Rule-based definition of muscle bundles in patient-specific models of the left atrium

Figures

• 

  FIGURE 1. Top: Preprocessing steps: (A) Segmentation extracted from the patient computed tomography images. (B) Preprocessing of the endocardial surface after chopping the pulmonary veins opens and opening the mitral valve ring. (C) Thickened and retopologized atrial surface. Bottom: final preprocessed left atrial surfaces of eight patients who underwent WATCHMAN device implantation. We remark that most of these patients have accessory right pulmonary veins and two of them a common left pulmonary trunk. We label the anatomies using F and M, to indicate patients’ gender, followed by their age.

• 

  FIGURE 2. Boundary conditions and corresponding harmonic fields for M75. The field ϕ 0 captures the distance from the endocardial and epicardial surfaces, respectively g = 0 and g = 1, and its gradient defines the transmural direction s . Imposing g = 0 at the tip of the LAA and g = 1 at the center of the FO, the field ϕ 1 sweeps from the LAA to the FO. Setting g = 0 on the left PVs and g = 1 on the right PVs, the field ϕ 2 define the fibers on the anterior and posterior walls. With g = 1 on the superior PVs and g = 0 on the inferior PVs and intermediate values on the auxilliary PVs, the field ϕ 3 separates the anterior and posterior walls. The field ϕ 4 defines the Bachmann’s bundle, imposing g = 1 on the MV ring, g = 0.5 in the LAA and FO regions, and g = 0 on the major PVs and g = 0.1 on the right middle PVs. The field ϕ 5 identifies the left and right antras setting g = 0 on the left PVs and MV ring, g = 0.5 on the LAA, and g = 1 on the right PVs. The field ϕ 6 defines the fiber direction in the anterior wall, setting g = 0 on the left PVs, right inferior PV, and around the MV ring, g = 0.05 on the LAA, and g = 1 on the right PVs.

• 

  FIGURE 3. Region selection in M75. The left panel shows the regions common to the endocardial and epicardial layers that are first extracted by the algorithm After those are defined, the endocardial anterior is split into three regions and the epicardial anterior wall is split into four regions. Then, the lateral and posterior walls are defined in both layers. Notice that, in the epicardium, the inferior part of the septum is defined as separate subregion.

• 

  FIGURE 4. Endocardial (top) and epicardial (bottom) fiber fields, activation times and conduction velocities on M75. The Bachmann’s bundle on the epicardial layer wraps around the left atrial appendage. Note that the orientation of the fibers in the left and right carina and in the left lateral ridge are an improvement over existing methods in representing the anatomical muscle bundles. Similarly to Fastl et al. (2018), the fibers in the right posterior pulmonary veins are set longitudinally instead of circumferentially. The activation times and the conduction velocities show two main paths of activations: one circumferential through the Bachmann’s bundle and another superior and then posterior through the septoatrial bundle.

• 

  FIGURE 5. Boundary data and harmonic solutions on M52. We set g = 0 on the right inferior PV and g = 1 right superior PV when solving for ϕ 3. The accessory PVs are set to intermediate values between 0 and 1. On the left common pulmonary trunk we impose natural boundary conditions. This field is used to define the anterior and posterior walls. The boundary conditions for ϕ 4 are g = 0 on the right superior, inferior, and left common PVs. The value of g on the three right PVs that lie between the superior-most and inferior-most is 0.1. The boundary condition on the MV ring is g = 1, and the LAA and FO regions are set to 0.5.

• 

  FIGURE 6. Endocardial (top) and epicardial (bottom) fiber fields, activation times and conduction velocities on M52. The presence of the left common pulmonary trunk is easily accounted by the algorithm. The Bachmann’s bundle on the epicardial layer wraps around the left atrial appendage. Note that the orientation of the fibers in the right carina and in the left lateral ridge are an improvement over existing methods in representing the anatomical muscle bundles. Similarly to Fastl et al. (2018) the fibers in the right posterior pulmonary veins are set longitudinally instead of circumferentially. The activation times and the conduction velocities show two main path of activations: one circumferential through the Bachmann’s bundle and another superior and then posterior through the septoatrial bundle.

• 

  FIGURE 7. Fibers and local activation times for all geometries other than M75 and M52. Notice we show the final fiber architecture, with endocardial and epicardial layers superposed, in this visualization. Although the size of the geometries look similar, the sizes of the LA are different. That is evident by denser isolines and longer activation times in the LAA and PVS for larger geometries, such as M71.

• 

  FIGURE 8. Comparison of the results obtained using the proposed fiber construction algorithm and previously proposed by Fastl et al. (2018) and Piersanti et al. (2021). Using one of the three geometries provided by Fastl et al. (2018), we have built the fibers using the method proposed by Piersanti et al. (2021) using two possible threshold values for the parameter τ mv defining the extent of the Bachmann’s bundle. The fiber direction for the Fastl et al. (2018) model construction were available with the mesh. This comparison shows that the proposed algorithm for the definition of the fiber field on the left atrium capture the essential features of the complex algorithm proposed by Fastl et al. (2018), while maintaining the simplicity of the Piersanti et al. (2021). Because the simple algorithm proposed by Piersanti et al. (2021) considers only a single layer of fibers, the activation times on the anterior wall show a higher degree of anisotropy. Note that with this algorithm, the right superior pulmonary vein is one of the last regions to be activated, whereas propagation in the LAA does not follow the expected ostium-to-tip route.

• 

  FIGURE 9. Comparison of the results obtained using the proposed fiber construction algorithm and the atlas based method proposed by Roney et al. (2021). Using the first of the geometries provided by Roney et al. (2021), we built our approximation to the fiber field based on the endocardial and epicardial surfaces. This comparison shows that the major physiological fiber bundles can be captured by our algorithm on any given geometry in contrast to the mapping achieved using the atlas-based method. The resulting fibers generates different activation times, especially on the endocardial surface. Note that the smoothness of the fiber field is reflected in the final activation times.

• 

  FIGURE 10. Comparison of the results obtained using the proposed fiber construction algorithm and previously proposed by Wachter et al. (2015). Using the geometry provided by Loewe et al. (2016), we have built our approximation to the left atrial fiber architecture. Notice that the epicardial fiber structure proposed by Wachter et al. (2015) is dominated by the septopulmonary bundle in the anterior wall. The Bachmann’s bundle is defined in a narrower area than in the proposed algorithm. Therefore, the proposed algorithm yields an activation pattern with a pronounced horizontal component when compared to the model created by Wachter et al. (2015). In contrast with the model proposed by Wachter et al. (2015), the proposed algorithm yields longitudinal fibers in the inferior part of the epicardial septal region. This difference results in earlier activation of the left inferior PV in the former model than in the latter one. Besides that, in the model by Wachter et al. (2015), the myocardial strands cross the posterior wall in a higher position than the proposed model. This leads to a more oblique activation pattern in the posterior wall of the former model than in the latter one.