Calcium is the primary signalling component of excitation-contraction coupling, the process linking electrical excitability of cardiac muscle cells to coordinated contraction of the heart. Understanding [Formula: see text] handling processes at the cellular level and the role of intercellular communication in the emergence of multicellular synchronization are key aspects in the study of arrhythmias. To probe these mechanisms, we have simulated cellular interactions on large scale arrays that mimic cardiac tissue, and where individual cells are represented by a mathematical model of intracellular [Formula: see text] dynamics. Theoretical predictions successfully reproduced experimental findings and provide novel insights on the action of two pharmacological agents (ionomycin and verapamil) that modulate [Formula: see text] signalling pathways via distinct mechanisms. Computational results have demonstrated how transitions between local synchronisation events and large scale wave formation are affected by these agents. Entrainment phenomena are shown to be linked to both intracellular [Formula: see text] and coupling-specific dynamics in a synergistic manner. The intrinsic variability of the cellular matrix is also shown to affect emergent patterns of rhythmicity, providing insights into the origins of arrhythmogenic [Formula: see text] perturbations in cardiac tissue in situ.