cardiac function curve depicts the systemic flow (Q) pumped by the heart as a function of P v ; i.e., P v is the independent variable and Q. the dependent variable. In accordance with the usual convention, P v is plotted along the abscissa and Q. along the ordinate. This curve will be shifted downward by a decrease in contractility or by an increase in afterload and will be shifted upward by the opposite changes in contractility and afterload. A given cardiac function curve Q (l/min) P v (mmhg) tardiac FUNCTION VASCULAR FUNCTION FIGURE 5 The cardiac function curve (A) expresses how systemic flow (Q) changes as a function of the central venous pressure (P v ); it represents the Frank- Starling mechanism. The vascular function curve (B) expresses how P v changes as a function of 0. Note that, for curve A, P v is the independent variable and 0 the dependent variable; for curve B the opposite is true. represents the intersection of the response surface in Figure 3 with the vertical plane, parallel to the MRAP axis, that represents the prevailing arterial pressure. With respect to the block diagram in Figure 2, the cardiac function curve represents the operation of block A. The vascular function curve (B, Fig. 5) depends on blood volume, peripheral resistance, venomotor tone, and vascular compliance, as shown by Guyton and his coworkers (Guyton, 1955; Guyton et al., 1955, 1957, 1973) in an extensive series of studies. Because the curve does depend in part on blood volume, "hemovascular function curve" would be a more comprehensive, but a more cumbersome, designation, and therefore will not be used herein. The vascular function curve is independent of the characteristics of the heart; it may be derived experimentally by totally replacing the heart by an artificial pump. Guyton and his collaborators designated this curve the "venous return curve," because they considered that P is an important determinant of VR. Hence in their plots P v was considered to be the independent variable and Q the dependent variable. From their viewpoint, plotting P v along the abscissa and Q. along the ordinate, as in Figure 5, would conform to the usual convention. It may be questioned, however, whether the identification of P v as the independent variable and Q. as the dependent variable for curve B is the most judicious selection. The development of a mathematical model is an abstraction, and hence the assignment of dependent and independent variables may be arbitrary. If the model is devised to improve our understanding of a specific problem, however, the optimal designation of dependent and indepen-

6 744 CIRCULATION RESEARCH VOL. 44, No. 6, JUNE 1979 dent variables may be critical, because it usually implies a certain relationship between cause and effect. With respect to the two variables that are related by curve B (Fig. 5), for example, the choice of designations involves the question of whether a change in P v is an important cause of a change in VR or the result of some change in Q around the circuit. Guyton and his associates (Guyton, 1955; Guyton et al., 1973) consider that small changes in P v may have enormous effects on VR. They argue that the difference between Pms and P ra is the "pressure gradient for venous return." Pms is a weightedaverage pressure and equals the static pressure for the systemic circulation, as stated above. Normally, P ms is about 7 mm Hg, and P ra is only slightly less than that. Therefore, Guyton and his collaborators have reasoned that a rise in P ra of only about 5 mm Hg would halt VR and reduce Q to zero, if Pms were held constant. The theoretical analysis presented above and summarized in Figure 4 suggests that the level of P v (or P ra ) is actually a consequence of the rate of Q around the circuit. It is, of course, also a determinant of Q, but principally through its effect on the filling of the heart (block A, Fig. 2). It probably is not an important determinant of "venous return" by virtue of any "back-pressure" effects. A rise in P v of only a few mm Hg would reduce the (P a P v ) gradient only slightly at normal levels of P a. From Equation 2, therefore it would be expected that a small reduction in the pressure gradient per se would produce only a small, proportionate reduction in Q. With respect to the hypothetical "pressure gradient for venous return" (i.e., P v Pms), Figure 4 does indeed show that 0 and (P v Pms) are proportional to each other. However, the theoretical analysis indicates that any change in P v Pms was evoked by a change in Q, and not the converse. Stated in another way, P v Pms represents a "pressure gradient caused by flow," rather than a "pressure gradient for venous return." Guyton et al. (1957, 1973) conducted a series of experiments on the mechanical factors that control VR. They used a right-heart bypass preparation, in which all of the VR to the right atrium was pumped mechanically into the cannulated pulmonary artery; i.e., an artificial pump replaced the right ventricle. Thin, collapsible tubing was included in the line between the right atrium and the pump, and the pump was adjusted to keep the tubing in a "semi-collapsed condition." To produce new values of Pra and Q, the hydrostatic level of the collapsible tubing was changed and the pump was readjusted to produce the same semicollapsed state in the thin tubing. Raising the level of the collapsible tubing and decreasing the pumping rate until the thin tubing returned to the semicollapsed state resulted in an elevation of P ra and a decline of Q. The investigators (Guyton et al., 1957, 1973) asserted that the collapsible tubing permitted direct control of the level of P ra, and that the changes in Q were a consequence of the experimentally induced change in P ra. Hence, they identified P ra as the independent variable ("stimulus") and Q as the dependent variable ("response"). However, the necessity of adjusting both the level of the collapsible tube and the pumping rate prior to making a measurement did introduce ambiguity in the identification of the independent and dependent variables. Did adjustment of the height of the collapsible tube set the level of P ra, which then determined the rate of VR, or did adjustment of the pumping rate (Q) produce the resultant level of P ra? These experiments on the right-heart bypass preparation recently were repeated in our laboratory in an open-chest, anesthetized dog. A roller pump was used to transport the blood returning to the right atrium into the pulmonary artery over a range of pumping rates. The only critical difference in our experimental system from that of Guyton and his coworkers was that the collapsible tube was excluded. As stepwise changes were made in the pumping rate (Q), there were parallel alterations in P a, but there were concomitant, inverse changes in P v and P ra, as shown in Figures 6 and 7. Similar results have been reported previously by Grodins et al. (1960) in a group of eight dogs. Elimination of the collapsible tubing in the experiment shown in Figures 6 and 7 and in the experiments by Grodins and his collaborators averted the ambiguity in the identification of the independent and dependent variables. The pumping rate was the factor that was altered experimentally; hence, Q was the independent variable, by definition. Changes in Q evoked changes in P a and P v, which then constituted the dependent variables. A series of experiments also was carried out by Guyton (1955) on a total heart bypass preparation. A collapsible tube was not included in the experimental design. Changes in Q produced by the arti- FIGURE 6 The changes in arterial (P a ) and central venous (P v ) pressures produced by changes in systemic blood flow (Q) in a canine right-heart bypass preparation. Stepwise changes in Q were produced by altering the rate at which blood was mechanically pumped from the right atrium to the pulmonary artery.

7 CARDIAC OUTPUT REGULATION/Leuy 745 mmhg vasculature. Hence, the graphs of P v as a function of Q (Figs. 4 and 7) reflect the influence of blood volume and certain critical vascular factors on the prevailing flow rate to produce a specified level of P v. They do not represent the effect that a change in P v will have on Q. Therefore, it is preferable that such curves be called "vascular function curves," rather than "venous return curves." mmhg Q (l/min) FIGURE 7 Graphs of arterial (P a ) and central venous (P v ) pressures as functions of the systemic blood flow (Q) for the experiment shown in Figure 6. Note that the scales for P a and P v are not the same. Pms is the mean systemic pressure, i.e., the value of P a and P v that prevails when Q = 0. ficial pump that replaced the heart were associated with inverse changes in P v. The change in Q was initiated by the investigator (Guyton, 1955), and the inverse change in P v was the response noted in the animal. It is apparent, therefore, that the change in P v was a consequence of the experimentally induced change in Q. Note that the experimental data plotted in Figure 7 are qualitatively similar to those derived theoretically in Figure 4. The curves that represent the experimentally derived levels of P a and P v as functions of Q are not linear, principally because C a, C v, and R are not constants in vivo, as they were assumed to be in the model. Also, the level of Pms was abnormally high, principally because of overhydration and reflexly induced venoconstriction. Directionally, however, changes in Q evoked concordant changes in P a and inverse changes in P v, just as in the theoretical model. Similar results have also been obtained by Grodins et al. (1960). Although the data in individual animals were nonlinear in their experiments, the composite data for the group of eight animals indicated that P a and P v were virtually linear functions of Q. The experimentally derived plot of P v as a function of Q (lower half of Fig. 7) may be considered to reflect the interaction between the vascular factors and the flow generated by the pump. With reference to Figure 2, this graph represents the actions of blocks B and C on Q; that is, with a given flow, a certain level of P v will be achieved, depending on the blood volume and the characteristics of the Graphic Analysis of CO Control Guyton and his coworkers (Guyton, 1955; Guyton et al., 1973) made a monumental contribution to the analysis of cardiovascular control by showing that, at equilibrium, the levels of CO and P ra are defined by the point of intersection of the two independent curves shown in Figure 5. The cardiac function curve (A) depicts the systemic flow (Q) pumped by the heart as a function of P ra or P v ; i.e., P v is the independent variable and is plotted along the abscissa, whereas Q is the dependent variable, and is plotted along the ordinate, in accordance with convention. The vascular function curve (B, Fig. 5) depends on blood volume, peripheral resistance, venomotor tone, and vascular compliance, as shown by Guyton and his coworkers (Guyton, 1955; Guyton et al., 1973). According to the arguments presented above, it reflects how these characteristics of the vascular system produce a certain value of P v for a given level of Q. Hence, for curve B (Fig. 5), P v and Q are the dependent and independent variables, respectively. To include this curve and curve A on the same set of axes, the usual plotting convention must be reversed for one of these curves. The axes have arbitrarily been reversed for the vascular function curve. To interpret the interactions between these two functions properly, curve A must be considered to represent the level of Q that would prevail at a given level of P v, and curve B to reflect the level of P v that would prevail at a given level of Q. At equilibrium, only one pair of values of P v and Q satisfy the two relationships. This pair of values are the coordinates of the point of intersection of the two curves, as originally enunciated by Guyton and his colleagues (Guyton, 1955; Guyton et al., 1973). After a transient perturbation, the levels of P v and Q may deviate temporarily from their equilibrium values. However, given a constant state of the heart and vasculature, the levels of P v and Q would approach that same equilibrium value in a series of diminishing steps. Each step would involve the processes represented by a complete circuit of the feedback loop shown in Figure 2. References Fermoso JC, Richardson TQ, Guyton AC: Mechanism of decrease in cardiac output caused by opening the chest. Am J Physiol 207: , 1964 Frank 0: Zur Dynamik des Herzmuskels. Z Biol 32: , 1895

8 746 CIRCULATION RESEARCH VOL. 44, No. 6, JUNE 1979 Grodins FS: Integrative cardiovascular physiology: A mathematical synthesis of cardiac and blood vessel hemodynamics. Q Rev Biol 34: , 1959 Grodins FS, Stuart WH, Veenstra RL: Performance characteristics of the right heart bypass preparation. Am J Physiol 198: , 1960 Guyton AC: Determination of cardiac output by equating venous return curves with cardiac response curves. Physiol Rev 35: , 1955 Guyton AC, Lindsey AW, Kaufmann BN: Effect of mean circulatory filling pressure and other peripheral circulatory factors on cardiac output. Am J Physiol 180: , 1955 Guyton AC, Lindsey AW, Abernathy B, Richardson T: Venous return at various right atria] pressures and the normal venous return curve. Am J Physiol 189: , 1957 Guyton AC, Jones CE, Coleman TG: Circulatory Physiology: Cardiac Output and Its Regulation, ed 2. Philadelphia, WB Saunders, 1973 Hemdon CW, Sagawa K: Combined effects of aortic and right atrial pressures on aortic flow. Am J Physiol 217: 65-72, 1969 Patterson SW, Piper H, Starling EH: The regulation of the heart beat. J Physiol (Lond) 48: , 1914 Sagawa K: The use of control theory and systems analysis in cardiovascular dynamics. In Cardiovascular Fluid Dynamics, vol 1, edited by DG BergeL London, Academic Press, 1972, pp Sagawa K: The circulation and its control. I: Mechanical properties of the cardiovascular system. In Engineering Principles in Physiology, vol 2, edited by JHU Brown, DS Gann. London, Academic Press, 1973, pp Editors' note: Dr. Arthur Guyton was one of the referees for this Special Article. He provided the following comments, which were judged to merit publication: This paper by Dr. Levy shows a high degree of insight into the interrelationships between cardiac and peripheral vascular factors for determining overall function of the circulation. It is clear from the paper that most of the concepts presented are similar to those that we have discussed in previous papers, but with the addition of new ways of looking at the problem. Having worked in this field for a number of years, I find myself in complete agreement with Dr. Levy on all but two minor points, neither of which is important conceptually and both of which justify discussion only from a semantic point of view. These are: First, Dr. Levy has suggested that, in the analysis of the venous return curve, venous pressure is a dependent variable and venous return is an independent variable. I agree wholeheartedly that venous pressure is a dependent variable. However, I would not quite agree that venous return is an independent variable, but instead is just as much a dependent variable as is venous pressure. This lack of independence becomes especially clear when one develops a relatively complete mathematical model of the circulation and then runs the model on a computer (Guyton et al., Annu Rev Physiol 34: 13-41, 1972). One immediately finds that both venous pressure and venous return are dependent variables. When one considers the mechanics of the circulation (leaving out reflexes, hormonal factors, and so forth), the independent variables are such factors as resistance and capacitance of each segment of the circulation, contractility of the heart, heart rate, and so forth. On the other hand, there is no possible way in such a model to make venous return, cardiac output, venous pressure, or arterial pressure independent variables. Instead, all of these are dependent on the independent variables listed above. When one considers the reflexes and the hormones as well even some of the "independent" variables listed above then also become dependent variables. On the other hand, it often is very useful in analyses of the circulation to set up "what if" types of function curves. In our own early analyses we asked ourselves the two questions: (1) What would happen to cardiac output if the venous pressure changed through a range of values? (2) What would happen to venous return if the venous pressure changed through the same range of values? Then, using the two derived curves, we were able to show that the point of intersection defines both the cardiac output and the right atrial pressure at the same time, neither one of these two being an independent variable but instead both being dependent variables. On the other hand, we could equally as well have constructed these same two curves by asking the following two questions: (1) What would happen to the venous pressure if the cardiac output increased from zero up to and above the normal operating level? (2) What would happen to the venous pressure if the systemic blood flow changed through a range of values from zero up to and above the normal operating level? If we had analyzed cardiac output and systemic venous pressure using these two questions, the analysis would have worked out to be exactly the same. However, in using these two separate approaches to cardiac output analysis, in one instance we make the theoretical assumption that the systemic venous pressure is an independent variable and that cardiac output (and venous return, which is equal to cardiac output) is the dependent variable. In the other type of analysis we make the assumption that cardiac output (and venous return) is the independent variable and systemic venous pressure is the dependent variable. However, in the actual circulation, neither of these two theoretical assumptions for independence holds true. Instead, both the cardiac output and the systemic venous pressure are dependent variables. The second semantic point on which I might differ with Dr. Levy is on the use of the terms "cardiac function curve" and "vascular function

9 COMMENTS ON SPECIAL ARTICLE 747 curve." Actually, in several editions of my Textbook of Medical Physiology (W.B. Saunders Co., 1966 and 1971), I used the terms "cardiac function curve" and "systemic function curve." The term "systemic function curve" was used instead of Dr. Levy's more encompassing "vascular function curve" to delineate the fact that the systemic circulation and the pulmonary circulation are different vascular elements. However, in using these two terms I found that they created confusion because there are many other types of cardiac function curves and many other types of systemic function curves. Therefore, from experience in teaching this subject to students, I found it much better to use more specific terms, which explains why I prefer to use the terms "cardiac output curve" and "venous return curve." When I chose to use these more specific terms, I also consciously remembered a dictum from my writing course in the University that whenever several alternative terms might be used, the more specific one almost always has a more definitive meaning and is more useful in discussions. This has been my experience after an unsuccessful period of using the more general terms which were almost identical to those that are now suggested by Dr. Levy. Therefore, I hope that we can stick to the more specific terms, even though I have no conceptual disagreement with the less specific terms. In any event, the terms and the different analytical approaches are merely tools to help us understand more fully the basic function of the circulation. What is truly important is the conceptual framework that Dr. Levy has presented in this paper, and also, I hope, the slightly different framework that we have attempted to present in the past. The subject of cardiac output regulation is so important that all possible analytical approaches to its understanding deserve widespread support and exploration. Dr. Arthur C. Guyton Department of Physiology and Biophysics University of Mississippi Medical Center Jackson, Mississippi 39216