INTRODUCTION

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ENERGY UTILIZATION by contracting myocardium includes several components. Energy is required for the maintenance of cell homeostasis independent of stimulation or contraction (basal metabolism). Additional energy is required to depolarize and repolarize the sarcolemma (activation energy), to support calcium release and reuptake, and for cross-bridge activity. Once basal metabolism is subtracted, the remaining three terms are related to the generation of a contraction. The ratio of work performed by a contraction to the sum of these contraction-related energy requirements has been termed net mechanical efficiency (7), whereas the ratio of external plus potential work to the energy required for cross-bridge cycling alone is referred to as contractile efficiency (21). For isometrically contracting isolated muscles, external work is zero and the force-length area provides a measure of potential work (12).

Peak force and force-time integral also have been correlated with energy consumption and employed in energetic studies. Because these measures do not have units of work, ratios involving them are not efficiencies; in the case of force-time integral the term economy has been used instead (2). By nature of their definitions, we would expect force-length area to be most useful for analysis of shortening contractions and force-time integral for analysis of force-frequency studies. Neither measure has a clear theoretical advantage for isometric studies. Hisano and Cooper (12) showed that peak force, force-length area, and force-time integral were all equally effective correlates of myocardial oxygen consumption (MO₂) (correlation coefficients 0.952, 0.965, and 0.970, respectively) during isometric contractions of ferret papillary muscles, whereas force-length area was a significantly better correlate when isometric and various shortening protocols were considered together (12).

The use of correlations between these mechanical quantities and oxygen consumption over the range of lengths and loading conditions likely encountered by in vivo myocardium assumes that economy and efficiency are independent of length. At the ventricular level, the concept of length-independent efficiency was advanced by Suga and co-workers (21) based on the correlation of pressure-volume area (PVA) to MO₂. At the cross-bridge level, length-independent economy is suggested by the fact that the ratio of tetanized force to ATP consumption in maximally activated skinned fibers is constant over the normal working sarcomere length (23). However, Higashiyama and co-workers (11), using a 2,3-butanedione (BDM) partitioning method to measure nonmechanical oxygen consumption in isovolumically contracting isolated rabbit hearts, found that economy was significantly higher at the higher of two volumes tested.

We therefore tested the hypothesis that economy and efficiency are independent of length in intact isolated cardiac muscle over its normal working range. We used low-dose BDM to partition oxygen consumption into its tension-dependent and tension-independent parts in isometrically contracting rabbit right ventricular papillary muscles (1, 11, 24), allowing us to calculate economy and efficiency at each muscle length and test this hypothesis. In agreement with Higashiyama's results (11) in the isolated rabbit heart and in disagreement with results in skinned rat trabeculae, we found that economy and efficiency increased significantly as the muscle was stretched from 90% to 100% of L_max.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

This investigation conforms to the Guide for the Care and Use of Laboratory Animals published by the National Institutes of Health (NIH Publication No. 85-23, Revised 1996).

Papillary muscle isolation. Right ventricular papillary muscles were harvested from New Zealand White rabbits (2.2-2.8 kg body wt) as follows. The animals were euthanized, the abdomen was opened in the midline just below the xyphoid, and the chest was entered via cuts through the diaphragm and ribs on each side of the sternum. The great vessels and atria were transected immediately above the atrioventricular valve rings. The ventricles were placed in a cold (0°C) oxygenated Krebs-Ringer solution containing (mM) 152 Na⁺, 3.6 K⁺, 135 Cl, 25 HCO, 1.3 H₂PO, 0.6 SO, 0.6 Mg²⁺, 2.5 Ca²⁺, and 11.2 glucose, with 10 IU/l insulin and 30 mM BDM to inhibit cross-bridge cycling. Ventricles were gently rinsed to clear remaining blood. The time from death to BDM solution was ~2 min. After at least 15 min in cold BDM solution, the right ventricle was opened under a dissecting microscope. Right ventricular papillary muscles were isolated by first dividing the chordae tendinae at the muscle tip and then freeing the muscle base and a small amount of surrounding myocardium from the ventricular wall. Only long, thin, uniformly cylindrical muscles were used.

Experimental protocol. Muscles were placed into the measurement apparatus (Muscle Research System, Scientific Instruments; Heidelberg, Germany) and clamped at both ends at a length well below slack length. Muscle length was precisely manipulated and measured by micrometers graduated in 0.01-mm intervals. Muscles were perfused with Krebs-Ringer solution (composition as above without BDM) bubbled with 95% O₂-5% CO₂ and warmed to 37.0°C. Muscles were stretched just beyond slack length and stimulated to contract isometrically with a 5-ms pulse applied end to end at a voltage 25% above threshold and a frequency of 1 Hz. Muscles were allowed to equilibrate for 30 min before proceeding. After equilibration, muscles were stretched in 0.05-mm steps until additional stretch did not produce an increase in developed force; this length was taken as L_max. From earlier experience with this preparation, a developed force of greater than 10 mN/mm² at L_max was required for inclusion in this study. Force parameters and oxygen consumption (see below) were measured under steady-state conditions at 90%, 95%, and 100% of L_max in a random order determined by coin toss. Force parameters were additionally measured at 85% L_max to improve the accuracy of force-length area calculations. BDM was added to the perfusate to achieve a concentration of 2 mM, and the measurement sequence was repeated. Finally, basal oxygen consumption was measured at L_max in the presence of 30 mM BDM.

Measurement of mechanical parameters. Isometric force was acquired digitally at 1.6-ms intervals from the force transducer (KG4, Scientific Instruments); the raw data from three consecutive twitches were averaged before analysis. Diastolic force was defined as the minimum force between two contractions, total force as the maximum force reached during an isometric contraction, and developed force as the difference between these two. Force-time integral was calculated as the area under the twitch force curve but above the diastolic force (Fig. 1A). All force parameters were normalized by muscle cross-sectional area, calculated as blotted muscle weight divided by muscle length. Force-length area was calculated as the area between the systolic and the diastolic force-length curves (12) and normalized by blotted muscle weight (Fig. 1B). Linear systolic and piecewise linear diastolic force-length curves were assumed.

View larger version (17K): [in this window] [in a new window]   Fig. 1.   Calculation of mechanical parameters in a typical experiment. A: force-time integral (FTI) was calculated as the area under the twitch force curve and above the diastolic force curve and normalized by muscle cross-sectional area. B: force-length area (FLA) was calculated as the area enclosed by a linear end-systolic force-length relation (dashed line), a piecewise linear end-diastolic force-length relation (lower solid curve), and isometric force at each length (solid vertical line), in this example Lmax.

Measurement of oxygen consumption. The method used to measure oxygen consumption was described and validated previously (17). Briefly, a miniature oxygen electrode continuously measured PO₂ in the experimental chamber close to the muscle surface. When the flow of perfusate was stopped, the chamber was unstirred and free of convective currents and of oxygen leaks in the vicinity of the muscle. An oxygen concentration gradient developed that depended on the size of the muscle, its rate of oxygen consumption, the distance between the probe tip and the muscle surface, and the diffusion constants of oxygen in the muscle and the surrounding solution. The drop in PO₂ at the probe tip was measured over 20 s and compared with precalculated theoretical profiles to determine the rate of oxygen consumption of the muscle (i.e., MO₂).

Partitioning of oxygen consumption. Terms were defined by analogy to standard heat-based energetics terms (10). Basal MO₂ referred to the oxygen consumption measured in an unstimulated muscle in the presence of 30 mM BDM to completely inhibit cross-bridge cycling. Nonbasal MO₂ (total MO₂  basal MO₂) reflected oxygen costs associated with contraction and was further separated into two components: tension-independent MO₂ (MO_2TI), oxygen consumed to support electrical events and calcium cycling, and tension-dependent MO₂ (MO_2TD), the oxygen consumed for cross-bridge cycling.

View larger version (17K): [in this window] [in a new window]   Fig. 2.   Partitioning of myocardial oxygen consumption (MO2) into tension-dependent (MO2TD), and tension-independent (MO2TI) components. Data are from a single experiment at 100% Lmax. A: single twitches before and after 2,3-butanedione (BDM) treatment. 2 mM BDM inhibits approximately one-half of the cross bridges, reducing developed force by ~50%. B: oxygen consumption plotted against FTI for the two twitches shown in A. A line connecting these points represents a line of decreasing number of active cross bridges. Its intercept indicates the oxygen consumed independent of force generation; subtracting basal MO2 gives MO2 TI.

Statistics. All results are reported as means ± SE unless otherwise specified. Trends in each parameter with length were assessed by one-way repeated measures ANOVA using the generalized linear model procedure in SAS 6.1 (SAS Institute, Cary, NC). P values reported are based on the univariate F statistic; the Huyn-Feldt adjusted F statistic was used for data sets for which sphericity was rejected. If the overall trend with length was significant, values at 100% and 95% L_max were each compared with the reference value at 90% L_max using paired t-tests with the Bonferroni correction for multiple comparisons. Single comparisons were made with standard paired t-tests. A P value <0.05 was considered significant for all tests.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Eight uniformly cylindrical papillary muscles generating at least 10 mN/mm² at L_max were studied. Each muscle was taken from a separate animal. Muscle length averaged 3.51 ± 0.26 mm, weight 1.05 ± 0.17 mg, and radius 0.31 ± 0.03 mm.

Mechanical parameters. Diastolic and developed force, force-time integral, and force-length area all increased significantly with muscle length (Fig. 3A). There was no difference between resting (unstimulated) and basal (unstimulated, 30 mM BDM) force (3.39 ± 0.69 vs. 3.17 ± 0.57 mN/mm² at L_max, P = 0.14).

View larger version (29K): [in this window] [in a new window]   Fig. 3.   Effect of length on mechanical performance and oxygen cost in 8 isometrically contracting rabbit right ventricular papillary muscles. A: developed force (Fdev/10, graphed divided by 10 to equalize scales, mN/mm2), FTI (mN · s/mm2), and FLA (mJ/g) increased by factors of 2.4, 2.7, and 4.8, respectively, as the muscles were stretched from 90% to 100% Lmax. Fdia, diastolic force (mN/mm2). B: total MO2, nonbasal MO2, and MO2 TD increased significantly but less dramatically with length (factors of 1.3, 1.6, and 1.6). * Statistically significant increase with length by ANOVA.

Oxygen consumption. As muscle length increased from 90% to 100% of L_max, MO₂ increased from 3.58 ± 0.40 to 4.77 ± 0.64 ml O₂ · min¹ · 100 g¹ (Fig. 3B). This represented a 33% increase in total oxygen consumption and a 63% increase in nonbasal MO₂. The MO_2TD component of nonbasal MO₂ also increased with length (ANOVA P = 0.03), whereas the tension-independent (MO_2TI) component did not change significantly (ANOVA P = 0.13).

Economy and efficiency. As shown in Fig. 3, the length-dependent increases in force-time integral and force-length area were proportionally greater than the measured increases in tension-dependent MO₂, indicating increased economy and efficiency. Calculated economy was 7.3 ± 0.6 mN · s · g/mm² · µl O₂ at 90%, 10.6 ± 1.1 mN · s · g/mm² · µl O₂ at 95%, and 12.2 ± 1.0 mN · s · g/mm² · µl O₂ at 100% L_max (ANOVA P = 0.04). Economy was significantly increased at 100% (P < 0.01) but not at 95% L_max (P = 0.06) compared with 90% L_max. Contractile efficiency was 0.10 ± 0.01 at 90%, 0.22 ± 0.02 at 95%, and 0.33 ± 0.03 at 100% L_max (ANOVA P = 0.002) and was significantly increased at both 95% (P < 0.01) and 100% L_max (P < 0.001) compared with 90% L_max.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Does the close correlation of oxygen consumption with force-time integral and force-length area across a range of conditions (lengths, frequencies, and afterload) imply that economy and efficiency are constant for a given muscle across those conditions? We and other investigators have assumed this to be the case. However, the current study demonstrates that both economy and efficiency change significantly with muscle length in isometrically contracting rabbit papillary muscles. Gibbs and Chapman (8) have pointed out that most muscle models would not predict a constant contractile efficiency and suggested an autoregulatory process may explain the linearity of the MO₂-PVA relationship. Higashiyama et al. (11) suggested that a population of nonforce-producing cross bridges may exist and consume an amount of oxygen that is linearly proportional to PVA.

Length-dependent changes in economy. There are a number of differences between whole heart and isolated muscle studies that might have explained the difference between the results of Higashiyama (11), who found increased economy at a larger volume in isolated rabbit hearts, and studies reporting length-independent economy in skinned fibers (14, 23). Isolated hearts may work at lower sarcomere lengths, may undergo different shape changes during isovolumic contraction at different volumes [an effect demonstrated by Rankin and co-workers (20) in closed-chest dogs], or may display preload-dependent changes in synchrony of contraction of various ventricular regions. However, a highly significant increase in economy was observed with increased muscle length in the present study of isolated muscle, suggesting that length-dependent changes in economy are a basic property of intact cardiac muscle. Great care was taken to ensure adequate oxygenation of the muscles in this experiment (see METHODS), making shifts in the ratio of ATP production to oxygen consumption unlikely. Because the force-time integral is a sum over the entire muscle of mechanical events at the cellular level, the observed increase in the ratio force-time integral to MO_2TD therefore indicated either an increase in the amount of cross-bridge work performed per ATP consumed or an increase in the efficiency of transducing cross-bridge work into force generation. Data from previous studies on skinned muscle preparations provide little support for either possibility.

Length-dependent changes in contractile efficiency. Regression of PVA against nonbasal MO₂ across contractions at multiple volumes assumes length-independent efficiency and interprets the PVA-MO₂ correlation intercept as MO_2TI, the portion used for activation and calcium handling (21). In this study, using 2 mM BDM to deactivate approximately half the cross bridges and extrapolating to a point of no cross-bridge activity to estimate MO_2TI gave values half the intercept of the force-length area-MO₂ regression line (Fig. 4A). This is in direct agreement with the studies by Yaku et al. (24) and Higashiyama et al. (11), who reported that mechanically unloaded O₂ was twice their O₂-force-time integral intercept. We conclude that roughly half the nonbasal energy expenditure of an unloaded contraction at the length at which no force is developed (L₀) or the analogous volume V₀ can be attributed to activation and calcium cycling, with the other half consumed by cross-bridge activity. This provides an alternate explanation for the data of de Tombe et al. (6), who reported in agreement with our data that low-dose BDM altered the intercept but not the slope of the PVA-MO₂ regression line in isovolumically contracting isolated blood-perfused canine ventricles (Fig. 4B). The authors concluded that low-dose BDM did not act as expected for a calcium-desensitizing agent because it altered MO_2TI; their data are equally explained by the finding that the PVA-MO₂ intercepts include substantial consumption for cross-bridge activity in addition to MO_2TI.

View larger version (24K): [in this window] [in a new window]   Fig. 4.   Alternate interpretation of the relationship between the FLA/MO2 intercept and tension-independent MO2. A: nonbasal MO2 plotted against FLA for a single muscle. At each muscle length, one solid and one open symbol represent data acquired without and with 2 mM BDM, respectively (squares, 90% Lmax; triangles, 95% Lmax; diamonds, 100% Lmax). Intersections of these lines estimate tension-independent MO2 as the oxygen consumed by a beat with no cross-bridge activity. This method gives MO2 TI estimates roughly half the value of the FLA-MO2 regression intercept, in agreement with previous studies by Yaku et al. (24) and Higashiyama et al. (11) B: grouping data from all lengths and muscles according to absence (solid circles) or presence (open circles) of 2 mM BDM masks the effects of length on contractile efficiency and suggests the conclusion that BDM alters the intercept but not the slope of the FLA-MO2 regression line. Very similar data were presented in Fig. 2 of de Tombe et al. (6) based on studies in isolated canine hearts; see DISCUSSION for explanation.

Partitioning of MO₂. Our calculations of economy and efficiency rely on the ability to accurately partition MO₂ into basal, tension-independent, and tension-dependent parts. Basal oxygen consumption was measured directly and agrees well with the literature. Our value of 1.65 ± 0.17 ml · min¹ · 100 g¹ in rabbit right ventricular papillary muscles was identical to that of 1.66 ± 0.15 reported by Goto et al. (9) in potassium-arrested isolated rabbit hearts. Similar values were reported in canine isolated heart and open-chest preparations, including 2.0 ml · min¹ · 100 g¹ by McKeever et al. (16), 1.43 by Boerth et al. (3), and 1.02 ± 0.42 by Nozawa et al. (18) during potassium arrest. Significantly higher values were reported in unstimulated cat papillary muscle preparations [4.73 ml · min¹ · 100 g¹ by Cranefield and Greenspan (5) and 4.13 by Coleman (4)].

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Limitations and sources of error. The principal source of error in measurements of both mechanical parameters and MO₂ was the determination of muscle radius. Radius was confirmed optically with a calibrated eyepiece grid in the microscope used to observe the muscle chamber; optical radius differed by no more than 10% from the radius calculated from blotted muscle weight. There was no evidence for systematic errors in muscle radius, with good repeatability between investigators and no consistent trend in differences between optical and calculated radii. However, at small radii even a 10% error has substantial consequences. For example, at an actual radius of 0.3 mm, an underestimation of 10% would result in a 23% overestimation of force per cross-sectional area, a 10% underestimation of oxygen consumption, and consequent 27% underestimation of economy.