The present paper is concerned with the problem of excitation propagation in a multicomponent excitable medium, which is considered as a model of neuron nets of the syncytial type. The best example is the cardiac tissues, which form a heterogeneous system of different units with common axoplasma. The sundry cardiac tissues differ quantitatively in their properties such as excitation threshold and refractory time. If units of each type are uniformly distributed in space and sufficiently "mixed" with one another, the medium proves to be macroscopically homogeneous. In the first part of the paper a method is described which is suitable for consideration of an excitable medium. In the case of a one-component system the velocity of excitation and profile of nerve impulse is obtained by this method. It is interesting to note that the impulse can have two velocities, but only the larger velocity proves to be stable. In the second part of the paper, complicated types of excitation in a two-component medium are considered. It is generally assumed that the complex behaviour of excitation of the echo or rhythm transformation type may arise only in macroscopically inhomogeneous media. In this paper is shown that similar phenomena can be observed also in macroscopically homogeneous media consisting of units of different types. In a two-component medium a moving "ectopic centre" arises, which is a source of nerve impulses. This theory explains some experimental results on cardiac arrhythmia.
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- Biochemistry, Genetics and Molecular Biology(all)
- Immunology and Microbiology(all)
- Agricultural and Biological Sciences(all)
- Applied Mathematics