Conformal Microwave Tomography using a Broadband Non-Contacting Monopole Antenna Array
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1 Conformal Microwave Tomography using a Broadband Non-Contacting Monopole Antenna Array Epstein NR, Golnabi AG, Meaney PM, Paulsen KD Thayer School of Engineering Dartmouth College Hanover NH, USA neil.r.epstein@dartmouth.edu Abstract Microwave imaging has shown clinical value based on its ability to detect a wide range of dielectric properties. Tomographic microwave images are traditionally reconstructed using a uniform mesh. Dartmouth College s microwave tomographic imaging system requires that imaged volumes be submerged in the system s coupling medium. Due to the fact that the electrical properties of the coupling medium are known, we have investigated a conformal imaging technique that deploys the reconstruction mesh directly to the imaged zone, such that all reconstruction nodes lie on or within the volume of interest. The broadband nature of the system [.5 3 GHz] allows the use of a frequency-hopping, phase-unwrapping technique, where low frequency phase information is used to guide the phase unwrapping at higher frequencies. In this paper we present the results from a simulation and phantom experiment to verify the use of conformal microwave imaging with our current imaging system. Keywords-breast cancer; confomal meshing; dielectric properties; image reconstruction; microwave tomography; phase unwrapping I. INTRODUCTION In the United States, 1 in 8 women are expected to develop an invasive breast cancer over the course of their lifetime [1]. In 2011, there were approximately 39,520 breast cancer related deaths, with an estimated 226,870 new cases of invasive breast cancer expected in 2012 [1,2]. Current screening techniques such as X-ray mammography suffer from complications related to the use of ionizing radiation, over diagnosis, and the identification of false-positives and false negatives. It is estimated that radiation induced breast mutations are responsible for 9 32 breast cancer cases per 10,000 women [3,4]. In 2011, over diagnosis and the treatment of insignificant abnormalities accounted for 33% of mammography detected breast cancers [5]. Furthermore, false positive and false negative rates can reach as high as 50% [6] depending on breast density [7,8] and cancer growth rates [9]. The limitations in current screening modalities have been a driving factor in the development of alternative breast cancer imaging techniques such as near infrared imaging (NIR), electrical impedance tomography (EIT), magnetic resonance elastography (MRE) and microwave imaging spectroscopy (MIS). Researchers at Dartmouth College (Hanover, NH USA) This work was supported in part by NIH grant P01-CA Fig. 1. Dartmouth s imaging system showing: (a)-antenna Array, (b) illumination chamber, (c) coupling medium. have been pioneers in investigating the used of these model based imaging approaches [10]. MIS represents a particularly attractive alternative imaging modality based on its ability to detect the relatively large contrast that exists between the dielectric properties (permittivity and conductivity) of healthy and abnormal breast tissue [11,12,13], as well as its potential to offer specificity information regarding non-cancerous and malignant abnormalities [13]. As shown in Fig. 1, Dartmouth s microwave tomographic (MT) imaging system utilizes a 16- element monopole antenna array and associated coupling medium to transmit microwave signals through a volume of interest [15]. We have previously shown that conformal microwave imaging has the ability to improve the accuracy of the recovered property distributions when a saline-based liquid is used as a coupling medium [16]. More recent experiments have indicated our log-transform reconstruction algorithm has improved convergence characteristics over the previous technique. In addition to suppressing unwanted multipath signals [17], the dielectrically tailored glycerin couplingmedium reduces reflections at the object under test (OUT) OUT-bath boundary. One result from this phenomenon is the obscuring of the boundary in the reconstructed image. To overcome this feature, we are currently developing a conformal /12/$ IEEE 192 ICUWB 2012
2 Fig. 3a. Phantom set-up showing breast (light green) and tumor inclusion (blue). Fig. 2. Experimental schematic of s within imaging domain: Region1- Coupling Medium, Region2a Breast, Region2b Tumor. microwave imaging system coupled to an optical surface scanner [18]. This scanner will be used for obtaining the desired boundary information required in the conformal microwave imaging reconstruction process (CMIRP). The remainder of this paper will focus on the conformal meshing technique in microwave imaging. We present both simulation and phantom results that demonstrate the power and effectiveness of using the approach with our current imaging system and reconstruction algorithm. Furthermore, we present an error metric for assessing overall image quality as a function of mismatch between the computed zone and the actual target. II. METHODS A. Phantom Material and Experimental Set-up The simulated and measured data was generated using experimental setups that were identical in geometry and dielectric property distribution. For these experiments, the imaging domain, shown in Fig. 2, consisted of the system s coupling medium ( 1) and the OUT ( 2). Furthermore, the OUT ( 2) was divided into two sub domains, with 2a representing a breast-like and 2b representing a breast-like inclusion. Table 1 summarizes the position and property information of all zones within the experimental imaging domain. The dielectric property values of the phantom materials were measured using a slim-form dielectric probe kit and associated Agilent measurement software [19]. Region # TABLE 1 REGION PROPERTY INFORMATION AT 1300 MHZ Center [cm] Radius [cm] Glycerin [%] Relative permittivity Conductivity [S/m] 1 Bath (0,0) 11 80% a Breast 2b tumor (0,0) % (3,0) 1 50% Phantom s were created using plastic containers (Fig. 3a) holding various concentrations of glycerin:water solutions. Fig. 3b. Image of MT imaging system with phantom setup submerged in the imaging field. This technique allows the creation of dielectrically contrasting phantom zones intended to mimic the permittivity contrast of healthy and abnormal breast tissue. B. MIS Image Acquisition Our MT imaging system uses a 16-element monopole antenna array and associated coupling medium housed in an illumination chamber. The antenna array, capable of operating from 500 MHz to 3 GHz, is attached to a linear-actuator controlled mounting plate that allows the system s array to transmit and receive microwave signals at multiple heights within the illumination chamber (Fig. 3b). The lossy coupling medium resistively loads the antenna elements, effectively increasing the operational bandwidth by decreasing the quality factor [20]. The monopole antenna elements utilized in the imaging system have been thoroughly characterized in [21]. The measured microwave signals related to the OUT are calculated by subtracting a homogeneous calibration data set taken with only coupling medium in the imaging system from the heterogeneous microwave signals obtained with the OUT submerged in the coupling medium. These calibrated microwave signals are used as inputs for a Gauss-Newton iterative reconstruction algorithm with a log-transformation [22]. The system utilizes a frequency-hopping, phaseunwrapping technique where the low frequency 500 MHz phase measurement information is used to guide the unwrapping of phase data at higher frequencies as part of the log-transformation. The forward solution at each iteration was calculated using a finite difference time domain (FDTD) method. A custom LabVIEW program has been developed to automate the entire microwave imaging data acquisition process, allowing the extraction of the desired magnitude and 193
3 (4a) (4b) Fig MHz reconstructed permittivity images of simulated data using 7cm radius mesh (4a) and 5.5cm radius mesh (4b). phase measurements through a software-based lock-in amplifier technique. The simulated measurements used for these experiments were generated using a finite element method (FEM) technique that has been described previously [23]. C. Conformal Meshing Technique The electric field distributions of the total imaging domain are acquired using a FDTD reconstruction algorithm that utilizes a uniform finite difference (FD) grid to compute the forward solution [22]. When using the conformal meshing technique it is necessary to separate the imaging domain into its two distinct s: the coupling-medium and the OUT, shown as 1 and 2 in Fig. 2. In order to produce accurate information regarding the OUT, all nodes in the conformed mesh should be contained on and within the OUT, with no nodes extending into the coupling medium zone. Adhering to this fundamental requirement allows the reconstruction mesh to be constructed in any shape at any location within the antenna array [16]. Additionally, an assessment of the recovered permittivity as a function of the mismatch between the reconstruction mesh and the actual boundary will be developed as a tool for verification of optimal mesh scaling. III. RESULTS A. Simulation Results Fig. 4a and 4b show reconstructed images generated from simulated data using the standard 7 cm radius mesh and the 5.5 cm radius conformed mesh, respectively. The conformal meshing technique generated a 2.08% increase in the average permittivity recovered over the inclusion as compared to the standard reconstructed image. Additionally, there is approximately a 1% decrease in the error of the recovered permittivity values over the entire breast. The error has been calculated as: where n is the number of nodes in the of interest, Meas(i) is the data at the i th node, and Exact (i) is the exact probe measurements at the i th node. Furthermore, the error has been normalized to the number of nodes in the breast for the specific mesh used in the image reconstruction process. (1) (5a) (5b) Fig MHz reconstructed permittivity images using a 7cm (5a) and a 5.cm (5b) reconstruction mesh. (6a) (6b) (6c) (6d) (6e) Fig. 6. Reconstructed images using reconstruction meshes of radius (6a) 7.0cm, (6b) 6.0cm, (6c) 5.5cm, (6d) 5.0cm, (6e) 4.5cm. B. Phantom Results Reconstructed images of the corresponding phantom experiment with a treast-like inclusion using both the standard 7 cm radius mesh and the conformed 5.5 cm radius mesh are shown in Fig. 5a and 5b respectively. The use for the conformal meshing technique tends to decrease the smoothing effects that occur near zone boundaries resulting from the reconstruction algorithm s least square fitting technique [24]. As a result of using the conformal meshing technique, there is a 10.64% increase in the average recovered permittivity value of the tumor and a 4.72% decrease in the error of the recovered permittivity values over the entire breast. Fig. 6 shows the reconstructed phantom images for a range of meshes used for analyzing image quality as a function of mismatch between the computed zone and the target. The recovered permittivity values along with the corresponding error values are summarized in table 2. Deviations in reconstruction mesh radii can significantly impact the recovered property results. Approaching the exact boundary has shown to increase the accuracy of the average recovered permittivity value over the tumor, and decrease the error over the entire breast. 194
4 TABLE 2. RECOVERED PHANTOM PROPERTIES AT 1300 MHZ Radius of reconstruction mesh [cm] % Error over breast Mean % recovered Max Fig. 7. The maximum recovered permittivity values of the tumor as a function of the mesh mismatch (blue) and the exact value of the tumor (red). Also shown is the optimal OUT-Mesh mismatch (green). Fig. 7 plots the maximum recovered permittivity of the tumor as a function of the mesh mismatch. In this experiment, the use of a reconstruction mesh that approached the exact OUT boundary generated results that most accurately match the exact solution. Furthermore, the percentage of the total permittivity recovered over the tumor improved as the reconstruction mesh conformes to the exact OUT boundary. IV. CONCLUSION We have demonstrated the effectiveness of using a conformal microwave image reconstruction technique with our current microwave imaging system through both simulation and phantom representations of breast-like s with a breast-like inclusion surrounded by coupling medium. In this experiment, conforming the reconstruction mesh to the OUT boundary increased the accuracy of the recovered permittivity values in both simulated and measured data. Currently, a new microwave imaging system with mounted laser scanner is being developed for the purpose of detecting the OUT boundary. This boundary information will be used for biomedical applications related to breast and bone imaging. REFERENCES [1] U.S. breast cancer statistics. Internet: symptoms/understand_bc/statistics.jsp, Mar. 1, 2012 [Oct. 19,2011]. [2] American Cancer Society Cancer Facts and Fig.s Atlanta, GA: American Cancer Society, [3] C. M. Ronckers, C. A. Erdmann, and C. E. 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