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Extended Bidomain Modeling of Defibrillation: Quantifying Virtual Electrode Strengths in Fibrotic Myocardium

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Extended Bidomain Modeling of Defibrillation: Quantifying Virtual Electrode Strengths in Fibrotic Myocardium

Jean Bragard et al. Front Physiol.

Abstract

Defibrillation is a well-established therapy for atrial and ventricular arrhythmia. Here, we shed light on defibrillation in the fibrotic heart. Using the extended bidomain model of electrical conduction in cardiac tissue, we assessed the influence of fibrosis on the strength of virtual electrodes caused by extracellular electrical current. We created one-dimensional models of rabbit ventricular tissue with a central patch of fibrosis. The fibrosis was incorporated by altering volume fractions for extracellular, myocyte and fibroblast domains. In our prior work, we calculated these volume fractions from microscopic images at the infarct border zone of rabbit hearts. An average and a large degree of fibrosis were modeled. We simulated defibrillation by application of an extracellular current for a short duration (5 ms). We explored the effects of myocyte-fibroblast coupling, intra-fibroblast conductivity and patch length on the strength of the virtual electrodes present at the borders of the normal and fibrotic tissue. We discriminated between effects on myocyte and fibroblast membranes at both borders of the patch. Similarly, we studied defibrillation in two-dimensional models of fibrotic tissue. Square and disk-like patches of fibrotic tissue were embedded in control tissue. We quantified the influence of the geometry and fibrosis composition on virtual electrode strength. We compared the results obtained with a square and disk shape of the fibrotic patch with results from the one-dimensional simulations. Both, one- and two-dimensional simulations indicate that extracellular current application causes virtual electrodes at boundaries of fibrotic patches. A higher degree of fibrosis and larger patch size were associated with an increased strength of the virtual electrodes. Also, patch geometry affected the strength of the virtual electrodes. Our simulations suggest that increased fibroblast-myocyte coupling and intra-fibroblast conductivity reduce virtual electrode strength. However, experimental data to constrain these modeling parameters are limited and thus pinpointing the magnitude of the reduction will require further understanding of electrical coupling of fibroblasts in native cardiac tissues. We propose that the findings from our computational studies are important for development of patient-specific protocols for internal defibrillators.

Keywords: cardiac tissue; computational modeling; defibrillation; fibrosis; multidomain modeling.

Figures

Figure 1
Figure 1
Geometry of (A) 1D and (B,C) 2D models of rabbit ventricular tissue with central fibrotic patch. The sites of extracellular current application are marked in black. Fibrotic patches are shown in grey.
Figure 2
Figure 2
Representative plots of (A) ϕe, (B) Vmyo, and (C) Vfibfor intracellular pacing and subsequent extracellular current application in the 1D model with the average fibrosis patch, σ¯fib of 0.1 S/m and Rmyo,fib of 40 GΩ. Spatial distribution of (D) ϕe, (E) Vmyo, and (F) Vfib at the end of application of extracellular currents. The extracellular current led to alterations of Vmyo and Vfib not only at the application site, but also at the left and right border of the fibrotic patch.
Figure 3
Figure 3
Measurement of effects of extracellular current application on Vmyo using the 1D model with the average fibrosis patch. Before application of extracellular currents, Vmyo at the (A) left and (C) right border of the fibrotic patch was marginally affected by Rmyo,fib and σ¯fib. (B) At the end of current application, the left patch border exhibited a positive ΔVmyo. (D) In contrast, the right patch border exhibited a negative ΔVmyo.
Figure 4
Figure 4
Measurement of effects of extracellular current application on Vfib using the 1D model with the average fibrosis patch. Before application of extracellular currents, Vfib at the (A) left and (C) right border of the fibrotic patch was strongly affected by Rmyo,fib and σ¯fib. At the end of current application, the (B) left and (D) right border exhibited a ΔVfib with magnitude and sign modulated by Rmyo,fib and σ¯fib.
Figure 5
Figure 5
Measurement of effects of extracellular current application on Vmyo using the 1D model with the large fibrosis patch. Before application of extracellular currents, Vmyo at the (A) left and (C) right border of the fibrotic patch was marginally affected by Rmyo,fib and σ¯fib. (B) At the end of current application, the left patch border exhibited a positive ΔVmyo. (D) In contrast, the right patch border exhibited a negative ΔVmyo.
Figure 6
Figure 6
Measurement of effects of extracellular current application on Vfib using the 1D model with the large fibrosis patch. Before application of extracellular currents, Vfib at the (A) left and (C) right border of the fibrotic patch was strongly affected by Rmyo,fib and σ¯fib. At the end of current application, the (B) left and (D) right border exhibited a ΔVfib with magnitude and sign modulated by Rmyo,fib and σ¯fib.
Figure 7
Figure 7
Assessment of effects of extracellular current application on Vmyo and Vfib simulated in 1D models with a patch of varying degrees of fibrosis. The degree of fibrosis ranged from average (α = 0) to large (α = 1). We also varied Rmyo,fib. σ¯fib was set to 0.1 S/m. The effects on the magnitude of ΔVmyo at the (A) left and (B) right boundary increased with the degree of fibrosis. Similarly, effects of ΔVfib at the (C) left and (D) right boundary increased with the degree of fibrosis for small Rmyo,fib. Marginal effects were present for larger Rmyo,fib.
Figure 8
Figure 8
Effects of patch length Wp on (A,B) Vmyo and (C,D) Vfib at the boundary of the patch in response to application of the extracellular current. We varied Rmyo,fib, but σ¯fib was set on 0.1 S/m. For small Wp, Vmyo, and Vfib were greatly reduced.
Figure 9
Figure 9
Spatial distribution of (A) ϕe, (B) Vmyo, and (C) Vfib at the end of extracellular current application in the 2D model with the square-shaped average fibrosis patch, σ¯fib of 0.1 S/m and Rmyo,fib of 1 GΩ. Close-ups of the spatial distribution for (D) ϕe, (E) Vmyo, and (F) Vfib. The extracellular current led to alterations of Vmyo and Vfib not only at the application site, but also at the left and right border of the patch.
Figure 10
Figure 10
Spatial distribution of (A) ϕe, (B) Vmyo, and (C) Vfib at the end of extracellular current application in the 2D model with the disk-shaped average fibrosis patch, σ¯fib of 0.1 S/m and Rmyo,fib of 1 TΩ. Close-ups of the spatial distribution for (D) ϕe, (E) Vmyo, and (F) Vfib at the end of application of extracellular currents. The extracellular current led to alterations of Vmyo and Vfib not only at the application site, but also at the left and right border of the patch.
Figure 11
Figure 11
Comparison of (A,B) Vmyo and (C,D) Vfib from the 1D simulations and the 2D simulations with disk and square patch geometries. The square and circle symbols refer to the results for the respective square and disk patch geometry.

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