The Role of the Frank–Starling Law in the Transduction of Cellular Work to Whole Organ Pump Function: A Computational Modeling Analysis

We have developed a multi-scale biophysical electromechanics model of the rat left ventricle at room temperature. This model has been applied to investigate the relative roles of cellular scale length dependent regulators of tension generation on the transduction of work from the cell to whole organ pump function. Specifically, the role of the length dependent Ca2+ sensitivity of tension (Ca50), filament overlap tension dependence, velocity dependence of tension, and tension dependent binding of Ca2+ to Troponin C on metrics of efficient transduction of work and stress and strain homogeneity were predicted by performing simulations in the absence of each of these feedback mechanisms. The length dependent Ca50 and the filament overlap, which make up the Frank-Starling Law, were found to be the two dominant regulators of the efficient transduction of work. Analyzing the fiber velocity field in the absence of the Frank-Starling mechanisms showed that the decreased efficiency in the transduction of work in the absence of filament overlap effects was caused by increased post systolic shortening, whereas the decreased efficiency in the absence of length dependent Ca50 was caused by an inversion in the regional distribution of strain.

[1]  Paul M L Janssen,et al.  Measurement of myofilament calcium sensitivity at physiological temperature in intact cardiac trabeculae. , 2006, American journal of physiology. Heart and circulatory physiology.

[2]  B. Roth.  Electrical conductivity values used with the bidomain model of cardiac tissue , 1997, IEEE Transactions on Biomedical Engineering.

[3]  Saleh Saleh,et al.  Active myocyte shortening during the 'isovolumetric relaxation' phase of diastole is responsible for ventricular suction; 'systolic ventricular filling'. , 2006, European journal of cardio-thoracic surgery : official journal of the European Association for Cardio-thoracic Surgery.

[4]  F. Yin,et al.  Ventricular wall stress. , 1981, Circulation research.

[5]  Jeffrey W Holmes,et al.  Energetics of the Frank-Starling effect in rabbit myocardium: economy and efficiency depend on muscle length. , 2002, American journal of physiology. Heart and circulatory physiology.

[6]  G. Aurigemma,et al.  Serial echocardiographic-Doppler assessment of left ventricular geometry and function in rats with pressure-overload hypertrophy. Chronic angiotensin-converting enzyme inhibition attenuates the transition to heart failure. , 1995, Circulation.

[7]  Nikolaos Stergiopulos,et al.  The effect of a myocardial infarction on the normalized time-varying elastance curve. , 2007, Journal of applied physiology.

[8]  Koji Kashihara,et al.  A self-calibrating telemetry system for measurement of ventricular pressure-volume relations in conscious, freely moving rats. , 2004, American journal of physiology. Heart and circulatory physiology.

[9]  F W Prinzen,et al.  Mapping of regional myocardial strain and work during ventricular pacing: experimental study using magnetic resonance imaging tagging. , 1999, Journal of the American College of Cardiology.

[10]  Masashi Komeda,et al.  Estimation of regional left ventricular wall stresses in intact canine hearts. , 1998, American journal of physiology. Heart and circulatory physiology.

[11]  T J Brady,et al.  Myocardial fiber shortening in humans: initial results of MR imaging. , 2000, Radiology.

[12]  Andrew J. Pullan,et al.  A Finite Element Method for an Eikonal Equation Model of Myocardial Excitation Wavefront Propagation , 2002, SIAM J. Appl. Math..

[13]  J. Bogaert,et al.  Regional nonuniformity of normal adult human left ventricle. , 2001, American journal of physiology. Heart and circulatory physiology.

[14]  J. Omens,et al.  Mechanical regulation of myocardial growth during volume-overload hypertrophy in the rat. , 1997, The American journal of physiology.

[15]  Andrew D McCulloch,et al.  Laminar fiber architecture and three-dimensional systolic mechanics in canine ventricular myocardium. , 1999, American journal of physiology. Heart and circulatory physiology.

[16]  J. Covell,et al.  Relation Between Transmural Deformation and Local Myofiber Direction in Canine Left Ventricle , 1988, Circulation research.

[17]  Paul Steendijk,et al.  Right and left ventricular function after chronic pulmonary artery banding in rats assessed with biventricular pressure-volume loops. , 2006, American journal of physiology. Heart and circulatory physiology.

[18]  J. Ulrich.  [Physiology of the heart]. , 1950, Zeitschrift fur Kreislaufforschung.

[19]  Yves Lecarpentier,et al.  Mechanics of Relaxation of the Human Heart. , 2000, News in physiological sciences : an international journal of physiology produced jointly by the International Union of Physiological Sciences and the American Physiological Society.

[20]  F W Prinzen,et al.  Regional fibre stress : fibre strain area as an estimate of regional blood flow and oxygen demand in the canine heart , 2005 .

[21]  Andrew D. McCulloch,et al.  Transmural Distribution of Three-Dimensional Systolic Strains in Stunned Myocardium , 2001, Circulation.

[22]  R. E. Davies,et al.  Chemical and mechanical changes during stretching of activated frog skeletal muscle , 1973 .

[23]  D L Prior,et al.  Load-sensitive measures may overestimate global systolic function in the presence of left ventricular hypertrophy: a comparison with load-insensitive measures. , 2006, American journal of physiology. Heart and circulatory physiology.

[24]  Neil B. Ingels,et al.  Torsional Deformation of the Left Ventricular Midwall in Human Hearts With Intramyocardial Markers: Regional Heterogeneity and Sensitivity to the Inotropic Effects of Abrupt Rate Changes , 1988, Circulation research.

[25]  G M Hutchins,et al.  Relation of regional cross-fiber shortening to wall thickening in the intact heart. Three-dimensional strain analysis by NMR tagging. , 1994, Circulation.

[26]  H Suga,et al.  Total mechanical energy of a ventricle model and cardiac oxygen consumption. , 1979, The American journal of physiology.

[27]  G Cooper,et al.  Correlation of Force‐Length Area With Oxygen Consumption in Ferret Papillary Muscle , 1987, Circulation research.

[28]  R M Heethaar,et al.  Regional timing of myocardial shortening is related to prestretch from atrial contraction: assessment by high temporal resolution MRI tagging in humans. , 2005, American journal of physiology. Heart and circulatory physiology.

[29]  Xiao-Ping Yang,et al.  Increased Systolic Performance With Diastolic Dysfunction in Adult Spontaneously Hypertensive Rats , 2003, Hypertension.

[30]  Y C Fung,et al.  Residual strain in rat left ventricle. , 1990, Circulation research.

[31]  P. Douglas,et al.  Differential cardiac effects of growth hormone and insulin-like growth factor-1 in the rat. A combined in vivo and in vitro evaluation. , 1996, Circulation.

[32]  O. Morel,et al.  Regional assessment of wall curvature and wall stress in left ventricle with magnetic resonance imaging. , 1999, The American journal of physiology.

[33]  P. Hunter,et al.  Laminar structure of the heart: ventricular myocyte arrangement and connective tissue architecture in the dog. , 1995, The American journal of physiology.

[34]  H Suga,et al.  Oxygen-saving effect of negative work in dog left ventricle. , 1988, The American journal of physiology.

[35]  Denis Chemla,et al.  Validation of echocardiographic and Doppler indexes of left ventricular relaxation in adult hypertensive and normotensive rats. , 2005, American journal of physiology. Heart and circulatory physiology.

[36]  N B Ingels,et al.  Regional epicardial and endocardial two-dimensional finite deformations in canine left ventricle. , 1991, The American journal of physiology.

[37]  W. Giles,et al.  A mathematical model of action potential heterogeneity in adult rat left ventricular myocytes. , 2001, Biophysical journal.

[38]  P. Hunter,et al.  Laminar structure of the heart: a mathematical model. , 1997, The American journal of physiology.

[39]  P. Hunter,et al.  Modelling the mechanical properties of cardiac muscle. , 1998, Progress in biophysics and molecular biology.

[40]  P. Hunter,et al.  A Deformable Finite Element Derived Finite Difference Method for Cardiac Activation Problems , 2003, Annals of Biomedical Engineering.

[41]  J D Humphrey,et al.  Constitutive Relations and Finite Deformations of Passive Cardiac Tissue II: Stress Analysis in the Left Ventricle , 1989, Circulation research.

[42]  F. Rademakers,et al.  Noninvasive measurement of shortening in the fiber and cross-fiber directions in the normal human left ventricle and in idiopathic dilated cardiomyopathy. , 1997, Circulation.

[43]  A. McCulloch,et al.  Comparison of two techniques for measuring two-dimensional strain in rat left ventricles. , 1996, The American journal of physiology.

[44]  H. T. ter Keurs,et al.  Velocity of sarcomere shortening in rat cardiac muscle: relationship to force, sarcomere length, calcium and time. , 1984, The Journal of physiology.

[45]  P. Hunter,et al.  Computational mechanics of the heart : From tissue structure to ventricular function , 2000 .

[46]  Li Li,et al.  Hibernator Citellus undulatus maintains safe cardiac conduction and is protected against tachyarrhythmias during extreme hypothermia: possible role of Cx43 and Cx45 up-regulation. , 2005, Heart rhythm.

[47]  R M Heethaar,et al.  Timing of cardiac contraction in humans mapped by high-temporal-resolution MRI tagging: early onset and late peak of shortening in lateral wall. , 2004, American journal of physiology. Heart and circulatory physiology.

[48]  P. Hunter,et al.  Mathematical model of geometry and fibrous structure of the heart. , 1991, The American journal of physiology.

[49]  A. McCulloch,et al.  Measurement of strain and analysis of stress in resting rat left ventricular myocardium. , 1993, Journal of biomechanics.

[50]  Shigeru Sugano,et al.  Studies on the positive T Wave on ECG in the Rat-Based on the Analysis for Direct Cardiac Electrograms in the Ventricle , 1993 .

[51]  Jeffrey W Holmes,et al.  Candidate mechanical stimuli for hypertrophy during volume overload. , 2004, Journal of applied physiology.

[52]  B. Kirn,et al.  Contraction wave in axial direction in free wall of guinea pig left ventricle. , 2004, American journal of physiology. Heart and circulatory physiology.

[53]  P. Hunter,et al.  Computational Mechanics of the Heart , 2000 .

[54]  D. Kass,et al.  Mechanical dyssynchrony in dilated cardiomyopathy with intraventricular conduction delay as depicted by 3D tagged magnetic resonance imaging. , 2000, Circulation.

[55]  L D Hall,et al.  Magnetic resonance imaging analysis of left ventricular function in normal and spontaneously hypertensive rats , 1998, The Journal of physiology.

[56]  Hiroshi Ashikaga,et al.  Transmural left ventricular mechanics underlying torsional recoil during relaxation. , 2004, American journal of physiology. Heart and circulatory physiology.

[57]  P. Hunter,et al.  A quantitative analysis of cardiac myocyte relaxation: a simulation study. , 2006, Biophysical journal.

[58]  H. E. Keurs,et al.  The Sarcomeric Control of Energy Conversion , 2005, Annals of the New York Academy of Sciences.

[59]  H. T. ter Keurs,et al.  Comparison between the Sarcomere Length‐Force Relations of Intact and Skinned Trabeculae from Rat Right Ventricle: Influence of Calcium Concentrations on These Relations , 1986, Circulation research.

[60]  A. Garnier,et al.  Heart failure: a model of cardiac and skeletal muscle energetic failure , 2006, Pflügers Archiv.

[61]  Sheng-Kwei Song,et al.  Regional ventricular wall thickening reflects changes in cardiac fiber and sheet structure during contraction: quantification with diffusion tensor MRI. , 2005, American journal of physiology. Heart and circulatory physiology.

[62]  E Erdmann,et al.  The failing human heart is unable to use the Frank-Starling mechanism. , 1994, Circulation research.

[63]  A. Huxley,et al.  The variation in isometric tension with sarcomere length in vertebrate muscle fibres , 1966, The Journal of physiology.

[64]  E. Myhre,et al.  Left ventricular dysfunction following rewarming from experimental hypothermia. , 1998, Journal of applied physiology.

[65]  A. Katz,et al.  Homogeneity out of heterogeneity. , 1989, Circulation.

[66]  R N Vaishnav,et al.  Stress distribution in the canine left ventricle during diastole and systole. , 1970, Biophysical journal.

[67]  A D McCulloch,et al.  Effect of residual stress on transmural sarcomere length distributions in rat left ventricle. , 1993, The American journal of physiology.

[68]  S. Niederer,et al.  A mathematical model of the slow force response to stretch in rat ventricular myocytes. , 2007, Biophysical journal.

[69]  Karl A. Tomlinson,et al.  Cardiac Microstructure: Implications for Electrical Propagation and Defibrillation in the Heart , 2002, Circulation research.

[70]  R. Barr,et al.  Current flow patterns in two-dimensional anisotropic bisyncytia with normal and extreme conductivities. , 1984, Biophysical journal.

[71]  A. Tanskanen,et al.  A simplified local control model of calcium-induced calcium release in cardiac ventricular myocytes. , 2004, Biophysical journal.

[72]  C. Stevens,et al.  A Computational Model of Cardiac Electromechanics , 2006, 2006 International Conference of the IEEE Engineering in Medicine and Biology Society.

[73]  S. Niederer,et al.  An improved numerical method for strong coupling of excitation and contraction models in the heart. , 2008, Progress in biophysics and molecular biology.

[74]  P. Hofmann,et al.  Effect of length and cross-bridge attachment on Ca2+ binding to cardiac troponin C. , 1987, The American journal of physiology.

[75]  Frank Langer,et al.  Transmural sheet strains in the lateral wall of the ovine left ventricle. , 2005, American journal of physiology. Heart and circulatory physiology.

[76]  L. E. Malvern.  Introduction to the mechanics of a continuous medium , 1969 .

[77]  Antonio Guill,et al.  Analyzing the electrophysiological effects of local epicardial temperature in experimental studies with isolated hearts , 2008, Physiological measurement.

[78]  Andrew D McCulloch,et al.  Asynchrony of ventricular activation affects magnitude and timing of fiber stretch in late-activated regions of the canine heart. , 2007, American journal of physiology. Heart and circulatory physiology.

[79]  Roy C. P. Kerckhoffs,et al.  Computational Methods for Cardiac Electromechanics , 2006, Proceedings of the IEEE.

[80]  David J. C. Alders,et al.  Assessing heterogeneous distribution of blood flow and metabolism in the heart , 2001, Basic Research in Cardiology.

[81]  W Müller,et al.  Fast optical monitoring of microscopic excitation patterns in cardiac muscle. , 1989, Biophysical journal.

[82]  Theo Arts,et al.  Optimizing ventricular fibers: uniform strain or stress, but not ATP consumption, leads to high efficiency. , 2002, American journal of physiology. Heart and circulatory physiology.

[83]  Andrew D McCulloch,et al.  Glycated collagen cross-linking alters cardiac mechanics in volume-overload hypertrophy. , 2003, American journal of physiology. Heart and circulatory physiology.

[84]  J. Seward,et al.  Apex-to-base dispersion in regional timing of left ventricular shortening and lengthening. , 2006, Journal of the American College of Cardiology.

[85]  E. Marbán,et al.  Myofilament Ca2+ sensitivity in intact versus skinned rat ventricular muscle. , 1994, Circulation research.

[86]  E. Leifer,et al.  Transmural dispersion of myofiber mechanics: implications for electrical heterogeneity in vivo. , 2006, Journal of the American College of Cardiology.