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.

Uncovering cross-bridge properties that underlie the cardiac active complex modulus using model linearisation techniques.

The properties underlying cardiac cross-bridge kinetics can be characterised by a muscle's active complex modulus. While the complex modulus can be described by a series of linear transfer functions, the biophysical mechanisms underlying these components are represented inconsistently among existing cross-bridge models. To address this, we examined the properties commonly implemented in cross-bridge models using model linearisation techniques and assessed their contributions to the complex modulus. From this analysis, we developed a biophysical model of cross-bridge kinetics that captures the three components of the active complex modulus: (1) the elastic modulus at low frequencies that arises from allowing the proportion of cross-bridges in the post-power stroke state to increase with sarcomere length, (2) the increase in elastic modulus at high frequencies that arises from the dependence of cross-bridge strain on sarcomere velocity, and (3) the negative viscous modulus which signifies the production of work by cross-bridges arises from either a sarcomere length or strain dependence, or both, on the rate of change of cross-bridge proportion in the post-power stroke state. While a model that includes all these features can theoretically reproduce the cardiac complex modulus, analysis of their transfer functions reveals that the relative contributions of these components are often not taken into account. As a result, the negative viscous component that signifies work production is not visible because the complex modulus is dominated by the effects of sarcomere velocity on cross-bridge strain.

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.

Slower shortening kinetics of cardiac muscle performing Windkessel work-loops increase 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.NEW & NOTEWORTHY Cardiac muscle samples were allowed to describe their natural shortening dynamics while performing force-length work and liberating heat. The muscle shortened more slowly and produced greater force and work output against a time-varying "Windkessel" load than during conventional constant-force shortening, thereby yielding greater mechanical efficiency. A key finding is that the slower shortening kinetics developed in the face of a time-varying load enhances the mechanical efficiency of cardiac muscle during work-loop contractions.

Cross-bridge 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.

Heat production in quiescent cardiac muscle is length, velocity and muscle dependent: Implications for active heat measurement.

NEW FINDINGS: What is the central question of this study? Intracellular energetic processes in quiescent cardiac muscle release 'basal' heat; during contraction, a much larger amount of 'active' heat is also produced. Previously, measurement challenges have constrained researchers to assume that basal heat rate remains constant during contraction and shortening. Is this assumption correct? What is the main finding and its importance? We show that basal heat rate is modulated by the extent and velocity of muscle shortening. Their relative contributions are muscle specific. We apply a method with which researchers can now disentangle, for each experiment, changes in basal heat from active heat production, providing more precise measures of the individual energetic processes underlying cardiac muscle contraction. ABSTRACT: Separating the variations in cardiac basal heat rate from variations in active heat rate is necessary to determine cardiac muscle energy consumption accurately during the performance of active work. By developing a model of cardiac muscle basal heat rate, we aimed to investigate changes in basal heat rate when cardiac muscle performs work. Experiments were conducted on 10 isolated rat cardiac trabeculae subjected to both active (work-loops) and quiescent (length-change and velocity) interventions. Muscle force, length and heat output rate were measured simultaneously in a flow-through work-loop calorimeter. Quiescent muscle characteristics were used to parameterize muscle-specific models of change in basal heat rate, thereby to predict dynamic changes in basal heat rate during active work-loop contraction. Our data showed that the quiescent heat characteristics of cardiac muscle varied between samples, displaying dependence on both the extent and the rate of change in muscle length. We found a moderate correlation between muscle dimensions (cross-sectional area and volume) and the length-dependent basal heat parameter (P = 0.0330 and P = 0.0242, respectively), but no correlation with the velocity-dependent parameter. These findings lead us to conclude that the heat output of cardiac muscle at quiescence varies with both the extent and the velocity of shortening, to an extent that is muscle specific, and that this variation must be measured and accounted for in each specimen when assessing active energetics.

Right-sided heart failure is also associated with transverse tubule remodeling in the left ventricle.

Right-sided heart failure is a common consequence of pulmonary arterial hypertension. Overloading the right ventricle results in right ventricular hypertrophy, which progresses to failure in a process characterized by impaired Ca2+ dynamics and force production that is linked with transverse (t)-tubule remodeling. This also unloads the left ventricle, which consequently atrophies. Experimental left-ventricular unloading can result in t-tubule remodeling, but it is currently unclear if this occurs in right-sided heart failure. In this work, we used a model of monocrotaline (MCT)-induced right heart failure in male rats, using confocal microscopy to investigate cellular remodeling of t-tubules, junctophilin-2 (JPH2), and ryanodine receptor-2 (RyR2). We examined remodeling across tissue anatomical regions of both ventricles: in trabeculae, papillary muscles, and free walls. Our analyses revealed that MCT hearts demonstrated a significant loss of t-tubule periodicity, disruption of the normal sarcomere striated pattern with JPH2 labeling, and also a disorganized striated pattern of RyR2, a feature not previously reported in right heart failure. Remodeling of JPH2 and RyR2 in the MCT heart was more pronounced in papillary muscles and trabeculae compared with free walls, particularly in the left ventricle. We find that these structures, commonly used as ex vivo muscle preparations, are more sensitive to the disease process.NEW & NOTEWORTHY In this work, we demonstrate that t-tubule remodeling occurs in the atrophied left ventricle as well as the overloaded right ventricle after right-side heart failure. Moreover, we identify that t-tubule remodeling in both ventricles is linked to sarcoplasmic reticulum remodeling as indicated by decreased labeling periodicity of both the Ca2+ release channel, RyR2, and the cardiac junction-forming protein, JPH2, that forms a link between the sarcoplasmic reticulum and sarcolemma. Studies developing treatments for right-sided heart failure should consider effects on both the right and left ventricle.

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.

Thermodynamic inconsistency disproves the Suga-Sagawa theory of cardiac energetics.

The theory proposed by Suga and Sagawa, encompassing the concepts of 'time-varying elastance', 'pressure-volume area' and 'isoefficiency', has been widely applied in cardiac research - albeit not without contention. In this Review, we commence with a brief history of striated muscle energetics as a prelude to re-visiting the Suga-Sagawa Theory. We conclude our discussion by including recent insights into the fundamental flaw underlying the metabolic component of the Theory.

Re-visiting the Frank-Starling nexus.

Well over a century ago, Otto Frank, working at Carl Ludwig's Institute of Physiology in Munich, studying the isolated, blood-perfused, frog heart preparation, demonstrated that there are two distinct pressure-volume relations in the heart: one for isovolumic twitches and a second (located inferiorly) for afterloaded twitches. Whereas Starling, working at UCL two decades later, referenced Frank's publication (to the extent of re-printing its seminal Figure), he appeared not to have tested Frank's finding. Hence, he remained silent with respect to Franks' contention that cardiac pressure-volume relations are contraction-mode-dependent. Instead, he concluded that "The energy of contraction, however measured, is a function of the length of the muscle fibre" - a conclusion that has become known (at least in the English-speaking world) as 'Starling's Law of the Heart'. This provides us with at least three conundra: (i) why did Starling present only one pressure-volume relation whereas Frank had previously found two, (ii) why, then, do we speak of The Frank-Starling relation, and (iii) how did Frank become largely forgotten for twelve decades among English speakers? This review will attempt to address and comment on these conundra.

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.

Perspective - life and death of a photon: an intuitive non-equilibrium thermodynamic distinction between photochemistry and thermochemistry.

Neither the thermodynamically determined probability isotherm nor its kinetically manifest rate isotherm can be applied to photo-absorptive reactions such that the participants, including photons, may be treated as if they were chemical reactants. Photons and chemical reactants differ from each other fundamentally: firstly, a photon's energy is absolute and, in all instances of practical relevance to the present paper, independent of its surrounding electrochemical field, while the energy of a chemical reactant is relative and defined by its surrounding field; secondly, while both photons and chemical reactants can and do engage in entropy creation, only chemical reactants can engage in entropy exchange. Clarification of these differences requires identification and abandonment of fundamental historical errors in photochemical thought deriving from inappropriate overreach of analogies drawn between light and ideal gases, and including: treatment of photo-absorption as a reversible chemical reaction; attribution to light of thermal potential, or temperature (as distinct from the idealised abstraction of a 'temperature signature'); attribution to light of exchangeable entropy content. We begin by addressing widespread misapprehensions concerning the perennially misunderstood concept of entropy and the frequently overlooked distinction between entropy creation and entropy exchange. Armed with these clarifications, we arrive at a useful perspective for understanding energy absorption and transfer in photosynthetic processes which, through the chemical 'kidnapping' of metastable excited states within structured metabolic pathways, achieves outcomes which the Second Law denies to thermal chemical reactions.

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.

Insights From Computational Modeling Into the Contribution of Mechano-Calcium Feedback on the Cardiac End-Systolic Force-Length Relationship.

In experimental studies on cardiac tissue, the end-systolic force-length relation (ESFLR) has been shown to depend on the mode of contraction: isometric or isotonic. The isometric ESFLR is derived from isometric contractions spanning a range of muscle lengths while the isotonic ESFLR is derived from shortening contractions across a range of afterloads. The ESFLR of isotonic contractions consistently lies below its isometric counterpart. Despite the passing of over a hundred years since the first insight by Otto Frank, the mechanism(s) underlying this protocol-dependent difference in the ESFLR remain incompletely explained. Here, we investigate the role of mechano-calcium feedback in accounting for the difference between these two ESFLRs. Previous studies have compared the dynamics of isotonic contractions to those of a single isometric contraction at a length that produces maximum force, without considering isometric contractions at shorter muscle lengths. We used a mathematical model of cardiac excitation-contraction to simulate isometric and force-length work-loop contractions (the latter being the 1D equivalent of the whole-heart pressure-volume loop), and compared Ca2+ transients produced under equivalent force conditions. We found that the duration of the simulated Ca2+ transient increases with decreasing sarcomere length for isometric contractions, and increases with decreasing afterload for work-loop contractions. At any given force, the Ca2+ transient for an isometric contraction is wider than that during a work-loop contraction. By driving simulated work-loops with wider Ca2+ transients generated from isometric contractions, we show that the duration of muscle shortening was prolonged, thereby shifting the work-loop ESFLR toward the isometric ESFLR. These observations are explained by an increase in the rate of binding of Ca2+ to troponin-C with increasing force. However, the leftward shift of the work-loop ESFLR does not superimpose on the isometric ESFLR, leading us to conclude that while mechano-calcium feedback does indeed contribute to the difference between the two ESFLRs, it does not completely account for it.

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.

Mechanical loading of isolated cardiac muscle with a real-time computed Windkessel model of the vasculature impedance.

To date, the mechanical loads imposed on isolated cardiac muscle tissue in vitro have been oversimplified. Researchers typically applied loads that are time-invariant, resulting in either isometric and auxotonic contractions, or flat-topped (isotonic shortening) work-loops. These contraction types do not fully capture the dynamic response of contracting tissues adapting to a variable load, such as is experienced by ventricular tissue in vivo. In this study, we have successfully developed a loading system that presents a model-based, time-varying, continuously updated, load to cardiac tissue preparations. We combined a Windkessel model of vascular fluid impedance together with Laplace's Law and encoded it in a real-time hardware-based force-length control system. Experiments were carried out on isolated rat left ventricular trabeculae; we directly compare the work-loops arising from this protocol with those of a typical simplified isotonic shortening work-loop system. We found that, under body conditions, cardiac trabeculae achieved greater mechanical work output against our new loading system, than with the simplified isotonic work-loop protocol. We further tested whether loading the tissue with a mechanical impedance defined by "diseased" Windkessel model parameters had an effect on the performance of healthy trabeculae. We found that trabecula shortening decreased when applying the set of Windkessel parameters describing the hypertensive condition, and increased in the hypotensive state. Our implementation of a real-time model of arterial characteristics provides an improved, physiologically derived, instantly calculated load for use in studying isolated cardiac muscle, and is readily applicable to study various disease conditions.

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.

Solving a century-old conundrum underlying cardiac force-length relations.

In the late 19th century, Otto Frank presented a diagram (Frank O. Z Biol 37: 483-526, 1899) showing that cardiac end-systolic pressure-volume relations are dependent on the mode of contraction: one for isovolumic contractions that locate above that for afterloaded ejecting contractions. Conflicting results to Frank's have been subsequently demonstrated in various species, both within and among preparations, ranging from the whole hearts to single myocytes, showing a single pressure-volume or force-length relation that is independent of the mode of contraction. Numerous explanations for these conflicting results have been proposed but are mutually contradictory and hence unsatisfying. The present study aimed to explore how these conflicting findings can be reconciled. We thus explored the cardiac force-length relation across a wide spectrum of both preloads and afterloads, encompassing the physiological working range. Experiments were performed using isolated ventricular trabeculae at physiological temperature and stimulus frequency. The force-length relation obtained from isometric contractions was indeed located above a family of those obtained from shortening contractions. Low preload conditions rendered the relation contraction mode independent. High afterload conditions also showed a comparable effect. Our exploration allowed us to reveal the loading conditions that can explain the apparent single, contraction mode-independent, force-length relation that is in contrast with that presented by Frank. Resolving this century-old cardiac conundrum highlights the caution that must be taken when using the end-systolic force-length relation to illustrate as well as to understand the concepts of the Frank-Starling law of the heart, "potential energy," and cardiac contractility. NEW & NOTEWORTHY Our exploration of the cardiac force-length relation under wide ranges of preload and afterload has allowed us to reconcile conflicting results in the literature regarding its length dependency. We show that the relation is dependent on the mode of contraction but can appear to be otherwise under certain conditions. This finding highlights the need for caution when using the force-length relation to understand key concepts in cardiac physiology.

The slow force response to stretch: Controversy and contradictions.

When exposed to an abrupt stretch, cardiac muscle exhibits biphasic active force enhancement. The initial, instantaneous, force enhancement is well explained by the Frank-Starling mechanism. However, the cellular mechanisms associated with the second, slower phase remain contentious. This review explores hypotheses regarding this "slow force response" with the intention of clarifying some apparent contradictions in the literature. The review is partitioned into three sections. The first section considers pathways that modify the intracellular calcium handling to address the role of the sarcoplasmic reticulum in the mechanism underlying the slow force response. The second section focuses on extracellular calcium fluxes and explores the identity and contribution of the stretch-activated, non-specific, cation channels as well as signalling cascades associated with G-protein coupled receptors. The final section introduces promising candidates for the mechanosensor(s) responsible for detecting the stretch perturbation.