Three-dimensional microwave tomography: experimental prototype of the system and vector born reconstruction method

A Deep Learning Approach for Diagnosis Support in Breast Cancer Microwave Tomography

In this paper, a deep learning technique for tumor detection in a microwave tomography framework is proposed. Providing an easy and effective imaging technique for breast cancer detection is one of the main focuses for biomedical researchers. Recently, microwave tomography gained a great attention due to its ability to reconstruct the electric properties maps of the inner breast tissues, exploiting nonionizing radiations. A major drawback of tomographic approaches is related to the inversion algorithms, since the problem at hand is nonlinear and ill-posed. In recent decades, numerous studies focused on image reconstruction techniques, in same cases exploiting deep learning. In this study, deep learning is exploited to provide information about the presence of tumors based on tomographic measures. The proposed approach has been tested with a simulated database showing interesting performances, in particular for scenarios where the tumor mass is particularly small. In these cases, conventional reconstruction techniques fail in identifying the presence of suspicious tissues, while our approach correctly identifies these profiles as potentially pathological. Therefore, the proposed method can be exploited for early diagnosis purposes, where the mass to be detected can be particularly small.

An End-to-End Deep Learning Approach for Quantitative Microwave Breast Imaging in Real-Time Applications

(1) Background: In this paper, an artificial neural network approach for effective and real-time quantitative microwave breast imaging is proposed. It proposes some numerical analyses for the optimization of the network architecture and the improvement of recovery performance and processing time in the microwave breast imaging framework, which represents a fundamental preliminary step for future diagnostic applications. (2) Methods: The methodological analysis of the proposed approach is based on two main aspects: firstly, the definition and generation of a proper database adopted for the training of the neural networks and, secondly, the design and analysis of different neural network architectures. (3) Results: The methodology was tested in noisy numerical scenarios with different values of SNR showing good robustness against noise. The results seem very promising in comparison with conventional nonlinear inverse scattering approaches from a qualitative as well as a quantitative point of view. (4) Conclusion: The use of quantitative microwave imaging and neural networks can represent a valid alternative to (or completion of) modern conventional medical imaging techniques since it is cheaper, safer, fast, and quantitative, thus suitable to assist medical decisions.

Calibrated Frequency-Division Distorted Born Iterative Tomography for Real-Life Head Imaging

The clinical use of microwave tomography (MT) requires addressing the significant mismatch between simulated environment, which is used in the forward solver, and real-life system. To alleviate this mismatch, a calibrated tomography, which uses two homogeneous calibration phantoms and a modified distorted Born iterative method (DBIM), is presented. The two phantoms are used to derive a linear model that matches the forward solver to real-life measurements. Moreover, experimental observations indicate that signal quality at different frequencies varies between different antennas due to inevitably inconsistent manufacturing tolerance and variances in radio-frequency chains. An optimum frequency, at which the simulated and measured signals of the antenna present maximum similarity when irradiating the calibrated phantoms, is thus calculated for each antenna. A frequency-division DBIM (FD-DBIM), in which different antennas in the array transmit their corresponding optimum frequencies, is subsequently developed. A clinical brain scanner is then used to assess performance of the algorithm in lab and healthy volunteers' tests. The linear calibration model is first used to calibrate the measured data. After that FD-DBIM is used to solve the problem and map the dielectric properties of the imaged domain. The simulated and experimental results confirm validity of the presented approach and its superiority to other tomographic method.

A Versatile and Shelf-Stable Dielectric Coupling Medium for Microwave Imaging

OBJECTIVE

To develop a new class of emulsions using a protein-based emulsifier as the coupling fluid for microwave imaging systems.

METHODS

In this paper, we provide a theoretical basis for engineering shelf-stable dielectric fluids, a step-by-step formulation method, and measurements of complex dielectric properties in the frequency range of 0.5-3 GHz, which can be applicable for many of the recent microwave imaging systems.

RESULTS

This medium was primarily designed for long-term stability while providing a controllable range of complex dielectric permittivities given different fractions of its constituents. Consequently, this emulsion shows dielectric stability in open air throughout a 7-day experiment and temperature insensitivity over the range of 0 to 60 Celsius degree.

CONCLUSIONS

This control over dielectric permittivity enables formulations that tune the background-to-target contrast to the linearizable regime of iterative inverse scattering algorithms. Accordingly, the emulsion conductivity can also be controlled and reduced to maintain the required signal-to-noise ratio within the dynamic range of the imaging system. The new formulation overcomes the practical challenges of engineering coupling fluids for microwave imaging systems, e.g., temporal stability, non-toxic, low sensitivity to temperature variation, and easy formulation from readily available and inexpensive materials.

SIGNIFICANCE

The achieved properties associated with this new fluid are of particular benefit to microwave imaging systems used in thermal therapy monitoring.

Discrete Dipole Approximation-Based Microwave Tomography for Fast Breast Cancer Imaging

This paper describes a fast microwave tomography reconstruction algorithm based on the two-dimensional discrete dipole approximation. Synthetic data from a finite-element based solver and experimental data from a microwave imaging system are used to reconstruct images and to validate the algorithm. The microwave measurement system consists of 16 monopole antennas immersed in a tank filled with lossy coupling liquid and a vector network analyzer. The low-profile antennas and lossy nature of system make the discrete dipole approximation an ideal forward solver in the image reconstructions. The results show that the algorithm can readily reconstruct a 2D plane of a cylindrical phantom. The proposed forward solver combined with the nodal adjoint method for computing the Jacobian matrix enables the algorithm to reconstruct an image within 6 seconds. This implementation provides a significant time savings and reduced memory requirements and is a dramatic improvement over previous implementations.

Electromagnetic Torso Scanning: A Review of Devices, Algorithms, and Systems

The past decade has witnessed a surge into research on disruptive technologies that either challenge or complement conventional thoracic diagnostic modalities. The non-ionizing, non-invasive, compact, and low power requirements of electromagnetic (EM) techniques make them among the top contenders with varieties of proposed scanning systems, which can be used to detect wide range of thoracic illnesses. Different configurations, antenna topologies and detection or imaging algorithms are utilized in these systems. Hence, to appreciate their progress and assess their potential, a critical review of EM thoracic scanning systems is presented. Considering the numerous thoracic diseases, such as fatty liver disease, lung cancer, respiratory and heart related complications, this paper will exclusively focus on torso scanning systems, tracing the early foundation of research that studied the possibility of using EM waves to detect thoracic diseases besides exploring recent progresses. The advantages and disadvantages of proposed systems and future possibilities are thoroughly discussed.

Full-Vectorial 3D Microwave Imaging of Sparse Scatterers through a Multi-Task Bayesian Compressive Sensing Approach

In this paper, the full-vectorial three-dimensional (3D) microwave imaging (MI) of sparse scatterers is dealt with. Towards this end, the inverse scattering (IS) problem is formulated within the contrast source inversion (CSI) framework and it is aimed at retrieving the sparsest and most probable distribution of the contrast source within the imaged volume. A customized multi-task Bayesian compressive sensing (MT-BCS) method is used to yield regularized solutions of the 3D-IS problem with a remarkable computational efficiency. Selected numerical results on representative benchmarks are presented and discussed to assess the effectiveness and the reliability of the proposed MT-BCS strategy in comparison with other competitive state-of-the-art approaches, as well.

Electrical Characterization of Glycerin: Water Mixtures: Implications for Use as a Coupling Medium in Microwave Tomography

We examine the broadband behavior of complex electrical properties of glycerin and water mixtures over the frequency range of 0.1 - 25.0 GHz, especially as they relate to using these liquids as coupling media for microwave tomographic imaging. Their combination is unique in that they are mutually miscible over the full range of concentrations which allows them to be tailored to dielectric property matching for biological tissues. While the resultant mixture properties are partially driven by differences in the inherent low frequency permittivity of each constituent, relaxation frequency shifts play a disproportionately larger role in increasing the permittivity dispersion while also dramatically increasing the effective conductivity over the frequency range of 1 to 3 GHz. For the full range of mixture ratios, the relaxation frequency shifts from 17.5 GHz for 0% glycerin to less than 0.1 GHz for 100% glycerin. Of particular interest is the fact that the conductivity stays above 1.0 S/m over the 1-3 GHz range for glycerin mixture ratios (70-90% glycerin) we use for microwave breast tomography. The high level of attenuation is critical for suppressing unwanted multipath signals. This paper presents a full characterization of these liquids along with a discussion of their benefits and limitations in the context of microwave tomography.

Microwave tomography of extremities: 1. Dedicated 2D system and physiological signatures

Microwave tomography (MWT) is a novel imaging modality which might be applicable for non-invasive assessment of functional and pathological conditions of biological tissues. Imaging of the soft tissue of extremities is one of its potential applications. The feasibility of this technology for such applications was demonstrated earlier. This is the first of two companion papers focused on an application of MWT for imaging of the extremity's soft tissues. The goal of this study is to assess the technical performance of the developed 2D MWT system dedicated for imaging of functional and pathological conditions of the extremity's soft tissues. Specifically, the system's performance was tested by its ability to detect signals associated with physiological activity and soft tissue interventions (circulatory related changes, blood flow reduction and a simulated compartmental syndrome)--the so-called physiological signatures. The developed 2D MWT system dedicated to the imaging of animal extremities demonstrates good technical performance allowing for stable and predictable data acquisition with reasonable agreement between the experimentally measured electromagnetic (EM) field and the simulated EM field within a measurement domain. Using the system, we were able to obtain physiological signatures associated with systolic versus diastolic phases of circulation in an animal extremity, reperfusion versus occlusion phases of the blood supply to the animal's extremity and a compartment syndrome. The imaging results are presented and discussed in the second companion paper.

Microwave tomography of extremities: 2. Functional fused imaging of flow reduction and simulated compartment syndrome

Medical imaging has recently expanded into the dual- or multi-modality fusion of anatomical and functional imaging modalities. This significantly improves the diagnostic power while simultaneously increasing the cost of already expensive medical devices or investigations and decreasing their mobility. We are introducing a novel imaging concept of four-dimensional (4D) microwave tomographic (MWT) functional imaging: three dimensional (3D) in the spatial domain plus one dimensional (1D) in the time, functional dynamic domain. Instead of a fusion of images obtained by different imaging modalities, 4D MWT fuses absolute anatomical images with dynamic, differential images of the same imaging technology. The approach was successively validated in animal experiments with short-term arterial flow reduction and a simulated compartment syndrome in an initial simplified experimental setting using a dedicated MWT system. The presented fused images are not perfect as MWT is a novel imaging modality at its early stage of the development and ways of reading reconstructed MWT images need to be further studied and understood. However, the reconstructed fused images present clear evidence that microwave tomography is an emerging imaging modality with great potentials for functional imaging.

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 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.

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.

Using a priori information for regularization in breast microwave image reconstruction

Regularization methods are used in microwave image reconstruction problems, which are ill-posed. Traditional regularization methods are usually problem-independent and do not take advantage of a priori information specific to any particular imaging application. In this paper, a novel problem-dependent regularization approach is introduced for the application of breast imaging. A real genetic algorithm (RGA) minimizes a cost function that is the error between the recorded and the simulated data. At each iteration of the RGA, a priori information about the shape of the breast profiles is used by a neural network classifier to reject the solutions that cannot be a map of the dielectric properties of a breast profile. The algorithm was tested against four realistic numerical breast phantoms including a mostly fatty, a scattered fibroglandular, a heterogeneously dense, and a very dense sample. The tests were also repeated where a 4 mm x 4 mm tumor was inserted in the fibroglandular tissue in each of the four breast types. The results show the effectiveness of the proposed approach, which to the best of our knowledge has the highest resolution amongst the evolutionary algorithms used for the inversion of realistic numerical breast phantoms.

Microwave tomography for functional imaging of extremity soft tissues: feasibility assessment

It is important to assess the viability of extremity soft tissues, as this component is often the determinant of the final outcome of fracture treatment. Microwave tomography (MWT) and sensing might be able to provide a fast and mobile assessment of such properties. MWT imaging of extremities possesses a complicated, nonlinear, high dielectric contrast inverse problem of diffraction tomography. There is a high dielectric contrast between bone and soft tissue in the extremities. A contrast between soft tissue abnormalities is less pronounced when compared with the high bone-soft tissue contrast. The goal of this study was to assess the feasibility of MWT for functional imaging of extremity soft tissues, i.e. to detect a relatively small contrast within soft tissues in closer proximity to high contrast boney areas. Both experimental studies and computer simulation were performed. Experiments were conducted using live pigs with compromised blood flow and compartment syndrome within an extremity. A whole 2D tomographic imaging cycle at 1 GHz was computer simulated and images were reconstructed using the Newton, MR-CSI and modified Born methods. Results of experimental studies demonstrate that microwave technology is sensitive to changes in the soft tissue blood content and elevated compartment pressure. It was demonstrated that MWT is feasible for functional imaging of extremity soft tissues, circulatory-related changes, blood flow and elevated compartment pressure.

Microwave image reconstruction from 3-D fields coupled to 2-D parameter estimation

An efficient Gauss-Newton iterative imaging technique utilizing a three-dimensional (3-D) field solution coupled to a two-dimensional (2-D) parameter estimation scheme (3-D/2-D) is presented for microwave tomographic imaging in medical applications. While electromagnetic wave propagation is described fully by a 3-D vector field, a 3-D scalar model has been applied to improve the efficiency of the iterative reconstruction process with apparently limited reduction in accuracy. In addition, the image recovery has been restricted to 2-D but is generalizable to three dimensions. Image artifacts related primarily to 3-D effects are reduced when compared with results from an entirely two-dimensional inversion (2-D/2-D). Important advances in terms of improving algorithmic efficiency include use of a block solver for computing the field solutions and application of the dual mesh scheme and adjoint approach for Jacobian construction. Methods which enhance the image quality such as the log-magnitude/unwrapped phase minimization were also applied. Results obtained from synthetic measurement data show that the new 3-D/2-D algorithm consistently outperforms its 2-D/2-D counterpart in terms of reducing the effective imaging slice thickness in both permittivity and conductivity images over a range of inclusion sizes and background medium contrasts.

Inverse scattering for a three-dimensional object in the time domain

An iterative inverse-scattering approach to reconstruction of electrical parameter distributions of a three-dimensional object by using time-domain field data is presented. The approach is the extension of the forward-backward time-stepping algorithm previously proposed for a two-dimensional object. Numerical examples of simulation data are given to assess the effectiveness of the proposed approach.

Microwave breast imaging: 3-D forward scattering simulation

Active microwave imaging (MWI) is emerging as a promising technique for the detection of biomedical anomalies such as breast cancer because of the high electrical contrasts between malignant tumors and normal tissue. Previously, we have developed fast two-dimensional forward and inverse scattering algorithms for MWI systems. In this paper, we report the full three-dimensional (3-D) forward scattering simulation in order to account for 3-D effects and to provide a fast solver in future 3-D nonlinear inverse scattering methods. The 3-D fast forward method is based on the stabilized biconjugate-gradient fast Fourier transform (BCGS-FFT) algorithm. The method has been validated for various MWI measurement scenarios. Using this fast simulation method, we demonstrate the importance of accounting for 3-D effects in MWI, and we compare numerical results with the measurements from an experimental prototype.

Quantification of 3-D field effects during 2-D microwave imaging

Two-dimensional (2-D) approaches to microwave imaging have dominated the research landscape primarily due to the moderate levels of measurement data, data-acquisition time, and computational costs required. Three-dimensional (3-D) approaches have been investigated in simulation, phantom, and animal experiments. While 3-D approaches are certainly important in terms of the potential to improve image quality, their associated costs are significant at this time. In addition, benchmarks are needed to evaluate these new generation systems as more 3-D methods begin to appear. In this paper, we present a systematic series of experiments which assess the capability of our 2-D system to image classical 3-D geometries. We demonstrate where current methods suffer from 3-D effects but also identify situations where they remain quite useful. Comparisons between reconstructions utilizing phantom measurements and simulated 3-D data are also shown to validate the results. These findings suggest that for certain biomedical applications, 2-D approaches remain quite attractive.

Three-dimensional microwave tomography: initial experimental imaging of animals

The purpose of this study was to construct a microwave tomographic system capable of conducting experiments with whole scale biological objects and to demonstrate the feasibility of microwave tomography for imaging such objects using a canine model. Experiments were conducted using a three-dimensional (3-D) microwave tomographic system with working chamber dimensions of 120 cm in diameter and 135 cm in height. The operating frequency was 0.9 GHz. The object under study was located in the central area of the tomographic chamber filled with a salt solution. Experimentally measured attenuation of the electromagnetic field through the thorax was about -120 dB. To obtain images, we used various two-dimensional and 3-D reconstruction schemes. Images of the canine were obtained. In spite of imperfections, the images represent a significant milestone in the development of microwave tomography for whole body imaging and demonstrate its feasibility.

A two-stage microwave image reconstruction procedure for improved internal feature extraction

We have developed a two-stage Gauss-Newton reconstruction process with an automatic procedure for determining the regularization parameter. The combination is utilized by our microwave imaging system and has facilitated recovery of quantitatively improved images. The first stage employs a Levenberg-Marquardt regularization along with a spatial filtering technique for a few iterations to produce an intermediate image. In effect, the first set of iterative image reconstruction steps synthesizes a priori information from the measurement data versus actually requiring physical prior information on the interrogated object. Because of the interaction of the Levenberg-Marquardt regularization and spatial filtering at each iteration, the intermediate image produced from the first reconstruction stage represents an improvement in terms of the least squared error over the initial uniform guess; however, it has not completely converged in a least squared sense. The second stage involves using this distribution as a priori information in an iteratively regularized Gauss-Newton reconstruction with a weighted Euclidean distance penalty term. The penalized term restricts the final image to a vicinity (determined by the scale of the weighting parameter) about the intermediate image while allowing more flexibility in extracting internal object structures. The second stage makes use of an empirical Bayesian/random effects model that enables an optimal determination of the weighting parameter of the penalized term. The new approach demonstrates quantifiably improved images in simulation, phantom and in vivo experiments with particularly striking improvements with respect to the recovery of heterogeneities internal to large, high contrast scatterers such as encountered when imaging the human breast in a water-coupled configuration.

Microwave imaging using the finite-element method and a sensitivity analysis approach

A method for reconstructing the constitutive parameters of two-dimensional (2-D) penetrable scatterers from scattered field measurements is presented. This method is based on the differential formulation of the forward scattering problem, which is solved by applying the finite-element method (FEM). Given a set of scattered field measurements, the objective is to minimize a cost function which consists of two terms. The first is the standard error term, which is related to the measurements and their estimates, while the second term, which is related to the Tikhonov regularization, is used to heal the ill posedness of the inverse problem. The iterative Polak-Ribière nonlinear conjugate gradient algorithm is applied to the minimization of the cost function. During each iteration of the algorithm, the direction of correction is computed by using a sensitivity analysis approach, which is carried out by an elaborate finite-element scheme. The adoption of the finite-element method results in sparse systems of equations, while the computational burden is further reduced by applying the adjoint state vector methodology. Finally, a microwave medical imaging application, which is related to the detection of proliferated bone marrow, is examined, while the robustness of the proposed technique in the presence of noise and for different regularization levels is investigated.