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Mesh structure-independent modeling of patient-specific atrial fiber orientation

  • Andreas Wachter EMAIL logo , Axel Loewe , Martin W Krueger , Olaf Dössel and Gunnar Seemann
Published/Copyright: September 12, 2015
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Current Directions in Biomedical Engineering
From the journal Current Directions in Biomedical Engineering Volume 1 Issue 1

Abstract

The fiber orientation in the atria has a significant contribution to the electrophysiologic behavior of the heart and to the genesis of arrhythmia. Atrial fiber orientation has a direct effect on excitation propagation, activation patterns and the P-wave. We present a rule-based algorithm that works robustly on different volumetric meshes composed of either isotropic hexahedra or arbitrary tetrahedra as well as on 3-dimensional triangular surface meshes in patient-specific geometric models. This method fosters the understanding of general proarrhythmic mechanisms and enhances patient-specific modeling approaches.

Keywords: fiber orientation; atrial modeling; anisotropy; surface mesh; volumetric mesh

1 Introduction

The fiber orientation in the atria has a significant effect on the spread of depolarization. Thus, it is important to include fiber orientation in computational models to understand the development and perpetuation of atrial arrhythmias. Atrial flutter is sustained along flutter paths which are usually aligned with the fibers. To predict e.g. the effect of radio frequency ablation in-silico, it is better to have realistic fiber orientation in patient-specific anatomical models.

Earlier, we presented an algorithm working on hexahedral meshes with fixed resolution [1]. On that base, a new algorithm was developed that works on volumetric structures composed of either hexahedra or tetrahedra as well as on triangular surface meshes. The rules used in the algorithm are based on [3–5]. In this paper, we present a complete and comprehensive description of the method and selected results.

Figure 1 Initial seed points in the RA and the LA.
Figure 1

Initial seed points in the RA and the LA.

2 Methods

2.1 Seed points

The algorithm works on the same 22 seed points, as the algorithm in [1, 2]. The seed points are marked in a preprocessing step by the user or a segmentation tool. Points are defined as centroids of cells yielding an approach independent of mesh structure. The seed points comprise 9 points in the right atrium (RA) and 13 points in left atrium (LA) (see Figure 1).

R1, R2, R3 mark the superior vena cava (SVC). R1 lies medial, close to R4. R2 lies anterior, in direction of the tricuspid valve. R3 is located at the junction of the SVC and the right atrial appendage (RAA). R4 and R5 mark the inferior vena cava (IVC) and lie at the junction of the atrial wall and the IVC. R6 marks the tip of the RAA. R7, R8 and R9 mark the tricuspid valve (TV). R7 is localized superior, apical, R8 inferior and R9 medial and close to the LA.

L1, L2 and L3 mark the mitral valve (MV) with L1 being localized close to the left atrial appendage (LAA), L2 lies posterior and L3 close to the RA. L5, L7, L9 and L12 define the left pulmonary veins (LPVs). L5, L7 and L9 form a line across the LPVs. L5, L7, L12 mark left superior pulmonary vein (LSPV). L5 is located superior, at the junction of the LAA and the LSPV. L7 is localized right lateral, between the LPVs, L12 left lateral, between the LPVs and the LAA. L12, L7 and L9 mark the left inferior pulmonary vein (LIPV) together with a later defined and computed additional point. L9 is located at the inferior border of the LSPV. L4, L6, L8 and L13 define the right pulmonary veins (RPVs). L4, L6 and L8 form a line on the RPVs. L4 is located superior, left lateral of the right superior pulmonary vein (RSPV). L6, L8, L13 mark the right inferior pulmonary vein (RIPV). L6 is located superior, at the beginning of the junction of the RSPV and the RIPV. L8 is located inferior of the RSPV, L13 right lateral, close to the RA. L10 marks the end of Bachmann’s Bundle (BB) in the LA and L11 marks the tip of the LAA.

2.2 Connecting paths

Paths are defined as connections between two points on the mesh. An auxiliary path (aPath) is calculated only to define a point on it but is not used to define fiber orientation. Paths are named using the start point, intermediate points if existent and the end point. Paths are calculated using a modified Dijkstra algorithm penalizing deviations from the direct connecting line:

min⁡(∑i=0n(‖ai+1−ai‖+‖an−a0×(ai+1−a0)‖‖(an−a0)‖))

A path with an equal start and end point is named as circular path (cPath). Paths are dilated radially into unmarked tissue to obtain the desired width of the muscular bundle represented by the path. Orientation is defined by the vector between two adjacent points along a path. Orientation and material class are saved for each cell. Paths are smoothed using orientation averaging of the 5 previous and 5 succeeding cell orientations on the path.

The paths in RA are shown in Figure 2. The cPath SVC runs from R1 via R2 and R3 to R1 and is dilated to a width (w) of 8.58 mm. The cPath TV runs from R8 via R7 and R9 to R8 (w = 12.54 mm). The path from the SVC to the TV runs from R12, placed at 3 % of PathR3R1, to R7 (w = 7,92 mm). The Crista Terminalis (CT) runs from R3 via R12, R4, R14 to R16. R14 is placed at 60 % of PathR4R5. PathR4R5 runs from R4 to R5. R16 is placed at 25 % of PathR14R15. R15 is placed at 20 % of PathR12R7. PathR12R4 is restricted to a 3D plane defined by R4, R12 and R14. The width of the first part of the CT (R3, R12 and R4) decreases linearly from 7.92 mm at R3 to 5.28 mm at R4. The second part of CT has a constant width of 5.28 mm. PathR16R15 is dilated to w = 9.24mm. PathR13R17 runs from the SVC to the top of the RAA (w = 3.96 mm). R13 is placed at 85 % of PathR2R3. R17 is placed at 6.6 mm from R13 along the aPathR13R6. The 15 pectinate muscles (PM) run from a part of the CT (origin path) to a part of PathR7R8 (destination path). The origin path runs from 10 % of PathR7R8 to the end. The destination path runs from 3 % to 100 % of the PathR12R4 and is extended by PathR4R14. The first muscle runs from the begining of the origin path to the begining of the destination path (w = 2.64 mm) at the first 4.95 mm of the path. The rest is of widthw = 1.32 mm. The other muscles begin and end at every 7.143 %. The remaining PMs arew = 1.32 mm. The PathR1R20 (w = 5.28 mm) is the superior border of the intercaval bundle (ICB). R20 is placed at 20 % of PathR12R4.

Figure 2 Calculated paths and points in the RA and in the endocar-dial layer of the LA.
Figure 2

Calculated paths and points in the RA and in the endocar-dial layer of the LA.

The inferior border of the ICB (w = 7.92 mm) runs from R2 via R23 (placed at 50 % of PathR1R2) to R28 (placed at 90 % of PathR12R4). The paths covering the RAA are described below. The LA wall is subdivided in two layers. 40 % of the wall is considered the endocardial layer (EnL) and 60 % the epicardial layer (EpL). The fiber orientation is defined separately for each layer.

The paths in the EnL are shown in Figure 2. cPathL1L2L3L1 marks the MV (w = 9.9 mm). All other paths from the EnL are set tow = 5.28 mm with dilation restricted to the EnL. cPathL4L6L8L13L4 marks the RPVs. cPathL5L7L9L31L12L5 marks the LPVs. L31 is placed at 30 % of aPathL1L9. PathL1L32L12L7 divides the LPVs in the LSPV and the LIPV. The middle-line between the LPVs and the RPVs runs from L18 via L19 to L21. L18 is placed at 50 % of aPathL5L4. L19 is placed at 50 % of aPathL7L6. L21 is placed at 50 % of aPathL19L20. L20 is placed at 50 % of aPathL9L8. The middle-line is subdivided into two paths: one from L21 to L9 and one from L21 to L8. The first connecting path between the MV and LPVs runs from L1 via L16 to L5. L16 is placed at 50 % of aPathL1L4. The second path runs from L14 to L4, L14 is placed at 80 % of aPathL2L3.

The paths in the EpL are shown in Figure 3. cPathL1L2L3L1 marks the MV (w = 9.9 mm). All other paths are set to w = 6.6 mm with dilation restricted to the EpL. An additional dilation restricted to the EnL (w = 8.58 mm) is performed. cPathL6L8L13L6 marks the RIPV. PathL26L24L22L4L6 encircles a part of the RPVs. L26 is placed at 20 % of aPathL9L1. L24 is placed at 10 % of aPathL8L2. L22 is placed at 10 % of aPathL4L14. L14 is placed at 80 % of aPathL2L3. PathL8L24 links the RIPV with PathL26L24L22L4L6. cPathL5L12L26L9L7L5 encircles the LPVs. A horizontal path runs from L5 via L23, L25 and L27 to L12. L23 is placed at 80 % of aPathL4L14. L25 is placed at 80 % of aPathL8L2. L27 is placed at 75 % of aPathL9L1. PathL26L33L12L7 also encircles the LIPV. L33 is placed at 5 % of aPathL26L1. The paths covering the LAA are described below.

Figure 3 Paths and points in the RA, the epicardial layer of the LA. Dashed straight lines between RA and LA indicate interatrial bridges.
Figure 3

Paths and points in the RA, the epicardial layer of the LA. Dashed straight lines between RA and LA indicate interatrial bridges.

2.3 Pulmonary veins & appendages

If an outward-oriented trunk of the vein is included in the model, the center point of the orifice is computed as the center of a path’s bounding box. For the LSPV, cPathL5L7L12L5 is used. For the LIPV, cPathL7L9L26L12L7; for the RSPV cPathL4L6L13L4; and for the RIPV cPathL6L8L13L6. To define an external point of the vein, the outwardly-oriented normal vector of the orifice plane is calculated. The path at the base of the vein is repeated towards that point. Smoothing is performed using all adjacent cells.

To mark the appendages, the border path at the base of the appendage is calculated first. Then, it is dilated up to the tip of the appendage. The supporting points (SPs) in the RA are R17, R21, R22, R23 and R26. R21 is placed at 55 % of PathR12R7. R22, R23 and R26 are placed at 59 %, 43 % and 20 % of the first PM. R17, R22, R23 are moved at least 0.66 mm towards R6. It means that the SP are moved until the path length of cells with no fiber orientation is equal with the distance covered. R21 and R26 are moved at least 1.32 mm towards R6. The border path runs from R17 via R22, R23, R26 and R21 to R17. It is dilated transmurally to separate the appendage from the rest of the RA. The border plane is dilated tow = 5.28 mm and up to R6. The SPs in the LA are L1, L5, L10, and L12. L1 is moved at least 7.26 mm towards L11 in the EpL. L5 and L10 are moved at least 0.99 mm in EpL towards L11. L12 is moved at least 6 mm or more in the EpL towards the recently moved point L1. The border path runs from L1 via L12, L5 and L10 to L1 regardless of the layer. The border plane is dilated transmurally tow = 5.2 mm in both layers and up to L11.

2.4 Region growing

The fiber orientation of cells which are not marked by any path are set using region growing. In isolated areas surrounded by only one type of material, the cells adopt the orientation of the closest border cell. If the area is surrounded by more than one type of material, the cells adopt the averaged orientation of the different material classes weighted by the inverse distance. The regions interpolated using two paths in the RA are: the areas between the PMs and the area between the first PM and the RAA; the area between the superior ICB and the inferior ICB; the area between PathR12R7 extended by PathR7R8R9; and the 15th PM extended by PathR14R16. PathR16R15 is only grown in the area which lies in direction of R7 of the plane defined by R14, R17 and R4. The region not lying in the direction of R7 but in direction of R20 from the plane defined by R28, R2 and R38 are defined as non-isthmus. The cells lying in direction of R7 from the plane defined by R18, R16 and R32 and having no orientation are defined as the isthmus region with an undefined orientation. In the LA, the areas between the middle-line and the LPVs, respectively RPVs are interpolated. Before the region can be grown, it must be isolated from the rest of the EnL. Therefore aPathL5L4 is calculated (w = 5.28 mm). Then, the path is deleted and the area between PathL1L16L5 and PathL14L4 is interpolated. For the rest of remaining areas, cross-layer interpolation is allowed. The area between PathL4L6L8L24 and PathL26L9L7L5 is interpolated after being isolated from the rest of the EnL and EpL by aPathL5L6 (w = 7.26 mm in both layers). Then, this path is deleted and the area between PathL5L23L25L27L12 and PathL26L24L22L4L6 is interpolated. The remaining orientation holes are closed using interpolation between material classes.

2.5 Interatrial bridges

The algorithm can set up to 6 interatrial bridges as their presence differs interindividually and can mostly not be extracted from imaging data. A bridge is defined by an LA point and an RA point, the width of the bridge and a search radius (r) for the breakthrough point (BTP). The direct line between the given RA and LA points is dilated by the search radius. Then, the closest RA point (R*) to the given LA point within that region is identified and vice versa (L*). The BTPs in the RA and the LA are identified as the closest points to the midpoint between R* and L*. The BTPs are the start and the end point of the bridge. The BB extends into both atria. In the RA, it runs from R3 via R30 to R7. R30 is placed at 40 % of PathR12R7. Hence, the BB surrounds the RAA partially. R30 is the start point of the actual bridge, L10 is the end point. The search radius is 2.31 mm. The right BTP is connected with the closest point on PathR3R30R7 and the left BTP is connected with L10. From L10, the BB runs to L5 and from L10 to L1, thus it partially surrounds the LAA. The superior posterior bridge runs from L13 to R29, the middle posterior bridge from L8 to R4, the coronary sinus (CS) bridge from L2 to R14, the middle anterior bridge from L10 to R2 and the inferior anterior bridge from L3 to R21. The search radius is 0.66 mm for all bridges except for the middle anterior bridge (2.31 mm).

Figure 4 Annotated fiber orientation in a volumetric structured hexahedral model including interatrial bridges. Colors correspond to paths in Figures 2 and 3.
Figure 4

Annotated fiber orientation in a volumetric structured hexahedral model including interatrial bridges. Colors correspond to paths in Figures 2 and 3.

Figure 5 Annotated fiber orientation in a trianguler surface mesh including interatrial bridges. Colors correspond to paths in Figures 2 and 3.
Figure 5

Annotated fiber orientation in a trianguler surface mesh including interatrial bridges. Colors correspond to paths in Figures 2 and 3.

3 Results

The algorithm was tested on two different geometries with three different mesh types each (hexahedra, tetrahedra and triangles). The resulting fiber orientation show that the algorithm allows fiber crossing in the meshes (see Figure 4 for hexahedral mesh and Figure 5 for triangular surface mesh). For hexahedral meshes the fiber orientation its comparable to previous results. For surface meshes, EnL and EpL results were saved in different containers. The CS orifice and IVC orifice were not marked as they are not covered by seed points. For setting interatrial bridges, each mesh type has its own method to include new elements. The height of the BB in the surface mesh does not reduce with increasing distance to the BTP.

4 Conclusion

We presented a complete and comprehensive description of a rule-based algorithm to annotate the atrial fiber orientation and bridges. Our method works independent from the underlying mesh structure (triangles, tetrahedra, hexahedra). Based on 22 seed points, the fiber architecture was defined layer-specifically resulting in a smooth fiber orientation for different mesh structures and models. To ensure robustness regarding patient-specific geometries, the seed points must be placed in a reproducible way. The fiber orientation in the pulmonary veins are not marked exactly radial due to the dilation from the base of the veins. Anatomic differences like different numbers of pulmonary veins are currently not handled by the algorithm leaving room for future development.

In conclusion, the presented method provides a tool to enhance computational models. On the one hand, this augments patient-specific modeling. On the other hand, it may eventually help to understand principal pro-arrhythmic mechanisms.

Author’s Statement

  1. Conflict of interest: Authors state no conflict of interest. Material and Methods: Informed consent: Informed consent has been obtained from all individuals included in this study. Ethical approval: The research related to human use has been complied with all the relevant national regulations, institutional policies and in accordance the tenets of the Helsinki Declaration, and has been approved by the authors’ institutional review board or equivalent committee.

References

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[2] Krueger, M. W., Seemann, G., Rhode, K., et al.: Personalization of atrial anatomy and electrophysiology as a basis for clinical modeling of radio-frequency ablation of atrial fibrillation. Medical Imaging, IEEE 2013; 32(1): 73–8410.1109/TMI.2012.2201948Search in Google Scholar PubMed

[3] Papez J. W.: Heart musculature of the atria. American Journal of Anatomy 1920; 27: 255–28610.1002/aja.1000270302Search in Google Scholar

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Published Online: 2015-9-12
Published in Print: 2015-9-1

© 2015 by Walter de Gruyter GmbH, Berlin/Boston

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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https://doi.org/10.1515/cdbme-2015-0099
Keywords for this article
fiber orientation; atrial modeling; anisotropy; surface mesh; volumetric mesh
Creative Commons
BY-NC-ND 3.0

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