Abstract: Despite its recognized value in detecting and characterizing breast disease, X-ray mammography has important limitations that motivate the quest for alternatives to augment the diagnostic tools that are currently available to the radiologist. The rationale for pursuing electromagnetic methods are based on the significant dielectric contrast between normal and cancerous breast tissues, when exposed to microwaves. The present study analyzes two-dimensional microwave tomographic imaging on normal and malignant breast tissue samples extracted by mastectomy, to assess the suitability of the technique for early detection of breast cancer. The tissue samples are immersed in matching coupling medium and are illuminated by 3 GHz signal. 2-D tomographic images of the breast tissue samples are reconstructed from the collected scattered data using distorted Born iterative method. Variations of dielectric permittivity in breast samples are distinguishable from the obtained permittivity profiles, which is a clear indication of the presence of malignancy. Hence microwave tomographic imaging is proposed as an alternate imaging modality for early detection of breast cancer.
Introduction
Breast cancer affects many women and early detection aids in fast and effective treatment. X-ray mammography is currently the most effective imaging method for detecting clinically occult breast cancer. However, despite significant progress in improving mammographic techniques for detecting and characterizing breast lesions, mammography reported high false-negative rates (Huynh et al., 1998) and high false-positive rates (Elmore et al., 1998). These difficulties are attributed to the intrinsic contrast between normal and malignant tissues at X-ray frequencies. In X-ray tomography a tissue is differentiated based on density. However in most cases, tissue density does not depend on tissue physiological state. Important tissue characteristics such as temperature, blood content, blood oxygenation and ischemia cannot be differentiated by X-ray tomography. For soft tissues like human breast, X-ray cannot image the breast anomalies at an early stage, as there is no significant variation in density between normal and malignant breast tissues (Fear et al., 2000).
Microwave imaging is a new technology, which has potential applications in the field of diagnostic medicine (Fear et al., 2002a, b). The basic motivation for this is improved physiologic and pathophysiologic correlation, especially in soft tissue. This expectation is based on the molecular (dielectric) rather than atomic (density) based interactions of the microwave radiation with the target when compared with X-ray imagery. When exposed to microwaves, the high water content of malignant breast tissues cause significant microwave scattering than normal fatty breast tissues that have low water content. It is reported that dielectric permittivity and conductivity increase for cancerous breast tissue is three or more times greater than the host tissue (Chaudhary et al., 1981). Due to the improved dielectric contrast, better tissue characterization too is possible.
Microwaves can be used effectively for the detection of biological anomalies like tumor at an early curable stage itself. At microwave frequencies the sensitivity, specificity and the ability to detect small tumors is the dielectric contrast between normal and malignant breast tissues (Semenov et al., 1996). Malignant breast tissues exhibit considerable increase in bound water content compared to the normal tissues and hence a high value of permittivity. When exposed to microwaves, the high water content of malignant breast tissues cause significant microwave scattering than normal fatty breast tissues that have low water content.
Some benign tumors too respond to microwaves similar to that of malignant tumors (Rangayyan et al., 1997). However, characterizing and analyzing such benign tumors is not considered in this study.
Many prototypes of active microwave imaging has been reported by Semenov et al. (1996) and Meaney et al. (2000). The need for using suitable coupling medium, to enhance the coupling of electromagnetic energy to the object as well as to increase the resolution is emphasized (Meaney et al., 2003). A suitable coupling medium accomplishes wavelength contraction without propagation loss penalty associated with increased frequency. In near field microwave medical imaging environment, resolution is determined by the aperture dimensions of the antenna, which can be generalized to far field by using a suitable coupling medium. A contrast in the dielectric properties of the object and the coupling medium decreases the measurement accuracy, increases the attenuation, creates temperature drifts and unpredictable local temperature gradients (Foti et al., 1986).
This study analyzes two-dimensional microwave tomographic imaging as an alternate imaging modality for early detection of breast cancer. Microwave studies are performed on normal and malignant breast tissues in the presence of a matching coupling medium. The reconstructed 2-D tomographic images from the collected fields show that microwave tomographic imaging could detect breast cancer with a high rate of accuracy.
Materials and Methods
The study was performed at the Microwave Tomography and Materials Research Laboratory of the Department of Electronics, Cochin University of Science and Technology, Cochin, India. Breast tissue samples for the study were collected from Department of Surgery, Lourde Hospital, Cochin, within 30 min of mastectomy.
System Configuration
The designed prototype of 2-D microwave imaging is shown in Fig.
1. The breast sample supported on a PVC holder is mounted on a circular
platform capable of circular motion in the horizontal plane. The platform along
with samples is kept inside a tomographic chamber of radius 12 cm and height
30 cm, coated inside with suitable absorbing material. The chamber is filled
with coupling medium. Suspended bowtie antennas are used for both transmission
and reception of microwave energy.
| Fig. 1: | Experimental setup |
All measurements are done using HP 8510 C network analyzer; interfaced with Compaq work station SP 750 using GPIB bus.
Coupling Medium
The coupling medium used here is corn syrup. Dielectric parameters of the
material in the frequency range of 2-4 GHz are done using cavity perturbation
technique (Bindu et al., 2004a, Mathew and Rareendranth,1999). This frequency
range is adopted, as the resonant frequency of the antenna used in our microwave
imaging studies is 3 Ghz. Also it conveniently includes the Industrial Scientific
and Medical (ISM) applications band of 2450 MHz. The dielectric permittivity
and conductivity variations of corn syrup in the frequency range of 2-4 GHz
are shown in Fig. 2. It is observed that for corn syrup, the
dielectric permittivity decreases and conductivity increases, with the increase
of frequency. This result coincides with the studies on dielectric properties
of biological tissues (Gabriel et al., 1996).
The complex permittivity of the medium can be written as
| (1) |
where εr' is the dielectric permittivity and εr" is the dielectric loss of the medium
The loss tangent
| (2) |
The propagation constant
| (3) |
where α represents the attenuation factor and β the phase factor. The conductivity σ is given by
| (4) |
Substituting Eq. 1, 2 and 4 in 3 and simplifying, we get
| (5) |
and
| (6) |
If the wave is considered traveling in the + z direction, e-αz represents the decaying envelope of the wave and e-βz represents the sinusoidal nature of the wave whose phase is βz. The total loss encountered by the wave over a distance z consists of dissipation loss Ldiss due to conduction currents being excited in the medium and diffusion loss Ldiff due to the spherical spreading of energy (Foti et al., 1986).
They are given by,
| (7) |
| (8) |
Hence the total loss
| (9) |
| Table 1: | Propagation loss parameters of water, corn syrup and saline at 3 GHz at a distance of 12 cm from the transmitter |
| Fig. 2: | Variation of dielectric permittivity and conductivity for corn syrup |
| Fig. 3: | Propagation loss characteristics of corn syrup |
Figure 3 shows the propagation loss characteristics of corn syrup. It is seen that losses increase with frequency, which is due to the increase of conductivity. Table 1 compares the loss parameters of distilled water and saline (Foti et al., 1986) with corn syrup at 3 GHz, at a distance of 12 cm from the transmitter. The loss values are acceptable when compared to the loss parameters of conventional coupling medium like distilled water and saline (Foti et al., 1986). It is reported that in water the rate of increase of loss vs. distance is much higher due to the dominant dissipation loss.
Antenna Design
Coplanar strip line fed bowtie antennas generating TM01 mode
are designed for both transmission and reception of microwave signals. The experimental
investigation (Bindu et al., 2004b,c) shows that the designed antenna,
in air, exhibits a center frequency of 3 GHz, enhanced 2:1 VSWR bandwidth of
~ 46% in the operational band of 1.850-3.425 GHz and a return loss of-53 dB.
In corn syrup, the bandwidth is enhanced to 91% in the range of 1.215-3.810
GHz with resonant frequency of 2.855 GHz and return loss of-41 dB. Figure
4a and b show the radiation characteristics of the antenna.
It is observed from the figures that the antenna exhibits maximum forward radiation
and less back radiations at 3 GHz.
Samples
Samples of breast tissues of four patients are subjected to the study. Cancerous
tissue of ~ radius 0.5 cm inserted in normal tissue of ~ radius 1 cm, of patient
1, is taken as sample 1. Samples 2 and 3 consists of four tumorous inclusions
of ~ radius 0.25 cm each inserted in normal tissue of ~ radius 1 cm, of patients
2 and 3. Scattered inclusions of cancerous tissue of ~ radius 0.1 cm each inserted
in normal tissue, of patient 4 is treated as sample 4. The samples are supported
on a cylindrical PVC holder (tan δ = 0.0018 and εr = 2.4
at 3 GHz) of height 15 cm at the center of the measurement set up as shown in
Fig. 1.
2-D Microwave Tomographic Imaging
The problem of microwave tomographic imaging has been a topic of theoretical
and experimental study for many years. Several research groups are investigating
microwave tomography for breast cancer detection (Meaney et al., 1996,
1998, Dun Li et al., 2004, Bulyshev et al., 2001).
| Fig. 4a: | Radiation characteristics of bowtie antenna |
| Fig. 4b: | Radiation pattern of the antenna measured at 3 GHz |
Data Acquisition
For data acquisition, the breast sample is illuminated by bow-tie antenna
at a frequency of 3 GHz. As shown in Fig. 1, the transmitting
antenna is fixed at a radius of 6 cm on the circular rail, while the receiving
antenna is rotated around the object at 6 cm radius. The platform upon which
the sample is mounted is rotated from 0° to 360° in steps of 10°
and the receiving antenna is rotated from 30° to 330° in steps of 10°.
For every 10° rotation of the platform with the sample, the receiving antenna
makes the measurement in steps of 10°.
Reconstruction Algorithm
The contrast in the dielectric properties of the object creates multiple
scattering of the wave inside the object. This poses a non linear inverse scattering
problem which is formulated in terms of Fredholm integral equation of the second
kind (Taflove, 1998). The object is considered inhomogeneous in the xy plane
but homogeneous in the z direction. For an incident TM wave, the total electric
field at the receiver (Taflove, 1998) is given by,
| (10) |
where r stands for a point in the measurement domain and r' for the object domain. φinc,b (r) is the incident field in the presence of the background inhomogeneity and the integral term is the scattered field due to the dielectric contrast between the scatterer and the background medium.
| (11) |
is called as the object function, gb (r, r') the Green’s function and φ(r') the total electric field inside the scatterer. Equation 10 is used for both the forward and inverse solutions. In the forward problem, both the medium properties and the domain of inhomogeneity are known and the equation is solved to obtain the total electric field. In the inverse problem, scattered fields are measured at discrete points and the medium properties are the unknowns to be determined. The problem is linearized using distorted Born approximation (Chew et al., 1990) by replacing φ(r') with φinc,b (r). As the background medium is inhomogeneous, Green’s function is solved numerically (Richmond, 1965). Discretization of the integral equation in the inverse problem yields vector representations of the scattered field and the object profile. As the inverse problem is ill posed, a regularization procedure (Taflove, 1998; Chew et al., 1990) is employed where an optimization technique is adopted to minimize the error by minimizing a cost functional. The non-uniqueness and instability of the problem is thus circumvented and an adequate solution is provided. The obtained δε is used to improve εb(r) which in turn is used to update the parameters in Eq. 10. The iteration is continued until convergence is reached. The imaging area is restricted to 16 x 16 pixels due to computational complexity. The sampling rate considered is 0.1λ.
Results and Discussion
Corn syrup sample of dielectric permittivity and conductivity as 18.7 and 0.64 S/m at 3 GHz is used as the coupling medium in this study. In order to check the compatibility of corn syrup with breast tissue samples, dielectric properties of the breast tissue samples are measured using cavity perturbation technique and are compared with that of the corn syrup at a frequency of 3 Ghz.
| Table 2: | Dielectric parameters of breast tissue samples and corn syrup measured using cavity perturbation technique at 3 GHz |
| Table 3: | Dielectric parameters and loss factors of corn syrup with frequency |
| Fig. 5: | Sample 1-a) 2D microwave tomographic image. b) Dielectric permittivity profile |
Table 2 shows the comparison. The measured dielectric parameters of breast tissues match with the literature data too (Chaudhary et al., 1981, Campbell et al., 1992). When corn syrup is used as coupling medium for imaging normal breast tissue with cancerous inclusion, good resolution is achieved as the dielectric permittivity of corn syrup matches with that of the normal breast tissue as seen in Table 2. As the conductivity of the medium is less than that of the actual tissue sample, loss tangent decreases and hence the propagation loss. Table 3 shows the tabulated form of the graphs shown in Fig. 2 and 3. The frequencies mentioned in the table are the resonant frequency of the cavity used in the cavity perturbation study.
The reconstructed 2-D tomographic images for the breast samples 1-4 are shown in Fig. 5-8. The dielectric contrast of the samples is clearly distinguishable from the images as well as from the permittivity profiles. Samples 1-3 are having ~ circular cross section without any cover, where as sample 4 is covered in a thin conical polythene study.
| Fig. 6: | Sample 2-a) 2 D microwave tomographic image. b) Dielectric permittivity profile |
| Fig. 7: | Sample 3-a) 2 D microwave tomographic image. b) Dielectric permittivity profile |
| Fig. 8: | Sample 4-a) 2 D microwave tomographic image. b) Dielectric permittivity profile |
This is done to check whether the shape of the sample too is reconstructed properly. As the dielectric permittivity of the coupling medium and the normal breast tissue samples are in good match, the tumor inclusions are clearly visible in Fig. 5-8. In Fig. 8, the shape of the sample too is reconstructed and is seen with a black border. This is due to the fact that polythene paper exhibits a very low permittivity of εr' 2.2 at 3 GHz. Scattered tumor inclusions are clearly distinguishable in the image. A resolution of 2 mm is achieved in this reconstruction with the use of corn syrup as the coupling medium. A comparison of the obtained permittivity values of the breast samples from Fig. 5-8 with that measured using cavity perturbation technique reported in Table 2 shows good agreement.
Sources of Error and Accuracy Conditions
Early stage tumor detection is the attractive feature of the proposed microwave medical imaging. So care is taken to eliminate all possible types of errors. In the present study HP 8510 network analyzer is used. Accuracy of this instrument is 0.001dB for power measurement, 1 Hz for frequency measurement (HP 8510C Manual, 1988). Main sources of experimental errors are 1) Edge reflections from the antenna: The FDTD computed end-reflections observed at the feed point of the bowtie antenna relative to the exciting pulse is as low as-24 dB. 2) Reflections from the sample holder: The tissue samples are supported on a low loss PVC pipe having loss tangent (tan δ) 0.002. Hence reflections are negligible. 3) Medium reflections: As the tumor under study is immersed in a matching coupling medium, reflections are minimized and good resolution of the reconstructed image is ensured. 4) Error in using distorted Born approximation to linearize the inverse scattering problem: This method is adopted to reduce the computational complexity. Acceptable values of permittivity profiles are obtained with in vitro breast studies. The matter has to be further investigated with strong scatterers and fast forward iterative solvers. 5) Convergence: To ensure that global convergence is achieved, we performed five iterations and the same profile as with the fourth iteration was obtained.
Conclusions
Microwave tomographic imaging is explored as an imaging modality for early detection of breast cancer. In vitro studies on normal and malignant breast tissues suggest that microwave tomographic imaging could satisfactorily image the tissues showing clear discrimination in terms of dielectric permittivity. The presence of breast cancer can be easily determined by analyzing the dielectric permittivity profiles, as cancerous tissues exhibit higher value of dielectric permittivity compared to normal tissues even at early curable stage itself. This is an advantage of the technique compared with conventional X-ray mammography. Hence microwave imaging can be considered for early stage breast cancer detection.
Acknowledgement
Authors G. Bindu and Anil Lonappan thankfully acknowledge Council of Scientific and Industrial research, Govt. of India for providing Senior Research Fellowships.