Does the intercept of the heat-stress relation provide an accurate estimate of cardiac activation heat?

Resolving an inconsistency in the estimation of the energy for excitation of cardiac muscle contraction

In the excitation of muscle contraction, calcium ions interact with transmembrane transporters. This process is accompanied by energy consumption and heat liberation. To quantify this activation energy or heat in the heart or cardiac muscle, two non-pharmacological approaches can be used. In one approach using the "pressure-volume area" concept, the same estimate of activation energy is obtained regardless of the mode of contraction (either isovolumic/isometric or ejecting/shortening). In the other approach, an accurate estimate of activation energy is obtained only when the muscle contracts isometrically. If the contraction involves muscle shortening, then an additional component of heat associated with shortening is liberated, over and above that of activation. The present study thus examines the reconcilability of the two approaches by performing experiments on isolated muscles measuring contractile force and heat output. A framework was devised from the experimental data to allow us to replicate several mechanoenergetics results gleaned from the literature. From these replications, we conclude that the choice of initial muscle length (or ventricular volume) underlies the divergence of the two approaches in the estimation of activation energy when the mode of contraction involves shortening (ejection). At low initial muscle lengths, the heat of shortening is relatively small, which can lead to the misconception that activation energy is contraction mode independent. In fact, because cardiac muscle liberates heat of shortening when allowed to shorten, estimation of activation heat must be performed only under isometric (isovolumic) contractions. We thus recommend caution when estimating activation energy using the "pressure-volume area" concept.

Work and oxygen consumption of isolated right ventricular papillary muscle in experimental pulmonary hypertension

Right-sided myocardial mechanical efficiency (work output/metabolic energy input) in pulmonary hypertension can be severely reduced. We determined the contribution of intrinsic myocardial determinants of efficiency using papillary muscle preparations from monocrotaline-induced pulmonary hypertensive (MCT-PH) rats. The hypothesis tested was that efficiency is reduced by mitochondrial dysfunction in addition to increased activation heat reported previously. Right ventricular muscle preparations were subjected to 5 Hz sinusoidal length changes at 37°C. Work and suprabasal oxygen consumption (V ̇ O 2 ${\dot{V}}_{{{\rm{O}}}_{\rm{2}}}$ ) were measured before and after cross-bridge inhibition by blebbistatin. Cytosolic cytochrome c concentration, myocyte cross-sectional area, proton permeability of the inner mitochondrial membrane and monoamine oxidase and glucose 6-phosphate dehydrogenase activities and phosphatidylglycerol/cardiolipin contents were determined. Mechanical efficiency ranged from 23% to 11% in control (n = 6) and from 22% to 1% in MCT-PH (n = 15) and correlated with work (r2  = 0.68, P < 0.0001) but not withV ̇ O 2 ${\dot{V}}_{{{\rm{O}}}_{\rm{2}}}$ (r2  = 0.004, P = 0.7919).V ̇ O 2 ${\dot{V}}_{{{\rm{O}}}_{\rm{2}}}$ for cross-bridge cycling was proportional to work (r2  = 0.56, P = 0.0005). Blebbistatin-resistantV ̇ O 2 ${\dot{V}}_{{{\rm{O}}}_{\rm{2}}}$ (r2  = 0.32, P = 0.0167) and proton permeability of the mitochondrial inner membrane (r2  = 0.36, P = 0.0110) correlated inversely with efficiency. Together, these variables explained the variance of efficiency (coefficient of multiple determination r2  = 0.79, P = 0.0001). Cytosolic cytochrome c correlated inversely with work (r2  = 0.28, P = 0.0391), but not with efficiency (r2  = 0.20, P = 0.0867). Glucose 6-phosphate dehydrogenase, monoamine oxidase and phosphatidylglycerol/cardiolipin increased in the right ventricular wall of MCT-PH but did not correlate with efficiency. Reduced myocardial efficiency in MCT-PH is a result of activation processes and mitochondrial dysfunction. The variance of work and the ratio of activation heat reported previously and blebbistatin-resistantV ̇ O 2 ${\dot{V}}_{{{\rm{O}}}_{\rm{2}}}$ are discussed. KEY POINTS: Mechanical efficiency of right ventricular myocardium is reduced in pulmonary hypertension. Increased energy use for activation processes has been demonstrated previously, but the contribution of mitochondrial dysfunction is unknown. Work and oxygen consumption are determined during work loops. Oxygen consumption for activation and cross-bridge cycling confirm the previous heat measurements. Cytosolic cytochrome c concentration, proton permeability of the mitochondrial inner membrane and phosphatidylglycerol/cardiolipin are increased in experimental pulmonary hypertension. Reduced work and mechanical efficiency are related to mitochondrial dysfunction. Upregulation of the pentose phosphate pathway and a potential gap in the energy balance suggest mitochondrial dysfunction in right ventricular overload is a resiult of the excessive production of reactive oxygen species.

Cardiac efficiency and Starling's Law of the Heart

The formulation by Starling of The Law of the Heart states that 'the [mechanical] energy of contraction, however measured, is a function of the length of the muscle fibre'. Starling later also stated that 'the oxygen consumption of the isolated heart … is determined by its diastolic volume, and therefore by the initial length of its muscular fibres'. This phrasing has motivated us to extend Starling's Law of the Heart to include consideration of the efficiency of contraction. In this study, we assessed both mechanical efficiency and crossbridge efficiency by studying the heat output of isolated rat ventricular trabeculae performing force-length work-loops over ranges of preload and afterload. The combination of preload and afterload allowed us, using our modelling frameworks for the end-systolic zone and the heat-force zone, to simulate cases by recreating physiologically feasible loading conditions. We found that across all cases examined, both work output and change of enthalpy increased with initial muscle length; hence it can only be that the former increases more than the latter to yield increased mechanical efficiency. In contrast, crossbridge efficiency increased with initial muscle length in cases where the extent of muscle shortening varied greatly with preload. We conclude that the efficiency of cardiac contraction increases with increasing initial muscle length and preload. An implication of our conclusion is that the length-dependent activation mechanism underlying the cellular basis of Starling's Law of the Heart is an energetically favourable process that increases the efficiency of cardiac contraction. KEY POINTS: Ernest Starling in 1914 formulated the Law of the Heart to describe the mechanical property of cardiac muscle whereby force of contraction increases with muscle length. He subsequently, in 1927, showed that the oxygen consumption of the heart is also a function of the length of the muscle fibre, but left the field unclear as to whether cardiac efficiency follows the same dependence. A century later, the field has gained an improved understanding of the factors, including the distinct effects of preload and afterload, that affect cardiac efficiency. This understanding presents an opportunity for us to investigate the elusive length-dependence of cardiac efficiency. We found that, by simulating physiologically feasible loading conditions using a mechano-energetics framework, cardiac efficiency increased with initial muscle length. A broader physiological importance of our findings is that the underlying cellular basis of Starling's Law of the Heart is an energetically favourable process that yields increased efficiency.

Crossbridge thermodynamics in pulmonary arterial hypertensive right-ventricular failure

Right-ventricular (RV) failure is an event consequent to pathological RV hypertrophy commonly resulting from pulmonary arterial hypertension. This pathology is well characterized by RV diastolic dysfunction, impaired ejection, and reduced mechanical efficiency. However, whether the dynamic stiffness and cross-bridge thermodynamics in the failing RV muscles are compromised remains uncertain. Pulmonary arterial hypertension was induced in the rat by injection of monocrotaline, and RV trabeculae were isolated from RV failing rats. Cross-bridge mechano-energetics were characterized by subjecting the trabeculae to two interventions: 1) force-length work-loop contractions over a range of afterloads while measuring heat output, followed by careful partitioning of heat components into activation heat and cross-bridge heat to separately assess mechanical efficiency and cross-bridge efficiency, and 2) sinusoidal-perturbation of muscle length while trabeculae were actively contracting to interrogate cross-bridge dynamic stiffness. We found that reduced mechanical efficiency is correlated with increased passive stress, reduced shortening, and elevated activation heat. In contrast, the thermodynamics, specifically the efficiency of, and the stiffness characteristics of, cross bridges did not differ between the control and failing trabeculae and were not correlated with elevated passive stress or reduced shortening. We thus conclude that, despite diastolic dysfunction and mechanical inefficiency, cross-bridge stiffness and thermodynamics are unaffected in RV failure following pulmonary arterial hypertension.

NEW & NOTEWORTHY This study characterizes cross-bridge mechano-energetics and dynamic stiffness of right-ventricular trabeculae isolated from a rat model of pulmonary hypertensive right-ventricular failure. Failing trabeculae showed increased passive force but normal active force. Their lower mechanical efficiency is found to be driven by an increase in the energy expenditure arising from contractile activation. This does not reflect a change in their cross-bridge stiffness and efficiency.

Cardiac mechanical efficiency is preserved in primary cardiac hypertrophy despite impaired mechanical function

Increased heart size is a major risk factor for heart failure and premature mortality. Although abnormal heart growth subsequent to hypertension often accompanies disturbances in mechano-energetics and cardiac efficiency, it remains uncertain whether hypertrophy is their primary driver. In this study, we aimed to investigate the direct association between cardiac hypertrophy and cardiac mechano-energetics using isolated left-ventricular trabeculae from a rat model of primary cardiac hypertrophy and its control. We evaluated energy expenditure (heat output) and mechanical performance (force length work production) simultaneously at a range of preloads and afterloads in a microcalorimeter, we determined energy expenditure related to cross-bridge cycling and Ca²⁺ cycling (activation heat), and we quantified energy efficiency. Rats with cardiac hypertrophy exhibited increased cardiomyocyte length and width. Their trabeculae showed mechanical impairment, evidenced by lower force production, extent and kinetics of shortening, and work output. Lower force was associated with lower energy expenditure related to Ca²⁺ cycling and to cross-bridge cycling. However, despite these changes, both mechanical and cross-bridge energy efficiency were unchanged. Our results show that cardiac hypertrophy is associated with impaired contractile performance and with preservation of energy efficiency. These findings provide direction for future investigations targeting metabolic and Ca²⁺ disturbances underlying cardiac mechanical and energetic impairment in primary cardiac hypertrophy.

Disruption of transverse-tubular network reduces energy efficiency in cardiac muscle contraction

AIM

Altered organization of the transverse-tubular network is an early pathological event occurring even prior to the onset of heart failure. Such t-tubular remodelling disturbs the synchrony and signalling between membranous and intracellular ion channels, exchangers, receptors and ATPases essential in the dynamics of excitation-contraction coupling, leading to ionic abnormality and mechanical dysfunction in heart disease progression. In this study, we investigated whether a disrupted t-tubular network has a direct effect on cardiac mechano-energetics. Our aim was to understand the fundamental link between t-tubular remodelling and impaired energy metabolism, both of which are characteristics of heart failure. We thus studied healthy tissue preparations in which cellular processes are not altered by any disease event.

METHODS

We exploited the "formamide-detubulation" technique to acutely disrupt the t-tubular network in rat left-ventricular trabeculae. We assessed the energy utilization by cellular Ca²⁺ cycling and by crossbridge cycling, and quantified the change of energy efficiency following detubulation. For these measurements, trabeculae were mounted in a microcalorimeter where force and heat output were simultaneously measured.

RESULTS

Following structural disorganization from detubulation, muscle heat output associated with Ca²⁺ cycling was reduced, indicating impaired intracellular Ca²⁺ homeostasis. This led to reduced force production and heat output by crossbridge cycling. The reduction in force-length work was not paralleled by proportionate reduction in the heat output and, as such, energy efficiency was reduced.

CONCLUSIONS

These results reveal the direct energetic consequences of disrupted t-tubular network, linking the energy disturbance and the t-tubular remodelling typically observed in heart failure.

An Equivocal Final Link - Quantitative Determination of the Thermodynamic Efficiency of ATP Hydrolysis - Sullies the Chain of Electric, Ionic, Mechanical and Metabolic Steps Underlying Cardiac Contraction

Each beat of the heart completes the final step in a sequence of events commencing with electrical excitation-triggered release of Ca2+ from the sarcoplasmic reticulum which, in turn, triggers ATP-hydrolysis-dependent mechanical contraction. Given that Thermodynamics is inherently detail-independent, the heart can be thus be viewed as a mechanical pump - the generator of pressure that drives blood through the systemic and pulmonary circulations. The beat-to-beat pressure-volume work (W) of the heart is relatively straightforward to measure experimentally. Given an ability to measure, simultaneously, the accompanying heat production or oxygen consumption, it is trivial to calculate the mechanical efficiency: ε = W/ΔH where ΔH is the change of enthalpy: (W + Q), Q representing the accompanying production of heat. But it is much less straightforward to measure the thermodynamic efficiency: η = W/ΔG ATP , where ΔG ATP signifies the Gibbs Free Energy of ATP hydrolysis. The difficulty arises because of uncertain quantification of the substrate-dependent yield of ATP - conveniently expressed as the P/O2 ratio. P/O2 ratios, originally ("classically") inferred from thermal studies, have been considerably reduced over the past several decades by re-analysis of the stoichiometric coefficients separating sequential steps in the electron transport system - in particular, dropping the requirement that the coefficients have integer values. Since the early classical values are incompatible with the more recent estimates, we aim to probe this discrepancy with a view to its reconciliation. Our probe consists of a simple, thermodynamically constrained, algebraic model of cardiac mechano-energetics. Our analysis fails to reconcile recent and classical estimates of PO2 ratios; hence, we are left with a conundrum.

The relation between sarcomere energetics and the rate of isometric tension relaxation in healthy and diseased cardiac muscle

Full muscle relaxation happens when [Ca²⁺] falls below the threshold for force activation. Several experimental models, from whole muscle organs and intact muscle down to skinned fibers, have been used to explore the cascade of kinetic events leading to mechanical relaxation. The use of single myofibrils together with fast solution switching techniques, has provided new information about the role of cross-bridge (CB) dissociation in the time course of isometric force decay. Myofibril’s relaxation is biphasic starting with a slow seemingly linear phase, with a rate constant, slow k_REL, followed by a fast mono-exponential phase. Sarcomeres remain isometric during the slow force decay that reflects CB detachment under isometric conditions while the final fast relaxation phase begins with a sudden give of few sarcomeres and is then dominated by intersarcomere dynamics. Based on a simple two-state model of the CB cycle, myofibril slow k_REL represents the apparent forward rate with which CBs leave force generating states (g_app) under isometric conditions and correlates with the energy cost of tension generation (ATPase/tension ratio); in short slow k_REL ~ g_app ~ tension cost. The validation of this relationship is obtained by simultaneously measuring maximal isometric force and ATP consumption in skinned myocardial strips that provide an unambiguous determination of the relation between contractile and energetic properties of the sarcomere. Thus, combining kinetic experiments in isolated myofibrils and mechanical and energetic measurements in multicellular cardiac strips, we are able to provide direct evidence for a positive linear correlation between myofibril isometric relaxation kinetics (slow k_REL) and the energy cost of force production both measured in preparations from the same cardiac sample. This correlation remains true among different types of muscles with different ATPase activities and also when CB kinetics are altered by cardiomyopathy-related mutations. Sarcomeric mutations associated to hypertrophic cardiomyopathy (HCM), a primary cardiac disorder caused by mutations in genes encoding sarcomeric proteins, have been often found to accelerate CB turnover rate and increase the energy cost of myocardial contraction. Here we review data showing that faster CB detachment results in a proportional increase in the energetic cost of tension generation in heart samples from both HCM patients and mouse models of the disease.

Energy turnover in mammalian skeletal muscle in contractions mimicking locomotion: effects of stimulus pattern on work, impulse and energetic cost and efficiency

Active muscle performs various mechanical functions during locomotion: work output during shortening, work absorption when resisting (but not preventing) lengthening, and impulse (force-time integral) whenever there is active force. The energetic costs of these functions are important components in the energy budget during locomotion. We investigated how the pattern of stimulation and movement affects the mechanics and energetics of muscle fibre bundles isolated from wild rabbits (Oryctolagus cuniculus). The fibres were from muscles consisting of mainly fast-twitch, type 2 fibres. Fibre length was held constant (isometric) or a sinusoidal pattern of movement was imposed at a frequency similar to the stride frequency of running wild rabbits. Duty cycle (stimulation duration×movement frequency) and phase (timing of stimulation relative to movement) were varied. Work and impulse were measured as well as energy produced as heat. The sum of net work (work output-work input) and heat was taken as a measure of energetic cost. Maximum work output was produced with a long duty cycle and stimulation starting slightly before shortening, and was produced quite efficiently. However, efficiency was even higher with other stimulation patterns that produced less work. The highest impulse (considerably higher than isometric impulse) was produced when stimulation started while the muscle fibres were being lengthened. High impulse was produced very economically because of the low cost of producing force during lengthening. Thus, locomotion demanding high work, high impulse or economical work output or impulse requires a distinct pattern of stimulation and movement.

Energy expenditure for isometric contractions of right and left ventricular trabeculae over a wide range of frequencies at body temperature

We studied the energy expenditure of isometric contractions using both right-ventricular (RV) and left-ventricular (LV) trabeculae isolated from the rat heart. The energy expenditure under isometric contraction presents entirely as heat liberation. Preparations were challenged to perform at various rates of energy demand while accounting for their inevitable time-dependent decline of performance. They were electrically stimulated to contract at 37 °C with a frequency order (between 0.1 Hz and 10 Hz) dictated by a fully-balanced Latin-Square experimental design. We measured, simultaneously, their stress production and heat output. As functions of stimulus frequency, active stress and heat were not significantly different between RV and LV trabeculae. However, contraction kinetics, indexed as the maximal rate of rise and fall of twitch, were lower in the LV trabeculae. The ratio of heat to stress was greater in the LV trabeculae, suggesting that the economy of contraction of the LV trabeculae is lower. Their lower economy became more pronounced at high stimulus frequencies. Our results allow us to assess whether slowing of kinetics is a causative mechanism for improvement of economy of contraction.

Pulmonary arterial hypertension reduces energy efficiency of right, but not left, rat ventricular trabeculae

KEY POINTS

Pulmonary arterial hypertension (PAH) triggers right ventricle (RV) hypertrophy and left ventricle (LV) atrophy, which progressively leads to heart failure. We designed experiments under conditions mimicking those encountered by the heart in vivo that allowed us to investigate whether consequent structural and functional remodelling of the ventricles affects their respective energy efficiencies. We found that peak work output was lower in RV trabeculae from PAH rats due to reduced extent and velocity of shortening. However, their suprabasal enthalpy was unaffected due to increased activation heat, resulting in reduced suprabasal efficiency. There was no effect of PAH on LV suprabasal efficiency. We conclude that the mechanism underlying the reduced energy efficiency of hypertrophied RV tissues is attributable to the increased energy cost of Ca²⁺ cycling, whereas atrophied LV tissues still maintain normal mechano-energetic performance.

ABSTRACT

Pulmonary arterial hypertension (PAH) greatly increases the afterload on the right ventricle (RV), triggering RV hypertrophy, which progressively leads to RV failure. In contrast, the disease reduces the passive filling pressure of the left ventricle (LV), resulting in LV atrophy. We investigated whether these distinct structural and functional consequences to the ventricles affect their respective energy efficiencies. We studied trabeculae isolated from both ventricles of Wistar rats with monocrotaline-induced PAH and their respective Control groups. Trabeculae were mounted in a calorimeter at 37°C. While contracting at 5 Hz, they were subjected to stress-length work-loops over a wide range of afterloads. They were subsequently required to undergo a series of isometric contractions at various muscle lengths. In both protocols, stress production, length change and suprabasal heat output were simultaneously measured. We found that RV trabeculae from PAH rats generated higher activation heat, but developed normal active stress. Their peak external work output was lower due to reduced extent and velocity of shortening. Despite lower peak work output, suprabasal enthalpy was unaffected, thereby rendering suprabasal efficiency lower. Crossbridge efficiency, however, was unaffected. In contrast, LV trabeculae from PAH rats maintained normal mechano-energetic performance. Pulmonary arterial hypertension reduces the suprabasal energy efficiency of hypertrophied right ventricular tissues as a consequence of the increased energy cost of Ca²⁺ cycling.

Left-Ventricular Energetics in Pulmonary Arterial Hypertension-Induced Right-Ventricular Hypertrophic Failure

Pulmonary arterial hypertension (PAH) alters the geometries of both ventricles of the heart. While the right ventricle (RV) hypertrophies, the left ventricle (LV) atrophies. Multiple lines of clinical and experimental evidence lead us to hypothesize that the impaired stroke volume and systolic pressure of the LV are a direct consequence of the effect of pressure overload in the RV, and that atrophy in the LV plays only a minor role. In this study, we tested this hypothesis by examining the mechanoenergetic response of the atrophied LV to RV hypertrophy in rats treated with monocrotaline. Experiments were performed across multiple-scales: the whole-heart in vivo and ex vivo, and its trabeculae in vitro. Under the in vivo state where the RV was pressure-overloaded, we measured reduced systemic blood pressure and LV ventricular pressure. In contrast, under both ex vivo and in vitro conditions, where the effect of RV pressure overload was circumvented, we found that LV was capable of developing normal systolic pressure and stress. Nevertheless, LV atrophy played a minor role in that LV stroke volume remained lower, thereby contributing to lower LV mechanical work output. Concomitantly lower oxygen consumption and change of enthalpy were observed, and hence LV energy efficiency was unchanged. Our internally consistent findings between working-heart and trabecula experiments explain the rapid improvement of LV systolic function observed in patients with chronic pulmonary hypertension following surgical relief of RV pressure overload.

Do right-ventricular trabeculae gain energetic advantage from having a greater velocity of shortening?

KEY POINTS

We designed a study to test whether velocity of shortening in right-ventricular tissue preparations is greater than that of the left side under conditions mimicking those encountered by the heart in vivo. Our experiments allowed us to explore whether greater velocity of shortening results in any energetic advantage. We found that velocity of shortening was higher in the rat right-ventricular trabeculae. These results at the tissue level seem paradoxical to the velocity of ventricular ejection at the organ level, and are not always in accord with shortening of unloaded cells. Despite greater velocity of shortening in right-ventricular trabeculae, they neither gained nor lost advantage with respect to both mechanical efficiency and the heat generated during shortening.

ABSTRACT

Our study aimed to ascertain whether the interventricular difference of shortening velocity, reported for isolated cardiac tissues in vitro, affects interventricular mechano-energetic performance when tested under physiological conditions using a shortening protocol designed to mimic those in vivo. We isolated trabeculae from both ventricles of the rat, mounted them in a calorimeter, and performed experiments at 37°C and 5 Hz stimulus frequency to emulate conditions of the rat heart in vivo. Each trabecula was subjected to two experimental protocols: (i) isotonic work-loop contractions at a variety of afterloads, and (ii) isometric contractions at a variety of preloads. Velocity of shortening was calculated from the former protocol during the isotonic shortening phase of the contraction. Simultaneous measurements of force-length work and heat output allowed calculation of mechanical efficiency. The shortening-dependent thermal component was quantified from the difference in heat output between the two protocols. Our results show that both extent of shortening and velocity of shortening were higher in trabeculae from the right ventricle. Despite these differences, trabeculae from both ventricles developed the same stress, performed the same work, liberated the same amount of heat, and hence operated at the same mechanical efficiency. Shortening heat was also ventricle independent. The interventricular differences in velocity of shortening and extent of shortening of isolated trabeculae were not manifested in any index of energetics. These collective results underscore the absence of any mechano-energetic advantage or disadvantage conferred on right-ventricular trabeculae arising from their superior velocity of shortening.

Experimental and modelling evidence of shortening heat in cardiac muscle

KEY POINTS

Heat associated with muscle shortening has been repeatedly demonstrated in skeletal muscle, but its existence in cardiac muscle remains contentious after five decades of study. By iterating between experiments and computational modelling, we show compelling evidence for the existence of shortening heat in cardiac muscle and reveal, mechanistically, the source of this excess heat. Our results clarify a long-standing uncertainty in the field of cardiac muscle energetics. We provide a revised partitioning of cardiac muscle energy expenditure to include this newly revealed thermal component.

ABSTRACT

When a muscle shortens against an afterload, the heat that it liberates is greater than that produced by the same muscle contracting isometrically at the same level of force. This excess heat is defined as 'shortening heat', and has been repeatedly demonstrated in skeletal muscle but not in cardiac muscle. Given the micro-structural similarities between these two muscle types, and since we imagine that shortening heat is the thermal accompaniment of cross-bridge cycling, we have re-examined this issue. Using our flow-through microcalorimeter, we measured force and heat generated by isolated rat trabeculae undergoing isometric contractions at different muscle lengths and work-loop (shortening) contractions at different afterloads. We simulated these experimental protocols using a thermodynamically constrained model of cross-bridge cycling and probed the mechanisms underpinning shortening heat. Predictions generated by the model were subsequently validated by a further set of experiments. Both our experimental and modelling results show convincing evidence for the existence of shortening heat in cardiac muscle. Its magnitude is inversely related to the afterload or, equivalently, directly related to the extent of shortening. Computational simulations reveal that the heat of shortening arises from the cycling of cross-bridges, and that the rate of ATP hydrolysis is more sensitive to change of muscle length than to change of afterload. Our results clarify a long-standing uncertainty in the field of cardiac muscle energetics.