Mucoepidermoid carcinoma (MEC) is an invasive tumor that has been reported in many organs, such as the salivary glands, lungs, esophagus, and thymus; however, it rarely affects the breast. Here, we report a case of primary breast MEC with imaging, including mammography, ultrasonography, and magnetic resonance imaging.

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The acoustic wave equation is an important basis for seismic wave propagation, imaging, and migration. This equation has led to the development of finite difference methods, but these methods are prone to numerical instability and grid dispersion problems, with the issue of dispersion being the most vital. Optimization methods can improve the accuracy across a large range of wavenumbers or frequencies. In this paper, we present a novel evolutionary optimization scheme for the acoustic wave equation. Our approach involves combining the fruit fly optimization algorithm (FOA) and sampling approximation (SA) to obtain the optimal difference operator for a wide range of wavenumbers. The difference coefficients are optimized to be extracted by the FOA, and the function of fitness, which is used to introduce an iterative process to determine the best smells, is evaluated by acoustic wave simulations. Based on the space-domain dispersion relation, we prove that the accuracy with which the absolute error is minimized is the same as that of the relative error. Within a given range of wavenumbers, we propose a fitness function by minimizing the absolute errors of the space-domain dispersion relation, and the dispersion analysis reveals that this scheme is superior to the Taylor-expansion scheme. We conduct two experiments by applying homogeneous and complex models, respectively. Further, the modeling results indicate that the fruit fly optimization approach in conjunction with sampling approximation preserve a higher accuracy for a small operator length and reduce the numerical artifacts.