A mathematical study of a muscle contraction model in which the fibre is a continuum of elements

In the framework of the sliding-filament theory of muscle contraction, we introduce and study a model which assumes the muscle fibre to be a continuum of elastic and contractile elements. Using the contracting mapping principle, we prove existence and uniqueness of the solution of the nonlinear and nonlocal hyperbolic equation related to the model.

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

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

[3]  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.

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

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

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

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

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

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

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

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

[12]  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.

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

[14]  K. Edman,et al.  Absence of plateau of the sarcomere length-tension relation in frog muscle fibres. , 1984, Acta physiologica Scandinavica.

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