Spiral waves of voltage signaling in cardiac tissue are widely recognized to play an important role in the genesis of lethal heart rhythm disorders. Previous modeling studies have shown that the breakup of such waves, which has been proposed as a mechanism for heart fibrillation, can be mediated by a generic period doubling bifurcation. This bifurcation leads to beat-to-beat changes of action potential duration known as alternans. I will present a study of the spatial patterns of alternans before spiral breakup. It is found numerically that the line defects, the location of the points where the dynamics has period one, can form either as a one- or a three-arm spiral pattern where each arm corresponds to a line defect emanating from the spiral core. These findings are interpreted analytically using a simple theory where spiral wave unstable modes with different numbers of line defects correspond to quantized solutions of a Helmholtz equation. Furthermore, the slow inward rotation of spiral line defects is described in different regimes.