Mechanism for Mechanical Wave Break in the Heart Muscle

Using a reaction-diffusion-mechanics model we identify a mechanism for mechanical wave break in the heart muscle. For a wide range of strengths and durations an external mechanical load causes wave front dissipation leading to formation and breakup of spiral waves. We explain the mechanism, and discuss under which conditions it can cause or abolish cardiac arrhythmias.

Figure 1

Pulse of external mechanical load causes wave break. Upper panel—regime $\mathbf{I}$: wave break is caused by a short pulse (50 ms, 23.5 kPa). Lower panel—regime $\mathbf{I}\mathbf{I}$: wave break is caused by release of a long pulse (350 ms, 17.0 kPa). Arrows symbolize applied external stretch.

Figure 2

CV vs stretch. (a) Stretch application. A wave is initialized at one end of the unstretched fiber at time 7 s, constant stretch ($\lambda ={\lambda }_{\max }$) is applied 50 ms later for different $G_s$. (b) Release of stretch. The fiber is held stretched for different $G_s$, at time 7 s a wave is initialized at one end of the fiber, 1.0 s later stretch is released ($\lambda =0$). 6 s prior experiments’ waves were started at one end of the fiber with 2 Hz for different $G_s$.

Figure 3

Wave front dissipation at a wave back vs $I_{\mathrm{sac}}$. (a) Setup: moving inexcitable block (rectangle) in a cable of cardiac tissue (line) forces wave S1 to propagate at “forced CV.” Wave S2 is interacting with the wave back of S1. (b) S2 wave front dissipation at wave back S1. Upstroke shape (upper panel) and sodium channel availability (lower panel) of S2 waves vs time for different forced CV values. Time was shifted for different simulations so that maximal availability of sodium channels is at 0 s. (c) Regimes of S2 propagation vs forced CV and $G_s$. Insets: time space plots; dotted lines illustrate moving block. (d) Prediction of border to wave break after a release of stretch using critical and normal CV vs direct computations.

Figure 4

Wave break in 2D model vs strength, duration of stretch. Dots indicate outcomes for individual simulations. Colored: wave break causes or annihilates spirals—red: regime $\mathbf{I}$; green: regime $\mathbf{I}\mathbf{I}$. Ciphers: number of new spiral wave sources 0.5 s after release of stretch. Black contours: annihilation of spiral wave. Black dots: no formation or annihilation of spiral waves. (a) Point source setup. (b) Spiral wave setup.

Figure 5

Pulse of external mechanical load causes wave formation and break via regime $\mathbf{I}$. Setup similar to Fig. 1 was used, but waves were started in the upper, left corner with a longer period of 500 ms. Stretch is applied at time 7450 ms with strength 24.0 kPa and duration 25 ms.