Anisotropic conduction in the myocardium due to fibrosis: the effect of texture on wave propagation

Figures

• 

  Figure 1. A part of the texture with elongated fibrosis, wave propagation comes from the upper side of the square. The light color indicates activated cells, the dark color (brown) indicates non-activated cells and the black color indicates fibrosis. The wavefront is marked as a red line and the gap locations are marked at the edges with the purple color.

• 

  Figure 2. An example of point stimulus and elliptic wave propagation (red) for 15% fibrosis area with the obstacles size 0.25 × 0.75 mm.

• 

  Figure 3. An example of wave propagation through the fibrosis texture across (upper) and along (lower) the obstacles orientation for t = 25, 70, 115 msec. Fibrosis area is 20% and the fibrosis (obstacles) size is 0.25 × 1 mm. Activated areas are shown in the red color.

• 

  Figure 4. Wavefront velocity depending on fibrosis area in two wavefront directions. Error bars show the standard deviation of the wavefront velocity in 20 fibrosis pattern samples for each obstacle length.

• 

  Figure 5. Wavefront velocity normalized by the values of diffuse fibrosis.

• 

  Figure 6. Wavefront velocity normalized to values of diffuse (size = 0.25 mm) fibrosis depending on fibrosis length in two wavefront directions.

• 

  Figure 7. The shortest path from point (0, 50) to the opposite side in longitudinal direction (a) and from point (47, 0) to the opposite side in transversal direction (b) for the same matrix with 30% fibrosis area and 0.25 × 1 mm fibrosis size.

• 

  Figure 8. Normalized histograms of the shortest path for the longitudinal propagation (a) and transversal propagation (b) for 0.25 × 1 mm length fibrosis and for diffuse fibrosis (c). 5000 trajectories calculated in 20 fibrosis matrices of 30% are used for each histogram.

• 

  Figure 9. Ratio in conduction velocity between the longitudinal and transversal wavefront direction as a characteristic of the fibrotic texture anisotropy. Error bars show the standard deviation of the velocity’s ratio for 20 repeats with unique fibrosis matrices.

• 

  Figure 10. Wavefront velocities depending on the polar angle for 20 simulations with the same 15% fibrosis matrix with the obstacles size 0.25 × 1 mm. The red line shows the average value of the velocity, while the purple area limits its maximum and minimum value.

• 

  Figure 11. Effect of fibrosis texture on pre-existing anisotropy of cardiac tissue. (a) effect of diffuse fibrosis. Points show predictions for anisotropy based on results of Fig. 9 (further explanation are in the text); (b) schematic representation of normal (the upper pannel) and scaled (the lower pannel) textures; (c) Effect of fibrosis on anistropy for textures generated by obstacles of various size.

• 

  Figure 12. Dependence of the wavefront t-length on fibrosis density for longitudinal and transversal wave propagation. Error bars show the standard deviation of the t-length for 20 simulations for each fibrosis texture.