Cardiac resonant oscillations in terms of finite-dimensional group representation in atrial parasystole.

Abstract

In order to understand the variation of the atrial parasystolic cycle lengths and mutual interactions of sinus node and atrial parasystolic pacemakers, a representation theory for finite groups of invertible linear transformation on a vector space is considered. A quantitative description of manifest atrial parasystolic cycles can be provided by the mapping in the group multiplication with the use of numerical factors of 2, 4 square root of 2 pi, 2/ 4 square root of 2 pi and 2 4 square root of 2 pi. These represent operators of a linear transformation in matrix multiplication of the similarity transformation representing an isomorphism.