Mechanical Characterization of Breast Compression with Cancerous Tissue Using an Axisymmetric Numerical Model

Resumo

Breast cancer is the leading cause of cancer-related deaths among women in Brazil and the second leading cause worldwide. Detecting the disease in its early stages is an effective way to increase survival rates. Ultrasound elastography is a non-invasive procedure used for this purpose, capable of providing data on tissue stiffness based on compression applied by an external force to the breast. Cancerous tissue is stiffer than the surrounding healthy tissue, and the nonlinear strain behavior of the compressed breast can be used to determine the nature of the inclusion using this approach. Since the relationship between applied forces and observed strains is essential for an accurate diagnosis, the mechanical characterization of the procedure becomes relevant. In this work, a numerical axisymmetric breast model is proposed. A simplified tissue distribution is modeled, incorporating a cancerous inclusion parameterized by its size and stiffness to represent different stages of the disease and tumor types (benign or malignant). The tissues were modeled as nonlinear elastic materials, and the breast model was compressed by a rigid spherical indenter to simulate the clinical elastography test, in which large strains and nonlinear geometric effects take place. The Finite Element Method was used for the numerical evaluation of the model, and parametric results were obtained by considering different cancerous inclusions and breast tissue distributions. While the results for tumors with small inclusions indicate no significant strain increase in the surrounding cancerous tissue compared to the healthy case, noticeable variations are observed for medium-sized and large tumors as stiffness increases. A relationship between applied forces and the increase in stiffness due to cancer characteristics is discussed and presented. The obtained results were compared with simplified theoretical analytical solutions for spherical indentation in a homogeneous material, as well as with results from other authors using different three-dimensional numerical models. As a result, the present simplified axisymmetric model shows good agreement in the mechanical characterization of the effect of cancerous inclusions on breast compression, while considering a simplified geometry and tissue distribution model, enabling fast and parametric analysis.