Energetics of stress production in isolated cardiac trabeculae from the rat

Methods for assessing cardiac myofilament calcium sensitivity

Myofilament calcium (Ca2+) sensitivity is one of several mechanisms by which force production of cardiac muscle is modulated to meet the ever-changing demands placed on the heart. Compromised Ca2+ sensitivity is associated with pathologies, which makes it a parameter of interest for researchers. Ca2+ Sensitivity is the ratio of the association and dissociation rates between troponin C (TnC) and Ca2+. As it is not currently possible to measure these rates in tissue preparations directly, methods have been developed to infer myofilament sensitivity, typically using some combination of force and Ca2+ measurements. The current gold-standard approach constructs a steady-state force-Ca2+ relation by exposing permeabilised muscle samples to a range of Ca2+ concentrations and uses the half-maximal concentration as a proxy for sensitivity. While a valuable method for steady-state investigations, the permeabilisation process makes the method unsuitable when examining dynamic, i.e., twitch-to-twitch, changes in myofilament sensitivity. The ability of the heart to transiently adapt to changes in load is an important consideration when evaluating the impact of disease states. Alternative methods have been proffered, including force-Ca2+ phase loops, potassium contracture, hybrid experimental-modelling and conformation-based fluorophore approaches. This review provides an overview of the mechanisms underlying myofilament Ca2+ sensitivity, summarises existing methods, and explores, with modelling, whether any of them are suited to investigating dynamic changes in sensitivity. We conclude that a method that equips researchers to investigate the transient change of myofilament Ca2+ sensitivity is still needed. We propose that such a method will involve simultaneous measurements of cytosolic Ca2+ and TnC activation in actively twitching muscle and a biophysical model to interpret these data.

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.

Slower shortening kinetics of cardiac muscle performing Windkessel work‑loops increases mechanical efficiency

Conventional experimental methods for studying cardiac muscle in vitro often do not expose the tissue preparations to a mechanical impedance that resembles the in vivo hemodynamic impedance dictated by the arterial system. That is, the afterload in work‑loop contraction is conventionally simplified to be constant throughout muscle shortening, and at a magnitude arbitrarily defined. This conventional afterload does not capture the time‑varying interaction between the left ventricle and the arterial system. We have developed a contraction protocol for isolated tissue experiments that allows the afterload to be described within a Windkessel framework that captures the mechanics of the large arteries. We aim to compare the energy expenditure of cardiac muscle undergoing the two contraction protocols: conventional versus Windkessel loading. Isolated rat left‑ventricular trabeculae were subjected to the two force-length work‑loop contractions. Mechanical work and heat liberation were assessed, and mechanical efficiency quantified, over wide ranges of afterloads or peripheral resistances. Both extent of shortening and heat output were unchanged between protocols, but peak shortening velocity was 39.0 % lower and peak work output was 21.8 % greater when muscles contracted against the Windkessel afterload than against the conventional isotonic afterload. The greater work led to a 25.2 % greater mechanical efficiency. Our findings demonstrate that the mechanoenergetic performance of cardiac muscles in vitro may have been previously constrained by the conventional, arbitrary, loading method. A Windkessel loading protocol, by contrast, unleashes more cardiac muscle mechanoenergetic potential, where the slower shortening increases efficiency in performing mechanical work.

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.

Compensating for changes in heart muscle resting heat production in a microcalorimeter

The heat production of cardiac muscle, determined by calorimetry, can be used as a measure of cardiac metabolism. However, heat produced while a muscle is actively-shortening, thereby performing force-length work, comprises both active and basal metabolic processes. In this paper, we present a method for post-experimental processing of calorimetric measurements of muscle heat production, that uncovers and compensates for the measured basal heat rate during work. In this method, the relationships between muscle length, velocity of length change and muscle heat output are coupled with a simulation of the measurement instrument, providing a model-based estimate of change of measured basal heat while the muscle is performing work. We demonstrate the use of this technique in an experiment conducted on a working cardiac muscle sample. The ability to identify the various components of heat release in these muscles provides useful insight into their mechanical and energetic capabilities.

Energetics Equivalent of the Cardiac Force-Length End-Systolic Zone: Implications for Contractility and Economy of Contraction

We have recently demonstrated the existence of a region on the cardiac mechanics stress-length plane, which we have designated "The cardiac end-systolic zone." The zone is defined as the area on the pressure-volume (or stress-length) plane within which all stress-length contraction profiles reach their end-systolic points. It is enclosed by three boundaries: the isometric end-systolic relation, the work-loop (shortening) end-systolic relation, and the zero-active stress isotonic end-systolic relation. The existence of this zone reflects the contraction-mode dependence of the cardiac end-systolic force-length relations, and has been confirmed in a range of cardiac preparations at the whole-heart, tissue and myocyte levels. This finding has led us to speculate that a comparable zone prevails for cardiac metabolism. Specifically, we hypothesize the existence of an equivalent zone on the energetics plane (heat vs. stress), and that it can be attributed to the recently-revealed heat of shortening in cardiac muscle. To test these hypotheses, we subjected trabeculae to both isometric contractions and work-loop contractions over wide ranges of preloads and afterloads. We found that the heat-stress relations for work-loop contractions were distinct from those of isometric contractions, mirroring the contraction mode-dependence of the stress-length relation. The zone bounded by these contraction-mode dependent heat-stress relations reflects the heat of shortening. Isoproterenol-induced enhancement of contractility led to proportional increases in the zones on both the mechanics and energetics planes, thereby supporting our hypothesis.

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.

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.

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

KEY POINTS

The heat of activation of cardiac muscle reflects the metabolic cost of restoring ionic homeostasis following a contraction. The accuracy of its measurement depends critically on the abolition of crossbridge cycling. We abolished crossbridge activity in isolated rat ventricular trabeculae by use of blebbistatin, an agent that selectively inhibits myosin II ATPase. We found cardiac activation heat to be muscle length independent and to account for 15-20% of total heat production at body temperature. We conclude that it can be accurately estimated at minimal muscle length.

ABSTRACT

Activation heat arises from two sources during the contraction of striated muscle. It reflects the metabolic expenditure associated with Ca²⁺ pumping by the sarcoplasmic reticular Ca²⁺ -ATPase and Ca²⁺ translocation by the Na⁺ /Ca²⁺ exchanger coupled to the Na⁺ ,K⁺ -ATPase. In cardiac preparations, investigators are constrained in estimating its magnitude by reducing muscle length to the point where macroscopic twitch force vanishes. But this experimental protocol has been criticised since, at zero force, the observed heat may be contaminated by residual crossbridge cycling activity. To eliminate this concern, the putative thermal contribution from crossbridge cycling activity must be abolished, at least at minimal muscle length. We achieved this using blebbistatin, a selective inhibitor of myosin II ATPase. Using a microcalorimeter, we measured the force production and heat output, as functions of muscle length, of isolated rat trabeculae from both ventricles contracting isometrically at 5 Hz and at 37°C. In the presence of blebbistatin (15 μmol l^-1 ), active force was zero but heat output remained constant, at all muscle lengths. Activation heat measured in the presence of blebbistatin was not different from that estimated from the intercept of the heat-stress relation in its absence. We thus reached two conclusions. First, activation heat is independent of muscle length. Second, residual crossbridge heat is negligible at zero active force; hence, the intercept of the cardiac heat-force relation provides an estimate of activation heat uncontaminated by crossbridge cycling. Both results resolve long-standing disputes in the literature.

Cardiac muscle energetics: Improved normalisation of heat using optical coherence tomography

Heat liberated from isolated cardiac muscle has been used to inform us of thermo-mechanical processes that occur during a contraction. However, for comparisons between different samples to be useful, the heat output needs to be normalized to volume. We have implemented an optical coherence tomograph (OCT), together with a flow-through calorimeter, to accurately determine both muscle volume and heat in the same measurement chamber. The heat rate for multiple stimulation frequencies were recorded and normalized to the volume captured by the OCT. There was a ~15 % difference in the volume estimated by the OCT compared to the standard 1D approximation, suggesting the need for this imaging system, especially for irregularly shaped muscles.

Cardiac activation heat remains inversely dependent on temperature over the range 27-37°C

The relation between heat output and stress production (force per cross-sectional area) of isolated cardiac tissue is a key metric that provides insight into muscle energetic performance. The heat intercept of the relation, termed "activation heat," reflects the metabolic cost of restoring transmembrane gradients of Na(+) and K(+) following electrical excitation, and myoplasmic Ca(2+) concentration following its release from the sarcoplasmic reticulum. At subphysiological temperatures, activation heat is inversely dependent on temperature. Thus one may presume that activation heat would decrease even further at body temperature. However, this assumption is prima facie inconsistent with a study, using intact hearts, which revealed no apparent change in the combination of activation and basal metabolism between 27 and 37°C. It is thus desired to directly determine the change in activation heat between 27 and 37°C. In this study, we use our recently constructed high-thermal resolution muscle calorimeter to determine the first heat-stress relation of isolated cardiac muscle at 37°C. We compare the relation at 37°C to that at 27°C to examine whether the inverse temperature dependence of activation heat, observed under hypothermic conditions, prevails at body temperature. Our results show that activation heat was reduced (from 3.5 ± 0.3 to 2.3 ± 0.3 kJ/m(3)) at the higher temperature. This leads us to conclude that activation metabolism continues to decline as temperature is increased from hypothermia to normothermia and allows us to comment on results obtained from the intact heart by previous investigators.

Muscle heat: a window into the thermodynamics of a molecular machine

The contraction of muscle is characterized by the development of force and movement (mechanics) together with the generation of heat (metabolism). Heat represents that component of the enthalpy of ATP hydrolysis that is not captured by the microscopic machinery of the cell for the performance of work. It arises from two conceptually and temporally distinct sources: initial metabolism and recovery metabolism. Initial metabolism comprises the hydrolysis of ATP and its rapid regeneration by hydrolysis of phosphocreatine (PCr) in the processes underlying excitation-contraction coupling and subsequent cross-bridge cycling and sliding of the contractile filaments. Recovery metabolism describes those process, both aerobic (mitochondrial) and anaerobic (cytoplasmic), that produce ATP, thereby allowing the regeneration of PCr from its hydrolysis products. An equivalent partitioning of muscle heat production is often invoked by muscle physiologists. In this formulation, total enthalpy expenditure is separated into external mechanical work (W) and heat (Q). Heat is again partitioned into three conceptually distinct components: basal, activation, and force dependent. In the following mini-review, we trace the development of these ideas in parallel with the development of measurement techniques for separating the various thermal components.

A high-resolution thermoelectric module-based calorimeter for measuring the energetics of isolated ventricular trabeculae at body temperature

Isolated ventricular trabeculae are the most common experimental preparations used in the study of cardiac energetics. However, the experiments have been conducted at subphysiological temperatures. We have overcome this limitation by designing and constructing a novel calorimeter with sufficiently high thermal resolution for simultaneously measuring the heat output and force production of isolated, contracting, ventricular trabeculae at body temperature. This development was largely motivated by the need to better understand cardiac energetics by performing such measurements at body temperature to relate tissue performance to whole heart behavior in vivo. Our approach uses solid-state thermoelectric modules, tailored for both temperature sensing and temperature control. The thermoelectric modules have high sensitivity and low noise, which, when coupled with a multilevel temperature control system, enable an exceptionally high temperature resolution with a noise-equivalent power an order of magnitude greater than those of other existing muscle calorimeters. Our system allows us to rapidly and easily change the experimental temperature without disturbing the state of the muscle. Our calorimeter is useful in many experiments that explore the energetics of normal physiology as well as pathophysiology of cardiac muscle.

Multiscale measurement of cardiac energetics

Herein we describe our laboratories' experimental methods for interrogating cardiac energetics at the organ (whole heart), tissue (trabecula) and perforated fibre (mitochondrial) levels. In whole heart and trabecula experiments, we focus on measuring pressure-volume (force-length) work and oxygen consumption (heat production) from which mechanical efficiency is derived. In both preparations (i.e. across scales differing by three orders of magnitude) we find efficiency values of 10%-15%. Mitochondrial experiments invoke a trio of titration protocols to yield information on oxygen consumption, ATP flux, membrane potential, electron leak and reactive oxygen species production, the latter two of which index energy transfer inefficiencies.

Streptozotocin-induced diabetes prolongs twitch duration without affecting the energetics of isolated ventricular trabeculae

BACKGROUND

Diabetes induces numerous electrical, ionic and biochemical defects in the heart. A general feature of diabetic myocardium is its low rate of activity, commonly characterised by prolonged twitch duration. This diabetes-induced mechanical change, however, seems to have no effect on contractile performance (i.e., force production) at the tissue level. Hence, we hypothesise that diabetes has no effect on either myocardial work output or heat production and, consequently, the dependence of myocardial efficiency on afterload of diabetic tissue is the same as that of healthy tissue.

METHODS

We used isolated left ventricular trabeculae (streptozotocin-induced diabetes versus control) as our experimental tissue preparations. We measured a number of indices of mechanical (stress production, twitch duration, extent of shortening, shortening velocity, shortening power, stiffness, and work output) and energetic (heat production, change of enthalpy, and efficiency) performance. We calculated efficiency as the ratio of work output to change of enthalpy (the sum of work and heat).

RESULTS

Consistent with literature results, we showed that peak twitch stress of diabetic tissue was normal despite suffering prolonged duration. We report, for the first time, the effect of diabetes on mechanoenergetic performance. We found that the indices of performance listed above were unaffected by diabetes. Hence, since neither work output nor change of enthalpy was affected, the efficiency-afterload relation of diabetic tissue was unaffected, as hypothesised.

CONCLUSIONS

Diabetes prolongs twitch duration without having an effect on work output or heat production, and hence efficiency, of isolated ventricular trabeculae. Collectively, our results, arising from isolated trabeculae, reconcile the discrepancy between the mechanical performance of the whole heart and its tissues.

Dietary pre-exposure of rats to fish oil does not enhance myocardial efficiency of isolated working hearts or their left ventricular trabeculae

Numerous epidemiological studies, supported by clinical and experimental findings, have suggested beneficial effects of dietary fish or fish oil supplementation on cardiovascular health. One such experimental study showed a profound (100%) increase in myocardial efficiency (i.e. the ratio of work output to metabolic energy input) of the isolated whole heart, achieved by a corresponding decrease in the rate of myocardial oxygen consumption. However, a number of other investigations have returned null results on the latter energetic index. Such conflicting findings have motivated us to undertake a re-examination. To that effect, we investigated the effects of dietary fatty acid supplementation on myocardial mechano-energetics, with our primary focus on cardiac efficiency. We used both isolated hearts and isolated left ventricular trabeculae of rats fed with one of three distinct diets: reference (REF), fish oil-supplemented (FO) or saturated fat-supplemented (SFA). For all three groups, and at both spatial levels, we supplied 10 mm glucose as the exogenous metabolic substrate. In the working heart experiments, we found no difference in the average mechanical efficiency among the three dietary groups: 14.8 ± 1.1% (REF), 13.9 ± 0.6% (FO) and 13.6 ± 0.7% (SFA). Likewise, we observed no difference in peak mechanical efficiency of left ventricular trabeculae among the REF, FO and SFA groups: 13.3 ± 1.4, 11.2 ± 2.2 and 12.5 ± 1.5%, respectively. We conclude that there is no effect of a period of pre-exposure to a diet supplemented with either fish oil or saturated fatty acids on the efficiency of the myocardium at either spatial level: tissue or whole heart.

An investigation into the viability of image processing for the measurement of sarcomere length in isolated cardiac trabeculae

A preliminary investigation was performed into the viability of using frequency domain image processing techniques to determine sarcomere length from bright-field images of isolated cardiac trabecula in real-time. Hardware based data processing was used to compute the average sarcomere length in a cardiac trabecula undergoing stretch. Our technique estimated the increase in mean sarcomere length with increasing muscle length as the trabecula was stretched to and beyond the normal physiological limit of 2.4 µm. The standard error in the mean sarcomere length extracted from each image was typically10 nm.

Interventricular comparison of the energetics of contraction of trabeculae carneae isolated from the rat heart

We compare the energetics of right ventricular and left ventricular trabeculae carneae isolated from rat hearts. Using our work-loop calorimeter, we subjected trabeculae to stress-length work (W), designed to mimic the pressure-volume work of the heart. Simultaneous measurement of heat production (Q) allowed calculation of the accompanying change of enthalpy (H = W + Q). From the mechanical measurements (i.e. stress and change of length), we calculated work, shortening velocity and power. In combination with heat measurements, we calculated activation heat (Q(A)), crossbridge heat (Q(xb)) and two measures of cardiac efficiency: 'mechanical efficiency' ((mech) = W/H) and 'crossbridge efficiency' ((xb) = W/(H - Q(A))). With respect to their left ventricular counterparts, right venticular trabeculae have higher peak shortening velocity, and higher peak mechanical efficiency, but with no difference of stress development, twitch duration, work performance, shortening power or crossbridge efficiency. That is, the 35% greater maximum mechanical efficiency of right venticular than left ventricular trabeculae (13.6 vs. 10.2%) is offset by the greater metabolic cost of activation (Q(A)) in the latter. When corrected for this difference, crossbridge efficiency does not differ between the ventricles.

Myocardial twitch duration and the dependence of oxygen consumption on pressure-volume area: experiments and modelling

We tested the proposition that linear length dependence of twitch duration underlies the well-characterised linear dependence of oxygen consumption (V(O(2)) ) on pressure–volume area (PVA) in the heart. By way of experimental simplification, we reduced the problem from three dimensions to one by substituting cardiac trabeculae for the classically investigated whole-heart. This allowed adoption of stress–length area (SLA) as a surrogate for PVA, and heat as a proxy for V(O(2)) . Heat and stress (force per cross-sectional area), at a range of muscle lengths and at both 1 mM and 2 mM [Ca(2+)](o), were recorded from continuously superfused rat right-ventricular trabeculae undergoing fixed-end contractions. The heat–SLA relations of trabeculae (reported here, for the first time) are linear. Twitch duration increases monotonically (but not strictly linearly) with muscle length. We probed the cellular mechanisms of this phenomenon by determining: (i) the length dependence of the duration of the Ca(2+) transient, (ii) the length dependence of the rate of force redevelopment following a length impulse (an index of Ca(2+) binding to troponin-C), (iii) the effect on the simulated time course of the twitch of progressive deletion of length and Ca(2+)-dependent mechanisms of crossbridge cooperativity, using a detailed mathematical model of the crossbridge cycle, and (iv) the conditions required to achieve these multiple length dependencies, using a greatly simplified model of twitch mechano-energetics. From the results of these four independent investigations, we infer that the linearity of the heat–SLA relation (and, by analogy, the V(O(2))–PVA relation) is remarkably robust in the face of departures from linearity of length-dependent twitch duration.

An innovative work-loop calorimeter for in vitro measurement of the mechanics and energetics of working cardiac trabeculae

We describe a unique work-loop calorimeter with which we can measure, simultaneously, the rate of heat production and force-length work output of isolated cardiac trabeculae. The mechanics of the force-length work-loop contraction mimic those of the pressure-volume work-loops experienced by the heart. Within the measurement chamber of a flow-through microcalorimeter, a trabecula is electrically stimulated to respond, under software control, in one of three modes: fixed-end, isometric, or isotonic. In each mode, software controls the position of a linear motor, with feedback from muscle force, to adjust muscle length in the desired temporal sequence. In the case of a work-loop contraction, the software achieves seamless transitions between phases of length control (isometric contraction, isometric relaxation, and restoration of resting muscle length) and force control (isotonic shortening). The area enclosed by the resulting force-length loop represents the work done by the trabecula. The change of enthalpy expended by the muscle is given by the sum of the work term and the associated amount of evolved heat. With these simultaneous measurements, we provide the first estimation of suprabasal, net mechanical efficiency (ratio of work to change of enthalpy) of mammalian cardiac trabeculae. The maximum efficiency is at the vicinity of 12%.

Radius-dependent decline of performance in isolated cardiac muscle does not reflect inadequacy of diffusive oxygen supply

The study of cardiac energetics commonly involves the use of isolated muscle preparations (papillary muscles or trabeculae carneae). Their contractile performance has been observed to vary inversely with thickness. This inverse dependence has been attributed, almost without exception, to inadequate diffusion of oxygen into the centers of muscles of large diameter. It is thus commonly hypothesized that the radius-dependent diminution of performance reflects the development of an anoxic core. We tested this hypothesis theoretically by solving a modification of the diffusion equation, in which the rate of oxygen consumption is a sigmoidal function of the partial pressure of oxygen. The model demonstrates that sufficiently thick muscles, operating at sufficiently high rates of oxygen demand or sufficiently low ambient partial pressures of oxygen, will indeed show diminished energetic performance, whether indirectly indexed as stress (force per cross-sectional area) development or as the rate of heat production. However, such simulated behavior requires the adoption of extreme parameter values, often differing by an order of magnitude from their experimental equivalents. We thus conclude that the radius-dependent diminution of muscle performance in vitro cannot be attributed entirely to an insufficient supply of oxygen via diffusion.

A work-loop calorimeter for measuring the force-length-heat relationship of working excised cardiac muscle fibers

Isolated cardiac trabeculae are convenient specimens with which to study the properties of cardiac muscle under a variety of controlled conditions in vitro. We have developed an instrument for measuring the mechanical and energetic properties of continuously-superfused cardiac trabeculae. Our instrument is capable of dynamically transitioning between fixed-length, isometric and isotonic modes of control during the time-course of a muscle twitch, allowing us to impart force-length work-loops that mimic the behaviour of cardiac muscle in vivo. Simultaneously, sensitive temperature transducers quantify muscle heat production. The combination of these interventions and measurements yields unique insight into the energetic efficiency of living cardiac muscle.