Thyroid nodules are a common clinical problem. Ultrasonography (US) is the main tool used to sensitively diagnose thyroid cancer. Although US is non-invasive and can accurately differentiate benign and malignant thyroid nodules, it is subjective and its results inevitably lack reproducibility. Therefore, to provide objective and reliable information for US assessment, we developed a CADx system that utilizes convolutional neural networks and the machine learning technique. The diagnostic performances of 6 radiologists and 3 representative results obtained from the proposed CADx system were compared and analyzed.

This paper utilizes the Picard method and Newton's method to linearize the stationary incompressible Navier-Stokes equations and then uses an LL* approach, which is a least-squares finite element method applied to the dual problem of the corresponding linear system. The LL* approach provides an L 2-approximation to a given problem, which is not typically available with conventional finite element methods for nonlinear second-order partial differential equations. We first show that the proposed combination of linearization scheme and LL* approach provides an L 2-approximation to the stationary incompressible Navier-Stokes equations. The validity of L 2-approximation is proven through the analysis of the weak problem corresponding to the linearized Navier-Stokes equations. Then, the convergence is analyzed, and numerical results are presented.

No abstract