INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

ALTHOUGH ENERGY USE by and efficiency of cardiac muscle can be estimated in vivo, accurate quantitative measurements of energy use can only be obtained from isolated muscle preparations. In general, there has been quite good agreement between measurements of oxygen consumption by working hearts in vivo and total enthalpy output from cardiac papillary muscles in vitro (4, 12, 33). In the former, the cardiac cells undergo their normal pattern of length changes during each contraction, but it is difficult to measure the rate of oxygen uptake precisely. Conversely, in the in vitro myothermic experiments, energy use can be measured very accurately from beat to beat, but it must be acknowledged that the pattern of length changes is probably not very realistic. The majority of myothermic studies have employed either isometric (30, 33) or afterloaded isotonic contractions, with muscle length set to that at which active force generation is maximal (12, 28, 35). These studies have followed the classical energetic approach developed by Hill (14).

There seems little doubt that papillary muscles provide a good linear model of the ejecting heart. Suga (42) demonstrated that there is a linear relationship between the heart's oxygen consumption and the area enclosed by a plot of its pressure development as a function of ventricular volume: pressure-volume area (PVA; for a review, see Ref. 43). PVA consists of the work loop and a potential energy term. Several groups have shown that for papillary muscles from several species, a similar relation exists between energy used per twitch and area enclosed by a plot of active force as a function of muscle length [force length area (FLA), the linear analog of PVA] (17, 21, 30).

Recently, another way of analyzing the mechanical response of both skeletal and cardiac muscle has been developed whereby preparations are subjected to cyclical, sinusoidal length changes and phasic stimulation at physiological frequencies (1, 5, 19, 47). In these types of experiments, the power output of a muscle can be calculated from the area enclosed by a "work loop" created by plotting force as a function of muscle length. The form of the work loops (e.g., see Ref. 47, Fig. 6) is very reminiscent of the pressure-volume diagrams of ejecting hearts (31, 38, 44). It is also noteworthy that the cyclical length changes produce length and force changes that closely resemble the in vivo dynamics of papillary muscles (16, 40).

In the present paper, we have used the work-loop protocol to investigate the energetics of rat papillary muscles. With the use of such preparations, it was possible to compare mechanical and energetic results obtained in this study with those from our previous studies (12, 21, 28), which used afterloaded isotonic contractions at relatively low stimulus rates. Despite the protocol differences, the work and energy output per twitch were in good agreement in the two types of experiments.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Papillary Muscle Preparation

In two recent papers, it has been shown that it is possible to make good mechanical recordings from rat trabeculae at 37°C and to use physiological twitch frequencies (4-8 Hz; Refs. 24 and 25). The preparations in those studies were sufficiently small (cross-sectional area ~0.2 mm²) that diffusive oxygen supply would probably have been adequate under the conditions used. There are considerable technical difficulties in making myothermic measurements with such small preparations, so in the current study we elected to use larger papillary muscle preparations, comparable to those used in previous myothermic studies (mass ~5 mg, cross-sectional area ~0.8 mm²) and to perform the experiments at a lower temperature (27°C). We have used stimulus rates appropriate to the lower temperature (i.e., about one-half of those observed in vivo).

Experimental Recordings

Work output was calculated by integrating force with respect to the change in muscle length (which, over a whole cycle, corresponds to the area enclosed by the work loop). Heat output was determined from the measurements of muscle temperature. Temperature signals were corrected for heat lost from the preparation during recording (see Ref. 50, p. 184) and were then converted to heat output by multiplication of temperature by muscle heat capacity. The rate of heat loss and muscle heat capacity were calculated from the time course of cooling of the preparation after it had been heated, using the Peltier effect (see Ref. 50, p. 187-188). No correction was made for heat produced by the stimulus pulses (0.5-ms duration, 4-6 V amplitude), as this was <5% of the heat produced during a twitch.

Experimental Protocols

The purpose of this study was to determine the energetics of papillary muscles by using a contraction protocol in which muscle length was varied in a sinusoidal pattern with one stimulus delivered to the muscle in each length cycle (19, 24). Cycles were defined as starting and finishing at the length midway between the extreme lengths reached in each cycle. Cycle amplitude was ±5% of the length at the start of the cycle (24). A series of preliminary experiments was performed to establish the stimulus phase that produced maximum work output at each cycle frequency and the range of cycle frequencies that spanned the frequency at which power output was maximal (see Table 2). At each frequency, a series of length changes were performed without stimulating the muscle; the pattern of force changes in this protocol allowed the work done on passive elastic elements to be measured.

After the equilibration period, stimulation was stopped, and the rate of heat production of the resting muscle was measured by using the method described by Gibbs et al. (12). Note that resting metabolism was not included in calculations of mechanical efficiency. Next, the isometric force-muscle length relationship was determined by performing sets of 10 twitches (frequency 0.16 Hz) at 0.1-mm-length increments, starting from the length at which passive force was ~5 mN. The average of the maximum active forces in the last five twitches was calculated, and the length at which isometric force was maximal (L_max) was determined. At each length, the muscle also performed a series of 40 twitches with sinusoidal length changes (19). The frequency of the length changes was 2 Hz, stimulus phase was 80° (where 90° corresponded to the point at which length was maximal), and cycle amplitude was ±5% of the resting length at the start of the cycles. Maximum work was defined as the maximum average work performed in five successive cycles. Typically, this occurred somewhere between cycles 5 and 20, depending on cycle frequency. The muscle length at which maximum work was greatest was called L_opt. As reported previously (23), L_opt was significantly shorter than L_max and was 96.1 ± 0.5% (n = 8) of L_max.

All subsequent measurements of energy output at different cycle frequencies were performed with muscle length at the start of each set of cycles set to L_opt. Cycle frequencies from 1 to 4 Hz and length changes of ±5% L_opt were used (see Table 2). An 8-min interval was allowed between runs at different cycle frequencies. Cycle frequencies were given in ascending order (n = 4) or in descending order (n = 4).

Calculations

Data normalization. At the end of each experiment, the lengths of muscle beyond the ties were cut off, the muscle was lightly blotted, and its mass was determined by using an electronic balance. Average cross-sectional area was calculated [mass/(length × density)], with the assumption of a density of 1.06 g/cm³ (39). Force was normalized by cross-sectional area. The average power output per cycle is the product of net work per cycle and cycle frequency. The average rate of heat output is the product of net heat produced per cycle and cycle frequency. The rate of enthalpy output is the sum of power output and rate of heat output. Power output and rates of heat and enthalpy output were normalized by muscle mass.

Calculation of efficiency. Net mechanical efficiency was defined as

where W_net is the sum of the net work output from all the contractions, Q_total is the total, suprabasal heat produced during and after the series of twitches, and H_total is the total enthalpy output. H_total included both initial energy output (i.e., energy from processes that consume ATP and PCr) and recovery energy output (i.e., energy from oxidative reversal of initial processes) but not basal metabolism. The contraction protocols used in this study were too brief for an energetic steady state to be established. This was evident from the continued rise in muscle temperature throughout the period for which the muscles were contracting (e.g., see Fig. 1C); if a steady state had been achieved, muscle temperature would have been the same at the start of successive cycles (34). As a consequence of the muscle not being in a steady state, overall efficiency could not be calculated on a cycle-to-cycle basis. Instead, to include all the metabolism associated with the contractions, efficiency had to be calculated on the basis of the total enthalpy produced during and after the series of contractions.

Statistical analysis. The statistical significance of variations of measured variables with cycle frequency was assessed using one-way analysis of variance. Where appropriate, post hoc analysis was performed using Dunnett's multiple comparisons test to compare mean values at cycle frequencies >1 Hz with that at 1 Hz. Statistical significance was determined with respect to the 95% level of confidence.

Modeling Diffusive Oxygen Supply

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

The aim of this study was to investigate the papillary muscle energetics during a contraction protocol involving sinusoidal length changes. The protocol is illustrated in Fig. 1. Muscles performed a series of 40 contractions at a frequency equal to the frequency of the imposed length changes (i.e., 1 twitch/length cycle). Total muscle force output (i.e., active + passive) and changes in muscle temperature were recorded. In a separate run, the protocol was repeated without stimulating the muscle, allowing just passive force changes to be measured. The pattern of force changes illustrated in Fig. 1B was typical of papillary muscles, starting a series of twitches after a period of rest. The force produced in the first twitch was greater than that in subsequent contractions and, as can be seen from the incomplete relaxation after this twitch, the contraction was of longer duration than subsequent twitches. The force produced in the second twitch was substantially smaller than that in the first, but during the next 10-15 twitches, force increased, eventually reaching a steady level that was maintained for the remainder of the protocol.

View larger version (59K): [in this window] [in a new window]   Fig. 1.   An example of recordings of applied muscle length change (A), force output (B), and muscle temperature change (C) during a series of 40 contractions. The frequency of applied length changes and contractions was 2.2 Hz. C: measured temperature change and signal after correction for heat lost from preparation during recording. Inset: complete time course of corrected heat production. Vertical dashed line indicates time at which contractions ended. Heat continued to be produced at a rate greater than basal rate for ~60 s after contraction series ended. Mass of papillary muscle was 5.1 mg, and initial length was 4.54 mm. Lopt, muscle length at which maximum work was greatest.

The measured muscle temperature (i.e., the thermopile output) increased throughout the contraction protocol. The temperature signal is also shown after correction for heat lost during the recording. Heat is continually lost from the muscle along the thermocouple wires that make up the thermopile. The rate of heat loss was accurately characterized before each series of contractions, enabling the corrected temperature to be calculated. Heat was produced not only while the muscles were contracting but also for ~60 s after the contractions ended. This is illustrated by the continued increase in corrected muscle temperature during the 60 s after the end of the series of contractions (Fig. 1C, inset).

Effects of Cycle Frequency on Work, Heat, and Enthalpy Output

View larger version (16K): [in this window] [in a new window]   Fig. 2.   Examples of time course of energy output from a papillary muscle performing 40 contractions at cycle frequencies of 1, 1.2, 2.2, and 4 Hz. Time courses of enthalpy output (A), heat output (B), and work output (C) are shown. Enthalpy output is sum of heat and work outputs. Total enthalpy output was similar at all frequencies shown except for 4 Hz, at which point less enthalpy was produced. Work output was greater at 2.2 Hz than at other frequencies illustrated. The records are from same muscle as those in Fig. 1.

View larger version (29K): [in this window] [in a new window]   Fig. 3.   Examples of active and passive work loops (force-length diagrams) at different cycle frequencies. Passive work loops (dashed) were recorded when length changes were applied without stimulating muscle. Time progresses around passive work loops in a clockwise direction (see arrows in 3-Hz example), indicating that work was absorbed by muscle. Active loops (solid) were recorded when muscle was stimulated once in each length cycle. Timing of stimulus in each cycle was adjusted to produce maximum work output at each frequency. Active loops proceed in a counterclockwise direction, indicating that net work was performed by muscle. Active and passive records were made in successive recording runs. Each record shows work loops from 5 successive cycles superimposed. The 5 cycles are centered around that in which steady state (i.e., excluding first cycle) net work output was maximum at that frequency.

Enthalpy output is the sum of the work and heat outputs. The combined effects of variations in work and heat output can be seen in the enthalpy output (Fig. 2A). At all frequencies below ~3 Hz, the total enthalpy produced in response to 40 cyclic contractions was similar. However, in the example shown, substantially less enthalpy was produced at 4 Hz than at lower cycle frequencies. These characteristics are summarized, with the use of the combined data from eight muscles, in Fig. 4. In this figure, total energy output has been divided by the number of contractions, which is a common style for presenting energetic data in the cardiac literature, and expressed as the rate of energy output (i.e., energy/cycle). The rate of work output was significantly greater at frequencies from 2 to 2.5 Hz than at either higher or lower cycle frequencies. Both the mean rates of heat and enthalpy output were independent of cycle frequency below 3.5 Hz, but significantly less heat and enthalpy were produced per cycle at 3.5 and 4 Hz. Rate of enthalpy output was maximum at a frequency of 2 Hz and was 5.9 ± 0.3 mJ · g¹ · cycle¹ (n = 8).

View larger version (20K): [in this window] [in a new window]   Fig. 4.   Effects of cycle frequency on rates of work output (), heat output (), and enthalpy output (). Note that all rates are expressed as amount of energy produced per cycle. Symbols are means ± SE. * Significant difference (P < 0.05) from value at 1 Hz.

Net mechanical efficiency was defined as the relative contribution of mechanical work to the total enthalpy produced. Efficiency varied significantly with cycle frequency and was highest between 2 and 2.5 Hz (Fig. 5). The maximum overall efficiency was 15.5 ± 0.6% (n = 8) at 2.2 Hz. At frequencies below 2 Hz and above 2.5 Hz, efficiency was ~10%; that is, there was a marked elevation in efficiency between 2 and 2.5 Hz. As there was no significant difference in enthalpy output between 1 and 3 Hz, the variations in efficiency over this frequency range can be entirely attributed to variations in work output. The independence of enthalpy output, but not work output, from cycle frequency between 1 and 3 Hz also supports the idea that at all but the highest frequencies used, net mechanical work output was not an important determinant of energetic cost.

View larger version (16K): [in this window] [in a new window]   Fig. 5.   Variation in net mechanical efficiency with cycle frequency. Net efficiency was calculated by dividing the total work output performed during 40 contractions by total enthalpy output. Total enthalpy output included all heat produced in excess of basal metabolism both during and after contraction protocol. Symbols are means ± SE. * Significant difference (P < 0.05) from value at 1 Hz.

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

These experiments constitute the first in which enthalpy output from cardiac muscle has been measured using a sinusoidal length change protocol. The main findings were that 1) the relationship between net mechanical efficiency and cycle frequency showed a distinct maximum at cycle frequencies between 2 and 2.5 Hz, and 2) the maximum net mechanical efficiency was ~15%. The basis of the higher efficiency at frequencies of 2-2.5 Hz was that the work output per cycle was also maximal at these frequencies (Fig. 4). Thus at these cycle frequencies, the frequency of the applied length changes was well matched to the kinetics of force generation; active force generation occupied the entire shortening phase, but relaxation was complete before substantial relengthening had occurred.

Analysis of the response of rat papillary muscles (at 24°C) to length perturbations has showed that dynamic stiffness has a minimum value at a frequency of 2 Hz (37). This observation was interpreted as indicating that during isometric contraction, the average cross-bridge cycling rate is ~2 Hz; that is, the average cross-bridge cycle time was ~500 ms. Although this frequency compares favorably with that at which efficiency was maximal (Fig. 5), it must be remembered that when contracting at 2 Hz in the current study, muscles were only active for just over one-half of each cycle (~260 ms, taking account of the stimulus phase). Clearly, shortening reduced the duration of each twitch (isometric twitch duration was 400-500 ms), and this probably reflects more rapid cross-bridge cycling, shortening-induced deactivation (23), or some combination of these two effects.

Comparison With Efficiency Measured by Use of Afterloaded Contractions

Two factors could have contributed to the lower work output in the current study compared with the earlier afterloaded studies. First, the muscles used in the current study had a higher cross-sectional area than those in the earlier isotonic studies. Maximum developed stress (i.e., force output/cross-sectional area) in papillary muscles is inversely related to cross-sectional area (but not related to development of an anoxic core, Ref. 27), and high stress development is associated with high work output per twitch (e.g., Refs. 20 and 25). Some of the lower work output in the current study could, therefore, have been due to the relatively large cross-sectional area of the preparations used. However, it might also be expected that enthalpy output would vary in a similar manner to work output (20), reducing any effect of work output on efficiency. Second, it is conventional, with afterloaded contractions, to use the total force (i.e., active + passive) to calculate work done; that is, both preload and afterload are included (41). This is almost certainly a simplification of the true situation. A fraction of the preload, which varies with the extent of shortening, will be borne by the parallel elastic elements during shortening, making the average load on the contractile element slightly less than the total force (11). On the other hand, there also appears to be some component that behaves as though it is an elastic component that is compressed during shortening, increasing the load on the contractile element (3). Given this complexity and the likelihood of corrections that would counter each other, the assumption that the total force corresponds to the load experienced by the contractile apparatus is probably reasonable. In the work-loop analysis, only active force is included in the work calculation. This difference in definition of work reflects the different mechanical arrangements employed in the two protocols. In afterloaded contractions, the muscle must develop sufficient force to overcome the afterload before shortening can commence, and then as shortening progresses, the preload is progressively transferred from the parallel elastic component to the contractile element (11). Work is then performed against something close to the total load. In the work-loop protocol, work against the preload is performed by the ergometer rather than by the muscle. Thus each method for calculating work is quite appropriate for the respective protocols.

The question as to which model is relevant to the in vivo function of papillary, or other cardiac, muscle is difficult to assess. It is worth noting, however, that there is considerable evidence that the efficiency of animal (7) and human (for a review, see Ref. 8) hearts is likely to be at least 20%. For example, the work output per beat of the human heart is well established at ~1 J/beat for the left ventricle, and myocardial oxygen consumption is ~8 ml · min¹ · 100 g¹. If allowance is made for a resting oxygen consumption of 2 ml · min¹ · 100 g¹, then the net mechanical efficiency of a 200 g left ventricle would be between 20 and 25%. There is even some evidence that the oxygen consumption measurement may be too high (8), leading to even higher calculated efficiencies. Because efficiency of cardiac muscle seems to vary relatively little between species (28), it seems reasonable to expect that a value of ~20% would also be applicable to rat cardiac muscle. If the typical preload is subtracted from the total force used to calculate work in afterloaded contractions, then maximum net efficiency would be reduced to between 16 and 17%, similar to the values in the current work-loop study.

Efficiency of isolated preparations may be slightly lower than that of the whole heart as a result of internal work performed in isolated muscles that contributes to energy cost but is not included in the measured external work. A source of additional internal work in isolated papillary muscles that would be absent in vivo are compliant regions at the ends of the preparations where some damage results from tying the muscle to the apparatus. Consequently, undamaged central regions of the muscle can shorten against the more compliant regions (6), and the total work performed by the contractile apparatus is greater than that calculated from the overall length change. This would have little effect on comparison between different protocols, using isolated papillary muscles, but may account for some difference between efficiency of isolated muscles and whole hearts.

Comparison With Other Sinusoidal Protocols

There is excellent agreement between our mechanical data and the data of Layland et al. (24). It should be noted, however, that their studies were done at 37°C and included twitch frequencies up to 9 Hz. The higher temperature and higher stimulus frequencies necessitated the use of much smaller preparations to avoid development of an anoxic region in the center of the preparations. Later in the DISCUSSION we show calculations relating to the adequacy of tissue oxygenation in the current experiments. The effect of cycle frequency is very evident in their studies, as the work output per beat rises from ~0.75 mJ/g at 1 Hz to near 1.8 mJ/g at 3 Hz. In Tables 1 and 2, we have set out our results in a manner comparable with that used in the studies of Layland et al. (24, 25). When the likely effects of the lower temperature that we used (27°C) are taken into account, the relationships of work and power output to frequency are similar, and the stimulation phase shifts found necessary to optimize work output are also similar, although our range is more limited (from 130° at 1.0 Hz to 60° at 4 Hz) because of the reduced cycle range.

The maximum work output per beat per cycle of 0.75 mJ · g¹ · cycle¹ in this study is low compared with the maximum work output per beat per cycle of 1.9 mJ · g¹ · cycle¹ in the work of Layland et al. (24), and in our view, this probably reflects the lower stress-generating capabilities of muscles with larger cross-sectional areas.

There is only one previous investigation in which an energetic analysis of cardiac muscle has been carried out with the use of a work-loop analysis. In that study (46), frog ventricular trabeculae preparations were used, and their mechanical power output and oxygen consumption were measured at 20°C over a narrow range of cycle frequencies (0.4-0.9 Hz). In contrast to the current results, net efficiency was independent of cycle frequency but did depend on both length and strain. Syme's preparations (46) were small and developed high twitch forces (~60 mN/mm²), but his highest net efficiency was only 13%. Again, this value is low compared with those obtained from toad ventricular strips performing afterloaded contractions (18-20%; Ref. 18) but does not differ greatly from that obtained in the current study.

Comparison Between Whole Heart PVA and Work Loops

View larger version (27K): [in this window] [in a new window]   Fig. 6.   Active work loops from one muscle recorded at different initial lengths or preloads. Length (L) is expressed relative to length at which active isometric twitch force was maximal (Lmax). The amplitude of length changes was ±5% of initial length. Net work output was maximum for this muscle when initial length was 0.94 Lmax. Each loop shown is average of the last 5 loops in a series of 40 contractions at 2.2 Hz. Dashed line is fitted by linear regression through maximum force values for each loop.

The interrelationship between mechanical efficiency, as measured in this paper, and contractile efficiency (43) has been discussed by us in a recent review (9). Suga et al. (44) have shown that the relationship between the rate of oxygen consumption and PVA is virtually the same at different heart rates, but it would be interesting to do an FLA analysis at cycle frequencies where mechanical efficiency was clearly different (e.g., 1 and 2.5 Hz in the current study).

Adequacy of Diffusive Oxygen Supply

Rates of oxygen consumption for resting and contracting muscle were calculated from the mean rates of enthalpy output measured in this study. For contracting muscles, mean rates of enthalpy output during the last five cycles at each cycle frequency were used. These were the highest rates of enthalpy output achieved at each cycle frequency. The metabolic rates used are given in Table 3, and the predicted PO₂ profiles are shown (see Fig. 7B). The simulations indicate that at all but the highest contraction frequencies used, diffusive oxygen supply would have been adequate to meet the oxygen requirements of the muscles during steady-state activity. This conclusion is drawn from the observation that the model predicted that PO₂ in the center of the muscle would be greater than that assumed to be low enough to decrease mitochondrial function. The assumed dependence of mitochondrial oxygen consumption on PO₂ is shown in Fig. 7A, and the critical PO₂ is indicated by the dotted line in Fig. 7B. At the highest contraction frequency used (4 Hz), the model predicts that a region with a radius of ~0.005 cm would have a PO₂ sufficiently low to impair mitochondrial oxygen consumption. However, it is unlikely that either the energetic or mechanical consequences of such a region, if it actually occurred, could be detected, as the putative hypoxic region would have an area of only 0.005²/0.05², equal to 1% of the total cross-sectional area. It should be noted that the contraction protocols used in the current study were not sufficiently long for an energetic steady state to be attained. This was deduced from records of muscle temperature. When an energetic steady state is attained, muscle temperature is the same at the start of successive contraction cycles (34) (i.e., rate of average heat production in each cycle is constant and equal to rate of heat loss from the recording system). However, this state was not reached during the protocols used in this study. Consequently, the predictions of the model would be conservative, underestimating the actual PO₂ at any radial location in the muscles.

View larger version (20K): [in this window] [in a new window]   Fig. 7.   A: assumed relationship between relative rate of mitochondrial O2 consumption and partial pressure of O2 (PO2). This relationship was used in computer simulations of diffusion of O2 into muscles during steady-state activity. Relationship is described by a sigmoidal curve with one-half-maximal rate at 0.01 atm and slope of 2. B: predicted PO2 profiles through cross section of cylindrical muscles during steady-state activity at indicated contraction frequencies. Horizontal dashed line indicates PO2 at muscle's surface, and dotted line indicates PO2 below which mitochondrial O2 consumption is assumed to be compromised. Simulations predict that only during steady-state activity of 4 Hz will PO2 in center of muscle decrease sufficiently to limit mitochondrial function. Note that area of assumed hypoxic region at 4 Hz only amounts to ~1% of muscle cross-sectional area.

Efficiency of Cardiac Muscle