  In healthy hearts myocytes are typically coupled to nearest neighbours
through gap junctions. Under pathological conditions such as fibrosis, or in
scar tissue, or across ablation lines myocytes can uncouple from their
neighbours. Electrical conduction may still occur via fibroblasts that not only
couple proximal myocytes but can also couple otherwise unconnected regions. We
hypothesise that such coupling can alter conduction between myocytes via
introduction of delays or by initiation of premature stimuli that can
potentially result in reentry or conduction blocks. To test this hypothesis we
have developed several $2$-cell motifs and investigated the effect of
fibroblast mediated electrical coupling between uncoupled myocytes. We have
identified various regimes of myocyte behaviour that depend on the strength of
gap-junctional conductance, connection topology, and parameters of the myocyte
and fibroblast models. These motifs are useful in developing a mechanistic
understanding of long-distance coupling on myocyte dynamics and enable the
characterisation of interaction between different features such as myocyte and
fibroblast properties, coupling strengths and pacing period. They are
computationally inexpensive and allow for incorporation of spatial effects such
as conduction velocity. They provide a framework for constructing scar tissue
boundaries and enable linking of cellular level interactions with scar induced
arrhythmia.
