Myocybernetic control models of skeletal muscle. Characteristics and applications.

*(English)*Zbl 0635.92003
Studia Mathematica, 4. Pretoria: University of South Africa. XI, 221 p. (1981).

A thorough literature search undertaken in the late 1960s convinced the author that none of the models proposed up to that time could justifiably be called a myocybernetic control model of skeletal muscle. Most modelling attempts had concentrated on the functional behaviour of the myo-structures with special reference to the sliding filament theory, but failed to incorporate the intricacies of the excitation and recruitment dynamics. However, a vast volume of experimental data was available which enabled the author over the past ten years successively to construct, refine and test a model which could be regarded a true control model of skeletal muscle.

The present monograph is designed to give a step-by-step exposition of this development. Detailed mathematical derivations have been transferred to the various appendices in order to make the mathematical treatment presented in the main text accessible to the average biologist with a moderate background in mathematics.

The book is organized into seven chapters and a number of appendices. Chapter one provides a historical background of theories and models of muscular contraction. In Chapter two we identify the structural elements of skeletal muscle. Chapter three is devoted to the description and modelling of the functional characteristics of the muscle elements, while in Chapter four these submodels are combined in the global myocybernetic control model. In Chapter five we describe methods for determining model parameters from measurements on living muscle, and Chapter six contains a comparison between simulation and corresponding experimental results. Finally, Chapter seven gives an exposition of various applications of the model.

Since simulation constitutes one of the main features of the present approach, computer programs are provided which enable the reader to perform his own model simulations and parameter determinations. The computer programs are written in ANSI FORTRAN IV and are listed in the appendices.

The present monograph is designed to give a step-by-step exposition of this development. Detailed mathematical derivations have been transferred to the various appendices in order to make the mathematical treatment presented in the main text accessible to the average biologist with a moderate background in mathematics.

The book is organized into seven chapters and a number of appendices. Chapter one provides a historical background of theories and models of muscular contraction. In Chapter two we identify the structural elements of skeletal muscle. Chapter three is devoted to the description and modelling of the functional characteristics of the muscle elements, while in Chapter four these submodels are combined in the global myocybernetic control model. In Chapter five we describe methods for determining model parameters from measurements on living muscle, and Chapter six contains a comparison between simulation and corresponding experimental results. Finally, Chapter seven gives an exposition of various applications of the model.

Since simulation constitutes one of the main features of the present approach, computer programs are provided which enable the reader to perform his own model simulations and parameter determinations. The computer programs are written in ANSI FORTRAN IV and are listed in the appendices.

##### MSC:

92Cxx | Physiological, cellular and medical topics |

92-02 | Research exposition (monographs, survey articles) pertaining to biology |

74L15 | Biomechanical solid mechanics |

92-04 | Software, source code, etc. for problems pertaining to biology |

92C05 | Biophysics |