Time course of aerobic recovery after contraction of rabbit papillary muscle

F. MAST AND G. ELZINGA Laboratory of Physiology, Free Unioersity, 1081

MAST, F., AND G. ELZINGA. Time course of aerobic recovery after contraction of rabbit papillary muscle. Am. J. Physiol. 253 (Heart Circ. Physiol. 22): H325-H332, 1987.-The time course of oxygen uptake after isometric twitch contractions of isolated rabbit papillary muscles was determined at 20°C by continuous polarographic measurement of the partial pressure of oxygen in a 219-p1 glass chamber in which the fluid circulated rapidly. The response time of the oxygen-measuring system was char- acterized by a delay of 1.1 s and a time constant of 2.1 s after that delay. Depending on the stimulation frequency (0.125-1.0 Hz) the total amount of oxygen uptake for 120 twitches varied from 5.3 to 32.7 nmol/mg dry wt, and the steady-state oxygen consumption rate varied from 0.4 to 8.5 nmol. min. mg dry wt-l. On the basis of a diffusion model we eliminated the effect of oxygen storage on the measured time course of oxygen consumption to determine the mitochondrial kinetics. We found a time constant of an average 19-22 s of mitochondrial off kinetics. By use of this time constant for the change in oxygen consumption rate after contraction, it can be estimated that 9-10% of the oxygen required to restore ATP levels is already taken up by the mitochondria during the twitch.

mitochondrial oxygen consumption; myocardial energy utili- zation; polarography; anoxia; lactate; oxygen diffusion

HEAT PRODUCTION by contracting isolated amphibian skeletal muscle shows that a separation in time exists between the initial chemical reactions, occurring during contraction, and the recovery processes, occurring there- after (15). The oxidative formation of ATP is for many cells the most important recovery process, and for frog muscle a close relationship has been demonstrated be- tween the time courses of recovery heat production and oxygen consumption (16). For the same species it has also been found that the onset of both recovery heat production (l&17) and oxygen consumption after tetanic contraction is delayed (11).

Based on this distinct temporal dissociation between initial and recovery processes, Bugnard (2) developed a technique that allows for a steady-state train of twitch contractions, the separation of initial (I) and recovery heat (R), and the assessment of their relative magnitude, i.e., the recovery ratio r = R/I.

Over the last few years the Bugnard technique has been used to study heat produced by isolated cardiac muscle (1, 18, 19). However, it is not yet clear if the temporal separation of initial and recovery processes, on which the method is based, also holds true for this special type of muscle with its relatively high oxidative capacity.

BT Amsterdam, The Netherlands

Based on the Bugnard method, Alpert and Mulieri (1) measured a recovery ratio of 1.37 for isolated rabbit muscle at Zl”C, whereas Chapman and Gibbs (6) esti- mated using a different approach but very similar exper- imental conditions, a value for r of 0.71. Such a discrep- ancy can be due to the fact that oxygen consumption in isolated cardiac muscle, the major recovery process, is relatively fast and may already start during contraction. This would imply, in contrast to what is known of amphibian skeletal muscle, that in heart muscle initial and recovery heat are generated in part simultaneously.

This study has been designed to measure the time course of oxygen consumption resulting from a train of twitch contractions of cardiac muscle to see how fast oxidative ATP generation follows hydrolysis and if the time course of oxygen consumption corresponds to the time course of recovery reported in the literature (5, 6). Measurements of the oxygen consumed by isolated car- diac muscle reported so far (7, 8, 12, 26) lack sufficient time resolution to answer that question.

METHODS

Preparation. Rabbits (3-6 kg) were injected intrave- nously with 150 IU heparin sodium. The animals were then killed by a blow to the neck, and their hearts were rapidly excised. The isolated hearts were exsanguinated in a series of six beakers containing an oxygenated so- lution at 37”C’of (in mM) NaCl, 128; KCl, 4.7; CaC12, 1.4; MgC12, 1.1; NaHC03, 20; NaH2P04, 0.4; and glucose, 11.1. Papillary muscles (length, 4.4-6.5 mm; diameter, 0.90-1.17 mm) were selected from the right ventricle and mounted in the oxygen chamber shown in Fig. 1.

Experiments were performed at 20°C in a solution containing (in mM) NaCl, 127; KCl, 2.3; MgSO,, 0.6; KH2P04, 1.3; NaHC03, 25; CaC12, 2.5; and glucose, 5.6. During 2 h before the start of the experiment, the oxygen chamber was perfused continuously with oxygenated so- lution, and the muscle was paced at a frequency of 0.2 Hz to allow the muscle to adapt to the experimental conditions.

The chamber used to measure oxygen consumption, shown in Fig. 1, consists of a glass cylinder with two vertical and two horizontal channels that together form a closed circuit with a volume of 219 ~1. The fluid in the chamber circulates rapidly driven by a magnetically cou- pled spinner.

An oxygen electrode (see below) faces the upper hori- zontal channel. The isolated papillary muscle is pulled

0363-6135/87 $1.50 Copyright 0 1987 the American Physiological Society H325

H326 TIME COURSE OF AEROBIC RECOVERY OF CARDIAC MUSCLE

force transducer

inlet

~~ ;;;;;rode /::I- stimulus lead

FIG. 1. Glass chamber used for measurement of oxygen consump- tion of isolated papillary muscle. Lower end of muscle is enclosed in ring at bottom, and upper end is attached to wire that leaves chamber via glass capillary. Wire is connected to force transducer mounted on micrometer (not shown). Circulation is achieved by magnetically cou- pled spinner. Oxygen is measured continuously by polarographic elec- trode. Temperature is controlled by circulating temperature-controlled water around chamber. Imet: response of electrode after rapid injection of 5 ~1 of a solution containing high oxygen concentration. Delay, 1.1 s; time constant, 2.1 s.

through a stainless steel ring that encloses the thicker proximal end of the muscle. Subsequently the ring is pressed into a slightly large r hollow cylinder at the bottom of the central channel. Ring and muscle are fixed to the cylinder with a short insect pin. The tendon end of the muscle is tied to a 0.2-mm diam stainless steel wire that leaves the oxygen chamber via a glass capillary (0 3 . mm wide, 1 .5 mm long) . The other end of the wire is suspended from a force transducer (Aksjeselskapet Mikro-Elektronikk, AE801). One stimulus electrode is connected to the cylindrical holder, the other to the inlet of the chamber. The muscle is stimulated by a single period of a sine wave of 200 Hz (amplitude 20-30 V) and contracts isometrically.

Temperature control within O.Ol”C is achieved bY a water jacket surrounding the glass cylinder.

Measurem fents. In our experimen ts oxygen tension was measured polarographic ally with a 2-mm diam electrode (20). Calibration of the electrode was carried out in the chamber by injecting solutions with different mixtures of oxygen and nitrogen. Concentrations were calculated from the solubility of oxygen in 128 mM NaCl at 20°C [29.9 ml 02/1 (25)]. The response time of the oxygen- measuring system, electrode and stirred chamber, was determined by rapid injection of 5~1 solution with a high (or low) oxygen concentration into the chamber. A delay of 1.1 t 0.4 s and a time constant of 2.1 t 0.3 s after that delay were found (see inset Fig. 1).

Resting oxygen consumption was measured by sub- tracting the oxygen decay in the chamber, without prep- aration, from the oxygen decay measured with a muscle present in the set up (n = 7). In two other experiments oxygen disappearance rate was measured with a muscle in the chamber before and after administration of 2 mM potassium cyanide. Potassium cyanide blocks all oxida- tive metabolism by inhibition of cytochrome-c oxidase.

m Muscle length an d diameter were assessed under the icroscope at X25 magnificati .on before mounting. At

the end of the experiment, length and diameter, at which maximum force was developed, were measured with the preparation in the oxygen chamber. The optical distor- tion of the glass cylinder was determined by placing various rods with known diameter in the chamber and relating that value to the measured one. In our calcula- tions, appropriate correction was made for this optical distortion. Blotted weight of the muscle and its dry weight were determined on an electrobalance (Cahn 29). It was found that wet weight equals 4.47 t 0.08 X dry weight (r = 0.90).

Lactate concentrations were determined in the cham- ber fluid via enzymatic analysis (30). Samples were taken before stimulation and when the oxygen tracing attained the resting level again after stimulation. This was done by infusing 100 ~1 of fresh Ringer in the chamber, which causes the same volume to appear in the reservoir (see Fig. 1). By use of a dye dilution technique, we found that concentration in the sample was 88% of the original concentration in the chamber, using an infusion velocity of 12 ml/h. Lactate measurements were done in 11 ex- periments.

Protocol and recording. After 2 h of equilibration, stim- ulation and perfusion were stopped, and the continuous decrease of oxygen in the chamber was recorded. In 11 muscles (one of which was used also for the measurement of lactate), random order trains of 120 stimuli were given at the following frequencies: 0.125, 0.14, 0.2, 0.33, 0.5, 0.67, and 1.0 Hz. The 95% 02-5% COz-gassed Krebs- Ringer solution was exchanged at least after every second stimulus train. The partial pressure of oxygen (PoJ at the start of the stimulus train varied in this way between 35 and 90 kPa.

Force and oxygen were recorded on a chart recorder. Both signals were also sampled by a Mint 11/23 com- puter (DEC) at sampling frequencies of 20 and 4 Hz, respectively.

Deconuolution. For a proper understanding of the ox- ygen consumption measurements it is essential to distin- guish between the time course of actual mitochondrial oxygen consumption (metabolism), which cannot be measured directly in our chamber, and the uptake of oxygen through the outer surface of the muscle (metab- olism and storage), which is measured as the decreasing oxygen concentration in the chamber.

We calculated for an homogeneous cylindrical muscle with a diameter of 1.0 mm the relation between the rate of mitochondrial oxygen consumption (Fig. 2A), total amount of oxygen used by these organelles (Fig. 2B), and the uptake of oxygen through the outer surface as a function of time (Fig. 2C). Due to diffusion processes in the muscle, the drawn out time course of the latter tracing does not resemble that of the mitochondrial oxygen consumption (Fig. 2B). On the basis of the math- ematical relationship between the tracings shown in Fig. 2, B and C, it is possible to obtain the time course of the mitochondrial oxygen consumption (Fig. 2B) from the oxygen uptake through the outer surface of the muscle by deconvolution. A more detailed account of this anal- ysis is given in the APPENDIX.

Units. Table 1 contains the symbols and the dimen-

TIME COURSE OF AEROBIC RECOVERY OF CARDIAC MUSCLE H327

stim. 0.5 Hz 240 s .

FIG. 2. Theoretical tracings for cylindrical muscle (1.0 mm diam). A: rate of mitochondrial oxygen consumption. B: amount of oxygen consumed by mitochondria. C: amount of oxygen taken up through outer surface of muscle.

TABLE 1. Summary of symbols used and their dimensions

Symbol Dimension

Muscle radius as a constant, R Muscle radius as a variable, r Steady-state oxygen consumption rate, A

Poststimulation oxygen uptake, P

Diffusion constant, K Time constant of mitochondrial activity, 7 Oxygen concentration in chamber or muscle, C Flux of oxygen, F Positive roots of Jo(a) = 0, a!

cm cm cm3 l crnm3. mine1

or nmol l min-l . mg

dry wt-’ cm3/cm3 or nmol/mg dry wt cm2/min min cm3/cm3 or kPa cm3. cm-‘. min-’

Jo, Bessel function of first kind and of zero order.

sions used. Flux of oxygen is not expressed per unit surface but per unit volume to provide a direct compari- son with oxygen consumption per unit wet weight.

RESULTS

Resting oxygen uptake. Oxygen consumption at rest, estimated by comparing oxygen decay in the chamber with and without a muscle, was 1.66 t 0.70 nmol l min-’ l

mg dry wt-’ (means t SD). From the two muscles that were blocked with 2 mM potassium cyanide, basal oxygen consumption rates of 1.40 and 1.22 nmol s min-’ l mg dry w-t-’ were obtained. On the basis of these results we used a value of 1.40 nmolmin-’ l mg dry wt -’ for the deter- mination of the maximum steady-state consumption rate a muscle could attain without becoming anoxic.

Oxygen uptake through the outer surface due to con- traction. An example of a recording of stress and oxygen is shown in Fig. 3A. On average, at stimulation frequen- cies ~0.2 Hz peak stress increased during the first 15 to 20 contractions and remained constant thereafter during the entire twitch train. For higher frequencies peak stress sometimes decreased after an initial rise depending on the muscle studied. This force decay was found for all

Oxygen concentration \ A

Oxygen consumed

above rest

+

4 t FIG. 3. A: experimental tracings of force and oxygen from train of

120 twitch contractions. Duration of stimulus train is indicated on oxygen tracings by vertical markers. B: oxygen tracing corrected for continuous decay during rest. Resulting graph represents oxygen con- sumption related to contraction.

TABLE 2. Peak stress development

Stimulaticm Frequency, Maximum Stress Stress of 120th

Twitch Mean Stress Hz

0.125 38.4k12.6 (10) 38.4t12.6 (10) 36.8~~12.3 (11) 0.14 48.7k20.6 (2) 48.7t20.6 (2) 42.5k22.8 (2) 0.2 40.9&15.1 (11) 40.0zk14.3 (11) 39.5k14.1 (11) 0.33 48.4H7.2 (11) 40.8k11.5 (11) 43.Ok14.9 (11) 0.5 52.5zk15.1 (11) 41.7k12.9 (11) 44.5k15.3 (11) 0.67 54.6k15.8 (7) 41.0t9.0 (9) 46.3k12.3 (8) 1.0 60.6k17.0 (9) 37.8klO.l (10) 42.2k13.4 (10)

Values are means & SD averaged for 11 muscles (mN/mm2). iVumber of observations is given in parentheses.

muscles at a stimulus frequency of 1 Hz. Maximum peak stress, peak stress of the last contraction of the train, and mean peak stress during the train are given for the 11 muscles in Table 2.

To determine the oxygen uptake related to contraction, a correction was made for the continuous decay of oxygen measured when the muscle was at rest, and tracings like the one shown in Fig. 3B were obtained. It was thus assumed that basal metabolism was not altered by con- tractile activity. The full amplitude of that tracing rep- resents the total amount of oxygen consumed due to contraction. For the various frequencies studied the total amount of oxygen uptake varied from 5.3 to 32.7 nmol/ mgdry~*

The slope of the corrected curve attained during steady-state stimulation is called the steady-state oxygen consumption rate. Steady state was reached within l-2

H328 TIME COURSE OF AEROBIC RECOVERY OF CARDIAC MUSCLE

min after the start of stimulation, and the rate varied from 0.4 to 8.5 nmol min-’ l mg dry wt? For the nor- moxie experiments, a linear relationship existed between stimulation frequency and oxygen consumption rate. The mean rates varied from 0.51 at 0.125 Hz to 2.45 nmol min-l .rng dry wt-l at 0.5 Hz.

The amount of oxygen taken up after the end of stimulation is referred to as poststimulation oxygen up- take.

We calculated (cf. APPENDIX) the maximum steady- state rate of oxygen consumption a muscle can have without becoming anoxic as a function of muscle radius. For the center of the muscle (r = 0) and during the steady state, Eq. A2 of the APPENDIX reduces to C = (Co - A) l

R2/4K, where C is the oxygen concentration in the muscle center, Co the oxygen concentration at the muscle sur- face, A the steady-state rate of oxygen consumption, R the muscle radius, and K the diffusion constant of oxygen in heart muscle. The critical steady-state rate that just leads to an anoxic core is then A = 4K Co l RD2. Normal- izing the rate with respect to the concentration of oxygen at the surface of the muscle, a single curve is obtained, when A/Co is plotted as a function of R. This line divides the x-y plane of muscle radius and steady-state oxygen consumption rate into an anoxic and a normoxic field (Fig. 4). In Fig. 4 we also plotted all the values obtained in the various experiments. For 45 out of 65 twitch trains the points were located above the line in Fig. 4, suggesting the presence of an anoxic core. In this calculation resting oxygen consumption was taken into account (see above).

To corroborate the occurrence of anoxia we measured lactate concentration in the chamber fluid before and after the twitch train to estimate lactate production. However, we found mean values of lactate production CO.1 nmol/mg dry wt with no correlation with stimula-

b

b

H

o.!ko

radius (mm1

FIG. 4. Drawn line indicates maximum steady-state rate allowed without center of muscle becoming anoxic as function of muscle radius. Rate is expressed relative to surface concentration to obtain single line. Normalized steady-state rates of various experiments (n = 11) are depicted with different symbols. Position of symbols relative to line indicates curve).

occurrence of normoxia (below curve) and anoxia (above

tion frequency. This then lead to the conclusion that the amount of lactate released into the chamber is negligible with respect to ATP formation.

Poststimulation oxygen consumption increased with steady-state oxygen consumption rate (Fig. 5). Normoxic and anoxic values are indicated by filled and open sym- bols, respectively. Because of the different muscle radii, the points do in theory not form a single straight line. Therefore we performed linear regression analysis on the individual muscles. The slopes of the regression lines through the origin varied from 0.54 to 1.20 when only normoxic points were used. When the anoxic points were included these two extreme values became 0.69 and 1.11, respectively. Thus the anoxic points appeared to be continuous with the normoxic relationships.

Mitochondrial oxygen consumption. Oxygen consump- tion causes oxygen gradients to occur in the muscle. These gradients change with changes of the consumption rate. Therefore during transients in metabolic activity the oxygen taken up by the muscle is not due to mito- chondrial oxygen usage only.

When the diffusion characteristics of the muscle in which the gradients occur are known it is possible to correct the measured uptake function for the change in oxygen stored. The information required for such a cor- rection can be obtained from the time course of oxygen uptake by the system when suddenly the surface concen- tration is changed. Unfortunately the experimental de- termination of this function was not possible in our setup because of the artifacts caused by injections of the vol- ume required. We therefore calculated this function on the basis of geometry (muscle radius) and diffusion of oxygen in heart muscle (cf. APPENDIX) and used that to correct the oxygen uptake tracings for changes in the amount of oxygen stored. An example of the results obtained when this analysis is used to determine the time course of mitochondrial oxygen uptake in a muscle is given in Fig. 6. It can be seen that oxygen flux through the muscle surface during transients lags behind the oxygen consumption of the mitochondria.

The initial part of eight deconvoluted oxygen uptake curves were averaged to display the time course of oxygen

0 O

0 0

FIG. 5. Poststimulation oxygen uptake plotted against steady-state rate of oxygen consumption ( MVO& for 11 muscles. Solid and open symbols indicate spectively.

occurrence of theoretical normoxia and anoxia, re-

TIME COURSE OF AEROBIC RECOVERY OF CARDIAC MUSCLE H329

O,- Consumption

’ . . . . - . . . . . . . . . . . . . . .*** * . .

t . a. . .

0. . .

. . . .

. .

. .

.

5s . .

stim. 0.5 Hz 4 4 240s

FIG. 6. Experimental recording of total amount of oxygen uptake before (a) and after deconvolution (b). Inset: initial part of 8 deconvo- luted oxygen uptake curves averaged to display time course of oxygen uptake immediately after onset of stimulation (arrow).

I 2 3 4 Steady-state M\iO, ~nmol.miti~m&J

FIG. 7. Mitochondrial oxygen consumption (MAO& as function of steady-state oxygen consumption rate. Only normoxic experiments are given. Slope of regression line through origin yields time constant of 20 s. Inset: assumed first-order kinetics if mitochondrial oxygen con- sumption rate, where A is the steady-state rate and T is time constant of aerobic recovery. Amount of oxygen consumed during recovery equals A x T (hatched area).

uptake immediately after onset of stimulation (Fig. 6 inset). This time course was not corrected for the delay (1.1 s) of the oxygen-measuring system. No appreciable delay of onset of consumption is present at the beginning of the twitch train.

By making use of the deconvolution analysis, the time course of mitochondrial oxygen consumption can be found from the oxygen consumption after the end of stimulation. Unfortunately the noise introduced by the deconvolution procedure made it virtually impossible to determine the most appropriate function to fit the time course of poststimul .ation oxygen uptake. Based on mea- surements on skeletal muscle (10, 11, 23, 31), we there- fore assumed first-order kinetics (Fig. 7 inset) and cal- culated the time constant from the slope of the relation- ship between poststimulation oxygen consumption and steady-state rate of oxygen uptake.

The 20 normoxic points in Fig. 7 were subjected to the Spearman’s rank correlation test. It came out that the

data pairs have a correlation coefficient of 0.60, which was significant (P < 0.01). The slope of the regression line through the data points and the origin yielded a time constant of 20 t 4 s (means t SD). When the time constant of an individual muscle was taken as one esti- mate, we found a time constant of 22 t 10 s.

By use of the same assumption of (pseudo)first-order kinetics of mitochondrial oxygen uptake, it can be shown that the oxygen consumed after stimulation (P) is deter- mined by P = A x 7 + AR2/8K, where A, R, and K are previously defined, and 7 is the time constant of aerobic recovery (for derivation of this equation see APPENDIX).

The first and second terms in this equation reflect the contribution of mitochondrial activity and storage, re- spectively. From this formula the time constant can be calculated because all other values are known. We found a time constant of 19.1 t 9.6 s (means t SD, n = 7).

The two methods used to determine the time constant of mitochondrial kinetics are essentially based on the same assumptions. It is therefore not surprising that they yield nearly the same result.

DISCUSSION

In this study we found on average a resting oxygen uptake of 1.40 nmol mine1 l mg dry wt-’ or 0.12 &s-log wet wt-l at 2O”C, corresponding to a resting heat pro- duction of 2.36 mW/g wet wt. This value compares well with the 0.12 to 0.14 ~1 l s-l l g wet wt-’ found from oxygen consumption of potassium-arrested rabbit hearts at tem- peratures from 17 to 27°C (27). The corresponding heat rate is also between the resting heat rate values measured by Alpert and Mulieri (1.74 mW/g wet wt at 21OC) (1) and by Loiselle and Gibbs (-2.6 mW/g wet wt at 20°C) (29) for isolated rabbit papillary muscle. However, esti- mates of resting metabolism of isolated cardiac muscle should be considered with great care because they vary, for instance, with the time of measurement after car- diectomy (28), the substrate added (6), the diameter of the preparation (29), and depend possibly also on other experimental circumstances (3).

Oxygen uptake during activity corresponded to an average of 8.3 mJ*beat-’ l g wet wt-‘, whereas in the literature 7.3 and 8.2 mJ=beat-leg wet wt-’ were found via a polarographic and a myothermic method, respec- tively (7).

As has been shown in a number of other studies (21, 33), we found in our experiments that, when stimulation frequency increases ‘above a critical value, peak force decays during the twitch train (Table 2). This force decay has been explained by the occurrence of an anoxic core at higher frequencies. However, at least two points within this argument require a more detailed consideration: 1) in theory the force decay during the twitch train can, for instance, be caused by accumulation of lactic acid and CO2 rather than by shortage of oxygen. 2) If myoglobin plays an important role in oxygen transport in the myo- cardium, one would expect a discrepancy between the occurrence of an anoxic core, as judged by simple diffu- sion calculations as we did here, and the measured force decay.

If force decay would be caused by something other

H330 TIME COURSE OF AEROBIC RECOVERY OF CARDIAC MUSCLE

than anoxia, a proportional decay of the steady-state rate of oxygen uptake would occur during the twitch train. This appeared not to be the case in our experiments where we found steady-state rates to occur also during anoxia. The occurrence of a decaying force together with a steady consumption rate suggests that force decay is caused by failure of cells in the center of the muscle, which produce less and less force because they lack sufficient means to provide ATP from sources other than the aerobic metabolism.

If, at low values of the oxygen tension, a significant amount of oxygen would be transported by myoglobin, differences would occur between the calculated critical value of the steady-state oxygen consumption rate and the force decay found during the twitch train. We there- fore related force decay and degree of anoxia (Fig. 8). Force decay was defined as the ratio of peak force of the last contraction and maximum peak force in a train (Table 2). As degree of anoxia the distance of the nor- malized steady-state uptake rate from its critical value (per minute) was used (cf. Fig. 4). It can be concluded that the occurrence of force decay corresponds with that of development of anoxia, and that force decay increases with the degree of anoxia. This can be interpreted as indirect evidence that the transport of oxygen by myo- globin may not be of major importance in these experi- ments.

The oxygen uptake through the muscle surface after the end of stimulation (solid circles in Fig. 5) can be compared with the mitochondrial oxygen consumption (Fig. 7). The slopes of the regression lines (not drawn) through the points of Fig. 5 varied from 0.54 to 1.20 min due to the variation in diameter. After deconvolution, the effect of diameter is abolished and an average slope of 0.33 min (7 = 20 s in Fig. 7) is found. We therefore can calculate that under aerobic conditions 28-62% of the oxygen taken up after a train of 120 contractions of isolated rabbit papillary muscle at 20°C is consumed by

h3st

FFWX 1.0

0.5

s

O.&O degree of anoxia (miri’l

8 1.00

FIG. 8. Force decay, expressed as ratio of peak force of last twitch (F& and maximum force during the train (F,,), plotted as function of degree of anoxia (see text). For each point stimulus interval in s is given.

the mitochondria. The decrease of the mitochondrial oxygen consumption rate after the twitch train occurred with a time constant of 19-22 s. This value is somewhat smaller than the time constant of 27.4 t 4.6 s that can be derived from the half time (t& of the off kinetics of NADH fluorescence of rabbit papillary muscle at 23°C reported by Chapman (5).

To obtain the time constant of aerobic recovery in our experiments the following assumptions were made.

1) To determine the time constant characterizing the time course of mitochondrial oxygen uptake following the twitch train, first-order kinetics were assumed. Since no lactate production was measured in the chamber solution, the aerobic recovery processes must have been dominant in our experiments. Although recovery metab- olism may in detail be more complex, it has been shown for various amphibian (11, 16, 24, 32) and mammalian muscles (9), which cover a wide range of aerobic capaci- ties, that under aerobic conditions the time course of oxygen consumption after contraction can indeed be described by a single exponential. In principle, the time course of mitochondrial oxygen consumption after the train of contractions can be assessed from the tracing obtained after deconvolution. In practice, however, this appeared not to be possible with sufficient accuracy because of the noise present after deconvolution.

2) There is some disagreement within the literature about what value for the diffusion constant to use for muscle. Grote and Thews (13) report a value of 6.0 x 10B4 cm2/min for rat heart slices at 20°C. Mahler et al. (32) found a value of 6.5 X low4 cm2/min for frog skeletal muscle at 22.8”C, criticizing the value.of 5.5 x 10m4 cm2/ min given by Hill (15), which had been based on the value of the Krogh constant (22) of 1.4 x low5 cm2. min-l l atm-’ (22). For rabbit myocardium no diffusion constant is reported in the literature. We decided to use the value given by Grote and Thews (13) because it was determined for heart muscle.

3) It was necessary to correct the time course of the measured oxygen uptake for the oxygen stored in the muscle. This correction was done using a diffusion model based on muscle dimensions. However, the possible ex- istence of an unstirred layer of solution around the muscle was not taken into account. An estimate of the thickness of this layer can be made from the response of the oxygen electrode to a rapid injection into the cham- ber. We then have to assume that the unstirred layer at the electrode surface resembles the unstirred layer at the muscle surface. In the worst case the difference between the measured time constant of that response (2.1 s) and what is found for the electrode in air (0.8 s) is entirely due to an increase in diffusion distance by the unstirred layer. This difference of 1.3 s would then have been caused by a layer of 0.018 mm. This would increase the effective radius of the diffusion cylinder by -4% and the time constants used for deconvolution by -7%. However, we found that the mixing process in the chamber can account for most of the time difference between the responses of the electrode in air and in the chamber (cf. plate 1 in Ref. 10). We therefore can assume that the effect of the unstirred layer on the measurements is

TIME COURSE OF AEROBIC RECOVERY OF CARDIAC MUSCLE H331

negligible. In contrast to what has been shown for frog skeletal

muscle (11) we did not find a finite delay between the first contraction of the train and the onset of oxygen consumption. The reason for this delay found in frog skeletal muscle is not clear, but its absence in cardiac muscle may indicate that its cause may not be an inher- ent mitochondrial property because if all mitochondria are the same the delay should be independent of the number of mitochondria and thus the same for frog skeletal muscle and rabbit papillary muscle.

The amount of oxygen consumed during the twitch depends on the duration of the twitch and the mitochon- drial time constant. The duration of the twitch varies from 1.7 s (at 0.5 Hz) to 2.1 s (at 0.125 Hz). On the basis of a time constant of 19-22 s for the change in oxygen consumption rate after contraction and assuming that all ATP required for a twitch is hydrolized during 2 s of force development, we estimated that at most 940% of the oxygen required to restore ATP levels is already consumed by the mitochondria during the twitch. This value is only slightly larger than the 7% contamination of initial heat with recovery heat reported by Alpert and Mulieri (1). If we assume that also 9-10% of the recovery heat is generated during the twitch an underestimation is made in the determination of the recovery ratio by using the Bugnard method. This would increase the value for r given by Alpert and Mulieri (1) from 1.37 to a value between 1.70 and 1.76, which emphasizes the discrepancy with the value given by Chapman and Gibbs (0.71) (6) even further.

APPENDIX

To characterize the muscle as a diffusion system the follow- ing assumptions were made. 1) The papillary muscle is a circular cylinder the radius of which is small compared with its length. 2) Diffusion of oxygen in muscle tissue is homogenous. The diffusion constant is K = 6.0 x 10m4 cm2/min (13). 3) The contribution of facilitated diffusion due to the presence of myoglobin is negligible. The dynamic behavior of a linear process can be described by a characteristic time function, i.e., the unit impulse-response function h(t). Input function z(t), output function y(t), and h(t) are related through the convo- lution integral

s

t y(t) = x(X).h(t - X)=&X (Al) 6

where X is a dummy variable of integration. From the assump- tions it follows (4) that

C(r, t) = co - A(R2 - r2)

1 TT 4fi

W) 2AR2 O” c expc-K&lm l Jo(rar?zlR3

+ K n=l &Jlk%J

This formula describes the oxygen concentration (C) in the muscle as a function of radius (r) and time (t), when there is a sudden increase of oxygen consumption (A) at t = 0 at a constant surface oxygen concentration (Co). JO and J1 are Bessel functions of the first kind and of zero and first order, respectively; CY, are the positive roots of J&Y) = 0.

The flux through the outer surface of the muscle is defined by

2K dc F(t) = - -y-$ (A3)

R

Combining ENS. A2 and A3 leads to

F(t) = ac exp( -Ka?,t/R2) -A + 4A c

a2 W) lZ=l n

which describes the flux after a step input of amplitude A. The unit impulse response h(t) is obtained by differentiation of Eq. A4 with respect to time (A = 1)

h(t) =- $ c exp(-K&/R2) (As) n-1

Eq. A5 can be used to calculate the amount of oxygen due to mitochondrial consumption. When the input goes from A to zero at t = 0 the flux response is given by

F(t) = O” exp(-Kac”, t/R2)

-4A c 2 646)

?Z=l Qrn The total amount of oxygen taken up after t = 0 integral from t = 0 to 01) and is given by Eq. A7

4AR2 O” 1 AR2 Area = 7 x 4 = 8~ (A71 n=l a?l

iS equal to the

If the downward step were not so abrupt but would follow an exponential decay with time constant 7, an extra amount A x 7 has to be added, yielding the equation P = A x T + AR2/8K.

Received 21 July 1986, accepted in final form 19 March 1987.

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