Spatiotemporal correlation uncovers characteristic lengths in cardiac tissue

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.

Key aspects for effective mathematical modelling of fractional-diffusion in cardiac electrophysiology: A quantitative study

“…On the experimental side, fractional diffusion indices have been correlated to the level of heterogeneity in myocardial microstructure through imaging analysis of ex vivo healthy rat ventricles [22], and fractional scaling was shown to characterise spatio-temporal correlation of cardiac electrical properties during paced excitation dynamics through the analysis of optically mapped canine ventricular preparations [23,24].…”

Efficient estimation of cardiac conductivities: A proper generalized decomposition approach

“…On the contrary, the PGD approximation is less accurate when the transmembrane potential sharply changes. In particular, the error is more significant in the interval [20,22] ms characterizing the wavefront propagation than in the interval [115,120] ms when waveback propagation occurs. This is confirmed by Fig.…”

“…The knowledge of the differential equations for the potential propagation in the cardiac tissue is quite consolidated, as witnessed by the specific literature (see, e.g., [14,15,16]). Modeling improvements are mainly devoted to the micro-, meso-and macroscopic (i.e., cell, tissue and organ levels) description of the ions dynamics at cellular and subcellular level [17], to their behavior at the cell-cell interface [18,19], and to the spatio-temporal coupling among the different cardiac components resulting in synchronized emerging phenomena [20]. These models feature parameters that are quite hard to measure in vivo and data assimilation procedures have been recognized as a viable approach [21,22].…”

In-silico study of the cardiac arrhythmogenic potential of biomaterial injection therapy

“…These border zones reportedly play a meaningful role in the propagation of action potentials, since they may promote the formation of abnormalities such as action potential alternans 10 and arrhythmias 43 . While recent multiscale models of cardiac tissue have been able to theoretically link the remodelling of gap-junction conductivity with reduced conduction velocity in cardiac tissue 44 , further studies should quantify in biophysical terms the level of remodelling found at the gel-intact tissue interface, in order to incorporate additional nonlinearities in the emerging cardiac behavior 45 – 48 . Another limitation is the absence of electromechanical coupling in our simulations.…”