Microwave tomography for early breast cancer detection based on the alternating direction implicit finite-difference time-domain method

Abstract

In microwave tomography (MWT), electric-parameter distributions of the breast can be reconstructed to detect the early-breast-cancer, which has a specific physical explanation and medical diagnostic value. In time-domain, the finite-difference time-domain (FDTD) method is usually applied to these problems. However, due to the constraint of Courant-Friedrich-Levy (CFL) stability condition, the time step should be small enough to well match the small fine cells, which begets an increasing computational cost, such as the central processing unit (CPU) time. For real-time clinical, it is very important and essential to look for efficient methods to improve the computational efficiency. The alternating-direction implicit finite-difference time-domain (ADI-FDTD) method, on the other hand, provides a larger time step than that the CFL stability condition limitation could set. In order to shorten the time of imaging and improve the detection efficiency, the ADI-FDTD method is first used for the early-breast-cancer detection in this paper. MWT for breast cancer detection requires solving nonlinear inverse scattering problems. Most nonlinear inversion algorithms require solving a number of forward scattering problems followed by an optimization procedure. Therefore, we turn the inverse scattering problem into an optimization question according to the least squares criterion. The optimization procedure aims at minimizing the error between measured scattered fields and estimated scattered fields by the forward solver. Nonlinear reconstruction algorithm is used to solve an update for the scattering object properties used in our breast model. This iteration process is repeated until the convergence between the measured and estimated data is obtained. The specific process of the iteration method is divided into two steps: the forward step, which is to solve a forward problem for a scattering object with estimated electrical properties, and the backward step, which is to solve adjoint fields by introducing the Lagrange multiplier penalty function. Both the forward and backward calculations are conducted by using the ADI-FDTD method. The algorithm is evaluated for a two-dimensional (2D) semicircle breast model with tumors. We compare the imaging results obtained by the ADI-FDTD method for various time steps with the results obtained by the conventional FDTD method and the real distribution. The results agree well, the simulation results prove that the imaging time by using this ADI-FDTD method can be reduced to 23% that by the conventional FDTD method. In addition, the simulation results suggest that the ADI-FDTD method can be more efficient if higher resolution is required, thus further enhancing the clinical applicability of MWT.