Extended Data Figure 8 : Anisotropy of electromechanical rotor patterns in elastic excitable media (computer simulation) and effect of mechanical inhomogeneity onto mechanical phase singularities.

From: Electromechanical vortex filaments during cardiac fibrillation

Extended Data Figure 8

a, b, d, Dependence of local strain rate amplitude and strain rate morphology on the direction of wave propagation relative to muscle fibres. The electrical spiral wave pattern (a) and corresponding elastomechanical strain rate patterns (b, d) form in two identically prepared simulation domains with differing underlying vertical (b) and horizontal (d) muscle fibre anisotropy (uniform transverse linear fibre orientation). c, The contractions along the fibre orientation produce stronger strain rate amplitudes when the wave propagates along the fibre orientation (green time-series in b, sampled from the green triangle) and weaker strain rate amplitudes when the wave propagates perpendicular to the fibre orientation (orange time-series in b, sampled from the orange triangle). Overall, the morphology of the strain rate pattern aligns with the fibre orientation and exhibits stronger gradients between dilating and contracting rates of deformation along the fibre orientation than perpendicular to it (polarization). The deformation data were obtained in quasi-2D electromechanical computer simulations with homogeneous active tension development and immediate electromechanical coupling and simulation domains with finite thickness (see Methods). eh, Sensitivity of phase singularity detection to external perturbations depending on the direction of wave propagation relative to fibres. e, Strain rate pattern superimposed with electrical (blue circle) and elastomechanical phase singularities (red circles) in a domain with uniform vertical fibre anisotropy. Perturbations caused by boundary conditions can distort the phase pattern and lead to the detection of spurious mechanical phase singularities, preferentially along the direction that is perpendicular to the fibre orientation. The spurious mechanical phase singularities propagate outwards away from the spiral wave core. f, Addition of a weak global strain perturbation exacerbates this effect in the direction that is perpendicular to the fibre orientation. g, Phase of strain rate shown in e used for the computation of the phase singularities also reveals anisotropy and polarization. h, The strong strain rate signal parallel to the fibre orientation (green time-series) is largely unaffected by a small perturbation, whereas, for the same perturbation amplitude, the strain rate signal in the low-amplitude region perpendicular to the fibre orientation is distorted more strongly (orange time-series). The deformation was obtained in simulations identical to those shown in ad. Phase singularities from both the electrical signal and the strain rate were calculated using Hilbert transforms.