Two-step inversion with a logarithmic transformation for microwave breast imaging

On the utilization of the adjoint method in microwave tomography

In microwave imaging, the adjoint method is widely used for the efficient calculation of the update direction, which is then used to update the unknown model parameter. However, the utilization and the formulation of the adjoint method differ significantly depending on the imaging scenario and the applied optimization algorithm. Because of the problem-specific nature of the adjoint formulations, the dissimilarities between the adjoint calculations may be overlooked. Here, we have classified the adjoint method formulations into two groups: the direct and indirect methods. The direct method involves calculating the derivative of the cost function, whereas, in the indirect method, the derivative of the predicted data is calculated. In this review, the direct and indirect adjoint methods are presented, compared, and discussed. The formulations are explicitly derived using the two-dimensional wave equation in frequency and time domains. Finite-difference time-domain simulations are conducted to show the different uses of the adjoint methods for both single source-multiple receiver, and multiple transceiver scenarios. This study demonstrated that an appropriate adjoint method selection is significant to achieve improved computational efficiency for the applied optimization algorithm.

Microwave Vertebrae Strength Probe Development: Robust and Fast Phase Unwrapping Technique

We have developed a new transmission-based, open-ended coaxial probe for assessing vertebrae strength during spinal fusion surgery. The approach exploits the fact that the probes are within the far field of each other implying that the phase varies linearly with respect to propagation distance. Determining the absolute phase is critical for recovering the associated tissue dielectric properties from which bone strength will be determined. Unfortunately, unwanted multi-path signals corrupt the signals at the lower end of the operating frequency range from which our conventional unwrapping strategy depends. Our new approach requires only three measurements within the prime frequency range and can be determined robustly with a minimum of computations. This will be vital to developing a commercial device since the signal levels will be extremely low power requiring longer than usual data acquisition times, which will be mitigated by measuring the data at only a few frequencies. Fast and efficient operation will be critical for clinical success.

Review and Analysis of Tumour Detection and Image Quality Analysis in Experimental Breast Microwave Sensing

This review evaluates the methods used for image quality analysis and tumour detection in experimental breast microwave sensing (BMS), a developing technology being investigated for breast cancer detection. This article examines the methods used for image quality analysis and the estimated diagnostic performance of BMS for image-based and machine-learning tumour detection approaches. The majority of image analysis performed in BMS has been qualitative and existing quantitative image quality metrics aim to describe image contrast-other aspects of image quality have not been addressed. Image-based diagnostic sensitivities between 63 and 100% have been achieved in eleven trials, but only four articles have estimated the specificity of BMS. The estimates range from 20 to 65%, and do not demonstrate the clinical utility of the modality. Despite over two decades of research in BMS, significant challenges remain that limit the development of this modality as a clinical tool. The BMS community should utilize consistent image quality metric definitions and include image resolution, noise, and artifacts in their analyses. Future work should include more robust metrics, estimates of the diagnostic specificity of the modality, and machine-learning applications should be used with more diverse datasets and with robust methodologies to further enhance BMS as a viable clinical technique.

Motion-based microwave tomographic measurement device for three-dimensional coverage in a magnetic resonance system

PURPOSE

We have developed a fully 3D data acquisition system for microwave breast imaging which can operate simultaneously inside a magnetic resonance imaging (MRI). MRI is used regularly for breast imaging to distinguish tumors from normal tissue. It generally has poor specificity unless used with a gadolinium contrast agent. Microwave imaging could fill this need because of the good endogenous tumor:normal tissue property contrast, especially in light of safety concerns for gadolinium. The antenna array consists of 16 monopole antennas positioned in a horizontal circle surrounding the breast which can then be moved vertically for 3D coverage of the breast. The tank system materials were chosen to minimize artifacts in the MR image within the specific shared imaging zone. The support rods are stainless steel, albeit positioned sufficiently far from the imaging target to have little effect. The mechanical motion parts are all 3D printed plastic. Unlike many conventional antennas, the monopoles consist of just the center conductor and insulator of the coaxial cable, making it one of the least possible metallic structures.

METHODS

Data were acquired both inside and outside of the MR bore to confirm that the MR bore did not have adverse effects on the microwave imaging process. The imaging tank was filled with a mixture of glycerin and water to both provide a reasonable property match to the phantom and to highly attenuate the fields which also acted to suppress multi-path signals. Microwave images were reconstructed using our Gauss-Newton scheme combined with a log transformation for a more linear convergence. MR images were also acquired to assess the effects of the microwave tank structures on the imaging.

RESULTS

The microwave measurement data were acquired in log magnitude and phase format at 200 MHz increments from 700-1900 MHz. Each antenna acted sequentially as a transmitter while the complement of 15 acted as a receiver. The single frequency images were reconstructed using a Gauss-Newton iterative technique with a standard log transformation to linearize the process. The data showed that the signal strengths were between 7-10 dB lower for the case when the array was inside the MRI versus when not. Notwithstanding, the image quality was still high because of the significant signal to noise ratio. The reconstructed images in both situations demonstrated good 3D object recovery of the vertically size and shaped varying object. The MR images were not adversely affected by the presence of antennas or feed structures.

CONCLUSIONS

We have demonstrated that our technique can recover high-quality images of a 3D varying object within an MRI system. Compatibility issues have been addressed for both the microwave and MRI systems. The reduced SNR for the case operating in the MRI did not adversely affect the images. To the best of our knowledge, this is the first example of a microwave imaging system operating in an MRI with full 3D volumetric capability.

Impact of Skin on Microwave Tomography in the Lossy Coupling Medium

In microwave imaging, the effects of skin on recovering property distributions of tissue underneath the surface may be significant because it has high dielectric contrast with subcutaneous fat, which inevitably causes significant signal reflections. While the thickness of skin, especially relative to the wavelengths in use, would presumably have minor effects, it can introduce practical difficulties, for instance, in reflection-based imaging techniques, where the impact of the skin is large-often as high as two orders of magnitude greater than that of signals from underlying tumors in the breast imaging setting. However, in tomography cases utilizing transmission-based measurement data and lossy coupling materials, the situation is considerably different. Accurately implementing a skin layer for numerical modeling purposes is challenging because of the need to discretize the size and shape of the skin without increasing computational overhead substantially. In this paper, we assess the effects of the skin on field solutions in a realistic 3D model of a human breast. We demonstrate that the small changes in transmission field values introduced by including the skin cause minor differences in reconstructed images.

3D-printed gear system for antenna motion in an MR environment: initial phantom imaging experiments

We have developed a microwave imaging device for breast cancer imaging that can be used concurrently inside an MR imaging system. The microwave measurement system is comprised of a horizontal array of 16 monopole antennas that can be moved vertically for full 3D coverage of the breast. All compatibility issues have been addressed. The motion is achieved using a novel 3D printed gearing device. Initial results demonstrate that the system is capable of accurately recovering the size, shape, location and properties of a 3D shape varying object. This is a critical step towards clinical microwave breast imaging in the MR.

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.

Expansion of the Nodal-Adjoint Method for Simple and Efficient Computation of the 2D Tomographic Imaging Jacobian Matrix

This paper focuses on the construction of the Jacobian matrix required in tomographic reconstruction algorithms. In microwave tomography, computing the forward solutions during the iterative reconstruction process impacts the accuracy and computational efficiency. Towards this end, we have applied the discrete dipole approximation for the forward solutions with significant time savings. However, while we have discovered that the imaging problem configuration can dramatically impact the computation time required for the forward solver, it can be equally beneficial in constructing the Jacobian matrix calculated in iterative image reconstruction algorithms. Key to this implementation, we propose to use the same simulation grid for both the forward and imaging domain discretizations for the discrete dipole approximation solutions and report in detail the theoretical aspects for this localization. In this way, the computational cost of the nodal adjoint method decreases by several orders of magnitude. Our investigations show that this expansion is a significant enhancement compared to previous implementations and results in a rapid calculation of the Jacobian matrix with a high level of accuracy. The discrete dipole approximation and the newly efficient Jacobian matrices are effectively implemented to produce quantitative images of the simplified breast phantom from the microwave imaging system.

Low Cost, High Performance, 16-Channel Microwave Measurement System for Tomographic Applications

We have developed a multichannel software defined radio-based transceiver measurement system for use in general microwave tomographic applications. The unit is compact enough to fit conveniently underneath the current illumination tank of the Dartmouth microwave breast imaging system. The system includes 16 channels that can both transmit and receive and it operates from 500 MHz to 2.5 GHz while measuring signals down to −140 dBm. As is the case with multichannel systems, cross-channel leakage is an important specification and must be lower than the noise floors for each receiver. This design exploits the isolation inherent when the individual receivers for each channel are physically separate; however, these challenging specifications require more involved signal isolation techniques at both the system design level and the individual, shielded component level. We describe the isolation design techniques for the critical system elements and demonstrate specification compliance at both the component and system level.

Use of multi-angle ultra-wide band microwave sounding for high resolution breast imaging

PURPOSE

This report proposes an approach to develop a method of microwave imaging for early, non-invasive diagnosis of breast tumors. Here we describe a data-processing method for obtaining radio images of biological heterogeneities and a new method for filtering static noise in received signals.

METHODS

A specialized radar system was developed in the present study and used to perform sounding of synthetic phantoms with the dielectric properties of breast tissue in the range of 2-8 GHz. Datasets thus contained synthetic structures that imitated the dielectric properties of breast tissues and tumors. The permittivity values of the created artificial materials were verified using a waveguide cell. Tumors were simulated via plastic balls with a diameter of 1 cm that were filled with saline. A special ultra-wide band (UWB) radar system developed at Tomsk State University was used to register radar responses from the phantoms. The radar system included the vector reflectometer, the UWB antenna, and the mechanical scanner that provided sounding in the hemisphere. We also used the time-domain signals processing method to obtain the radio image signals. In this method, all signals received during scanning in the hemisphere are added with calculated delay for the given focus point. Special filtering of the constant components of the signal at each of the angular sounding latitudes was used to eliminate clutter in the received signal. This solution allowed us to account for additive clutter in the received signal from structural elements during scanning in the hemisphere. The influence of the number of angles on the quality of the resulting radio image was evaluated.

RESULTS

The phantoms of a female breast and a malignant tumor from artificial materials with electrophysical characteristics close to those of real tissues have been developed. This facilitated verification of the proposed method for constructing radio images under more clinically relevant conditions. The proposed filtering of the constant components of the signal effectively doubled the signal-to-noise ratio in the resulting radio image compared with the standard algorithm of clutter filtering. The influence of different numbers of scan points on the quality of the final radio image are presented herein. It is concluded that it is sufficient to use not more than 600-800 sounding points for acceptable image quality. A further increase in the number of angles does not significantly improve image quality despite increasing the scan time.

CONCLUSIONS

Scanning in the hemisphere of the breast phantom using the proposed method of clutter filtering show that multi-angle microwave imaging can form accurate three-dimensional (3D) images with double the level of signal-to-clutter compared with the standard filtering approach. The images of artificial tumors were obtained when sounding in the range of 2-8 GHz with the resolution of about 5-7 mm.

Full 3D Microwave Breast Imaging Using a Deep-Learning Technique

A deep learning technique to enhance 3D images of the complex-valued permittivity of the breast obtained via microwave imaging is investigated. The developed technique is an extension of one created to enhance 2D images. We employ a 3D Convolutional Neural Network, based on the U-Net architecture, that takes in 3D images obtained using the Contrast-Source Inversion (CSI) method and attempts to produce the true 3D image of the permittivity. The training set consists of 3D CSI images, along with the true numerical phantom images from which the microwave scattered field utilized to create the CSI reconstructions was synthetically generated. Each numerical phantom varies with respect to the size, number, and location of tumors within the fibroglandular region. The reconstructed permittivity images produced by the proposed 3D U-Net show that the network is not only able to remove the artifacts that are typical of CSI reconstructions, but it also enhances the detectability of the tumors. We test the trained U-Net with 3D images obtained from experimentally collected microwave data as well as with images obtained synthetically. Significantly, the results illustrate that although the network was trained using only images obtained from synthetic data, it performed well with images obtained from both synthetic and experimental data. Quantitative evaluations are reported using Receiver Operating Characteristics (ROC) curves for the tumor detectability and RMS error for the enhancement of the reconstructions.

Microwave imaging of breast cancer with factorization method: SPIONs as contrast agent

Female breast at macroscopic scale is a nonmagnetic medium, which eliminates the possibility of realizing microwave imaging of the breast cancer based on magnetic permeability variations. However, by administering functionalized, superparamagnetic iron oxide nanoparticles (SPIONs) as a contrast material to modulate magnetic permeability of cancer cells, a small variation on the scattered electric field from the breast is achievable under an external, polarizing magnetic field.

PURPOSE

We demonstrate an imaging technique that can locate cancerous tumors inside the breast due to electric field variations caused by SPION tracers under different magnetic field intensities. Furthermore, we assess the feasibility of SPION-enhanced microwave imaging for breast cancer with simulations performed on a multi-static imaging configuration.

METHODS

The imaging procedure is realized as the factorization method of qualitative inverse scattering theory, which is essentially a shape retrieval algorithm for inaccessible objects. The formulation is heuristically modified to accommodate the scattering parameters instead of the electric field to comply with the requirements of experimental microwave imaging systems.

RESULTS

With full-wave electromagnetic simulations performed on an anthropomorphically realistic breast phantom, which is excited with a cylindrical imaging prototype of 18 dipole antenna arranged as a single row, the technique is able to locate cancerous tumors for a experimentally achievable doses.

CONCLUSIONS

The technique generates nonanatomic microwave images, which map the cancerous tumors depending on the concentration of SPION tracers, to aid the diagnosis of the breast cancer.

A Discrete Dipole Approximation Solver Based on the COCG-FFT Algorithm and Its Application to Microwave Breast Imaging

We introduce the discrete dipole approximation (DDA) for efficiently calculating the two-dimensional electric field distribution for our microwave tomographic breast imaging system. For iterative inverse problems such as microwave tomography, the forward field computation is the time limiting step. In this paper, the two-dimensional algorithm is derived and formulated such that the iterative conjugate orthogonal conjugate gradient (COCG) method can be used for efficiently solving the forward problem. We have also optimized the matrix-vector multiplication step by formulating the problem such that the nondiagonal portion of the matrix used to compute the dipole moments is block-Toeplitz. The computation costs for multiplying the block matrices times a vector can be dramatically accelerated by expanding each Toeplitz matrix to a circulant matrix for which the convolution theorem is applied for fast computation utilizing the fast Fourier transform (FFT). The results demonstrate that this formulation is accurate and efficient. In this work, the computation times for the direct solvers, the iterative solver (COCG), and the iterative solver using the fast Fourier transform (COCG-FFT) are compared with the best performance achieved using the iterative solver (COCG-FFT) in C++. Utilizing this formulation provides a computationally efficient building block for developing a low cost and fast breast imaging system to serve under-resourced populations.

A 4-channel, vector network analyzer microwave imaging prototype based on software defined radio technology

We have implemented a prototype 4-channel transmission-based, microwave measurement system built on innovative software defined radio (SDR) technology. The system utilizes the B210 USRP SDR developed by Ettus Research that operates over a 70 MHz-6 GHz bandwidth. While B210 units are capable of being synchronized with each other via coherent reference signals, they are somewhat unreliable in this configuration and the manufacturer recommends using N200 or N210 models instead. For our system, N-series SDRs were less suitable because they are not amenable to RF shielding required for the cross-channel isolation necessary for an integrated microwave imaging system. Consequently, we have configured an external reference that overcame these limitations in a compact and robust package. Our design exploits the rapidly evolving technology being developed for the telecommunications environment for test and measurement tasks with the higher performance specifications required in medical microwave imaging applications. In a larger channel configuration, the approach is expected to provide performance comparable to commercial vector network analyzers at a fraction of the cost and in a more compact footprint.

3-D Microwave Tomography Using the Soft Prior Regularization Technique: Evaluation in Anatomically Realistic MRI-Derived Numerical Breast Phantoms

OBJECTIVE

Fusion of magnetic resonance imaging (MRI) breast images with microwave tomography is accomplished through a soft prior technique, which incorporates spatial information (from MRI), i.e., accurate boundary location of different regions of interest, into the regularization process of the microwave image reconstruction algorithm.

METHODS

Numerical experiments were completed on a set of three-dimensional (3-D) breast geometries derived from MR breast data with different parenchymal densities, as well as a simulated tumor to evaluate the performance over a range of breast shapes, sizes, and property distributions.

RESULTS

When the soft prior regularization technique was applied, both permittivity and conductivity relative root mean square error values decreased by more than 87% across all breast densities, except in two cases where the error decrease was only 55% and 78%. In addition, the incorporation of structural priors increased contrast between tumor and fibroglandular tissue by 59% in permittivity and 192% in conductivity.

CONCLUSION

This study confirmed that the soft prior algorithm is robust in 3-D and can function successfully across a range of complex geometries and tissue property distributions.

SIGNIFICANCE

This study demonstrates that our microwave tomography is capable of recovering accurate tissue property distributions when spatial information from MRI is incorporated through soft prior regularization.

A Transmission-Based Dielectric Property Probe for Clinical Applications

We have developed a transmission-based, open-ended coaxial dielectric probe that can be used in clinical situations and overcomes many of the limitations related to the typical reflection-based dielectric probes. The approach utilizes the low profile, open-ended coaxial cables enabling clinicians to still probe relatively compact spaces. The sensing depth can be extended to as large as 1.5 to 2 cm compared with the more typical range of 0.3 mm for conventional probes and is dramatically less affected by measurement technique variability including poor sample contact and cable bending. As a precursor to an actual clinical implementation, we study the technique in a range of homogeneous liquids with substantially varying dielectric properties. The initial results demonstrate good agreement between the transmission-based probe and commercial, reflection-based probes and pave the way for more substantial clinical implementation.

Effects of the Plastic of the Realistic GeePS-L2S-Breast Phantom

A breast phantom developed at the Supelec Institute was interrogated to study its suitability for microwave tomography measurements. A microwave measurement system based on 16 monopole antennas and a vector network analyzer was used to study how the S-parameters are influenced by insertion of the phantom. The phantom is a 3D-printed structure consisting of plastic shells that can be filled with tissue mimicking liquids. The phantom was filled with different liquids and tested with the measurement system to determine whether the plastic has any effects on the recovered images or not. Measurements of the phantom when it is filled with the same liquid as the surrounding coupling medium are of particular interest. In this case, the phantom plastic has a substantial effects on the measurements which ultimately detracts from the desired images.

Image Registration for Microwave Tomography of the Breast Using Priors From Nonsimultaneous Previous Magnetic Resonance Images

Microwave imaging is a low-cost imaging method that has shown promise for breast imaging and, in particular, neoadjuvant chemotherapy monitoring. The early studies of microwave imaging in the therapy monitoring setting are encouraging. For the neoadjuvant therapy application, it would be desirable to achieve the most accurate possible characterization of the tissue properties. One method to achieve increased resolution and specificity in microwave imaging reconstruction is the use of a soft prior regularization. The objective of this study is to develop a method to use magnetic resonance (MR) images, taken in a different imaging configuration, as this soft prior. To enable the use of the MR images as a soft prior, it is necessary to register the MR images to the microwave imaging space. Registration fiducials were placed around the breast that are visible in both the MRI and with an optical scanner integrated into the microwave system. Utilizing these common registration locations, numerical algorithms have been developed to warp the original breast MR images into a geometry closely resembling that in which the breast is pendant in the microwave system.

Addressing Multipath Signal Corruption in Microwave Tomography and the Influence on System Design and Algorithm Development

In developing a microwave tomography system, we started by examining the fundamental signal measurement challenges-i.e., how to interrogate the target while suppressing unwanted multi-path signals. Beginning with a lossy coupling bath to suppress unwanted surface waves, we have developed a robust and reliable system that is both simple and low profile. However, beyond the basic measurement configuration, the lossy coupling medium concept has also informed our choice of array antenna and imaging algorithms. The synergism of these concepts has produced a novel concept which is embodied in a system that has been successfully translated to the clinic.