An active microwave imaging system for reconstruction of 2-D electrical property distributions

A Tuned Microwave Resonant System for Subcutaneous Imaging

A compact and planar imaging system was developed using a flexible polymer substrate that can distinguish subcutaneous tissue abnormalities, such as breast tumors, based on electromagnetic-wave interactions in materials where permittivity variations affect wave reflection. The sensing element is a tuned loop resonator operating in the industrial, scientific, and medical (ISM) band at 2.423 GHz, providing a localized high-intensity electric field that penetrates into tissues with sufficient spatial and spectral resolutions. The resonant frequency shifts and magnitudes of the reflection coefficients indicate the boundaries of abnormal tissues under the skin due to their high contrasts to normal tissues. The sensor was tuned to the desired resonant frequency with a reflection coefficient of -68.8 dB for a radius of 5.7 mm, with a tuning pad. Quality factors of 173.1 and 34.4 were achieved in simulations and measurements in phantoms. An image-processing method was introduced to fuse raster-scanned 9 × 9 images of resonant frequencies and reflection coefficients for image-contrast enhancement. The results showed a clear indication of the tumor's location at a depth of 15 mm and the capability to identify two tumors both at the depth of 10 mm. The sensing element can be expanded to a four-element phased array for deeper field penetration. Field analysis showed the depths of -20 dB attenuation were improved from 19 to 42 mm, giving wider coverage in tissues at resonance. Results showed that a quality factor of 152.5 was achieved and a tumor could be identified at a depth of up to 50 mm. In this work, simulations and measurements were conducted to validate the concept, showing great potential for subcutaneous imaging in medical applications in a noninvasive, efficient, and lower-cost way.

Effect of Coupling Medium on Penetration Depth in Microwave Medical Imaging

In microwave medical imaging, the human skin reflects most of microwave energy due to the impedance mismatch between the air and the body. As a result, only a small portion of the microwave energy can enter the body and work for medical purpose. One solution to tackle this issue is to use a coupling (or matching) medium, which can reduce unwanted reflections on the skin and meanwhile improve spatial imaging resolution. A few types of fluids were measured in this paper for their dielectric properties between 500 MHz and 13.5 GHz. Measurements were performed by a Keysight programmable network analyzer (PNA) with a dielectric probe kit, and dielectric constant and conductivity of the fluids were presented in this paper. Then, quantitative computations were exercised to present the attenuations due to the reflection on the skin and to the loss in each coupling medium, based on the measured liquid dielectric values. Finally, electromagnetic simulations verified that the coupling liquid can allow more microwave energy to enter the body to allow for a more efficient medical examination.

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.

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.

Review of Microwaves Techniques for Breast Cancer Detection

Conventional breast cancer detection techniques including X-ray mammography, magnetic resonance imaging, and ultrasound scanning suffer from shortcomings such as excessive cost, harmful radiation, and inconveniences to the patients. These challenges motivated researchers to investigate alternative methods including the use of microwaves. This article focuses on reviewing the background of microwave techniques for breast tumour detection. In particular, this study reviews the recent advancements in active microwave imaging, namely microwave tomography and radar-based techniques. The main objective of this paper is to provide researchers and physicians with an overview of the principles, techniques, and fundamental challenges associated with microwave imaging for breast cancer detection. Furthermore, this study aims to shed light on the fact that until today, there are very few commercially available and cost-effective microwave-based systems for breast cancer imaging or detection. This conclusion is not intended to imply the inefficacy of microwaves for breast cancer detection, but rather to encourage a healthy debate on why a commercially available system has yet to be made available despite almost 30 years of intensive research.

Recent technological advancements in thermometry

Thermometry is the key factor for achieving successful thermal therapy. Although invasive thermometry with a probe has been used for more than four decades, this method can only detect the local temperature within the probing volume. Noninvasive temperature imaging using a tomographic technique is ideal for monitoring hot-spot formation in the human body. Among various techniques, such as X-ray computed tomography, microwave tomography, echo sonography, and magnetic resonance (MR) imaging, the proton resonance frequency shift method of MR thermometry is the only method currently available for clinical practice because its temperature sensitivity is consistent in most aqueous tissues and can be easily observed using common clinical scanners. New techniques are being proposed to improve the robustness of this method against tissue motion. MR techniques for fat thermometry were also developed based on relaxation times. One of the latest non-MR techniques to attract attention is photoacoustic imaging.

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.

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.

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.

Recent Advances in Microwave Imaging for Breast Cancer Detection

Breast cancer is a disease that occurs most often in female cancer patients. Early detection can significantly reduce the mortality rate. Microwave breast imaging, which is noninvasive and harmless to human, offers a promising alternative method to mammography. This paper presents a review of recent advances in microwave imaging for breast cancer detection. We conclude by introducing new research on a microwave imaging system with time-domain measurement that achieves short measurement time and low system cost. In the time-domain measurement system, scan time would take less than 1 sec, and it does not require very expensive equipment such as VNA.

3D microwave tomography of the breast using prior anatomical information

PURPOSE

The authors have developed a new 3D breast image reconstruction technique that utilizes the soft tissue spatial resolution of magnetic resonance imaging (MRI) and integrates the dielectric property differentiation from microwave imaging to produce a dual modality approach with the goal of augmenting the specificity of MR imaging, possibly without the need for nonspecific contrast agents. The integration is performed through the application of a soft prior regularization which imports segmented geometric meshes generated from MR exams and uses it to constrain the microwave tomography algorithm to recover nearly uniform property distributions within segmented regions with sharp delineation between these internal subzones.

METHODS

Previous investigations have demonstrated that this approach is effective in 2D simulation and phantom experiments and also in clinical exams. The current study extends the algorithm to 3D and provides a thorough analysis of the sensitivity and robustness to misalignment errors in size and location between the spatial prior information and the actual data.

RESULTS

Image results in 3D were not strongly dependent on reconstruction mesh density, and the changes of less than 30% in recovered property values arose from variations of more than 125% in target region size-an outcome which was more robust than in 2D. Similarly, changes of less than 13% occurred in the 3D image results from variations in target location of nearly 90% of the inclusion size. Permittivity and conductivity errors were about 5 times and 2 times smaller, respectively, with the 3D spatial prior algorithm in actual phantom experiments than those which occurred without priors.

CONCLUSIONS

The presented study confirms that the incorporation of structural information in the form of a soft constraint can considerably improve the accuracy of the property estimates in predefined regions of interest. These findings are encouraging and establish a strong foundation for using the soft prior technique in clinical studies, where their microwave imaging system and MRI can simultaneously collect breast exam data in patients.

Surface wave multipath signals in near-field microwave imaging

Microwave imaging techniques are prone to signal corruption from unwanted multipath signals. Near-field systems are especially vulnerable because signals can scatter and reflect from structural objects within or on the boundary of the imaging zone. These issues are further exacerbated when surface waves are generated with the potential of propagating along the transmitting and receiving antenna feed lines and other low-loss paths. In this paper, we analyze the contributions of multi-path signals arising from surface wave effects. Specifically, experiments were conducted with a near-field microwave imaging array positioned at variable heights from the floor of a coupling fluid tank. Antenna arrays with different feed line lengths in the fluid were also evaluated. The results show that surface waves corrupt the received signals over the longest transmission distances across the measurement array. However, the surface wave effects can be eliminated provided the feed line lengths are sufficiently long independently of the distance of the transmitting/receiving antenna tips from the imaging tank floor. Theoretical predictions confirm the experimental observations.

Microwave tomography in the context of complex breast cancer imaging

The notion of applying microwave imaging to breast cancer imaging has been studied at various levels by numerous scientists. The earliest appeal of this concept related to the presumably high property contrast between benign and malignant tissue that was unique to the breast. Subsequent published studies have shown that this assumption was overly simplistic and that the tissue property heterogeneity is considerable within the breast. As we have expanded the clinical use of our microwave tomographic system, we are now using this approach to monitor tumor progressions during neoadjuvant chemotherapy. In these cases, while we can still characterize and track the tumor progression, we have observed a new phenomenon. Very often these cancer patients exhibit skin thickening near the tumor site. Our images have reconstructed elevated dielectric properties along the breast surface associated with the accompanying edema. These observations further add to the complex nature of breast dielectric properties and the challenges for imaging them using microwave interrogation.

Dual-Band Miniaturized Patch Antennas for Microwave Breast Imaging

We present a miniaturized, dual-band patch antenna array element that is designed for use in a 3-D microwave tomography system for breast imaging. Dual-band operation is achieved by manipulating the fundamental resonant mode of the patch antenna and one of its higher-order modes. Miniaturization and tuning of the resonant frequencies are achieved by loading the antenna with non-radiating slots at strategic locations along the patch. This results in a compact, dual-band antenna with symmetric radiation patterns and similar radiation characteristics at both bands of operation. The performance of the antenna in a biocompatible immersion medium is verified experimentally.

On verification of hyperthermia treatment planning for cervical carcinoma patients

PURPOSE

The aim of this study was to verify hyperthermia treatment planning calculations by means of measurements performed during hyperthermia treatments. The calculated specific absorption rate (SAR(calc)) was compared with clinically measured SAR values, during 11 treatments in seven cervical carcinoma patients.

METHODS

Hyperthermia treatments were performed using the 70 MHz AMC-4 waveguide system. Temperatures were measured using multisensor thermocouple probes. One invasive thermometry catheter in the cervical tumour and two non-invasive catheters in the vagina were used. For optimal tissue contact and fixation of the catheters, a gynaecological tampon was inserted, moisturized with distilled water (4 treatments), or saline (6 treatments) for better thermal contact. During one treatment no tampon was used. At the start of treatment the temperature rise (DeltaT(meas)) after a short power pulse was measured, which is proportional to SAR(meas). The SAR(calc) along the catheter tracks was extracted from the calculated SAR distribution and compared with the DeltaT(meas)-profiles.

RESULTS

The correlation between DeltaT(meas) and SAR(calc) was on average R = 0.56 +/- 0.28, but appeared highly dependent on the wetness of the tampon (preferably with saline) and the tissue contact of the catheters. Correlations were strong (R approximately 0.85-0.93) when thermal contact was good, but much weaker (R approximately 0.14-0.48) for cases with poor thermal contact.

CONCLUSION

Good correlations between measurements and calculations were found when tissue contact of the catheters was good. The main difficulties for accurate verification were of clinical nature, arising from improper use of the gynaecological tampon. Poor thermal contact between thermocouples and tissue caused measurement artefacts that were difficult to correlate with calculations.

Log transformation benefits parameter estimation in microwave tomographic imaging

Microwave tomographic imaging falls under a broad category of nonlinear parameter estimation methods when a Gauss-Newton iterative reconstruction technique is used. A fundamental requirement in using these approaches is evaluating the appropriateness of the regression model. While there have been numerous investigations of regularization techniques to improve overall image quality, few, if any, studies have explored the underlying statistical properties of the model itself. The ordinary least squares (OLS) approach is used most often, but there are other options such as the weighted least squares (WLS), maximum likelihood (ML), and maximum a posteriori (MAP) that may be more appropriate. In addition, a number of variance stabilizing transformations can be applied to make the inversion intrinsically more linear. In this paper, a statistical analysis is performed of the properties of the residual errors from the reconstructed images utilizing actual measured data and it is demonstrated that the OLS algorithm with a log transformation (OLSlog) is clearly advantageous relative to the more commonly used OLS approach by itself. In addition, several high contrast imaging experiments are performed, which demonstrate that different subsets of data are emphasized in each method and may contribute to the overall image quality differences.

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

A tomographic time-domain reconstruction algorithm for solving the inverse electromagnetic problem is described. The application we have in mind is dielectric breast cancer detection but the results are of general interest to the field of microwave tomography. Reconstructions have been made from experimental and numerically simulated data for objects of different sizes in order to investigate the relation between the spectral content of the illuminating pulse and the quality of the reconstructed image. We have found that the spectral content is crucial for a successful reconstruction. The work has further shown that when imaging objects with different scale lengths it is an advantage to use a multiple step procedure. Low frequency content in the pulse is used to image the large structures and the reconstruction process then proceed by using higher frequency data to resolve small scale lengths. Good agreement between the results obtained from experimental data and simulated data has been achieved.

Model-based microwave image reconstruction: simulations and experiments

We describe an integrated microwave imaging system that can provide spatial maps of dielectric properties of heterogeneous media with tomographically collected data. The hardware system (800-1200 MHz) was built based on a lock-in amplifier with 16 fixed antennas. The reconstruction algorithm was implemented using a Newton iterative method with combined Marquardt-Tikhonov regularizations. System performance was evaluated using heterogeneous media mimicking human breast tissue. Finite element method coupled with the Bayliss and Turkel radiation boundary conditions were applied to compute the electric field distribution in the heterogeneous media of interest. The results show that inclusions embedded in a 76-diameter background medium can be quantitatively reconstructed from both simulated and experimental data. Quantitative analysis of the microwave images obtained suggests that an inclusion of 14 mm in diameter is the smallest object that can be fully characterized presently using experimental data, while objects as small as 10 mm in diameter can be quantitatively resolved with simulated data.

Microwave thermal imaging: initial in vivo experience with a single heating zone

The deployment of hyperthermia as a routine adjuvant to radiation or chemotherapy is limited largely by the inability to devise treatment plans which can be monitored through temperature distribution feedback during therapy. A non-invasive microwave tomographic thermal imaging system is currently being developed which has previously exhibited excellent correlation between the recovered electrical conductivity of a heated zone and its actual temperature change during phantom studies. To extend the validation of this approach in vivo, the imaging system has been re-configured for small animal experiments to operate within the bore of a CT scanner for anatomical and thermometry registration. A series of 5-7 day old pigs have been imaged during hyperthermia with a monopole antenna array submerged in a saline tank where a small plastic tube surgically inserted the length of the abdomen has been used to create a zone of heated saline at pre-selected temperatures. Tomographic microwave data over the frequency range of 300-1000 MHz of the pig abdomen in the plane perpendicular to the torso is collected at regular intervals after the tube saline temperatures have settled to the desired settings. Images are reconstructed over a range of operating frequencies. The tube location is clearly visible and the recovered saline conductivity varies linearly with the controlled temperature values. Difference images utilizing the baseline state prior to heating reinforces the linear relationship between temperature and imaged saline conductivity. Demonstration of in vivo temperature recovery and correlation with an independent monitoring device is an important milestone prior to clinical integration of this non-invasive imaging system with a thermal therapy device.

Inverse scattering from phaseless measurements of the total field on a closed curve

A new approach for quantitative electromagnetic imaging of scatterers located in free space from phaseless data is proposed and discussed. The procedure splits the problem into two steps. In the first one, we solve a phase-retrieval problem for the total field, thus estimating the amplitude and phase of the scattered field. Careful analysis of properties and possible representations of both scattered and incident fields allow us to introduce a criterion for an optimal choice of the measurement setup and a successful retrieval. Then the complex permittivity profile is reconstructed in the second step by use of the estimated scattered field. Numerical examples are provided to check the whole chain in the presence of noise-corrupted data.

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.

Three-Dimensional Nonlinear Image Reconstruction for Microwave Biomedical Imaging

Active microwave imaging has attracted significant interests in biomedical applications, in particular for breast imaging. However, the high electrical contrasts in breast tissue also increases the difficulty of forming an accurate image because of the increased multiple scattering. To model such strong three-dimensional (3-D) multiple scattering effects in biomedical imaging applications, we develop a full 3-D inverse scattering algorithm based on the combination of the contrast source inversion and the fast Fourier transform algorithm. Numerical results show that our algorithm can accurately invert for the high-contrast media in breast tissue.

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.

Pre-scaled two-parameter Gauss-Newton image reconstruction to reduce property recovery imbalance

Gauss-Newton image reconstruction in microwave imaging can be formulated in terms of a single complex quantity, the wave number squared (k2), with the understanding that the relative permittivity and conductivity images can be extracted afterwards through a simple constitutive relationship. However, this approach ignores the fact that the magnitude of the average real and imaginary components can be considerably out of balance depending on the operating frequency and tissue characteristics which can inadvertently imbalance the process in favour of one parameter over the other. In an effort to achieve property recovery which is balanced, we introduce a pre-scaling procedure at the property update stage of the reconstruction. Utilization of this concept in conjunction with our two-step regularization process for both simulation and phantom experiments demonstrates that the penalty term weighting parameters for the optimal mean-squared property errors for the two recovered distributions (relative permittivity and conductivity) together with that yielding the lowest least-squared electric field error coincide only when the scaling is applied. The scheme provides a means for simultaneous optimization of the two permittivity and conductivity images.

Experimental validation of a linear model for data reduction in chirp-pulse microwave CT

Chirp-pulse microwave computerized tomography (CP-MCT) is an imaging modality developed at the Department of Biocybernetics, University of Niigata (Niigata, Japan), which intends to reduce the microwave-tomography problem to an X-ray-like situation. We have recently shown that data acquisition in CP-MCT can be described in terms of a linear model derived from scattering theory. In this paper, we validate this model by showing that the theoretically computed response function is in good agreement with the one obtained from a regularized multiple deconvolution of three data sets measured with the prototype of CP-MCT. Furthermore, the reliability of the model as far as image restoration in concerned, is tested in the case of space-invariant conditions by considering the reconstruction of simple on-axis cylindrical phantoms.

Microwave image reconstruction utilizing log-magnitude and unwrapped phase to improve high-contrast object recovery

Reconstructing images of large high-contrast objects with microwave methods has proved difficult. Successful images have generally been obtained by using a priori information to constrain the image reconstruction to recover the correct electromagnetic property distribution. In these situations, the measured electric field phases as a function of receiver position around the periphery of the imaging field-of-view vary rapidly often undergoing changes of greater than pi radians especially when the object contrast and illumination frequency increase. In this paper, we introduce a modified form of a Maxwell equation model-based image reconstruction algorithm which directly incorporates log-magnitude and phase of the measured electric field data. By doing so, measured phase variation can be unwrapped and distributed over more than one Rieman sheet in the complex plane. Simulation studies and microwave imaging experiments demonstrate that significant image quality enhancements occur with this approach for large high-contrast objects. Simple strategies for visualizing and unwrapping phase values as a function of the transmitter and receiver positions within our microwave imaging array are described. Metrics of the degree of phase variation expressed in terms of the amount and extent of phase wrapping are defined and found to be figures-of-merit which estimate when it is critical to deploy the new image reconstruction approach. In these cases, the new algorithm recovers high-quality images without resorting to the use of a priori information on object contrast and/or size as previously required.

Image restoration in chirp-pulse microwave CT (CP-MCT)

Chirp-pulse microwave computed tomography (CP-MCT) is a technique for imaging the distribution of temperature variations inside biological tissues. Even if resolution and contrast are adequate to this purpose, a further improvement of image quality is desirable. In this paper, we discuss the blur of CP-MCT images and we propose a method for estimating the corresponding point spread function (PSF). To this purpose we use both a measured and a computed projection of a cylindrical phantom. We find a good agreement between the two cases. Finally the estimated PSF is used for deconvolving data corresponding to various kinds of cylindrical phantoms. We use an iterative nonlinear deconvolution method which assures nonnegative solutions and we demonstrate the improvement of image quality which can be obtained in such a way.

Nonactive antenna compensation for fixed-array microwave imaging--Part I: Model development

Fixed-array microwave imaging with multisensor data acquisition can suffer from nonactive antenna element interactions which cause distortions in the measurements. In Part I of a two-part paper, we develop a nonactive antenna compensation model for incorporation in model-based near-field microwave image reconstruction methods. The model treats the nonactive members of the antenna array as impedance boundary conditions applied over a cylindrical surface of finite radius providing two parameters, the effective antenna radius and impedance factor, which can be determined empirically from measured data. Results show that the effective radius and impedance factor provide improved fits to experimental data in homogeneous phantoms where measurements are obtained with and without the presence of the nonactive antenna elements. Once deduced, these parameters are incorporated into the nonactive antenna compensation model and lead to systematic data-model match improvements in heterogeneous phantoms. While the improvements afforded by the nonactive antenna model are small on a per measurement basis, they are not insignificant. As shown in Part II, inclusion of this new model for nonactive antenna compensation produces significantly higher quality image reconstructions from measurements obtained with a fixed-array data acquisition system over the frequency band 500-900 MHz.

Non-invasive thermal assessment of tissue phantoms using an active near field microwave imaging technique

An active microwave imaging system for non-invasive temperature sensing has been developed and evaluated. The system is designed to assess biological tissues undergoing thermal therapy. This paper presents results that demonstrate the imaging capabilities of the microwave method using simulated and experimental phantom materials. Results from both numerical studies and laboratory experiments have been analysed and are presented. The imaging system uses a 16 channel fixed monopole array transceiver unit operating over a bandwidth of 300-900 MHz. The annular array diameter is 14.75 cm and is immersed in a 0.9% saline solution. Standard heterodyning principles are used for signal detection leading to a dynamic range of the system of better than 115dB. Image formation is accomplished with a 2-D finite element based, near-field iterative technique. This allows the simultaneous reconstruction of both the real and imaginary components of the dielectric property distribution in tissue equivalent phantoms. Data acquisition currently captures 144 complex field measurements per image. Image reconstruction requires approximately 2 min per iteration with a typical convergence in less than 10 steps. Experiments performed to evaluate the temperature dependence of biological phantoms (saline with variable salt concentrations) are described. The numerical accuracy and precision of the reconstruction algorithm based upon these phantom studies are presented. Simple laboratory models of localized hyperthermia have been used to evaluate the experimental accuracy and precision of the imaging system. A numerical precision of 0.02 degrees C and an accuracy of 0.37 degrees C have been observed with the current algorithm. In laboratory experiments, images have been reconstructed at different target temperatures and target saline concentrations. The effect of placing high contrast biological phantoms (i.e. bone/fat simulants) along with the heated objects have also been studied. Localized heating of the biological phantom is achieved by pumping a saline solution of pre-selected concentration through enclosed ends of hollow dielectric cylinders having approximately 5cm inner diameter and 4 mm wall thickness. The temperature of the heated zone is preset and maintained to +/-0.2 degrees C by an external heater and circulator. The results currently show that a maximum temperature precision of 0.98 degrees C and maximum relative accuracy of 0.56 degrees C has been achieved in the laboratory using the current generation of the prototype system.

Quantitative microwave imaging with a 2.45-GHz planar microwave camera

This paper presents microwave tomographic reconstructions of the complex permittivity of lossy dielectric objects immersed in water from experimental multiview near-field data obtained with a 2.45-GHz planar active microwave camera. An iterative reconstruction algorithm based on the Levenberg-Marquardt method was used to solve the nonlinear matrix equation which results when applying a moment method to the electric field integral representation. The effects of uncertainties in experimental parameters such as the exterior medium complex permittivity, the imaging system geometry and the incident field at the object location are illustrated by means of reconstructions from synthetic data. It appears that the uncertainties in the incident field have the strongest impact on the reconstructions. A receiver calibration procedure has been implemented and some ways to access to the incident field at the object location have been assessed.

Initial in vivo experience with EIT as a thermal estimator during hyperthermia

Thermal imaging experiments using electrical impedance tomography (EIT) have been conducted during hyperthermia treatments delivered to two human patients and one animal subject. Coplanar and circumferential arrays of 16 and 32 tin-plated copper electrodes etched on a 0.005" polyimide sheet were used to inject 12.5 KHz current patterns of increasing sinusoidal spatial frequencies and subsequent potential distributions were recorded at each electrode site. Image reconstruction was achieved with a finite element method and difference images of conductivity changes during the course of treatment were formed. An assumed linear relationship (2%/degree C increase) between tissue impedance change and temperature change was used to produce thermal images of the treatment field in patients whereas an empirically measured nonlinear relationship obtained from excised tissue samples was applied retrospectively in the animal subject case. Reconstructed conductivity changes are shown to be possible given electrical data measured in vivo during hyperthermia delivery with conventional equipment (spiral microstrip applicator at 433 MHz). These correlated well with direct temperature measurements and demonstrated quantitative levels of agreement to the extent that estimated temperature accuracies were approximately 1.5 degrees C; although large errors (> 5 degrees C) did exist. This work suggests that EIT is a potentially useful tool for hyperthermia treatment monitoring and assessment. The relationship between tissue impedance and temperature is complex and confounds the ability to make simple correlations between conductivity and temperature changes. Further, study is required to discern whether this will ultimately limit EIT as a thermal estimator or whether it will lead to more fundamental uses of impedance as an indicator of thermal effect.

Microwave imaging for tissue assessment: initial evaluation in multitarget tissue-equivalent phantoms

A prototype microwave imaging system is evaluated for its ability to recover two-dimensional (2-D) electrical property distributions under transverse magnetic (TM) illumination using multitarget tissue equivalent phantoms. Experiments conducted in a surrounding lossy saline tank demonstrate that simultaneous recovery of both the real and imaginary components of the electrical property distribution is possible using absolute imaging procedures over a frequency range of 300-700 MHz. Further, image reconstructions of embedded tissue-equivalent targets are found to be quantitative not only with respect to geometrical factors such as object size and location but also electrical composition. Quantitative assessments based on full-width half-height criteria reveal that errors in diameter estimates of reconstructed targets are less than 10 mm in all cases, whereas, positioning errors are less than 1 mm in single object experiments but degrade to 4-10 mm when multiple targets are present. Recovery of actual electrical properties is found to be frequency dependent for the real and imaginary components with background values being typically within 10-20% of their correct size and embedded object having similar accuracies as a percentage of the electrical contrast, although errors as high as 50% can occur. The quantitative evaluation of imaging performance has revealed potential advantages in a two-tiered receiver antenna configuration whose measured field values are more sensitive to target region changes than the typical tomographic type of approach which uses reception sites around the full target region perimeter. This measurement strategy has important implications for both the image reconstruction algorithm where there is a premium on minimizing problem size without sacrificing image quality and the hardware system design which seeks to economize on the amount of measured data required for quantitative image reconstruction while maximizing its sensitivity to target perturbations.

A dual mesh scheme for finite element based reconstruction algorithms

The finite element (FE) method has found several applications in emerging imaging modalities, especially microwave imaging which has been shown to be potentially useful in a number of areas including thermal estimation. In monitoring temperature distributions, the biological phenomena of temperature variations of tissue dielectric properties is exploited. By imaging these properties and their changes during such therapies as hyperthermia, temperature distributions can be deduced using difference imaging techniques. The authors focus on a microwave imaging problem where the hybrid element (HE) method is used in conjunction with a dual mesh scheme in an effort to image complex wavenumbers, k(2). The dual mesh scheme is introduced to improve the reconstructed images of tissue properties and is ideally suited for systems using FE methods as their computational base. Since the electric fields typically vary rapidly over a given body when irradiated by high-frequency electromagnetic sources, a dense mesh is needed for these fields to be accurately represented. Conversely, k(2) may be fairly constant over subregions of the body which would allow for a less dense sampling of this parameter in those regions. In the dual mesh system employed, the first mesh, which is uniformly dense, is used for calculating the electric fields over the body whereas the second mesh, which is nonuniform and less dense, is used for representing the k(2) distribution within the region of interest. The authors examine the 2-D TM polarization case for a pair of dielectric distributions on both a large and small problem to demonstrate the flexibility of the dual mesh method along with some of the difficulties associated with larger imaging problems. Results demonstrate the capabilities of the dual mesh concept in comparison to a single mesh approach for a variety of test cases, suggesting that the dual mesh method is critical for FE based image reconstruction where rapidly varying physical quantities are used to recover smoother property profiles, as can occur in microwave imaging of biological bodies.