performed at 50 kHz by a commercial impedance analyzer through stainless steel needles. A needle stays ..... London Stoc
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 56, NO. 5, MAY 2009
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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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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 56, NO. 5, MAY 2009
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
