Electrophysiological properties of cardiac tissue change as a function of position. We define the 'excitability' as the propagation velocity of an excitation pulse through the tissue, and study a simple FitzHugh-Nagumo (FHN) model of heart tissue whose excitability changes with position. The propagation velocity is shown to be a good continuous measure of the excitability for both limit cycle and excitable tissues. The influence of the spatial dependence of the excitability is examined for several normal and pathological situations. A novel transient effect is observed for a train of pulses propagating across an excitability step.