Local Gradients in Electrotonic Loading Modulate the Local Effective Refractory Period: Implications for Arrhythmogenesis in the Infarct Border Zone

Abstract

Ectopic electrical activity that originates in the peri-infarct region can give rise to potentially lethal re-entrant arrhythmias. The spatial variation in electrotonic loading that results from structural remodelling in the infarct border zone may increase the probability that focal activity will trigger electrical capture, but this has not previously been investigated systematically. This study uses in-silico experiments to examine the structural modulation of effective refractory period on ectopic beat capture. Informed by 3-D reconstructions of myocyte organization in the infarct border zone, a region of rapid tissue expansion is abstracted to an idealized representation. A novel metric is introduced that defines the local electrotonic loading as a function of passive tissue properties and boundary conditions. The effective refractory period correlates closely with local electrotonic loading, while the action potential duration, conduction, and upstroke velocity reduce in regions of increasing electrotonic load. In the presence of focal ectopic stimuli, spatial variation in effective refractory period can cause unidirectional conduction block providing a substrate for reentrant arrhythmias. Consequently, based on the observed results, a possible novel mechanism for arrhythmogenesis in the infarct border zone is proposed.

Fig. 1

Histology (from [3]) showing surviving myocyte bundle expansions through the thickness, encapsulated in collagen.

Fig. 2

Schematics of the computational domains and imposed fiber directions for the θ ∈ {0, 30, 60, 90}° funnels. (a) Schematic of the computational domains and stimulus locations (note that, although only four locations are shown, the s₂ stimuli were applied at each vertex coinciding with the symmetry line). The reference frame and origin are shown in blue. (b) Example of the imposed fiber directions.

Fig. 3

Variation in APD and max{dV/dt} for the θ = 0° geometry for large variations in σ_b . The bidomain variations in APD and max{dV/dt}, for different bath conductivities are small and correspond closely with the monodomain results.

Fig. 4

Nondimensional EL(x) for each vertex in the domain. EL(x) reaches a maximum just above the funnel expansion in the θ > 0° funnels. In the θ = 0° funnel the maximum value is located at the centroid of the domain, due to the symmetry.

Fig. 5

Local variation in ERP (with dotted markers), APD, and EL for points along the vertical (y) axis of the funnels. The ERP reaches a maximum above the funnel expansion for the θ = {30, 60, 90}° funnels, whereas it is maximum at the mid-point of the symmetrical (θ = 0°) funnel. The ERP varies by approximately 20 ms in the θ = 90° funnel and 0.5 ms for the θ = 0° funnel. The maxima in EL(x) is approximately colocated with the maxima in ERP for each funnel.

Fig. 6

(a) Wavefronts for the different funnel geometries shown at t = 3, 4, 5 and 6 ms. When the wavefront approaches the funnel expansion (for the θ > 0° funnels), the anisotropic conductivity coupled with the varying fiber directions causes the wavefront to become concave. (b) Lower plot: APs recorded at the centre of the funnels (x = y = 0). Upper plot: a zoom-in of the AP upstrokes. (a) Activation wavefronts for the different funnels. (b) Lower: APs recorded at point x = y = 0. Upper: zoom-in of AP upstrokes.

Fig. 7

CV and max{dV/dt} for the different funnels. (a) CV is approximately constant, at 50.6 cm · s⁻¹ for the θ = 0° funnel, but retards at ≈ 525µm below the expansion for the θ > 0° funnels to reach a minimum just above the expansion for each case. (b) max{dV/dt} is approximately constant, at 145.5 mV for the θ = 0° funnel, but reduces at ≈ 525µm below the expansion for the θ > 0° funnels to reach a minimum just above the expansion for each case.

Fig. 8

Spatial rate of change of APDs for the different funnels. |∂/∂y(APD)| is approximately constant for the θ = 0° funnel at 1.7ms/mm. |∂/∂y(APD)| is slightly lower for the θ > 0° funnels between approximately 700 and 250µm below the funnel expansion before it starts to increase, reaching a maximum just above the expansion for each case.

Fig. 9

ERP (marker dots), APD and EL for the θ > 0° funnels with an isotropic conductivity. The maxima in the ERP again roughly correspond to the maxima in EL.

Fig. 10

ERP (marker dots) and APD for the θ > 0° funnels, with the s₁ pacing stimuli applied at the vertices along the top edge of the funnels.

Fig. 11

Unidirectional wavefront propagation from stimuli at the mid-point of the funnel at t = t_ERP for each funnel. (a) θ = 30° funnel. Stimulation is applied at the mid-point at t = 155 ms. (b) θ = 60°. Stimulation is applied at the mid-point at t = 156 ms. (c) θ = 90°. Stimulation is applied at the mid-point at t = 158 ms.

Fig. 12

Schematic of how unidirectional block may arise due to SD in a region with a spatial gradient in ERP. The symmetry plane implies 2-D symmetry or 3-D cylindrical symmetry. The opacity of the red shading illustrates the magnitude of the local ERP.

Fig. 13

Emergence of circus movement from stimulation at the local ERP in an idealized isthmus geometry. s₁ stimulation was applied at vertices along the top of the domain and s₂ stimulation was applied at a points corresponding to the s₂ location show in Fig. 12; the stimulus can be seen at t = 200 ms. Unidirectional propagation from the s₂ stimulus occurs due to the large gradient in ERP, resulting in a re-entrant circuit (t > 200 ms). The slowed propagation in the middle of the domain is due to the lower conductivity imposed in that region to replicate slow tortuous conduction through the central isthmus [33].