  Complex spatiotemporal patterns of action potential duration have been shown
to occur in many mammalian hearts due to a period-doubling bifurcation that
develops with increasing frequency of stimulation. Here, through
high-resolution optical mapping and numerical simulations, we quantify voltage
length scales in canine ventricles via spatiotemporal correlation analysis as a
function of stimulation frequency and during fibrillation. We show that i)
length scales can vary from 40 to 20 cm during one to one responses, ii) a
critical decay length for the onset of the period-doubling bifurcation is
present and decreases to less than 3 cm before the transition to fibrillation
occurs, iii) fibrillation is characterized by a decay length of about 1 cm. On
this evidence, we provide a novel theoretical description of cardiac decay
lengths introducing an experimental-based conduction velocity dispersion
relation that fits the measured wavelengths with a fractional diffusion
exponent of 1.5. We show that an accurate phenomenological mathematical model
of the cardiac action potential, fine-tuned upon classical restitution
protocols, can provide the correct decay lengths during periodic stimulations
but that a domain size scaling via the fractional diffusion exponent of 1.5 is
necessary to reproduce experimental fibrillation dynamics. Our study supports
the need of generalized reaction-diffusion approaches in characterizing the
multiscale features of action potential propagation in cardiac tissue. We
propose such an approach as the underlying common basis of synchronization in
excitable biological media.
