Mathematical modelling for contracting muscle (

An overview of the results obtained from the collaboration of mathematicians and physiologists in mathematical simulation of muscle contraction is presented. Next a mathematical model taking into account the heterogeneity of the muscle, is presented. A mathematical analysis of the model is given along with a numerical approach and some physiological implications.

[1]  A. Huxley,et al.  The relation between stiffness and filament overlap in stimulated frog muscle fibres. , 1981, The Journal of physiology.

[2]  A mathematical model of heterogeneous behavior of single muscle fibres , 1986, Journal of mathematical biology.

[3]  A uniqueness result for a nonlinear hyperbolic equation , 1984 .

[4]  G H Pollack,et al.  The cross-bridge theory. , 1983, Physiological reviews.

[5]  K. Edman,et al.  Redistribution of sarcomere length during isometric contraction of frog muscle fibres and its relation to tension creep. , 1984, The Journal of physiology.

[6]  J. E. Wood,et al.  A sliding-filament cross-bridge ensemble model of muscle contraction for mechanical transients , 1981 .

[7]  V. Comincioli,et al.  A mathematical study of a continuum-state cross-bridge model of muscle contraction , 1988 .

[8]  R. Minelli,et al.  The analysis of some mechanical properties of quiescent myocardium. , 1979, Journal of biomechanics.

[9]  On a nonlinear and nonlocal evolution equation related to muscle contraction , 1989 .

[10]  C. Reggiani,et al.  The sarcomere length‐tension relation determined in short segments of intact muscle fibres of the frog. , 1987, The Journal of physiology.

[11]  Pierluigi Colli,et al.  A mathematical study of a muscle contraction model in which the fibre is a continuum of elements , 1988 .

[12]  A. Huxley Muscle structure and theories of contraction. , 1957, Progress in biophysics and biophysical chemistry.

[13]  T. L. Hill,et al.  Cross-bridge model of muscle contraction. Quantitative analysis. , 1980, Biophysical journal.

[14]  V. Comincioli,et al.  A four-state cross bridge model for muscle contraction. Mathematical study and validation , 1984, Journal of mathematical biology.

[15]  R. Hammond,et al.  Histochemical and Fatigue Characteristics of Conditioned Canine Latissimus Dorsi Muscle , 1986, Circulation research.

[16]  K. Edman,et al.  Differences in maximum velocity of shortening along single muscle fibres of the frog. , 1985, The Journal of physiology.

[17]  L. Gastaldi,et al.  A nonlinear and nonlocal evolution equation describing the muscle contraction , 1987 .

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

[19]  A. Huxley,et al.  Reflections on Muscle , 1981 .

[20]  S. Glantz A three-element description for muscle with viscoelastic passive elements. , 1977, Journal of biomechanics.

[21]  V. Comincioli,et al.  Mathematical aspects of the cross-bridge mechanism in muscle contraction , 1983 .

[22]  Numerical methods for a model of cardiac muscle contraction , 1983 .

[23]  T. L. Hill,et al.  A cross-bridge model of muscle contraction. , 1978, Progress in biophysics and molecular biology.

[24]  J. Thorson,et al.  The kinetics of muscle contraction , 1975 .

[25]  T. L. Hill,et al.  Theoretical formalism for the sliding filament model of contraction of striated muscle. Part I. , 1974, Progress in biophysics and molecular biology.

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