The Efficiency of Frog Ventricular Muscle

In general, heart rate and blood pressure (or wall tension or muscle force) have been identified as the primary determinants of oxygen cost in working myocardium, with muscle shortening playing a lesser role (e.g. Braunwald, 1971; Weber and Janicki, 1977; Cooper, 1990). The rate of oxygen consumption of working cardiac muscle has been studied using both intact working hearts (e.g. Weber and Janicki, 1977; Farrell et al. 1985; Cooper, 1990; Suga, 1990; Agnisola and Houlihan, 1991) and, in a few instances, using linear segments of isolated cardiac muscle (Whalen, 1961; Gibbs et al. 1967; Coleman et al. 1969; Hisano and Cooper, 1987). Results from intact working hearts provide information about the organ’s mechanical and metabolic performance, but only indirect information about the muscle itself. Interpretation of the energetics of the muscle using results from intact hearts is complicated by the complex geometry and asynchronous time course of activation of the heart, by non-homogeneous fibre stress and strain throughout the chamber wall, and by the requirement for assumptions about the relative contributions of different regions of the heart to the work and oxygen consumption. Direct information on cardiac muscle performance can be obtained from isolated preparations such as trabecular or muscle strips. With appropriate isolated muscle segments, the fibres are relatively parallel; all fibres are activated simultaneously; and muscle length, muscle shortening and loading are known and are under direct experimental control. The power output and oxygen consumption can be measured with certainty as to their source and sink. In the few studies in which work was measured from isolated muscle segments (see above), afterloaded isotonic contractions were used to determine the effects of load and length on oxygen consumption. These studies measured only the work done during muscle shortening, which is but part of the mechanical balance sheet.

The present study was undertaken to evaluate the metabolic cost of mechanical power output from small bundles of ventricular trabeculae undergoing oscillatory contractions. Power was altered by changing the muscle length, strain (amount of shortening) and/or cycle frequency (heart rate). Power was measured using the work-loop technique (Josephson, 1985), allowing assessment of both the work done by the muscle while shortening and the work done on the muscle to lengthen it. Metabolic energy expenditure was calculated from the oxygen consumed by the muscle. The muscle’s efficiency is compared with results from intact working hearts, mammalian papillary muscle and skeletal muscle.

Animal husbandry and muscle preparation have been described previously (Syme, 1993). Briefly, frogs (Rana pipiens) were double-pithed followed by decapitation. The heart was removed and the ventricle opened along the dorsal midline. Bundles of trabecular muscle were isolated from the ventricle; bundles with as few side branches as possible were selected to minimize the contribution of non-working and damaged muscle to oxygen consumption. The bundle mass was approximately 0.3 mg, and the length was approximately 3.3 mm. One end of the bundle was tied, using single strands of silk from braided 6-0 suture, to a small stainless-steel hooked pin (76 μm diameter), which was in turn attached to a glass support rod via a pair of links of fine gold chain (Fig. 1). The other end of the muscle bundle was tied to a second hooked pin attached to a longer stainless-steel insect pin (000) via a pair of gold links (Fig. 1). After the muscle had been fixed in place, the free tissue outside the tied ends was trimmed close to the knots. Muscles that did not give a vigorous twitch, or that were spontaneously active, were discarded.

The composition of the saline was similar to that described in Syme (1993), except that 5 mmol l⁻¹ NaHCO₃ was used to maintain the pH at 7.5 in ambient air, and 5000 i.u. ml⁻¹ penicillin, 5 mg ml⁻¹ streptomycin and 12 μg ml⁻¹ amphotericin B (Sigma no. A7292) were added to prevent bacterial growth. The chamber was rinsed routinely in 0.075% benzalkonium chloride to minimize bacterial growth on the chamber walls.

The oxygen chamber (Fig. 1) was built from a section of glass tubing 40 mm long and 5 mm in diameter. The bottom of the tube was sealed to the face of a Radiometer E5047-0 polarographic oxygen electrode, connected to a Radiometer PHM73 blood gas monitor (Radiometer America Inc., Ohio, USA). The analogue output of the PHM73 oxygen meter was connected to a 100X, low-pass (-3 dB frequency=1.6 Hz), d.c. amplifier. The oxygen electrode calibration was checked using dilutions of air- and nitrogen-saturated saline. The electrode/meter/amplifier combination was accurate over the range 2.67–20.68 kPa; the slope of the relationship between output voltage and real was linear (r>0.999, N=7). Oxygen volumes were corrected to STPD.

A small magnetic stir bar was sealed in glass capillary tubing and rested on the rubber seal around the face of the oxygen electrode at the bottom of the chamber. The stir bar created a vortex current in the chamber sufficient to cause swirling of particles at the chamber surface.

The lid of the chamber (Fig. 1) was milled from Perspex. The lid fitted snugly into the glass chamber and was inserted down the tube to a depth of 5 mm. Only the bottom face of the lid was exposed to the saline. The glass rod that supported one end of the muscle was attached to the bottom of the lid. The insect pin, attached to the other end of the muscle, passed through a small hole in the centre of the lid. A second hole in the lid, large enough to allow the insertion of PE-20 polyethylene tubing (o.d. 1.1 mm), was used for injecting saline into the chamber. Two chloride-coated silver wires, used to stimulate the muscle, passed through the lid into the chamber to a depth of 3 cm. The chamber volume, with the lid in place, was 1.026 ml (measured as the increase in chamber mass when filled with water).

After the lid and muscle had been inserted into the chamber, the pin, which was attached to one end of the muscle and passed through the lid, was linked to a pair of force transducers mounted on the end of the servomotor arm (Cambridge Technology, model 350, Massachusetts, USA) (Fig. 1). The transducers formed two arms of a Wheatstone bridge circuit. The stimulating electrodes were attached to a current source with a battery-driven and optically isolated output. The stimuli were single, 1 ms, square pulses. The direction of current flow was reversed with each successive stimulus in order to avoid polarization of the stimulating electrodes and to reduce the possibility of net current flow induced in the oxygen electrode by the stimulating circuit. Passing current between the electrodes at the same intensity and for the same duration as used in experiments, but with no muscle present, had no detectable influence on the current in the oxygen electrode.

The chamber and over half of the shaft of the oxygen electrode were enclosed in a water jacket for temperature regulation (Fig. 1). A circulating water bath and heating coil, placed at the entrance to the water jacket, maintained the chamber temperature at about 20°C. The temperature, measured inside the oxygen chamber, was constant to within ±0.02°C. The oxygen electrode had a temperature coefficient of 6%°C⁻¹. Using air-saturated saline, a 0.02°C change in temperature would result in the equivalent of a 25.36 Pa change in ⁠. The smallest recorded changes in during experimental trials, from the beginning to end of a bout of work, were about 333 Pa. Therefore, error due to temperature drift could be about 7.5% of the O₂ consumed by the muscle while working. The actual error is likely to be very much smaller as temperature did not drift consistently up or down, but fluctuated about 20°C, and as most decrements in during experimental trials were larger than 333 Pa.

Work was measured using the work-loop technique (for a thorough account of the method and rationale, see Josephson, 1985, 1993; also see Syme, 1993 for further details of its application to frog cardiac muscle). Briefly, the muscle’s length was cycled continuously in a sinusoidal fashion about its resting length. A sinusoidal pattern was chosen for simplicity; it is not known whether this is the ideal trajectory for maximizing power output in cardiac muscle; ramp shortening has been estimated to increase power by only 20% or less relative to sinusoidal shortening (Josephson, 1989), and the effect on efficiency is unknown.

Because there was not a distinct optimum length for work and the muscle was easily damaged if over-stretched, the length at which work reached or closely approached a plateau was chosen as the optimum length, L_opt. The strain (amplitude of the sinusoidal length cycle) and the frequency of cycling were controlled with a sine-wave generator connected to the servomotor. Strain is expressed relative to muscle length (i.e. strain=peak-to-peak amplitude/muscle length).

The muscle was activated with a single, 1 ms, stimulus pulse, given at the time during the length cycle (the phase) that resulted in the muscle doing maximum net work; active force was generated primarily while the muscle was shortening, and the muscle was inactive during most of the lengthening part of the cycle. When the strain or cycle frequency were changed, the stimulus phase was readjusted to maximize net work. See Syme (1993) for representative force–length plots and details concerning the effects of strain, cycle frequency and stimulus phase on work output in frog heart muscle.

Muscle power output was changed in three ways. (1) Changing resting muscle length: muscle length was set to 85%, 90%, 100% or 110% L_opt. The strain was maintained at 20% and the cycle frequency at 0.7 Hz. (2) Changing cycle frequency: cycle frequency was set to 0.4, 0.55, 0.7 or 0.9 Hz. The strain was maintained at 20% and muscle length at 100% L_opt. (3) Changing strain amplitude: strain was varied between 0% (isometric) and approximately 25%. Muscle length was maintained at 100% L_opt and cycle frequency at either 0.55 or 0.7 Hz (results from these two frequencies were pooled as they were not significantly different). Recordings of power and were made from 8–20 different muscle strips under each of the above conditions.

The range of muscle lengths used (85–110%L_opt) encompasses the length for which work was about 50% maximal to the longest length, above which damage to the muscle was probable. The range of strain amplitudes used (0–25%) reaches values for which work was at, or near, maximum. The cycle frequencies used (0.4–0.9 Hz) range from a relatively slow frequency to the highest for which the muscle could still just respond to every twitch stimulus.

The muscle was allowed to rest for 1–2 h after initial mounting in the chamber. At the onset of each experimental trial, the oxygen chamber was flushed several times with air-saturated saline at 20°C. The experimental trial began approximately 10 min later, when a stable, resting had been attained. Recording of resting continued for 10–15 min before the muscle was stimulated. The muscle was then stimulated, at the optimum phase for net work output, for 210 cycles. This number of cycles was found to result in a change in that could be resolved easily (see Fig. 2). Stimulating the muscle for longer periods did not affect the efficiency; muscles working for 5 min had the same efficiency as those working for 10 min. After stimulation had ended, the recording of continued until resting was again attained and remained stable for 10–15 min.

Before, during and after stimulation, the net work done by the muscle (described below), and the minimum and maximum force during each cycle, were calculated on a computer and stored, along with the chamber and time, at about 4 s intervals. The muscle length was cycled continuously, both while it was resting and while doing work. The above procedure was repeated, beginning with flushing the chamber with fresh saline, for each trial. Most muscle preparations could be tested under 7–8 experimental conditions (about 9 h of experimentation) before work declined below about 85% of its initial value.

Net work is the difference between the work done by the muscle while it shortens and the work done on the muscle to lengthen it, and equals the product of muscle force and displacement over a complete length cycle. Net work is the best estimate of work done by the cross-bridges during a cycle (see Josephson and Stevenson, 1991). Work was calculated by computer integration of the force/length recordings. The total work done during a bout of stimulation is the sum of the recorded net work values and the values interpolated for cycles between those that were recorded (two or three interpolated values per recorded value). Power output (Ė_p), the rate of doing work, is the total work done divided by the duration of the work bout and is standardized to muscle wet mass (J min⁻¹ kg⁻¹).

The oxygen consumed by the muscle as a result of doing work was calculated by extending the pre-stimulus portion of the curve forward in time, and measuring the vertical separation between the pre-stimulus and the post-stimulus value (Fig. 2B). This yields the change in ⁠, above that for a resting muscle, associated with the stimulation and work done (i.e. the net oxygen consumption). The change in as a result of muscle stimulation was multiplied by the saline capacitance (13.788 nmol O₂ ml⁻¹ kPa⁻¹ STPD for 8.4 ‰ salinity at 20°C; Cameron, 1986) and the chamber volume to obtain moles of oxygen consumed. The molar oxygen consumption was converted into volume (22.4 l mol⁻¹ O₂) or joule equivalents (4.79 ×10⁻⁴ J nmol⁻¹ O₂) assuming a respiratory quotient (RQ) of 1 (glucose was the only exogenous fuel source). If the true RQ was 0.9, assuming some lipid metabolism, the error in the estimated energy consumption would be only 3%. The rate of muscle oxygen consumption was expressed as ml O₂ min⁻¹ kg⁻¹ or converted to rate of energy utilization and expressed as J min⁻¹ kg⁻¹. The resting and (both pre- and post-stimulus) were calculated from the slopes of the versus time curves after correction for chamber effects (see below and Fig. 2).

In subsequent discussions, will refer to the energy equivalent of ⁠, and Ė_p to the mechanical power output. Following Stainsby et al. (1980), I will distinguish three kinds of efficiency; each has a different significance for understanding underlying contractile mechanisms (discussed later): gross efficiency = Ė_p/(net + resting ⁠); net efficiency = ⁠; delta efficiency = ⁠.

The pin that connected the muscle to the servomotor passed through a hole in the cap. This formed a leak pathway for oxygen. It was not feasible to fill the hole with a substance that would reduce the leak for two reasons. (1) The forces produced by the muscles were very small (1–7 mN), and any increase in resistance or viscosity caused by filling the hole would substantially degrade the force signal measured at the arm of the servomotor. (2) At the beginning of each trial it was necessary to flush the chamber with fresh saline, which was introduced through a second hole in the lid and exited through the pin hole. Any substance filling either hole would be flushed both into and out onto the chamber each time the chamber was recharged (every 30–45 min).

where P_t is the chamber at time t, P₀ is the initial ⁠, P_a is the asymptotic ⁠, and k is the rate constant of the change in ⁠. Values for the constants k and P_a were obtained using an iterative process; least-squares regressions were performed on the log-transformed (linearized) form of the above equation using estimated values of P_a, and real data from a chamber with no muscle in it. The P_a value giving the smallest residual error was identified, and a new set of estimates for P_a was selected for another series of linear regression calculations, etc. The mean value for k was 4.23×10⁻⁴ ±4.31×10⁻⁵ V s⁻¹ (S.E.M., N=8) and that for P_a was 18.42±0.227 kPa (S.E.M.).

The equation was used to correct the measured change in for changes due to the leak and oxygen consumption by the chamber (see Fig. 2). For example, and using typical values, if the declined from 18.6830 to 18.6697 kPa over a 4 s interval, and the equation for the empty chamber predicted d/dt at 18.6763 kPa (midway between the interval) to be -0.400 Pa 4 s⁻¹, the corrected change in (that due to oxygen consumption by the muscle alone) was 18.6830 to 18.6701 kPa. This procedure was repeated for each sample point in each experiment. All results refer to data that have been subjected to the correction.

As the decreased, the rate of decline in due to the chamber effects decreased, and therefore the rate of decline in at rest after muscle stimulation appeared to be slower than before stimulation (Fig. 2A). When a correction was made for the chamber effects, as described above, the rate of decline in after stimulation, that due only to oxygen consumption by the resting muscle, closely matched that before stimulation (Fig. 2B). Efficiencies calculated after the correction were usually less than those prior to correction. Paired comparisons from a series of efficiencies calculated using data both with and without the correction had an absolute mean difference in net efficiency of 1.0±1.2% (S.D., N=15) (P<0.05).

To determine whether anaerobic metabolism was a significant source of energy in these preparations, lactate production was measured. Ventricles were isolated, cut in half in the frontal plane, and washed with saline. The hemi-chambers were pinned open in small wells coated with Sylgard 184 silicone elastomer (Dow Corning). 0.2 ml of saline was added to each well, enough to cover the muscle. The saline was stirred for 5 s every 30 s with air bubbled through polyethylene tubing. One half of each heart was used as an unstimulated control, and the other half was subjected to 5 min of twitch stimulation at 0.5 Hz. Immediately after stimulation ended, the saline was withdrawn from the wells and frozen in polypropylene vials.

The muscles were quickly covered with 0.2 ml of ice-cold 0.6 mol l⁻¹ trichloroacetic acid and homogenized with a glass mortar and pestle. The samples were centrifuged for 10 min and frozen in vials. The lactate concentrations in the saline and the supernatant from the muscle homogenate were determined using Sigma diagnostic kit no. 826-A (NADH endpoint, 340 nm absorbance measured on a Beckman DU-70 spectrophotometer). The assay was found to be linear between 0.01 and 1.0 mmol l⁻¹ lactate (r>0.999). The average lactate concentration in the samples was 0.22 mmol l⁻¹. The total lactate content of the muscle homogenate and saline was calculated using the lactate concentrations and sample volumes. The lactate content of the working muscle was then compared with that of the control, resting muscle.

One of the variables investigated was the effect on efficiency of the amplitude of the imposed length change (strain). Length change, measured in millimetres, was converted to strain, measured as a fraction of the optimum muscle length (L_opt). L_opt varied between preparations and therefore so did the fractional strain corresponding to a given absolute length change. In order that data and the effects of strain could be better presented, the data were grouped into approximately 5% strain bins and averaged.

Curves were fitted to the data using linear regressions, second-order polynomial regressions or line segments, where appropriate. One-way analysis of variance (ANOVA) was used to test for differences at different strains, lengths and frequencies, and LSD range tests (Steel and Torrie, 1980) were used to locate differences if they were present. Differences were considered significant at or below the 5% level. Graphs show means and standard errors.

The mean mass of the working ventricles used for measuring lactate content was 35.2±2.67 mg (S.D., N=5), and that of the resting muscle was 35.3±3.28 mg (S.D., N=5). The mean lactate content in the working muscles at the end of 5 min of stimulation was 2.54±1.24 nmol mg⁻¹ (S.D.) and that in the control, resting muscle was 2.44±1.11 nmol mg⁻¹ (S.D.). The mean paired difference in lactate content between working and resting hemi-chambers was small and not significant (0.11±0.38 nmol mg⁻¹, S.D., P>0.5). Apparently, most or all of the contractile activity of the heart is supported by aerobic metabolism. Even if all the lactate in working muscle was produced as a result of exercise (which it clearly is not, given the equal concentration in the unstimulated muscle), it would contribute only (2.54 nmol lactate mg⁻¹ 5 min⁻¹) × (1 mol ATP mol⁻¹ lactate) × (29.3 kJ mol⁻¹ ATP) = 15 J min⁻¹ kg⁻¹. This compares with an aerobic metabolic rate of about 400 J min⁻¹ kg⁻¹ at an intermediate power output (see Fig. 4). Coulson (1976) noted that anaerobic metabolic rate in rabbit heart was less than 5% of the total energy production and was independent of the level of activity. Lazou and Beis (1986) found that, after 30 min of work, lactate levels in frog (R. ridibunda) hearts were not significantly different from levels in resting hearts. Collectively, these results indicate that there is a basal level of lactate present in the heart which does not change with work if the heart is well oxygenated. In the present study, of muscle strips recovered to pre-stimulus levels in only 3–4 min after the end of stimulation. Thus, even if lactate had been produced, it was rapidly oxidized after work ceased and there was no long-term oxygen debt. It has been demonstrated that aerobic cardiac muscle has an extremely high affinity for lactate as an energy substrate (Katz, 1992), and any lactate produced should be quickly oxidized. On the basis of the above evidence, anaerobic metabolism was considered to be insignificant and was disregarded.

The in the chamber declined over the course of an experiment. It was possible that could be affected by the changing ⁠. To determine whether this was an important factor, efficiency was measured when the saline in the chamber was not replaced between work trials and the was allowed to drop below the minimal (18.68 kPa) normally encountered during experiments. The efficiency of muscle working near a of 18.68 kPa was 4.4%, compared with 4.6% for muscle working near a of 20.02 kPa; a difference of only 4%. Efficiencies are low as a relatively small strain was used for this comparison. Work output was the same under both conditions. Thus, the rate of oxygen consumption appears not to be dependent on under the conditions of these experiments.

The mean pre-stimulus (resting) of ventricular muscle at 20°C was 6.54±0.46 ml O₂ min⁻¹ kg⁻¹ (S.E.M., N=68) (equivalent ⁠, S.E.M.), and the post-stimulus (resting) was 7.33±0.48 ml O₂ min⁻¹ kg⁻¹ (S.E.M., N=68) (equivalent ⁠, S.E.M.). The paired difference between pre- and post-stimulus values was not significant (P>0.5). There was no elevation in the resting due to the imposed length cycling. A resting of 150 J min⁻¹ kg⁻¹ will be used in calculations of gross efficiency in the following discussions.

Mechanical power output (Ė_p) and net increased with increasing cycle frequency at low frequencies, but neither Ė_p nor net changed significantly as the frequency was increased beyond 0.55 Hz (Fig. 3). Net efficiency remained constant at about 11% as the cycle frequency was varied (Fig. 3), indicating that changes in Ė_p were matched by proportional changes in ⁠. When plots of versus Ė_p were made using data sets from each frequency plotted separately, the slopes and intercepts of the linear regression lines from the separate data sets were not significantly different (P>0.1). The regression through the pooled versus Ė_p data for all frequencies (Fig. 4) had a significant (P<0.001) slope of 3.86, and intercept of 231 J min⁻¹ kg⁻¹. The slope of the line is the change in for a change in Ė_p as they are altered by changing the cycle frequency. The reciprocal of the slope is the delta efficiency and equals 26%.

Mechanical power (Ė_p) and net increased significantly as mean muscle length was increased from 85 to 100%L_opt (Fig. 5). There was no change in either Ė_p or as length was increased further to 110%L_opt. Net efficiency increased from 8 to 13% as muscle length was increased from 85 to 100%L_opt (Fig. 5). There was no change in efficiency as muscle length was increased from 90 to 110%L_opt. When was plotted as a function of Ė_p, the slopes of the linear regression lines through the data from each length plotted separately did not differ (P>0.1). The linear regression (not shown) through the pooled versus Ė_p data for all muscle lengths had a significant (P<0.001) slope of 4.09. The slope is the change in for a change in Ė_p when they are altered by changing the muscle length. The reciprocal of the slope is the delta efficiency and equals 24%. The intercept of the linear regression through the versus Ė_p data at 85%L_opt was smaller than that from data at other muscle lengths (0.025<P<0.05). Thus, a second-order polynomial was fitted to the pooled versus Ė_p data in order to give appropriate emphasis to the short-length (low-power) points in estimating the zero-power intercept (Fig. 6). The intercept, which was 137 J min⁻¹ kg⁻¹, equals the cost of a slack (unloaded) contraction above the cost of resting metabolism.

Mechanical power output (Ė_p) increased with increasing strain over the range studied (Fig. 7). Net also increased with increasing strain; however, the proportional increase in was less than that for Ė_p (Fig. 7). increased slightly above the isometric (0% strain) cost as strain was increased from zero to 10%, and remained relatively constant between strains of 5 and 20%. increased significantly between 15% and 25% strain, the largest strain studied.

Net efficiency increased from 0% at zero strain, to 12–13% at strains of 15–25% (Fig. 7). The increase in net efficiency with increasing strain was greatest at smaller strains. The linear regression through the versus Ė_p data had a significant (P<0.001) slope of 2.32 and an intercept of 328 J min⁻¹ kg⁻¹ (Fig. 8). The slope is the change in for a change in Ė_p when they are altered by changing the strain amplitude. The reciprocal of the slope is the delta efficiency and equals 43%. The intercept is the cost, above resting metabolism, of an isometric contraction at L_opt and was 328 J min⁻¹ kg⁻¹.

The principal goal of this study was to determine the efficiency of muscle from frog heart in converting metabolic energy into mechanical energy. I distinguish three kinds of efficiency (gross, net and delta) as defined earlier (see Materials and methods).

Gross efficiency, the ratio of the work done to the total metabolic energy expenditure, is a measure of the relative cost of maintaining and operating a muscle, including the costs of resting metabolism, activation (membrane depolarization, ion movements within/across the cell, etc.) and the energy consumed by cycling cross-bridges. The gross efficiency of frog ventricular muscle was about 9% at an intermediate power output (Table 1). Whalen (1961) recorded gross efficiencies of 6–9.7% using isotonic contractions of cat papillary muscle. Reports of gross efficiency from working hearts at moderate power outputs include 10–12% for octopus (Houlihan et al. 1987; Agnisola and Houlihan, 1991), 18% for a fish, the sea raven (Farrell et al. 1985), 12–15% for dogfish (Davie and Franklin, 1992) and 8–13% for the dog (Nozawa et al. 1988). On the basis of this interspecific comparison, which is limited because of non-standardized conditions for work between the various studies, the gross efficiency of isolated frog cardiac muscle does not appear to be different from values previously reported for intact working hearts. The similarity between the gross efficiency of cardiac muscle found for frog ventricle and that reported for working hearts is concordant with observations that the mass-specific work done by the muscle of the chamber wall, based on in vivo measurements of work from segments of the heart wall, is equivalent to the pressure–volume work done by the ejecting heart (Goto et al. 1988; Arts et al. 1992). It should be noted, however, that Britman and Levine (1964) and Kedem et al. (1989) found pressure–volume work to be only poorly correlated with, or unrelated to, the work done by the muscle of the chamber wall.

Net efficiency, the ratio of the work done to the metabolic energy expenditure above resting level, is a measure of the relative cost to operate, but not maintain, the muscle and includes the costs of activation and the energy consumed by cycling cross-bridges. Net efficiency in frog cardiac muscle remained constant at about 11% as the cycle frequency was varied (Fig. 3, Table 1). Kedem et al. (1989) also found the efficiency of regional contractile work (work done by the chamber wall) of dog hearts to be largely independent of heart rate. This constant cost of doing work, irrespective of changes in heart rate, might be expected if there were a decrease in the diastolic interval only, with no change in the rate, duration or amplitude of force development. During isometric contraction of frog ventricle, twitch amplitude increases and twitch duration declines with increasing cycle frequency (e.g. Syme, 1993). However, the force developed by the muscle during the work-loop trials of the present study (maximum force minus minimum force during the cycle) did not change as the cycle frequency was varied over the range studied (P>0.1, data not shown), and the work per cycle remained relatively constant with changes in cycle frequency over the range studied (Syme, 1993). As appears to be determined by, or correlated with, force (e.g. Braunwald, 1971; Weber and Janicki, 1977; Cooper, 1990; Takaoka et al. 1993), and force and work per cycle do not change with cycle frequency, then efficiency should also remain relatively constant as the cycle frequency changes. Constant net efficiency with changing cycle frequency was observed in the present study (Fig. 3).

Both Kedem et al. (1989) and Berglund et al. (1958) noted that the efficiency of external pressure–volume work declined as heart rate increased. It has been suggested that efficiency may be reduced at high heart rates as a result of the increased amount of internal work done to deform the chamber wall with each beat (less external work and more internal work is done per beat) (e.g. Berglund et al. 1958; Katz, 1992). With small bundles of fibres, as used in the present study, the energy lost to internal work is likely to be considerably less than that lost in the complex wall of a heart chamber, which may explain why a decrease in efficiency with increasing operating frequency is not observed in small, parallel-fibred muscle bundles (Fig. 3).

Net efficiency increased slightly with increased muscle length (Fig. 5) and substantially with increased strain (Fig. 7). Because the costs of activation are significant (14% of the cost of an isometric twitch in cat papillary muscle, crudely estimated as the difference between isometric and unloaded costs; Cooper, 1979), their relative contribution to can have a considerable influence on efficiency. At short muscle lengths and small strains, work output is low (Figs 5 and 7) and the costs of activation will be a large component of the total cost; thus, efficiency will be low. As work output increases, the costs of activation become a proportionately smaller component of the energy consumed, more of the energy is used for work and efficiency increases.

Delta efficiency, the slope of the relationship between mechanical power output (Ė_p) and metabolic energy expenditure ⁠, is a measure of the change in power output for a change in energy expenditure. Because the changes can occur over an infinitely small interval, changes in the costs of activation can be assumed to be zero; thus, delta efficiency represents the cost incurred to produce power by cycling cross-bridges alone. The delta efficiency of frog ventricular muscle was 24–43% (Table 1). Values from intact working hearts include 26% for sea raven (Farrell et al. 1985), 18% and 14% for octopus (Houlihan et al. 1987; Agnisola and Houlihan, 1991), 26% for dogfish (Davie and Franklin, 1992) and 36% for dog (Britman and Levine, 1964). The similarity of the delta efficiencies from the present study, using isolated muscle segments, and those from intact hearts again suggests that the efficiency of converting metabolic energy into mechanical work is the same, whether work is measured directly from the muscle or after transduction into hydraulic work; there appears to be little loss of mechanical energy in the conversion.

The average resting of mammalian ventricular muscle at 37°C is about 20.5 ml O₂ min⁻¹ kg⁻¹ (Lochner et al. 1968). Given a Q₁₀ of 2.5 for resting metabolic rate, the expected of mammalian ventricular muscle at 20°C is about 4.3 ml O₂ min⁻¹ kg⁻¹. Gibbs et al. (1967) found the measured of rabbit papillary muscle at 20°C to be slightly higher, 5.2 ml O₂ min⁻¹ kg⁻¹. The mean resting of frog ventricular muscle at 20°C measured here was 6.9 ml O₂ min⁻¹ kg⁻¹, which is 30% and 60% higher than values measured and predicted, respectively, for mammalian muscle. However, the range of values reported for mammalian hearts (Lochner et al. 1968), corrected for temperature differences, encompasses the value found for frog heart. Even if the relatively high resting of frog heart is due to muscle trauma, it would have only a small influence on the observed gross efficiency, because resting metabolic rate accounted for only about 20% of the working metabolic rate in these muscles (see below).

In the present study, net power was used when calculating all efficiencies. Net power is the difference between the power output of the muscle during shortening and the power required to lengthen the muscle; it is a measure of the mean power available from the contractile machinery during a complete cycle. The maximum net efficiency observed (calculated using net power) was about 13%. The only other reports of efficiency calculated using net work are those for locust flight muscle (4–10%, Josephson and Stevenson, 1991) and dogfish white muscle (41%, Curtin and Woledge, 1993). The locust muscle was operating at 20 Hz, substantially faster than the frog ventricular muscle. Josephson and Stevenson (1991) suggest that the relatively low efficiency found in the locust muscle may reflect the high costs of rapid activation and relaxation in a muscle with a high operating frequency. The value of 41% reported by Curtin and Woledge was calculated using the molar enthalpy of the splitting of phosphocreatine (–34 kJ mol⁻¹); had they based their calculation on the fuel (glucose) energy available, as was done in the present study, their maximum efficiency would have been approximately 20%. Typical values reported for net efficiency of mammalian and frog skeletal muscle, calculated using shortening (not net) work, range from 15 to 30% (see Josephson and Stevenson, 1991; Curtin and Woledge, 1993). Even allowing for the use of net and not shortening power when calculating the efficiency of frog ventricular muscle, it is apparent that the efficiency falls at the lower end of the range reported for skeletal muscle. The relatively low efficiency of frog cardiac muscle suggests either that the costs of activation in cardiac muscle are substantially higher than in most skeletal muscles or that the contractile machinery of cardiac muscle is less efficient at converting energy from the hydrolysis of ATP into mechanical work.

The relationships between and mechanical power output (Ė_p) in frog ventricular muscle as strain, muscle length and cycle frequency were changed were similar to results obtained from mammalian hearts. Heart rate (cycle frequency) and blood pressure (muscle tension or length) contribute approximately equally to (Badeer, 1963; Shaddy et al. 1989; equivalent slopes in Figs 4 and 6). Efficiency increases as power output increases (Whalen, 1961; Neely et al. 1967; Nozawa et al. 1988; Table 1). is linearly related to power output (Ė_p) (Berglund et al. 1958; Britman and Levine, 1964; Coleman et al. 1969; Kedem et al. 1989; Figs 4, 6 and 8). Power output is also linearly related to in non-mammalian hearts (octopus, Houlihan et al. 1987; Agnisola and Houlihan, 1991; sea raven, Farrell et al. 1985; dogfish, Davie and Franklin, 1992) and, in anaerobic turtle heart, to lactate production (Reeves, 1963). The metabolic responses of hearts to changes in power output are remarkably similar in a wide variety of taxa. There are too few relevant studies on skeletal muscle to conclude that the similarities found among cardiac muscles are common to striated muscle in general.

Gross efficiency must be less than net efficiency, and net efficiency less than delta efficiency. In frog ventricular muscle, net efficiency was about 1.2 times greater than gross efficiency (Table 1). This indicates that the cost of resting metabolic rate was about 20% of the total cost to maintain and operate the muscle, which agrees with results from mammalian hearts (e.g. Braunwald, 1971).

Delta efficiency was 2–4 times greater than net efficiency at an intermediate power output (Table 1), indicating that the cost of unloaded or isometric contraction (costs of activation plus any internal cross-bridge work) accounted for 50–75% of the energy used by the muscle working at an intermediate power output. In agreement with this observation, the intercepts of the versus Ė_p curves (Figs 4, 6 and 8), which represent the cost of activating the muscle with zero power output, were at least half of the total cost at intermediate power output. How much of the energy used during unloaded or isometric contraction can be attributed to the costs of activation, and how much to cycling cross-bridges that do not result in external work, cannot be estimated from the present study.

That there is a greater cost associated with tension development than with muscle shortening has been observed widely by others (e.g. Neely et al. 1967; Braunwald, 1971; Weber and Janicki, 1977; Cooper, 1990) as well as in the present study. The zero-power intercepts of the versus Ė_p curves, when length or strain were altered (Figs 6 and 8), were significantly different (P<0.001). At zero strain, the muscle contracted isometrically and the cost was 328 J min⁻¹ kg⁻¹ (8.7 J beat⁻¹ kg⁻¹) (Fig. 8). Extrapolation to zero power when length is altered yields the cost of unloaded or slack contraction, and was 137 J min⁻¹ kg⁻¹ (3.7 J beat⁻¹ kg⁻¹) (Fig. 6; 5.4 J beat⁻¹ kg⁻¹ if a linear regression is used to fit the data). The cost (above resting) of unloaded shortening was thus only 42% of the cost of an isometric contraction, even though the power output was zero in both cases; if resting metabolism is included, the cost of unloaded contraction was about 60% of that for isometric contraction. Hisano and Cooper (1987) also found that the total cost of unloaded contraction in ferret papillary muscle was less than the cost of isometric contraction (about 50%), and Cooper (1979) found that the oxygen consumed during unloaded shortening of cat papillary muscle was only 14% of that used during isometric contractions.

The greater cost of isometric contraction suggests that more cross-bridge cycles are completed during an isometric twitch contraction than during an unloaded twitch contraction. The smaller number of cross-bridge cycles during unloaded twitch contractions may be a consequence of decreased levels of activation resulting from muscle shortening (e.g. Jewell, 1977; Edman, 1980).

In support of the observation that isometric costs are greater than unloaded costs, the increase in metabolic cost with an increase in power output when muscle length (force) was increased was greater than the increase in cost when strain (shortening or stroke volume) was increased (the slope in Fig. 6 is greater than that in Fig. 8, P<0.001); pressure loading is more costly than volume loading. In contrast, results from sea raven hearts suggest that pressure loading and volume loading have equivalent effects on (Farrell et al. 1985), although the authors comment that the circumstances under which volume loading was altered leaves this observation uncertain. In the octopus heart, volume loading (varied input pressure with constant pressure differential between input and output) is more costly than pressure loading (varied pressure differential with constant aortic output) (Houlihan et al. 1987). Similarly, volume loading was found to be more costly than pressure loading in the dogfish heart (Davie and Franklin, 1992). Davie and Franklin (1992) suggest that volume loading (greater amount of muscle shortening) causes the sarcomeres to operate over non-optimal regions of overlap, which results in decreased efficiency. However, it has yet to be demonstrated whether myofilament overlap is related to economy of force generation. An explanation for the absence of similar observations (higher cost of volume loading) in mammalian myocardium is lacking.

Thanks to Professor Robert Josephson and Professor Al Bennett for critical comments on techniques and the manuscript and the kind loan of their equipment. Supported by NSF through Professor R. K. Josephson and NSERC of Canada through D.A.S.

A recent study by Barclay (1994), in which efficiency measurements were made using sinusoidal work loop analysis (10% strain) and initial heat production in vitro at 31°C, shows the maximum efficiency of mouse soleus and extensor digitorum longus muscle to be 52% and 34% respectively. Efficiencies were relatively constant over a range of cycle frequencies, but declined at very slow frequencies. Note that these efficiencies were calculated using the energy liberated from the hydrolysis of ATP (i.e. initial heat+work), and are thus about twofold greater than had they been calculated as in the present study, using the energy liberated by the substrate glucose.