Computational Modeling of Ventricular Mechanics and Energetics

[+] Author and Article Information
Nicolas Smith, Carey Stevens, Peter Hunter

Bioengineering Institute, University of Auckland, Auckland, New Zealand

Appl. Mech. Rev 58(2), 77-90 (Apr 06, 2005) (14 pages) doi:10.1115/1.1859794 History: Online April 06, 2005
Copyright © 2005 by ASME
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Opie, L. H., 1998, The Heart: Physiology, from Cell to Circulation, New York, third, edition, Lippincott-Raven.
Nielsen  P. M. F., Le Grice  I. J., Smaill  B. H., and Hunter  P. J., 1991, “Mathematical Model of Geometry and Fibrous Structure of the Heart,” Am. J. Physiol., 260(29), pp. H1365–H1378.
Stevens C., Remme E., LeGrice I. J., and Hunter P. J., 2002, “Ventricular Mechanics in Disatole: Material Parameter Sensitivity,” J. Biomech., pp. 737–748.
Le Grice  I. J., Smaill  B. H., Chai  L. Z., Edgar  S. G., Gavin  J. B., and Hunter  P. J., 1995, “Laminar Structure of the Heart: Ventricular Myocyte Arrangement and Connective Tissue Architecture in the Dog,” Am. J. Physiol., 269(38), pp. H571–H582.
Beyar  R., and Sideman  S., 1984, “A Computer Study of the Left Ventricular Performance Based on Fiber Structure, Sarcomere Dynamics, and Transmural Electrical Propagation Velocity,” Circ. Res., 55(3), pp. 358–375.
Bovendeerd  P. H. M., Arts  T., Huyghe  J. M., van Campen  D. H., and Reneman  R. S., 1992, “Dependence of Local Left Ventricular Wall Mechanics on Myocardial Fiber Orientation: A Model Study,” J. Biomech., 25(10), pp. 1129–1140.
Bovendeerd  P. H. M., Huyghe  J. M., Arts  T., van Campen  D. H., and Reneman  R. S., 1994, “Influence of Endocardial-Epicardial Crossover of Muscle Fibers on Left Ventricular Wall Mechanics,” J. Biomech., 27(7), pp. 941–951.
Guccione, J. M., and McCulloch, A. D., 1991, “Finite Element Modeling of Ventricular Mechanics,” edited by L. Glass, P. J. Hunter, and A. D. McCulloch, Theory of Heart: Biomechanics, Biophysics, and Nonlinear Dynamics of Cardiac Function, Springer, New York, pp. 121–124.
Arts  T., Veenstra  P. C., and Reneman  R. S., 1982, “Epicardial Deformation and Left Ventricular Wall Mechanics During Ejection in the Dog,” Am. J. Physiol., 243(12), pp. H379–H390.
Rijcken  J., Bovendeerd  P. H., Schoofs  A. J., van Campen  D. H., and Arts  T., 1997, “Optimization of Cardiac Fiber Orientation for Homogeneous Fiber Strain at Beginning of Ejection,” J. Biomech., 30(10), pp. 1041–1049.
Vendelin  M., Bovendeerd  P. H., Engelbrecht  J., and Arts  T., 2002, “Optimizing Ventricular Fibers: Uniform Strain or Stress, but Not ATP Consumption, Leads to High Efficiency,” Am. J. Physiol., 283(3), pp. H1072–H1081.
Vetter  F. J., and McCulloch  A. D., 2000, “Three-Dimensional Stress and Strain in Passive Rabbit Left Ventricle: A Model Study,” Ann. Biomed. Eng., 28(7), pp. 781–792.
Nash  M. P., and Hunter  P. J., 2000, “Compuatational Mechanics of the Heart,” J. Elast., 61, pp. 112–141.
Omens  J. H., May  K. D., and McCulloch  A. D., 1991, “Transmural Distribution of Three-Dimensional Strain in the Isolated Arrested Canine Left Ventricle,” Am. J. Physiol., 261(30), pp. H918–H928.
Waldman  L. K., Fung  Y. C., and Covell  J. W., 1985, “Transmural Myocardial Deformation in the Canine Left Ventricle: Normal In Vivo Three-Dimensional Finite Strains,” Circ. Res., 57(1), pp. 152–163.
Waldman  L. K., Nossan  D., Villareal  F., and Covell  J. W., 1988, “Relation Between Transmural Deformation and Local Myofiber Direction in the Canine Left Ventricle,” Circ. Res., 63, pp. 550–562.
Huyghe  J. M., van Campen  D. H., Arts  T., and Heethaar  R. M., 1991, “A Two-Phase Finite Element Model of the Diastolic Left Ventricle,” J. Biomech., 24(7), pp. 527–538.
Yang  M., and Taber  L. A., 1991, “The Possible Role of Poroelasticity in the Apparent Viscoelastic Behavior of Passive Cardiac Muscle,” J. Biomech., 24(7), pp. 587–597.
Smaill, B. H., and Hunter, P. J., 1991, “Structure and Function of the Diastolic Heart: Material Properties of Passive Myocardium,” edited by L. Glass, P. J. Hunter, and A. D. McCulloch, Theory of Heart: Biomechanics, Biophysics, and Nonlinear Dynamics of Cardiac Function, Springer, New York, pp. 1–29.
MacKenna  D. A., Omens  J. H., and Covell  J. W., 1996, “Left Ventricular Perimysial Collagen Fibers Uncoil Rather Than Stretch During Diastolic Filling,” Basic Res. Cardiol., 91(2), pp. 111–122.
Dokos  S., Smaill  B. H., Young  A. A., and LeGrice  I. J., 2002, “Shear Properties of Passive Ventricular Myocardium,” Am. J. Physiol., 283(6), pp. H2650–2659.
Dokos  S., LeGrice  I. J., Smaill  B. H., Kar  J., and Young  A. A., 2000, “A Triaxial-Measurement Shear-Test Device for Soft Biological Tissues,” J. Biomech., 122(5), pp. 471–478.
Guccione  J. M., McCulloch  A. D., and Waldman  L. K., 1991, “Passive Material Properties of Intact Ventricular Myocardium Determined From a Cylindrical Model,” ASME J. Biomech. Eng., 113, pp. 42–55.
Emery J. L., Omens J. H., and McCulloch A. D., 1997, “Biaxial Mechanics of the Passively Overstretched Left Ventricle,” Am. J. Physiol., pp. 2299–2305.
Usyk  T. P., Mazhari  R., and McCulloch  A. D., 2000, “Effect of Laminar Orthotropic Myofiber Architecture on Regional Stress and Strain in the Canine Left Ventricle,” J. Elast., 61, pp. 143–164.
Usyk  T. P., LeGrice  I. J., and McCulloch  A. D., 2002, “Computational Model of Three-Dimensional Cardiac Electromechanics,” Comput. Visual Sci.,4, pp. 249–257.
Hunter  P. J., Smaill  B. H., and Hunter  I. W., 1995, “A ‘Pole-Zero’ Constitutive Law for Myocardium,” ASME J. Biomech. Eng., 382, pp. 303–18.
Demer  L. L., and Yin  F. C. P., 1983, “Passive Biaxial Mechanical Properties of Isolated Canine Myocardium,” J. Physiol. (London), 339, pp. 615–630.
Yin  F. C. P., Strumpf  R. K., Chew  P. H., and Zeger  S. L., 1987, “Quantification of the Mechanical Properties of Noncontracting Canine Myocardium Under Simultaneous Biaxial Loading,” J. Biomech., 20, pp. 577–589.
Humphrey  J. D., Strumpf  R. K., and Yin  F. C. P., 1990, “Determination of a Constitutive Relation for Passive Myocardium: I. A New Functional Form,” ASME J. Biomech. Eng., 112, pp. 333–339.
Novak  V. P., Yin  F. C. P., and Humphrey  J. D., 1994, “Regional Mechanical Properties of Passive Myocardium,” J. Biomech., 27(4), pp. 403–412.
Nevo  E., and Lanir  Y., 1994, “The Effect of Residual Strain on the Diastolic Function of the Left Ventricle as Predicted by a Structural Model,” J. Biomech., 27(12), pp. 1433–1446.
Costa  K. D., May-Newman  K., Farr  D., O’Dell  W. G., McCulloch  A. D., and Omens  J. H., 1997, “Three-Dimensional Residual Strain in Midanterior Canine Left Ventricle,” Am. J. Physiol., 273, pp. H1968–H1976.
Omens  J. H., McCulloch  A. D., and Criscione  J. C., 2003, “Complex Distributions of Residual Stress and Strain in the Mouse Left Ventricle: Experimental and Theoretical Models,” Biomechan. Modeling Mechanobiolog,1(4), pp. 267–277.
Rodriguez  E. K., Hoger  A., and McCulloch  A. D., 1994, “Stress-Dependent Finite Growth in Soft Elastic Tissues,” J. Biomech., 27(4), pp. 455–467.
Hill  A. V., 1938, “Time Heart of Shortening and the Dynamic Constants of Muscle,” Proc. R. Soc. London, Ser. B, 126, pp. 136–195.
Huxley  A. F., 1957, “Muscle Structure and Theories of Contraction,” Prog. Biophys. Biophys. Chem., 7, pp. 255–318.
Wong  A. Y. K., 1972, “Mechanics of Cardiac Muscle Based on Huxley’s Model: Mathematical Simulation of Isometric Contraction,” J. Biomech., 4, pp. 520–540.
Tözeren  A., 1985, “Continuum Rheology of Muscle Contraction and Its Application to Cardiac Contractility,” Biophys. J., 47, pp. 303–309.
Pinto  J. G., 1987, “A Constitutive Description of Contracting Papillary Muscle and Its Implications to the Dynamics of the Heart,” ASME J. Biomech. Eng., 109, pp. 181–191.
ter Keurs  H. E. D. J., Rijnsburger  W. H., van Heuningen  R., and Nagelsmit  M. J., 1980b, “Tension Development and Sarcomere Length in Rat Cardiac Trabeculae: Evidence of Length-Dependent Activation,” Circ. Res., 46(5), pp. 703–714.
ter Keurs  H. E. D. J., Rijnsburger  W. H., and van Heuningen  R., 1980a, “Restoring Forces and Relaxation of Rat Cardiac Muscle,” Eur. Heart J., 1, pp. 67–80.
Rice  J. J., Jafri  M. S., and Winslow  R. L., 2000, “Modeling Short-Term Interval-Force Relations in Cardiac Muscle,” Am. J. Physiol., 278, pp. H913–H931.
Hunter  P. J., McCulloch  A. D., and ter Keurs  H. E. D. J., 1998, “Modeling the Mechanical Properties of Cardiac Muscle,” Prog. Biophys. Mol. Biol., 69, pp. 289–331.
Guz, A., Bergel, D. H., and Brutsaert, D. L., 1974, The Physiological Basis of Starling’s Law of the Heart, Elsevier, New York.
Hill T. L., 1975, “Theoretical Formalism for the Sliding Filament Model of Contraction of Striated Muscle, Part II,” Prog. Biophys. Mol. Biol., pp. 105–159.
Smith  D. A., 1998, “A Strain-Dependent Ratchet Model of [Phosphate]- and [ATP]-Dependent Muscle Contraction,” J. Muscle Res. Cell Motil., 19, pp. 189–211.
Piazzesi  G., and Lombardi  V., 1995, “A Cross-Bridge Model That is Able to Explain Mechanical and Energetic Properties of Shortening Muscle,” Biophys. J., 68(5), pp. 1966–1979.
Zahalak  G. I., 1981, “A Distribution-Moment Approximation for Kinetic Theories of Muscular Contraction,” Math. Biosci., 55, pp. 89–114.
Zahalak  G. I., and Ma  S.-P., 1990, “Muscle Activation and Contraction: Constitutive Relations Based Directly on Cross-Bridge Kinetics,” ASME J. Biomech. Eng., 112, pp. 52–62.
Guccione  J. M., Motabarzadeh  I., and Zahalak  G. I., 1998, “A Distribution-Moment Model of Deactivation in Cardiac Muscle,” J. Biomech., 31(11), pp. 1069–73.
Bergel, D. A., and Hunter, P. J., 1979, “The Mechanics of the Heart,” edited by N. H. C. Hwang, D. R. Gross, and D. J. Patel, Quantitative Cardiovascular Studies, Clinical and Research Applications of Engineering Principles, University Park Press, Baltimore, Chap. 4, pp. 151–213.
Hunter, P. J., 1995, “Myocardial Constitutive Laws for Continuum Mechanics Models of the Heart,” edited by S. Sideman and R. Beyar, Molecular and Subcellular Cardiology: Effects of Structure and Function, Plenum, New York, Chap. 30, pp. 303–318.
Kawai  M., and W  B. P., 1980, “Sinusoidal Analysis: A High-Resolution Method for Correlating Biochemical Reactions With Physiological Processes in Activated Skeletal Muscles of Rabbit, Frog, and Crayfish,” J. Muscle Res. Cell Motil., 3, pp. 279–303.
Kawai  M., Zhao  Y., and Halvorson  H., 1993b, “Elementary Steps of Contraction Probed by Sinusoidal Analysis Technique in Rabbit Psoas Fibers,” Circ. Res., 332, pp. 567–580.
Saeki  Y., Kawai  M., and Zhao  Y., 1991, “Comparison of Cross-Bridge Dynamics Between Intact and Skinned Myocardium From Ferret Right Ventricles,” Circ. Res., 68(3), pp. 772–781.
Kawai  M., Saeki  Y., and Zhao  Y., 1993a, “Cross-Bridge Scheme and the Kinetic Constants of Elementary Steps Deduced From Chemically Skinned Papillary and Trabecular Muscles of the Ferret,” Circ. Res., 73, pp. 35–50.
Hunter  P. J., 1974, “Development of a Mathematical Model of the Left Ventricle,” J. Physiol. (London), 241, pp. 87–88.
Hunter  P. J., and Smaill  B. H., 1988, “The Analysis of Cardiac Function: A Continuum Approach,” Prog. Biophys. Mol. Biol., 52, pp. 101–164.
Hunter, P. J., McCulloch, A. D., Nielsen, P. M. F., and Smaill, B. H., 1988, “A Finite Element Model of Passive Ventricular Mechanics,” edited by R. L. Spilker and B. R. Simon, Computational Methods in Bioengineering, ASME, BED, New York, Chap. 9, pp. 387–397.
Hunter, P. J., Nash, M. P., and Sands, G. B., 1997, “Computational Electromechanics of the Heart,” edited by A. V. Panfilov and A. V. Holden, Computational Biology of the Heart, Wiley, West Sussex, England, Chap. 12, pp. 345–407.
Atkin, R. J., and Fox, N., 1980, An Introduction to the Theory of Elasticity, Longman, London.
Malvern, L. E., 1969, Introduction to the Mechanics of a Continuous Medium, Prentice–Hall, Englewood Cliffs, New Jersey.
Zienkiewicz, O. C., and Taylor, R. L., 1994, The Finite Element Method. I. Basic Formulation and Linear Problems, McGraw–Hill, fourth edition, Berkshire, UK.
Oden, J. T., 1972, Finite Elements of Nonlinear Continua, McGraw–Hill, New York.
Bovendeerd  P. H., Arts  T., Delhaas  T., Huyghe  J. M., van Campen  D. H., and RS  R. S. R., 1996, “Regional Wall Mechanics in the Ischemic Left Ventricle: Numerical Modeling and Dog Experiments,” Am. J. Physiol., 270(1), 398–410.
Mazhari  R., and McCulloch  A. D., 2000, “Integrative Models for Understanding the Structural Basis of Regional Mechanical Dysfunction in Ischemic Myocardium,” Ann. Biomed. Eng., 28(8), pp. 979–990.
Mazhari  R., Omens  J. H., Waldman  L. K., and McCulloch  A. D., 1998, “Regional Myocardial Perfusion and Mechanics: A Model-Based Method of Analysis,” Ann. Biomed. Eng., 26(5), pp. 743–755.
Mazhari  R., Covell  J. H. O. J. W., and McCulloch  A. D., 2000, “Structural Basis of Regional Dysfunction in Acutely Ischemic Myocardium,” Cardiovasc. Res., 47(2), pp. 284–293.
Smith  N. P., Pullan  A. J., and Hunter  P. J., 2002, “An Efficient Finite Difference Model of Transient Coronary Blood Flow in the Heart,” SIAM J. Appl. Math.,62, pp. 990–1018.
Ch’en  F. F. T., Vaughan-Jones  R. D., Clark  K., and Noble  D., 1998, “Modeling Myocardial Ischaemia and Reperfusion,” Prog. Biophys. Mol. Biol., 69, pp. 497–515.
Mulquiney  P. J., and Kuchel  P. W., 1997, “Model of the ph Dependence of the Concentrations of Complexes Involving Metabolites, Haemoglobin, and Magnesium Ions in the Human Erythrocyte,” Eur. J. Biochem., 245(1), pp. 71–83.
Bassingthwaighte, J. B., Liebovitch, L. S., and West, B. J., 1994, Fractal Physiology, Oxford University Press, Oxford, U.K.
Wang  C. Y., Bassingthwaighte  J. B., and Weissman  L. J., 1992, “Bifurcating Distributive System Using Monte Carlo Method,” Math. Comput. Modell., 16(3), pp. 91–98.
Beard  D. A., and Bassingthwaighte  J. B., 2000, “The Fractal Nature of Myocardial Blood Flow Emerges From a Whole-Organ Model of Arterial Network,” J. Vasc. Res., 37, pp. 282–296.
Kassab  G. S., Rider  C. A., Tang  N. J., and Fung  Y. C., 1993, “Morphometry of Pig Coronary Arterial Trees,” Am. J. Physiol., 265, pp. H350–H365.
Kassab  G. S., Rider  C. A., Tang  N. J., and Fung  Y. C., 1994b, “Topology and Dimensions of Pig Coronary Capillary Network,” Am. J. Physiol., 267, pp. H319–H325.
Kassab  G. S., Lin  D. H., and Fung  Y. C., 1994a, “Morphometry of Pig Coronary Venous System,” Am. J. Physiol., 267, pp. H2100–H2113.
Kassab  G. S., Berkley  J., and Fung  Y. C., 1997, “Analysis of Pig’s Coronary Arterial Blood Flow With Detailed Anatomical Data,” Ann. Biomed. Eng., 25, pp. 204–217.
Smith  N. P., Pullan  A. J., and Hunter  P. J., 2000, “The Generation of an Anatomically Accurate Geometric Coronary Model,” Ann. Biomed. Eng., 28, pp. 14–25.
Downey  J. M., and Kirk  E. S., 1975, “Inhibition of Coronary Blood Flow by a Vascular Waterfall Mechanism,” Circ. Res., 36, pp. 753–760.
Spaan  J. A. E., Breuls  N. P. W., and Laird  J. D., 1981, “Diastolic-Systolic Coronary Flow Differences are Caused by Intramyocardial Pump Action in the Anesthetised Dog,” Circ. Res., 49, pp. 584–593.
Krams  R., Sipkema  P., and Westerhof  N., 1989, “Varying Elastance Concept May Explain Coronary Systolic Flow Impediment,” Am. J. Physiol., 257, pp. H1471–H1479.
Vis  M. A., Sipkema  P., and Westerhof  N., 1997b, “Modeling Pressure-Flow Relations in Cardiac Muscle in Diastole and Systole,” Am. J. Physiol., 272, pp. H1516–H1526.
Vis  M. A., Bovendeerd  P. H., Sipkema  P., and Westerhof  N., 1997a, “Effect of Ventricular Contraction, Pressure, and Wall Stretch on Vessels at Different Locations in the Wall,” Am. J. Physiol., 272, pp. H2963–H2975.
Huyghe  J. M., Arts  T., van Campen  D. H., and Reneman  R. S., 1992, “Porous Medium Finite Element Model of the Beating Left Ventricle,” Am. J. Physiol., 262(31), pp. H1256–H1267.
Spencer, A. J. M., 1980, Continuum Mechanics, Longman, London.
May-Newman  K., Omens  J. H., Pavelec  R. S., and McCulloch  A. D., 1994, “Three-Dimensional Transmural Mechanical Interaction Between the Coronary Vasculature and Passive Myocardium in the Dog,” Circ. Res., 74(6), pp. 1166.
McCulloch  A. D., Hunter  P. J., and Smaill  B. H., 1992, “Mechanical Effects of Coronary Perfusion in the Passive Canine Left Ventricle,” Am. J. Physiol., 262(31), pp. H523–H530.
Nash, M. P., Sands, G. B., Bullivant, D. P., and Hunter, P. J., 1996, “Modeling the Electromechanics of the Heart,” Electrocardiology ’96: From the Cell to the Body Surface. Procs. of the XXIII Intl. Congr. on Electrocardiology.
Nichols, W. W., and O’Rourke, M. F., 1990, McDonalds Blood Flow in Arteries: Theoretic, Experimental, and Clinical Principles, third edition, Hodder and Stoughton, London, Chap. 4, pp. 85–87.
Bassingthwaighte  J. B., King  R. B., and Roger  S. A., 1989, “Fractal Nature of Regional Myocardial Blood Flow Heterogeneity,” Circ. Res., 65, pp. 578–590.
Eisenberg  E., Hill  T. L., and Chen  Y. D., 1980, “Cross-Bridges Model of Muscle Contraction: Quantitative Analysis,” Biophys. J., 29, pp. 195–227.
Smith  D. A., 1990, “The Theory of Sliding Filament Models for Muscle Contraction III: Dynamics of the Five-State Model,” J. Theor. Biol., 146, pp. 433–466.
Salem  J. E., Saidel  G. M., Stanley  W. C., and Cabrera  M. E., 2002, “Mechanistic Model of Myocardial Energy Metabolism Under Normal and Ischemic Conditions,” Ann. Biomed. Eng., 30(2), pp. 202–216.
Yi  C. S., Fogelson  A. L., Keener  J. P., and Peskin  C. S., 2003, “A Mathematical Study of Volume Shifts and Ionic Concentration Changes During Ischemia and Hypoxia,” J. Theor. Biol., 220(1), pp. 83–106.
Muller  J. M., Davis  M. J., and Chilian  W. M., 1996, “Integrated Regulation of Pressure and Flow in the Coronary Microcirculation,” Circ. Res., 32(4), pp. 668–678.
Xu, X. Y., and Collins, M. W., 1999, Haemodynamics of Arterial Organs—Comparison of Computational Predictions With In Vitro and in Vivo Data, WIT Press, Southhampton, UK.
Verdonck, P., and Perktold, K., 2000, Intra and Extracorporeal Cardiovascular Fluid Dynamics, WIT Press, Southampton, UK, Vols. I and II.
McQueen,  D. M., and Peskin,  C. S. 2000, “A Three-Dimensional Computer Model of the Human Heart for Studying Cardiac Fluid Dynamics,” Comput. Graph 34, pp. 56–60.
Hughes,  T. J. R. and Zimmerman,  W. K. L. T. K., 1981, “Lagrangian-Eulerian Finte Element Formulation for Incompressible Viscous Flows,” Comput. Meth. Appl. Mechs. Eng., 29, pp. 329–349.
May-Newman,  K. and McCulloch,  A. D., 1998, “Homogenization Modeling for the Mechanics of Perfused Myocardium,” Prog. Biophys. Molec. Biol., 69, pp. 463–481.
Yang,  M., Taber,  L., and Clark,  E., 1994, “A Nonlinear Poroelastic Model for the Trabecular Embryonic Heart,” ASME J. Biomed. Eng.,116, pp. 213–223.
Nickerson,  D. P., Smith,  P., and Hunter,  P. J., 2001, “A Model of Cardiac Cellular Electromechanics,” Philos. Trans. R. Soc. London, 359, pp. 1159–1172.
Smith,  N. P., Mulquiney,  P. J., Nash,  M. P., Bradley,  C. P., Nickerson,  D. P., and Hunter,  P. J., 2001, “Mathematical Modeling of the Heart: Cell to Organ,” Chaos, Soluctions Fractals, 13 pp. 1613–1621.
Sands, G. B., and Hunter, P. J., 1996, “A Collocation-Multigrid Model of Bidomain Activation as a Component of a Complete Electrocardiology Model,” 23rd International Conference on Electrocardiography, Cleveland, OH.
Briggs, W. L., 1987, A Multigrid Tutorial, Society for Industrial and Applied Mathematics, Philadelphia, PA.


Grahic Jump Location
Relationship between regional work and coronary perfusion calculated at each Gauss point in the myocardium
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Epicardial blood flow velocity profiles
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Results of coupled cardiac mechanics and coronary blood flow model
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View of the heart mode where the total work performed by myocyte contraction through the heart cycle is shown at Gauss points in the myocardium (results are scales such that blue corresponds to 0 mJ/g and red corresponds to 50 mJ/g)
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Red squares indicate base and apex Gauss point positions in the septum and left and right ventricular free wall where work rate is calculated
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Regional work rate calculated at Gauss points shown in Fig. 1. The end of diastolic filling and isovolumic contraction are marked using vertical lines on each figure.
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Coordinate systems used in the kinematic analysis of large deformation mechanics
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(a) Tension recovery (lower figure) following a length step of Δλ of duration Δt (upper figure). Notice the different phases of the tension recovery. (b) Tension T1 reached at the end of the length step, divided by isometric tension T0, plotted against the magnitude of the length step Δλ. One curve is for a length step of 1 ms duration and the other for an idealized instantaneous step.
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Anatomically accurate canine and porcine finite element models. Two layers of streamlines (one on the outer epicardial surface and one midway through the wall) are used to visualize the epicardial and midwall fiber directions which continuously rotate through the wall.



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