Three‐dimensional microwave imaging of realistic numerical breast phantoms via a multiple‐frequency inverse scattering technique

Abstract

Breast density measurement has the potential to play an important role in individualized breast cancer risk assessment and prevention decisions. Routine evaluation of breast density will require the availability of a low-cost, nonionizing, three-dimensional (3-D) tomographic imaging modality that exploits a strong properties contrast between dense fibroglandular tissue and less dense adipose tissue. The purpose of this computational study is to investigate the performance of 3-D tomography using low-power microwaves to reconstruct the spatial distribution of breast tissue dielectric properties and to evaluate the modality for application to breast density characterization. State-of-the-art 3-D numerical breast phantoms that are realistic in both structural and dielectric properties are employed. The test phantoms include one sample from each of four classes of mammographic breast density. Since the properties of these phantoms are known exactly, these testbeds serve as a rigorous benchmark for the imaging results. The distorted Born iterative imaging method is applied to simulated array measurements of the numerical phantoms. The forward solver in the imaging algorithm employs the finite-difference time-domain method of solving the time-domain Maxwell's equations, and the dielectric profiles are estimated using an integral equation form of the Helmholtz wave equation. A multiple-frequency, bound-constrained, vector field inverse scattering solution is implemented that enables practical inversion of the large-scale 3-D problem. Knowledge of the frequency-dependent characteristic of breast tissues at microwave frequencies is exploited to obtain a parametric reconstruction of the dispersive dielectric profile of the interior of the breast. Imaging is performed on a high-resolution voxel basis and the solution is bounded by a known range of dielectric properties of the constituent breast tissues. The imaging method is validated using a breast phantom with a single, high-contrast interior scattering target in an otherwise homogeneous interior. The method is then used to image a set of realistic numerical breast phantoms of varied fibroglandular tissue density. Imaging results are presented for each numerical phantom and show robustness of the method relative to tissue density. In each case, the distribution of fibroglandular tissues is well represented in the resulting images. The resolution of the images at the frequencies employed is wider than the feature dimensions of the normal tissue structures, resulting in a smearing of their reconstruction. The results of this study support the utility of 3-D microwave tomography for imaging the distribution of normal tissues in the breast, specifically, dense fibroglandular tissue versus less dense adipose tissue, and suggest that further investigation of its use for volumetric evaluation of breast density is warranted.