Figure 3.

(A) Endocardial CVs as a function of the curvature when no bath-loading conditions are considered (ℓ_b = 0 mm) for muscle thicknesses ℓ_bm = 0.25 μm, 0.5, 1, 1.5, and 2 mm. Note that the construction of the domain leads to different geometries for positive and negative curvatures. This is because we keep the endocardial length fixed, but we allow the epicardial surface to become shorter or longer. When a planar wave travels on a curved domain, endocardial CV are faster for negative curvatures and slower for positive curvatures. Since the left atrial posterior wall has mostly positive curvature, endocardial CVs are expected to be slower than in a flat piece of muscle. The case of mucles thickness 25 μm correspends to the case of two-dimensional manifolds in three-dimensional simulations. (B) Relative change in conduction velocities (with respect to CVs in a straight muscle) as a function of curvature for three selected values of the longitudinal conductivity coefficients but fixed transveral conductivities. Muscle thickness was fixed at 1.5 mm. Relative changes in CVs are not influenced by longitudinal conductivities. (C) Relative change in conduction velocities (with respect to CVs in a straight muscle) as a function of curvature for four selected values of the transversal conductivity coefficients but fixed longitudinal conductivities. Muscle thickness was fixed at 1.5 mm. Even for isotropic conditions (purple) endocardial CVs change depending on the curvature. Relative changes in CVs are only slightly influenced by transversal conductivities.