  Spatially discordant alternans is a widely observed pattern of voltage and
calcium signals in cardiac tissue that can precipitate lethal cardiac
arrhythmia. Using spatially coupled iterative maps of the beat-to-beat
dynamics, we explore this pattern's dynamics in the regime of a
calcium-dominated period-doubling instability at the single cell level. We find
a novel nonlinear bifurcation associated with the formation of a discontinuous
jump in the amplitude of calcium alternans at nodal lines separating discordant
regions. We show that this jump unidirectionally pins nodal lines by preventing
their motion away from the pacing site following a pacing rate decrease, but
permitting motion towards this site following a rate increase. This
unidirectional pinning leads to strongly history-dependent nodal line motion
that is strongly arrhythmogenic.
