Abstract
Based on A. V. Hill's three-component model, mechanical properties of the contractile element (CE), such as velocity and tension, were determined as muscle shortening and loads in quick-release or afterloaded isotonic contraction. The method is applicable for studying cardiac mechanics, to obtain force-velocity data of the same CE length at varous afterloads.
Analysis of the energetics of cardiac muscle was based on simulation studies of cardiac mechanics (Wong 1971, 1972). By proper derivation, the conventional contractile element work (CEW) was found to be a minor energy determinant. The tension-time integral and tension-independent heat (Ricchiuti and Gibbs, 1965) represent energy utilization for activation and maintenance of tension, the primary energy determinant.
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Literature
Antic, R., L. J. Hirsch and L. N. Katz. 1965. “The Factors Controlling Myocardial Oxygen Consumption per Stroke per Minute.”Acta Cardiol.,20, 309–323.
Badeer, H. S. 1963. “Relative Influence of Heart Rate and Arterial Pressure on Myocardial Oxygen Uptake.” —Ibid.,18, 356–365.
Brady, A. J. 1965. “Time and Displacement Dependence of Cardiac Contractility: Problems in Defining the Active State and Force-Velocity Relations.”Fedn. Proc.,24, 1410–1420.
—. 1966. “Onset of Contractility in Cardiac Muscle.”J. Physiol.,184, 560–580.
— 1968. “Active State in Cardiac Muscle.”Physiol. Rev.,48, 570–600.
Britman, N. A. and H. J. Levine. 1964. “Contractile Element Work: A Major Determinant of Myocardial Oxygen Consumption.”J. Clin. Invest.,43, 1397–1408.
Chandler, B. M., E. H. Sonnenblick and P. E. Pool. 1968. “Mechanochemistry of Cardiac Muscle: III. Effects of Norepinephrine on the Utilization of High Energy Phosphates.”Circulation Res.,22, 729–735.
Coleman, H. N. 1967. “Role of Acetylstrophanthidin in Augmenting Myocardial Oxygen Consumption.” —Ibid.,21, 487–495.
— 1968. “Effect of Alterations in Shortening and External Work on Oxygen Consumption of Cat Papillary Muscle.”Am. J. Physiol.,214, 100–106.
— 1971. “Determinants of Myocardial Energy Utilization.” InCardiac Hypertrophy, N. R. Alpert, ed., 485–509. New York: Academic Press.
Covell, J. W., E. Braunwald, J. Ross, Jr. and E. H. Sonnenblick. 1966. “Studies on Digitalis. XVI. Effects on Myocardial Oxygen Consumption.”J. Clin. Invest.,45, 1535–1542.
Edman, K. A. P. and E. Nilsson. 1968. “The Mechanical Parameters of Myocardial Contraction Studied at a Constant Length of the Contractile Element.”Acta Physiol. Scand.,72, 205–219.
Fung, Y. C. 1970. “Mathematical Representation of the Mechanical Properties of the Heart Muscle.”J. Biomechanics,3, 381–404.
— 1971. “Comparison of Different Models of the Heart Muscle.” —Ibid.,4, 289–295.
Gibbs, C. L. 1967. “Role of Catecholamines in Heat Production in the Myocardium.”Circulation Res.,21, Suppl. 111, 223–242.
—, W. F. H. M. Mommaerts and N. V. Ricchiuti. 1967. “Energetics of Cardiac Contractions.”J. Physiol.,191, 25–46.
— and W. R. Gibson. 1969. “Effect of Ouabain on the Energy Output of Rabbit Cardiac Muscle.”Circulation Res.,24, 951–967.
Graham, T. P., Jr, J. Ross, Jr., J. W. Covell, E. H. Sonnenblick and R. L. Clancy. 1967. “Myocardial Oxygen Consumption in Acute Experimental Cardiac Depression.” —Ibid.,21, 123–138.
Gregg, D. E. 1963. The George E. Brown Memorial Lecture: “Physiology of the Coronary Circulation”.Circulation,27, 1128–1137.
Hartree, W. and A. V. Hill. 1921. “The Regulation of the Supply of Energy in Muscular Contraction.”J. Physiol.,55, 133–158.
Hefner, L. L. and T. E. Bowen, Jr. 1967. “Elastic Components of Cat Papillary Muscle.”Am. J. Physiol.,212, 1221–1227.
Hill, A. V. 1950. “Mechanics of the Contractile Element of Muscle.”Nature,166, 415–419.
Jewell, B. R. and D. R. Wilkie. 1958. “Analysis of the Mechanical Components in Frog's Striated Muscle.”J. Physiol.,143, 518–540.
Jewell, B. R. and J. R. Blinks. 1968. “Drugs and the Mechanical Properties of Heart Muscle.”Ann. Rev. Pharmacol.,8, 113–130.
Katz, L. N. and H. Feinberg. 1958. “The Relation of Cardiac Effort to Myocardial Oxygen Consumption and Coronary Flow.”Circulation Res.,6, 656–669.
Krasnow, N., E. L. Rolett, P. M. Yurchak, W. B. Hood, Jr. and R. Gorlin. 1964. “Isoproterenol and Cardiovascular Performance.”Am. J. Med.,37, 514–525.
Lee, K. S. 1960. “The Relationship of the Oxygen Consumption to the Contraction of the Cat Papillary Muscle.”J. Physiol.,151, 186–201
McDonald, R. H., Jr. 1966. “Developed Tension: A Major Determinant of Myocardial Oxygen Consumption.”Am. J. Physiol.,210, 351–356.
—, R. R. Taylor and H. E. Cingolani. 1966. “Measurement of Myocardial Developed Tension and Its Relation to Oxygen Consumption.” —Ibid.,211, 667–673.
Noble, M. I. M., T. E. Bowen and L. L. Hefner. 1969. “Force-Velocity Relationship of Cat Cardiac Muscle, Studied by Isotonic and Quick-Release Techniques.”Circulation Res.,24, 821–833.
Parmley, W. W. and E. H. Sonnenblick. 1967. “Series Elasticity in Heart Muscle: Its Relation to Contractile Element Velocity and Proposed Muscle Models.” —Ibid.,20, 112–123.
Pollack, G. H. 1970. “Maximum Velocity as an Index of Contractility in Cardiac Muscle: A Critical Evaluation.” —Ibid.,26, 111–127.
Pool, P. E. and E. H. Sonnenblick. 1967. “The Mechanochemistry of Cardiac Muscle: I. The Isometric Contraction.”J. Gen. Physiol.,50, 951–965.
—, B. M. Chandler, S. C. Seagren and E. H. Sonnenblick. 1968. “Mechanochemistry of Cardiac Muscle: II. The Isotonic Contraction.”Circulation Res.,22, 465–472.
Ricchiuti, N. V. and C. L. Gibbs. 1965. “Heat Production in a Cardiac Contraction.”Nature,208, 897–898.
Rodbard, S., F. Williams and C. Williams. 1959. “The Spherical Dynamics of the Heart (Myocardial Tension, Oxygen Consumption, Coronary Blood Flow and Efficiency).”Am. Heart J.,57, 348–360.
Sandberg, J. A. and F. D. Carlson. 1966. “The Length Dependance of Phosphorylcreatine Hydrolysis During an Isometric Tetanus.”Biochem. Z. 345, 212–231.
Sarnoff, S. J., E. Braunwald, G. H. Welch, Jr., R. B. Case, W. N. Stainsby and R. Macruz. 1958. “Hemodynamic Determinants of Oxygen Consumption of the Heart with Special References to the Tension-Time Index. “Am. J. Physiol.,192, 148–156.
Sonnenblick, E. H. 1962. “Implications of Muscle Mechanics in the Heart.”Fedn. Proc.,21, 975–990.
—. 1964. “Series Elastic and Contractile Elements in Heart Muscle: Changes in Muscle Length.”Am. J. Physiol.,207, 1330–1338.
—, J. Ross, Jr., J. W. Covell, G. A. Kaiser and E. Braunwald. 1965. “Velocity of Contraction as a Determinant of Myocardial Oxygen Consumption.” —Ibid.,209, 919–927.
— 1967. “Acxtive State in Heat Muscle: Its Delayed Onsest and Modification by Inotropic Agents.”J. Gen. Physiol.,50, 661–676.
— and A. C. Stam, Jr. 1969. “Cardiac Muscle: Activation and Contraction.”Ann. Rev. Physiol.,31, 647–674.
Ullrick, W. C. 1964. “Characteristic Force-Velocity Equation of Rat Heart Muscle.”Am. J. Physiol.,206, 1285–1290.
Whalen, W. J. 1957. “Oxygen Consumption and Tension of Isolated Heart Muscle During Rest and Activity Using a New Technic.”Circulation Res.,5, 556–561.
— 1960. “Some Factors Which Influence the Oxygen Consumption of Isolated Heart Muscle.”Am. J. Physiol.,198, 1153–1156.
Whalen, W. J. 1961. “The Relation of Work and Oxygen Consumption in Isolated Strips of Cat and Rat Myocardium.”J. Physiol.,157, 1–17.
Wong, A. Y. K. 1971. “Mechanics of Cardiac Muscle Based on Huxley's Model: Mathematical Simulation of Isometric Contraction.”J. Biomechanics,4, 529–540.
— 1972. “Mechanics of Cardiac Muscle Based on Huxley's Model: Simulation of Active State and Force-Velocity Relations.” —Ibid.,4, 107–117.
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Wong, A.Y.K. Some proposals in cardiac muscle mechanics and energetics. Bltn Mathcal Biology 35, 375–399 (1973). https://doi.org/10.1007/BF02458344
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DOI: https://doi.org/10.1007/BF02458344