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J Appl Physiol 89: 1903-1911, 2000;
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Vol. 89, Issue 5, 1903-1911, November 2000

Quantitative analysis of feedforward sympathetic coronary vasodilation in exercising dogs

Mark W. Gorman, Johnathan D. Tune, Keith Neu Richmond, and Eric O. Feigl

Department of Physiology and Biophysics, University of Washington School of Medicine, Seattle, Washington 98195-7290


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

Recent experiments demonstrate that feedforward sympathetic beta -adrenoceptor coronary vasodilation occurs during exercise. The present study quantitatively examined the contributions of epinephrine and norepinephrine to exercise coronary hyperemia and tested the hypothesis that circulating epinephrine causes feedforward beta -receptor-mediated coronary dilation. Dogs (n = 10) were chronically instrumented with a circumflex coronary artery flow transducer and catheters in the aorta and coronary sinus. During strenuous treadmill exercise, myocardial oxygen consumption increased by ~3.9-fold, coronary blood flow increased by ~3.6-fold, and arterial plasma epinephrine concentration increased by ~2.4-fold over resting levels. At arterial concentrations matching those during strenuous exercise, epinephrine infused at rest (n = 6) produced modest increases (18%) in flow and myocardial oxygen consumption but no evidence of direct beta -adrenoceptor-mediated coronary vasodilation. Arterial norepinephrine concentration increased by ~5.4-fold during exercise, and coronary venous norepinephrine was always higher than arterial, indicating norepinephrine release from cardiac sympathetic nerves. With the use of a mathematical model of cardiac capillary norepinephrine transport, these norepinephrine concentrations predict an average interstitial norepinephrine concentration of ~12 nM during strenuous exercise. Published dose-response data indicate that this norepinephrine concentration increases isolated coronary arteriolar conductance by ~67%, which can account for ~25% of the increase in flow observed during exercise. It is concluded that a significant portion of coronary exercise hyperemia (~25%) can be accounted for by direct feedforward beta -adrenoceptor coronary vascular effects of norepinephrine, with little effect from circulating epinephrine.

coronary blood flow; norepinephrine; epinephrine


    INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

THE SYMPATHETIC NERVOUS SYSTEM affects coronary blood flow via three mechanisms: 1) local metabolic vasodilation secondary to the increase in myocardial oxygen consumption by activation of cardiac myocyte beta -adrenoceptors and the resulting increases in heart rate and contractility; 2) alpha -adrenoceptor-mediated vasoconstriction; and 3) beta -adrenoceptor-mediated coronary vasodilation. Direct beta -adrenoceptor-mediated vasodilation in the coronary circulation has been demonstrated during intracoronary norepinephrine infusion (18) and during treadmill exercise in pigs (8) and dogs (11). Those experiments separated beta -adrenoceptor vasodilation from the accompanying local metabolic vasodilation using either adrenergic receptor blockade or by increasing oxygen consumption with cardiac pacing. The balance between oxygen delivery (blood flow) and oxygen consumption, reflected by coronary venous oxygen tension, was lower when coronary vascular beta -adrenoceptor effects were not present (8, 11). Such experiments demonstrate the presence of sympathetic beta -adrenoceptor-mediated vasodilation during exercise, but it is difficult to translate the changes in coronary venous oxygen tension into terms of coronary blood flow. Furthermore, elevated catecholamine concentrations after alpha - or beta -adrenoceptor blockade (12, 21) tend to exaggerate the remaining unblocked alpha -adrenoceptor vasoconstriction or beta -adrenoceptor vasodilation.

The present study was designed to estimate the magnitude of sympathetic beta -adrenoceptor coronary vasodilation during exercise. Circulating catecholamine concentrations were measured at rest and during exercise, and the myocardial interstitial norepinephrine concentration was estimated. These concentrations were then compared with published dose-response curves for norepinephrine in isolated coronary arterioles. Catecholamine measurements were also taken to determine the relative contributions of norepinephrine and epinephrine to feedforward beta -adrenoceptor vasodilation during exercise.


    METHODS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

Exercise studies. Data for the hemodynamic portion of the present study during exercise are described in the accompanying study (11). Briefly, 10 dogs were surgically instrumented with a flow probe on the circumflex coronary artery, an aortic catheter, and a coronary sinus catheter. Arterial and coronary sinus blood samples for catecholamine analysis were collected at rest and during treadmill exercise at three different exercise levels during steady-state hemodynamic conditions. Samples for blood-gas analysis were also drawn at the same time. Exercise bouts lasted ~2 min, and the dogs rested between periods. The exercise experiments were repeated on separate days during intravenous alpha -adrenoceptor blockade with phentolamine (1 mg/kg) and again during intravenous alpha  + beta -adrenoceptor blockade with phentolamine plus propranolol (1 mg/kg, each).

Epinephrine infusion studies. Epinephrine infusion experiments were performed in 4 of the 10 dogs in the exercise group and in 2 additional dogs. Epinephrine experiments were separated from exercise studies by at least 2 days. The animals were studied while standing in a sling. A catheter was placed in a leg vein for epinephrine or saline infusion. After baseline blood samples of arterial and coronary sinus blood during saline infusion were collected, epinephrine was infused at sequential doses of 0.025, 0.05, 0.1, 0.2, 0.4, and 0.8 µg · kg-1 · min-1. After at least 5 min at each dose and during steady-state hemodynamic conditions, arterial and coronary sinus blood samples were collected. Because epinephrine release from cardiac sympathetic nerves is negligible (9), only arterial catecholamine concentrations were measured during epinephrine infusion.

Catecholamine assay. Arterial and coronary venous plasma catecholamine concentrations were measured using HPLC with an electrochemical detector (3). Three- or five-milliliter blood samples were added to prechilled tubes containing antioxidant solution (20 µl/ml blood). The antioxidant solution consisted of 225 mM glutathione, 93 µM EDTA, 1,660 U/ml heparin, and 250 pmol/ml isoproterenol, as an internal standard, in saline. Blood collection tubes were immediately centrifuged at 4°C for 2 min at 15,000 rpm, and the plasma was removed and stored in a covered ice container. Plasma samples were analyzed on the day of the experiment or frozen at -70°C for later analysis.

Plasma catecholamines were adsorbed on powdered alumina (25 mg/ml plasma) after addition of 1 M Tris buffer with 2% EDTA (pH 8.6; 400 µl/ml plasma). The tubes were agitated for 5 min and centrifuged; the plasma was aspirated; and the alumina pellet was washed twice with 1 ml of distilled water. Catecholamines were eluted from the alumina under acid conditions with 150 µl 0.1 N HClO4 by vortexing the tubes for 2 min. One hundred microliters of the supernatant were analyzed on a Hewlett-Packard 1100 HPLC system and electrochemical detector (HP 1049A). Catecholamines were eluted isocratically at a flow of 0.75-1.0 ml/min using a 125- × 4-mm LiCrospher 100 column. The mobile phase consisted of 20 mM citric acid, 100 mg/l octanesulfonic acid, 0.2 mM EDTA, and 8-10% methanol, and pH was adjusted to 5.0 with NaOH. The electrochemical detector used a glassy carbon electrode at a potential of 0.6 V. Epinephrine and norepinephrine peaks were identified and quantified by comparison of retention times and peak areas to those of known standards. The detection limit is 0.2 pmol for both catecholamines, which is equivalent to a plasma concentration of ~0.2 nM. Concentrations in each sample were corrected for recovery [69.0 ± 1.2% (SE), n = 18] using the isoproterenol internal standard.

Estimation of interstitial norepinephrine concentration. To estimate the effect of the plasma norepinephrine concentrations measured at rest and during exercise, it is first necessary to estimate the norepinephrine concentration in the vicinity of the coronary vascular smooth muscle receptors in the interstitium. Interstitial concentration is different from either arterial or venous concentration due to two major factors. 1) Interstitial norepinephrine arrives directly from cardiac sympathetic nerves as well as via the circulation, and 2) the endothelium acts as a barrier to norepinephrine diffusion between plasma and interstitial fluid (6).

These factors and others have been accounted for in a model of cardiac norepinephrine transport previously developed by Cousineau et al. (5). This model is described in detail in the APPENDIX. Model calculations of myocardial interstitial norepinephrine concentrations used coronary plasma flow and norepinephrine concentrations from the present study, together with the capillary transport parameters for norepinephrine measured previously, in dog hearts, by Cousineau et al. (5).

The model makes the following assumptions. 1) Neuronal norepinephrine release is uniformly distributed along the length of the capillary. 2) Segmented plasma flow between red blood cells occurs within the capillary. 3) Radial concentration gradients within the interstitium and plasma are negligible due to the short distances involved. 4) Axial (longitudinal) diffusion is negligible (compared with bulk flow). 5) Norepinephrine crosses the endothelial cell barrier by diffusion and is not taken up by endothelial cells. 6) Steady-state conditions ensure that the concentrations at any given point along the capillary are not changing at the time measurements are made.

With these assumptions, it is possible to derive an equation for interstitial norepinephrine concentration at any point along the capillary length (see APPENDIX). This is a distributed model, as opposed to a compartmental model, meaning that concentration gradients between the arterial and venous ends of the capillary will exist in both plasma and interstitium whenever arterial and venous norepinephrine concentrations are different. The average interstitial concentration over the length of the capillary (<A><AC>C</AC><AC>&cjs1171;</AC></A>isf) is reported.

Data analysis. Unless stated otherwise, results are presented as mean ± SE. Formal statistical testing was limited to the catecholamine concentrations in the control exercise experiments, in accordance with the primary hypothesis of the study. Catecholamine concentrations in the adrenoceptor blockade experiments are not central to the experimental goals but are presented, for completeness, without statistical tests to avoid inappropriate multiple comparisons. To determine whether catecholamine concentrations increased with myocardial oxygen consumption, linear regression lines were fit individually for each dog, and the slopes were averaged. A standard t-test with nine degrees of freedom was used to test each average slope against zero. The regression lines shown in the figures use this average slope with the regression line centered at the mean oxygen consumption and mean catecholamine concentration of the data set being plotted. Arterial and venous catecholamine concentrations at each exercise level were compared using a paired t-test with a Bonferroni correction factor of 4 for multiple comparisons. In the epinephrine infusion experiments, results at each epinephrine dose were compared with saline infusion using ANOVA followed by Dunnett's test.


    RESULTS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

Exercise experiments. The hemodynamic results during treadmill exercise are presented in the accompanying paper (11). Plasma catecholamine concentrations are presented in Fig. 1 and Table 1. Both arterial and venous epinephrine concentrations increased linearly with myocardial oxygen consumption, and the arterial concentration was always higher than coronary venous concentration. The increase in plasma norepinephrine concentration with myocardial oxygen consumption was more marked than epinephrine, and coronary venous norepinephrine concentration was always higher than arterial concentration, indicating norepinephrine release. Systemic alpha -adrenoceptor blockade and combined alpha  + beta -adrenoceptor blockade both led to substantial increases in arterial and coronary venous plasma catecholamine concentrations (Table 1).


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  		Fig. 1.   Arterial and coronary venous plasma concentrations of norepinephrine (A) and epinephrine (B), at rest and during 3 levels of treadmill exercise, plotted vs. myocardial oxygen consumption. All catecholamine concentrations increased with oxygen consumption, as indicated by slopes >0 (P < 0.05). Coronary venous norepinephrine concentration was higher than arterial levels, indicating net cardiac norepinephrine release. Coronary venous epinephrine concentration was lower than arterial, indicating cardiac epinephrine uptake. r values: 0.85 arterial norepinephrine; 0.79 venous norepinephrine; 0.52 arterial epinephrine; 0.49 venous epinephrine. * Venous vs. arterial, paired t-test with Bonferroni adjustment (P < 0.05).


                              
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  		Table 1.   Catecholamine results during graded treadmill exercise

Epinephrine infusion experiments. The effects of epinephrine infusion on myocardial oxygen consumption and coronary blood flow are shown in Fig. 2. Epinephrine produced moderate increases in both variables at low infusion rates. These effects plateaued at the higher doses. The arterial epinephrine concentration achieved during exercise produced a modest increase in myocardial oxygen consumption and coronary blood flow. Further hemodynamic results are presented in Table 2.


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  		Fig. 2.   Coronary blood flow and oxygen consumption responses to intravenous epinephrine infusion. The arterial epinephrine concentration reached during the highest level of exercise (dashed line) produced only small increases in coronary blood flow and oxygen consumption. MVO2, myocardial oxygen consumption. See Table 2 for statistical comparisons to resting values.


                              
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  		Table 2.   Results of epinephrine infusion experiments

Figure 3 presents coronary venous oxygen tension as a function of myocardial oxygen consumption during epinephrine infusion and during exercise in the presence of alpha  + beta -adrenoceptor blockade. Coronary sinus oxygen tension is used as an index of the balance between myocardial oxygen supply and consumption. The alpha  + beta -adrenoceptor blockade data define the relationship between these variables, free of direct alpha - or beta -adrenoceptor effects on the coronary vasculature. At the higher epinephrine doses, coronary sinus oxygen tension increased markedly with little change in myocardial oxygen consumption, indicating beta -adrenoceptor-mediated coronary vasodilation. However, at arterial epinephrine concentrations matching the highest arterial concentrations reached during exercise, coronary sinus oxygen tension was not increased (Fig. 3).


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  		Fig. 3.   Coronary venous oxygen tension vs. myocardial oxygen consumption during intravenous epinephrine infusion. Values are means ± SE. Coronary venous oxygen tension is an index of the balance between myocardial blood flow and oxygen consumption. Exercise during alpha  + beta -adrenoceptor blockade is used to define the slope of this relationship during a purely metabolic vasodilation (11). The coronary blood flow response to epinephrine includes both metabolic vasodilation and feedforward beta -adrenergic vasodilation. Epinephrine-induced feedforward vasodilation is manifest when the slope of the relationship during epinephrine infusion becomes more positive than the slope during metabolic vasodilation alone, as happens at the higher epinephrine concentrations (higher oxygen consumptions). At the point indicated by the arrow, the arterial epinephrine concentration closely matches the concentration during the highest level of exercise. At this concentration, there is no evidence of feedforward vasodilation.

Interstitial norepinephrine concentrations. The estimates of average interstitial norepinephrine concentrations during normal exercise, presented in Fig. 4 and Table 1, are higher than the corresponding venous concentrations. The effects of interstitial norepinephrine on coronary blood flow will be detailed in the DISCUSSION. Estimated interstitial norepinephrine concentrations and neuronal norepinephrine release rates during exercise with adrenergic blockade are also presented in Table 1.


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  		Fig. 4.   Model estimates of myocardial interstitial norepinephrine concentration at rest and during treadmill exercise, plotted vs. myocardial oxygen consumption. Estimated interstitial norepinephrine concentration increases with increasing oxygen consumption during exercise, as indicated by the positive slope (P < 0.05). The threshold value for coronary vasodilation is from isolated vessels in the study of Zuberbuhler and Bohr (23).


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

The present study is the first to quantify the contribution of feedforward sympathetic vasodilation to coronary exercise hyperemia and to separate the roles of epinephrine and norepinephrine. These experiments also estimated the contribution of circulating epinephrine to increased coronary blood flow and myocardial oxygen consumption in exercising dogs. As discussed below, circulating epinephrine is responsible for ~6% of the increase in oxygen consumption and coronary blood flow during strenuous exercise and does not contribute to feedforward beta -adrenoceptor coronary vasodilation. Under the same conditions, norepinephrine reaches myocardial interstitial concentrations that directly relax coronary smooth muscle and accounts for ~25% of the increase in coronary blood flow.

Role of epinephrine in feedforward sympathetic vasodilation. The arterial concentration of epinephrine increased during exercise. The coronary venous concentrations of epinephrine were lower than arterial concentrations, indicating net epinephrine uptake by the heart. This is consistent with the observation that the epinephrine content of cardiac sympathetic nerves is only 1.5% of norepinephrine content (9). Therefore, the vast majority of epinephrine affecting the heart arrives via the circulation, rather than from the cardiac sympathetic nerves. Thus cardiac effects of circulating epinephrine concentrations during exercise can be approximated by intravenous infusions that cause equivalent arterial concentrations. Therefore, epinephrine dose-response experiments were performed (Fig. 2).

Interpolation of the dose-response curves to intravenous epinephrine (Fig. 2, Table 2) reveals that the arterial epinephrine concentration (2.9 nM) during strenuous exercise causes increases of ~18% in both myocardial oxygen consumption and coronary blood flow. However, these epinephrine-induced increases are only a small fraction (~6%) of the increases seen during strenuous exercise, in which myocardial oxygen consumption increased 290% and coronary flow increased 260% (11). These results are consistent with a study by Young et al. (22) in which epinephrine was found to make only a small contribution to increased cardiac contractility in exercising dogs.

The exercise observations alone do not evaluate epinephrine's contribution to beta -adrenoceptor-mediated coronary vasodilation. To separate the direct coronary vasodilator effect of epinephrine from the metabolic vasodilation due to increased myocardial oxygen consumption, coronary sinus oxygen tension was plotted vs. myocardial oxygen consumption (Fig. 3). The relationship between these variables during relatively "pure" metabolic vasodilation is revealed by the data obtained during exercise in the presence of alpha  + beta -adrenoceptor blockade (11). Epinephrine infusion includes both the local metabolic component plus a beta -adrenoceptor vasodilator component. The direct beta -adrenoceptor vasodilation is revealed when the slope of the plot during epinephrine infusion exceeds the slope of the local metabolic plot, i.e., when the oxygen supply/consumption relationship increases. At the epinephrine dose that closely matched the maximal arterial plasma concentration during exercise (2.9 ± 0.8 nM; Fig. 3), the curve is at an inflection point. Above this epinephrine concentration, there is an ever-increasing amount of beta -adrenoceptor vasodilation, but there is no evidence of such dilation up to this point. The 2.9 nM plasma value is also below the ~4.5 nM threshold for epinephrine relaxation of small, isolated, canine coronary arteries (23). Therefore, it can be concluded that epinephrine is not causing feedforward beta -adrenoceptor vasodilation at the concentrations reached during exercise.

Role of norepinephrine in feedforward sympathetic vasodilation. The above conclusion strongly suggests that norepinephrine is the source of direct beta -adrenoceptor coronary vasodilation during exercise. However, matching the exercising arterial concentrations via intravenous infusion is insufficient for norepinephrine. Unlike epinephrine, much of the interstitial norepinephrine is released directly into the interstitial space by sympathetic nerves. Norepinephrine infused to match arterial exercise concentrations would therefore produce lower myocardial interstitial concentrations than during exercise and would underestimate the true effects. It is also necessary to separate the direct feedforward beta -adrenoceptor vasodilator effect of norepinephrine from the accompanying local metabolic vasodilation. Graphs such as Fig. 3 expose the presence or absence of this feedforward dilation but do not translate readily into terms of coronary blood flow. An alternative approach is needed that will allow this quantitation.

The first step in a quantitative approach is to use the plasma norepinephrine concentrations and coronary flows, together with a previously published mathematical model (5), to estimate myocardial interstitial norepinephrine concentrations. The resulting interstitial concentrations (Fig. 4) are slightly higher than the coronary venous concentrations (Table 1, Fig. 1). This is consistent with the release of norepinephrine from cardiac sympathetic fibers within the interstitial space, the endothelial diffusion barrier for norepinephrine between plasma and interstitium (6) and the fact that the coronary venous norepinephrine concentration was always higher than the arterial concentration. During strenuous exercise (level three) the estimated interstitial norepinephrine concentration was 12.2 nM. The relatively small interstitial-venous gradient agrees with a recent study that used microdialysis to estimate cardiac interstitial norepinephrine concentration (14).

The direct vascular effects of norepinephrine concentration can be estimated from dose-response curves to norepinephrine in isolated coronary blood vessels. Whereas large coronary arteries contract in response to norepinephrine, small coronary arteries relax under the same conditions (19, 23). The relaxation is mediated almost entirely by beta -adrenoceptors, with a small contribution from endothelial mechanisms (19). Because small arteries and arterioles are the primary site of vascular resistance, the direct net effect of norepinephrine on the coronary vasculature is likely to be vasodilation.

Using arterial strips from 400-µm diameter coronary arteries of dogs, Zuberbuhler and Bohr (23) found significant relaxation to norepinephrine at 0.6 nM (1 µg/l). This suggests that the myocardial interstitial concentrations during exercise are in the vasoactive range. However, it is difficult to extrapolate data from tension changes in helical vessel strips to changes in vessel diameter. Quillen et al. (19) measured diameter changes in 80- to 200-µm-diameter porcine coronary arteries perfused at 20 mmHg and precontracted with leukotriene D4. Norepinephrine relaxed these vessels with a 50% effective concentration (EC50) of 47 nM. On the basis of that study's dose-response curve and vessel diameters, the estimated interstitial norepinephrine concentration during strenuous exercise in the present study (12.2 nM) would increase vessel diameter from 67 to 79.5 µm, an 18.6% increase.

The 18.6% increase in diameter will have much larger effects on coronary blood flow. Poiseuille's law states that flow is proportional to the fourth power of vessel diameter under appropriate hemodynamic conditions. However, such conditions do not exist in vivo. In the rat cremaster circulation, blood flow varies with the cube of vessel diameter across a wide range of diameters (17). Assuming a similar cubic relationship in the coronary circulation, an 18.6% diameter increase would result in a flow increase of 67%. Because coronary blood flow increased by 260% at the highest exercise level, the direct vascular effect of norepinephrine may account for ~25% (67/260%) of the increase. As an upper bound, if the diameter to the fourth power is used, the comparable figure is ~37%. These values assume that the in vitro data may be used to estimate in vivo resistance changes.

Neuronal norepinephrine release rate. Estimated neuronal norepinephrine release rate and plasma norepinephrine concentrations were significantly increased during exercise after alpha -adrenoceptor blockade (Table 1). This is consistent with previous plasma catecholamine measurements in exercising dogs (12) and results, in part, from blockade of presynaptic alpha -adrenoceptors that normally inhibit norepinephrine release in a negative feedback manner (15). The fall in arterial pressure during exercise after alpha -adrenoceptor blockade also triggers the baroreceptor reflex, which contributes to the elevated norepinephrine release. Neuronal norepinephrine release and plasma norepinephrine concentrations increased even further during exercise after alpha  + beta -adrenoceptor blockade (Table 1).

Chilian et al. (4) were unable to find a difference in alpha -adrenoceptor-mediated coronary vasoconstriction in regionally denervated and intact areas of the left ventricle in exercising dogs. This led to the conclusion that alpha -adrenoceptor vasoconstriction is due to circulating catecholamines and not to norepinephrine released by sympathetic nerves in the heart. Although arterial norepinephrine concentration increased during exercise in the present study (presumably due to spillover from skeletal muscle, gut, and kidney, as well as heart), coronary venous norepinephrine concentration consistently exceeded the arterial concentration. This demonstrates that cardiac interstitial norepinephrine concentration exceeds the arterial concentration and that cardiac sympathetic nerves probably play a role in alpha - and beta -adrenoceptor-mediated coronary effects.

Study limitations. We assume that the coronary effects of circulating epinephrine during exercise can be reproduced by an intravenous infusion under resting conditions that matches the arterial concentration during exercise. Epinephrine's extracardiac source makes it one of the few native vasoactive compounds for which this approach is reasonable. It is difficult to separate the contributions of epinephrine and norepinephrine by other means. The full effects of exercise are not reproduced during epinephrine infusion; therefore, it is possible that the arterial epinephrine concentration during exercise is more effective than estimated in the present study.

A second major assumption is that the in vivo effects of the estimated interstitial norepinephrine concentrations can be approximated from their effects on isolated arterioles in vitro. The in vitro results are valuable because they provide a clean separation of vascular norepinephrine effects from metabolic norepinephrine effects. However, extrapolation from in vitro dose-response curves to coronary blood flow is, at best, an approximation.

Transmitter criteria. Six criteria for chemical transmitters have been suggested (10), and it is useful to evaluate feedforward norepinephrine control of coronary blood flow in terms of these criteria.

1) The proposed transmitter is released under appropriate conditions, and it can be recovered from the tissue under those conditions. This is documented in the present experiments in which coronary venous norepinephrine concentration consistently exceeded the arterial concentration during exercise.

2) Transmitter substance artificially infused into the target tissue should faithfully mimic physiological activation. beta -Adrenoceptor-mediated coronary vasodilation was demonstrated by Miyashiro and Feigl (18) with intracoronary norepinephrine infusions during prolonged diastoles to avoid the inotropic and chronotropic effects of norepinephrine.

3) The biochemical apparatus for production of the proposed transmitter is present in the tissue in an appropriate location. The synthesis and release mechanisms for norepinephrine in sympathetic nerves is well established (16).

4) A mechanism for inactivation and/or uptake of the transmitter is present at an appropriate location in the tissue. The degradation and/or reuptake of norepinephrine by sympathetic nerves is also well documented (16).

5) The action of various inhibitors and blocking agents on synthesis release, target-organ receptor function, or transmitter inactivation should have effects consistent with the hypothesis. Blocking agents should give the same effect whether the transmitter is released physiologically or artificially applied. The blocking action of selective beta 1- and beta 2-adrenoceptor antagonists on feedforward norepinephrine-induced coronary vasodilation was demonstrated by Miyashiro and Feigl (18). The blocking action of combined beta 1- and beta 2-adrenoceptor blockade on the balance between coronary oxygen delivery and myocardial oxygen consumption during exercise is documented in the accompanying study (11).

6) Quantitative studies should indicate that the amount and time course of the transmitter released under physiological conditions is appropriate to give the indicated effect. The present study presents evidence that the myocardial interstitial norepinephrine concentration during exercise is in the vasoactive range and accounts for ~25% of exercise coronary hyperemia. The present results were obtained during steady-state exercise and do not provide information on the time course of norepinephrine release.

In summary, circulating epinephrine contributes only modestly to increases in myocardial oxygen consumption and blood flow in exercising dogs and does not reach concentrations that directly relax coronary blood vessels. Norepinephrine released from cardiac sympathetic nerves reaches vasoactive concentrations in the myocardial interstitial space during exercise and accounts for ~25% of the increase in coronary blood flow during exercise.


    APPENDIX
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

This is the distributed mathematical model of Cousineau et al. (5), with the addition of explicit solutions for interstitial norepinephrine concentration and neuronal release rate in a single capillary-tissue unit. The terminology and units for mass transport and exchange suggested by Bassingthwaighte et al. (1) have been adopted. Figure 5 shows a schematic capillary-tissue unit with labels indicating the variables and parameters used in the model.


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  		Fig. 5.   Schematic diagram of myocardial tissue unit used in modeling interstitial norepinephrine (NE) concentration, as detailed in the APPENDIX. Although not indicated in the figure, plasma NE and interstitial NE concentrations (Cp and Cisf, respectively) are functions of distance along the capillary. The difference between Cp and Cisf is largely determined by the ratio of flow (Fp) to permeability-surface area product (PSg), and the difference between arterial and venous plasma NE concentrations (Ca and Cv, respectively). GNE, rate constant for reuptake/degradation of NE within the interstitium; RNE, rate of efflux of NE from sympathetic nerve terminals; Vp, volume of plasma space; Visf, volume of interstitial space.

Glossary


Ca   arterial plasma norepinephrine concentration, nmol/l
Cisf   interstitial norepinephrine concentration, nmol/l
Cp(x)   plasma norepinephrine concentration at distance x along the capillary, nmol/l
Cv   venous plasma norepinephrine concentration, nmol/l
Fp   plasma flow rate, ml · min-1 · g-1
GNE   rate constant for reuptake/degradation of norepinephrine within the interstitium, ml · min-1 · g-1
L   capillary length, mm
PSg   permeability-surface area product for norepinephrine diffusion across the endothelium, ml · min-1 · g-1
RNE   rate of efflux of norepinephrine from sympathetic nerve terminals, pmol/min
Vp   volume of plasma space, ml/g
Visf   volume of interstitial space, ml/g

PSg and GNE are parameters that were estimated by Cousineau et al. (5, 6) using multiple-indicator dilution experiments in closed-chest dog hearts. In multiple-indicator dilution experiments, a bolus of radiolabeled albumin, sucrose, and norepinephrine is injected into a coronary artery while multiple sequential venous samples are collected. Analysis of the indicator concentrations in the venous outflow allows calculation of PSg and GNE (2, 5, 6). The parameter values reported by Cousineau et al. (5) in units of ml · s-1 · ml interstitial fluid-1 were converted to ml · min-1 · g-1 by multiplying by 8.85 (20).

In the following equations, plasma and interstitial fluid norepinephrine concentrations, Cp(x) and Cisf(x), are both functions of distance x along the capillary. For the sake of brevity, they will be abbreviated simply as Cp and Cisf. Conservation of mass equations can be written for norepinephrine content in the plasma space
V<SUB>p</SUB> <FR><NU>dC<SUB>p</SUB></NU><DE>d<IT>t</IT></DE></FR><IT>=</IT>−F<SUB>p</SUB><IT>L </IT><FR><NU>dC<SUB>p</SUB></NU><DE>d<IT>x</IT></DE></FR><IT>−PS</IT><SUB>g</SUB>(C<SUB>p</SUB><IT>−</IT>C<SUB>isf</SUB>) (1)
and for the interstitial fluid space
V<SUB>isf</SUB> <FR><NU>dC<SUB>isf</SUB></NU><DE>d<IT>t</IT></DE></FR><IT>=</IT>−<IT>PS</IT><SUB>g</SUB>(C<SUB>isf</SUB><IT>−</IT>C<SUB>p</SUB>)<IT>+</IT>R<SUB>NE</SUB><IT>−</IT>G<SUB>NE</SUB>C<SUB>isf</SUB> (2)
During steady-state conditions, these concentrations are not changing, so the left-hand side of both equations becomes zero. From Eq. 2, we can then formulate an expression for Cisf
C<SUB>isf</SUB><IT>=</IT><FR><NU>R<SUB>NE</SUB><IT>+PS</IT><SUB>g</SUB>C<SUB>p</SUB></NU><DE><IT>PS</IT><SUB>g</SUB><IT>+</IT>G<SUB>NE</SUB></DE></FR> (3)
To calculate Cisf, it now remains to derive expressions for Cp and RNE. From Eq. 1, under steady-state conditions
F<SUB>p</SUB><IT>L </IT><FR><NU>dC<SUB>p</SUB></NU><DE>d<IT>x</IT></DE></FR><IT>=</IT>−<IT>PS</IT><SUB>g</SUB>(C<SUB>p</SUB><IT>−</IT>C<SUB>isf</SUB>) (4)
Substituting Eq. 3 for Cisf in Eq. 4, rearranging to get all Cp terms on the left side
F<SUB>p</SUB><IT>L </IT><FR><NU>dC<SUB>p</SUB></NU><DE>dx</DE></FR>+C<SUB>p</SUB><FENCE><IT>PS</IT><SUB>g</SUB><IT>−</IT><FR><NU><IT>PS</IT><SUP><IT>2</IT></SUP><SUB>g</SUB></NU><DE><IT>PS</IT><SUB>g</SUB><IT>+</IT>G<SUB>NE</SUB></DE></FR></FENCE><IT>=</IT><FR><NU><IT>PS</IT><SUB>g</SUB>R<SUB>NE</SUB></NU><DE><IT>PS</IT><SUB>g</SUB><IT>+</IT>G<SUB>NE</SUB></DE></FR> (5)
and dividing by Fp
L <FR><NU>dC<SUB>p</SUB></NU><DE>d<IT>x</IT></DE></FR><IT>+</IT>C<SUB>p</SUB><FENCE><FR><NU><IT>PS</IT><SUB>g</SUB></NU><DE>F<SUB>p</SUB></DE></FR><IT>−</IT><FR><NU><IT>PS</IT><SUP><IT>2</IT></SUP><SUB>g</SUB></NU><DE>F<SUB>p</SUB>(<IT>PS</IT><SUB>g</SUB><IT>+</IT>G<SUB>NE</SUB>)</DE></FR></FENCE><IT>=</IT><FR><NU><IT>PS</IT><SUB>g</SUB>R<SUB>NE</SUB></NU><DE>F<SUB>p</SUB>(<IT>PS</IT><SUB>g</SUB><IT>+</IT>G<SUB>NE</SUB>)</DE></FR> (6)
Eq. 6 can be simplified by abbreviating two of the terms, which are constants during steady-state conditions
A=<FR><NU>PS<SUB>g</SUB></NU><DE>F<SUB>p</SUB></DE></FR><IT>−</IT><FR><NU><IT>PS</IT><SUP><IT>2</IT></SUP><SUB>g</SUB></NU><DE>F<SUB>p</SUB>(<IT>PS</IT><SUB>g</SUB><IT>+</IT>G<SUB>NE</SUB>)</DE></FR>

B=<FR><NU>PS<SUB>g</SUB>R<SUB>NE</SUB></NU><DE>F<SUB>p</SUB>(<IT>PS</IT><SUB>g</SUB><IT>+</IT>G<SUB>NE</SUB>)</DE></FR>
so that Eq. 6 may be rewritten as
L <FR><NU>dC<SUB>p</SUB></NU><DE>d<IT>x</IT></DE></FR><IT>+A</IT>C<SUB>p</SUB><IT>=B</IT> (7)
Solving this differential equation and incorporating the fact that Cp = Ca at x = 0 
C<SUB>p</SUB>(<IT>x</IT>)<IT>=</IT><FR><NU><IT>B</IT></NU><DE><IT>A</IT></DE></FR><IT>+</IT><FENCE>C<SUB>a</SUB><IT>−</IT><FR><NU><IT>B</IT></NU><DE><IT>A</IT></DE></FR></FENCE><IT>e<SUP>−Ax/L</SUP></IT> (8)
Because Cp = Cv at x = L, from Eq. 8
C<SUB>v</SUB><IT>=</IT><FR><NU><IT>B</IT></NU><DE><IT>A</IT></DE></FR><IT>+</IT><FENCE>C<SUB>a</SUB><IT>−</IT><FR><NU><IT>B</IT></NU><DE><IT>A</IT></DE></FR></FENCE><IT>e<SUP>−A</SUP></IT> (9)
The constant A can be calculated from measured variables and known model parameters. Equation 9 allows calculation of the value of constant B in terms of known variables and parameters
B=<FR><NU>A[C<SUB>v</SUB><IT>−</IT>C<SUB>a</SUB>(<IT>e<SUP>−A</SUP></IT>)]</NU><DE><IT>1−e<SUP>−A</SUP></IT></DE></FR> (10)
From the definition of B and Eq. 10, RNE can also be expressed in terms of known values
R<SUB>NE</SUB><IT>=</IT><FR><NU>F<SUB>p</SUB><IT>A</IT>(<IT>PS</IT><SUB>g</SUB><IT>+</IT>G<SUB>NE</SUB>)(C<SUB>v</SUB><IT>−</IT>C<SUB>a</SUB>(<IT>e<SUP>−A</SUP></IT>))</NU><DE><IT>PS</IT><SUB>g</SUB>(<IT>1−e<SUP>−A</SUP></IT>)</DE></FR> (11)
Equations 8 and 11 give values for Cp and RNE that can be used in Eq. 3 to calculate Cisf at any fractional distance (x/L) along the capillary. In practice, the average value <A><AC>C</AC><AC>&cjs1171;</AC></A>isf is calculated using the average plasma concentration, <A><AC>C</AC><AC>&cjs1171;</AC></A>p, where
<OVL>C<SUB>p</SUB></OVL><IT>=</IT><FR><NU><IT>1</IT></NU><DE><IT>L</IT></DE></FR> <LIM><OP>∫</OP><LL><IT>0</IT></LL><UL><IT>L</IT></UL></LIM> C<SUB>p</SUB>(<IT>x</IT>)d<IT>x</IT>
From the definition of <A><AC>C</AC><AC>&cjs1171;</AC></A>p and Eq. 8
<OVL>C<SUB>p</SUB></OVL><IT>=</IT><FR><NU><IT>1</IT></NU><DE><IT>L</IT></DE></FR> <LIM><OP>∫</OP><LL><IT>0</IT></LL><UL><IT>L</IT></UL></LIM> <FENCE><FR><NU><IT>B</IT></NU><DE><IT>A</IT></DE></FR><IT>+</IT><FENCE>C<SUB>a</SUB><IT>−</IT><FR><NU><IT>B</IT></NU><DE><IT>A</IT></DE></FR></FENCE><IT>e<SUP>−Ax/L</SUP></IT></FENCE><IT>=</IT><FR><NU><IT>B</IT></NU><DE><IT>A</IT></DE></FR><IT>+</IT><FR><NU>C<SUB>a</SUB><IT>−</IT><FR><NU><IT>B</IT></NU><DE><IT>A</IT></DE></FR></NU><DE><IT>A</IT></DE></FR> (<IT>1−e<SUP>−A</SUP></IT>) (12)
Finally, using <A><AC>C</AC><AC>&cjs1171;</AC></A>p in Eq. 3 results in the average interstitial concentration over the length of the capillary, <A><AC>C</AC><AC>&cjs1171;</AC></A>isf.

Effects of changing flow on model parameters. As coronary vasodilation occurs during exercise, the number of perfused capillaries increases and the capillary permeability-surface area product PSg increases somewhat. Cousineau et al. (7) have previously determined the relationship between sucrose PSg and myocardial plasma flow in closed-chest dogs during pacing. Their equation and the coronary plasma flows from the current experiments were used to determine a sucrose PSg in each dog during each condition. The sucrose PSg was then multiplied by the ratio of PSg for norepinephrine to PSg for sucrose (1.2), which was determined by Cousineau et al. (5). The resulting PSg for norepinephrine was used in calculations of interstitial norepinephrine concentration.

The unidirectional rate constant for GNE was assumed to be the same at rest and during exercise (3.5 ml · min-1 · g-1). This assumption has not been explicitly tested experimentally. Reduction in myocardial oxygen consumption and blood flow during pacing by the addition of alprenolol did not significantly reduce GNE (5), suggesting that this parameter is relatively constant. The value of GNE does not influence the estimates of <A><AC>C</AC><AC>&cjs1171;</AC></A>isf, because changes in GNE must be balanced by changes in RNE to match the measured venous concentration. A simulated 10-fold increase in GNE changed the estimated <A><AC>C</AC><AC>&cjs1171;</AC></A>isf at exercise level three by <1%.

The equations above describe an explicit solution for <A><AC>C</AC><AC>&cjs1171;</AC></A>isf in a single capillary-tissue unit. The heart consists of many such units in parallel with heterogeneous flows. An explicit solution for whole organ <A><AC>C</AC><AC>&cjs1171;</AC></A>isf incorporating flow heterogeneity is not possible, but an iterative solution may be obtained. To examine the effect of flow heterogeneity on <A><AC>C</AC><AC>&cjs1171;</AC></A>isf, the heart was modeled as 10 parallel units, identical except for flow, connected to a common artery and vein. Each unit was assigned a flow and a fractional tissue mass based on a previous microsphere deposition study (13). A lagged normal density curve was used to describe flow distribution, with a relative dispersion (SD/mean) of 0.52, skewness of 1.02, and kurtosis of 4.58. Individual unit flows ranged from 0.055 to 3.55 times the measured mean flow. Each unit was assigned the same arbitrary RNE value, resulting in a different venous concentration from each pathway. The value of RNE was varied until the weighted, average venous concentration of the model matched the measured venous concentration in that situation. The whole organ <A><AC>C</AC><AC>&cjs1171;</AC></A>isf was calculated as the weighted average of the 10 individual unit <A><AC>C</AC><AC>&cjs1171;</AC></A>isf values.

At the highest exercise level, the <A><AC>C</AC><AC>&cjs1171;</AC></A>isf incorporating flow heterogeneity in 10 dogs was 12.0 nM, as opposed to 12.2 nM without flow heterogeneity. Heterogeneity raised the resting estimate of <A><AC>C</AC><AC>&cjs1171;</AC></A>isf from 2.9 to 3.1 nM. The differences were even smaller at intermediate exercise levels. Although the assumption of homogeneous coronary flow is incorrect, physiological levels of heterogeneity have little effect on estimated interstitial norepinephrine concentration. The simpler, single-unit (homogeneous) solutions for <A><AC>C</AC><AC>&cjs1171;</AC></A>isf are reported in the RESULTS.


    ACKNOWLEDGEMENTS

We thank Pamela Campbell for expert technical and editorial assistance in all phases of this research and Julie Kleeberger for help during the animal surgeries.


    FOOTNOTES

This work was supported by National Heart, Lung, and Blood Institute Grants HL-49170 and HL-07403 and National Center for Research Resources Grant RR-01243.

Address for reprint requests and other correspondence: M. W. Gorman, Dept. of Physiology and Biophysics, Univ. of Washington School of Medicine, Box 357290, Seattle, WA 98195-7290 (E-mail: mgorman{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.

Received 21 April 2000; accepted in final form 8 June 2000.


    REFERENCES
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
APPENDIX
REFERENCES

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