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Reprinted from Circulation Research,VoL 44, No. 6 June 1979

767

The Role of Potassium in the MetabolicControl of Coronary Vascular Resistance

of the Dog

PAUL A. MURRAY, FRANCIS L. BELLONI, AND HARVEY V. SPARKS

SUMMARY We tested the hypothesis that potassium ion (K+) is involved in the local control of thecoronary circulation. The left coronary artery was perfused at constant flow in closed-chest, anesthe-tized dogs. Step increases in heart rate caused transient (six dogs) or sustained (three dogs) increasesin coronary sinus plasma [K+] averaging 0.63 mEq/liter. When the effects of vascular transit delaywere accounted for, we found that [K+] changes preceded the vasodilation seen with increased heartrate. We used a mathematical model to calculate changes in interstitial [K+] from arterial and venous[K+] and K+ release rate. The magnitude of the changes in interstitial [K+] appeared to be sufficient toaccount for a considerable portion but not all of the initial changes in coronary vascular resistanceassociated with increased heart rate. Thus potassium seems to be involved at least transiently, and, inthree of nine dogs, for a more sustained period, in heart rate-induced coronary vasodilation. Cessations(for 15 seconds) of coronary blood flow resulted in transient postischemic increases of coronary sinus[K+] averaging 0.55 mEq/liter. In this case, correction for vascular transit disclosed that the recoveryof [K+] preceded the return of vascular tone to baseline for only the second half of the recovery,implying only a limited role for potassium in this response. Potassium appears to play a significant buttransient role in the local control of the coronary circulation. Ore Res 44: 767-780, 1979

THE POTASSIUM ion (K+) has long been consid-ered a possible controller of coronary vascular re-sistance (Katz and Lindner, 1938). The simplestform of such a hypothesis is that, with increasedmetabolic activity of the heart, there is an increasedflux of intracellular K+ across the myocardial mem-brane into the surrounding interstitial fluid.The increase in interstitial fluid K+ concentration([K+]) then would decrease the vasomotor tone ofthe coronary arterioles, producing a vasodilation.This mechanism would permit the heart to matchan increase in metabolic demand with an increasein nutrient supply. Several types of evidence offersupport for this theory. Potassium is a coronaryvasodilator over a certain concentration range(Cohen, 1936; Katz and Lindner, 1938; Driscol andBerne, 1958; Scott et al., 1961; Konold et al., 1967;Norton and Detar, 1972; Gellai and Detar, 1974;Bunger et aL, 1976; Murray and Sparks, 1978),

From the Department of Physiology, The University of MichiganMedical School, Ann Arbor, Michigan.

The work reported in this article was submitted by Dr. Murray inpartial fulfilment of the requirements for the degree of Doctor of Philos-ophy at the University of Michigan.

Supported by Grant HL 16760 from the National Institutes of Health,VS. Public Health Service.

Dr. Belloni was supported by National Research Service Award HL05015 from the National Heart, Lung, and Blood Institute. His presentaddress is: Department of Physiology, University of Virginia School ofMedicine, Charlottesville, Virginia 22901.

Dr. Murray's current address is: Harvard Medical School, New Eng-land Regional Primate Research Center, Southborough, Massachusetts01772.

Address for reprints: Harvey V. Sparks, M.D., Department of Physi-ology, Michigan State University, East Lansing, Michigan 48824.

Received September 5, 1978; accepted for publication December 22,1978.

although its vasodilator action may be only transi-tory (Gellai and Detar, 1974; Bunger et al., 1976).Potassium efflux from myocardium is enhanced byincreases in heart rate (Wilde, 1957; Wood andConn, 1958; Sybers et al., 1965; Langer and Brady,1966; Grupp et al., 1967; Gilmore and Gerlings, 1969;Parker et al., 1970) and by limitations of oxygensupply (Cherbakoff et al., 1957; Harris et al., 1958;Cummings, 1960; Jennings et al., 1964; Gerlings etal., 1969; Parker et al., 1970; Case, 1971; Scott andRadawski, 1971). Driscol and Berne (1958) failed tofind a steady state correlation between myocardialK+ loss and coronary blood flow. However, thisstudy neglected the possibility, which is suggestedby other work (Gerlings et al., 1969), that K+ effluxchanges only transiently following alterations inmyocardial activity. The goal of this study, then,was to determine whether changes in interstitialfluid [K+] elicited by changes in myocardial activity(step increases in heart rate) and by changes inoxygen supply (15-second cessations of coronaryblood flow) were (1) large enough in magnitude and(2) fast enough in their time course to explain atleast part of the coronary vascular responses tothese interventions.

MethodsGeneral

Male mongrel dogs ranging in weight from 25 to39 kg were anesthetized with morphine sulfate (4-7mgAg subcutaneous injection) and sodium pento-barbital (25 mg/kg or to effect, iv). Smaller doses of

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768 CIRCULATION RESEARCH VOL. 44, No. 6, JUNE 1979

sodium pentobarbital were administered through-out the course of the experiment to maintain ade-quate surgical anesthesia. Positive pressure venti-lation was achieved through a cuffed endotrachealtube with a large-animal respirator (Harvard Ap-paratus). Respiratory pump rate and tidal volumewere adjusted so that an arterial PCO2 of 44 ± 2 mmHg (mean ± SEM) was achieved (n = 16 dogs).Esophageal temperature was maintained with elec-tric heating pads between 38° and 39°C throughoutthe course of each experiment. A femoral arterywas isolated and cannulated for systemic bloodpressure measurement (Statham model P23 DC).Following a priming dose of sodium heparin (500-750 U/kg), a solution containing sodium bicarbon-ate (15 mg/ml) and sodium heparin (50 U/ml) wasinfused intravenously at a constant rate (60-120ml/hour) throughout the course of the experimentto counteract acidosis and prevent coagulation.

The left main coronary artery of the closed-chestdogs was pump-perfused with blood at a constantflow rate. A ballon-tipped, stainless steel cannula(compliments of Drs. D.E. Mohrman and E.O.Feigl) was passed down the right common carotidartery into the aorta and guided into the left maincoronary artery. Blood obtained from the dog'sright femoral artery was passed through an extra-corporeal circuit (Silastic tubing) containing a var-iable speed roller pump (Cole-Parmer model 7598),and constant flow perfusion was thus obtained. Theperfusion line included a blind-end side tube ofSilastic tubing between the pump and the heart.When partially filled with air, this side tube actedas a windkessel and filtered out the pressure pulsesgenerated by the pump. The dynamics of the wind-kessel were such (time constant ~ 0.5 second) thatit allowed flow to vary with each cardiac cycle anddid not interfere with the time course of the ob-served changes in coronary vascular resistance,myocardial oxygen consumption, or myocardial in-terstitial fluid K+ concentration. The perfusion linealso contained an access port between the pumpand the heart that permitted the sampling of arte-rial blood. The coronary cannula had an internaldiameter of 3 mm and contained two smaller di-ameter stainless steel tubes in its lumen, each witha separate exteriorized access port. One of thesesmaller internal tubes was connected to a Silasticballoon around the distal end of the main cannula.Inflation of the balloon achieved a complete seal ofthe coronary ostium around the main stem of theperfusion cannula, thus permitting constant flowperfusion of the coronary artery. The distal tip ofthe other internal tube lay at the opening of themain cannula. The proximal end of this inner cath-eter was connected to a pressure transducer (Sta-tham model P23 DC) to measure coronary perfu-sion pressure.

Both jugular veins were isolated. A bipolar pacingelectrode and radio-opaque catheter were passeddown the jugulars and, with the aid of fluoroscopy,

were positioned in the right atrium and coronarysinus, respectively.

Blood from the coronary sinus cannula wasdrawn at a constant rate (16 ml/min) through anoximeter cuvette (Waters model 0-600). The elec-trical signal from the oximeter was proportional tothe oxygen content of blood, given a constant he-moglobin concentration and ignoring the smallamount of oxygen dissolved in the blood. The he-moglobin concentration in the blood was measuredspectrophotometrically (Hycel Cyanmethemo-globin Kit) in each experiment and was found to beconstant (±10%) during the 1- to 2-hour period ofactual experimental manipulations. The electricaloutput of the oximeter was calibrated for total bloodoxygen content by determining the oxygen contentof anaerobically sampled blood with an electro-chemical oxygen analyzer (Lexington Instrumentsmodel Lex-O2-Con). Arterial blood was also drawnthrough the cuvette and analyzed for oxygen con-tent at 30- to 90-minute intervals throughout theexperiment. This allowed calculation of arterial-ve-nous oxygen content differences across the left ven-tricular myocardium and, since coronary blood flowwas known, calculation of myocardial oxygen con-sumption.

Arterial and coronary sinus plasma [K+] weremeasured by collecting blood samples at timed in-tervals (usually 6 seconds) into microhematocritcapillary tubes. These tubes were centrifugedwithin 5 minutes, and 20 fd of plasma were drawnfrom each tube into calibrated disposable glass cap-illary pipettes. These samples were then diluted1:100 for determination of [K+] by flame photome-try. The standard deviation of duplicate determi-nations of the same sample was ±0.03 mEq/liter.

The outputs of the pressure transducers and ox-imeter were recorded on an ink-writing oscillograph(Grass model 7 B). Heart or pace rate was measuredand recorded on the oscillograph with a tachographchannel (Grass model 7 P4D) using either the sys-temic pressure measurement signal or an ECG sig-nal (standard limb lead) as input.

Experimental ProtocolAfter the initial placement of the coronary can-

nula, the preparation was allowed to stabilize. Dur-ing this period, the coronary flow was set by ad-justing the pump rate so that coronary perfusionpressure approximately equalled systemic arterialblood pressure (within 10 mm Hg). An acceptablepositioning of the coronary cannula and seal of thecoronary ostium was achieved when the followingcriteria were met:

1. Coronary perfusion pressure fell smoothly andrapidly (less than 10 seconds) to 15 mm Hg or lessduring a 15-second cessation of coronary blood flow.

2. Coronary sinus oxygen content returned toapproximately preocclusion levels with the reinsti-tution of flow following a 15-second cessation ofcoronary blood flow. A large overshoot of this signal


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beyond its baseline level was interpreted as indicat-ing an increase in coronary flow due to influx ofblood around the cannula tip.

3. Coronary perfusion pressure and coronarysinus oxygen content fell smoothly to new steadystate levels and returned smoothly to prestimula-tion levels in response to step changes in heart rate.

4. Coronary pump flow had to be at least 50 ml/min, with a perfusion pressure equal to systemicarterial pressure. Any smaller value was interpretedas indicating cannulation of only one major branchof the left coronary artery.

The cannula position was confirmed by postmor-tem examination, as described later.

When perfusion pressure had reached an accept-able and steady level, the following maneuvers wereperformed:

Step Increase in Heart RateHeart rate was increased in a single step by 75

± 7 beats/min (range: 50-100 beats/min) above theunpaced rate. The elevated rate was maintained fora period of 2.5-3.0 minutes. This maneuver wasperformed from one to three times in each of ninedogs.

Fifteen-Second Cessation of Coronary BloodFlow (15-Second Ischemia)

The pump perfusing the left common coronaryartery was turned off for 15 seconds. At the end ofthe 15-second period, flow was restored to the pre-cessation level. Throughout this entire sequence,heart rate either spontaneously remained un-changed or was maintained at a constant level bypacing the heart at a rate slightly above the inher-ent rate. This maneuver was performed two to threetimes in each of six dogs.

Timed arterial and coronary sinus plasma [K+]measurements were made just before and duringthe periods of decreased coronary vascular resist-ance that were elicited by either a step increase inheart rate or a 15-second cessation of coronaryblood flow. Blood samples were collected at 5-sec-ond intervals starting 30 seconds prior to theseexperimental maneuvers and continuing for 2.5-3.0minutes. No samples were collected during the 15seconds of complete ischemia.

The distribution of intravascular transit timeswas obtained in each preparation by injecting anintravascular dye (indigo carmine) as a bolus intothe coronary artery through the coronary perfusionpressure cannula and then monitoring with theoximeter the relative concentration of the dye inthe coronary sinus blood. For each preparation fromthree to five dye curves were obtained. The coro-nary blood flow rate was always the same as that atwhich the heart rate steps or cessations of flow wereperformed.

At the termination of each experiment a solutioncontaining crystal violet stain was injected into theperfusion line. Five to 10 seconds after injection of

the stain, the dog was killed by the rapid injectionof a saturated potassium chloride solution and thecessation of the coronary perfusion. The chest wasopened and the heart exposed. The postions of thecoronary cannula, the coronary sinus catheter, andthe pacing electrode were confirmed by visual in-spection. The heart was then excised and examined.As a further check on the proper placement of thecoronary artery cannula and the complete seal ofthe coronary ostium, the following criteria had tobe met for an acceptable experimental preparation:(1) There could be no staining of the walls of theaorta with crystal violet in the area of the coronaryostium. (2) Both the circumflex artery and leftanterior descending artery vascular beds had to bestained. (3) The septal artery had to be stained. Allnine dogs used for data analysis met these criteria.

Data Analysis and Presentation

DigitizationThe curvilinear oscillograph records of coronary

perfusion pressure and coronary sinus oxygen con-tent were digitized, using a clear plastic overlayinggrid. Values for the two variables were determinedat 0.6-second intervals starting at 6.0 seconds priorto and ending 150-180 seconds after the experimen-tal intervention.

NormalizationEach individual digitized response of coronary

perfusion pressure and coronary sinus oxygen con-tent and each coronary sinus plasma [K+] timecourse was normalized in the following mannerprior to any averaging:

Step Increase in Heart Rate. The baseline valueof the variable was defined as the average of thevalues of the variable determined at the points from—6 seconds (-30 seconds for [K+] only) up to andincluding time 0 and was set equal to 0. The post-step value that corresponded to the peak change ofthe variable was set equal to 100. The values of thevariable at all points of that particular responsewere then adjusted to conform to this 0-100 scale.

Fifteen-Second Cessation of Flow. The releasepoint (corresponding to the point at which flow wasreinstituted after a 15-second cessation of flow) wasdefined as time 0. The peak coronary sinus plasma[K+] following the 15-second ischemia was dennedas 0. The steady state level to which coronary sinusplasma [K+] returned after recovery from the 15-second ischemia was defined as 100. This value wasobtained by averaging values of [K+] over a 30-second period immediately following the return ofthis variable to a steady state leveL The values atall the points of that particular response were thenadjusted to conform to this 0-100 scale.

The rapid initial rise in coronary perfusion pres-sure immediately following the reinstitution of flow(Fig. 5) is due to the passive refilling of the coronaryvascular bed and will not be considered. After this


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initial rise, the perfusion pressure begins a moregradual return to its baseline value. We defined thestart of this gradual return as being the point atwhich, following reinstitution of flow, perfusionpressure changed less than 5 mm Hg from onedigitization point to the next (i.e., less than 5 mmHg/0.6 sec). This point occurred 1.6 ± 0.2 seconds(n = 16 interventions; range: 0.6-3.0 seconds) afterreinstitution of flow. The normalized value of per-fusion pressure at this point was set equal to 0. Thesteady state level to which perfusion pressure re-turned after the 15-second cessation of flow was setequal to 100. This value was obtained by averagingthe digitized values of perfusion pressure for a 10-second period immediately following the return ofperfusion pressure to a steady level. The values atall the digitized points of that particular responsewere then adjusted to conform to this 0-100 scale.

The units of this scale (i.e., 0-100) can be thoughtof as: (1) the percent of the peak change of thevalue of the variable for heart rate steps and (2) thepercent of return of the variables from their peakvalues to the post-step steady state values duringrecovery from 15 seconds of ischemia. This normal-ization of the magnitude of the responses allowedus to compare their time courses.

GroupingResponses of coronary perfusion pressure, coro-

nary sinus oxygen content, and coronary sinusplasma [K+] to either step increases in heart rate or15-second cessations of coronary blood flow weregrouped for averaging, adjustment for transit effects(see below), and statistical analysis as follows:

1. For each preparation, the average response ofthe individually normalized responses (as describedabove) for each variable in response to an experi-mental intervention was obtained by averaging,point by point, the corresponding values from eachof the individually normalized responses. This pro-duced one data set per intervention per preparation.There was a total of nine data sets of step increasesin heart rate (involving 21 individual steps) fromnine dogs. There was a total of six data sets ofpostischemic recovery (involving 16 individual in-terventions) from six dogs. These data sets wereused as the basic units for statistical analysis. Thetime course parameters (described below) were alsoobtained from these data sets. And, finally, theperfusion pressure components of the data sets werethe functions used in the convolution integral (de-scribed below).

2. The overall average responses of coronary per-fusion pressure, coronary sinus oxygen content, andcoronary sinus plasma [K+] to either step increasesin heart rate or 15-second cessations of flow wereobtained by point-by-point averaging of the datasets, so that the responses from individual dogswere weighted equally for graphical display.

Time Course ParametersWe used the parameters tio, tso, and teo to describe

the time courses of the responses of our variablesto our experimental interventions. These were de-fined as the times after time 0 at which the averagedata set response of the variable in question hadchanged by 10, 50, or 90% of the final peak changefor step increases in heart rate, or at which thevariable had returned 10, 50, or 90% to its steadystate level from its peak change following 15 secondsof ischemia. The values for tio, Uo, and tso wereobtained by linear interpolation between adjacentpoints from the average data set responses of coro-nary perfusion pressure, coronary sinus oxygen con-tent, coronary sinus plasma [K+], and the convo-luted functions described below.

Comparison of Time CoursesIt is inappropriate to draw conclusions concern-

ing the relative time courses of myocardial intersti-tial fluid [K+] on the one hand and coronary vas-cular resistance on the other from a comparison ofthe time courses of coronary sinus plasma [K+] andcoronary perfusion pressure. This is because thecoronary sinus plasma [K+] time course reflects notonly changes in myocardial interstitial fluid [K+]but also (1) the gradient and the delay associatedwith transport of potassium across the capillaryendothelium and (2) the delay and dispersion intro-duced by vascular transit of blood from the capillaryto the site where coronary sinus blood samples werecollected for subsequent analysis of plasma [K+].For the purpose of considering the relative speed ofpotassium and vascular transients, we have ignoredthe effects of capillary wall transport. We did cor-rect for the vascular transit effects, as has beenpreviously described in detail (Belloni and Sparks,1977). Briefly, we estimated the delaying and dis-persive effects of vascular transit through capillariesand veins from the distribution of intravasculartransit times obtained for each preparation. Weused indigo carmine dye as our intravascularmarker. Its concentration in coronary sinus bloodwas measured continuously with our cuvette oxi-meter. We assumed that 91.1% of the trans-coronary transit of dye occurred in capillaries andveins. This figure is based on previous measure-ments of precapillary and transcoronary transittime distributions (Belloni and Sparks, 1977). Theestimated effects of capillary and venous vasculartransit were imposed onto the time course of coro-nary vascular resistance by use of the convolutionintegral:

CVR*(t) = ^/h(t - T) CVR(T) dT,

where h(t) is the function describing the distribu-tion of intravascular transit times through capillar-ies and veins (i.e., the impulse response of thissystem), CVR(t) is the time course of coronary


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vascular resistance (i.e., coronary perfusion pres-sure divided by the constant flow rate), and T isthe dummy variable of integration. The result ofthis convolution, CVR*(t), then, included the ef-fects of vascular transit as well as the basic timecourse of changes in coronary vascular resistance.It is with this function that we compared the timecourse of coronary sinus plasma [K+], which inher-ently included the effects of vascular transit as wellas the basic time course of changes in K+ release(or uptake) by the heart. Since K+ release or uptakeshould follow changes in interstitial [K+], we maydraw conclusions about the relative time courses ofvascular resistance and interstitial [K+] from thiscomparison of CVR*(t) with coronary sinus plasma[K+].

This approach dictated our use of constant flowperfusion in these studies. To use the convolutionintegral as we have, the intravascular transit func-tion, h(t), must be time-invariant. Since the abso-lute level of blood flow through the vascular bed isa major determinant of intravascular transit times,changes in flow during the experimental interven-tion would violate our assumption of stationarity.Hence, we used a constant flow protocol.

Estimation of Interstitial [IC]

We wished to decide whether changes in inter-stitial [K+] were of sufficient magnitude to explainsome or all of the vasodilation seen with changes inheart rate. To this end we constructed a mathe-matical model of the myocardium, which includedrepresentation of vascular transit effects and ex-change of K+ across the capillary wall. Details ofthis model are presented in the Appendix to thisarticle. We assumed reasonable values for capillarypermeability-surface area product (PScP) (Zieglerand Goresky, 1971; Tancredi et aL, 1975) and otherparameters and an arbitrary interstitial [K+] timecourse as a forcing function to drive the model.Then we determined the interstitial [K+] timecourse which resulted in a simulated coronary sinusplasma [K+] time course that closely fit the coro-nary sinus plasma [K+] time course observed ineach of the experiments reported herein. We deter-mined the peak or plateau interstitial [K+] for eachof these close-fit simulations.

In a previous study, we had observed the effectof a bolus injection of 40 junol of potassium chlorideon coronary vascular resistance (Murray andSparks, 1978). To calculate the change in interstitial[K+] caused by this injection, we modified ourmodel by adding a cellular compartment whichacted as an infinite sink for K+. Assuming a reason-able value for the permeability-surface area productof myocardial cell membranes (PScm) (Ziegler andGoresky, 1971; Tancredi et aL, 1975), we simulatedthe injection of 40 junol K+ and observed the peakchange in interstitial [K+] in our model. This wascompared to the previously estimated changes in

interstitial [K+] that accompanied heart rate steps.

Statistical AnalysesAll statistical tests performed on the time course

parameters (defined above) used Student's t distri-bution for paired samples (Dixon and Massay,1969). Statistical analyses were performed on anAmdahl 470V/6 computer and the Michigan Inter-active Data Analysis System (MIDAS). Groupmeans ± one standard error of the mean are pre-sented throughout the text. Model simulations wereperformed with the Amdahl 470V/6 computer andthe Continuous System Modeling Program (IBMProgram 360A-CS-16X).

ResultsIncreases in Heart Rate

A typical record of the responses to a step in-crease in heart rate is shown in Figure 1. In general,when heart rate was increased, systemic blood pres-sure did not change. Coronary vascular resistancegradually fell to a new steady state level. Coronarysinus oxygen content remained unchanged for sev-eral seconds after the heart rate increase (reflectingthe delay introduced by vascular transit) and thengradually fell to a new steady state value. Thisreflects an increased myocardial oxygen consump-tion. Coronary sinus plasma [K+] also remainedunchanged for several seconds following the heartrate increase and then gradually increased to a peakvalue or a temporary plateau value before returningto about the control level during the period ofincreased heart rate. In three of the nine prepara-tions the coronary sinus plasma [K+] remainedelevated throughout the period of increased heartrate. The average increase in heart rate was 75 ± 6beats/min. This resulted in a decrease of 0.51 ±0.12 PRUioo in coronary vascular resistance, an

0IMCTEASt/

hCAffT'HATE

3 0 6 0

TIME

9 0

tSKOOdiJ

FIGURE 1 A typical record of the responses of coronarysinus oxygen content, coronary vascular resistance, andcoronary sinus plasma fK*] to a step increase (60 beats/min) in heart rate. Coronary blood flow was held con-stant at 89.5 ml/min per 100 g.


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increase of 2.19 ± 0.36 ml/min per 100 g in myocar-dial oxygen consumption, and an increase of 0.53± 0.07 mEq/liter in coronary sinus plasma [K+].Coronary blood flow averaged 86.1 ± 3.8 ml/minper 100 g (see Table 1).

The average time courses of changes in coronarysinus [K+] following step increases in heart rate areshown in Figure 2 for two groups of experiments.The ordinate of this graph reflects our normalizedscale in which 0 is the baseline value and 100 thepeak or plateau value. Coronary sinus [K+] rosefollowing a step increase in heart rate in all ninedogs studied. In three dogs this rise was sustainedthroughout the period of increased heart rate. Inthe remaining six dogs coronary sinus [K+] returnedtoward its prestimulation level while the increasedheart rate was maintained. It is apparent in Figure2 that the time course of the initial rise in coronarysinus [K+] is very similar for these two groups ofdogs. Therefore, for the purpose of comparing po-tassium and vascular dynamics following heart ratesteps, no distinction was made between the dogswhose coronary sinus [K+] plateaued and those inwhich it returned towards baseline during the pe-riod of increased heart rate.

Figure 2 also shows the average time course ofthe transit-adjusted coronary vascular resistance(CVR*) seen in response to step increases in heartrate. It is apparent in Figure 2 that the rise incoronary sinus [K+] preceded the vasodilation fol-

60 90 120TIME (Stamtt)

FIGURE 2 Average time courses of coronary sinusplasma [K*] and CVR* following step increases in heartrate. Heart rate increases were induced at time 0 andsustained throughout the time period shown. See text forexplanation of transit correction and normalization.Upward deflection of CVR* indicates vasodilation. ForCVR*, n — 9 dogs; for coronary sinus [K*] (heavy lines),n = 3; and for coronary sinus fK*J (light lines), n = 6.

lowing a step increase in heart rate. In Table 2 wehave summarized the parameters that characterizethe time courses of these responses. The tio and Uofor coronary sinus [K+] are significantly lower (i.e.,faster) than the corresponding parameters that

TABLE 1 Absolute Values: Heart Rate Steps

DogHeart rate (beate/

min)Coronary blood flow(ml/min per 100 g)

Coronary vascularresistance (PRU.oo)

Coronary sinusO, content (vol%)

Myocardial Oi con-sumption (ml/min per

100 g)Coronary sinus plasma

[K+] (mEq/liter)

Baseline values before step increases in heart rate

2-32-52-243-53-93-103-123-304-1

Mean± SEM

2-32-52-243-53-93-103-123-304-1

Mean±SEM

9010011016080

160160105160

12511

200190200220150210220190220

2007

77.280.588.284.474.289.574.4

101106

86.13.8

Peak or plateau

77.280.688.284.474.289.574.4

101106

86.13.8

1.511.751.111.321.731.401.331.321.00

1.400.08

values during

1.240.740.770.730.611.130.930.710.90

0.890.07

8.876.416.633.843.074.013.675.428.43

5.540.73

increased heart rate

3.961.734.611.720.503.321.952.636.59

3.000.62

3.969.058.62

10.028.11

11.588.937.03

12.25

8.840.82

7.7512.8210.4011.8110.0212.2110.219.83

14.20

11.030.64

4.654.003.994.983.903.504.363.144.28

4.090.19

5.124.794.475.304.823.904.833.724.64

4.620.17


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TABLE 2 Comparison of Time Courses: Heart RateSteps

(seconds)

t.o t«o

CVR*Coronary sinusplasma [K+]

24.5 ± 1.415.3 ± 1.8

0.007

32.6 ± 2.026.5 ± 1.2

0.011

53.3 ± 5.443.8 ± 14

0.14

P values are for paired (-test statistics comparing CVR* to [K*]; n —9 data sets.

characterize the CVR* time course. The tio, t«>, andtgo for coronary sinus oxygen content are signifi-cantly lower (i.e., faster) than the correspondingparameters for CVR*. Moreover, the decrease incoronary sinus oxygen content produced by theincreased heart rate is sustained throughout theperiod of elevated heart rate (Table 3).

Fifteen-Second Cessations of Coronary BloodFlow

A typical record showing the responses of coro-nary sinus oxygen content, coronary vascular re-sistance, and coronary sinus plasma [K+] to a 15-second cessation of flow (ischemia) is shown inFigure 3. At —15 seconds, as indicated on the ab-scissa, the pump delivering blood to the left com-mon coronary artery was stopped. Coronary perfu-sion pressure fell immediately and rapidly (less than10 seconds) to a very low value and remained atthis level throughout the period of ischemia. After15 seconds of ischemia (i.e., at time 0 on the abscissaof Figure 3) pump flow was reinstituted at theconstant, baseline rate. The flow value for perfusionpressure after the recommencement of flow indi-cates that a considerable vasodilation had occurredduring the period of ischemia. Perfusion pressurerose quickly following reinstitution of flow to aboutone-third of its preischemia level as the vascularbed was refilled with blood. Perfusion pressure thengradually returned toward its control leveL It is thissecond phase, reflecting the gradual return of cor-onary vascular resistance to its control level follow-ing the reinstitution of flow, that is of primaryinterest in this study. Coronary sinus oxygen con-tent remained unchanged for several seconds fol-lowing the onset of ischemia and then gradually

TABLE 3 Comparison of Corrected Time Courses:Heart Rate Increase

(seconds)

tto tw

CVR*Coronary sinusOj content

24.5 ± 1.418.4 ± 0.5

<0.005

32.6 ± 2.024.0 ± 0.6

<0.005

53.3 ± 5.440.7 ± 4.6

0.016

P values are for paired (-test statistics comparing CVR* to coronarysinus O, content; n •» 9 data sets.

FIGURE 3 A typical record of the responses of coronarysinus oxygen content, coronary vascular resistance, andcoronary sinus plasma [K*J to a 15-second cessation ofcoronary blood flow. The pump used to perfuse the leftcommon coronary artery with blood at a constant ratewas turned off at —15 seconds, and turned back on attime 0. Heart rate was held constant by external pacing.

decreased to a minimum value before returning toits control level. This decrease in coronary sinusoxygen content no doubt reflects increased extrac-tion of oxygen from the blood within the myocardialvessels during and perhaps after the ischemic pe-riod. Coronary sinus plasma [K+] also remainedunchanged for several seconds until, some timeafter recommencement of flow, it began a gradualincrease to a peak value before returning toward itscontrol level. Heart rate was constant throughoutthis entire time. Sometimes electrical pacing wasused to attain this constancy.

Table 4 contains the minimum postischemic cor-onary vascular resistance, the peak postischemiccoronary sinus plasma [K+], and preischemic, base-line values of these variables for the six experimentsin which the 15-second ischemic challenge wasgiven. Vascular resistance fell by 1.25 ± 0.22 PRUioo-Coronary sinus plasma [K+] increased in each ofthe six dogs studied by an average of 0.55 ± 0.09mEq/liter.

Figure 4 depicts the average time course ofchanges in coronary sinus [K+] produced by 15seconds of ischemia. In this figure, an upward de-flection of the [K+] curve indicates a decrease in[K+]. Here the ordinate value 0 indicates the peakof the [K+] response to ischemia, and 100 indicatesthe recovery [K+]. Coronary sinus plasma [K+]reached a peak value approximately 25—40 secondsafter the reinstitution of flow and returned to itscontrol level 35-50 seconds later.

The average time course of CVR* to 15 secondsof ischemia is also shown in Figure 4. Here theordinate value 0 indicates the minimum resistanceat the beginning of the postdschemia recovery pe-riod, and 100 indicates the steady state recoveryvascular resistance. Consider now the return of both[K+] and CVR* to their respective baselines values,


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TABLE 4 Steady State and Transient Data: 15-Second Cessation of Flow

DogCoronary blood

flow (ml/min per100 g)

Coronary vascu-lar resistance

(PRU.oo)

Coronary sinus plasma [K1](mEq/liter)

2-32-42-52-112-132-24

Mean± SEM

Baseline values before cessation of flow

77.211781.055.152.088.2

78.49.7

1.540.961.282.272.041.04

1.520.22

4.594.517.225.264.824.46

5.140.43

2-32-42-52-112-132-24

Mean± SEM

Peak changes after cessation of flow

71211781.056.152.088.2

78.49.7

0.310.390.310.290.290.08

0.280.04

5.085.248.135.615.174.94

5.700.50

i.e., the rising phases of the curves in Figure 4. Itappears that the CVR* time course preceded thecoronary sinus [K+] changes initially, but that the[K+] changes preceded the CVR* time course overapproximately the second half of the return course.The time course parameters summarized in Table5 confirm this impression. The tio, teo, and tgo forcoronary sinus plasma [K+] were significantly

- 2 5 -

CORONARY SINUSPLASMA K*

CORONARY VASCU.ARRESISTANCE •

START' FLOW

120

TIME (Stconds)

2 4 0

FIGURE 4 Average time courses of coronary sinusplasma [K*] and CVR* following 15 seconds of is-chemia. Flow was reinstituted at time 0. Normalizationprocedure is described in text. In this figure, upwarddeflection of the [K*J curve indicates fall in coronarysinus [K*J, and upward deflection in the CVR* curveindicates vasoconstriction. Transit correction is ex-plained in text; n = 6 dogs. Vertical bars indicate oneSEM.

slower, not different, and significantly faster, re-spectively, than the corresponding parameters thatcharacterized the CVR* time courses.

Calculation of the Magnitude of Changes inInterstitial [K+]

The assessment of whether interstitial [K+]changes were of adequate magnitude to explain theobserved vasodilation required two calculations.First, we calculated how much interstitial [K+]changes following an intracoronary injection of KCl.In a previous study, intracircumflex artery injectionof 40 /unol of KCl caused a 34-48% fall in coronaryvascular resistance (Murray and Sparks, 1978). Us-ing the model described in the Appendix to thisarticle, we calculated that interstitial [K+] wouldhave been increased by 1.1-2.2 mEq/liter by thisinjection. This range exists because of uncertaintyabout the values of three parameters. As seen inFigure 5, the size of the interstitial space and thePS can each explain about half of this range whenthey are varied within their physiological limits

TABLE 5Ischemia

Comparison of Time

t»

Courses:

(seconds)

tto

Recovery from

CVR*Coronary sinusplasma [K+]

33.8 ± 3.843.6 ± 3.0

0.041

69.2 ± 7.861.0 ± 1.9

0.143

132 ± 2 378.2 ± 4.7

0.019

P values are for paired (-test statistics comparing CVR* to [K*J; n •6 data sets.


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2 4

_ 2 0_ J

UJ

E 1.6

s_ J< I 2

0.8

0.4

M K < " INJECTION

^ ^ P S C . - 0 5

LpPSc»' l I

6 .8 10 1.2CAPILLARY PS (ml/min/ty

FIGURE 5 Calculations of changes in interstitial [K*]due to postassium injections (shaded bands) or heartrate steps (lines). The shaded bands show the range ofinterstitial [K*] increments possible with variation ofvarious parameters within their physiological range asindicated in the figure. PScm ~ permeability surface areaof myocardial cell membranes in ml/min per g. V/SF =volume of interstitial space in ml/g. The lines show thepeak or plateau value of interstitial [K*] needed tomatch coronary sinus plasma [K*] data. Each linerepresents a single dog and contains three points rep-resenting three different values of capillary PS. Thebroken lines represent the dogs in which K* efflux wassustained for the duration of the increased heart rate.

(Ziegler and Goresky, 1971; Tancredi et al., 1975).Variation of myocardial cell membrane PS withinits physiological limits (Ziegler and Goresky, 1971;Tancredi et al., 1975) has less effect on the intersti-tial [K+] attained.

The second step in our assessment of interstitial[K+] was to calculate the [K+] reached during heartrate steps. Using the model described in the Appen-dix, we calculated that interstitial [K+] rose by 0.3-1.4 mEq/liter. This range is due primarily to vari-ability in potassium efflux from dog and secondarilyto uncertainty about the true value of capillary PS(Fig. 5). Thus the interstitial [K+] increments dur-ing heart rate steps seem to be less than thosecaused by potassium injection. Assuming an inter-mediate PScp of 0.8 ml/min per g, the averageinterstitial [K+] increment caused by heart ratesteps in 0.68 mEq/liter. This is 30-60% of the incre-ment calculated to occur with injections. The cor-onary vascular resistance fell by 36% (range: 10-65%) with the heart rate steps, which fall is ofsimilar magnitude to the vasodilation observed withpotassium injections (Murray and Sparks, 1978).

DiscussionWe have attempted in this study to evaluate one

possible mechanism for the local regulation of the

coronary circulation. The criteria we have used toevaluate this hypothesis, that potassium ion is acoronary vasoregulatory agent, are enumerated anddiscussed below. The major problem we had to facein this study was our inability to measure directlyone variable of interest, i.e., the concentration ofpotassium ion to which the arteriolar vascularsmooth muscle is exposed. In the absence of stand-ing gradients in the interstitial space, it would befair to call this variable of interest the interstitial[K+]. Our approach, then, was to measure what wecould, in this case coronary sinus plasma [K+], andto make certain assumptions about and ancillarymeasurements of the processes relating interstitial[K+] to coronary sinus plasma [K+]. We then usedexplicit mathematical models of these intermediaryprocesses so that we could use our indirectly ob-served variable (coronary sinus plasma [K+]) tolearn something about the variable of direct interest(interstitial [K+]) and its relation to coronary vas-cular resistance.

The processes that influence the relationship ofinterstitial [K+] to coronary sinus plasma [K+] are(1) movement of potassium across the myocardialcapillary wall, (2) vascular transit of plasma con-taining potassium from the myocardial capillariesto the coronary sinus, and (3) uptake of plasmapotassium into red blood cells. This third processhas been found to be very slow in dog blood (Frazieret al., 1954), and we have assumed it to be ofnegligible importance in our experiments.

The effect of the transcapillary exchange is toblunt and slightly slow the changes in end-capillaryplasma [K+] following a change in interstitial[K+]. The effect of vascular transit is to slow con-siderably the changes in coronary sinus plasma [K+]after a change in end-capillary plasma [K+]. Vas-cular transit also blunts the appearance of briefpeaks of end-capillary [K+] in coronary sinus [K+],but sustained changes in end-capillary [K+] arefully reflected in coronary sinus [K+]. We asked twobasic questions in this study, which are discussedbelow. Briefly, we asked whether interstitial [K+]changes were (1) fast enough and (2) big enough toaccount for the vascular changes seen in two situ-ations. To answer the first question, a time coursequestion, we modeled only the vascular transit proc-ess, since the capillary exchange process has onlyrelatively slight slowing effects. To answer the mag-nitude question, we modeled both of these proc-esses, since both could affect the magnitude ofcoronary sinus plasma [K+] changes.

Our model of coronary vascular transit and ouralgorithm for correction of vascular transit effectshave been discussed in detail previously (Belloniand Sparks, 1977). Briefly, the distribution oftranscoronary vascular transit times was measuredwith an intravascular tracer. Postarteriolar vasculartransit effects were calculated from the tracer databy ascribing 91.1% of its transit to postarteriolarvessels (Sparks and Belloni, 1977). These postarter-


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iolar vascular transit effects were then appended tothe coronary vascular resistance time course via theconvolution integral. The resulting CVR* reflects(1) the time course of resistance changes and (2)the effects of vascular transit. The coronary sinusplasma [K+] reflects (1) the time course of capillary[K+] and (2) the effects of vascular transit. If theeffects of vascular transit are equally represented inthe time courses of CVR* and coronary sinusplasma [K+], their temporal relation to each otherreflects the temporal relation of unadjusted vascu-lar resistance and capillary plasma [K+]. The timecourse of interstitial [K+] must be, if anything,faster than that of capillary [K+]. Since we foundthat potassium changes preceded vascular changesafter correction was made only for vascular transit,further correction for the slight slowing effects oftranscapillary exchange was unnessary, as our con-clusion would not have been affected.

The source of greatest potential error in thisanalysis is our assignment of 91.1% of the trans-coronary vascular transit effects to postarteriolarvessels. Obviously, assignment of a larger fractionto adjust the resistance time course would onlyfurther slow the CVR* time course. But if thevascular transit effects of interest were substantiallysmaller than those we used in calculating CVR*,our conclusion might be in error. Our assignmentfigure, 91.1%, was obtained from the mean of severalmeasurements in a previous study (Belloni andSparks, 1977). The 95% confidence interval for thisparameter was approximately 80-100%. We calcu-late that our conclusion that potassium changesprecede vascular changes still would have beenreached if we had used only 80% of the total transiteffects in the calculation of CVR*. It seems unlikelyto us, therefore, that our estimates of capillary andvenous transit effects would be so inaccurate as toobscure a temporal precedence of vascular changesover potassium changes.

Our use of the convolution integral assumes thatthe system is stationary; i.e., the transit effects donot change over time. As already noted, this re-quirement dictated the use of constant flow perfu-sion in our experiments. It is possible that changesin myocardial activity could result in changes incapillary density or vascular volume, for example,sufficient to alter the pattern of intravascular tran-sit times. Smaller heart rate changes (20 beats/min)than those used in the present study were shown tohave no effect on intravascular transit through theheart (Belloni and Sparks, 1977). Similarly, incre-ments of 35% in myocardial oxygen consumptioninduced by catecholamines were without significanteffect on vascular transit in the heart (Smith et aL,1978). In the present study, oxygen consumptionwas increased by an average of 31% by raising heartrate. It seems probable, therefore, that statdonaritywas achieved during the heart rate steps. It is lesscertain that our assumption of stationarity was metduring and immediately after the 15-second is-chemic challenges. The myocardial vascular volume

must fall somewhat during the period of no flowand must rise again with reinstitution of perfusion.Exactly what effect this emptying and refilling hadupon the intravascular transit pattern during theearly postischemic period is a matter for specula-tion. The fast initial rise in perfusion pressure uponrecommencement of flow seems likely to representrefilling of vascular spaces. This phase takes only asecond or two, which agrees well with estimates offilling time based on vascular volumes and flowrates. It appears likely, then, that nonstationaritymay exist only briefly, although its consequencesmay persist for some seconds, i.e., until a completeturnover of the intravascular volume has takenplace.

The caveats concerning the vascular transit ef-fects apply also to their inclusion in our estimationof the magnitude of interstitial [K+] changes duringheart rate steps. However, the critical element hereis the magnitude of the capillary PS. The exchangeof potassium across the capillary wall is diffusion-ally limited, but the correspondence between inter-stitial and end-capillary concentrations is ratherclose. As seen in Figure 5, a doubling of capillaryPS causes only relatively small changes in the cal-culated peak or plateau interstitial [K+]. This isbecause the magnitude of interstitial [K+] and cor-onary sinus plasma [K+] are fairly close even in thelow PScp range. Other parameters in our model,such as the estimate of capillary plasma space,cause only slight changes in the behavior of themodel when their values are varied. This is due tothe predominance of the high PScP values in deter-mining the overall behavior of the model. Our val-ues for PScap span the range measured by twodifferent groups (Ziegler and Goresky, 1971; Tan-credi et al., 1975). It has also been found thatmyocardial capillary PS for sodium varies less than2-fold with large variations in myocardial oxygenconsumption (Duran et aL, 1977).

The hypothesis that potassium ion is involved inthe control of coronary vascular resistance holdsthat, in association with an increase in myocardialmetabolic activity or a decrease in oxygen supplyto the heart, there is an increase in the [K+] of theinterstitial space. The elevated interstitial [K+] inturn causes relaxation of the coronary arteriolarvascular smooth muscle. If potassium is a compo-nent of the myocardial vasoregulatory system, thefollowing criteria must be met: (1) Potassium mustbe a coronary vasodilator. (2) The [K+] in theenvironment of the arteriolar vascular smooth mus-cle must increase at least as fast as the associateddecreases in coronary vascular resistance. (3) Theinterstitial [K+] changes must be of sufficient mag-nitude to account for at least some portion of theassociated vascular response. That is, the dose-re-sponse relationship between interstitial [K+] andvascular resistance must be known, and the inter-stitial [K+] changes must fall into the appropriaterange.

Potassium has been shown to be a dilator of


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coronary vessels. The data presented in this studyindicate that, in at least two situations, interstitial[K+] transients are fast enough so that a vasoregu-latory role for potassium is possible. Following stepincreases in heart rate, the rise in coronary sinusplasma [K+] preceded the coronary vasodilationonce the latter time course was adjusted to includethe effects of vascular transit. This observationleads us to conclude that interstitial [K+] rose morequickly than the vascular resistance fell. In thesecond situation studied, the return-to-control timecourses of coronary sinus plasma [K+] and CVR*crossed each other. The CVR* time course precededthe [K+] time course for roughly the first half of thereturn of both variables, and the situation wasreversed for the second half of the return. Weconclude from this that interstitial [K+] may beplaying a partial role in determining the time courseand magnitude of postischemic vasodilation, al-though the participation of other mechanisms isalso suggested. Thus the present data appear tosatisfy the time course criterion.

The calculations made to assess whether inter-stitial [K+] changes were of sufficient magnitude toexplain the vasodilation seen following heart ratesteps are explained in the Results and the Appendix.From our calculation we can say that potassiuminjections which caused a 34-48% fall in coronaryvascular resistance (Murray and Sparks, 1978)probably caused a 1.1-2.2 mEq/liter increment ininterstitial [K+]. During the increased heart rateperiods of the present study, coronary resistancefell by 36% on the average. We calculated thatinterstitial [K+] must have risen by 0.3-1.4 mEq/liter to a peak or a plateau. If we assume an inter-mediate PScap of 0.8 ml/min per g, the average risewould have been 0.68 mEq/liter. We conclude thatinterstitial [K+] may rise enough during heart ratesteps to account for a considerable fraction of thecoronary vasodilation seen (very roughly about one-half) . It does not appear that potassium can accountfor all of the coronary vasodilation seen with theseheart rate steps, although better information on thedose dependency relationship between [K+] andcoronary vascular resistance is needed before a finalconclusion is possible.

We did not make detailed calculations of inter-stitial [K+] during 15 seconds of ischemia. Frominspection of Table 4, it can be seen that coronarysinus plasma [K+] changes were very similar tothose seen with heart rate steps (mean change •=+0.55 mEq/liter). The vasodilation seen with the15-second ischemic challenges was greater than thatseen with heart rate steps, with resistance falling anaverage of 80%. It seems as if potassium must playonly a relatively minor role in causing the ischemicvasodilation seen in these experiments. It may playa more important role during the later stages of thepostischemic vasodilation.

Our criteria for assessment of the potassium hy-pothesis for coronary vasoregulation all have been

partially met. Potassium is a coronary vasodilator.Following step increases in heart rate, interstitial[K+] changes appear to precede vasodilation andalso appear to be of sufficient magnitude to explainroughly one-half of the resistance fall. After a 15-second period of ischemia, there appears to beconsiderably more coronary vasodilation than canbe accounted for solely by potassium. During thelater stages of the postischemic vasodilation, how-ever, interstitial [K+] recovery appears to precedethe recovery of coronary vascular tone. This sug-gests that interstitial potassium may be an impor-tant determinant of coronary vascular resistance atthis stage of postischemic vasodilation.

This collection of evidence strongly suggests thatpotassium ion participates in the local regulation ofthe coronary circulation. This in no way rules outthe participation of other mechanisms. In fact,other mechanisms are needed to explain severalaspects of the present results, namely: (1) the sus-tained vasodilation following heart rate steps seenin the absence of a sustained increment in coronarysinus [K+] and, presumably, interstitial [K+] (Fig.2); (2) the vasodilation seen with heart rate stepsand 15 seconds of ischemia, which cannot be ex-plained by increments in interstitial [K+]; and (3)the early phase of the recovery from ischemic vaso-dilation which precedes interstitial [K+] recovery(Fig. 4).

The transient nature of the interstitial [K+] risewith increased heart rate suggests that potassiumparticipates in the initiation of the coronary vaso-dilation seen in this situation but is not responsiblefor the maintained, steady state vasodilation. Thistype of role for potassium is also suggested by thetransient nature of its action on isolated vessels(Gellai and Detar, 1974) or on resting, in situ coro-nary vascular resistance (McKeever et al., 1960).

In three experiments, however, potassium effluxwas maintained for the 2.5 minutes of increasedheart rate. These three dogs had a significantlylower coronary sinus oxygen content during theelevated heart rate than did the six dogs in whichthe potassium release was only transient (1.69 ±0.63 vs. 3.66 ± 0.76 vol%, P < 0.05). It may be thatthe combination of increased metabolic activity andinadequate oxygen supply is the cause of a sustainedincrease in interstitial [K+] (Gerlings et al., 1969;Parker et al., 1970). A more prolonged participationof potassium in coronary vasoregulation cannot beruled out for this situation. Even this prolongedincrease in interstitial [K+] can explain no morethan about half of the vasodilation seen. We need,therefore, at least one other vasoregulatory mech-anism to account for all or part of the sustainedvasodilation seen with increased heart rate.

Several other proposed vasoregulatory mecha-nisms have received attention (Sparks and Belloni,1978). One class of mechanism, those closely linkedto oxidative metabolism (e.g., mechanisms involv-ing oxygen or adenosine), has been examined for


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possible transient involvement in coronary vaso-regulation. Small steps in heart rate (20 beats/min)were found to be followed by changes in myocardialoxygen uptake which preceded vascular changes(Belloni and Sparks, 1977). This finding has beenextended to the larger heart rate steps used in thepresent study (Table 3). It appears, then, that theremay be two (or more) mechanisms that initiate thecoronary vascular response to increased metabolicactivity, one being a rise in interstitial [K+] and theother more tightly linked to oxidative metabolism.These mechanisms may act in simple concert withtheir effects being summed. Alternatively, theremay be a true redundancy of action in which onemechanism fully compensates for the induced orpathological absence of the other. This problemremains to be resolved. If there is no redundancy,one might predict that the speed but not the steadystate magnitude of the coronary vascular changesduring increased metabolic activity or postischemicvasodilation would be affected by aberrations ofpotassium transport or metabolism.

Appendix

Model of Myocardial K+ Efflux during StepChange in Heart Rate

We constructed a compartmental model of themyocardium as shown in Figure 6. We representedthe capillary bed of the heart by three compart-ments in series, each capable of exchanging materialwith the single compartment used to represent theinterstitial space. The remainder of the vascularspace was represented by a single arterial and asingle venous compartment placed in series withthe capillary compartments. The venous compart-ment also represents the plasma space of the coro-nary sinus catheter. Since coronary blood flow pergram of myocardium was measured in each experi-ment, the value of this parameter in our model wasfixed for the simulation of that experiment. In orderthat our model behave like the corresponding ex-perimental preparation with respect to intravascu-lar transit time distribution, we adjusted the vol-umes of the vascular compartments. Myers andHonig (1964) found a myocardial blood content ofabout 0.06 mg/g for the dog. We assigned 40% ofthis space (i.e., 0.024 ml/g) to the capillary com-partments and 5% (0.003 ml/g) to the arterial com-partment. The behavior of this model was found tobe rather insensitive to the value of these param-eters. The remaining vascular space plus catheterspace was assigned to the venous compartment andwas varied to obtain a good fit of model behavior tothe experimentally obtained dye curves. Since theintravascular marker used, indigo carmine dye,binds to plasma proteins, it is assumed to be con-fined to the plasma space. Plasma spaces wereobtained by multiplying each of the blood spacesby (1 — HT), where HT was the hematocrit of bloodwithin the tissue. Because of the differential linear

ARTERIES CAPILLARYVEINS +

CATHETER

FIGURE 6 Mathematical model used to calculate inter-stitial [K*]. The cell compartment was included only inthe simulations of potassium injections.

velocity of red cells and plasma in small vessels, thetissue hematocrit was taken to equal one-half thelarge-vessel hematocrit (Gibson et al., 1948). Wealso introduced an adjustable delay to mimic the10-16 seconds that passed in our experiments beforeany dye appeared in the coronary sinus plasma. Anexample of how closely we could simulate the ex-perimentally observed intravascular transit timedistribution is shown in Figure 7A. We minimizedthe sum of squared differences between simulatedand observed curves until this sum changed by lessthan 5% with a 5% or greater change in the param-eter being estimated, or until the sum fell below

08

06

.04

O2

0

0

if \VMT'/ Vv i r -

/ ^

S 12 18 24 30SECONDS

ULATKM

> ^

36 42

A

1 '48 34

4 8

4.6

4 2

(T 40<

3 820 40 60 80

SECONDS100 120 140 160

FIGURE 7 Comparison of data (solid lines) and modelsimulations (broken lines). A: Distribution of intravas-cular transit times. B: Coronary sinus plasma fK*J witha step increase in heart rate. Both comparisons are fordogs 2-5.


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POTASSIUM AND CORONARY VASODILATION/Murrajy et al. 779

0.002, which indicated an average absolute devia-tion between simulated and observed curves of lessthan 0.0004/sec per point.

The next step was to simulate the observed timecourse of coronary sinus plasma [K+]. We used thevascular volume parameters found to simulate bestthe intravascular transit curves for each prepara-tion. We set capillary permeability-surface areaproduct (PScp) equal to 0.6, 0.8, or 1.2 ml/min perg. These values span the range of values for PScapfound for dog heart by Trancredi et al. (1975) andZiegler and Goresky (1971). For each PScp, wechose a time course for interstitial [K+]. We used aseries of ramp functions which allowed us to simu-late linear rises and falls as well as plateaus asneeded to match our simulated coronary sinusplasma [K+] time course with the observed timecourse. An example of such a match is shown inFigure 7B. We minimized the sum of squared dif-ferences between simulated and observed curvesuntil this sum changed less than 5% or fell below0.15, which indicated an average deviation of lessthan 0.01 mEq/liter per point. In general, as mightbe expected, the value of PScP did not affect thegeneral shape of the interstitial [K+] functionneeded to obtain a close fit to the data. Rather,only the magnitude of the interstitial [K+] changeswas altered to obtain good fits at different PScPvalues. For each PSc«p for each preparation, thepeak interstitial [K+] was obtained. In the case ofthe three preparations in which coronary sinusplasma [K+] levels remained elevated for the dura-tion of the increased heart rate period (see Results),the plateau level of interstitial [K+] was obtained.These values are shown in Figure 5.

Model of Interstitial [K+] during KC1Injection

In a previously reported study, we injected 40jtmol of potassium chloride into the coronary arter-ies of several dogs and observed a considerabletransient coronary vasodilation (Murray andSparks, 1978). We wanted to estimate how great achange in interstitial [K+] would occur with suchan injection. For this purpose, we kept arterial andcapillary vascular volumes equal to those in ourprevious model stages. Venous and catheter spacesand pure transit delay were unimportant param-eters at this stage. Blood flow was set equal to 0.86ml/min per g, which was the average flow rate forthe heart rate step dogs. Capillary PS was set equalto either 0.6 or 1.2 ml/min per g. A new compart-ment and parameter were introduced to representthe uptake of K+ into myocardial cells. Althoughthese are shown in Figure 6, they have not beenincluded in previous stages of our modeling. Thenew parameter, PScm, is the permeability-surfacearea product for myocardial cell membranes. Weassigned it the values of 0.5, 0.8, or 1.1 ml/min perg; these values span the range measured by Tan-credi et al. (1975) and Ziegler and Goresky (1971).

We assumed an interstitial volume of 0.2 or 0.3 ml/g (Page, 1962). Finally, we assumed a tissue weightof 60 g as the portion of myocardium supplied bythe circumflex artery into which the 40 jtmol of K+

was injected. We forced our model with a 1-secondinjection of 40/^mol K+ and observed the peakinterstitial [K+], which occurred about 4 secondsafter the simulated injection. This model behavedsuch that 38-59% of the injected K+ is taken up bythe intracellular compartment, which acts as aninfinite sink here. This agrees well with the obser-vations of Ziegler and Goresky (1971) for dog heart.

AcknowledgmentsWe wish to thank Thorn Rooke and David Harlan for their

help with these experiments, and Susan Koch and NanolynHowell for their secretarial assistance.

ReferencesBelloni FL, Sparks HV: Dynamics of myocardial oxygen con-

sumption and coronary vascular resistance. Am J Physiol 233:H34-H43, 1977.

Bunger R, Haddy FJ, Querengasser A, Gerlach E: Studies onpotassium induced coronary dilation in the isolated guinea pigheart. Pfluegers Arch 363: 27-31, 1976

Case RB: Ion alterations during myocardial ischemia. Cardiology56: 246-262, 1971

Cherbakoff A, Toyama S, Hamilton WF: Relation between cor-onary sinus plasma potassium and cardiac arrhythmia. CircRes 5: 517-521, 1957

Cohen SE: The influence of the Ca and K ions on tonus andadrenaline response of the coronary arteries. Arch Int Phar-macodyne Ther 64: 1-16, 1936

Cummings JR: Electrolyte changes in heart tissue and coronaryarterial and venous plasma following coronary occlusion. CircRea 8: 865-869, 1960

Dixon WJ, Massay FJ: Introduction to Statistical Analysis. NewYork, McGraw-Hill, 1969

Driscol TE, Berne RM: Role of potassium in regulation ofcoronary blood flow. Proc Soc Exp Biol Med 96: 505-508,1958

Duran WN, Marsicano TH, Anderson RW: Capillary reserve inisometrically contracting dog hearts. Am J Physiol 233: H276-H281, 1977

Frazier HS, Sicular A Solomon AK: Potassium uptake by dogerythrocyte. J Gen Physiol 37: 631-641, 1954

Gellai M, Detar R: Evidence in support of hypoxia but againsthigh K+ and hyperosmolality as possible mediators of sus-tained vasodilation in rabbit cardiac and skeletal muscle. CircRes 35: 681-691, 1974

Gerlings ED, Miller DT, Gilmore JP: Oxygen availability: Adeterminant of myocardial potassium balance. Am J Physiol216: 559-562, 1969

Gibson JG, Seligman AM, Peacock WC, Aub JC, Fire J, EvansRD: The distribution of red cells and plasma in large andminute vessels of the normal dog, determined by radioactiveisotopes of iron and iodine. J Clin Invest 25: 848-857, 1948

Gilmore JP, Gerlings ED: Influence of interstimulus interval onmyocardial potassium balance. Am J Physiol 217: 136-141,1969

Grupp G, Acheson GH, Charles A: Heart and paired ventricularstimulation: Effects on contractile force and K+ exchange. AmJ Physiol 212: 607-611, 1967

Harris AL, Toth LA, Hoey TE: Arrhythmic and anti-aiThythmiceffects of sodium, potassium and calcium salts and of glucoseinjected into coronary arteries of infarcted and normal hearts.Circ Res 6: 570-579, 1958

Jennings RB, Sommers HM, Kaltenbach JP, West JJ: Electro-lyte alterations in acute myocardial ischemic injury. Circ Res14: 260-269, 1964

Katz LN, Lindner E: The action of excess Na+, Ca*+, and K+ onthe coronary vessels. Am J Physiol 124: 156-160, 1938


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Konold P, Gebert G, Brecht K: The mechanical response ofisolated arteries to potassium. Experentia 24: 247-248, 1967

Langer GA, Brady AJ: Potassium in dog ventricular muscle:Kinetic studies of distribution and effects of varying frequencyof contraction and potassium concentration of perfusate. CircRes 18: 164-177, 1966

McKeever WP, Braun H, Coder D, Croft J: The local effect ofpotassium on different segments of the coronary vascular bed.Clin Res 3: 188, 1960

Murray PA, Sparks HV: The mechanism of K+-induced vasodilation of the coronary vascular bed of the dog. Circ Res 42:35-42, 1978

Myers WW, Honig CR: Number and distribution of capillariesas determinants of myocardial oxygen tension. Am J Physiol207: 653-660, 1964

Norton JM, Detar R: Potassium and isolated coronary vascularsmooth muscle. Am J Physiol 222: 474-479, 1972

Page E: Cat heart muscle in vitro. III. The extracellular space.J Gen Physiol 46: 201-213, 1962

Parker JO, Chiong MA, West RO, Case RB: The effect ofischemia and alterations of heart rate on myocardial potassiumbalance in man. Circulation 42: 205-217, 1970

Scott JB, Frohlich ED, Hardin RA, Haddy FJ: Na*, K+, Ca++,and Mg++ action on coronary vascular resistance in the dog

heart. Am J Physiol 201: 1095-1100, 1961Scott JB, Radawski D: Role of hyperosmolarity in the genesis of

active and reactive hyperemia. Circ Res 28: (suppl 1): 26-32,1971

Smith RE, Belloni FL, Sparks HV: Coronary vascular resistanceand myocardial oxygen consumption dynamics in response tocatecholamines infusion. Cardiovasc Res 12: 391-400, 1978

Sparks HV, Belloni FL: The peripheral circulation: Local regu-lation. Am Rev Physiol 40: 67-92, 1978

Sybers RG, Sybers HD, Helmer PR, Murphy QR: Myocardialpotassium balance during cardioaccelerator nerve and atrialstimulation. Am J Physiol 209: 699-701, 1965

Tancredi RG, Yipintsoi T, Bassingthwaighte JF: Capillary an<J_cell wall permeability to potassium in isolated dog hearts. AmJ Physiol 229: 537-544, 1975

Wilde WS: Pulsatile nature of the release of potassium fromheart muscle during systole. Ann NY Acad Sci 65: 693-699,1957

Wood JC, Conn HL: Potassium transfer kinetics in the isolateddog heart. Influence of contraction rate, ventricular fibrilla-tion, high serum potassium and acetylcholine. Am J Physiol195: 451-458, 1958

Ziegler WH, Goresky CA: Kinetics of rubidium uptake in theworking dog heart. Circ Res 29: 208-220, 1971


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P A Murray, F L Belloni and H V SparksThe role of potassium in the metabolic control of coronary vascular resistance of the dog.

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