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Linear Superposition Electrical Impedance Tomography Imaging With Multiple Electrical/Biopsy Probes Antoni Ivorra, Mohanad Shini∗ , and Boris Rubinsky

Abstract—In medical diagnostics, tissue is often examined with multiple discrete biopsies taken under ultrasound placement. In a previous theoretical study, we have suggested that the linear nature of the equations used in electrical impedance tomography (EIT) can be employed with the conventional practice of biopsy sampling to produce an image of the tissue between the biopsy samplings. Specifically, the biopsy probes can be used to record EIT-type electrical data during the discrete tissue sampling. The location of the discrete biopsy needle insertions available from the ultrasound placement of the probes can be combined with the electrical measurement data and used with linear superposition to produce a complete EIT image of the tissue between the sampled sites. In this study, we explore the concept experimentally using gel phantoms to simulate tissue and heterogeneities in the tissue. The experiments are performed in 2-D and 3-D configurations, and data are taken discretely, one at a time, through single electrical probe insertions. In the 2-D configuration, we were able to produce images of reasonable quality for heterogeneities with a diameter larger than 3 mm (conductivity ratio 1:5) and with relative conductivity differences above 50% (diameter 5 mm). Index Terms—Biopsy, electrical impedance tomography (EIT), minimally invasive medical imaging.

I. INTRODUCTION ISSUE biopsies are the “gold standard” of medical diagnostics for many pathologies. Biopsies are performed with a biopsy needle that is inserted into the body, usually under ultrasound imaging guidance, to remove tissue samples, which are then analyzed with a variety of histochemical tests, e.g., [1]. A drawback of the biopsy method for diagnostics is that the tissue is sampled only at the discrete location from which it is taken

T

Manuscript received June 10, 2008; revised October 23, 2008 and December 5, 2008. First published February 2, 2009; current version published May 22, 2009. This work was supported in part by the Israel Science Foundation under Grant 403/06 and in part by the U.S. National Institutes of Health (NIH) under Grant NIH RO1 RR018961. A. Ivorra and M. Shini have contributed equally to this work. Asterisk indicates corresponding author. A. Ivorra is with the Departments of Mechanical Engineering and Bioengineering, University of California at Berkeley, Berkeley, CA 94720 USA (e-mail: [email protected]). ∗ M. Shini is with the Center for Bioengineering in the Service of Humanity and Society, School of Engineering and Computer Science, Hebrew University of Jerusalem, Jerusalem 91904, Israel, and also with the University of California at Berkeley, Berkeley, CA 94720 USA (e-mail: [email protected]). B. Rubinsky is with the Departments of Mechanical Engineering and Bioengineering, University of California at Berkeley, Berkeley, CA 94720 USA, and also with the Center for Bioengineering in the Service of Humanity and Society, School of Engineering and Computer Science, Hebrew University of Jerusalem, Jerusalem 91904, Israel (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TBME.2009.2013821

and it does not provide information from the adjacent tissue. In order to produce diagnostic information on the entire tissue, biopsy needle samplings need to be taken from a large number of biopsy sites [2]–[7]. For instance, conventional biopsy sampling of the prostate guided by transrectal ultrasonography (TRUS) involves biopsies from 6 to 12 sampling sites. However, since needle biopsies still produce only discrete information on the location from which they are taken, in some cases it may be interesting to sample a much larger number of sites. In the case of the prostate, it has been shown that by increasing the number of sampled sites to about 100 tumors were identified in over 50% of the patients that had been inaccurately labeled negative by the more traditional method based on a lower number of biopsies [7]. These saturation biopsy techniques employ a grid placed over the peritoneum to sample multiple cores at 5 mm intervals under ultrasound guidance [6]. This has found use in the precise treatment of the prostate known as “male lumpectomy” [8]. Nevertheless, the use of single or multiple biopsies remains a discrete site sampling technique and, regardless of the number of sampling sites, malignancies can remain hidden between the sites. Furthermore, increasing the number of biopsies increases cost and the complexity of the procedure. Therefore, any procedure that is able to detect potential tumors between sampling sites would be of great interest. Recently, we have produced a theoretical study that suggested a possible solution to the inherent problems of discrete tissue sampling through the use of biopsy needle probes as electrodes for electrical impedance tomography (EIT) [9]. EIT produces an image of the spatial distribution of the electrical impedivity of an object from electrical transimpedance measurements made with an electrode array on its periphery [10]–[12]. Image reconstruction in EIT is an inverse problem in which the electrical impedance of a domain is determined from the solution of the electrical field equation with the boundary conditions specified by electrode measurements. In a typical procedure, electric current is injected and drained through a pair of electrodes, while the resulting potentials are measured at other electrodes. A variety of combinations of injecting and measuring electrodes from among the electrodes surrounding the targeted tissue or organ are used. An impedivity distribution in the targeted tissue is sought that provides the solution of the electrical field equation that best satisfies all the boundary conditions obtained from the electrode measurements. Increasing the number of electrodes and the number of current injection pair combinations as well as decreasing the distance between electrodes can improve the

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quality of the EIT image [13]. Further details on the technique can be found in a recent book [14]. In our previous study, it occurred to us that the linear nature of the mathematical problem solved in EIT can be used advantageously with the way in which taking discreet needle biopsies is practiced [9]. We suggested that the discrete biopsy needles could be also used, in addition to taking biopsy samples, to take electrical measurements of the EIT type. Due to the facts that the governing equations are linear and the information on the location of the electrode/biopsy probes is accurately known (by the use of ultrasound imaging and biopsy insertion templates), the entire electrical data from all the biopsies can be combined and used to produce an EIT image of the entire sampled tissue. Our previous study was theoretical and has demonstrated the feasibility of the concept through mathematical analysis. In this study, we explore the concept experimentally using gel phantoms to simulate tissue and heterogeneities in the tissue. The experiments are performed in 2-D and 3-D configurations, and data are taken discretely, one at a time, through single probe insertions. These data are then linearly combined in a conventional EIT reconstruction algorithm and the image compared with the phantom. II. MATERIALS AND METHODS A. Agar Gels Agar gel is commonly used by researchers in the EIT field to implement phantoms that mimic the conductive properties of living tissues [15]–[17]. Such phantoms are built by combining a variety of gel pieces with different electrical conductivities so that the macroscopic heterogeneity of living tissues can be emulated. The electrical conductivity for each piece is adjusted by varying the concentration of ionic salts in the solution from which the gel is prepared. Here, we produced simple phantoms in which one or more inclusions are embedded within a base gel. This sort of phantoms is useful to model solid tumors within a normal tissue. Due to morphological differences at microscopic scale, tumors exhibit different passive electrical properties from surrounding healthy tissues. These differences depend on the frequency at which impedance is measured and are manifested both in the magnitude and in the phase angle. This study is only focused on impedance magnitude changes at a specific frequency. Therefore, such changes can be modeled with regions of different dc conductivity, as is the case of the gels with ionic salts. The process to prepare conductive gels starts with a solution of NaCl. Then, 1.5 g of agar powder is added per 100 ml of solution, and the mixture is heated until boiling point for proper agar dissolution. Finally, the solution is cooled down to room temperature (25 ◦ C); jellification occurs at around 35 ◦ C. The conductivity (σ, expressed in millisiemens per centimeter) of the prepared gel follows a linear relationship with the concentration (C) of the NaCl solution [18] σ = AC + σ0 .

(1)

The agar gel employed here (reference A7002 from Sigma– Aldrich Company) has a residual conductivity of 0.3 mS/cm

when no salts are added. This residual conductivity is probably due to impurities within the agar powder. Conductivity of gel prepared from a 0.9% NaCl solution is 14.1 mS/cm. Therefore, in (1), the parameter σ0 is 0.3 mS/cm and the parameter A is 15.3 mS/(cm·%). For the base gel, we chose a 0.09% NaCl solution (σ = 1.7 mS/cm). A variety of other gels were prepared so that we had the following ratios of conductivities between the base gel and the inclusion (base gel:inclusion): 1:0.5, 1:2, 1:5, and 1:10. These gels were stored until each phantom was built. Ions can diffuse quite fast in and out of gels embedded within other gels or solutions, altering the original conductivity ratios [18], [19]. Because of this, we performed all our measurements within 20 min after the construction of the phantoms. The choices of the electrical properties of the gel inserts come from the following considerations. At low and intermediate frequencies (up to 100 kHz), most cancers cause a decrease in the impedance magnitude [20], [21]. This has been explained as due to an impaired tight packaging of cells [22]. In other sorts of cancers, an opposite effect has been observed [23] that has been attributed to an inflammatory response due to the loss of the ability of the tissue to seal [24]. In the case of the breast, significant differences between the impedance magnitude of normal tissues and that of tumors (either malignant or benign) have been found around the frequency employed here (50 kHz). For instance, Jossinet [25] reported differences between normal tissues (connective tissues and subcutaneous adipose tissues) and tumors (carcinomas and fibroadenomas) of up to 800% (lower conductivity for normal tissues) at 62 kHz. Differences in the case of the prostate seem to be less significant. Halter et al. [23] have reported impedance magnitude differences of up to 100% between normal tissues and tumors at frequencies around 50 kHz (in this case, the lower conductivity is for tumors). We have chosen for this study conductivity ratios between the base gel and the inclusion (base gel:inclusion—1:0.5, 1:2, 1:5, and 1:10) to be in the overall range of the reported data.

B. Impedance Measurements Two-electrode impedance measurements are prone to errors due to the electrode–electrolyte interface impedance. Such impedance appears at the interface between a metallic electrode and an electrolyte. When no dc currents are involved and the magnitude of ac currents is small, its electrical behavior can be roughly modeled by a capacitance (one for each electrode) in series with the impedance of interest, i.e., the electrode–electrolyte interface distorts the measurement as an additive error, particularly at low frequencies. A possible method to reduce its impact on the measurement is to enlarge the effective surface area of the electrodes; here, we sanded the stainless steel needles used as electrodes (gauge 21, outer diameter = 0.81 mm, model 305167 by Becton, Dickinson and Company, Corporation) so that their surface roughness was increased. At the frequency employed in all the following experiments, 50 kHz, such interface impedance was insignificant when compared to the impedance of interest

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IVORRA et al.: LINEAR SUPERPOSITION EIT IMAGING WITH MULTIPLE ELECTRICAL/BIOPSY PROBES

Fig. 1. (a) Schematic representation of the setup employed to perform 2-D experiments with gel phantoms. Two-electrode impedance measurements are performed at 50 kHz by a commercial impedance analyzer through stainless steel needles. A needle stays in the same position during the whole measurement procedure (reference electrode), whereas the other needle is inserted sequentially at different locations separated by 5 mm. An insertion template is on top of the phantom to facilitate positioning of the electrodes. (b) Top view of the insertion pattern; numbers indicate the order in which measurements are taken.

(contribution to measured values <0.5% of the measurement) [26, Ch. 2]. All impedance measurements reported here were performed with a commercial impedance analyzer (Precision Impedance Analyzer 4294 A by Agilent Technologies, Inc., Santa Clara, CA). For the excitation source, we selected a constant voltage amplitude of 100 mV. A single frequency of 50 kHz was analyzed. Magnitude and phase angle were recorded at this frequency but only magnitude was employed as input data for the EIT reconstruction algorithms; phase angle was only employed to detect aberrant data (phase angle from the measurement of the impedance of saline solutions, or saline gels, must be close to 0◦ for frequencies below 1 MHz, we rejected data when phase angle was below −1◦ ). In all the experiments, the induced current amplitudes ranged from 50 to 300 µA, which are common values in clinical EIT setups [27]. C. 2-D Configuration The setup employed for the 2-D experiments is depicted in Fig. 1. Phantoms consisted of a base gel, which filled a plastic petri dish (thickness = 13 mm), and a variety of heterogeneities shaped as gel cylinders of different diameters and conductivities that were embedded within the base gel. On top of the phantom,

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we placed a needle insertion template made of acrylic glass (thickness = 9 mm). A bare hypodermic needle was inserted through the template into the location noted as “reference electrode” in Fig. 1(b), and stayed there for the whole measurement procedure. Another needle (“probe electrode”) was inserted sequentially into all the other locations (separation between insertion points = 5 mm). Impedance was measured continuously between both needles. The whole measurement process took 4 min (the probe electrode was inserted into each location for 3 s approximately). Impedance data were recorded as a single file with 500 measurement points (approximately two samples per second) by the commercial impedance analyzer. That file was then downloaded to a PC and valid data segments were automatically identified by custom-programmed routines that detected insertions and extractions of the probe needle. Such detection was performed by comparing measured magnitude and phase angle to predefined thresholds (e.g., when impedance magnitude was larger than 100 kΩ, it was considered that the probe needle was out of the gel). For each location, a segment was identified. Of the approximately six valid measurements per location (3 s × 2 samples per second), only the one closest to midpoint of the segment was considered for EIT reconstruction. (We tried to do an average of the four samples closest to the midpoint but it did not produce any significant improvement.) Therefore, 64 measurements were extracted and employed by the EIT algorithms to reconstruct the conductivity map. D. 3-D Configuration The setup employed for the 3-D experiments is depicted in Fig. 2. In this case, the phantom was mounted on the base of the micropositioning system of a microscope (Model 3111700 by Edmund Scientific, Inc.) so that it was possible to control its relative position to the probe needle (anchored to the microscope chassis). The pattern of insertion points is shown in Fig. 2(b) and (c). The separation between insertion points was 10 mm. In the simulations performed in [9], resistances were “measured” between two point electrodes. However, because of the interface impedance issue mentioned earlier in Section II-B, here it was required that the electrodes had a minimum area: the needles were covered with Teflon tape down to the last 4 mm. Hence, the total electrode length was 4 mm and its diameter was 0.81 mm. The reference electrode needle was attached to the phantom through the whole measurement procedure. The active electrode area (4 mm uncovered at the tip) was located at the bottom of the phantom. Insertion points on the x–y plane were indicated by a paper template with holes that was located on top of the phantom (not shown in Fig. 2). Insertion depth was measured with a digital caliper (model 700-125 by Mitutoyo Corporation, Kawasaki, Japan) that was fixed to the microscope chassis. Measurements were taken at four depths: 2, 6, 10, and 14 mm. Therefore, the total number of measurements was 64 (16 insertion points × 4 depths). In this case, measurements were taken manually and it took about 5 min to perform the whole measurement procedure.

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Fig. 2. (a) Schematic representation of the setup employed to perform 3-D experiments with gel phantoms. Two-electrode impedance measurements are performed at 50 kHz by a commercial impedance analyzer through stainless steel needles covered with Teflon tape down to the last 4 mm at the tip. A needle stays in the same position during the whole measurement procedure (reference electrode), whereas the other needle is inserted sequentially at different locations separated by 10 mm. (b) Top view of the insertion pattern. (c) Top view of the insertion pattern superimposed on a picture of a phantom with an inclusion at the center of the insertion pattern.

E. Image Reconstruction Image reconstruction follows the method developed in [9]. It is the same for the 2-D and 3-D configurations. Briefly, we first specify the shape of the body and the location of electrodes in the experiment. This information is used with COMSOL Multiphysics for mesh generation. Then, we specify the location of the reference electrode and the order in which the various insertion sites (nodes) are probed by the single electrode. The information on the mesh and the location of the discrete electrode measurements is used to specify objects in Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software (EIDORS) [11], [28], [29]. The image reconstruction is based on EIDORS and employs the linearity of the field equation. The linearity allows us to combine the discrete measurement from single electrode pairs in a single data input file. The method of image reconstruction is identical to that in [9]. The only difference is that here the input data are taken from the experiment while in our previous study it was taken from simulations by EIDORS. The 2-D model used in this study is a circle of 80 mm in diameter. In this circle, we define 65 nodes that correspond to the locations from which measurements were taken. Among these nodes, 1 is for the reference electrode and 64 are for the 64 discrete measurements that we took. The position and the num-

Fig. 3. (a) 2-D impedance magnitude measurements from a homogeneous phantom (σ = 1.7 mS/cm). The 64 measurements are displayed along the abscissa in the same order that they are taken [Fig. 1(b)]. Data from two experiments are combined: (•) experiment 1 and (◦) experiment 2 (measured impedance values for second homogeneous sample have been scaled to equal those of first sample in order to cancel the differences due to the slight difference in the thickness of the slab). (b) Difference between both sets of measurements expressed in percentage.

bering of the nodes from which electrode measurements were taken are shown in Fig. 1(b). It is unique to our method that each measurement is taken separately between only two electrodes. Therefore, during each electrode insertion, we use the same electrode for current injection and voltage measurement; a total of 64 of voltage difference measurements are obtained. The 3-D model is a cylinder with a diameter of 80 mm and a height of 16 mm. In this cylinder, we also define the location of 65 nodes that correspond to the points from which the data were acquired. One of the nodes is at the location of the reference electrode. The reference electrode was 2 mm above the bottom surface of the body, at the location marked in Fig. 2(b). The other 64 nodes correspond to four discrete measurements taken at different locations along the needle insertion path during each of the 16 insertions of the electrodes in Fig. 2(b). III. RESULTS AND DISCUSSION A. Measurement Noise In our previous theoretical study, it was assumed that the measurement noise is on the order of 0.1%. However, here we have observed that the variability between consecutive measurement sets is significantly larger. If we compare the 2-D measurements recorded from two homogeneous phantoms (Fig. 3), it can be

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Fig. 5. Reconstructed conductivity 2-D image with two inclusions. (a) Representation of the phantom; the gray circles indicate location, shape, and size of the inclusions in relation to the insertion pattern and the base gel. (b) Obtained conductivity image. Color scale is adjusted so that white color represents the conductivity of the homogeneous case and black color indicates the maximum conductivity found during the reconstruction.

measurements. Electrical noise of any type and interferences can be ruled out as significant contributors to such variability because when measurements are performed continuously at the same gel site (even if we move the cables or the whole setup), standard deviation of values is much lower than 0.1%. We presume that the magnitude of the observed variability is due to geometrical errors when placing the needles at each specific site for measuring. We estimate that the geometrical tolerance of our needle insertion system is on the order of 0.5 mm, and this is the main reason for the measurement errors. We anticipate that better templates can be implemented so that this error will be substantially reduced in clinical scenarios. The resistance measured between two rods inserted in an infinite slab is [26, annex B] R=

Fig. 4. Examples of reconstructed conductivity 2-D images for single inclusions at the center of the insertion pattern. (a)–(d) Representation of the phantoms; the gray circle indicates location, shape, and size of the inclusion in relation to the insertion pattern and the base gel. Inclusion diameter and relative conductivities (base gel:inclusion) are noted on the left bottom corner. (e)–(h) Obtained conductivity images for each setup represented on the subfigures on the left. Color scale is adjusted for each image according to the reconstructed conductivities: white color represents the conductivity of the homogeneous case, whereas black color indicates extreme conductivities.

ln[(r + d)/r] ρ πt

(2)

where R is the measured resistance, r is the radius of the needle, d is the distance between the rods, t is the thickness of the slab, and ρ is the resistivity of the material (= 1/σ). When distance errors are in the order of 0.5 mm then the previous expression indeed provides variations in R that are in the order of 2% (e.g., if r = 0.4 mm, d = 5 mm, and ∆d = 0. 5 mm, then ∆R = 3.4%). Therefore, the hypothesis that needle placement tolerance induces the observed magnitude of variation seems quite plausible. Other artifacts, such as observed gel cracks or air bubbles when inserting the needles, cannot be completely ruled out but we think that their contribution is sporadic and much more noticeable: in some experiments, we have observed that one or two measurement points provided values with errors much larger than 10%. In these cases, we disregarded the whole dataset and repeated the measurement procedure. B. 2-D Results

noticed that differences between both sets of measurements are as high as 2% [Fig. 3(b)]. This, of course, will have a significant influence on the quality of the images. Here, we briefly discuss the reason or reasons for such large variation between

Fig. 4 shows the effect of inclusion size and relative conductivity on the ability of the technique to detect single inclusions (the experimental setup is shown in Fig. 1). Subfigures on the left column display the location of the inclusion and indicate its

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Fig. 6. Example of reconstructed conductivity 3-D map with a single cylindrical inclusion (diameter = 9 mm) at the center of the insertion pattern. Conductivity of the inclusion is ten times larger than the conductivity of the base gel. (a) and (b) Geometric representation of the phantoms; the gray circle indicates location, shape, and size of the inclusion in relation to the insertion pattern and the base gel. (c) Obtained conductivity map represented in nine sections at equally spaced depths (left top image at 0 mm, bottom right image at 16 mm). Color scale is adjusted for each 3-D reconstruction (the same for all cross sections) according to the reconstructed conductivities: white color represents the conductivity of the homogeneous case, whereas black color indicates extreme conductivities.

relative conductivity compared to the base gel (base gel:inclusion). Subfigures on the right show the reconstructed images produced with the EIDORS reconstruction algorithm. The bottom subfigures [Fig. 4(d) and (h)] represent a prostate multiple biopsy sampling procedure in which the distance between the probe insertion sites is 5 mm and there are a total of 64 sampling sites. It is interesting to note that the 5-mm-diameter tumor would be missed by the biopsy probes but would be

Fig. 7. Example of reconstructed conductivity 3-D map with a single cylindrical inclusion (diameter = 7 mm) at the center of the insertion pattern. See caption of Fig. 6 for further details.

clearly manifested by the technique presented here. Therefore, the physician in charge of biopsy sampling procedure would have the opportunity to take an extra biopsy sample at the suspicious area indicated by the EIT technique. It is evident that inclusion detection becomes harder as its size is reduced and its conductivity is more similar to that of the base gel. We were not able to produce reconstructed images of reasonable quality for inclusions smaller than 3 mm (conductivity ratio 1:5) and with relative conductivity differences below 50% (inclusion diameter 5 mm). Fig. 5 demonstrates the ability of the technique to detect and discern two isolated inclusions that would be missed by the biopsy probes.

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it is evident that some sort of heterogeneity exists. Once again, in the case of an actual biopsy procedure, the physician would have the opportunity to explore in more detail the central region by performing some extra biopsies. IV. CONCLUSION This experimental study has demonstrated experimentally the feasibility of detecting tissue heterogeneities, which would be missed during a multisite biopsy sampling, by means of EIT based on impedance data collected from the biopsy needles. In particular, this study shows that inclusions with impedance and size characteristics similar to those of prostate tumors could be revealed by the technique. It should be emphasized that the most important aspect of this technique is not necessarily producing a precise image of the tumor but rather the ability to detect the occurrence and rough location of tumors that may be missed by biopsy sampling. ACKNOWLEDGMENT The authors would like to thank C. Daniels for helping them with the implementation of the needle insertion template. B. Rubinsky has a financial interest in Excellin Life Sciences, a company in the field of electroporation. M. Shini and B. Rubinsky have potential interests in the revenues of pending patents relevant to this study held by the Hebrew University of Jerusalem. A. Ivorra and M. Shini have contributed equally to this work. REFERENCES

Fig. 8. Example of reconstructed conductivity 3-D map with a single cylindrical inclusion (diameter = 5 mm) at the center of the insertion pattern. See caption of Fig. 6 for further details.

C. 3-D Results Experiments with 3-D phantoms are of particular interest because the simulations in our previous paper [9] were carried out under the assumption of point electrodes, whereas here our electrodes consist of a rod with a diameter of 0.8 mm and a length of 4 mm. Figs. 6–8 examine the effect of the inclusion size on the quality of the reconstructed images (inclusion location and conductivity ratio are the same in the three cases; the experimental setup is shown in Fig. 2). Note that the three inclusions would be missed by the biopsy probes but they are clearly manifested in the reconstructed images. Even in the case of the smallest inclusion (Fig. 8, diameter 5 mm), in which the reconstructed image fails to provide the correct z-positioning of the inclusion,

[1] H. D. Bear, “Image-guided breast biopsy—How, when, and by whom?,” J. Surg. Oncol., vol. 67, pp. 1–5, 1998. [2] H. S. Lee, C. T. Shun, L. L. Chiou, C. H. Chen, G. T. Huang, and J. C. Sheu, “Hydroxyproline content of needle biopsies as an objective measure of liver fibrosis: Emphasis on sampling variability,” J. Gastroenterol. Hepatol, vol. 20, pp. 1109–1114, 2005. [3] R. Rosenblatt, S. A. Fineberg, J. A. Sparano, and R. N. Kaleya, “Stereotactic core needle biopsy of multiple sites in the breast: Efficacy and effect on patient care,” Radiology, vol. 201, pp. 67–70, 1996. [4] S. Jhavar, C. M. Corbishley, D. Dearnaley, C. Fisher, A. Falconer, C. Parker, R. Eeles, and C. S. Cooper, “Construction of tissue microarrays from prostate needle biopsy specimens,” Br. J. Cancer, vol. 93, pp. 478–482, 2005. [5] W. E. Barzell and M. R. Melamed, “Appropriate patient selection in the focal treatment of prostate cancer: The role of transperineal 3-dimensional pathologic mapping of the prostate—A 4-year experience,” Urology, vol. 70, pp. S27–S35, 2007. [6] E. D. Crawford, S. S. Wilson, K. C. Torkko, D. Hirano, J. S. Stewart, C. Brammell, R. S. Wilson, N. Kawata, H. Sullivan, M. S. Lucia, and P. N. Werahera, “Clinical staging of prostate cancer: A computer-simulated study of transperineal prostate biopsy,” BJU Int., vol. 96, pp. 999–1004, 2005. [7] G. Onik and W. Barzell, “Transperineal 3D mapping biopsy of the prostate: An essential tool in selecting patients for focal prostate cancer therapy,” Urol. Oncol. Semin. Original Investig., vol. 26, pp. 506–510, 2008. [8] G. Onik, “The male lumpectomy: Rationale for a cancer targeted approach for prostate cryoablation. A review,” Technol. Cancer Res. Treat., vol. 3, pp. 365–370, 2004. [9] M. Shini and B. Rubinsky, “Multiple biopsy probe sampling enabled minimally invasive electrical impedance tomography,” Physiol. Meas., vol. 29, pp. 109–126, 2008. [10] K. Boone, D. Barber, and B. Brown, “Imaging with electricity: Report of the European concerted action on impedance tomography,” J. Med. Eng. Technol., vol. 21, pp. 201–232, 1997.

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[11] N. Polydorides and W. R. B. Lionheart, “A MATLAB toolkit for threedimensional electrical impedance tomography: A contribution to the electrical impedance and diffuse optical reconstruction software project,” Meas. Sci. Technol., vol. 13, pp. 1871–1883, 2002. [12] R. H. Bayford, “Bioimpedance tomography (electrical impedance tomography),” Annu. Rev. Biomed. Eng., vol. 8, pp. 63–91, 2006. [13] M. Tang, W. Wang, J. Wheeler, M. McCormick, and X. Dong, “The number of electrodes and basis functions in EIT image reconstruction,” Physiol. Meas., vol. 23, pp. 129–140, 2002. [14] D. S. Holder, Electrical Impedance Tomography: Methods, History and Applications. Bristol, PA: Inst. Phys. Publishing, 2005. [15] M. Cheney, D. Isaacson, and J. C. Newell, “Electrical impedance tomography,” SIAM Rev., vol. 41, pp. 85–101, 1999. [16] D. M. Otten and B. Rubinsky, “Cryosurgical monitoring using bioimpedance measurements—A feasibility study for electrical impedance tomography,” IEEE Trans. Biomed. Eng., vol. 27, no. 10, pp. 1376–1381, Oct. 2000. [17] D. S. Holder and B. H. Brown, “Biomedical applications of EIT: A critical review,” in Clinical and Physiological Applications of Electrical Impedance Tomography, D. S. Holder, Ed. London, U.K.: Taylor & Francis, 1993, ch. 2. [18] M. J. Hamamura, L. T. Muftuler, O. Birgul, and O. Nalcioglu, “Measurement of ion diffusion using magnetic resonance electrical impedance tomography,” Phys. Med. Biol., vol. 51, pp. 2753–2762, 2006. [19] D. S. Holder and A. Khan, “Use of polyacrylamide gels in a saline-filled tank to determine the linearity of the Sheffield Mark 1 electrical impedance tomography (EIT) system in measuring impedance disturbances,” Physiol. Meas., vol. 15, pp. 45–50, 1994. [20] Y. Zou and Z. Guo, “A review of electrical impedance techniques for breast cancer detection,” Med. Eng. Phys., vol. 25, pp. 79–90, 2003. [21] S. R. Smith, K. R. Foster, and G. L. Wolf, “Dielectric properties of VX2 carcinoma versus normal liver tissue,” IEEE Trans. Biomed. Eng., vol. BME-33, no. 5, pp. 522–524, May 1986. [22] B. H. Brown, J. A. Tidy, K. Boston, A. D. Blackett, R. H. Smallwood, and F. Sharp, “Relation between tissue structure and imposed electrical current flow in cervical neoplasia,” Lancet, vol. 355, pp. 892–895, 2000. [23] R. J. Halter, A. Hartov, J. A. Heaney, K. D. Paulsen, and A. R. Schned, “Electrical impedance spectroscopy of the human prostate,” IEEE Trans. Biomed. Eng., vol. 54, no. 7, pp. 1321–1327, Jul. 2007. [24] D. C. Walker, R. H. Smallwood, A. Keshtar, B. A. Wilkinson, F. C. Hamdy, and J. A. Lee, “Modelling the electrical properties of bladder tissue— Quantifying impedance changes due to inflammation and oedema,” Physiol. Meas., vol. 26, pp. 251–268, 2005. [25] J. Jossinet, “Variability of impedivity in normal and pathological breast tissue,” Med. Biol. Eng. Comput., vol. 34, pp. 346–350, 1996. [26] A. Ivorra. (2005). Contributions to the measurement of electrical impedance for living tissue ischemia injury monitoring, Ph.D. dissertation in electronic engineering, Univ. Polit`ecnica de Catalunya (UPC), Barcelona, Spain [Online]. Available: http://www.tdx.cat/TDX-0302105– 135356. [27] G. J. Saulnier, “EIT instrumentation,” in Electrical Impedance Tomography: Methods, History and Applications, D. S. Holder, Ed. Bristol, PA: Inst. Phys. Publishing, 2005, pp. 65–104. [28] M. Vauhkonen, W. R. Lionheart, L. M. Heikkinen, P. J. Vauhkonen, and J. P. Kaipio, “A MATLAB package for the EIDORS project to reconstruct two-dimensional EIT images,” Physiol. Meas., vol. 22, pp. 107–111, 2001. [29] A. Adler and W. R. Lionheart, “Uses and abuses of EIDORS: An extensible software base for EIT,” Physiol. Meas., vol. 27, pp. S25–S42, 2006.

Antoni Ivorra was born in Barcelona, Spain, in 1974. He received the Ph.D. degree in electrical engineering from the Polytechnic University of Catalunya, Barcelona, in 2005. During 1998–2005, he was with the Biomedical Applications Group, Centro Nacional de Microelectr´onica, Barcelona. He is currently a Postdoctoral Fellow at the University of California at Berkeley, Berkeley. He was engaged in the measurement of the electrical impedance of living tissues. His current research interests include electroporation, bioimpedance, and electrical impedance tomography.

Mohanad Shini was born in Maghar village, Israel, in 1983. He received the B.Sc. degree in computer engineering from Hebrew University of Jerusalem, Jerusalem, Israel, in 2006, and the M.Sc. degree in computer science in 2007 from the Center for Bioengineering in the Service of Humanity and Society, Hebrew University of Jerusalem, where he is currently working toward the Ph.D. degree. He is currently a Research Scholar at the University of California at Berkeley, Berkeley. His current research interests include medical diagnostic using electrical measurements.

Boris Rubinsky was born in Romania. He received the Ph.D. degree from Massachusetts Institute of Technology (MIT), Cambridge. Since 1980, he has been a Professor of the Graduate School, University of California at Berkeley. He is also the Director of the Center for Bioengineering in the Service of Humanity and Society, School of Engineering and Computer Science, Hebrew University of Jerusalem, Jerusalem, Israel. His current research interests include the field of bioengineering that encompasses a large range of topics from numerical analysis, medical imaging, cryobiology, tissue engineering, biological energy, biological heat and mass transfer, and bioelectronics. He has authored or coauthored over 250 peer-reviewed articles and has over 20 issued patents. He has cofounded nearly ten biotech startups, some of which are on the National Association of Securities Dealers Automated Quotation (NASDAQ) and London Stock Exchange.

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