period waves with the frequency of the free spiral wave in the model, i.e. [11.36]{}. [[With the isotropic diffusivity ($\Ppar=\Port=1$) equal to the geometric mean between the faster and the slower anisotropic diffusivities ($\Ppar=2, \Port=1/2$), the isotropic conduction velocity 1.89 was almost exactly the same as the geometric mean 1.89 of the faster and slower (2.68 and 1.34 respectively) anisotropic conduction velocities, chosen in order to minimize the maximal relative difference between the isotropic and anisotropic propagation speeds.]{}]{}

All the computer simulations presented here were done using the [BeatBox]{} [@bbx-2017-PONE] software package with the explicit time-step Euler scheme, on the Cartesian regular grid with space step discretization $\Delta x=0.1$, time step discretisation $\Delta t=0.001$; 5-point stencil for isotropic, and 9-point stencil for anisotropic Laplacian approximation in 2D simulations; 7-point stencil for isotropic, and 27-point stencil for anisotropic Laplacian approximation in 3D simulations. The re-entry was initiated by the phase distribution method [@chaos]: in the 2D simulations, at a prescribed location of the cross section of the DT-MRI based anatomical model; in the 3D simulations, at a prescribed location of the full DT-MRI based whole heart anatomical model.

\[RESULTS\]Results
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\[2D\] 2D MRI-based “slice” simulations
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![image](Fig2.pdf)

In the 2D simulations, 