Desarrollo de un modelo matemático que determine el espesor de pared para diseño de prótesis mamarias externas

Abstract

The design of external breast prostheses is often based on empirical methods or suggestions from printing software, which can result in inadequate wall thicknesses: too thin, leading to easy deformation, or too thick, making them heavy and uncomfortable. In this work, a mathematical model is developed based on bending stress analysis to calculate the optimal wall thickness, relating geometric dimensions and mechanical properties of the material. The model considered the prosthesis divided into two geometric sections (half of an elliptical cone and a quarter of an ellipsoid) and calculated the bending moment, the moment of inertia, and the distance to the neutral axis to determine the required thickness. It was evaluated through finite element simulations in different mechanical design software, using digital prototypes from real 3D scans and applying a geometric correction factor to compensate for anatomical asymmetry. The results showed that the thickness increases with cup size and applied pressure or force, and that the adjusted model achieves an accuracy with an error of less than 22%. Additionally, a financial analysis is presented, confirming the commercial viability of the product with a competitive price and an attractive return on investment. Key Words: External breast prostheses, mathematical model, wall thickness, finite element simulation, additive manufacturing. II