Modeling the role of the coronary vasculature during external field stimulation

Abstract

The exact mechanisms by which defibrillation shocks excite cardiac tissue far from both the electrodes and heart surfaces require elucidation. Bidomain theory explains this phenomena through the existence of intramural virtual electrodes (VEs), caused by discontinuities in myocardial tissue structure. In this study, we assess the modeling components essential in constructing a finite-element cardiac tissue model including blood vessels from high-resolution magnetic resonance data and investigate the specific role played by coronary vasculature in VE formation, which currently remains largely unknown. We use a novel method for assigning histologically based fiber architecture around intramural structures and include an experimentally derived vessel lumen wall conductance within the model. Shock-tissue interaction in the presence of vessels is assessed through comparison with a simplified model lacking intramural structures. Results indicate that VEs form around blood vessels for shocks > 8 V/cm. The magnitude of induced polarizations is attenuated by realistic representation of fiber negotiation around vessel cavities, as well as the insulating effects of the vessel lumen wall. Furthermore, VEs formed around large subepicardial vessels reduce epicardial polarization levels. In conclusion, we have found that coronary vasculature acts as an important substrate for VE formation, which may help interpretation of optical mapping data.

Fig. 1

Computational model generation. (a) Axial slice through the raw MR rabbit data set, showing the selected region of the LV free wall used to produce the wedge model and the final segmentation of this area with papillary muscles manually removed. (b) Identification of artery (red) and vein (blue) vessel trees within the finite element wedge model. (c) Example of tagged elements within the mesh representing the vessel lumen wall (black) as distinct from the surrounding myocardium (blue) or other extracellular bath region (yellow).

Fig. 2

Results of Laplace-Dirichlet solves within the wedge model with electrodes placed to produce circumferential (a) and apex-base (b) fields. In each case, vectors representing explicit field gradients are shown in horizontal and vertical slices through the model, respectively.

Fig. 3

Final representation of fibre vectors within the wedge model visualised in a slice along the xy-plane. Colour-bar represents the out-of-plane component of the fibre vectors.

Fig. 4

(a) Electrode set-up for pacing and delivery of external field stimuli. (b) Discontinuous representation of fibre architecture within the complex model, highlighting the same region shown in Fig. 3(b).

Fig. 5

Shock-end V_m distributions within the complex (top) and simplified (bottom) models following application of external stimuli of varying SS.

Fig. 6

Quantitative analysis of transmural V_m profile. (a) Bi-sectional cut through complex wedge model along xy-planes showing positions of transmural lines for plotting V_m values. (b) & (c) Variation in V_m along transmural line A for SS of −10 V (yellow), 1 V (black), 4 V (green), 10 V (red) and 20 V (blue) in the complex (b) and simple (c) model. (d) Variation in maximum δV_m of tissue (on ground side) adjacent to 3 different diameter vessels with SS.

Fig. 7

Histograms showing the percentage of nodes in the intramural region (left) with δV_m levels < −10 mV (blue), between −10 and 10 mV (green), and > 10 mV (yellow); and, epicardial region (right) with δV_m levels < 50 mV (blue), between 50 and 150 mV (green), and > 150 mV (yellow), for different SS for complex and simple models.

Fig. 8

(a) (left) Shock-end V_m distribution (SS 20 V) within complex model for the case where the reduced conductivity of the lumen wall (Fig. 1(d)) has not been represented (i.e. $g_e^{lum}=1.0$ S/m). (right) Difference map of V_m distribution for normal case ($g_e^{lum}=1.0$ S/m, left panel) minus that of experimentally-derived case ($g_e^{lum}=0.010$ S/m), with selected region in vicinity of large vessel highlighted. (b) Difference maps of V_m distributions (SS 20 V) for varying $g_e^{lum}$ conductivities minus V_m distribution of experimentally-derived case (Fig. 5), with selected region in vicinity of large vessel highlighted.

Fig. 9

(a) Shock-end V_m distribution (SS 20 V) within complex model with discontinuous fibre architecture, with distribution near large blood vessel highlighted (bottom, left) and corresponding V_m distribution with continuous fibre architecture from Fig. 5 (SS 20 V, complex model) (bottom, right). (b) Difference map of V_m distribution of panel (a) minus that of Fig. 5 (SS 20 V, complex model), with selected regions near large vessels highlighted right.