Reconstruction Quality and Spectral Content of an Electromagnetic Time-Domain Inversion Algorithm

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.

Three-Dimensional Holographic Electromagnetic Imaging for Accessing Brain Stroke

The authors recently developed a two-dimensional (2D) holographic electromagnetic induction imaging (HEI) for biomedical imaging applications. However, this method was unable to detect small inclusions accurately. For example, only one of two inclusions can be detected in the reconstructed image if the two inclusions were located at the same XY plane but in different Z-directions. This paper provides a theoretical framework of three-dimensional (3D) HEI to accurately and effectively detect inclusions embedded in a biological object. A numerical system, including a realistic head phantom, a 16-element excitation sensor array, a 16-element receiving sensor array, and image processing model has been developed to evaluate the effectiveness of the proposed method for detecting small stroke. The achieved 3D HEI images have been compared with 2D HEI images. Simulation results show that the 3D HEI method can accurately and effectively identify small inclusions even when two inclusions are located at the same XY plane but in different Z-directions. This preliminary study shows that the proposed method has the potential to develop a useful imaging tool for the diagnosis of neurological diseases and injuries in the future.

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.

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.

Antenna modeling and reconstruction accuracy of time domain-based image reconstruction in microwave tomography

Nonlinear microwave imaging heavily relies on an accurate numerical electromagnetic model of the antenna system. The model is used to simulate scattering data that is compared to its measured counterpart in order to reconstruct the image. In this paper an antenna system immersed in water is used to image different canonical objects in order to investigate the implication of modeling errors on the final reconstruction using a time domain-based iterative inverse reconstruction algorithm and three-dimensional FDTD modeling. With the test objects immersed in a background of air and tap water, respectively, we have studied the impact of antenna modeling errors, errors in the modeling of the background media, and made a comparison with a two-dimensional version of the algorithm. In conclusion even small modeling errors in the antennas can significantly alter the reconstructed image. Since the image reconstruction procedure is highly nonlinear general conclusions are very difficult to make. In our case it means that with the antenna system immersed in water and using our present FDTD-based electromagnetic model the imaging results are improved if refraining from modeling the water-wall-air interface and instead just use a homogeneous background of water in the model.

On the forward scattering of microwave breast imaging

Microwave imaging for breast cancer detection has been of significant interest for the last two decades. Recent studies focus on solving the imaging problem using an inverse scattering approach. Efforts have mainly been focused on the development of the inverse scattering algorithms, experimental setup, antenna design and clinical trials. However, the success of microwave breast imaging also heavily relies on the quality of the forward data such that the tumor inside the breast volume is well illuminated. In this work, a numerical study of the forward scattering data is conducted. The scattering behavior of simple breast models under different polarization states and aspect angles of illumination are considered. Numerical results have demonstrated that better data contrast could be obtained when the breast volume is illuminated using cross-polarized components in linear polarization basis or the copolarized components in the circular polarization basis.

Image reconstruction in microwave tomography using a dielectric Debye model

In this paper, quantitative dielectric image reconstruction based on broadband microwave measurements is investigated. A time-domain-based algorithm is derived where Debye model parameters are reconstructed in order to take into account the strong dispersive behavior found in biological tissue. The algorithm is tested with experimental and numerical data in order to verify the algorithm and to investigate improvements in the reconstructed image resulting from the improved description of the dielectric properties of the tissue when using broadband data. The comparison is made in relation to the more commonly used conductivity model. For the evaluation, two examples were considered, the first was a lossy saline solution and the second was less lossy tap water. Both liquids are strongly dispersive and used as a background medium in the imaging examples. The results show that the Debye model algorithm is of most importance in the tap water for a bandwidth of more than 1.5 GHz. Also the saline solution exhibits a dispersive behavior but since the losses restrict the useful bandwidth, the Debye model is of less significance even if somewhat larger and stronger artifacts can be seen in the conductivity model reconstructions.

Time-reversal focusing in microwave hyperthermia for deep-seated tumors

A fast beam-forming method for hyperthermia treatment of deep-seated tumors is described and verified. The approach is based on the time-reversal characteristics of Maxwell equations. The basic principle of the method is coupling of the electromagnetic modeling of the system with the actual application. In this modeling the wavefront of the source is propagated through a patient-specific model from a virtual antenna placed in the tumor of the model. The simulated radiated field is then captured using a computer model of the surrounding antenna system. The acquired amplitudes and phases are then used in the real antenna system. The effectiveness of this procedure is demonstrated by calculating the power absorption distribution using FDTD electromagnetic simulations of a realistic 2D breast model as well as a 2D neck model. Several design parameters, i.e. number of antennas, operating frequency and dimensions, have been evaluated by performance indicators. The promising results suggest that the development of this technique is pursued further.

Advances in the 3-D forward-backward time-stepping (FBTS) inverse scattering technique for breast cancer detection

This paper presents recent advances in a 3-D inverse scattering technique, called forward-backward time-stepping (FBTS), applied to the reconstruction of the microwave properties of the breast. The FBTS algorithm is utilized for a numerical-based study of a 3-D breast model based on an MRI. Several illumination schemes, based on different microwave transmitter/receiver configurations, are compared based on the quality of the reconstructed images of the breast model. A combination of cylindrical and planar arrays is shown to provide accurate estimates of the model electrical parameters that delineate the various regions of the breast. Although further analysis with this combination array demonstrates that tumors of reduced size and reduced contrast with the surrounding fibroglandular region are much more difficult (and in some cases not possible) to reconstruct, the study presents some promising initial results of a reconstruction technique for breast imaging and cancer detection.

Development of anatomically realistic numerical breast phantoms with accurate dielectric properties for modeling microwave interactions with the human breast

Computational electromagnetics models of microwave interactions with the human breast serve as an invaluable tool for exploring the feasibility of new technologies and improving design concepts related to microwave breast cancer detection and treatment. In this paper, we report the development of a collection of anatomically realistic 3-D numerical breast phantoms of varying shape, size, and radiographic density which can readily be used in finite-difference time-domain computational electromagnetics models. The phantoms are derived from T1-weighted MRIs of prone patients. Each MRI is transformed into a uniform grid of dielectric properties using several steps. First, the structure of each phantom is identified by applying image processing techniques to the MRI. Next, the voxel intensities of the MRI are converted to frequency-dependent and tissue-dependent dielectric properties of normal breast tissues via a piecewise-linear map. The dielectric properties of normal breast tissue are taken from the recently completed large-scale experimental study of normal breast tissue dielectric properties conducted by the Universities of Wisconsin and Calgary. The comprehensive collection of numerical phantoms is made available to the scientific community through an online repository.

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.

Two-dimensional time-domain inverse scattering for quantitative analysis of breast composition

Forward-backward time-stepping is a unique approach for solving electromagnetic inverse scattering problems in the time domain. In this paper, the technique is applied to a realistic, heterogeneous breast model. The ability to detect a 5-mm diameter malignancy and provide substantial quantitative information about the breast's composition is demonstrated.

Characterization of an Implicitly Resistively-Loaded Monopole Antenna in Lossy Liquid Media

Microwave tomographic imaging of the breast for cancer detection is a topic of considerable interest because of the potential to exploit the apparent high-dielectric property contrast between normal and malignant tissue. An important component in the realization of an imaging system is the antenna array to be used for signal transmission/detection. The monopole antenna has proven to be useful in our implementation because it can be easily and accurately modeled and can be positioned in close proximity to the imaging target with high-element density when configured in an imaging array. Its frequency response is broadened considerably when radiating in the liquid medium that is used to couple the signals into the breast making it suitable for broadband spectral imaging. However, at higher frequencies, the beam patterns steer further away from the desired horizontal plane and can cause unwanted multipath contributions when located in close proximity to the liquid/air interface. In this paper, we have studied the behavior of these antennas and devised strategies for their effective use at higher frequencies, especially when positioned near the surface of the coupling fluid which is used. The results show that frequencies in excess of 2 GHz can be used when the antenna centers are located as close as 2 cm from the liquid surface.