关于乳腺癌检测的IEEE文章

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 47, NO. 5, MAY 1999 783 Three-Dimensional FDTD Analysis of a Pulsed Microwave Confocal System for Breast Cancer Detection: Design of an Antenna-Array Element Susan C. Hagness, Member, IEEE, Allen Taflove, Fellow, IEEE, and Jack E. Bridges, Life Fellow, IEEE Abstract—We are investigating a new ultrawide-band (UWB) microwave radar technology to detect and image early-stage malignant breast tumors that are often invisible to X rays. In this paper, we present the methodology and initial results of three-dimensional (3-D) finite-difference time-domain (FDTD) simulations. The discussion concentrates on the design of a single resistively loaded bowtie antenna element of a proposed confocal sensor array. We present the reflection, radiation, and scattering properties of the electromagnetic pulse radiated by the antenna element within a homogeneous, layered half-space model of the human breast and the polarization and frequency- response characteristics of generic tumor shapes. We conclude that the dynamic range of a sensor array comprised of such elements in conjunction with existing microwave equipment is adequate to detect small cancerous tumors usually missed by X-ray mammography. Index Terms—Antenna array, cancer, FDTD methods. I. INTRODUCTION Apotentially important strategy for reducing breast cancermortality is the detection of early-stage tumors [1]. X-ray mammography is currently the most effective screening modal- ity for detecting clinically occult breast cancers. However, approximately 10–30% of breast cancers are missed by mam- mography [2], [3]. The significant number of false negatives may be attributed to the limitations of mammography in: 1) assessing dense glandular tissue and regions located close to the chest wall or underarm and 2) imaging very early-stage tumors that do not yet exhibit microcalcifications. Another concern is the high rate of false positives in screening mam- mograms [3], [4]. These statistics indicate a critical need for complementary modalities with high sensitivity and specificity for early detection through low-cost screening. Ultrasound and contrast-enhanced MRI are effective in the diagnostic evalu- ation of mammographically detected breast lesions. However, Manuscript received July 29, 1998; revised December 2, 1998. This work was supported in part by the Small Business Innovative Research Grant 1-R43-CA67598-D1A2 from the National Institute of Health and by internal funding from Interstitial, Inc. Computing resources were provided by Cray Research, Inc. S. C. Hagness is with the Department of Electrical and Computer Engi- neering, University of Wisconsin-Madison, Madison, WI 53706 USA. A. Taflove is with the Department of Electrical and Computer Engineering, McCormick School of Engineering and Applied Science, Northwestern Uni- versity, Evanston, IL 60208 USA. J. E. Bridges is with Interstitial, Inc., Park Ridge, IL 60068 USA. Publisher Item Identifier S 0018-926X(99)04839-5. these modalities are either not sensitive/specific enough or are too costly for mass screening purposes [5]–[8]. We are investigating an ultrawide-band (UWB) microwave radar technology to detect early-stage breast cancer. The cardinal feature of this technology is the differential microwave backscatter response from tissues based on their water content, a tissue-radiation interaction mechanism that is distinct from density-based attenuation of X rays. According to the literature, the differing water content of normal and malignant breast tissues results in an order-of-magnitude dielectric-property contrast at microwave frequencies. The system under consideration has the potential to detect very small noncalcified cancers, including those in radiographically dense breasts and in regions near the chest wall or underarm. Furthermore, this approach avoids exposure to ionizing radiation, is noninvasive, and does not require breast compression. The radio-frequency exposure is well within the safety limits set by ANSI/IEEE [9]. The safety, comfort, ease-of-use, and low-cost features of the new approach should permit frequent screening of the general public and regular monitoring of patients with detected abnormalities. Augmenting X-ray mammography in this manner could help to reduce the number of false negatives and false positives. The new modality is based on the principle of the confocal optical microscope [10], an instrument that selectively images small particles in a translucent medium having multiple scat- tering sources. It reduces the problem of background clutter by providing spatial selectivity of both the illuminating and backscattered waves. Our UWB pulsed adaptation achieves a range-gated microwave focus at potential tumor locations through the use of an electronically scanned antenna array of elements. Here, an ultrawide-band antenna element located at a particular position on the surface of the breast is excited and the backscattered waveform is collected, digitized, and stored within the computer. Via electronic switching, this is repeated in sequence for the other elements in the array. As a postprocessing step, the set of backscattered waveforms are then variably time-shifted to achieve coherent addition for a desired virtual focal point within the breast in a manner analogous to the signal processing performed for geophysical seismic prospecting [11]. Backscatter from the in-breast focal point adds coherently in this process, while returns from off- focus scatterers add incoherently and are thereby suppressed. 0018–926X/99$10.00  1999 IEEE 784 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 47, NO. 5, MAY 1999 The position of the focal point is scanned throughout the breast by adjusting the assumed distribution of time shifts of the stored backscatter waveforms. The spatial selectivity of the pulsed confocal microwave technology addresses a central problem in applying electrical or microwave techniques to tumor detection: the heteroge- neous nature of the breast. Published microwave backscat- ter methods [12], [13] that illuminate the breast with large unfocused beams suffer because returns from a tumor can be masked by clutter from adjacent breast regions. Matrix schemes using microwave or impedance measurements [14], [15] suffer because errors in the data can be amplified by the matrix-inversion process. Alternative matrix schemes are under development for microwave imaging of objects embed- ded in lossy media [16]. Our approach has no relation to matrix schemes or techniques involving passive thermography or active tomography [17]. Three wide-ranging U.S. patents for our technology were awarded recently [18]–[20]; additional U.S. patents are pending. Previously, we reported extensive two-dimensional (2-D) finite-difference time-domain (FDTD) simulations of the op- eration of the pulsed confocal technology [21]–[24]. In this paper, we present the methodology and results from three- dimensional (3-D) FDTD modeling of key system aspects relating to the UWB antenna-element design, the propagation and scattering of the electromagnetic impulse radiated by this element within a simple model of the breast, and the polarization and spectral characteristics of the backscatter response of generic tumor shapes. The results reported here and in [21]–[24] indicate that a system realized with existing microwave equipment has sufficient sensitivity and dynamic range to detect small tumors less than 5 mm in diameter located within 5 cm of the skin surface. II. SUMMARY OF BREAST TISSUE DIELECTRIC PROPERTIES Breast-tissue differentiation using the pulsed microwave confocal approach is based upon two fundamental physical properties. 1) The high-water content of malignant tumors causes them to have significantly larger microwave scattering cross sections than normal fatty breast tissues that have low- water content. The vascularization of malignant tumors further increases the scattering cross section. 2) Microwave attenuation in normal breast tissue is low enough (less than 4 dB/cm up to 10 GHz) to permit con- structive addition of wide-bandwidth backscattered re- turns using broad-aperture confocal-imaging techniques. Specifically, Gabriel et al. [25]–[27] reported that the rel- ative dielectric permittivity, , and conductivity, , of high- water-content tissues such as muscle are about an order of magnitude greater than those found for low-water-content tissues such as fat. This contrast persists throughout the entire RF spectrum up through millimeter waves. Foster and Schepps [28], Rogers et al. [29], and Peloso et al. [30] reported that the dielectric properties of malignant tumors are almost the same as those found for normal high-water-content tissues such as muscle. Joines et al. [31] and Chaudhary et al. [32] performed a large number of measurements up to 3 GHz of both normal and malignant human breast tissues. They found that the dielectric properties of normal breast tissues are similar to (but somewhat greater than) fat, while the properties of malignant breast tumors are similar to muscle. According to their measured data, the dielectric properties of normal breast tissue properties vary in an approximate 10% range about and S/m, whereas for malignant tumors, and S/m. Extrapolation of these values to higher frequencies using either the Debye model or an empirical model [33] shows that normal breast tissue exhibits path losses of less than 4 dB/cm up to 10 GHz. Swarup et al. [35] studied the onset of the high values of and in malignant tumors by measuring MCA1 fibrosarcoma mouse tumors at 7, 15, and 30 days after inception. No significant variation of and was seen with tumor age. While the larger tumors exhibited a necrotic interior, they showed little difference in and above 0.5 GHz. Surowiec et al. [36] performed measurements of centimeter- size malignant human breast tumors and adjacent tissues and found an increase in and of the normal breast tissue near malignant tumors. This effect may be caused by infiltration or vascularization. It could enlarge the microwave scattering cross section and thereby aid in the confocal microwave detection of the tumor. Campbell and Land [34] also measured the dielectric prop- erties of breast tissues with tumors. However, their data are not in agreement with the work cited above. Such discrepancies most likely are due to their experimental protocol which: 1) did not consider possible vascularization surrounding the tumors and 2) introduced air gaps in the very small dielectric-sample test chamber. Some benign tumors may also have a high-water content and could produce a backscatter response similar to that generated by malignant tumors. However, at present, there exists little reliable data regarding the dielectric properties of benign tumors. Characterizing and analyzing such benign tumors is an extensive subject by itself and will be considered in future papers. Here, we focus only on the dielectric properties of malignant tumors. III. ULTRALOW REVERBERATION ANTENNA DESIGN FOR BIOLOGICAL SENSING Video pulse radars operated at the air–earth interface have been used to detect buried structures such as pipes, cables, and mines [37]. Versions of these radars were proposed as means to detect and possibly image internal biological tissues [38]. However, a problem arises in that small or weakly- scattering tissue structures adjacent to an impulsively excited antenna can be obscured by the reflections from the ends of the antenna. (Early-time reflection due to impedance mismatch between the source cable and the antenna is assumed to be fully decayed before the end reflections.) For the case of free-space radiation of ultrawide-band video pulses, resistively loaded conical, and bowtie antennas have been reported [39], [40] having end reflections 40–50 dB below the exciting pulse. HAGNESS et al.: 3-D FDTD ANALYSIS OF PULSED MICROWAVE CONFOCAL SYSTEM 785 (a) (b) Fig. 1. Geometry of the bowtie antenna backed with a lossy dielectric slab, located at the surface of the breast tissue half-space (skin: � r = 36:0, � = 4:0 S/m, thickness = 1:0 mm; normal breast tissue: � r = 9:0, � = 0:4 S/m): (a) plan view and (b) side view. As demonstrated in Section IV, this reflection level is too high for detecting tumors in the breast. We recently reported the design of a wide-band bowtie antenna suitable for near-surface biological sensing [41]. The design procedure involved 3-D FDTD modeling [42], [43] in the manner of [39], [40], and [44]. In fact, the design was based upon a modification of the continuous resistive loading examined in [39], [40] in combination with the use of a zero dc Gaussian-pulse modulated carrier excitation and the location of the antenna at the interface of the biological tissue half- space. Here, we present the design of the antenna for use as an element in the pulsed microwave confocal array. Fig. 1 shows the antenna configuration. A bowtie antenna with a flare length of cm and a flare angle of 53 is located at the surface of the breast. The breast model is comprised of a 1-mm-thick layer of skin ( and S/m)1 and a half-space of normal breast tissue ( and S/m). The antenna is comprised of a material that has the following conductivity: S/m (1) where is the normalized axial distance along the bowtie, is determined by the choice of the metal used at the feed point and is chosen to give the desired level of suppression of the reflected pulse. As noted in [41], this taper is a modification of that used in [40]. Here, is a function of the axial distance from the center of the bowtie, rather than a function of the radial distance. Also, in our design so that the conductivity at the center of the bowtie is large but finite. At the ends of the bowtie antenna ( ), the conductivity goes to zero. The antenna is embedded within a large block of lossy dielectric material that matches the dielectric parameters of normal breast tissue. The excitation to the antenna is of the form V (2) where GHz, ns, and . This pulse has a temporal width of 0.22 ns (full width at half maximum—FWHM), an amplitude spectral width of 4 GHz (FWHM), and zero dc content. Although very wide-band, this excitation differs significantly from that used in [39] and [40]. Here, the excitation spectrum is a bandpass Gaussian function (centered about 6 GHz), which nulls out the low-frequency energy and minimizes the resulting exponential field decay in the surrounding lossy medium. In the FDTD analysis, the slanted edges of the bowtie an- tenna are approximated using staircasing with a submillimeter spatial-grid resolution. The excitation is implemented as a 1-V, 50- resistive voltage source at the antenna feedpoint [45]. The FDTD grid is terminated with a perfectly matched layer absorbing boundary condition [46]. Fig. 2(a) graphs the FDTD-computed exciting pulse as observed at the feed point. The magnetic field recorded in this simulation circulates about the -directed voltage source and is, therefore, proportional to the induced current. Fig. 2(b) graphs the FDTD computed-end reflections as observed at the feed point of the all-metal bowtie antenna. The end reflection is seen to be 63 dB relative to the exciting pulse. Evidently, the lossy nature of the skin provides a substantial amount of suppression of the end reflections. For example, in our previously reported work, which did not include the skin layer, the reflection from the ends of the all-metal antenna was seen to be 40 dB [41]. Fig. 2(c) graphs the FDTD computed-end reflections as observed at the feed point of the resistively loaded bowtie antenna for which S/m (the conductivity of a typical metal) and S/m (a sheet resistance of 1000 1Gabriel et al. [25]–[27] found that, for either wet or dry skin, 30 < � r < 40 and 1 < � < 10 S/m from 1–10 GHz. 786 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 47, NO. 5, MAY 1999 (a) (b) (c) Fig. 2. Time-domain fields observed at the feed point of the bowtie antenna shown in Fig. 1. (a) Exciting pulse. (b) Pulse reflected from the ends of the all-metal antenna. (c) Pulse reflected from the ends of the resistively loaded antenna. , assuming an antenna thickness of 1 mm). The resistive loading together with the lossy nature of the biological tissue and the bandpass nature of the excitation drops the antenna reverberation to 125 dB relative to the exciting pulse. In comparison to Fig. 2(b), the resistive loading is seen to provide an additional 60 dB of dynamic range beyond that which is Fig. 3. Time-domain fields observed at a depth of 1.0 cm in the breast tissue half-space. The fields radiated by the resistively loaded bowtie antenna (solid line) are reduced in amplitude by 1 dB relative to the all-metal bowtie antenna (dotted line). available with the all-metal version of the antenna in Fig. 1. Further, the resistive loading causes little loss of radiating efficiency for the electric fields penetrating the tissue half- space. Fig. 3 graphs the FDTD computed -directed electric fields at a depth of 1 cm below the feed point. The pulse radiated by the resistively loaded antenna into the breast is reduced by only 1.0 dB relative to the all-metal antenna. As shown in Section IV, this ultralow reverberation antenna permits the sensing of tumors less than 5 mm in diameter at depths as great as 5.0 cm. IV. DYNAMIC RANGE The principal performance specification is the system dy- namic range; that is, the ratio of the peak pulse power of the source to the system noise floor due to reverberations and thermal noise. The dynamic range should be large enough to permit detection of a tumor of specified size and depth. We note that the backscatter collected by a single antenna element is augmented by the processing gain of the -position synthetic-aperture array, which yields an improvement in the signal-to-noise ratio of dB. Assuming , the processing gain would range between 10–20 dB. Using the resistively loaded bowtie antenna, we have per- formed benchmark simulations to estimate the dynamic range requirements of the microwave system. The 3-D FDTD model used for this study is similar to that shown in Fig. 1, except that here a spherical malignant tumor is embedded within the breast tissue half-space. The depth of a typical normal, nonlactating human breast is on the order of 5 cm [47]–[49]. This suggests that a flattened breast of a patient in supine position would span less than 5 cm between the skin surface and the rib cage. Further, almost 50% of all breast tumors occur in the quadrant near the underarm where the breast is less than about 2.5 cm deep [50]. Accordingly, we have based our computational models of the confocal microwave system on detecting tumors to depths of up to 5 cm with a typical depth of 3–4 cm. To determine the dynamic range required to detect a tumor of a specific diameter and depth, the peak-to-peak amplitude of the backscattered response of the tumor is compared with the peak-to-peak amplitude of the exciting pulse. Fig. 4 graphs the HAGNESS et al.: 3-D FDTD ANALYSIS OF PULSED MICROWAVE CONFOCAL SYSTEM 787 (a) (b) Fig. 4. Time-domain fields observed at the feed point of the bowtie antenna. A 0.5-cm-diameter spherical tumor is located in the breast tissue half-space at a depth of 4.0 cm directly below the feedpoint. (a) Exciting pulse. (b) Backscattered response of tumor. FDTD-computed magnetic field circulating the feed point for the case of a 5.28-mm-diameter tumor located at a depth of 4.0 cm directly below the feed point. The backscatter from the tumor [Fig. 4(b)] observed in the 1.0-ns time window immediately following the excitation [Fig. 4(a)] is seen to be 92 dB relative to the exciting pulse. This simulation was performed for tumor diameters of 5.28, 3.52, and 1.76 mm at depths of 3.0, 4.0, and 5.0 cm. The backscatter response levels are tabulated in