Aims: The wavelength of a cardiac reentry represents the spatial extent of refractory regions and may be estimated as action potential duration x conduction velocity. We assessed an instantaneous measure of geometric wavelength (GWL) applicable to monitoring the effect of externally-driven variations in acetylcholine concentration (ACh) at a shorter time scale than action potential duration.
Methods: A stable reentry was simulated in a ring (4-cm diameter; 628 cells with Ramirez et al. kinetics). ACh time course was set to a predefined exponential profile composed of a release and a degradation phase (2000 ms each phase) and characterized by its maximum ACh level (30 values between 0 and 0.03 µM) and the time constant (τ) of ACh release and degradation (30 values from 50 to 1000 ms). Reentry GWL was defined as the length of the region with membrane potential above -70 mV. Quasi-static GWL was the steady-state GWL that would be measured if ACh concentration remained constant. Time to 90% adaptation (T90) for the time course of dynamic and quasi-static GWL during ACh release and degradation were documented.
Results: In the 900 simulations, the time scale of variations in dynamic GWL was faster than ACh time constant τ during ACh release and slower during degradation (T90 / τ = 0.58 ± 0.21 vs 4.54 ± 1.13; p<0.001). This was partially explained by the nonlinear relationship between ACh and quasi-static GWL. The resulting hysteresis was quantified by the area of the dynamic vs quasi-static GWL loop, normalized by the square of GWL range. This relative area was strongly correlated to τ (Spearman's rho = -0.99) independently from ACh maximum level, and varied from 50% (τ = 50 ms) to 15% (τ = 1000 ms).
Conclusion: Geometric wavelength provides an instantaneous measure to describe fast time-scale dynamic changes in refractoriness.