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

Computational Modelling of Cardiac Trabecula Mechanics

Cardiac trabeculae are thin strips of muscle within the ventricles that can be readily excised and used to investigate contractile mechanics of cardiac muscle. Recently, the Auckland Bioengineering Institute has developed a novel cardiac myometer that simultaneously measures force, length and shape of actively contracting isolated cardiac trabeculae. Here we have developed a muscle-specific computational model based on optical coherence tomography geometric surface data that replicates passive mechanics of trabecula. We hypothesised that the muscle's surface geometry data, in addition to force-length data, would improve the fit between the model simulated mechanics and the experimental data. The trabecula model was optimised using two different objective functions (muscle length or shape) driven by a pressure boundary condition. For both objective functions, there was a region of optimal parameters the optimiser tended towards but, due to the coupling between parameters, the ability to find the true optimal parameters was hindered. Due to the limitations of the data, we found that the addition of surface data did not improve parameter estimation and that using only the force-length data provided sufficient information to produce an optimal fit. References A. Anderson. The Cardiac Myometer: Measuring Matters of the Heart. PhD thesis, University of Auckland, 2016. K. F. Augenstein, Brett R. Cowan, Ian J. LeGrice, Poul M. F. Nielsen, and Alistair A. Young. Method and apparatus for soft tissue material parameter estimation using tissue tagged Magnetic Resonance Imaging. Journal of Biomechanical Engineering, 127(1):148–157, February 2005. C. Bradley, Andy Bowery, Randall Britten, Vincent Budelmann, Oscar Camara, Richard Christie, Andrew Cookson, Alejandro F. Frangi, Thiranja Babarenda Gamage, Thomas Heidlauf, Sebastian Krittian, David Ladd, Caton Little, Kumar Mithraratne, Martyn Nash, David Nickerson, Poul Nielsen, Oyvind Nordbo, Stig Omholt, Ali Pashaei, David Paterson, Vijayaraghavan Rajagopal, Adam Reeve, Oliver Rohrle, Soroush Safaei, Rafael Sebastian, Martin Steghofer, Tim Wu, Ting Yu, Heye Zhang, and Peter Hunter. OpenCMISS: A multi-physics and multi-scale computational infrastructure for the VPH/Physiome project. Progress in Biophysics and Molecular Biology, 107(1):32–47, October 2011. doi:http://dx.doi.org/10.1016/j.pbiomolbio.2011.06.015 M. L. Cheuk, A. J. Anderson, J. C. Han, N. Lippok, F. Vanholsbeeck, B. P. Ruddy, D. S. Loiselle, P. M. F. Nielsen, and A. J. Taberner. Four-Dimensional Imaging of Cardiac Trabeculae Contracting In Vitro Using Gated OCT. IEEE Transactions on Biomedical Engineering, 64(1):218–224, January 2017. doi:http://dx.doi.org/10.1109/TBME.2016.2553154 M. L. Cheuk, N. Lippok, A. W. Dixon, B. P. Ruddy, F. Vanholsbeeck, P. M. F. Nielsen, and A. J. Taberner. Optical coherence tomography imaging of cardiac trabeculae. In 2014 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, pages 182–185, August 2014. doi:http://dx.doi.org/10.1109/EMBC.2014.6943559 J. M Guccione, Andrew D McCulloch, and LK Waldman. Passive material properties of intact ventricular myocardium determined from a cylindrical model. J Biomech Eng, 113(1):42–55, 1991. J. C. Han, Andrew J. Taberner, Robert S. Kirton, Poul M. Nielsen, Nicholas P. Smith, and Denis S. Loiselle. A unique micromechanocalorimeter for simultaneous measurement of heat rate and force production of cardiac trabeculae carneae. Journal of Applied Physiology, 107(3):946–951, September 2009. doi:http://dx.doi.org/10.1152/japplphysiol.00549.2009 M. P. Nash and P. J. Hunter. Regional mechanics of the beating heart. In Cardiac Perfusion and Pumping Engineering, volume Volume 1 of Clinically-Oriented Biomedical Engineering, pages 83–127. WORLD SCIENTIFIC, July 2007. doi:http://dx.doi.org/10.1142/9789812775597_0004 J. H. Omens, D. A. MacKenna, and A. D. McCulloch. Measurement of strain and analysis of stress in resting rat left ventricular myocardium. Journal of Biomechanics, 26(6):665–676, June 1993. doi:http://dx.doi.org/10.1016/0021-9290(93)90030-I V. Y. Wang, H. I. Lam, Daniel B. Ennis, Brett R. Cowan, Alistair A. Young, and Martyn P. Nash. Modelling passive diastolic mechanics with quantitative MRI of cardiac structure and function. Medical Image Analysis, 13(5):773–784, October 2009. doi:http://dx.doi.org/10.1016/j.media.2009.07.00

The ineluctable constraints of thermodynamics in the aetiology of obesity

We exploit the detail-independence feature of thermodynamics to examine issues related to the development of obesity. We adopt a 'global' approach consistent with focus on the first law of thermodynamics - namely that the metabolic energy provided by dietary foodstuffs has only three possible fates: the performance of work (be it microscopic or macroscopic), the generation of heat, or storage - primarily in the form of adipose tissue. Quantification of the energy expended, in the form of fat metabolised, during selected endurance events, reveals the inherent limitation of over-reliance on exercise as a primary agent of weight loss. This result prompts examination of various (non-exercise based) possibilities of increasing the rate of heat loss. Since these, too, give little cause for optimism, we are obliged to conclude that obesity can be prevented, or weight loss achieved, only if exercise is supplemented by reduction of food intake

The efficiency of muscle contraction

When a muscle contracts and shortens against a load, it performs work. The performance of work is fuelled by the expenditure of metabolic energy, more properly quantified as enthalpy (i.e., heat plus work). The ratio of work performed to enthalpy produced provides one measure of efficiency. However, if the primary interest is in the efficiency of the actomyosin cross-bridges, then the metabolic overheads associated with basal metabolism and excitation-contraction coupling, together with those of subsequent metabolic recovery process, must be subtracted from the total heat and work observed. By comparing the cross-bridge work component of the remainder to the Gibbs free energy of hydrolysis of ATP, a measure of thermodynamic efficiency is achieved. We describe and quantify this partitioning process, providing estimates of the efficiencies of selected steps, while discussing the errors that can arise in the process of quantification. The dependence of efficiency on animal species, fibre-type, temperature, and contractile velocity is considered. The effect of contractile velocity on energetics is further examined using a two-state, Huxley-style, mathematical model of cross-bridge cycling that incorporates filament compliance. Simulations suggest only a modest effect of filament compliance on peak efficiency, but progressively larger gains (vis-a-vis the rigid filament case) as contractile velocity approaches Vmax. This effect is attributed primarily to a reduction in the component of energy loss arising from detachment of cross-bridge heads at non-zero strain

A thermodynamic model of the cardiac sarcoplasmic/endoplasmic Ca(2+) (SERCA) pump

We present a biophysically based kinetic model of the cardiac SERCA pump that consolidates a range of experimental data into a consistent and thermodynamically constrained framework. The SERCA model consists of a number of sub-states with partial reactions that are sensitive to Ca(2+) and pH, and to the metabolites MgATP, MgADP, and Pi. Optimization of model parameters to fit experimental data favors a fully cooperative Ca(2+)-binding mechanism and predicts a Ca(2+)/H(+) counter-transport stoichiometry of 2. Moreover, the order of binding of the partial reactions, particularly the binding of MgATP, proves to be a strong determinant of the ability of the model to fit the data. A thermodynamic investigation of the model indicates that the binding of MgATP has a large inhibitory effect on the maximal reverse rate of the pump. The model is suitable for integrating into whole-cell models of cardiac electrophysiology and Ca(2+) dynamics to simulate the effects on the cell of compromised metabolism arising in ischemia and hypoxia

Reduced contraction strength with increased intracellular [Ca2+] in left ventricular trabeculae from failing rat hearts

Intracellular calcium ([Ca2+](i)) and isometric force were measured in left ventricular (LV) trabeculae from spontaneously hypertensive rats (SHR) with failing hearts and normotensive Wistar-Kyoto (WKY) controls. At a physiological stimulation frequency (5 Hz), and at 37 degrees C, the peak stress of SHR trabeculae was significantly (P <or = 0.05) reduced compared to WKY (8 +/- 1 mN mm(-2) (n = 8) vs. 21 +/- 5 mN mm(-2) (n = 8), respectively). No differences between strains in either the time-to-peak stress, or the time from peak to 50 % relaxation were detected. Measurements using fura-2 showed that in the SHR both the peak of the Ca2+ transient and the resting [Ca2+](i) were increased compared to WKY (peak: 0.69 +/- 0.08 vs. 0.51 +/- 0.08 microM(P <or = 0.1) and resting: 0.19 +/- 0.02 vs. 0.09 +/- 0.02 microM(P <or = 0.05), SHR vs. WKY, respectively). The decay of the Ca2+ transient was prolonged in SHR, with time constants of: 0.063 +/- 0.002 vs. 0.052 +/- 0.003 s (SHR vs. WKY, respectively). Similar results were obtained at 1 Hz stimulation, and for [Ca2+ ](o) between 0.5 and 5 mM. The decay of the caffeine-evoked Ca2+ transient was slower in SHR (9.8 +/- 0.7 s (n = 8) vs. 7.7 +/- 0.2 s (n = 8) in WKY), but this difference was removed by use of the SL Ca2+ -ATPase inhibitor carboxyeosin. Histological examination of transverse sections showed that the fractional content of perimysial collagen was increased in SHR compared to WKY (18.0 +/- 4.6 % (n = 10) vs. 2.9 +/- 0.9 % (n = 11) SHR vs. WKY, respectively). Our results show that differences in the amplitude and the time course of the Ca2+ transient between SHR and WKY do not explain the reduced contractile performance of SHR myocardium per se. Rather, we suggest that, in this animal model of heart failure, contractile function is compromised by increased collagen, and its three-dimensional organisation, and not by reduced availability of intracellular Ca2+

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