Based on the histologic whole slide images and the presented tissue characterization, we carried out manual segmentations of the different tissue classes and built 3D models. Our pipeline is presented in Fig.  6.

Concept for the reconstruction of 3D meshes for the patient-specific wall thickness and wall composition based on the segmented 2D histologic images. a image segmentation, b virtual inflation of segmented images, c contours derived from segmented and inflated images, d contours combined to 3D point clouds, e surface meshes from point clouds

In order to use a surface model from an arbitrary image modality for any kind of fluid or structural simulation, it must meet certain requirements. The surface must be closed and should not contain any non-manifolds or duplicate faces for easy processing. In addition, unrealistically sharp edges must be avoided; otherwise, this can lead to singular points with locally wrong solutions. But at the model edges, which represent a system boundary, a clear edge is necessary. These are, for example, the virtual slice planes where a model section is cut out from the surrounding structure. Therefore, a separate boundary condition is applied at these cut planes, which requires a clear demarcation from other boundaries like mechanically free surfaces.

The first step is the segmentation of the histologic images. Different segmentations were carried out manually: a segmentation of the inner and outer contour of the IA’s walls and a segmentation of the different tissue classes, as described in “Tissue classification in histologic images” section. While the histologic images contain small details, like cell nuclei, the segmented images comprise larger, uniformly colored areas. Therefore, the image resolution is reduced by 85%. On the segmented images, a virtual inflation as described by Glaßer et al. [11] is performed. For the virtual inflation, the inner contour is projected to a circle in order to account for deflation during the postmortem explanation of the specimens. We do not use the perfect circular inner contour, but use the interpolation step of 4/10, which was empirically determined to be a suitable interpolation step.

After the virtual inflation, the contours of the segmented areas are determined. For each tissue class, a binary mask is generated. Next, a connected component analysis is applied to the binary mask and the boundaries of each component are extracted with the Moore neighbor tracing algorithm using Jacob’s stopping criteria [12]. As a result, we obtain closed 2D contours for each 2D histologic whole slide image and the comprised tissue categories.

The next step is a point cloud generation from these 2D contours that represent different tissue types. During the slicing and scanning of the slides, the orientation of each individual histologic slice can vary. Therefore, an affine registration using the coherent point drift algorithm [19] with up to 40 iterations is carried out. After registration, the algorithm searches for corresponding contours in consecutive slices. The contours are re-sampled to have the same number of points as the contours of the previous slide. The distance between the centers of two contours as well as the average distance between corresponding points of two contours is calculated. Only contours of the same tissue class are considered for matching. Matching contours are summarized in 3D point clouds, where the z-coordinate depends on the slice number and slice distance.

The resulting point clouds have flat endings. While it is not visible in the data, we assume that abrupt changes are uncommon in human tissue. To generate a realistic model and avoid artifacts during simulation due to unnatural sharp edges, a cap is added to the start and end of the point clouds. The first and last contour of a point cloud are determined by the smallest and largest z-values, respectively. In addition, their midpoints are determined. While keeping the midpoint of the contour constant, several smaller contours are generated and added above/below the last/first contour. The factor for decreasing the contour is based on a parabolic function, and therefore, the resulting smaller contours form a cap. For this procedure, the midpoint has to be inside the contour. To ensure this, the contour is transformed to a binary image and a thinning algorithm yielding the centerline of the shape is applied [12]. The points of this centerline are the candidates for the midpoint of the contour. The point with the largest distance to the nearest contour point is chosen as the midpoint (see Fig. 7).

a Last contour of a tissue segment (contour of the tissue in the last slide where this tissue segment was visible) as 3D point cloud; b corresponding binary image, red line: points left after thinning, blue circle: center of the contour; c example of a dome added to a contour in 3D, red: top contour blue: added points for the dome

In the last step, each point cloud is converted to a mesh by iterative fitting a start mesh to the points [20]. Due to tears in the tissue, folding of the tissues and impurities the contours from the images and the meshes might contain some noise. The meshes were manually smoothed to correct these problems. This results in meshes of the inner and outer contour and several meshes of larger regions of the same tissue type. Small intersections of the meshes may occur due to the mesh generation and smoothing. This can cause problems in applications like structural simulations. Boolean operations were used in this study to clear intersections and create distinct interfaces between meshes.

A structural simulation is generally based on simplifications and modeling assumptions. The solution is calculated only at discrete points. The number of these solution points depends on the spatial discretization and affect the computational effort. Therefore, the underlying surface model should only contain that level of detail, which can be spatial resolved by the simulation. In this investigation, structures smaller than 1mm3 are neglected.

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