Spatiotemporal correlation uncovers fractional scaling in cardiac tissue
arXiv:1806.04507 · doi:10.1103/PhysRevE.100.020201
Abstract
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.
arXiv comment8 pages, 6 figures
References in corpus (9)
- Magnitude and Sign Correlations in Heartbeat Fluctuations
- Characterizing microstructure of living tissues with time-dependent diffusion
- Noise Effects on the Complex Patterns of Abnormal Heartbeats
- A note on stress-driven anisotropic diffusion and its role in active deformable media
- Competing mechanisms of stress-assisted diffusivity and stretch-activated currents in cardiac electromechanics
- Drift of scroll waves in thin layers caused by thickness features: asymptotic theory and numerical simulations
- A modeling framework for contact, adhesion and mechano-transduction between excitable deformable cells
- Inter-Scale Information Flow as a Surrogate for Downward Causation That Maintains Spiral Waves
- Causal Unit of Rotors in a Cardiac System