Jacob D. Shea

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

PURPOSE 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. METHODS 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 Maxwells 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. RESULTS 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. CONCLUSIONS 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.

Contrast-enhanced microwave imaging of breast tumors: a computational study using 3D realistic numerical phantoms

The detection of early-stage tumors in the breast by microwave imaging is challenged by both the moderate endogenous dielectric contrast between healthy and malignant glandular tissues and the spatial resolution available from illumination at microwave frequencies. The high endogenous dielectric contrast between adipose and fibroglandular tissue structures increases the difficulty of tumor detection due to the high dynamic range of the contrast function to be imaged and the low level of signal scattered from a tumor relative to the clutter scattered by normal tissue structures. Microwave inverse scattering techniques, used to estimate the complete spatial profile of the dielectric properties within the breast, have the potential to reconstruct both normal and cancerous tissue structures. However, the ill-posedness of the associated inverse problem often limits the frequency of microwave illumination to the UHF band within which early-stage cancers have sub-wavelength dimensions. In this computational study, we examine the reconstruction of small, compact tumors in three-dimensional numerical breast phantoms by a multiple-frequency inverse scattering solution. Computer models are also employed to investigate the use of exogenous contrast agents for enhancing tumor detection. Simulated array measurements are acquired before and after the introduction of the assumed contrast effects for two specific agents currently under consideration for breast imaging: microbubbles and carbon nanotubes. Differential images of the applied contrast demonstrate the potential of the approach for detecting the preferential uptake of contrast agents by malignant tissues.

Three-Dimensional Microwave Breast Imaging: Dispersive Dielectric Properties Estimation Using Patient-Specific Basis Functions

Breast imaging via microwave tomography involves estimating the distribution of dielectric properties within the patients breast on a discrete mesh. The number of unknowns in the discrete mesh can be very large for 3-D imaging, and this results in computational challenges. We propose a new approach where the discrete mesh is replaced with a relatively small number of smooth basis functions. The dimension of the tomography problem is reduced by estimating the coefficients of the basis functions instead of the dielectric properties at each element in the discrete mesh. The basis functions are constructed using knowledge of the location of the breast surface. The number of functions used in the basis can be varied to balance resolution and computational complexity. The reduced dimension of the inverse problem enables application of a computationally efficient, multiple-frequency inverse scattering algorithm in 3-D. The efficacy of the proposed approach is verified using two 3-D anatomically realistic numerical breast phantoms. It is shown for the case of single-frequency microwave tomography that the imaging accuracy is comparable to that obtained when the original discrete mesh is used, despite the reduction of the dimension of the inverse problem. Results are also shown for a multiple-frequency algorithm where it is computationally challenging to use the original discrete mesh.

Estimating the Breast Surface Using UWB Microwave Monostatic Backscatter Measurements

This paper presents an algorithm for estimating the location of the breast surface from scattered ultrawideband (UWB) microwave signals recorded across an antenna array. Knowing the location of the breast surface can improve imaging performance if incorporated as a priori information into recently proposed microwave imaging algorithms. These techniques transmit low-power microwaves into the breast using an antenna array, which in turn measures the scattered microwave signals for the purpose of detecting anomalies or changes in the dielectric properties of breast tissue. Our proposed surface identification algorithm consists of three procedures, the first of which estimates points on the breast surface given channels of measured microwave backscatter data. The second procedure applies interpolation and extrapolation to these points to generate points that are approximately uniformly distributed over the breast surface, while the third procedure uses these points to generate a 3-D estimated breast surface. Numerical as well as experimental tests indicate that the maximum absolute error in the estimated surface generated by the algorithm is on the order of several millimeters. An error analysis conducted for a basic microwave radar imaging algorithm (least-squares narrowband beamforming) indicates that this level of error is acceptable. A key advantage of the algorithm is that it uses the same measured signals that are used for UWB microwave imaging, thereby minimizing patient scan time and avoiding the need for additional hardware.

A TSVD Analysis of Microwave Inverse Scattering for Breast Imaging

A variety of methods have been applied to the inverse scattering problem for breast imaging at microwave frequencies. While many techniques have been leveraged toward a microwave imaging solution, they are all fundamentally dependent on the quality of the scattering data. Evaluating and optimizing the information contained in the data are, therefore, instrumental in understanding and achieving optimal performance from any particular imaging method. In this paper, a method of analysis is employed for the evaluation of the information contained in simulated scattering data from a known dielectric profile. The method estimates optimal imaging performance by mapping the data through the inverse of the scattering system. The inverse is computed by truncated singular-value decomposition of a system of scattering equations. The equations are made linear by use of the exact total fields in the imaging volume, which are available in the computational domain. The analysis is applied to anatomically realistic numerical breast phantoms. The utility of the method is demonstrated for a given imaging system through the analysis of various considerations in system design and problem formulation. The method offers an avenue for decoupling the problem of data selection from the problem of image formation from that data.

MRI-Derived 3-D-Printed Breast Phantom for Microwave Breast Imaging Validation

We propose a 3-D-printed breast phantom for use in preclinical experimental microwave imaging studies. The phantom is derived from an MRI of a human subject; thus, it is anthropomorphic, and its interior is very similar to an actual distribution of fibroglandular tissues. Adipose tissue in the breast is represented by the solid plastic (printed) regions of the phantom, while fibro glandular tissue is represented by liquid-filled voids in the plastic. The liquid is chosen to provide a biologically relevant dielectric contrast with the printed plastic. Such a phantom enables validation of microwave imaging techniques. We describe the procedure for generating the 3-D-printed breast phantom and present the measured dielectric properties of the 3-D-printed plastic over the frequency range 0.5-3.5 GHz. We also provide an example of a suitable liquid for filling the fibroglandular voids in the plastic.

Contrast-enhanced microwave breast imaging

Tomographic maps of the dielectric distribution of breast tissue can be made at microwave frequencies by applying nonlinear optimization techniques to the electromagnetic inverse scattering problem. There is a mismatch between the resolution of UHF band microwaves and the feature size of fibroconnective and glandular breast tissues which fundamentally limits the ability of such imaging systems to clearly resolve these structures. Tumor detection is further challenged by the small intrinsic contrast between the dielectric properties of normal and malignant glandular tissues. The use of contrast agents to preferentially alter the properties of malignant tissues is a potential approach to improving detection performance. In this paper, we explore the information available to contrast-enhanced imaging of realistic numerical breast phantoms at microwave frequencies. Differential images are produced using three-dimensional tomographic reconstructions of the dielectric profiles before and after the introduction of a contrast agent to a malignant inclusion.

Numerical Study of Microwave Scattering in Breast Tissue via Coupled Dielectric and Elastic Contrasts

A computational investigation of microwave scattering in mechanically (or acoustically) excited breast tissue is conducted to explore the feasibility of combining dielectric and elastic properties contrasts to enhance breast cancer detection. The mechanical excitation induces tissue-dependent displacements in the heterogeneous breast interior, which modulate the scattered microwave signals. Sheet boundary conditions are implemented using the finite-difference time-domain (FDTD) method to efficiently compute the Doppler component of the scattered microwave signals. Simulation results for a 2D numerical phantom testbed demonstrate increased microwave scattering contrast between malignant and normal fibroglandular inclusions when elastic properties are exploited.

Three-dimensional microwave imaging of realistic breast phantoms via an inexact Gauss-Newton algorithm

Various microwave tomographic methods have been proposed for breast imaging and cancer detection (see for example [1] and references therein). Due to the very high computational cost associated with iterative inverse scattering algorithms, most studies to date have been limited to two-dimensional (2-D) reconstructions. Recent advances in three-dimensional (3-D) microwave inverse scattering are reviewed in [2].

Dielectric Characterization of PCL-Based Thermoplastic Materials for Microwave Diagnostic and Therapeutic Applications

We propose the use of a polycaprolactone (PCL)-based thermoplastic mesh as a tissue-immobilization interface for microwave imaging and microwave hyperthermia treatment. An investigation of the dielectric properties of two PCL-based thermoplastic materials in the frequency range of 0.5-3.5 GHz is presented. The frequency-dependent dielectric constant and effective conductivity of the PCL-based thermoplastics are characterized using measurements of microstrip transmission lines fabricated on substrates comprised of the thermoplastic meshes. We also examine the impact of the presence of a PCL-based thermoplastic mesh on microwave breast imaging. We use a numerical test bed comprised of a previously reported 3-D anatomically realistic breast phantom and a multi-frequency microwave inverse scattering algorithm. We demonstrate that the PCL-based thermoplastic material and the assumed biocompatible medium of vegetable oil are sufficiently well matched such that the PCL layer may be neglected by the imaging solution without sacrificing imaging quality. Our results suggest that PCL-based thermoplastics are promising materials as tissue immobilization structures for microwave diagnostic and therapeutic applications.