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Department of Physiology and Biophysics, University of Washington, Seattle, Washington 98195-7290
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ABSTRACT |
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 TOP
 ABSTRACT
 INTRODUCTION
HOW VENOUS RETURN CURVES...
ALTERNATIVE WAYS OF ACQUIRING...
SUMMARY
REFERENCES
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A. C. Guyton pioneered major advances in understanding cardiovascular equilibrium. He superimposed venous return curves on cardiac output curves to reveal their intersection at the one level of right atrial pressure (Pra) and flow simultaneously consistent with independent properties of the heart and vasculature. He showed how this point would change with altered properties of the heart (e.g., contractility, sensitivity to preload) and/or of the vasculature (e.g., resistance, total volume). In such graphical representations of negative feedback between two subdivisions of a system, one input/output relationship is necessarily plotted backward, i.e., with the input variable on the y-axis (here, the venous return curve). Unfortunately, this format encourages mistaken ideas about the role of Pra as a "back pressure," such as the assertion that elevating Pra to the level of mean systemic pressure would stop venous return. These concepts are reexamined through review of the original experiments on venous return, presentation of a hypothetical alternative way for obtaining the same data, and analysis of a simple model.
cardiac output; cardiovascular equilibrium; mean systemic pressure; peripheral vasculature; vascular function curves
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INTRODUCTION |
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TOP
ABSTRACT
INTRODUCTION
HOW VENOUS RETURN CURVES...
ALTERNATIVE WAYS OF ACQUIRING...
SUMMARY
REFERENCES
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WE OWE TO A. C.
GUYTON and co-workers major steps toward the understanding of the
mechanical coupling between the heart and peripheral vasculature. Their
experimental data, described graphically as "venous return curves"
(Fig. 1) revealed how right atrial
pressure (Pra) varied in relation to the rate of flow through the
peripheral vasculature (2, 5, 6). Guyton went on
(2) to combine this new information with extant
information about the relationship between Pra and cardiac output. He
pointed out that the dependence of cardiac output on Pra and the
functional relationship shown in a venous return curve together dictate
an equilibrium in the intact system at a specific Pra and cardiac
output. He illustrated the equilibrium graphically as the point of
intersection of the appropriate cardiac output curve with the
appropriate venous return curve, each appropriate in the sense of
representing specified states of the heart and vasculature,
respectively. He also focused on the pressure recorded with zero flow
through the vasculature, defined as mean systemic pressure (Pms), and
saw Pms as manifesting the total volume contained within the peripheral
vasculature in relation to the elastic properties of the complex
container comprised by the peripheral vasculature.
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The value of this approach to studying the cardiovascular system cannot be overestimated; the work of Guyton and his co-workers set the stage for the intervening decades of progressive expansion of knowledge about control of cardiac output (12). Yet some have misinterpreted features of venous return curves as applicable to analysis of the dynamics of venous return. Indeed, venous return implies a dynamic context. We would not need this separate term except for those situations in which cardiac output and venous return temporarily differ. In fact, Guyton et al. did not record venous return in dynamic states. They emphasized that their data were all taken from steady states (5).
Therefore, a physical model based on the sloped segment of venous return curves cannot apply to dynamic states. In that model, since taught to three generations of medical students, venous return is driven through a fixed hydraulic resistor connected between a pressure source fixed at Pms and an independently variable "back pressure" Pra. Clinicians and physiologists discuss venous return dynamics in these terms; the extreme example being the statement that elevation of Pra to Pms would stop venous return. This practice of taking the components of the model as having actual counterparts in the vasculature confuses a mathematical abstraction with reality.
In the hope of clarifying this issue, this article begins with a review of how venous return curves were obtained, followed by a brief discussion of features of the curves. Then, alternative ways of recording the relationship between Pra and venous return are discussed, including a hypothetical one. In this "thought" experiment, the experimental preparation differs slightly from the one employed by Guyton et al. to make it, perhaps, easier to see the consequence of maintaining fixed blood volume and to illustrate dynamic vs. steady-state conditions. Finally, the issue of mathematical abstraction vs. reality is discussed in terms of a simple physical model.
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HOW VENOUS RETURN CURVES WERE OBTAINED |
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TOP
ABSTRACT
INTRODUCTION
HOW VENOUS RETURN CURVES...
ALTERNATIVE WAYS OF ACQUIRING...
SUMMARY
REFERENCES
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How venous return curves were obtained.
Guyton and his colleagues obtained the data for their venous return
curves through the ingenious use of a Starling resistor to manipulate
Pra without altering the amount of volume circulating in the peripheral
vasculature. Their preparation, illustrated schematically in Fig.
2, is described in various papers; for a detailed description, see the 1957 paper (5).
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Procedure.
Note in Fig. 1 that flow was highest at low Pra. The authors emphasized
that Pra was kept at 
8 mmHg or lower most of the time to promote as
much venous return as possible (5) to forestall deterioration of the preparation. Data were recorded at the end of
brief periods (8-10 s) during which the Starling resistor
was elevated to obtain desired levels of Pra. Before and after these periods, which were just long enough for flow and pressures to reach a
new steady state (in their terms, after "an equilibrium rate of flow
had been established"; Ref. 5), the resistor was positioned below heart level to return to the starting subatmospheric Pra.
Necessity of changes in pump output. As shown in Fig. 1, blood flow through the vasculature fell during the periods of elevated Pra. Therefore, we know unequivocally that the outflow rate from the pump was reduced during these periods, because the flowmeter was on the pump outflow line.
What changed pump output is not clear in the 1957 paper (5). Elsewhere, descriptions of the same experiments specifically mention that the operators adjusted pump output. One paper refers to adjustment of pump output to maintain pressure at the pump end of the Starling resistor within a specific range of subatmospheric pressures (4). Another refers to controlling Pra "by increasing or decreasing the minute capacity of the pump" (2). These can be interpreted (see p. 744 in Levy's critical review; Ref. 8) to mean that the operators manually adjusted the pump after each elevation of the Starling resistor to obtain the desired state of partial collapse of the resistor tubing. However, it is conceivable that the throttling action of the Starling resistor determined pump output. Note that the pump consisted of a series of closely spaced mechanical fingers, side by side, that pressed on a length of flexible tubing in succession to create a kind of peristaltic action. Its output would have depended on the rate of sequencing of the fingers and also on how completely the tubing filled between compressions. Pump output would have been reduced if high resistance of the Starling resistor resulted in pressures in the supply line of the pump so low that the tubing would fail to fill during the fill cycle.Obligatory redistributions of volume associated with altered Pra and flow. Why the Starling resistor would at least temporarily have greater resistance to flow and why pump output had to fall after elevation of Pra can be better understood through consideration of the change in distribution of the blood volume necessarily associated with change in Pra.
With the Starling resistor placed well below heart level (solid lines for peripheral vasculature and connections to Starling resistor in Fig. 2), the great veins close to the right atrium were not fully distended, i.e., the volume contained within this segment of the vascular container was relatively low because the transmural pressures were low. One segment having less volume means that the reciprocal amount of blood has been transferred to other segments. Accordingly, the solid lines suggest that, with less of the total blood volume in the vessels near the right atrium, more of it is upstream. The dashed lines suggest the distribution of volume when the Starling resistor was positioned above heart level, when higher pressures in the vicinity of the right atrium obligated greater distention of the affected vessels, which was made possible through transfer of volume from upstream segments of the vasculature. These different distributions of volume are necessarily associated with different rates of flow. For example, when Pra was increased and blood accumulated within the central conduit veins to distend them sufficiently to bring pressures into equilibrium with the new Pra, the volume that accumulated had to come from compliant segments of the vasculature upstream. For that to happen, pressures in those upstream segments had to fall. In order for pressure in upstream segments to fall, pump rate had to fall, allowing a decline in pressure in the aorta and throughout the segments upstream of those that became relatively distended after the increase in Pra. This conclusion depends on the constraint that total volume contained within the peripheral vasculature remained constant. Other necessary restrictions include that regional compliances did not change, that flow was not redistributed among the parallel organ vasculatures, and that no other energy sources (muscle pumping, respiratory pumping) were coupled into the vasculature. Note the consequence for the Starling resistor of the volume dynamic initiated when it was elevated from the level that kept Pra subatmospheric during the rest periods. During the subsequent moments of diversion of venous return to distention of the large veins, the rate of inflow into the resistor would have been correspondingly reduced. Meanwhile, the rate of outflow was initially, at least, still at the high level set by the pump during the preceding rest period. Thus volume within the resistor tubing itself would have been reduced, increasing the tendency to collapse and obstruct flow with the consequence of reducing pressure in the inflow line of the pump. Collapse and perhaps fluttering of the resistor tubing would have been visual evidence of the need to adjust pump output. Alternatively, these changes in the Starling resistor might have sufficiently restricted inflow to the pump to reduce output to the level commensurate with the new level of Pra.What the sloped segment of classical venous return curves tells us. It makes no difference to the arguments of this paper whether pump output was adjusted manually or throttled by the Starling resistor. What matters is recognition that steady-state Pra and the rate at which blood passes through the peripheral vasculature are locked in a functional relationship. For each height of the Starling resistor, pump output had to settle at the cardiac output that would create the distribution of volume and pressure that would allow Pra to stabilize at the new level dictated by the height of the hydrostatic column.
Zero intercept of the sloped segment: Pms. The point at which the linear sloped segment intercepts zero flow is defined as Pms. For critical review of this concept and of mean circulatory pressures related to the volume of the entire cardiovascular system as opposed to that of the isolated vasculature, see Rothe (9, 10).
Horizontal segment. Guyton et al. (5) found that the Starling resistor could be positioned arbitrarily far below heart level with no change in flow, giving the series of data points for subatmospheric Pra (Fig. 1) at nearly constant flow described here as the horizontal segment of a venous return curve. This was interpreted as the consequence of partial venous collapse, i.e., the great veins functioned as Starling resistors and isolated upstream pressures from influence of progressively more negative Pra.
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ALTERNATIVE WAYS OF ACQUIRING DATA ON THE RELATIONSHIP BETWEEN PRA AND VENOUS RETURN |
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TOP
ABSTRACT
INTRODUCTION
HOW VENOUS RETURN CURVES...
ALTERNATIVE WAYS OF ACQUIRING...
SUMMARY
REFERENCES
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The relationship between Pra and steady-state flow through the vasculature discovered by Guyton and his co-workers has been reproduced in independent laboratories and with different methodologies (1, 7, 8).
Matthew Levy's vascular function curves. In particular, Matthew Levy (8) published data from experiments with a right-heart bypass preparation identical to that employed in the Guyton laboratory except that the Starling resistor was omitted. He set pump output at particular levels and recorded Pra.
Over the range of pump output from zero through maximal, he observed a progressive decline of Pra. He was not able to record a wide range of subatmospheric Pra at the upper limit of cardiac output because, without a Starling resistor to create ever more negative Pra, he could only drive Pra down to the level associated with the maximal level of output. Because Levy manually adjusted flow, it was natural to see Pra as the dependent variable and plot it on the y-axis, the format Levy referred to as a "vascular function curve." With this point of view, the natural focus falls on the steady-state cardiac output pumped through the vasculature as the determinant of Pra.A "thought" experiment.
What goes on in the collection of data for a venous return curve can
perhaps be understood more clearly if we imagine using a preparation
nearly identical to that employed by Guyton et al. (Fig. 2). In this
hypothetical preparation (Fig. 3), the
tubing conveying the venous return is allowed to overflow into a
reservoir rather than connecting to a Starling resistor. The pump that
forces flow through the peripheral vasculature is supplied from this reservoir rather than from the outflow of the Starling resistor. Further imagine that the peripheral vasculature under study is the one
characterized by the venous return curve illustrated in Fig. 1.
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Pra) is fixed, so, ignoring effects
of vessel diameters on resistance, pressure falls by the same amount
over the entire profile, as illustrated in Fig. 4. When all of the
excess volume has been removed, Pra is necessarily at 4 mmHg, the
pressure associated with Vo and a steady-state flow of 1 l/min in Fig.
1.
Successive upward adjustments of pump output and subsequent searches
(incremental lowering of the tubing end) for the level of Pra that
brings systemic volume back to Vo would map out the identical
relationship between Pra and flow shown in the sloped segment of the
venous return curve in Fig. 1.
The phenomenon that causes the horizontal segment of a venous return
curve can also be explored. In the sequential progression of upward
adjustments of pump output followed by lowering the tubing to bring
volume back to Vo, the tubing would eventually be set to a level below
the heart at which negative pressures in the large conduit veins
immediately upstream of the right atrium causes them to collapse
partially. Any further reduction of Pra has no influence on the
pressure profile upstream; it only causes further collapse. With no
transient increase in venous return due to passive volume removal, no
change in pump output is necessary to correct volume back to Vo, no
matter how much we lower Pra.
The hypothetical experiment could equally well have been carried out
with a sequence of changes in Pra and subsequent adjustments of flow to
reestablish volume at Vo. Either way obtains the same pressure-flow
relationship (Fig. 1) determined by the physical properties of this
particular vasculature at Vo because of the immutable functional
relationship between flow and Pra. Figure 5 illustrates the dynamics associated
with an elevation of Pra. As the tubing end is raised, volume
accumulates during the temporary disparity between cardiac output and
venous return (shaded area A); downward adjustment of pump
output is necessary to restore volume to Vo. Only in this rather
backward sense is venous return determined by Pra. Clearly, it is the
pump that causes the steady-state pressure profile.
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Venous return curves are not about venous return as distinct from cardiac output. To sum up, this paper offers absolutely no dispute against the validity of the obligatory relationship between steady-state flow through the vasculature and Pra under conditions of fixed systemic volume discovered by Guyton et al. (5). What it disputes is the idea that "venous return" curves describe venous return as distinct from cardiac output.
That they do not is revealed by study of the original papers. The authors clearly point out that data were obtained in steady states. The graphical presentations of the data could as legitimately have been named something like "dependence of pressure at the outflow of the peripheral vasculature on cardiac output," although it might not then have seemed natural to have Pra on the x-axis. Unfortunately, selection of the term venous return curve and of the format of the graphic evokes the misleading idea that, in the vascular subdivision of the cardiovascular system, Pra somehow determines venous return. It is true that a given level of Pra, over the range of the sloped segment, is necessarily associated with the corresponding level of flow, but it is not the cause, it is the effect. The thought experiment described above reveals that it is no more possible to turn around the drive and response sides of this relationship than it is to make the relationship between preload and cardiac output operate in reverse. Nonetheless, the approach pioneered by Guyton (2) of superimposing venous return curves on cardiac output curves is a convenient way to look at the negative feedback interaction between the major subdivisions of the cardiovascular system (Fig. 6).
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Utility of plots of the Pra-cardiac output relationship in descriptions of the negative feedback interaction between the heart and the vasculature. Cardiac output curves, as applied by Guyton (2), describe the influence of preload, expressed as Pra, on cardiac output under conditions of fixed heart rate, afterload, and contractility. Just as different venous return curves are plotted for different levels of systemic volume or different vasomotor states, families of cardiac output curves are used to illustrate influence of altered contractility or afterload.
Cardiac output curve data are obtained in the open-loop configuration, i.e., Pra is controlled independent of how the pressures in the vasculature are affected by the resultant cardiac output. So are venous return curve data, i.e., they describe the isolated vasculature, independent of any consequences of altered Pra on cardiac function. Putting these two functional relationships together should enable description of the closed-loop, steady-state equilibrium point of the intact cardiovascular system (Fig. 6). This was the advance contributed by Guyton's technique of superimposing cardiac output curves and venous return curves (Fig. 7). He made it easy to visualize consequences of changes in cardiac function or of properties of the systemic vasculature for equilibrium cardiac output and Pra (2).
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Models of the vasculature that predict the sloped segment. This paper does not dispute that the linear approximation of the sloped segment of a venous return curve for a particular volume is the pressure-flow relationship that would occur if venous return were driven by a fixed Pms and variable Pra, respectively, at the upstream and downstream ends of a fixed resistance. What it disputes is taking this model as having real counterparts. This misconception arises from a mathematical abstraction; the sloped segment appears this way because of the redistribution of a fixed total volume within the vasculature at different flow rates, not because there is a reservoir with pressure fixed at Pms.
Guyton and his co-workers certainly did not propose a two-pressure, one resistor arrangement as a model of the peripheral vasculature. They worked with networks of resistances and capacitances (6) intended to approximate properties of anatomically identifiable segments of the peripheral vasculature. From these, they derived quantitative solutions that adequately explained the sloped segment of venous return curves. Indeed, they showed that the apparent resistance indicated by the slope did not correspond to a physical resistance of any particular segment of the vasculature. In terms of the model, it could be identified as a composite of resistance and capacitance properties of the entire circuit. For example, in chapter 13 of his 1963 monograph (3), Guyton specifically describes the apparent resistance as a combination of arterial resistance (Ra) and arterial and venous capacitances of the system as well as venous resistance (Rv). Elsewhere, the term "venous impedance" was used (6). For simulations that come closer to the accurate prediction of the dynamics of the peripheral vasculature, including the consequences of regional vasomotor adjustments, more complex representations of properties of the vasculature are necessary [see, for example, Tsitlik et al. (15)]. But simple models like the one used by Guyton et al. (6) and the one Levy used in his critical review (8) suffice to show what underlies the obligatory decline in Pra with the increase in flow revealed in venous return curves.A simple model adequate for prediction of sloped segment data.
Models are not attractive if their components cannot be recognized as
having counterparts in the system to be described. The model
illustrated in Fig. 9 is perhaps the
simplest possible first approximation of peripheral vascular mechanics.
It is not offered as a new model for vascular dynamics, only for
illustration of points about the significance of Pms Pra that
seems apparent in a venous return curve.
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1 · min,
respectively, for Ra and Rv.
As an aside, capacitors do not accurately represent compliant vascular
compartments that contain volume at zero distending pressure, i.e.,
rest or unstressed volume. However, Pms can be modeled through initial
conditions of charge stored in the circuit. For network elements that
represent the complex, nonlinear properties of compliant segments of
the vasculature, see Tsitlik et al. (15).
The circuit is driven by a pure current source. It removes current from
the right atrial end at exactly the same rate that it forces current
into the arterial end.
With the current (blood flow) set at zero, voltages (pressures)
equilibrate, i.e., Pa = peripheral venous pressure (Ppv) = Pra, at a level that depends on the total charge (representing fixed
system volume) set as an initial condition. Charge distributes among
the capacitors in proportion to their capacitance. This uniform voltage
and distribution of charge is the analog of the zero-flow situation in
which Pms is seen. References to analogous quantities, henceforth, will
be in terms of blood flow, pressures, and volume.
At any other level of blood flow, the development of pressure gradients
causes increased volume in the arterial capacitor matched by an equal
decrease in the total volume in the venous capacitors. This volume
distributes between the two venous capacitors according to the pressure
profile set by flow rate. Changes in flow change the differences
between Pa and Ppv and Ppv and Pra, dictating progressive decreases in
Pra with progressive increases in flow.
The electrical circuit is readily analyzed with the aid of computer
simulation. For particular values of compliance and resistance chosen
to represent a 70-kg human, Pra is predicted to vary with flow as shown in Figs. 10 and
11. Figure 10 shows the details of how
Pra changes in time after each adjustment in flow. Figure 11 shows the
pressure-flow relationship plotted with Pra on the vertical axis
(Levy's vascular function curve format; Ref. 8). Data
from the simulation, plotted as a solid line, closely agree with data
points taken from the venous return curve of Fig. 1.
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What the math tells us about the apparent role of Pms in the sloped
segment.
The highly simplified model of Fig. 9 is sufficient to reveal the
obligatory relationship between Pra and cardiac output seen in the
sloped segment of experimentally obtained venous return or vascular
function curves. It predicts a flow-pressure relationship consistent
with the idea that flow in the sloped segment is driven by Pms Pra through a fixed resistance. We can see why by manipulating the
equations that describe the circuit, beginning with the relationship between total blood volume (V) and the pressure-capacitance products for each compartment
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SUMMARY |
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TOP
ABSTRACT
INTRODUCTION
HOW VENOUS RETURN CURVES...
ALTERNATIVE WAYS OF ACQUIRING...
SUMMARY
REFERENCES
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Guyton et al. (2, 5, 6) solved the problem of how to study the relationship between the steady-state rate of blood flow through the peripheral vasculature and Pra without the complication of changes in total intravascular volume. They presented their data in the format of venous return curves (Fig. 1), with Pra on the horizontal axis.
Alternative ways of obtaining the flow-Pra relationship (8) as well as a thought experiment presented here reveal the fallacy of taking their findings to say that Pra governs venous return through the hydraulic resistance of the venous system as a back pressure acting against Pms on the other end of the resistance. In the original experiments, it was the reduction of output that enabled Pra to come into equilibrium with the levels set by elevating their Starling resistor. What venous return curves really show is the steady-state relationship between the rate at which blood flows through the vasculature and Pra plotted backward, i.e., with the independent variable on the y-axis.
Cardiovascular equilibrium occurs through the negative feedback interaction between the subdivisions of the system: increasing Pra increases cardiac output in the cardiac part; increasing cardiac output reduces Pra in the vascular part (Fig. 6). Guyton introduced the technique of superimposing plots of these open-loop relationships to reveal the one point simultaneously consistent with both of them and, therefore, the point of equilibrium cardiac output and Pra. In this graphical technique, one relationship is necessarily plotted backward (Figs. 7 and 8).
During brief periods when venous return and cardiac output are not identical, but total vascular volume is fixed, the difference is made up by reciprocal exchange of volume between compliant compartments. (In a broader view than the focus in this paper, these include the pulmonary vasculature and chambers of the heart.) We can describe such transients by reasoning how the pressure profile changes when flow changes and how volume is thereby redistributed or, in a more advanced view, how pressure profiles in the parallel organ vasculatures change when cardiac output changes with Pa kept constant. We can alternatively take a quantitative approach with the aid of simple models like the one in Fig. 9 or more sophisticated ones with a better description of the components and their interconnections (15).
The equations that describe the steady-state behavior of simple models
can be manipulated into a form showing flow equal to (Pms Pra)/Req, which is consistent with the proportional relationship seen
in the sloped segment of a venous return curve. However, the apparent
resistance, Req, is a composite of all the resistances and capacitors
of the model, Pms does not remain constant at the upstream end of one
of the resistors, and the expression does not apply to situations in
which it is meaningful to speak of venous return as distinct from
cardiac output.
Allowance of the formality that steady-state venous return can be
described as proportional to Pms Pra to suggest that this two-pressure, one-resistance model has some correspondence to the
actual dynamics of venous return is worse than an oversimplification. Such an allowance overlooks the fact that it is the cardiac pump (together, in the real world, with the pumping action of skeletal and
respiratory muscles) that supplies the mechanical energy that creates
the pressure profile through the vasculature.
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ACKNOWLEDGEMENTS |
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The author thanks medical and graduate students whose confusion motivated probing this subject. The author also thanks Dr. Loring Rowell, Dr. Eric Feigl, and Alan Scher for many hours of discussion and editorial criticism, Dr. Matthew Levy for critical reading and encouragement, and Drs. Keith Richmond, Jonathan David Tune, and Mark Gorman for dissections of early drafts.
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FOOTNOTES |
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Address for reprint requests and other correspondence: G. L. Brengelmann, Box 357290, Dept. of Physiology and Biophysics, Univ. of Washington, Seattle, WA 98195 (E-mail: brengelm{at}u.washington.edu).
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
First published October 18, 2002;10.1152/japplphysiol.00868.2002
Received 23 September 2002; accepted in final form 12 October 2002.
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REFERENCES |
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TOP
ABSTRACT
INTRODUCTION
HOW VENOUS RETURN CURVES...
ALTERNATIVE WAYS OF ACQUIRING...
SUMMARY
REFERENCES
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G. L. Brengelmann COUNTERPOINT: THE CLASSICAL GUYTON VIEW THAT MEAN SYSTEMIC PRESSURE, RIGHT ATRIAL PRESSURE, AND VENOUS RESISTANCE GOVERN VENOUS RETURN IS NOT CORRECT J Appl Physiol, November 1, 2006; 101(5): 1525 - 1526. [Full Text] [PDF]
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G. L. Brengelmann The classical Guyton view that mean systemic pressure, right atrial pressure, and venous resistance govern venous return is/is not correct J Appl Physiol, November 1, 2006; 101(5): 1532 - 1532. [Full Text] [PDF]
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S. Magder Point:Counterpoint: The classical Guyton view that mean systemic pressure, right atrial pressure, and venous resistance govern venous return is/is not correct J Appl Physiol, November 1, 2006; 101(5): 1523 - 1525. [Full Text] [PDF]
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M. R. Pinsky, S. Permutt, Y.-Y. L. Wang, W.-K. Wang, R. D. Baker, C. Rothe, and W. Mitzner The classical Guyton view that mean systemic pressure, right atrial pressure, and venous resistance govern venous return is/is not correct J Appl Physiol, November 1, 2006; 101(5): 1528 - 1530. [Full Text] [PDF]
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M. V. Pancheva, V. S. Panchev, A. V. Suvandjieva, C. T. P. Krediet, J. J. van Lieshout, and W. Wieling Improved orthostatic tolerance by leg crossing and muscle tensing: indisputable evidence for the arteriovenous pump existence J Appl Physiol, October 1, 2006; 101(4): 1271 - 1272. [Full Text] [PDF]
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B. A. J. Reddi and R. H. S. Carpenter Venous excess: a new approach to cardiovascular control and its teaching J Appl Physiol, January 1, 2005; 98(1): 356 - 364. [Abstract] [Full Text] [PDF]
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K. Uemura, M. Sugimachi, T. Kawada, A. Kamiya, Y. Jin, K. Kashihara, and K. Sunagawa A novel framework of circulatory equilibrium Am J Physiol Heart Circ Physiol, June 1, 2004; 286(6): H2376 - H2385. [Abstract] [Full Text] [PDF]
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were scaled from Fig. 
