Three-dimensional Microwave Imaging with Incorporated Prior Structural Information

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1 Three-dimensional Microwave Imaging with Incorporated Prior Structural Information Amir H. Golnabi, Paul M. Meaney, Neil R. Epstein, Keith D. Paulsen Thayer School of Engineering at Dartmouth College, 14 Engineering Dr, Hanover, NH USA ABSTRACT Microwave imaging for biomedical applications, especially for early detection of breast cancer and effective treatment monitoring, has attracted increasing interest in last several decades. This fact is due to the high contrast between the dielectric properties of the normal and malignant breast tissues at microwave frequencies. The available range of dielectric properties for different soft tissue can provide important functional information about tissue health. Nonetheless, one of the limiting weaknesses of microwave imaging is that unlike conventional modalities, such as X-ray CT or MRI, it inherently cannot provide high-resolution images. The conventional modalities can produce highly resolved anatomical information but often cannot provide the functional information required for diagnoses. Previously, we have developed a regularization strategy that can incorporate prior anatomical information from MR or other sources and use it in a way to refine the resolution of the microwave images, while also retaining the functional nature of the reconstructed property values. In the present work, we extend the use of prior structural information in microwave imaging from D to 3D. This extra dimension adds a significant layer of complexity to the entire image reconstruction procedure. In this paper, several challenges with respect to the 3D microwave imaging will be discussed and the results of a series of 3D simulation and phantom experiments with prior structural information will be studied. Keywords: Microwave Imaging, Soft-prior Regularization, Multi-modality Imaging, Breast Cancer, and A-priori Information 1. INTRODUCTION Excluding skin cancer, breast cancer is the most commonly diagnosed cancer in the United States, and the second leading cause of cancer death in women, exceeded only by lung cancer. In fact, it is estimated that over 30,000 new cases of invasive breast cancer will be diagnosed among women in the U.S. in 011 [1].The National Cancer Institute (ACS) estimates that a woman in the United States has a 1 in 8 chance of developing invasive breast cancer during her lifetime [1]. Despite the overall decline in breast cancer mortality over the past decade, about 40,40 deaths are expected in 011 alone [1]. It has been shown that early detection of breast cancer is one of the most effective ways to improve patient s long-term survival. Today, X-ray mammography is the most prominent clinical imaging technique for detection and screening breast abnormalities. While mammography is effective for a wide range of breast types, it suffers from a significant false negative detection rate in younger women and those with radiographically higher density breasts []. In these cases, the increased levels of fibroglandular tissue can make the detection of small tumors difficult, and as a result, the overall sensitivity of mammography can be significantly reduced. In response to these limitations, new and complementary imaging techniques, such as tomographic microwave imaging, are being developed to improve both sensitivity and specificity of conventional imaging modalities. Microwave imaging is based on recovering the electrical properties of tissue. It has been shown that in the microwave frequency range (from high megahertz to low gigahertz), the electrical properties of malignant breast tissue are significantly different from those of healthy breast tissue [3, 4]. We have previously demonstrated that we can recover clinically useful microwave images for breast cancer detection and therapy monitoring purposes [5]. Nonetheless, due to the sub-centimeter resolution of microwave images, we have developed a regularization strategy, called soft-prior regularization, to incorporate structural information of the object being imaged into our reconstruction algorithm [6]. We showed that combining the functional information of the D microwave imaging (i.e. the dielectric property contrast) with the high spatial resolution of other imaging modalities, such as MR or X-ray CT, through the use of our soft-prior regularization can significantly improve the accuracy of the recovered dielectric property distributions and may potentially allow us to differentiate even smaller tumors [7, 8]. In this paper, we extend our investigation to 3D microwave imaging, which adds an additional layer of complexity to the reconstruction algorithm. We will study the Medical Imaging 01: Biomedical Applications in Molecular, Structural, and Functional Imaging, edited by Robert C. Molthen, John B. Weaver, Proc. of SPIE Vol. 8317, 83171L 01 SPIE CCC code: /1/$18 doi: / Proc. of SPIE Vol L-1

effectiveness of the soft-prior regularization in 3D simulation and phantom experiments using our clinical microwave imaging system located at the Advance Imaging Center at Dartmouth Hitchcock

1 3D microwave imaging In order to reduce to the computational complexity of microwave image reconstruction procedure, it is often assumed that the 3D scattering of electromagnetic waves can be

2 effectiveness of the soft-prior regularization in 3D simulation and phantom experiments using our clinical microwave imaging system located at the Advance Imaging Center at Dartmouth Hitchcock Medical Center (DHMC).. METHODS.1 3D microwave imaging In order to reduce to the computational complexity of microwave image reconstruction procedure, it is often assumed that the 3D scattering of electromagnetic waves can be reasonably represented as a simplified D model. Nonetheless, this assumption may impose excessive simplification, which can lead into image artifacts. Moreover, if the target is smaller than the space between two consecutive D imaging slices, the D reconstruction algorithm may not be able to detect the target accurately. Therefore, we have developed a viable 3D image reconstruction process, which is computationally feasible and balances the tradeoff between the accuracy and efficiency of the wave propagation model. We use MATLAB as the main platform for our image reconstruction algorithm. Additional features such as the Parallel Computing Toolbox, Graphical User Interface (GUI), and MEX-files are used to improve the performance of the algorithm. A more detailed description of our 3D reconstruction procedure can be found in [9]. The current microwave imaging system utilizes paired rotary motor-linear actuator complexes to control antenna subsets within the imaging antenna array. As illustrated in Figure 1, the 16-antenna array is sectioned into two sub-arrays, with alternating antennas residing in opposing array subsets; each subset is fixed to a separate designated mounting plate. The configuration allows independent control of the array subsets such that the transmitting antenna and receiving elements can lie in the same tomographic slice, known as an in-plane acquisition, as well as a cross-plane scenario, where the sub array associated with the transmitting antenna resides in a different plane than that of the receiving elements. It is this dual mounting plate scheme and the associated independent motor-actuator complex control of each mounting plate that gives rise to the system's true 3D capabilities by allowing the system to collect both in-plane and cross-plane scatter information. Figure 1. Antenna arrays mounted on two independently-moving plate Proc. of SPIE Vol L-

. Incorporating a priori structural information into the 3D image reconstruction algorithm Our 3D image reconstruction algorithm is a direct extension of the D algorithm, where the FDTD method is

3 . Incorporating a priori structural information into the 3D image reconstruction algorithm Our 3D image reconstruction algorithm is a direct extension of the D algorithm, where the FDTD method is used to calculate the forward solution, and dielectric properties of the object under investigation is estimated from the measured microwave excitations. In the latter process, we use an iterative Gauss-Newton scheme to minimize the data-model misfit [10]. That is the difference between the measured (acquired data) and computed electric field calculated using the forward model. The objective function Ω can be written as: Ω= Γ m Γ c (k ) +Φ m Φ c (k ) + λ L(k k 0 ) (1) where Γ m and Γ c are the log magnitudes and Φ m and Φ c are the phases of the measured and computed field values, respectively, λ is the Tikhonov regularization parameter, and L is a positive definite, dimensionless regularization matrix. k 0 is the prior estimate of k and. is the vector two-norm [10]. When no prior spatial information about the structure of the object being imaged is available, the regularization matrix L in equation (1) is set to be an identity matrix, which applies the same weight to all nodes of the reconstruction mesh (i.e. Levenberg-Marquardt (LM) scheme). However, when a priori spatial data is available from other sources such as MRI, the variation within regions that are assumed to have the same or similar dielectric properties can be penalized through the soft-prior (SP) regularization matrix [6, 7, 8]. Complete details about this regularization method can be found in [8]. Figure. Simulation Setup: A spherical inclusion of 1.5 cm radius centered at (x,y,z) = (3,0,0) cm, and surrounded by 11 monopole antennas configured in seven evenly spaced circles of 15. cm diameter and 1 cm separated from each other..3 Simulation experiment As a first step, we have conducted a simple-geometry simulation experiment where the location and size of the inclusion were known. As illustrated in Figure, 11 monopole antennas were configured in seven evenly spaced circles of 15. cm diameter and 1 cm separated from each other. A spherical inclusion of 1.5 cm radius was centered at (x,y,z) = (3,0,0) cm with respect to the center of the imaging domain located at the origin of the Cartesian coordinate system (0,0,0). The associated properties for the background medium and the target inclusion were set to: background ε r =.4, σ = 1.3 S/m; and inclusion ε r = 40.0, σ =.0 S/m. The simulated data (with -100 dbm synthetic noise) was generated using our 3D finite-difference time-domain (FDTD) forward solver. The images were then reconstructed at 1300 MHz the first set used a Levenberg-Marquardt (LM) regularization scheme on a uniformly distributed mesh composed of 3594 nodes and tetrahedral elements (3(a)), and the second applied a soft-prior regularization scheme on a customized mesh composed of 5187 nodes and 5747 tetrahedral elements (Figure 3(b)). Proc. of SPIE Vol L-3

4 (a) (b) (c) (d) Figure 3. 3D reconstruction meshes: (a) uniformly distributed cylindrical mesh composed of 3594 nodes and tetrahedral elements, (b) customized mesh composed of 5187 nodes and 5747 tetrahedral elements, (c) uniformly distributed cylindrical mesh composed of 5301 nodes and 3714 tetrahedral elements and, (d) customized mesh composed of 358 nodes and tetrahedral elements.4 Phantom experiment In order to study the effect of the soft-prior regularization in a more complex setup and on real measured data, the following phantom experiment was performed: As illustrated in Figure 4, a thin-walled plastic tube of 1.0 cm radius, filled with a 60:40 mixture of glycerin:water was inserted into an irregularly-shaped gelatin inclusion. An 86:14 solution of glycerin:water was used as a lossy background medium to minimize the multipath contributions at each receiver from reflections at the tank boundaries. The actual properties of different regions at 1300 MHz were: background ε r = 10.8, σ = 0.75 S/m; cylindrical inclusion ε r = 50.6, σ = 1.8 S/m; and gelatin inclusion ε r = 37.5, σ = 1.51 S/m. The images with no prior structural information were reconstructed on a uniformly distributed mesh composed of 5301 nodes and 3714 tetrahedral elements (Figure 3(c)). In order to obtain the precise structural information of the phantom for the softprior regularization, the same setup was imaged in MRI prior to the microwave data acquisition. The corresponding MR images were then used to create a 3D customized soft-prior mesh composed of 358 nodes and tetrahedral elements, as shown in Figure 3(d). Proc. of SPIE Vol L-4

Figure 4. Phantom inclusions: a thin-walled plastic tube of 1.

(top) and conductivity profiles of the simulation experiment with and without soft-prior

While the target inclusion is successfully detected in both cases, the reconstructed dielectric

values in both permittivity and conductivity images.

5 Figure 4. Phantom inclusions: a thin-walled plastic tube of 1.0 cm radius, filled with a 60:40 mixture of glycerin:water inserted into an irregularly-shaped gelatin inclusion 3. RESULTS 3.1 Simulation experiment Figures 5(a) and 5(b) show a D slice of the 3D reconstructed permittivity (top) and conductivity profiles of the simulation experiment with and without soft-prior regularization, respectively. While the target inclusion is successfully detected in both cases, the reconstructed dielectric property values of the images with soft-prior regularization are much closer to the actual property values in both permittivity and conductivity images. Moreover, the level of background artifacts is significantly reduced in the images with incorporated structural information. (a) (b) Figure MHz reconstructed permittivity (top) and conductivity (bottom) profiles of the simulation experiment with (a) soft-prior regularization and (b) LM regularization (i.e. no prior information) Proc. of SPIE Vol L-5

3. Phantom experiment The results of the phantom experiment with and without soft-prior regularization are shown in Figures 6(a) and 6(b), respectively.

information is used, they are not separable from each other.

More specifically, the recovered permittivity values of the cylindrical inclusion are higher than those of the gelatin inclusion, whereas, the counterpart conductivity values of the cylindrical

6 3. Phantom experiment The results of the phantom experiment with and without soft-prior regularization are shown in Figures 6(a) and 6(b), respectively. In order to compare the reconstructed dielectric properties, the permittivity and conductivity values in Figure 6 are extracted along a plane normal to the x-axis. In the reconstructed images with the soft-prior regularization (i.e. Figure 6(a)), both gelatin and plastic cylindrical inclusions are detected successfully; however, in Figure 6(b) when no prior structural information is used, they are not separable from each other. In terms of the recovered dielectric properties, soft-prior images are significantly superior to those without incorporated structural information. More specifically, the recovered permittivity values of the cylindrical inclusion are higher than those of the gelatin inclusion, whereas, the counterpart conductivity values of the cylindrical inclusion are lower than those of the gelatin inclusion, which agrees with the true dielectric property distributions reported in section.4. (a) (b) (c) (d) Figure MHz reconstructed permittivity (top) and conductivity (bottom) profiles of the phantom experiment: (a) soft-prior regularization, (b) LM regularization (i.e. no prior information) 4. CONCLUSIONS We have studied the effects of incorporating prior structural information into 3D microwave imaging, using the softprior regularization. Implementation of such regularization approach is appealing because it demonstrates that the microwave measurement data in combination with the anatomical knowledge can be a powerful tool to recover high Proc. of SPIE Vol L-6

7 fidelity dielectric properties of actual targets. This is an encouraging step as we work towards incorporating anatomical information of the breast (available from MRI) to our 3D reconstruction algorithm to produce the necessary spatial data. REFERENCES [1] A. C. Society, "Cancer Facts & Figures 011," American Cancer Society, Inc, Atlanta 011. [] Smith-Bindman, R., Chu, P., Miglioretti, D., Quale, C., Rosenberg, R. Cutter, G., Geller, B., Bacchetti, P., Sickles, E., and Kerlikowske, K., "Physician predictors of mammographic accuracy," Journal of the National Cancer Institute, 97, (005). [3] Chaudhary, S., Mishra, R., Swarup, A., and Thomas, J., Dielectric properties of normal & malignant human breast tissues at radiowave & microwave frequencies, Indian Journal of Biochemistry & Biophysics, 1(1), (1984). [4] Joines, W., Zhang, Y., Li, C., and Jirtle, R., The measured electrical properties of normal and malignant human tissues from 50 to 900 MHz, Medical Physics, 1(4), (1994). [5] Meaney, P., Fanning, M.,Raynolds, T., Fox, C., Fang, Q., Kogel, C., Poplack, S., and Paulsen, K., "Initial clinical experience with microwave breast imaging in women with normal mammography," Academic Radiology, 14, (007). [6] Golnabi, A., Meaney, P., Fanning, M., Geimer, S., and Paulsen, K., "Microwave imaging utilizing a soft prior constraint", Proc. SPIE 76, 76L (009). [7] Golnabi, A., Meaney, P., Geimer, S., and Paulsen, K., "Microwave imaging of the breast with incorporated structural information," Proc. SPIE 766, 7660 (010). [8] Golnabi, A., Meaney, P., Geimer, S., and Paulsen, K., "Comparison of No-Prior and Soft-Prior Regularization in Biomedical Microwave Imaging," Journal Medical Physics, 36, (011) [9] Golnabi, A., Meaney, P., Epstein, N., and Paulsen, K., " Microwave Imaging for Breast Cancer Detection - Advances in 3D Image Reconstruction," International Conference of the IEEE Engineering in Medicine and Biology Society, (011). [10] Kelley, C., [Iterative methods for linear and nonlinear equations], Society for Industrial and Applied Mathematics, Philadelphia, (1995). Proc. of SPIE Vol L-7

Microwave Imaging Utilizing a Soft Prior Constraint

Microwave Imaging Utilizing a Soft Prior Constraint Amir H. Golnabi, Paul M. Meaney, Shireen D. Geimer, Margaret W. Fanning, Keith D. Paulsen Thayer School of ngineering, Dartmouth College, Hanover, NH,