87 8 IEEE TRANSACTIONS ON BlOMEDlCAL ENGINEERING, VOL. 43, NO. 9, SEPTEMBER 1996

Microwave Imaging for Tissue Assessment: Initial Evaluation in Multitarget

Tissue-Equivalent Phantoms Paul M. Meaney,” Member, IEEE, Keith D. Paulsen, Member, IEEE,

Alexander Hartov, and Robert K. Crane, Fellow, IEEE

Abstract-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 compo- sition. 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 depen- dent 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 configu- ration 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.

I. INTRODUCTION

HE application of microwave imaging to various medical T problems may offer several benefits relative to tradi- tional imaging modalities [l], especially in terms of tissue contrast [21, [31. Of particular interest is the area of hy- perthermia cancer therapy, where electrical properties can

Manuscript received June 26, 1995; revised April 12, 1996. This work was supported by the National Institutes of Health under Grant #RO 1-CA55034. Asterisk indicates corresponding author.

“P. M. Meaney is with the Thayer School of Engineering, Dartmouth Col- lege, Hanover, NH 03755-8000 USA (e-mail: paul.meaney@dartmouth.edu).

K. D. Paulsen is with the Thayer School of Engineering and the Norris Cotton Cancer Center, Lebanon, NH 03766 USA.

A. Hartov is with the Radiation Oncology Department, Dartmouth Medical School, Lebanon, NH 03766 USA.

R. K. Crane is with the School of Meteorology, University of Oklahoma, Norman, OK 73019 USA.

Publisher Item Identifier S 0018-9294(96)06104-6.

vary with tissue temperature [4]-[6]. By monitoring these quantities during treatment, estimations of induced temperature field profiles may be extractable using difference imaging techniques [7]. Several investigators have sought to exploit microwave imaging in this context [SI, [9] and while fun- damental groundwork has been laid by these studies, the temperature imaging experiments that have been reported to date have been crude [S]-[11]. This work has demonstrated that some useful information about temperature distributions can be obtained through difference imaging techniques: the value of the images produced has been limited, however, by the inability to recover quantitative information about the electrical property distribution in an absolute sense. Perhaps the most important conclusion that has emerged from this initial experience is the fact that quantitative static imaging using absolute imaging procedures is an essential prerequisite to performing quantitative dynamic thermal profiling [SI, [lo].

Based on the overall strong rationale for medical microwave imaging, and the promising, but to date only qualitatively suc- cessful, preliminary work of others, we have been developing an imaging system with the goal of temperature estimation. As such, one of our primary foci has been the realization of an approach with quantitative imaging capabilities, especially in terms of recovering both the real and imaginary components of a static electrical property profile using absolute imaging procedures: a step which is essential to attaining meaningful dynamic thermal imaging, but which has been lacking in previously reported systems.

Central to our approach has been an image reconstruction al- gorithm [ 121 which is fundamentally unlimited by wavelength and contrast considerations because it is essentially a near- field technique that is not constrained by conventional far-field diffraction-limit arguments, but rather is ultimately restricted by signal-to-noise. This leads to the additional advantage that lower frequency illuminations can be utilized with this type of algorithm without severe degradation in resolution. Early estimates of optimal operating frequency for microwave imaging were driven by the diffraction limit which led to the need to design hardware systems functioning in the low-GHz regime [ I 31 . The limited penetration depths of electromagnetic signals at these frequencies dictated that either unrealistic dynamic ranges had to be achieved or imaging depths in tissue had to be restricted to clinically uninteresting dimensions. With the new class of imaging algorithm we employ, lower

0018-9294/96$05.00 0 1996 IEEE

MEANEY et al.: MICROWAVE IMAGING FOR TISSUE ASSESSMENT INITIAL EVALUATION IN MULTITARGET TISSUE-EQUIVALENT PHANTOMS 879

Boundary Element Integration Path

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Fig. 2. Reconstructed images of the real and imaginary components of the k2 distribution at 500 MHz for 4.3-cm and 2.5-cm fathone equivalent phantoms separated by 0.4, 1.7, and 4.2 cm. The data has been collected using the two-tiered receiver locations shown in Fig. 1.

frequencies can be utilized which reduce system dynamic range requirements and increase tissue depths that can be imaged without unduly compromising spatial resolution.

algorithms as well [ 141-[17]; the hypothesized advantages of these approaches, however, have only been demonstrated in theory using simulations and have not been shown to be viable with actual measured data. In this regard, we have realized a dual mesh concept [ 181 which decouples the field variables from the reconstruction parameters thereby minimizing the amount of observational data which is needed to recover electrical property profiles without sacrificing quality in the reconstructed images obtained from measured field amplitudes and phases. This in turn has allowed us to validate our image reconstruction algorithms with laboratory data which was collected at a single illumination frequency for simple high- contrast targets. The hardware system design used to carry out this initial phase of experimentation and its performance characteristics have been described in [19].

While we have discussed the conceptual foundation for our image reconstruction algorithm and demonstrated its per- formance with noisy simulated data elsewhere [ 121, [181 and we have described the hardware needed to perform the measurements required for image reconstruction in detail [ 191, we have not systematically investigated whether we can achieve absolute and quantitative image reconstruction of static targets. In this paper, we report an initial evaluation of an enhanced version of our complete system through a series of more complex multitarget phantom experiments involving several different frequencies, target contrast levels and target positions. The primary advantage of our latest approach is the utilization of a novel two-tiered reception mode, the imple- mentation of which has required modifications to our original reconstruction algorithm as described herein. The findings

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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 43, NO. 9, SEPTEMBER 1996

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Real and imaginary components of the k 2 distributlon plotted along a horizontal transect through the images in Fig. 2 comparing results using only

reported suggest that the quality of the static target images obtained is sufficient to provide a framework with which to proceed toward the more difficult problem of dynamic imaging of temperature distributions. These results are also significant because they represent the first thorough demonstration of the viability of near-field imaging algorithms based on actual laboratory data and they confirm the advantages of this type of approach which have previously only been hypothesized os demonstrated through simulations.

11. METHODS AND MATERIALS

A. Receiver Antenna Configuration

The reconstruction algorithm employed here is a total field formulation which differs significantly from other approaches [ 141-[ 171 where the total field is decomposed into its constitu- tive parts-the incident field and the scattered field-such that the scattered field is used in an integral formulation to recover the material property distribution. In addition to mathematical nuances which distinguish these two formulation strategies, measurement issues can also arise depending on the approach

that is taken. For example, in the highly conductive medium used in this work, the total field values at measurement sites which are located on the near-side of the target region with respect to the electromagnetic (EM) source have been shown to be due almost entirely to the source incident fields with very little contribution resulting from the scattered fields of the objects present [20]. As a result, within our reconstruction algorithm which uses a total field formulation, the measured data for points nearest the electromagnetic source produces almost no information about heterogeneities in the target region. In a scattered field formulation, subtraction of the incident field from the total field would yield relatively small scattered fields that might prove useful. In the presence of measurement and roundoff errors due to subtracting two large, nearly identical values, however, effective utilization of this data in the scattered field formulation can prove difficult.

Based on these observations, we have chosen not to use any near-source locations in our measurement data sets. Rec- ognizing that this significantly reduces the amount of measured data that is available for image reconstruction, which can directly effect the number of reconstruction parameters that

MEANEY et al.: MICROWAVE IMAGING FOR TISSUE ASSESSMENT INITIAL EVALUATION IN MULTITARGET TISSUE-EQUIVALENT PHANTOMS 88 I

can be accurately determined, we have sought to compensate for the decrease by increasing the amount of measurement data on the far-side (transmission side) of the target region. Specifically, we have utilized a combination of measurement sites on the target region perimeter along with a set of sites which are outside of this perimeter. Fig. 1 conceptually illustrates our receiver antenna positioning strategy relative to the more conventional tomographic measurement site config- uration which is also shown. Utilization of the two-tiered set of sites in Fig. 1 requires some modification to the hybrid element reconstruction algorithm [12].

B. Measurement Sites Outside the Target Region

Our original hybrid element reconstruction algorithm uti- lized measurement sites which coincide with boundary nodal positions in the finite element mesh. Thus, when the electric field distribution was calculated at each iteration, the computed electric field values were available at the measurement sites without any additional effort. In principle the finite element discretization can be extended beyond the perimeter of the predefined target region in order to encompass any new measurement sites which might be exterior to the target region (see Fig. 1). Unfortunately, this would significantly increase computational costs due to the unnecessary discretization of that exterior region which is not only homogeneous but also of known electrical properties. An alternative approach is to allow the new measurement sites to reside in the boundary element region of the problem (i.e., the homogeneous region exterior to the finite element mesh) which can be accomplished without sacrificing computational accuracy or increasing the size of the finite element mesh. Further, this strategy requires only minor additional computations at each iteration.

Our overall image reconstruction approach is cast as a non- linear optimization problem where we use Newton’s method to update an initial electrical property distribution by minimizing the squared error between computed and measured field values. As a result, the incorporation of exterior measurements is involved in 1) calculation of the electric fields for the current estimate of the electrical properties at these points and 2) calculation of the derivative of the field with respect to each reconstruction parameter which is required for construction of the Jacobian matrix that is needed for updating the electrical property profile at each iteration.

Calculation of the electric fields at “exterior” points is governed by solution of the matrix system [21]

where {E} and {F} are the discretized electric fields, E, and (n x H), within the exterior or boundary element region (external to the target area, see Fig. 1) of the problem domain; the subscripts b and s refer to those particular points which are located either along the boundary of the finite element region or the electromagnetic source, respectively; and the elements of the [C] and [D] matrices are integrations of known functions over the boundary element integration contour shown in Fig. 1. The electric fields at all points in vector X = {x1,22, . . . z,}~

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(e.g., at the locations illustrated in Fig. 1) can be calculated as an integral of boundary electric fields and fluxes by [22]

882 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 43, NO. 9, SEPTEMBER 1996

where the subscript z refers to the fact that the electric field is only oriented in the x-direction due to the assumed transverse magnetic (TM) illumination; G is the Green’s function for the two-dimensional (2-D) Helmholtz equation with singularity at 2,; and the subscript i refers to the ith member of X which is located exterior to the boundary elements comprising the perimeter of the target region. Integral equation (2) can be written in matrix form as

where {E,} is a vector of electric field values calculated at the points in X. It is important to note that the matrices [Q1] and [&2] are solely functions of the geometry and material properties in the boundary element region; hence, their values do not change with iteration as do the electrical properties within the interior finite element region which are iteratively updated; hence, the matrix elements in (3) can be calculated and stored by a preprocessing program.

In the existing algorithm, {E,} is initialized to a set of values appropriate for the type of radiator used which has been determined empirically and { E b } is calculated at every iteration in the present algorithm; hence, the only quantities needed to compute {E,} from (3) are { F b } and {F3}. Equation (1) can be rewritten as

(4)

where [GI = [D]-l [C] which has also already been calculated as part of the forward solution as described in [12]. Thus, { F b } and {F,} can be computed at nominal extra cost from a simple matrix-vector multiplication of a pre-existing matrix and vector. {E,} can then be calculated from the two matrix- vector multiplications as shown in (3).

The calculation of the derivatives of the field solution with respect to each member of the discrete set of parameters which define the k 2 distribution (where k is the complex- valued wavenumber) that are required to construct the Jacobian matrix are handled in very much the same manner. For example, differentiation of (3) with respect to the k 2 value for reconstruction parameter, j , yields

Again it is important to recognize that the matrices [&I] and [QZ] are not functions of the k 2 values within the finite element region, and are, therefore, treated as multiplicative constants during this differentiation. Since {E,} has also been dictated, it too, does not change with variations in I C 2 . Similarly to the forward solution, {q} has already been computed at each iteration as part of our original image reconstruction process and it follows that {q} and {q} can be found by differentiating (4) and recognizing that matrix, [GI, is also not a function of k 2 which means that these quantities are

a k ,

a k l a k ,

obtained by multiplying [GI by known vector {%}. Given

that {%} are precisely the terms needed in the Jacobian matrix when external measurement sites are included and that this vector can be obtained directly from (5) once { q} and

{ %} are known, it is clear that both calculation of the electric fields and their associated derivatives at external locations can be obtained during image reconstruction by matrixhector multiplies which pose no major computational load on our overall algorithm.

dk l

ah,

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C. Reconstructed Image Error Analysis

In addition to presenting reconstructed images and compar- ing one-dimensional (1-D) transects of the exact and recovered electrical property profiles through the region of interest (ROI) as methods of documenting imaging performance, we have also developed error analyzes to further quantify the results presented in Section 111. For this study, we have analyzed three quantities: 1) root-mean-square (rms) errors in the recovered k 2 values (where k 2 = w 2 p + j w p a is complex-valued having real and imaginary parts proportional to the electrical permittivity and conductivity, respectively) of the object and background subregions, 2) errors in the estimated diameters of the reconstructed and actual objects, and 3) errors in the locations of the reconstructed and actual objects.

rms Errors: In this case, we compute the square root of the averaged squared error between the reconstructed and exact real and imaginary components of k 2 , relative to the size of the electrical contrast for both the object and background regions (for the background the size of the electrical contrast is taken as unity). For this error measure, we consider all sample positions in the discrete sum which are inside the physical target dimensions and not the reconstructed target size which is determined from a full-width half-height criterion as described below. Diameter of Reconstructed Object: Because of the large contrast ratios that have been considered between the embedded objects and the saline background, a full- width-half-height criterion is employed to estimate a representative reconstructed target diameter. In this case, a mid-level k 2 value is determined by taking the average of the lowest and highest k 2 value in the selected object subregion and then the area of all finite elements whose centroidal k 2 value is below this thresh- old is summed to determine the total reconstructed object area. An effective diameter is then be calculated assuming a circular object shape. Location of the Reconstructed Object: The center of the reconstructed object is estimated in a manner similar to calculating its center of mass. In this case, the inverse (since the property values of the object are significantly less than those of the background) of the centroidal value of the property distribution for each element is weighted by the element area. This quantity is then multiplied by the ( L G , ~ ) coordinates of the element centroid, summed over all elements and normalized by

MEANEY et al.: MICROWAVE IMAGING FOR TISSUE ASSESSMENT INITIAL EVALUATION IN MULTITARGET TISSUE-EQUIVALENT PHANTOMS 883

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Real and imaginary components of the IC2 distribution plotted along a horizontal transect through the images in Fig. 4 for the target separation

this same sum obtained without the coordinate-value multiplication.

D. Phantom Muterials

Several materials with various electrical properties have been used during the experiments described herein. Their properties are listed in Table I. Values for the saline solu- tion were determined as a matter of course during system calibration [19]. All others were measured using the HP 85070B Dielectric Probe Kit in conjunction with the HP 8753C Network Analyzer. The agar and distilled (DI) water phantoms were held in cylindrical tubes of Plexiglas with inner diameter of 3.81 cm and outer diameter of 4.45 cm. The other two phantoms were solid cylinders constructed from a fathone equivalent material [2] and had diameters of 2.5 and 4.3 cm, respectively.

111. RESULTS This section presents reconstructed images obtained with

our imaging system operating at three different frequencies

(300, 500, and 700 MHz) using the receiver antenna con- figuration described in Section 11-A. The meshes used for the forward solution calculation and the image reconstruction consisted of 2342 and 143 nodes, respectively. Image recon- structions required approximately eight minutes per iteration (three to five iterations were used for the images shown herein) on an IBM RISC 6000 series workstation. Eight transmitter locations, which were positioned equidistantly from the target region center in angular increments of 45", and 32 receiver locations formed from two rings (each having 16 sites) of equi-angular positions (fixed at radii of 7.4 cm and 10.2 cm from the target region center, respectively) comprised the experimental system configuration. As discussed in !Section II- A, for each transmitter excitation only the 18 receiver positions (nine on each semicircular arc, see Fig. 1) directly opposite the transmitter have been used to form the measured data sets from which image reconstruction has been attained.

A. Use of Two-Tiered Receiver Sites

As an initial demonstration of system performance, we have compared reconstructions involving the use of only the nine

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Real and imaginary components of the k 2 distribution plotted along a horizontal transect through the images in pig. 4 for the target

TABLE I ELECTRICAL PROPERTIES OF THE TISSUE EQUIVALENT MATERIALS USED IN THE RECONSTRUCTION EXPERIMENTS

receiver sites from the inner arc with reconstructions based on the full 18 receiver sites from both measurement arcs. These configurations yield totals of 72 and 144 pieces of data, respectively. This comparison not only provides some

insight into the importance of the data from the outer arc, but also indicates how effective the algorithm can be in an under- determined least squares problem since it is reconstructing 143 separate parameters in both cases.

MEANEY et al.: MICROWAVE IMAGING FOR TISSUE ASSESSMENT INITIAL EVALUATION IN MULTITARGET TISSUE-EQUIVALENT PHALNTOMS 885

4.28 cm diam. Object

TABLE I1 AVERAGE RMS ERRORS FOR THE REAL AND IMAGINARY PARTS OF THE RECONSTRUCTED MATERIAL ELECTRICAL PROPERTIES FOR TEST PERFORMED AT

300-, SOO-, and 700-MHz. ERROR VALUE WERE AVERAGED FOR THE (a) 4.28-cm AND (b) 2.54-cm DIAMETER FATBONE EQUAVALENT CYLINDERS AT THREE DISTANCES (0.0, 2.54, AND 3.81 Cm) FROM THE CENTER OF THE TARGET REGION ALONG THE HORIZONTAL AXIS

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Fig. 2 shows images of 4.3-cm and 2.5-cm fathone equiv- alent cylinders separated by increasing distances for recon- structions based on 144 pieces of measurement data. One- dimensional horizontal transects of the recovered I C 2 values are shown in Fig. 3 and are compared with both the actual material distributions and the reconstructions obtained with only 72 measurement observations. In general, both reconstructions recover the larger object in the proper location; however, the images using the 144 measured values capture both objects much more effectively and their material properties much more accurately. This may partly be due to the raw increase in data; nonetheless, while the results from both sets of data are reasonably quantitative, there is a clear benefit from the extra information coming from the two-tiered measurement configu- ration. As a result, all of the remaining images reported in this section have been obtained with the two-tiered measurement scheme.

B. Frequency Variation While a variety of image reconstructions have been per-

formed at selected frequencies, only images from represen- tative cases involving multiple objects will be shown here. In general, the multitarget configurations pose more difficult reconstruction problems and more readily indicate system performance limitations in terms of ability to resolve object size, separation of objects and material contrasts. In this regard, Fig. 4(a) and (b) shows images obtained at illumination frequencies of 300, 500, and 700 MHz for 4.3-cm and 2.5-

cm fathone equivalent cylinders separated by distances of 0.4 and 1.7 cm, respectively. Fig. 5 displays I-D exact and reconstructed electrical property profiles along a horizontal transect across the images in Fig. 4 in order to provide a quantitative assessment of image quality.

C. Contrast Variation

A series of images are shown in Figs. 6-7 where a mul- titarget phantom is used but with variations in electrical contrasts between the two objects. The first case involves a target arrangement consisting of a 4.3-cm diameter fathone equivalent cylinder and a 3.8-cm diameter DI water cylinder. This is a particularly interesting situation because the DI water and saline background should demonstrate little difiFerence in their relative dielectric constants, E,, but their conductivity values, (7, should be strongly distinct. Fig. 6(a) shows images at 300 and 700 MHz for this multitarget case where the two objects are separated by a distance of 2.3 cm, respectively. One-dimensional transects of the recovered and exact property distributions for these images are shown in Fig. 7(a).

The second situation to be considered in detail here is the same as the previous one in terms of the object sizes and separations; however, in this case the DI water target is replaced with an agar gel (0.3% NaC1). The agar material has a dielectric constant that is slightly lower than that of the saline background, and a smaller conductivity value, but one not as dramatically different as that of the fathone equivalent targets (see Table I). Fig. 6(b) shows image reconstructions at

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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 43, NO. 9, SEF'TEMBER 1996

RMS ERRORS

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TABLE I11 AVERAGE RMS ERRORS FOR TWO CYLINDRICAL OBJECTS MADE OUT OF FAT/BONE EQUIVALENT MATERIAL WITH THE ACTUAL

DIAMETERS BEING (a) 4.28 cm AND (b) 2.54 Cm FOR THE LEFT AND RIGHT OBJECTS, RESPECTIVELY. AVERAGES WERE COMPILED FOR THREE TESTS CASES WHERE THE TWO OBJECTS WERE SEPARATED B Y 0.4, 1.7, AND 4.2 cm, RESPECTIVELY

300 500 700

exponetid decay 8.74 .201 ,433 7.70 ,261 .481 7.18 ,275 ,469

300 and 700 MHz for this situation with the corresponding 1- D horizontal transects comparing the exact and reconstructed electrical property profiles displayed in Fig. 7(b).

D. Image Quality

Analysis of imaging performance, in terms of the measures discussed in Section 11-C for both single and multitarget imaging experiments, are provided in Tables 11-V. In order to present a representative summary of the extensive experi- mentation that has been conducted, only image reconstructions involving the 4.3-cm and 2.5-cm fathone objects which consti- tute the difficult high contrast cases, are analyzed here. Similar findings have been noted for the other phantoms of varying contrast levels. Table I1 shows a summary of rms errors in the k 2 distribution (real and imaginary parts) for the single object experiments versus frequency for both the background and target regions whereas Table 111 provides the equivalent information for individual objects and the background in the multitarget experiments. Tables IV and V document the results of the diameter and center of object computations for the 4.3- cm and 2.5-cm fathone equivalent cylinders in both the single and multitarget experiments, respectively.

IV. DISCUSSION

For two objects of distinct size but having identical high- contrast material compositions, the results shown in Figs. 4 and 5 indicate that both objects can be discriminated quite

well when they are separated by a distance of 1.7 cm. Further, it is clear that the 700 MHz images have the most uniformity in the background medium and the sharpest resolution at material interfaces in this case. The images resulting from the smaller separation (0.4 cm.) are also quite informative. Reconstructions at all three frequencies contain what appears to be a rightward shift of an otherwise normally reconstructed large cylinder. Again, the 300-MHz case shows the greatest degree of blurring with the background, whereas, the 700- MHz results exhibit a sharper contrast and a more uniform background to the extent that the adjacent targets are beginning to appear distinct.

For the contrast variation cases shown in Figs. 6(a) and 7(a), the DI water object is correctly imaged at 700 MHz. The imaginary part of the image (corresponding to a) clearly shows the object, which is essentially not visible in the real part of the image (corresponding to q.). The situation is quite different at 300 MHz. The background is much less uniform than that at 700 MHz and a low-&, object emerges erroneously. It is important to note here that the very low-dielectric Plexiglas wall was roughly 0.3-cm thick, and may have had some influence in making the composite object (plastic wall plus DI water) appear as a lower-dielectric target. For the agar gel case shown in Figs. 6(b) and 7(b), the fathone equivalent cylinder is recognized quite well at both 300 and 700 MHz along with the conductivity of the agar gel. However, the results for the dielectric reconstructions of the agar gel are quite similar to the DI water tests in Figs. 6(a) and 7(a). At 700 MHz, the recovery

MEANEY et al.: MICROWAVE IMAGING FOR TISSUE ASSESSMENT INITIAL EVALUATION IN MULTITARGET TISSUE-EQUIVALENT PHANTOMS 887

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of the dielectric constant of the agar is fairly accurate whereas the results at 300 MHz still exhibit an erroneous detection of an object of significantly lower dielectric constant.

The image error analyses in Table 11 for the single target experiments indicate that there is a definite improvement in the quantitative recovery of electrical properties with frequency for the real part of the k 2 distribution in the background and in both sizes of object regions. It is not clear, however, that this trend holds true for the imaginary part of the electrical properties. For example, the electrical property composition errors actually increase with frequency for the larger 4.3-cm diameter target, whereas, they decrease for the smaller 2.5- cm diameter target. Similar behavior can be observed in the multitarget cases as shown in Table 111. Again recovery of the real part of the electrical property distribution (background and object regions) shows improvement with frequency, whereas the imaginary component exhibits some increased degradation with frequency. Some insight into this phenomenon may be gained by observing the mesh sampling rates shown in Tables 11 and III. In all cases, the number of samples per wavelength is greater than ten which is a benchmark estab-

300 500 700

TABLE IV AVERAGE DIAMETERS AND POSITION ERRORS FOR THE TWO FATBONE

EQUIVALENT CYLINDERS WITH THE ACTUAL DIAMERERS BEING 4.28 Cm AND 2.54 cm, RESPECTIVELY, DURING SINGLE-TARGET IMAGING EXPERIMENTS. VALUES

WERE AVERAGED FOR THE CYLINDERS AT THREE DISTANCES (0.0,2.54, AND 3.81 cm) FROM THE CENTER OF THE TARGEr REGION ALONG THE HORIZONTAL AXIS

14.28 cm dram. I 1

,061 ,068 .064

4.09 3.63 3.16

lished in [21] for accurately modeling the forward solution. However, as the frequency increases, the mesh sampling rate per exponential decay length much more closely approaches seven which is also a benchmark for accurate forward solution modeling. Hence, because of the high conductivity of the medium, a higher level of discretization than has been used here may be required for more accurate forwarid solution modeling in order to diminish the increase in rm:; errors in the imaginary component of k 2 that has been observed with increasing frequency.

Overall, however, the reconstructions are quantitative with respect to electrical property recovery. The property errors in the background range between 10-20% for most cases. A 5 1 0 % increase in error in the reconstructed background values is observed in the multitarget experimenl s relative to their single-target counterparts. In general, the property recovery errors are also in the 10-20% range for the embedded objects, although they are consistently worse than in the background which is not surprising given the high electrical contrast. Interestingly, the errors in recovered target property values are not as sensitive to the presence of multiple targets. While property errors in the objects can be near 50% in some cases, it is important to recognize that when assessing this image quality measure we have used the actual target size and not the estimated target size based on reconstruction as the region over which property errors have been computed (see Section 11-C). This represents a stringent worst-case scenario

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Fig. 7. agar gel cases. Solid line is the recovered property profile whereas the double-dashed line is the exact distribution.

Real and imaginary components of the k 2 distribution plotted along a horizontal transect through the images in Fig. 6 for the (a) DI water and (b)

which penalizes the reconstructions for both geometrical and property errors.

Based on the results shown in Tables IV and V, reconstruc- tion of the real part of the k 2 distribution more accurately captures the target diameters, especially for the larger of the two objects, with errors in diameter estimates being less than 1 cm in all cases for both object sizes. Interestingly, there is a steady improvement in reconstruction of object diameter with frequency (for both the real and imaginary parts) for the

smaller object-a trend which does not manifest itself clearly with the larger target. Further, it does not appear that the ability to accurately capture the object diameter is significantly different in either the single or multitarget cases. Recovery of the center of the object, however, shows a clear improvement when only one object is imaged at a time. In single-object cases, the positioning error is generally 1 mm or less for both object sizes at all three frequencies. In contrast, the errors in object position for the multitarget cases were generally

MEANEY et al.: MICROWAVE IMAGING FOR TISSUE ASSESSMENT INITIAL EVALUATION IN MULTITARGET TISSUE-EQUIVALENT PHANTOMS 889

300 500 700

TABLE V AVERAGE DIAMERERS AND POSITION ERRORS FOR THE TWO FATBONE

EQUIVALENT CYLINDERS WITH THE ACTUAL DIAMERERS BEING (a) 4.28 cm (LEFT OBJECT) AND (h) 2.54 cm (RIGHT OBJECT),

RESPECTIVELY, DURING MULTITARGET IMAGING EXPERIMENTS. AVERAGES WERE COMPILED FOR THREE TEST CASES WHERE THE TWO

OBJECTS WERE SEPARATED BY 0.4, 1.7, and 4.2 cm, RESPECTIVELY

2.96 0.75 1 3.14 0.828 2.94 0.830

300 500 700

between 4 and 10 mm with roughly 90% of these errors occurring along the common axis of the two objects. Thus, the accuracy of the object position is clearly affected by the presence of multiple heterogeneities.

3.27 0.857 2.81 0.973 2.38 0.973

V. CONCLUSION

A prototype microwave imaging system has been evaluated for its ability to reconstruct images of the material property distributions for a range of material contrasts over a band of relevant frequencies. Comparison of results at different frequencies demonstrated the capability of reconstructing rel- atively good images over the full 300-700-MHz frequency range with certain improvements occurring as the frequency is increased. However, not all aspects of imaging performance are found to improve monotonically with increasing frequency which suggests that multispectral imaging capability could prove to be a very valuable asset. These observations are based on quantitative analysis of the images produced in terms of material property composition, target size and location. In the more challenging multitarget experiments that were conducted, objects with a range of electrical properties were imaged. The results of these studies showed a clear advantage of the higher-frequency excitations in terms of simultaneous recovery of both the real and imaginary components of the electrical property distribution. In this case, both the dielectric constants

and conductivities were reconstructed quite well at 700 MHz, whereas, similar tests at 300 MHz were only able to recover the conductivities of the objects, although often more accurately than that achieved at 700 MHz. Electrical composition analysis showed that background and object property valuer, recovered simultaneously for both the real and imaginary components of the kz distribution were in error by only 10-20% in most cases. Object size and location analysis showed that both estimated target diameters and center positions were accurate to better than 1 cm in all cases with errors as small as 2-3 mm or less occurring in many circumstances.

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[ I ] L. E. Larsen and J. H. Jacobi, Medical Applications c f f icrowave Imaging. Piscataway, NJ: IEEE Press, 1986, pp. 118-137.

121 A. W. Guy, “Analyzes of electromagnetic fields induced in biological tissues by thermographic studies on equivalent phantom models,” IEEE Trans. Microwave Theory Tech., vol. MTT-19, no. 2, 1971.

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[4] H. P. Schwan and K. Li, “Capacity and conductivity of body tissues at ultrahigh frequencies,” in Proc. IRE, 1953, vol. 41, pp. 1735-1740.

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[6] E. C. Burdette, P. G. Friedrich, R. L. Seaman, and L. E Larsen, “In situ permitivity of canine brain: Regional variations and post-mortem changes,” IEEE Trans. Microwave Theory Tech., vol FdTT-34, pp. 38-50, 1986.

[7] M. J. Moskowitz, T. P. Ryan, K. D. Paulscn, and S. E. Mitchell, “Clinical implementation of electrical impedance tomography with hyperthermia,” Int. J. Hyperthernz., vol. 11, pp. 141-149, 1995.

[8] L. Jofre, M. S. Hawley, A. Broquetas, E. de 10s Reyes, M. Ferrando, and A. R. Elias-Fuste, “Medical imaging with a microwave tomographic scanner,” IEEE Trans. Biomed. Eng., vol. 37, pp. 303-312, 1990.

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[IO] J. J. Mallorqui, A. Broquetas, L. Jofre, and A. Cardama, “Noninvasive active microwave thermometry with a microwave tomographic scanner in hyperthermia treatments,” ACES Special Issue on Bioelec-tromagnetic Computations, A. H. J. Fleming and K. H. Joyner, Eds., ACES J . , vol. 7, pp. 121-127, 1992.

[ I11 J. M. Rius, C. Pichot, L. Jofre, J. C. Bolomey, N. Joachimowicz, A. Broquetas, and M. Ferrando, “Planar and cylindrical active microwave temperature imaging: Numerical simulations,” IEEE Trans. Med. Zmag.. vol. 11, pp. 457-469, 1992.

[I21 P. M. Meaney, K. D. Paulsen, and T. P. Ryan, “Two-dimensional hybrid element image reconstruction for TM illumination,” IEEE Trans. Antennas Propagat., vol. 43, pp. 239-247, 1995.

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[14] T. C. Guo and W. W. Guo, “Three-dimensional dielectric imaging by inverse scattering with resolution unlimited by wavelength,” in Proc. Con$ Elect. Insul. and Dielectric Phenomena, 1989, pp. 65-74.

[15] N. Joachimowicz, C. Pichot, and J. R. Hugonin, “Inverse scattering: An iterative numerical method for electromagnetic imaging,” .TEEE Trans. Antennas Propagat., vol. 39, pp. 1742-52, 1991.

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[I91 P. M. Meaney, K. D. Paulsen, A. Hartov, and R. K. Crane, “An active microwave imaging system for reconstruction of Z D electrical property distributions,” fEEE Trans. Biomed. Eng., vol. 42, pp. 1017-1026, 1995.

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Alexander Hartov was born on August 5, 1957 in Fontainebleau, France, and moved to the United States in 1979. He received the B.S.E.E degree from Northeastern University, Boston, MA, in 1984, and the M.Sc. and Ph.D. degrees in engineering Sciences from Dartmouth College, Hanover, NH, in 1988 and 1990, respectively.

In addition to his appointments as Research Assistant Professor of Surgery at Dartmouth Medical School and Adjunct Professor of Engineering at the Thayer School of Engineering, Dartmouth College, he is a consultant on research projects for clients in industrial and biomedical application.

Paul M. Meaney (M’91) received the A.B. de- gree in electrical engineering and computer science from Brown University, Providence, RI, in 1982, the M.S. degree in electrical engineering from the University of Massachusetts, Amherst, in 1985, and the Ph.D. degree in engineering from Dartmouth College, Hanover, NH, in 1995.

After working for Millitech Corporation and Al- pha Industries from 1985 to 1991, designing mil- limeter wave components and subsystems, he be- came a Research Assistant at the Thaver School

of Engineering at Dartmouth College, where he is a Postdoctoral Research Associate. His current research interest include antenna theory and inverse scattering problems, especially those related to the imaging of electrical property distributions in biological tissue.

Keith D. Paulsen (S’SM’86) received the B.S. degree in biomedical engineering from Duke Uni- versity, Durham, NC, in 1981 and the M.S. and Ph.D. degrees in engineering from Dartmouth Col- lege, Hanover, NH, in 1984 and 1986, respectively.

He is an Associate Professor in the Thayer School of Engineering at Dartmouth College. His current research interest include numerical electromagnetics for application in biomedical problems and remote sensing.

Robert K. Crane (SM’71-F’SO) received the B.S., M.S., and Ph.D. degrees from the Worchester Poly- technic Institute, Worchester, MA, all in electrical engineering.

He is Professor of Meteorology and Professor of Electrical Engineering at the University of Ok- lahoma, Norman. Prior to joining the faculty at the University of Oklahoma, he spent ten years as Research Professor of Engineering, Thayer School of Engineering, Dartmouth College. Prior to that he was Deputy Division Manager and Division Senior

Scientist at Environmental Research & Technology, Inc. (ERT) and prior to ERT, he was a staff member of Massachusetts Institute of Technology Lincoln Laboratory. He has spent his research career conducting studies in electromagnetic wave propagation through the atmosphere and in remote- sensing of precipitation via radio and radar techniques.

Dr. Crane is a member of the American Meteorological Society and the American Geophysical Union. He has been active in the work of Commission F of the International Union of Radio Science (URSI) and in the United States National Committee for URSI. He has also been active in the work of Study Group 5 of the International Radio Consultative Committee (CCIR).