Virtual electrodes around anatomical structures and their roles in defibrillation

Figures

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  Fig 1. Schematic of intracardiac RV electrode (blue), with an active “can” far from the RV electrode. The electric field around the RV electrode is shown in light-blue.

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  Fig 2. Cross-sectional slice of the rabbit ventricles [15] showing a highly trabeculated endocardial surface (left) and idealized geometries representing protrusions (middle) and grooves (right). The origin is located at the vertex of the parabolas.

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  Fig 3. Blood-vessel schematic. The fibre-field (given by Eq (6)) is shown by the grey lines and the stimulating field is aligned with the vertical axis (corresponding to the field-lines around the RV ICD electrode in Fig 1).

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  Fig 4. The non-dimensional transmembrane potential for the parabolic geometries with similar conductivities (left panel) and realistic conductivities (right-panel). The red lines show the streamlines of E. Note that here the transmembrane potentials for the protrusions (top row) were calculated using the semi-analytical scheme [9], whereas the FEM scheme (solving the full bidomain system) was used to calculate the transmembrane potentials for the grooves (bottom row).

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  Fig 5. The normalized depolarization (measured at the vertex) of domains with parabolic boundaries versus non-dimensional curvature. Data-points for positive curvatures (cλ > 0) were calculated using unstructured linear finite elements. Two sets of curves, corresponding to equal conductivities (solid line) and physiological conductivities (dashed line), are shown. Full bidomain results in a truncated domain are also shown (dotted line).

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  Fig 6. The value of the normalized VEs at r = a, θ = π/2 for the zeroth-order component (solid line), the first-order component (dot-dashed) and the resultant potential (dashed).

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  Fig 7. The VE pattern around a blood-vessel with an electric field aligned with the y axis. Red and blue colours indicate depolarization and hyperpolarization, respectively.

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  Fig 8. The steady-state bidomain solution for the transmembrane potential around blood-vessels of radius 0.5 mm (top row) and 3.0 mm (bottom row). The columns show the effects of the conductivities of the vessel cavity, in the case of no vessel wall (left column) and with a vessel wall (right column). The externally applied electric field was aligned with the vertical axis and had strength 10 V/cm; red lines show the streamlines of the electric field. The colorbar units are millivolts.

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  Fig 9. The steady-state bidomain solution for the transmembrane potential around insulators of radius 0.5 mm (left) and 3.0 mm (right). The externally applied electric field was aligned with the vertical axis and had strength 10 V/cm; red lines show the streamlines of the electric field. The colorbar units are millivolts.