Figure 3From left to right (a): original MRI slice; pixels with gray value higher than 0; pixels with gray value higher than 0 after curvature flow filter and low threshold. From left to right (b): C-means with 4 clusters; clusters with skin and dense tissue; …Final segmented image needed selleck chem inhibitor some improvements. Skin-dense tissue separation explained above can leave skin artifacts inside the breast, with a thickness value of one pixel or dense tissue artifacts with a thickness value of one pixel attached to the skin. Those artifacts are removed with a smoothness iterative filter applied inside the breast that searches skin pixels or dense pixels (in contact with skin) with 3 of its 4 connected neighbor pixels with a value that does not belong to skin or dense cluster, respectively.

Skin segmentation method described in this work is able to segment skin in 2D slices, but 3D nature of DICOM images leaves spaces between slices. Those interslice millimeters may produce zones in a 3D reconstruction without skin, leaving internal breast tissues in contact with exterior. To solve this problem, an iterative 3D search adds skin pixels to internal tissues in contact with background (Figure 4). The final pixels labeled as skin were used as a mask to delete skin from original MRI, letting it ready for studies and analysis without skin interaction.Figure 4From left to right: one thickness skin artifact (up) and skin growing effect after skin pixel addition (down); skin with holes; reconstructed skin.2.2.

Fat and Dense Tissue SegmentationWith the skin removed, a partition clustering algorithm (C-Means) that searches for an optimal partition of the data into 2 clusters was used. The objective of the algorithm is to minimize the sum of squared errors (SSE) of the partition into C clusters (2), where x X is a data element and mC is the cluster C mean:��i��j=||xi?mCj||2.(2)The data is distributed randomly into each cluster, and then the algorithm chooses an optimal partition minimizing the cluster SSE, thus, proving the impact in the SSE formula by moving each data element from one cluster to another and changing the cluster membership to the one that minimizes the SSE. This is, if ||x?mj||2 < ||x?mi||2, Entinostat data element x will belong to cluster mj instead of cluster mi. C-means performs an accurate segmentation of the breast tissues in fatty and dense clusters [16, 23].2.3. Biomechanical ModelFinite element methods (FEMs) are the most popular methods for biomechanical modeling of the soft tissues due to their capability to model irregular structures and complex boundary conditions. In this paper, FEMs are used to perform the simulation of the breast compression during an X-Ray mammography. These simulations were carried out in the commercial package ANSYS.

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