Theoretical analysis of the effects of a radial activation wave and twisting motion on the mechanics of the left ventricle

Abstract

The mechanical effects resulting from the normal transmural delay of electrical depolarization of the myocardium are investigated. An activation sequence having a finite radial propagation velocity is introduced into the equations of ventricular mechanics. The resulting system of coupled integral equations is solved using a perturbation method based on the small ratio of transmural propagation time to cardiac period. Numerical calculations are performed using cavity pressure and volume waveforms characteristic of the canine left ventricle (LV), for both simultaneous and delayed activation of fiber layers. The results show that a finite transmural electrical propagation velocity tends to: (i) equalize the transmural distribution of sarcomere length during systole; (ii) equalize the transmural distribution of fiber external work/vol; and (iii) insignificantly affect myocardial tissue pressure.

Calculations are also performed to investigate the mechanical effects resulting from the application of an externally applied moment that prevents LV torsion. Those results are highly dependent on the transmural distribution of sarcomere length in the stress-free reference state (unloaded diastole). When we assume a uniform distribution, then normal torsion acting with normal activation delay tends to: (i) increase the magnitude of fiber strain in the subendocardium and decrease it in the subepicardium; (ii) equalize the transmural distribution of fiber external work/vol; and (iii) lower myocardial tissue pressure. The normally occurring transmural delay of activation tends to lessen endocardial O₂ demand, while the normally occurring torsion further lessens that demand and improves O₂ supply.