Evaluating intramural virtual electrodes in the myocardial wedge preparation: simulations of experimental conditions

Abstract

While defibrillation is the only means for prevention of sudden cardiac death, key aspects of the process, such as the intramural virtual electrodes (VEs), remain controversial. Experimental studies had attempted to assess intramural VEs by using wedge preparations and recording activity from the cut surface; however, applicability of this approach remains unclear. These studies found, surprisingly, that for strong shocks, the entire cut surface was negatively polarized, regardless of boundary conditions. The goal of this study is to examine, by means of bidomain simulations, whether VEs on the cut surface represent a good approximation to VEs in depth of the intact wall. Furthermore, we aim to explore mechanisms that could give rise to negative polarization on the cut surface. A model of wedge preparation was used, in which fiber orientation could be changed, and where the cut surface was subjected to permeable and impermeable boundary conditions. Small-scale mechanisms for polarization were also considered. To determine whether any distortions in the recorded VEs arise from averaging during optical mapping, a model of fluorescent recording was employed. The results indicate that, when an applied field is spatially uniform and impermeable boundary conditions are enforced, regardless of the fiber orientation VEs on the cut surface faithfully represent those intramurally, provided tissue properties are not altered by dissection. Results also demonstrate that VEs are sensitive to the conductive layer thickness above the cut surface. Finally, averaging during fluorescent recordings results in large negative VEs on the cut surface, but these do not arise from small-scale heterogeneities.

Figure 1

Schematics of the experimental setup in the studies by Fast and co-workers (10–12) and of the computer model. In both model and experiment, the wedge preparation was paced via an electrode located at the preparation edge (STIM). Rectangular shocks were delivered via two large mesh electrodes located at opposite borders of the tissue-bath chamber. The direction of the applied electric field E is indicated by the arrows. The wedge model is of dimensions 1.2 × 1.2 cm of the endo- and epicardial surfaces, and a transmural thickness of 1 cm. The computer model panel also presents a schematic of how permeable and impermeable boundary conditions were implemented on the cut surface of the wedge in accordance with the experimental procedure.

Figure 2

Fiber orientation in the wedge model. Fibers rotate linearly in the transmural direction, from −60° at the endocardium (red lines) to +60° at the epicardium (green lines). The angle of rotation, α, is measured with respect to the y axis. Fibers in the middle of the wedge (midmyocardium, mid, dark blue lines) are orthogonal to the cut surface (yellow outline). Patterns of shock-induced VE are compared on the cut surface and on a intramural reference plane (thick black outline). The local coordinate system (the coordinate system attached to the fibers) is denoted x′,y′,z′ (shown in red and aligned with the fibers on the endocardium), while the global coordinate system is x,y,z (shown in black).

Figure 3

Maps of the shock-induced change in transmembrane potential, ΔV_m, at the end of the 10-ms shock on the intramural reference plane (top row) and on the cut surface (middle row) for three wedge preparations with different fiber orientation. (A) Fibers oriented parallel to the cut surface (arrow). (B) Fibers oriented perpendicularly to the cut surface (circle and dot). (C) Fibers rotating transmurally as shown in Fig. 2. In all three cases, impermeable boundary conditions are enforced on the cut surface. Field strength, E, is 28 V/cm. Plots of ΔV_m profiles (red and blue lines) along the dotted line (direction epi- to endocardium) in the middle of the ΔV_m maps are presented at the bottom. Vertical lines delineate areas of zero ΔV_m and their locations with respect to the epicardium.

Figure 4

Maps of the shock-induced change in transmembrane potential, ΔV_m, at shock-end on the cut surface for impermeable (top row) and permeable (bottom row) boundary conditions. Shock strength is 28 V/cm; fiber orientation is rotational (as in Fig. 2). Side views of ΔV_m distributions on the endo- and epicardial surfaces of the wedge are also shown. Middle panel shows a plot of ΔV_m profiles along the centrally located horizontal line (endo- to epicardium) in the middle of the ΔV_m maps. Individual traces of shock-induced responses on the plateau of the action potential at numbered locations along the same line are shown in vertical columns (locations denoted, in white, on the ΔV_m maps). Red lines refer to impermeable boundary conditions, while blue ones refer to permeable.

Figure 5

Maps of the shock-induced change in transmembrane potential, ΔV_m, at shock-end on the cut surface of the same wedge as in Fig. 4 as the thickness of the bath layer over it is increased from 0 to 2 mm, together with a plot of ΔV_m profiles along the centrally located horizontal line (endo- to epicardium) in the middle of the ΔV_m maps. The different colors correspond to the thickness of the bath layer as indicated under each ΔV_m map.

Figure 6

(Top row) Effect of small-scale resistive heterogeneities on the shock-induced ΔV_m distribution on the cut surface of the same wedge as in Fig. 4 for permeable and impermeable boundary conditions (right and left panels, respectively). Middle panel shows a plot of ΔV_m profiles, with and without small-scale heterogeneities, along the centrally located horizontal line (endo- to epicardium) in the middle of the ΔV_m maps. (Bottom row) Optical maps of ΔV_m (ΔV_opt) on the cut surface for permeable and impermeable boundary conditions (right and left panels, respectively). Dotted lines in the maps are zero iso-fluorescence lines. Middle panel shows a plot of ΔV_opt profiles, with and without small-scale heterogeneities, along the centrally located horizontal line (endo- to epicardium) in the middle of the ΔV_opt maps. Optical potentials are normalized as percent of normal action potential magnitude. Shock strength is 28 V/cm; fiber orientation is rotational (as in Fig. 2).

Figure 7

(Top) Map of ΔV_opt on the cut surface for a shock of 40 V/cm strength. Green (40 V/cm shock) and red (28 V/cm shock) dotted lines refer to locations where ΔV_m changes sign. (Bottom) Effect of the increase in shock strength from 28 V/cm to 40 V/cm on the optical ΔV_opt profile along a centrally located horizontal line (endo- to epicardium) on the cut surface of the same wedge as in Fig. 4, with permeable boundary conditions. Optical potentials are normalized as percent of normal action potential magnitude.