Parameters of the myocardium controlling vulnerability. Analysis of mathematical models

In a model of the Wiener type and the Noble model the authors study the conditions of onser of extrasystole induced by delivery of a stimulus in the phase of relative refractoriness (vulnerability). Two mechanisms of vulnerability are analysed: 1) circulation of the excitation wave: and 2) point source of impulsation (echo type). For the model of the Wiener type the dependence of the minimal size of the inhomogeneity for which vulnerability appears on the refractoriness R, wavelength λ = Rv (υ = speed of wave) and maximum latency of the response τ is found analytically. It is shown that the region of vulnerability does not tend to zero for dimensions of inhomogeneity less than the steady wavelength λ; in this case the minimum size of the inhomogeneity l_min is determined by the ratio τ R and l_min is smaller the larger τ R. Reduction of the region of vulnerability may be achieved: 1) by reducing the relative inhomogeneity in the refractoriness ΔR R; by reducing the characteristic dimensions l of the portion of inhomogeneity; and 3) by reducing τ R when the dimensions of inhomogeneity are small (l < λ). The dependence of the width of the region of vulnerability on the amplitude of the stimulus is calculated with a computer for a Noble model. In this model the dip-phenomenon is reproduced; the region of vulnerability is located above the zone of fall in threshold.