In-Vivo Electrical Properties Estimation of Biological Tissues by Means of a Multi-Step Microwave Tomography Approach.

The accurate quantitative estimation of the electromagnetic properties of tissues can serve important diagnostic and therapeutic medical purposes. Quantitative microwave tomography is an imaging modality that can provide maps of the in-vivo electromagnetic properties of the imaged tissues, i.e. both the permittivity and the electric conductivity. A multi-step microwave tomography approach is proposed for the accurate retrieval of such spatial maps of biological tissues. The underlying idea behind the new imaging approach is to progressively add details to the maps in a step-wise fashion starting from single-frequency qualitative reconstructions. Multi-frequency microwave data is utilized strategically in the final stage. The approach results in improved accuracy of the reconstructions compared to inversion of the data in a single step. As a case study, the proposed workflow was tested on an experimental microwave data set collected for the imaging of the human forearm. The human forearm is a good test case as it contains several soft tissues as well as bone, exhibiting a wide range of values for the electrical properties.

Generation of Prior Information in a Dual-Mode Microwave-Ultrasound Breast Imaging System.

A new breast imaging system capable of obtaining ultrasound and microwave scattered-field measurements with minimal or no movement of the breast between measurements has recently been reported. In this work, we describe the methodology that has been developed to generate prior information about the internal structures of the breast based on ultrasound data measured with the dual-mode system. This prior information, estimating both the geometry and complex-valued permittivity of tissues within the breast, is incorporated into the microwave inversion algorithm as a means of enhancing image quality. Several techniques to map reconstructed ultrasound speed to complex-valued relative permittivity are investigated. Quantitative images of two simplified dual-mode breast phantoms obtained using experimental data and the various forms of prior information are presented. Though preliminary, the results presented herein provide an understanding of the impacts of different forms of prior information on dual-mode reconstructions of the breast and can be used to inform future work on the subject.

Evaluating Performance of Microwave Image Reconstruction Algorithms: Extracting Tissue Types with Segmentation Using Machine Learning.

Evaluating the quality of reconstructed images requires consistent approaches to extracting information and applying metrics. Partitioning medical images into tissue types permits the quantitative assessment of regions that contain a specific tissue. The assessment facilitates the evaluation of an imaging algorithm in terms of its ability to reconstruct the properties of various tissue types and identify anomalies. Microwave tomography is an imaging modality that is model-based and reconstructs an approximation of the actual internal spatial distribution of the dielectric properties of a breast over a reconstruction model consisting of discrete elements. The breast tissue types are characterized by their dielectric properties, so the complex permittivity profile that is reconstructed may be used to distinguish different tissue types. This manuscript presents a robust and flexible medical image segmentation technique to partition microwave breast images into tissue types in order to facilitate the evaluation of image quality. The approach combines an unsupervised machine learning method with statistical techniques. The key advantage for using the algorithm over other approaches, such as a threshold-based segmentation method, is that it supports this quantitative analysis without prior assumptions such as knowledge of the expected dielectric property values that characterize each tissue type. Moreover, it can be used for scenarios where there is a scarcity of data available for supervised learning. Microwave images are formed by solving an inverse scattering problem that is severely ill-posed, which has a significant impact on image quality. A number of strategies have been developed to alleviate the ill-posedness of the inverse scattering problem. The degree of success of each strategy varies, leading to reconstructions that have a wide range of image quality. A requirement for the segmentation technique is the ability to partition tissue types over a range of image qualities, which is demonstrated in the first part of the paper. The segmentation of images into regions of interest corresponding to various tissue types leads to the decomposition of the breast interior into disjoint tissue masks. An array of region and distance-based metrics are applied to compare masks extracted from reconstructed images and ground truth models. The quantitative results reveal the accuracy with which the geometric and dielectric properties are reconstructed. The incorporation of the segmentation that results in a framework that effectively furnishes the quantitative assessment of regions that contain a specific tissue is also demonstrated. The algorithm is applied to reconstructed microwave images derived from breasts with various densities and tissue distributions to demonstrate the flexibility of the algorithm and that it is not data-specific. The potential for using the algorithm to assist in diagnosis is exhibited with a tumor tracking example. This example also establishes the usefulness of the approach in evaluating the performance of the reconstruction algorithm in terms of its sensitivity and specificity to malignant tissue and its ability to accurately reconstruct malignant tissue.

Enhanced Detection of Magnetic Nanoparticles Using a Novel Microwave Ferromagnetic Resonance Imaging System.

Objective: An aluminium faceted chamber designed for 3D microwave imaging (MWI) of the breast has been integrated into an electromagnet in order to carry out signal acquisition experiments for an inverse scattering-based ferromagnetic resonance imaging (FRI) system, or magnetic contrast-enhanced MWI system. METHODS: For this proof of concept, the chamber has been equipped with four wire monopole antennas, and low-contrast oil-based targets have been tested with varying concentrations of iron oxide magnetic nanoparticles (MNP) to serve as ferromagnetic contrast agents. The electromagnet is capable of sustaining a static polarizing magnetic field (PMF) greater than 0.2 Tesla (2000 Gauss) across the imaging chamber to modulate the MNPs' ferromagnetic response, effectively changing the targets' magnetic permeability. Differential scattered field data are then collected through the application and withdrawal of this PMF. RESULTS: This study has successfully characterized a particular narrow band of frequencies within the asymmetric faceted chamber that demonstrate significant differential responses corresponding to the weak magnetic signal physically isolated from the MNPs, tested on different sizes and positions of targets containing various concentrations of MNPs. CONCLUSION: Similar to ferromagnetic resonance (FMR) spectroscopy, in which detection of FMR phenomena is best achieved at probing frequencies coinciding with the structural resonant frequency of a metallic cavity, these resonant frequencies of interest yield a high level of sensitivity to MNP permeability changes and are suitable for imaging within the chamber. SIGNIFICANCE: These represent the first experimental results of a full-scale FRI system capable of detecting and eventually imaging MNPs at biologically relevant concentrations.

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.

Enhancement of Multimodal Microwave-Ultrasound Breast Imaging Using a Deep-Learning Technique.

We present a deep learning method used in conjunction with dual-modal microwave-ultrasound imaging to produce tomographic reconstructions of the complex-valued permittivity of numerical breast phantoms. We also assess tumor segmentation performance using the reconstructed permittivity as a feature. The contrast source inversion (CSI) technique is used to create the complex-permittivity images of the breast with ultrasound-derived tissue regions utilized as prior information. However, imaging artifacts make the detection of tumors difficult. To overcome this issue we train a convolutional neural network (CNN) that takes in, as input, the dual-modal CSI reconstruction and attempts to produce the true image of the complex tissue permittivity. The neural network consists of successive convolutional and downsampling layers, followed by successive deconvolutional and upsampling layers based on the U-Net architecture. To train the neural network, the input-output pairs consist of CSI's dual-modal reconstructions, along with the true numerical phantom images from which the microwave scattered field was synthetically generated. The reconstructed permittivity images produced by the CNN show that the network is not only able to remove the artifacts that are typical of CSI reconstructions, but can also improve the detectability of tumors. The performance of the CNN is assessed using a four-fold cross-validation on our dataset that shows improvement over CSI both in terms of reconstruction error and tumor segmentation performance.

Novel Stopping Criteria for Optimization-Based Microwave Breast Imaging Algorithms.

A discontinuous Galerkin formulation of the Contrast Source Inversion algorithm (DGM-CSI) for microwave breast imaging employing a frequency-cycling reconstruction technique has been modified here to include a set of automated stopping criteria that determine a suitable time to shift imaging frequencies and to globally terminate the reconstruction. Recent studies have explored the use of tissue-dependent geometrical mapping of the well-reconstructed real part to its imaginary part as initial guesses during consecutive frequency hops. This practice was shown to improve resulting 2D images of the dielectric properties of synthetic breast models, but a fixed number of iterations was used to halt DGM-CSI inversions arbitrarily. Herein, a new set of stopping conditions is introduced based on an intelligent statistical analysis of a window of past iterations of data error using the two-sample Kolmogorov-Smirnov (K-S) test. This non-parametric goodness-of-fit test establishes a pattern in the data error distribution, indicating an appropriate time to shift frequencies, or terminate the algorithm. The proposed stopping criteria are shown to improve the efficiency of DGM-CSI while yielding images of equivalent quality to assigning an often liberally overestimated number of iterations per reconstruction.

Integrating prior information into microwave tomography Part 1: Impact of detail on image quality.

PURPOSE: The authors investigate the impact that incremental increases in the level of detail of patient-specific prior information have on image quality and the convergence behavior of an inversion algorithm in the context of near-field microwave breast imaging. A methodology is presented that uses image quality measures to characterize the ability of the algorithm to reconstruct both internal structures and lesions embedded in fibroglandular tissue. The approach permits key aspects that impact the quality of reconstruction of these structures to be identified and quantified. This provides insight into opportunities to improve image reconstruction performance. METHODS: Patient-specific information is acquired using radar-based methods that form a regional map of the breast. This map is then incorporated into a microwave tomography algorithm. Previous investigations have demonstrated the effectiveness of this approach to improve image quality when applied to data generated with two-dimensional (2D) numerical models. The present study extends this work by generating prior information that is customized to vary the degree of structural detail to facilitate the investigation of the role of prior information in image formation. Numerical 2D breast models constructed from magnetic resonance (MR) scans, and reconstructions formed with a three-dimensional (3D) numerical breast model are used to assess if trends observed for the 2D results can be extended to 3D scenarios. RESULTS: For the blind reconstruction scenario (i.e., no prior information), the breast surface is not accurately identified and internal structures are not clearly resolved. A substantial improvement in image quality is achieved by incorporating the skin surface map and constraining the imaging domain to the breast. Internal features within the breast appear in the reconstructed image. However, it is challenging to discriminate between adipose and glandular regions and there are inaccuracies in both the structural properties of the glandular region and the dielectric properties reconstructed within this structure. Using a regional map with a skin layer only marginally improves this situation. Increasing the structural detail in the prior information to include internal features leads to reconstructions for which the interface that delineates the fat and gland regions can be inferred. Different features within the glandular region corresponding to tissues with varying relative permittivity values, such as a lesion embedded within glandular structure, emerge in the reconstructed images. CONCLUSION: Including knowledge of the breast surface and skin layer leads to a substantial improvement in image quality compared to the blind case, but the images have limited diagnostic utility for applications such as tumor response tracking. The diagnostic utility of the reconstruction technique is improved considerably when patient-specific structural information is used. This qualitative observation is supported quantitatively with image metrics.

Integrating prior information into microwave tomography part 2: Impact of errors in prior information on microwave tomography image quality.

PURPOSE: The authors have developed a method to combine a patient-specific map of tissue structure and average dielectric properties with microwave tomography. The patient-specific map is acquired with radar-based techniques and serves as prior information for microwave tomography. The impact that the degree of structural detail included in this prior information has on image quality was reported in a previous investigation. The aim of the present study is to extend this previous work by identifying and quantifying the impact that errors in the prior information have on image quality, including the reconstruction of internal structures and lesions embedded in fibroglandular tissue. This study also extends the work of others reported in literature by emulating a clinical setting with a set of experiments that incorporate heterogeneity into both the breast interior and glandular region, as well as prior information related to both fat and glandular structures. METHODS: Patient-specific structural information is acquired using radar-based methods that form a regional map of the breast. Errors are introduced to create a discrepancy in the geometry and electrical properties between the regional map and the model used to generate the data. This permits the impact that errors in the prior information have on image quality to be evaluated. Image quality is quantitatively assessed by measuring the ability of the algorithm to reconstruct both internal structures and lesions embedded in fibroglandular tissue. The study is conducted using both 2D and 3D numerical breast models constructed from MRI scans. RESULTS: The reconstruction results demonstrate robustness of the method relative to errors in the dielectric properties of the background regional map, and to misalignment errors. These errors do not significantly influence the reconstruction accuracy of the underlying structures, or the ability of the algorithm to reconstruct malignant tissue. Although misalignment errors do not significantly impact the quality of the reconstructed fat and glandular structures for the 3D scenarios, the dielectric properties are reconstructed less accurately within the glandular structure for these cases relative to the 2D cases. However, general agreement between the 2D and 3D results was found. CONCLUSION: A key contribution of this paper is the detailed analysis of the impact of prior information errors on the reconstruction accuracy and ability to detect tumors. The results support the utility of acquiring patient-specific information with radar-based techniques and incorporating this information into MWT. The method is robust to errors in the dielectric properties of the background regional map, and to misalignment errors. Completion of this analysis is an important step toward developing the method into a practical diagnostic tool.

Ultrasound tomography for simultaneous reconstruction of acoustic density, attenuation, and compressibility profiles.

A fast and efficient forward scattering solver is developed for use in ultrasound tomography. The solver is formulated so as to enable the calculation of scattering from large and relatively high-contrast objects with inhomogeneous physical properties that vary simultaneously in acoustic attenuation, compressibility, and density. It is based on the method of moments in conjunction with a novel implementation of the conjugate gradient algorithm which requires the use of the adjoints of the scattering operators. The solver takes advantage of the symmetric block Toeplitz matrix with symmetric Toeplitz blocks property of the Green's function matrix to increase efficiency and only stores the first row of this matrix to reduce memory requirements. This row is then used for the matrix-vector multiplication using the fast Fourier transform technique, thus, resulting in the computational complexity of O(n log n). The marching-on-source technique is also used to provide a good initial guess which allows the conjugate gradient technique to converge faster than initializing with an arbitrary guess. This feature is important in tomographic inversion algorithms which require that the object to be imaged be interrogated via several incident fields. Forward scattering and inversion examples, based on the Conjugate Gradient Least Squares regularized Born Iterative Method, are shown, in two-dimensions, for objects varying in all three physical properties.

Microwave imaging of human forearms: pilot study and image enhancement.

We present a pilot study using a microwave tomography system in which we image the forearms of 5 adult male and female volunteers between the ages of 30 and 48. Microwave scattering data were collected at 0.8 to 1.2 GHz with 24 transmitting and receiving antennas located in a matching fluid of deionized water and table salt. Inversion of the microwave data was performed with a balanced version of the multiplicative-regularized contrast source inversion algorithm formulated using the finite-element method (FEM-CSI). T1-weighted MRI images of each volunteer's forearm were also collected in the same plane as the microwave scattering experiment. Initial "blind" imaging results from the utilized inversion algorithm show that the image quality is dependent on the thickness of the arm's peripheral adipose tissue layer; thicker layers of adipose tissue lead to poorer overall image quality. Due to the exible nature of the FEM-CSI algorithm used, prior information can be readily incorporated into the microwave imaging inversion process. We show that by introducing prior information into the FEM-CSI algorithm the internal anatomical features of all the arms are resolved, significantly improving the images. The prior information was estimated manually from the blind inversions using an ad hoc procedure.

A study of matching fluid loss in a biomedical microwave tomography system.

PURPOSE: Effective imaging of human tissue with microwave tomography systems requires a matching fluid to reduce the wave reflections at the tissue boundary. Further, in order to match the idealized mathematical model used for imaging with the complicated physical measurement environment, loss must be added to the matching fluid. Both too little and too much loss result in low-quality images, but due to the nonlinear nature of the imaging problem, the exact nature of loss-to-image quality cannot be predicted a priori. Possible optimal loss levels include a single, highly sensitive value, or a broad range of acceptable losses. Herein, the authors outline a process of determining an appropriate level of loss inside the matching fluid and attempt to determine the bounds for which the images are the highest quality. METHODS: Our biomedical microwave tomography system is designed for 2D limb imaging, operating from 0.8 to 1.2 GHz. Our matching fluid consists of deionized water with various levels of loss introduced by the addition of table salt. Using two homogeneous tissue-mimicking phantoms, and eight different matching fluids of varying salt concentrations, the authors introduce quantitative image quality metrics based on L-norms, mean values, and standard deviations to test the tomography system and assess image quality. Images are generated with a balanced multiplicative regularized contrast source inversion algorithm. The authors further generate images of a human forearm which may be analyzed qualitatively. RESULTS: The image metrics for the phantoms support the claim that the worst images occur at the extremes of high and low salt concentrations. Importantly, the image metrics show that there exists a broad range of salt concentrations that result in high-quality images, not a single optimal value. In particular, 2.5-4.5 g of table salt per liter of deionized water provide the best reconstruction quality for simple phantoms. The authors argue that qualitatively, the human forearm data provide the best images at approximately the same salt concentrations. CONCLUSIONS: There exists a relatively large-range of matching fluid losses (i.e., salt concentrations) that provide similar image quality. In particular, it is not necessary to spend time highly optimizing the level of loss in the matching fluid.

A wideband microwave tomography system with a novel frequency selection procedure.

In this paper, we describe a 2-D wideband microwave imaging system intended for biomedical imaging. The system is capable of collecting data from 3 to 6 GHz, with 24 coresident antenna elements connected to a vector network analyzer via a 2 x 24 port matrix switch. As one of the major sources of error in the data collection process is a result of the strongly coupling 24 coresident antennas, we provide a novel method to avoid the frequencies where the coupling is large enough to prevent successful imaging. Through the use of two different nonlinear reconstruction schemes, which are an enhanced version of the distorted born iterative method and the multiplicative regularized contrast source inversion method, we show imaging results from dielectric phantoms in free space. The early inversion results show that with the frequency selection procedure applied, the system is capable of quantitatively reconstructing dielectric objects, and show that the use of the wideband data improves the inversion results over single-frequency data.

An ultra-wideband microwave tomography system: preliminary results.

We describe a 2D wide-band multi-frequency microwave imaging system intended for biomedical imaging. The system is capable of collecting data from 2-10 GHz, with 24 antenna elements connected to a vector network analyzer via a 2 x 24 port matrix switch. Through the use of two different nonlinear reconstruction schemes: the Multiplicative-Regularized Contrast Source Inversion method and an enhanced version of the Distorted Born Iterative Method, we show preliminary imaging results from dielectric phantoms where data were collected from 3-6 GHz. The early inversion results show that the system is capable of quantitatively reconstructing dielectric objects.

Enhancement of the Krylov subspace regularization for microwave biomedical imaging.

Although Krylov subspace methods provide fast regularization techniques for the microwave imaging problem, they cannot preserve the edges of the object being imaged and may result in an oscillatory reconstruction. To suppress these spurious oscillations and to provide an edge-preserving regularization, we use a multiplicative regularizer which improves the reconstruction results significantly while adding little computational complexity to the inversion algorithm. We show the inversion results for a real human forearm assuming the 2-D transverse magnetic illumination and a cylindrical object assuming the 2-D transverse electric illumination.