A Computer Study of the Left Ventricular Performance Based on Fiber Structure, Sarcomere Dynamics, and Transmural Electrical Propagation Velocity

A model of the left ventricle which combines a spheroidal geometry with a spatial fiber angle distribution is presented. The mechanics of each muscle fiber is described by its passive stress-strain relationship, active stress-strain relationship, and an activation function (half a sinusoid) which represents the time-dependent degree of activation of the fiber. A stress-strain rate relationship which characterizes the muscle fibers is used to calculate the mechanics of left ventricular contraction during ejection. Furthermore, a radial electrical signal propagation from the endocardium to the epicardium is used here as a first approximation to the actual depolarization sequence. The model is used to describe the process of contraction throughout the systole. The different calculated parameters and indices of left ventricular function are presented and discussed for different preloading, afterloading and contractility conditions. The maximum elastance is found to be an optimal macroscale parameter of contractility, as it is completely preload and afterload independent, and is a good reflection of the active microscale sarcomere stressstrain relationship.

[1]  S. Sideman,et al.  Model for left ventricular contraction combining the force length velocity relationship with the time varying elastance theory. , 1984, Biophysical journal.

[2]  Arthur J. Moss,et al.  The Heart, Arteries, and Veins , 1983 .

[3]  R. Chadwick,et al.  Mechanics of the left ventricle. , 1982, Biophysical journal.

[4]  G. Schuler,et al.  Noninvasive assessment of myocardial contractility in asymptomatic patients with sever aortic regurgitation and normal left ventricular ejection fraction at rest. , 1982, The American journal of cardiology.

[5]  C. A. Vinson,et al.  Computer modeling of the human left ventricle. , 1982, Journal of biomechanical engineering.

[6]  W. Welkowitz.  Indices of Cardiac Status , 1981, IEEE Transactions on Biomedical Engineering.

[7]  W H Pierce,et al.  Body forces and pressures in elastic models of the myocardium. , 1981, Biophysical journal.

[8]  G. Schuler,et al.  Noninvasive determination of the endsystolic pressure volume relation in patients with aortic regurgitation , 1981 .

[9]  V. Froelicher,et al.  Peak systolic blood pressure/end-systolic volume ratio: assessment at rest and during exercise in normal subjects and patients with coronary heart disease. , 1980, The American journal of cardiology.

[10]  E L Ritman,et al.  Derivation of myocardial fiber stiffness equation based on theory of laminated composite. , 1980, Journal of biomechanical engineering.

[11]  Weber Kt,et al.  The dynamics of ventricular contraction: force, length, and shortening. , 1980 .

[12]  C. Phillips,et al.  Contractile Filament Stress in the Left Ventricle and its Relationship to Wall Stress , 1979 .

[13]  T. Feit.  Diastolic pressure-volume relations and distribution of pressure and fiber extension across the wall of a model left ventricle. , 1979, Biophysical journal.

[14]  J S Janicki,et al.  The heart as a muscle--pump system and the concept of heart failure. , 1979, American heart journal.

[15]  D N Ghista,et al.  Finite element stress analysis of the human left ventricle whose irregular shape is developed from single plane cineangiocardiogram. , 1977, Computer programs in biomedicine.

[16]  H. Suga,et al.  Effects of Stroke Volume and Velocity of Ejection on End‐Systolic Pressure of Canine Left Ventricle: End‐Systolic Volume Clamping , 1977, Circulation research.

[17]  H Suga,et al.  Controls of ventricular contractility assessed by pressure-volume ration, Emax. , 1976, Cardiovascular research.

[18]  J C Greenfield,et al.  The Three‐Dimensional Dynamic Geometry of the Left Ventricle in the Conscious Dog , 1976, Circulation research.

[19]  J W Krueger,et al.  Myocardial sarcomere dynamics during isometric contraction. , 1975, The Journal of physiology.

[20]  W. Förster,et al.  A model for the assessment of left ventricular compliance: effect of hypertrophy and infarction. , 1975, Cardiovascular research.

[21]  W. Parmley,et al.  Comparative evaluation of the specificity and sensitivity of isometric indices of contractility. , 1975, The American journal of physiology.

[22]  E H Wood,et al.  Finite-element analysis of left ventricular myocardial stresses. , 1974, Journal of biomechanics.

[23]  A. Grimm,et al.  Deformation of the diastolic left ventricle--II. Nonlinear geometric effects. , 1974, Journal of biomechanics.

[24]  G. Pollack,et al.  Sarcomere length-active force relations in living mammalian cardiac muscle. , 1974, The American journal of physiology.

[25]  Hiroyukisuga,et al.  Instantaneous Pressure-Volume Relationships and Their Ratio in the Excised, Supported Canine Left Ventricle , 1974 .

[26]  A. Grimm,et al.  Deformation of the diastolic left ventricle. Nonlinear elastic effects. , 1973, Biophysical journal.

[27]  S. Awa,et al.  Role of Kinetic Energy in Pulmonary Valvar Pressure Gradients , 1973, Circulation.

[28]  A. Shoukas,et al.  Load Independence of the Instantaneous Pressure‐Volume Ratio of the Canine Left Ventricle and Effects of Epinephrine and Heart Rate on the Ratio , 1973, Circulation research.

[29]  J W Covell,et al.  Structural Basis for the Ascending Limb of Left Ventricular Function , 1973, Circulation research.

[30]  W. Gaasch,et al.  Left Ventricular Stress and Compliance in Man: With Special Reference to Normalized Ventricular Function Curves , 1972, Circulation.

[31]  R. Myerburg,et al.  Physiology of Canine Intraventricular Conduction and Endocardial Excitation , 1972, Circulation research.

[32]  G. Diamond,et al.  Dlastolic Pressure‐Volume Relationship in the Canine Left Ventricle , 1971 .

[33]  D. Durrer,et al.  Total Excitation of the Isolated Human Heart , 1970, Circulation.

[34]  I. Mirsky,et al.  Effects of anisotropy and nonhomogeneity on left ventricular stresses in the intact heart. , 1970, The Bulletin of mathematical biophysics.

[35]  A. Hill.  First and Last Experiments in Muscle Mechanics , 1970 .

[36]  A. Grimm,et al.  Relation of sarcomere length and muscle length in resting myocardium. , 1970, The American journal of physiology.

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

[38]  G. Pollack.  Maximum Velocity as an Index of Contractility in Cardiac Muscle: A CRITICAL EVALUATION , 1970, Circulation research.

[39]  J. Ross,et al.  Fiber Orientation in the Canine Left Ventricle during Diastole and Systole , 1969, Circulation research.

[40]  J Ross,et al.  Contractile State of the Left Ventricle in Man: Instantaneous Tension‐Velocity‐Length Relations in Patients With And Without Disease of the Left Ventricular Myocardium , 1968, Circulation research.

[41]  J W Covell,et al.  The Ultrastructure of the Heart in Systole and Diastole: >Changes In Sarcomere Length , 1967, Circulation research.

[42]  John Ross,et al.  Contractile State of the Heart Characterized by Force‐Velocity Relations in Variably Afterloaded and Isovolumic Beats , 1966 .

[43]  E. Sonnenblick,et al.  Relation of Ultrastructure to Function in the Intact Heart: Sarcomere Structure Relative to Pressure Volume Curves of Intact Left Ventricles of Dog and Cat , 1966, Circulation research.

[44]  D. Robinson,et al.  Quantitative Analysis of the Control of Cardiac Output in the Isolated Left Ventricle , 1965, Circulation research.

[45]  G L MADDOX,et al.  A critical evaluation , 2012 .

[46]  E. Sonnenblick,et al.  FINE STRUCTURAL CHANGES IN HEART MUSCLE IN RELATION TO THE LENGTH-TENSION CURVE , 1963 .

[47]  T. Sano,et al.  Directional Difference of Conduction Velocity in the Cardiac Ventricular Syncytium Studied by Microelectrodes , 1959, Circulation research.

[48]  A. Hill.  The heat of shortening and the dynamic constants of muscle , 1938 .

[49]  E. Feigl,et al.  Coronary physiology. , 1983, Physiological reviews.

[50]  A. Capelo,et al.  Study and parameters identification of a rheological model for excised quiescent cardiac muscle. , 1981, Journal of biomechanics.

[51]  J S Janicki,et al.  The dynamics of ventricular contraction: force, length, and shortening. , 1980, Federation proceedings.

[52]  J H van den Broek,et al.  Application of an ellipsoidal heart model in studying left ventricular contractions. , 1980, Journal of biomechanics.

[53]  S. Moskowitz.  On the mechanics of left ventricular diastole. , 1980, Journal of biomechanics.

[54]  M. Broek,et al.  Application of an ellipsoidal heart model in studying left ventricular contractions , 1980 .

[55]  A. Noordergraaf.  Circulatory System Dynamics , 1978 .

[56]  W. Welkowitz,et al.  Relation between computed zero-load aortic flow and cardiac muscle mechanics. , 1978, Journal of biomechanics.

[57]  Abraham Noordergraaf,et al.  Cardiovascular system dynamics , 1978 .

[58]  B. Deswysen,et al.  Parameter Estimation of a Simple Model of the Left Ventricle and of the Systemic Vascular Bed, with Particular Attention to the Physical Meaning of the Left Ventricular Parameters , 1977, IEEE Transactions on Biomedical Engineering.

[59]  S. Glantz.  A three-element model describes excised cat papillary muscle elasticity. , 1975, The American journal of physiology.

[60]  D. Ghista,et al.  Cardiac mechanics: Physiological, clinical, and mathematical considerations , 1974 .

[61]  G. Diamond,et al.  Diastolic pressure-volume relationship in the canine left ventricle. , 1971, Circulation research.

[62]  Gerard N. Burrow,et al.  Mechanisms of contraction of the normal and failing heart. , 1967, The New England journal of medicine.