the re-entrant circuit fails to fire the circuit is stopped and fibrillatory behaviour dissipates.[]{data-label="fig:propagation"}](cropped_normal_prop4.pdf){width="\linewidth"}

Dysfunctional cells can block propagation along the cell strands and leave an opening for the propagating wavefront to turn back in on itself forming a circuit (re-entry). If this circuit is long enough (which occurs when $\nu$ is sufficiently small), the signal can continuously propagate around the circuit forming a persistent driver of AF, see Fig. \[fig:rotorform\]. Figure \[fig:propagation\] shows the emergence of AF on a tissue wide scale. In the real myocardium, the transverse decoupling of muscle fibres is associated with the build up of fibrosis [@zahid2016; @haissaguerre2016; @matsuo2009]. Hence, the parameter $\nu$ can be thought of as a control for the degree of fibrosis in the myocardium. In previous work with the CMP model, we have shown how the increased prevalence of fibrosis (decreasing $\nu$) increases the risk of AF persisting, in agreement with clinical observation [@christensen2015; @manani2016].

It is helpful to understand the considerations behind the dysfunctional cell mechanism. The important detail is that the AF mechanism in the CMP model is possible using any mechanism of unidirectional conduction block - the stochastic failure of cells to depolarise is a simple way to 