A Two-Phase Nonlocal Integral Continuum Model Combined with Machine Learning for Flexural Wave Propagation in Small-Scale Breast Ducts

The majority of breast malignancies arise from breast ducts at the small-scale level. Understanding the wave characteristics of breast ducts may assist in developing new technologies to detect very early changes that precede breast cancer. In this study, a two-phase nonlocal integral model is developed to analyse the biomechanical behavior of breast ducts under flexural wave propagation. The influence of surface stiffness, surface residual stress, stress nonlocality, and stromal matrix is taken into consideration. The breast duct consists of different biological layers, including the basement membrane, myoepithelial cells, and luminal epithelial cells. Surface properties are calculated for the outer basement membrane and inner luminal epithelial cell layer. The results of the two-phase nonlocal integral model are validated using available molecular dynamics simulations. In addition, various machine learning algorithms, such as a neural network model, gradient boosting, random forest, logistic regression, and Ridge regression, are developed and integrated with the two-phase nonlocal model to better understand the flexural wave characteristics of breast ducts. Incorporation of two-phase nonlocal integral stress effects, surface energy, and residual stress reduces the root mean square error from 4.16 to 0.24 when compared against molecular dynamics simulation data.