COMPENSATED RADIOLUCENT ELECTRODE ARRAY AND METHOD FOR COMBINED EIT AND MAMMOGRAPHY

STATEMENT OF GOVERNMENT INTEREST The Government has certain rights to this invention.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority from U.S. Provisional Patent Applications 60/978,157 filed October 8, 2007, and 60/919,829 and 60/919,821 filed March 23, 2007, all three of which are incorporated here by reference.

FIELD AND BACKGROUND OF THE INVENTION

The present invention relates generally to medical imaging techniques and in particular to a method and apparatus for taking EIT (Electrical Impedance Tomography) and x-ray mammography data simultaneously and in registry with each other, for enhancing the value of images created by both types of data.

X-ray mammography is currently the gold standard imaging technique for breast cancer screening in clinical practice. The sensitivity of mammography has been reported to be 74%, however, with specificity 60%, which means a 26% false- negative rate and 40% false-positive rate. About 70-80% of women who undergo biopsy are found to have benign lesions. Mammograms also require cumulative x- ray exposure and they are difficult to interpret, especially with the dense breast tissue prominent in younger women. Accordingly, a way of enhancing the validity and true meaning of a mammogram would be very useful. Increasing evidence has been found showing significant differences in specific impedance between malignant breast tumors and normal tissues. Electrical impedance tomography or EIT, a non-invasive technique used to image the

electrical conductivity and permittivity within a body from measurements taken on the body's surface, might therefore be used as an indicator for breast cancer. Surowiec et al. (1988) studied the dielectric properties of breast tissue (Surowiec A J, Stuchly S S, Barr J R and Swamp A 1988 "Dielectric properties of breast carcinoma and the surrounding tissues" IEEE Trans. Biomed. Eng. 35 257-63).

Also see Soni et al (Soni N K, H. Dehghani, A. Hartov, K. D. Paulsen 2003 "A novel data calibration scheme for electrical impedance tomography" Physiol. Meas. 24 421 -35). Jossinet (1996) measured the impedance of breast tissues (Jossinet J 1996 "Variability of impedivity in normal and pathological breast tissue" Med. Biol. Eng. Comput. 34 346-50) and DaSilva et al (2000) used the impedance measurements to distinguish carcinomas from normal and benign tumors (DaSilva J E, de Sa J P and Jossinet J 2000 "Classification of breast tissue by electrical impedance spectroscopy" Med. Biol. Eng. Comput. 38 26-30). These studies have shown that EIT is a promising modality to image breasts for malignancies. Recently, reports have shown that the EIT technique can improve sensitivity and specificity when used as an adjunct to mammography.

Because of the low spatial resolution of EIT, combining it with other modalities may enhance its utility and since x-ray mammography is the standard screening technique for breast cancer detection, it is the first choice for that other modality. To combine these two techniques, one could take mammograms and EIT images separately and use a mapping-based method to co-register them. However, changes in the breast shape between the x-ray and EIT exams would make the registration mapping complex and difficult. An alternative is to use the same geometry in EIT and mammogram. Not only would it be easier to analyze the EIT images, but also the EIT images could augment the two-dimensional x-ray mammograms by providing three-dimensional images of the tissue being imaged. This could provide additional information on the location of the tumor. For this mammography geometry, EIT distinguishability has been studied experimentally by Kao et al (2003) (Kao T-J, Newell J C, Saulnier G J and Isaacson D 2003

"Distinguishability of inhomogeneities using planar electrode arrays and different patterns of applied excitation" Physiol. Meas. 24 403-1 1 ). A simplified reconstruction algorithm has been built and successfully tested in a saline-filled test tank by Choi et al (2004) (Choi M H, Kao T-J, Isaacson D, Saulnier G J and Newell J C 2007 "A reconstruction algorithm for breast cancer imaging with electrical impedance tomography in mammography geometry" IEEE Trans. Biomed. Eng. 54 700-10).

In order to take the x-ray and EIT measurements at the same time, the major task is to build electrodes that can allow the x-rays to pass through. As will be disclosed in detail below, one feature of the present invention is a radiolucent electrode array that can be attached to the compression plates of a mammography unit, enabling EIT and mammography data to be taken simultaneously and to co- register the images of these two modalities automatically.

Radiolucent electrodes have been disclosed by Steinberg et al. in 2004 (Published patent application US2004/0077944). Also see U.S. Patent 6,157,697 to Mertelmeier et al.

Researchers at Rensselaer Polytechnic Institute (RPI), including some of the inventors of the subject application, have developed an effective technique for EIT imaging referred to as Adaptive Current Tomography or ACT. There have been various ACT versions that can be used with the present invention, with the latest being the ACT4 technique. This technique is disclosed in U.S. Patents 5,284,142 to Goble et al., 5,544,662 to Saulnier et al. and 7,1 16,157 to Ross et al., as well as US published patent application US 2008/0001608 to Saulnier et al., all of which are incorporated here by reference for their teaching of the technique of applying voltage or current waveform patterns at multiple frequencies to multiple electrodes in an array that are in electrical contact with the surface of a volume, for measuring the resulting currents and/or voltages, and for using these measurements to calculate electrical impedance at different locations in the volume (voxels) which, in turn, is used to create a three dimensional impedance image of the volume.

A need remains for an effective radiolucent EIT electrode array, however, as well as better ways of operating the array and of distinguishing between normal and tumor tissue.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide an apparatus and method for use with an x-ray arrangement having a pair of spaced apart breast compression plates for compressing the breast of a subject there between, the subject's breast defining a volume between the compression plates containing a plurality of voxels lying in a plurality of layers, x-ray emission means on one side of the plates for directing x-rays through the plates, and x-ray imaging means on an opposite side of the plates for receiving the x-rays and for creating an x-ray image from the x-rays, the apparatus comprising a pair of facing arrays of electrodes on respective inner surfaces of the compression plates for making direct electrical contact with opposite surfaces of a subject's breast being compressed between the plates, and an adaptive current tomography device connected to the electrodes of each array for applying a plurality of current or voltage waveform patterns to the electrodes and for measuring resulting current or voltage waveform patterns from the electrodes for calculating an impedance of each voxel in at least one layer of the volume, and for creating an electrical impedance tomography image of the layer that is substantially simultaneous with and in spatial co-registry with the x-ray image.

Another object of the invention is to provide each electrode of each array to be a strip of aluminum layer of a first thickness having a contact area and a connection area extending toward an edge of one array, and a precious metal (e.g. gold) layer of a second thickness that is less than the first thickness, deposited on the aluminum layer only in the contact area for making electrical contact with a subject's breast.

A further object of the invention is to provide each array to be a rectilinear array of rows and columns of rectangular contact areas, each array including a

copper layer on the aluminum layer at an end of each aluminum layer that is spaced from and opposite the contact area, and a copper connecting lead extending from each copper layer for connection to the adaptive current tomography device.

The each column of each array is made up of a plurality of the strips of aluminum layer deposited on one insulating polymer substrate to form an electrode column, and a plurality of these electrode columns are stacked one above the other with the contact areas of one electrode column being spaced from the contact areas of a next electrode column in the stack to form rows of electrodes in each array, each array including an insulating layer of polymer with a conductive ground layer between each electrode column.

According to another object of the invention, each array comprises an insulating polymer, e.g. polyimide, substrate or film, on which a metal adhesion layer, e.g. titanium, is first deposited before each strip of aluminum layer is deposited on the adhesion layer, the adhesion, aluminum, precious metal and copper layers each being E-beam deposited.

The apparatus of the invention accumulates the connecting leads for each array into one or more cables wherein each cable and each array has an impedance, the apparatus including means for simply or complex modeling the array and cable impedance as a loss impedance that is parallel only, or partly parallel and partly in series to a load impedance to be measured from the contact areas by the adaptive current tomography device.

According to another object of the invention, the adaptive current tomography device includes tissue identification means for calculating a complex admittivity for each voxel in the at least one layer, at a plurality of frequencies, each complex admittivity including real and imaginary parts, the tissue identification means plotting the real and imaginary parts against each other for each frequency to form an electrical impedance spectrum (EIS) for each voxel with a curved plot being indicative of normal tissue and a straight plot being indicative of tumor tissue.

The tissue identification means can also transform each plot into a linear

correlation measure (LCM) of the relative curvature and linearity of each plot and creates an image for the linear correlation measure for each voxel, the image graphically distinguishing between curved plots that are indicative of normal tissue and may be darker in the image, and straight plots that are indicative of tumor tissue and may be lighter in the image.

The apparatus of the invention, in its adaptive current tomography device, may include scaling means for applying linearly independent patterns of voltage or current to the electrodes, the scaling means determining if an optimal set of patterns was applied to the medium, the scaling means using a mathematical transformation to compute the voltages that would have been obtained had the optimal set of current patterns been actually applied, for each measured pattern, computing a characteristic resistance of the medium for that pattern, based on the measured voltages, scaling the measured voltages such that a characteristic resistance of the volume matches exactly those theoretically obtained using an ave-gap model, then perform an image reconstruction using the scaled voltage patterns.

The various features of novelty that characterize the invention are pointed out with particularity in the claims annexed to and forming a part of this disclosure. For a better understanding of the invention, its operating advantages and specific objects attained by its uses, reference is made to the accompanying drawings and descriptive matter in which a preferred embodiment of the invention is illustrated.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings:

Fig. 1 is a schematic view of a dual mode EIT plus mammography arrangement of the present invention;

Fig. 2 is a graph plotting resistivity versus x-ray mass attenuation for various possible electrode materials;

Fig. 3 is a top plan view of a six electrode columns manufactured according to the present invention and used to create a flat, 6 x 6 electrode array according to

the present invention;

Fig. 4 is a side elevational view (not to scale) showing three stacked electrode columns of Fig. 3, forming one half of a 6 x 6 electrode array of the invention; Fig. 5 is an exploded top plan view of the 6 x 6 electrode array using six of the electrode columns of Fig. 3;

Fig. 6 is a schematic diagram of a simple compensation scheme of the present invention;

Fig. 7 is a schematic diagram of a complex compensation scheme of the present invention;

Fig. 8 is a composite image showing EIS plots for a biopsy patient's breast using EIT of the present invention on the left, and a spatially co-registered, simultaneous mammogram x-ray image of the same breast on the right, indicating the increased linearity of the EIS plots for areas containing invasive ductal carcinoma (as confirmed by biopsy) and more curved EIS plots for the surrounding normal tissue;

Fig. 9 is a composite image showing on the right, LCM (Linear Correlation Measure) gray scale values obtained by the corresponding EIS plots of voxels for a biopsy patient's breast, and a spatially co-registered, simultaneous mammogram x- ray image of the same breast on the left, indicating the whiter areas containing invasive ductal carcinoma and darker areas of surrounding normal tissue; and

Fig. 10 is a schematic illustration of the apparatus of Fig. 1 for making spatially co-registered EIT and x-ray images on the left, with a pattern of voxels for which EIS and LCM values are calculated based on measured EIT impedance values on the right.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring now to the drawings, in which like reference numerals are used to refer to the same or similar elements, Fig. 1 shows part of an apparatus for use with

an x-ray arrangement having a pair of spaced apart breast compression plates for compressing the breast of a subject there between, the subject's breast defining a volume illustrated also in Fig. 10, between the compression plates containing a plurality of voxels lying in a plurality of layers, x-ray emission means on one side to the plates for directing x-rays through the plates, and x-ray imaging means on an opposite side of the plates for receiving the x-rays and for creating an x-ray image from the x-rays.

The apparatus has a pair of facing arrays of electrodes on respective inner surfaces of the compression plates for making direct electrical contact with opposite surfaces of a subject's breast being compressed between the plates, and an adaptive current tomography device connected to the electrodes of each array for applying a plurality of current or voltage waveform patterns to the electrodes and for measuring resulting current or voltage waveform patterns from the electrodes for calculating an impedance of each voxel in at least one layer of the volume, and for creating an electrical impedance tomography image of the layer that is substantially simultaneous with and in spatial co-registry with the x-ray image.

Each electrode of each array, shown also in Fig. 3, 4 and 5, advantageously comprises a strip of aluminum layer of a first thickness having a contact area and a connection area extending toward an edge of its array, and a precious metal layer of a second thickness that is less that the first thickness, deposited on the aluminum layer only in the contact area for making electrical contact with a subject's breast.

Electrode modeling, tissue identification and scaling means and methods are also disclosed.

Mammography geometry:

In x-ray mammography, a breast 12 of a subject 10 is compressed between two plates 14 and 16, an x-ray emission device 20 sends a beam of x-rays 22 through the plates and the breast tissue, and an x-ray image of the breast is made in an imaging section 24 of the device in a known fashion and as shown in Fig 1.

In order to image the electrical impedance distribution in the volume of the breast 12, plural electrodes in upper and lower rectilinear electrode arrays 30 are provided and placed so that they are in physical contact with upper and lower flattened surfaces of the breast. To this end the arrays 30 are mounted to the lower surface of upper plate 14 and to the upper surface of lower plate 16. The electrode arrays must allow x-rays to pass through without significant attenuation, avoiding the need for an increase in radiological dose, or an artifact in the x-ray image. If a metal layer were to attenuate the x-ray to such an extent as to require an increase in the source power, this would not necessarily translate into an increased x-ray exposure to the patient, since half would be absorbed or attenuated in the upper metal layer, but image artifacts would likely remain.

Fabrication of Radiolucent Electrodes:

In selecting the materials for the electrode arrays, the inventors investigated the radiolucency and the resistivity of several metals. Fig. 2 shows the resistivity versus the x-ray mass attenuation coefficient with a photon energy of 250 keV for several candidate metals. The plot shows that aluminum has both a low radiodensity, i.e. has the lowest attenuation coefficient, and a low resistance.

However, aluminum oxide (AI ₂ O ₃ ), that would form on an aluminum electrode, has very poor conductivity. Consequently, to protect the surface from oxidation, each electrode contact area that is meant to contact the subject's skin, is covered by a thin (e.g. 20 to 80 nm) layer of gold to minimize the adverse effect on radiolucency and eliminate aluminum oxide formation. Although a thin gold protective layer is preferred, other precious, lower corrosion metals such as platinum or silver may be used instead.

Referring to Fig. 3, showing the top of one electrode column of strips of six electrodes for the array, and Fig. 4, showing the side of three such columns stacked on each other for creating one half of the array 30, after an initial deposition of strips of about 10 to 20nm thickness of titanium on the surface of a first Kapton (a

registered DuPont trademark) polyimide film 50 of 2 mil (50μμ) thickness using a known E-beam evaporation technique, corresponding strips of aluminum layers 52 of about 300 nm thickness are deposited using the same technique. The polyimide film is an electrical insulator with a high x-ray radiolucency and the titanium layer was used to increase the adhesion between the aluminum and the polyimide film. The active contact areas 54 near one end of each aluminum strip 52 then receives an E-beam deposited layer of gold of about 50nm and an opposite end of each aluminum strip at 56 each receives a thick copper layer that each extends into a connecting lead at 58 for connection to the ACT4 apparatus 60. To obtain the desired radiolucency for the electrode array 30, a very thin metal layer is used and is produced using the E-beam evaporation in the Microfabrication Clean Room (MCR) at RPI. The polyimide film is placed in a deposition chamber and once a vacuum in the chamber reaches approximately 5 x 10-7 Torr (53 μPa), a metallic target is heated to high temperature by the electron beam. This process leads to the evaporation of the metal and its deposition onto the film. The evaporation material is contained in a water cooled copper hearth eliminating problems related to crucible contamination. Isolated crystal rate sensors ensure process accuracy and reliability. A mask is placed over the film at the top of the deposition chamber to produce the desired metal patterns to form the electrode array. Several crucibles are available to enable multiple layers of different metals to be deposited sequentially on the film to create the array 30.

To produce the full array 30 of 6 x 6 electrodes of Fig. 5, three strip sets or electrode columns of Fig. 3 (each with 6 electrodes in the column) were stacked much like a multilayer printed circuit board and shown in Fig. 4. Each layer in this stack has a deposited aluminum ground layer 62 of about 200 nm in a pattern on a 2 mil polyimide separation layer 64. An example of a single layer, consisting of the 300 nm thick aluminum strips 52 which are extended with the thicker copper strips. A thick deposition of copper is used to make the narrow electrical leads from the electrode which have a low resistance. The gold on top of the aluminum in the

region that will form the electrode surface or actual contact area, reduces the contact impedance between skin and electrode. A further separation layer 64 of polyimide with an aluminum ground layer 62 is provide between each further six electrode column as shown in Fig. 4, to reduce noise and cross-talk between the electrodes. The thickness T of the stack of three electrode strips is about 0.5 mm but Fig. 4 is not to scale so that in practice all the contact surfaces 54 are effectively at the same plane for uniformly contacting the skin of the breast.

Two complete 6 x 6 electrode arrays 30 of 36 electrodes each in the mammography geometry of Figs. 1 and 5 is used, one at the top and one at the bottom, each facing the breast, with two associated ribbon cables 66 for each array. Each ribbon cable is connected to a bundle of coaxial cables with driven shields connected to channels of the EIT instrument 60 via a 75-circuit coaxial connector and an SMB connector.

Results:

The radiolucent electrode arrays were tested in the Department of Radiology at the Massachusetts General Hospital (MGH) with a tomosynthesis digital mammography machine. In the mammography images only the copper lead areas 58 were slightly visible while the electrode areas 54 were not visible at all. X-ray exposure time was not increased to obtain each mammogram. To test durability, adhesive tape was applied to the electrodes and peeled off slowly. The electrode array did not peel off from the polyimide film. In patient studies it was found that the electrode arrays can be used for approximately 5 to 10 studies before the electrode surface starts to wear away. The measured resistance of each electrode is less than 2 Ohms and the capacitance to ground from each electrode is between 300 pF and 550 pF.

Cable and array compensation:

The results show that the radiolucent electrode arrays present an electrical

impedance characterized by a significant series resistance and a large shunt capacitance. What may be even more critical is that this resistance and capacitance varies from electrode to electrode within the array, meaning that it must be accounted for if the impedance seen by the electrode is to be measured accurately.

The invention provided two approaches to modeling and compensating for these electrical characteristics of the arrays. In each case, each cable and electrode is characterized as a collection of one or more impedance values and these values are used to compute the voltage and current at the electrode from those measured at the instrument end of the cable.

Simple model:

In the simple model, the complete cable and electrode for each channel is characterized as the single complex impedance that is measured by the EIT instrument 60 when nothing is attached to the electrode. This measured impedance is then assumed to be in parallel with the load impedance applied to the electrode. This model is shown in Fig. 6, where the excitation source for the electrode drives the cable and electrode impedance, denoted as Zcable&array, in parallel with the unknown load resistance, Zload. The values of Zcable&array measured for the radiolucent electrode arrays are primarily capacitive.

Complex model:

A more accurate approach is to model both the cable and electrode as a series and shunt impedance as shown in Fig. 7. The individual impedances in this model are measured through a series of open- and short-circuit measurements.

The impedances for the cable, ZparC and ZserC, are determined by disconnecting the electrode array from the end of the cables and measuring the impedance seen by the source with the electrode array end open-circuited (ZparC) and short- circuited (ZparC in parallel with ZserC). Using the values for the cable impedances

along with open- and short-circuit impedances with the electrode array attached, the electrode array impedances, ZparA and ZserA, can be determined. The EIT apparatus 60 of the invention is modified to make it easy to short all electrodes to ground to facilitate easy measurement of the short-circuit impedances. Four complex impedance values are used directly in computing the voltage and current values at the load from those measured at the source. ZparC, however, for 2 m, shield-driven, coaxial cables is well modeled as a capacitor of approximately 7 pF while ZserC is well modeled as a small resistance (<1 Ohm) in series with an inductance of approximately 1 μH. At high frequencies, this series inductance has a significant impact on the measured impedance. The series and parallel impedances, ZserA and ZparA, for the electrode array were between 0.6 and 1.8 Ohms and between 280 and 570 pF across the 36 electrodes.

Measurement results: Graphs of the measured impedances when a 750 Ohm resistor was placed between three different pairs of electrodes on the radiolucent electrode array were plotted and the result was a nearly constant and linear value for both magnitude and angle of impedance across a frequency range of 1 kHz to 1000 kHz.

The resistor was attached to a pair of platinized platinum-iridium-surfaced titanium probes which were manually held in contact with the desired pair of electrodes for the measurements. The ACT4 system, without the lead cables, has an automated calibration system which calibrates all channels of the instrument to a common standard, meaning that without the variations introduced by the cables and electrodes, the same impedance should be measured when the resistor is placed between any pair of instrument channels. The plot of impedance magnitude in

Ohms showed the magnitude of the measured resistance as a function of frequency for each of the three channel pairs. Results were provided without any compensation for the cables/array, for compensation by the simple model and for compensation by the more complex model. Without any compensation, the

apparent magnitude of the impedance drops at high frequencies due to the large shunt capacitance within the electrode array. Furthermore, the variation between channel pairs is high due to the variation in this shunt capacitance from electrode to electrode. Using the simple model substantially improves the performance by reducing both the variation with frequency and the variation between channel pairs. However, there is still some loss in performance at high frequencies. The plot of impedance angle in degrees showed the measured angles for the 750 Ohm resistor. Without any compensation, the angle deviates greatly from the actual value of zero, while both compensation techniques bring the angles near zero. Once again, the more complex approach was better at high frequencies.

The radiolucent electrode array of the invention has been built and tested successfully. The electrical properties of the array are acceptable and can be compensated for after taking measurements with open- and short-circuited arrays. The invention has been applied to the ACT4 EIT system to perform regional impedance spectroscopy on breasts simultaneously and in co-register with mammograms. The system has been used to study breast cancer patients at Massachusetts General Hospital and the study involving a small number of patients undergoing biopsies, is meant to establish the ability of EIT to detect cancer by directly comparing EIT results with biopsy results as will become evident in the following further disclosures.

Distinguishing breast tissue based on EIS:

Noninvasive electrical impedance EIT measurements at a number of temporal frequencies are also used according to the invention the detect cancer in the breast based on the discovery that reconstructed Electrical Impedance Spectra or EIS plots of a breast containing tumors differ markedly from those of normal breasts. It was observed that, unlike the customary arc-like appearance of EIS (electrical impedance spectra) plots in the range of 5 kHz to 300 kHz or more generally 1 to 1000 kHz, the EIS spectra of tumor tissue more closely approximates

a straight line.

The invention includes a nonlinear transformation of the electrical impedance spectrum that, when visualized, can detect and localize tumors in the breast. A measure of the linearity of the electrical impedance spectrum (EIS) for the detection and localization of cancer using multi-frequency reconstructions of the body's electrical properties is also disclosed. One particularly effective measure of linearity according to the invention is referred to here as the LCM or Linear Correlation Measure.

The method for the detection of tumor tissue in a breast according to the invention is summarized as follows:

1. Apply patterns of currents or voltages to the exterior of the breast on a set of electrodes, at a set of temporal frequencies in the range of 1 kHz to 1 MHz.

2. Make use of a mathematical image reconstruction method to generate a three-dimensional map of the breast's conductivity and permittivity at each of the surveyed frequencies.

3. For each point in space, plot the real and the imaginary parts of the electrical impedance spectrum on the x and y axes respectively, parameterized by frequency to obtain the EIS for each volume increment or voxel, and compute the following transformation of the spectrum, which is here called the LCM (Linear Correlation Measure):

LCM = 1 / (1 - (|<Y,Ym>| / ||Y|| ||Ym|D) where Ym is a vector made up of the electrical permittivities actually reconstructed at each of the temporal frequencies and Y is a vector of permittivities predicted by the model Y =aX + b, where a and b are scalars and X is a vector of the conductivities at each of the temporal frequencies probed. <A,B> and IIAII denote the inner product and norm, respectively. The constants a and b are estimated by means of a least-squares fit. The LCM tends to approach infinity as the plot of permittivity vs. conductivity tends to a straight line. In a number of patient studies, it was found that directly visualizing the LCM at each point in space using a

gray scale image where white indicates a very linear EIS corresponding to tumor tissue, and black indicates a very curved EIS corresponding the normal tissue, provided a new method of detecting the presence of cancer in the breast. Fig. 8 graphically illustrated how analyzing the electrical impedance spectroscopy (EIS) data from each voxel of the breast with co-registered EIT images and tomosynthesis images can be used to confirm the presence of tumor and normal tissue. The simultaneous EIT and mammogram x-ray image of Fig. 8, is of a subject with areas containing invasive ductal carcinoma in her breast, as confirmed by a biopsy. The increased linearity of the EIS plots is clearly visible on the left for the areas containing tumor tissue, and the more curved EIS plots are evident for the surrounding normal tissue areas. A grid of the locations for the ACT4 EIT electrodes is shown on the right, on the spatially correlated x-ray image and the tumor tissue is evident as lighter areas.

By calculating LCM values for the EIS of each voxel, and converting to a gray scale where more linear EIS is lighter (closer to white) for a straight line, and more curved EIS is darker (closer to black) be a very curved EIS, Fig. 9 illustrates the even more graphic correlation between normal tissue and darker areas, and tumor tissue and lighter areas, for a biopsy patient's breast, and a spatially co-registered, simultaneous mammogram x-ray image of the same breast on the left, indicating the whiter areas containing invasive ductal carcinoma and darker areas of surrounding normal tissue.

The EIS plot is generated and displayed for each of the reconstructed voxels or mesh elements at 5 or 6 frequencies, i.e. 5, 10, 30, 100 and 300 kHz, and 1000 kHz (1 MHz). The distribution of the admittivity spectra for normal breast tissue from patients was compared with those from patients with breast tumor, as verified by the pathology report of a biopsy sample. This analysis can thus distinguish breast cancer from normal tissue with the admittivity data.

The ACT4 60 of Fig. 5 provided a high-speed, high-precision, multi- frequency, multi-channel instrument that supports up to 72 channels and electrodes

(although 64 electrodes were used in some experiments of the inventors and 60 electrodes were used in others). Each electrode is driven by a high precision voltage source, and has a circuit for measuring the resulting electrode current. These circuits are digitally controlled to produce and measure signals at approximately 5k, 10k, 30k, 100k, 300k and 1 MHz. The magnitude and phase of each source are controlled independently. As noted above, the system was used to study breast cancer patients at Massachusetts General Hospital in conjunction with the tomosynthesis machine 20, 24 of Fig. 1 , and with verification by biopsy. The EIT images are co-registered with tomosynthesis images since the EIT electrodes are placed on the mammograph plates as shown in Fig. 1.

In reconstructing the images of Fig. 8 and 9 from patient data, the goal is to provide a practical, useful, real time reconstruction algorithm. To accommodate a possible additional ill-posedness introduced by the geometry and contact variability in the patient data, a reconstruction mesh is used with non-uniform voxel thickness, having thicker voxels at the center and thinner voxels near the electrode arrays.

Fig. 10 shows the simplified geometry and the mesh for this algorithm where the apparatus of Fig. 1 for making spatially co-registered EIT and x-ray images is on the left, and a pattern of voxels for which EIS and LCM values are calculated based on measured EIT impedance values is on the right. In addition, the reconstruction mesh extends beyond the region of interest between the electrode arrays. The margin is used to account for the unknown boundary condition due to the different sizes and shapes of the breasts studied. These extra mesh elements are not displayed or used for data analysis. The thickness of the breast is divided into 7 layers. The top and bottom layer simulated the skin tissue with 2 mm thickness that will not be shown in the display image. The thicknesses of the other 5 layers are arranged by the ratio as 1 : 2: 4: 2: 1. The reason for this ratio is that the further the voxel is from the electrodes, the less its admittivity affects the data. Therefore, the actual region of the breast in the reconstructed image is 65 mm by 54 mm by the breast thickness of about 40 mm.

For this experiment each electrode array contained a 5 x 6 rectangular array of 10mm x 10 mm electrodes with 1 mm gaps.

The EIT, ACT4 device for Fig. 10, utilizes 60 electrodes and can produce 3-D volume distributions of conductivity and permittivity images at a 2.5 frame/sec rate using frequencies between 5 kHz and 1 MHz, presented as a series of slices.

Patterns of voltages are applied to the breast using two parallel planar arrays of the radiolucent electrodes that are attached to the compression plates of an x-ray mammography unit as in Fig. 1. The 59 voltage patterns applied to produce each image are calculated from the eigenvectors of the voltage-to-current map matrix for a homogeneous admittivity field. The maximum applied voltage at any time is +/- 0.5 V, and a software protection system is used to report overloaded voltage sources. Further, the maximum applied voltage is reduced to +/- 0.25 V for current patterns of high spatial frequency when the applied voltage is at 100 kHz and above. To reduce the surface or contact impedance, the skin of the breast was prepared by application of PrepTrode® conductive electrode skin preparation, a commercial spray skin preparation. This fluid, which has a conductivity of about 1500 mS/m, is designed to facilitate application of electrodes to the skin.

The method of the invention is robust and has produced results that clearly distinguish malignant from benign lesions and normal tissues in the patients studied to date. There are 30 electrodes on the top array and 30 opposite electrodes on the bottom array. This allows the maximum number of independent complex (real and imaginary) measurements to equal 1 ,770 (30 x 59).

In this way at most 1 ,770 independent conductivities and permittivities values are recovered for each frequency from these electrode arrays. The region is modeled as a rectangular solid volume bounded by the planes that contain the arrays but which extends at least one electrode width beyond the actual array. The volume is divided into 1 ,568 rectangular boxes or voxels of varying size within which are reconstructed approximations to the electrical conductivity and permittivity. The

choices of region or volume, boundary conditions, number of terms used in approximating the electrical potentials, and the dimensions and positioning of the voxels within the region of interest are important to the ability to make useful reconstructions that are as accurate as the ACT4 measurements allow, that have as many degrees of freedom as the number of measurements and the conditioning of the inversion problem allows, and that have small artifacts due to currents and fields that extend outside the region of interest.

Reconstruction algorithms: The reconstruction problem for EIT is to determine the electrical conductivity and the electrical permittivity at a point within the body from measurements of the potential due to an applied electric field made at angular frequency on a portion of the surface of the body.

The electric field and magnetic field inside a body with selected conductivity, permittivity and permeability values and at an angular frequency, satisfy Maxwell's equations inside the body but below 1 MHz, a quasi-static approximation is used so that a voltage inside the body can be calculated and a complex admittivity found by measuring voltage on the surface of the body surface, and as a function of the applied current density on the surface. The region of interest within the breast is modeled as a rectangular prism as in Fig. 10, an approximation which is very useful because the potential due to applied current densities on the top and bottom planes can be explicitly given. This geometric approximation has been validated using saline-tank experiments with a specially constructed breast-shaped tank (see Choi et al (2004) cited above). The application of currents on the electrodes of the top plane induces a current density distribution at the top plane. The current density distribution at the bottom plane can also be calculated and assuming there is no current flowing through the side walls there are four other boundary conditions for the dimensions of the rectangular medium.

Using the Ave-gap electrode model (Cheng, K-S., D. Isaacson, J. C. Newell and D. G. Gisser "Electrode models for electric current computed tomography" IEEE Trans. Biomed. Eng. 36:918-924, 1989.) and a rectangular geometry, one can compute the potential due to applied current densities on the top and bottom electrode planes. This potential is then integrated over the spatial extent of each electrode and divided by the electrode's area to give the measured potential on this electrode.

The inverse problem is to determine the complex admittivity from measurements of the potential on the electrodes resulting from applied current patterns. In fact, due to the difficulty of implementing current sources which can properly manage the capacitive load of the radiolucent electrode arrays, voltages are applied and measurements of both voltages and currents are taken on the electrodes. In the reconstruction, the voltages that would have resulted from application of a given set of current patterns can be synthesized. In the solution of the inverse problem, the canonical set of current patterns is used for the geometry used here (Kao, T-J, G.J. Saulnier, D. Isaacson and J. C. Newell "Distinguishability of lnhomogeneities Using Planar Electrode Arrays and Different Patterns of Applied Excitation" Physiol Meas. 24(2):403-412, 2003). The applied patterns correspond to the eigenvectors of the Neumann-to-Dirichlet or current-to-voltage map in the homogeneous case.

An algorithm was used to reconstruct an approximation to the complex admittivity within the body at each frequency and for each voxel so that the EIS plot could be made of each.

Analysis of patient data:

Figs. 8 and 9 graphically represent the effectiveness of the invention to distinguish between tumor tissue and normal tissue. They show the results of only one of a group of breast impedance distributions from a normal breast, and breasts with the pathologies of fibroadenoma (benign lesion), and invasive ductal

carcinomas. An analysis of their EIS plots provides a quantitative regional indication of malignancy.

To analyze the data, EIS admittivity loci were reconstructed from measurements made at 5 frequencies, (5, 10, 30, 100, 300 kHz), within each voxel. Fig. 8 shows one example of these EIS loci for voxels in the center (the central thickest layer in Fig. 10, right image) of the regions of interest. Each graph plots the angular frequency (ω) times the reconstructed permittivity (e) on the vertical axis vs. the reconstructed conductivities (σ) on the horizontal axis at each frequency. In this way each voxel contains a graph of permittivity vs. conductivity as a function of frequency with the same units, milliSiemens/meter, on both axes. It was noticed that voxels in locations corresponding to malignancies had impedance spectra that seem to approximate straight lines, whereas normal tissue had spectra that looked like arcs of a circle; benign lesions such as fibroadenoma had intermediate shapes.

The grid in Fig. 8 shows where the reconstructed voxels are located is superimposed over the tomosynthesis images. The EIS plots of each voxel were analyzed. The plots from two small regions of interest are displayed beside the x- ray image. The EIS plots of the normal regions at the top are all shown as arcs with good curvature. It was also found that the EIS plots of fibroadenoma regions resemble normal tissue. The plots of the invasive ductal carcinoma region, the bottom plots, resemble straight lines.

Particularly in the plots of Fig. 8, the plots in the normal region resemble arcs, with significant curvature arcs and the plots in the abnormal region are close to straight lines. Based on these qualitative observations, it was hypothesized that EIS graphs of malignant tissue should be highly correlated with straight lines. This hypothesis was tested by making a gray scale image for each patient of how correlated the EIS curve in each voxel is with a straight line. The measure of correlation is obtained by fitting the EIS curve to a line. This line is then used to predict the values of the scaled permittivities (vertical coordinates) denoted by the vector Y that correspond to the conductivities (horizontal coordinates). The

reconstructed permittivities are denoted by a vector Ym. This Linear Correlation Measure or LCM is defined as noted above.

An example of these measures in gray scale is shown in Fig. 9 on a gray scale of 0 to 700 for the voxels in the thickest voxel layer at the center of Fig. 10, right, for one of four patients. It is clear that these LCM images visually distinguish malignant lesions from non-malignant lesions and normal tissues. They also approximately localize the lesions within the low resolution of our electrode arrays and coarse meshes. These reconstructions and LCM images suggest that in this small set of patients the EIT reconstruction algorithms described above can distinguish between cancerous, normal, and benign tissue.

Pathology report, Grades, EIS spectra and LCM value:

Following is the reports for four subjects designated 1 -R, 2-R, 3-L and 4-L.

1 -R

Screening patient, normal breast, BIRADS: Category 1 , No biopsy report All EIS plots have good curvature. LCM < 137 for all regions. Minimum value of LCM:23. Maximum value of LCM: 137.

2-R

Hyalinized Fibroadenoma, no evidence of malignancy. Most EIS Plots have good curvature. LCM < 70 for the tumor region. Minimum value of LCM:18. Maximum value of LCM: 122.

3-L

Invasive ductal carcinoma, Ductal carcinoma in-situ. A few cylindrical to irregular tan-yellow soft tissue cores ranging from 0.3 to 1.2 cm in length and averaging 0.1 cm in diameter. Grade: 3/3 - EIS plots on bottom right corner are abnormal. Others have good curvature. LCM > 300 for the tumor region. Minimum

value of LCM:42. Maximum value of LCM: 905.

4-L

Invasive ductal carcinoma, (Proliferation is worrisome) Ductal carcinoma in- situ Atypical ductal hyperplasia. Tumor size: 1.1 x 0.9 x 0.7 cm and two satellite nodules, 0.14 cm and < 0.1 cm. Grade:3/3 - Most EIS plots are close to a straight line. LCM > 300 for most plots. Minimum value of LCM: 4. Maximum value of LCM: 1017.

The forgoing summarizes the pathology reports for the 4 breasts tested. The cancers are graded on a scale of 1 to 3: Grade 1 (Low Grade or Well Differentiated) where the cancer cells still look much like normal cells and are usually slow- growing, Grade 2 (Intermediate/Moderate Grade or Moderately Differentiated) where the cancer cells do not look like normal cells and are growing somewhat faster than normal cells, and Grade 3 (High Grade or Poorly Differentiated) where the cancer cells do not look at all like normal cells and are fast-growing.

The LCM parameter defined here has clearly identified the malignancies in these 4 patients. Using similar derived EIS parameters, such as the consistency of slopes between different frequencies and the distances from EIS plots to the predicted line, gives similar results.

Reducing boundary effects in static EIT images: A further feature of the invention reduces image artifacts due to modeling error and the layer structure of the tissue for three-dimensional electrical impedance tomography (EIT). In early clinical experiments, it was found to be difficult to ensure that all electrodes make sufficiently good contact with the breast. Quite often some subset of the electrodes experienced a relatively high impedance, perhaps due to local variation in the pressure applied to different portions of the breast under compression. If the ave-gap model is used, these high-impedance interfaces tend

to produce low-admittivity artifacts in the reconstructed images. The approach here is to use an automated criterion to detect poorly contacting electrodes, by considering the relative error of the voltages actually measured on these electrodes, as compared to the voltages that would have been expected given a homogeneous medium and the ave-gap model. Those electrodes that meet or exceed a given threshold for the relative error are excluded from the image reconstruction, where the exclusion is accomplished by replacing the measured data from these electrodes with data generated by the ave-gap model applied to a homogeneous medium. In order to detect electrodes making insufficiently good contact with the breast, one computes an error metric for each electrode as a function of a summation of the voltages on all the electrodes for a given current pattern, to identify electrodes that are making poor contact. The strategy is to ameliorate errors from poorly contacting electrodes by replacing measured data from these electrodes with values that would have been expected, given a homogeneous medium and the ave-gap model.

The set of electrodes for which the error metric is smaller than a predetermined threshold, e.g. 70%, was then used to create the EIT image, rather than all the electrodes. As noted above, in breast EIT, a number of electrodes are engaged with the exterior upper and lower surfaces of the breast and patterns of currents or voltages are applied to these electrodes, with the resulting voltages/currents being measured on these electrodes or, in some systems, on some subset of the electrodes). The electrodes are arranged in parallel plates as in Fig. 1 , above and below the breast and the ACT4 apparatus 60 of Fig. 5 is used to apply and read the voltage and/or current patterns.

The choice of current patterns used in the imaging procedure is important to obtain high-quality image reconstructions. Here an optimal set of current patterns was used for a somewhat idealized version of the parallel-plate mammography

geometry, based on the error metric. The invention thus uses current patterns that maximize average distinguishability, or, for the homogeneous rectangular medium of voxels as used here (Fig. 10, right) the optimal currents are the eigen-currents, where the voltages measured on the electrodes are just a linearly scaled version of the applied currents. In this imaging method, one computes the eigen-currents using an iterative procedure, assuming that the medium is homogeneous and that it has a specific shape. It is possible to also find the eigen-currents experimentally. The use of the optimal set of current patterns gives a particularly attractive way to conduct the measurements. Specifically, one arranges the current patterns in order of decreasing power, for a fixed input current, one will generally find the current patterns to be of increasing spatial frequency. For each eigen-current, one defines the characteristic resistance as the factor by which one must scale the input current pattern in order to obtain the measured voltage pattern.

Two of the co-inventors here (Kao and Isaacson) have described a method for reducing artifacts in a 2-D circular geometry, particularly for the case of a layered medium. By using a similar method here, the artifacts due to the layer structure of the tissue (especially the skin layer) can be largely eliminated and a linearized image reconstruction algorithm that assumes that the medium is homogeneous can be used, rather than needing to explicitly model a skin layer. This disclosure extends the method to three dimensions, for EIT imaging in a mammography geometry. In analyzing the clinical data, it has been observed that the effect of the skin is highly significant, as the limited-view 3-D image reconstruction problem is very ill-posed, with the consequence that reconstruction algorithms are very sensitive to noise and to modeling errors. The key to the efficacy of the process is the observation that different current patterns are affected in different ways by modeling errors. For example, it can be shown that higher spatial-frequency current patterns are considerably more affected by the presence of a high-impedance skin layer than those comprising lower spatial frequencies. In addition, the invention makes use of ave-gap model of electrical propagation in the body, which can be

computed in a very computationally efficient way, but the inventors have pioneered the use of the complete electrode model, which takes into account the interface between the medium and the electrodes considerably more accurately than the ave- gap model. The modeling error between the ave-gap model and the complete model differs as a function of the particular current pattern applied. It was experimentally found that many of the advantages of using the complete electrode model, which, in general, is computationally considerably more expensive than the ave-gap model, can be obtained by means of the use of the ave-gap model with the scaling method of the invention.

The scaling method of the invention comprises:

1. Affixing a set of electrodes to the exterior of a medium and apply patterns of currents/voltages. If there are L electrodes, then L- 1 linearly independent current/voltage patterns are applied. 2. If the optimal set of current patterns was not actually applied to the medium, use a mathematical transformation to compute the voltages that would have been obtained had the optimal set of current patterns been actually applied.

3. For each measured current pattern, compute the characteristic resistance of the medium for that pattern, based on the measured voltages. 4. Scale the measured voltages such that the medium's characteristic resistances match exactly those theoretically obtained using an ave-gap model.

5. Then perform an image reconstruction using the scaled voltage patterns.

The experimental setup is that of Fig. 10, left, but using a test tank as an analogy for the breast 12. The reconstruction mesh and thickness of each layer of the simulated mammography geometry test tank (Fig. 10, right) and two test targets in front of the electrodes, is as follows: the reconstruction mesh has the thickness of the five different layers - layer 1 (top) : 4 mm, layer 2 (next layer down) : 8 mm, Iayer3 (middle layer) : 16 mm, layer 4 (fourth layer down) : 8 mm, layer 5 (bottom

layer) : 4 mm.

As noted, the mesh layers are numbered from 1 at the top to 5 at the bottom. A 1 cm cubic copper target was placed about 5 mm in front of the electrode array, at the 3 o'clock position of the electrode array. Corresponding 3-D reconstructed images were improved by using the scaling vector and the dynamic range of the images was reduced because the artifact was reduced by the rescaling vector.

While specific embodiments of the invention have been shown and described in detail to illustrate the application of the principles of the invention, it will be understood that the invention may be embodied otherwise without departing from such principles.