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IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 22, NO. 5, MAY 2003

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Electrical Conductivity Imaging via Contactless Measurements: An Experimental Study Bas¸ak Ülker Karbeyaz, Student Member, IEEE, and Nevzat G. Gençer*, Member, IEEE

Abstract—A data-acquisition system has been developed to image electrical conductivity of biological tissues via contactless measurements. This system uses magnetic excitation to induce currents inside the body and measures the resulting magnetic fields. The data-acquisition system is constructed using a PC-controlled lock-in amplifier instrument. A magnetically coupled differential coil is used to scan conducting phantoms by a computer controlled scanning system. A 10 000-turn differential coil system with circular receiver coils of radii 15 mm is used as a magnetic sensor. The transmitter coil is a 100-turn circular coil of radius 15 mm and is driven by a sinusoidal current of 200 mA (peak). The linearity of the system is 7.2% full scale. The sensitivity of the system to conducting tubes when the sensor-body distance is 0.3 cm is 21.47 mV/(S/m). It is observed that it is possible to detect a conducting tube of average conductivity (0.2 S/m) when the body is 6 cm from the sensor. The system has a signal-to-noise ratio of 34 dB and thermal stability of 33.4 mV C. Conductivity images are reconstructed using the steepest-descent algorithm. Images obtained from isolated conducting tubes show that it is possible to distinguish two tubes separated 17 mm from each other. The images of different phantoms are found to be a good representation of the actual conductivity distribution. The field profiles obtained by scanning a biological tissue show the potential of this methodology for clinical applications. Index Terms—Contactless conductivity measurement, electrical impedance imaging, magnetic induction, medical imaging.

I. INTRODUCTION

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EASURING the magnetic fields of the induced currents in a conductive body provides a means to image the electrical conductivity of human tissues. Tomographic images of simple objects with limited resolution have been presented using saline phantoms in previous studies [1]–[3]. The use of the same measurement method was also proposed for subsurface imaging and its potential was shown numerically by three-dimensional (3-D) simulations [4], [5]. However, the performance of the methodology for subsurface imaging has not been demonstrated experimentally. Experimentation is necessary in order to investigate the assumptions of the technique and its limitations. This

Manuscript received September 27, 2002; revised December 17, 2002. This work was supported in part by the Middle East Technical University Research Fund under Project AFP 96-03-01-01 and in part by the Turkish Scientific and Technical Research Council TUBITAK under Project 101E013. The Associate Editor responsible for coordinating the review of this paper and recommending its publication was M. W. Vannier. Asterisk indicates corresponding author. B. Ülker Karbeyaz is with the Electrical and Electronics Engineering Department, Middle East Technical University, 06531 Balgat, Ankara, Turkey (e-mail: basak_ [email protected]). *N. G. Gençer is with the Electrical and Electronics Engineering Department, Middle East Technical University, 06531 Balgat, Ankara, Turkey (e-mail: [email protected]). Digital Object Identifier 10.1109/TMI.2003.812271

paper introduces a computer-controlled data-acquisition system developed for this purpose. The system operates at low frequency (11.6 kHz), and uses a single channel to collect data with a scanning mechanism. The system parameters, i.e., spatial resolution, signal-to-noise ratio (SNR), data-acquisition time, etc., are investigated in detail. Extensive use of these systems to image saline phantoms and biological tissues reveals that even measured field profiles can be used as a good representation of the underlying objects. This measurement methodology has been known for decades. Common applications include geophysical inspection, nondestructive testing, salt content measurements in sea water, and impurity measurements in semiconductors [6]. For medical purposes it was first proposed by Tarjan and McFee (in 1968) to determine the effective electrical resistivity (100 kHz) of the human torso and head, and to follow conductivity fluctuations as a result of cardiac activity and ventilation [7]. Almost 25 years later, Al-Zeibak and Saunders, proposed a tomographic imaging system, known as mutual inductance imaging, based on these contactless measurements. A small drive coil (2 MHz) and a distant pickup coil is used to scan saline phantoms. By employing computational algorithms used for X-ray computed tomography (CT), it was shown that fat and fat-free tissue can be differentiated and the internal and external geometry of simple objects can be determined [1]. Around the same period, Netz et al., introduced a miniaturized device (25-mm diameter) and showed a linear dependence between the subsurface measurements and the electrolytic content of saline solutions [8]. The ability to detect simulated cytotoxic oedema conditions in a skull model was also shown. Recently, a number of studies have reported images of saline phantoms using a similar method presented by Al-Zeibak and Saunders to produce tomographic conductivity images [the method is later named magnetic induction tomography (MIT)]. Griffiths et al. used a single-channel system operating at 10 MHz to present an image of a 9-cm beaker containing 2 S/m saline solution [2]. The beaker was located at the center of an image plane and data profiles were collected from 64 views. Korjenevsky et al. reported an experimental system operating at 20 MHz with 16 drive and detector coils encircling the object to be imaged [3]. In both studies, a filtered back-projection algorithm was used to generate images of saline solutions with conductivities in the range of biological tissues. Scharfetter et al. developed hardware for multifrequency MIT measurements [9] operating in the 20–370 kHz range. The system comprises of planar gradiometers and a high-resolution phase detector. The SNR of the system at 150 kHz is 20 dB. The feasibility of measuring the conductivity spectra of biological tissues

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was experimentally demonstrated on a potato. The authors concluded that on-line spectroscopy of tissue conductivity with low spatial resolution is feasible. The measurement methodology was also proposed for use in subsurface imaging, for instance allowing data to be collected from the upper surface of the human head [4], [5], [10]. At a single frequency, the basic field equations would be similar to those for MIT. However, the basic assumptions and the characteristics of the imaging system are different. For high frequencies: 1) the displacement currents in the conducting body are not negligible; 2) the propagation effects should be taken into account; and 3) the stray capacitances are effective in the measurements. Thus, both the theory and the experimental work is more complicated than the low frequency studies. High-frequency studies are conducted for tomographic images. In that case, the excitation coil is at one side of the object, and the receiver coil is at the other side, which is 20–25 cm away from the transmitter coil. In order to increase the signal strength at such a distance one method is to increase the excitation frequency. For subsurface imaging, however, the conductivity distribution at 5 cm distance from the transducer is of interest. The feasibility of this method was explored for safety conditions at 50 kHz [10]. Gencer and Tek calculated the magnetic fields for a miniaturized coil configuration (10-mm radius) over a uniformly conductive semi-infinite region. The magnetic fields were measured at about 10 V while the induced currents were well below the safety limit (1.6 mA cm at 50 kHz). Consequently, the measurement method is proposed for subsurface imaging and a mathematical formulation is proposed for the forward problem (i.e., the calculation of measurements for a given conductivity distribution) [4], [5]. A 3-D finite-element method (FEM) model was developed to solve the forward problem. The inverse problem, (i.e., the calculation of the unknown conductivity distribution using the measurements) was then formulated based on a sensitivity matrix which relates the changes in the measurements to the conductivity perturbations and 3-D images were reconstructed using the simulated data. The characteristics of the inverse problem are explored by analyzing the sensitivity matrix. Simulations studies using a specific 7 7 coil system nearby the upper surface of a cubic body revealed that it is possible to identify shallow perturbations, although, resolution decreases gradually for deeper conductivity perturbations. This paper will present experimental results utilizing the theoretical and numerical work on subsurface imaging presented in [4] and [5]. II. THEORETICAL BACKGROUND The theoretical formulation relating conductivity to magnetic measurements, given in [5] will be presented here briefly. In a linear isotropic nonmagnetic conductive medium, the electric field can be expressed as follows: (1) where is the radial frequency, is the magnetic vector potential, and is the scalar potential. Thus, the electric field has two sources: variation of the magnetic field with time, and surface and volume charges. Assuming that the magnetic vector

potential generated by the transmitter coil is equal to the primary vector potential , and the displacement currents are negligible, the vector potential term can easily be calculated for a certain coil configuration. Calculation of the scalar potential disfor the same coil configuration requires the solutribution tion to the following differential equation: (2) (3) is the normal component where denotes conductivity and of the magnetic vector potential on the surface of the conductive body. Given the assumptions stated above, the scalar potential has only an imaginary component. Thus, the electric field can , and the induced now be expressed as . current density in the conductive body is Let us assume that the excitation and detection coils are placed nearby a conducting body. The flux in the detector coil will be affected by the current in the excitation coil and the induced current distribution in the conductive body. Using the magnetic reciprocity theorem [11], it is possible to express this as follows: (4) is the magnetic vector potential created by the recipwhere in the detector coil. Here, is the current denrocal current sity in the excitation coil and is the induced current density in the conductive body. Flux in the detector coil can be obtained by taking the integrals in the corresponding volumes. The first term on the right-hand side of (4) is the primary flux directly coupled from the transmitter coil. The second term represents the flux caused by the induced currents. The electromotive force in the receiver coil can be expressed as

(5) (the magnetic lead field) repNote that the term resents the electric field that can be created by the detector coil, energized with a unit reciprocal current. The two terms on the and secondary right-hand side of (5) represent the primary , respectively. The in-phase component (out of a voltages minus sign) corresponds the secondary voltage that gives information about the conductivity of the conducting body. The quadrature component is the primary voltage and will be cancelled out using a proper measurement system. A simple cancellation can be obtained by employing a differential coil system. In a coaxial system, two oppositely wound receiver coils are placed at equal distances from the excitation coil, one of them which is at the body side and the other one removed from the conducting body. Because there are two receiver coils in this case, the above formulation should be modified as (6)

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where and are the magnetic vector potentials created and in the first and the second by the reciprocal currents detector coils, respectively. For a given excitation and detector coil configuration, the and are easily calculated. magnetic vector potentials However, the scalar potential distribution is a function of the unknown conductivity distribution. Thus, the relation between the secondary voltages in the detector coil and the conductivity distribution is nonlinear. One method to find an estimate of the conductivity distribution from a set of secondary voltage measurements is to linearize (6) around an initial conductivity distribution and obtain a linear relation between the perturbations in conductivity and the changes in the measurements. For measurements, if the conductive body is discretized into constant conductivity elements, it is possible to obtain the following matrix equation [5]: Fig. 1. Block diagram of the data-acquisition system.

(7) is an vector representing the changes in where is an vector representing the measurements and conductivity perturbations from an assumed initial conductivity value. represents the sensitivity matrix and can be calculated as explained in detail in [5]. Different methods that apply different optimization criterions can be employed to solve for . In this study, a least-squares solution is obtained using the is Steepest-Descent algorithm [12]. Once an estimate for obtained, it is possible to update the conductivity distribution. The accuracy in the solutions can be improved iteratively by calculating a new sensitivity matrix and solving a new system of equations at each iteration. Note that the calculation of requires the solution of the scalar potential distribution for an assumed conductivity distribution. For a body of arbitrary geometry, a numerical method, such as the (FEM) [5], must be employed for that purpose. However, for a specific body geometry and coil configuration, a two-dimensional (2-D) FEM can be used to reduce the computation time in image reconstruction. This is possible if: 1) the body has translationally uniform conductivity; 2) the boundary conditions at the edges has no depth dependency; and 3) the boundary conditions are zero on the upper and lower surfaces. When the conducting body is in the form of a thin slice, the conductivity distribution can be assumed to be translationally uniform in that slice. In electrical impedance tomography (EIT) studies, thin body slices (for example, of 1-cm thickness) are assumed translationally uniform and used as 2-D phantoms [13]. In EIT measurements, the electrodes used for excitation at the boundaries extend from the upper to lower surface imposing constant boundary conditions across the slice thickness. In this paper, tubes or vessels filled with saline solution (in air or in a saline solution) are used for experimental studies. They have translationally uniform conductivity distributions and since they are thin (1.8-cm height) the boundary conditions are assumed constant across the slice thickness. Since the coil is planar and its axis is vertical to the body, the boundary conditions (3) on ). Conthe upper and lower surfaces are zero (i.e, sequently, the conducting bodies used in the experiments are assumed as 2-D phantoms and 2-D algorithms are employed. As the thickness of the slice increases or the geometry of the

conducting body changes in depth, then the actual 3-D reconstruction problem should be solved by first identifying the 3-D geometry using other means. A fast approximate solution for can also be obtained by on measurements, thus avoiding neglecting the effects of FEM calculations. Note that in (6), the nonlinearity originates from the scalar potential term. If one neglects the scalar potential term in the electric field calculations, the relation between the measurements and conductivity becomes linear. In this case, can be obtained by solving a linear inverse problem. In this paper, the least-squares solutions to the linear inverse problem are obtained by using the steepest-descent algorithm that imposes nonnegativity on the solutions at each iteration. III. MEASUREMENT SYSTEM In this paper, a data-acquisition system is introduced that scans a conductive body and measures the magnetic fields of the induced currents. The system uses a differential-coil configuration and a computer-controlled lock-in amplifier instrument. The block diagram of the differential coil system is shown in Fig. 1. The coils are coaxial and 15 mm in radius. The receiver coils (1.36 H, 3.69 k , self resonance frequency 45.6 kHz) have 10 000-turns wound on a 6-mm-diameter delrin rod using 0.06-mm copper wire and separated 7 mm apart. The transmitter (488 mH, 1.58 , self resonance frequency 400 kHz) is a 100-turn coil wound with 0.5-mm copper wire and is the same size as the receiver coils. The oscillator output [1.5 V root-mean-square (rms), 11.60 kHz] of the EG&G Model 5209 lock-in amplifier instrument feeds the LM12 power amplifier (80 W, 0.01% total harmonic distortion), which excites the transmitter coil with 200 mA (peak). The transmitter coil is tuned to the operating frequency using a series resistance capacitance (RC) circuit. The time-varying magnetic field in the transmitter coil induces current in the receiver coils and the conductive body. The two receiver coils with opposite winding directions are connected in series to cancel out the voltage induced by direct coupling. The primary 35-V rms in the receiver coils can be approximately cancelled out with proper positioning. However, there

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Fig. 2.


Block diagram of the manually adjusted nulling circuitry.

is still a 5-V rms residual signal. Since the measured signal is usually small compared with the residual voltage, a nulling circuit is required to cancel its effects. For this purpose, a manual nulling circuit is designed to decrease the residual signal further when there is no conductive body. The signal on the monitor resistor R (4.7 ) is amplified with a wide-band (4 MHz), high slew rate (13 V s) and high input impedance (1 M ) amplifier (LF351N), and phase shifted to obtain a signal which is equal in magnitude and phase with the residual signal (Fig. 2). The resulting signal is subtracted from the residual signal, using a differential amplifier circuit with common mode rejection ratio (CMRR) of 70 dB. Initially 5-V rms of residue voltage is decreased by a factor of 900 using this nulling circuit. The output of the nulling circuitry is connected to the input of the lock-in amplifier for phase sensitive detection (the lock-in amplifier’s reference signal is fed with the transmitter coil current). The instrument is controlled by a PC (via RS232 by a computer code written in BASIC) as the data is acquired. Before each measurement, the auto-sensitivity function of the lock-in amplifier instrument is activated so that it is possible to achieve maximum sensitivity. One-hundred values are collected at each measurement point. Time required for a single measurement depends on the time-constant of the lock-in amplifier instrument. This is chosen to be 30 ms in order to improve SNR. Digital-to-analog (D/A) outputs of the lock-in amplifier instrument are also controlled by the PC, which feeds the XY scanner. To scan the phantom by the probe, a computer-controlled XY scanning system has been designed and implemented (Fig. 3). The motion is controlled by two step motors, which are controlled by the computer through a step motor driving circuit. The scanning system has a minimum step size of 0.4 mm. The operating frequency is selected to be lower than 100 kHz since the displacement currents are small and propagation terms are negligible in that frequency range [10]. This allows for the quasistatic behavior of electromagnetic fields and simplifies the forward problem calculations. From the experimental point of view, an operating frequency of 50 kHz is usually selected to avoid the stray capacitance effects in the measurements in most of the electrical impedance tomography studies [13]. Similarly, in this paper, although the secondary voltages increase with the square of the frequency, low frequency is desired to decrease the electric field pick-up. Low-frequency operation is also preferred to decrease the residue signal and minimize the efforts for nulling. In order to work with the minimum residue signal (when there is no conducting object near the transducer), the residue signal is recorded by sweeping the frequency of the ex-

Fig. 3. (a) Picture of the XY scanning system with the probe attached. The system is all made up of plastic materials to avoid artifacts. (b) Probe at a closer view. (c) Scanning pattern.

citation signal between 0–100 kHz. Due to the available electronics and coil characteristics, the minimum residue signal is achieved at 11.60 kHz and this frequency is chosen as the operating frequency.


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the system is evaluated by the relation , and are the variance of the signal and noise, rewhere spectively. The variances are calculated by obtaining 100 samples of data at a point in a frame of 10 cm 10 cm. The data is measured at 16 16 locations with a phantom of uniform conductivity (0.2 S/m). The SNR of the system is found as 34 dB when the distance between the conducting body and the sensor is 3 mm. If the distance increases the amplitude of the measurements decreases, thus, the SNR of the system becomes poor. It is observed that the system can detect the circular vessel used for the sensitivity calculations [filled with saline solution of average tissue conductivity (0.2 S/m)] when it is placed at a distance of 60 mm. C. Spatial Resolution Fig. 4.

Field measurements versus conductivity plot.

IV. RESULTS The results of several experiments are used to assess the system’s performance and explore its ability to reconstruct conductivity images of biological tissues. The following sections present our findings. A. Sensitivity In order to obtain the sensitivity of the system, measurements are made on a 45-mm-radius, 10-mm-deep circular vessel. For each measurement the vessel is filled with a saline solution of differing conductivities, spanning the range 0.2–6.72 S/m. The vessels are placed at a distance of 3 mm from the sensor. The linearity in the measurements with respect to the object conductivity is shown in Fig. 4. The linearity of the system is found as 7.2% full scale. The slope of this curve implies that the sensitivity of the system is 21.47 mV/(S/m). In order to compare this value with the theoretical predictions an analytical formula is used which is derived for a differential (coaxial) coil placed above a conducting ring [7]. Using this formula, it is possible to evaluate the received voltage when the coil is placed above a cylindrical conducting body. In that case, the conducting cylinder is considered as a sum of conducting rings (The coupling between the conducting rings is assumed negligible). When the method is applied for the coil configuration used in the experiments, the sensitivity value is obtained as 45.63 mV/(S/m), which is on the same order of magnitude with the sensitivity obtained using the measurements. It is assumed that the discrepancy primarily originates due to geometrical differences in the theoretical and numerical cases. The coil-body distances and coil configurations (coil thicknesses, coil radii, and coil-coil distances) used in the theoretical calculations may not exactly represent the geometry in the experimental studies. B. Signal-to-Noise Ratio The measured signal contains the noise component, as well as the true signal data which is obtained by the average value of the signal at each data point. The noise has been obtained by subtracting the average value from the measured signal. The SNR of

A commonly used method to measure the spatial resolution of an imaging system is to find the minimum separation between the two point or line objects that can be resolved by the imaging system. For this purpose, two 30-cm long, 8-mm wide tubes are used. The tubes are filled with 2 S/cm conductivity solution. The excitation and receiver coils have 6-mm inner radius, thus, it is possible to induce circulating currents in 8-mm wide tubes. The scanner system scans a 10 10 cm area at 17 17 data points. It is observed that it is possible to distinguish the bars with minimum separation of 17 mm (from center to center). The field profile (the measured voltages) and the reconstructed conductivity image is shown in Fig. 5(a) and (b). D. Thermal Stability Measurements are recorded by raising the ambient temperature (using heating fans) and recording the output of the system. It is observed that the output voltage changes by 33.4 mV for a 1 C rise in temperature (at a full scale of 1 V). E. Image Reconstruction The performance of the imaging system is tested using various phantoms and biological tissues. The practical way of obtaining a conductivity phantom is to fill glass tubes of differing shapes (cylinder, ring, cube, etc.) with saline solutions. The conductivity of the saline solution is chosen from the range of biological tissue conductivities. In order to test the algorithms, these tubes are also immersed into saline solutions to provide a perturbation from an otherwise uniform conductivity. Final experiments are conducted by scanning a raw lamb chop. The measured field profiles and reconstructed conductivity images are presented in the following sections. 1) Isolated Conducting Tubes: Fig. 6(a) shows the field profile of a conducting ring (the actual ring geometry is also shown in this figure). The conducting ring is obtained by filling a glass tube with saline solution of conductivity 2 S/m. Measurements are obtained scanning a 10 cm 10 cm area with 17 17 samples. The measurement field profile shows a circularly shaped object, however, it does not provide information about the size and actual ring geometry of the object. Fig. 6(b) shows the conductivity distribution of the object reconstructed by neglecting the effects of the scalar potential on the measurements, i.e., the

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Fig. 5. Experiment results of two 8-mm diameter, 17 mm apart saline solution filled rods. (a) Field profile. (b) Conductivity distribution.

Fig. 6. Experiment result of ring shaped phantom. (a) Field profile. (b) Conductivity distribution.

sensitivity matrix is obtained using only the magnetic vector potentials calculated for the transmitter and receiver coils. Note that the actual size and ring shape of the object is evident. In order to illustrate the spatial resolution of the system for isolated conducting objects, two conducting tubes are placed horizontally. The experimental details are described in Section IV-C. The 17 17 field profile is shown in Fig. 5(a). From the field profile it is apparent that there is a line object placed horizontally. The existence of two closely located conducting tubes is revealed by the solution of the inverse problem and is given in Fig. 5(b). 2) Isolated Conducting Object In Saline Solution: In this group of experiments, uniformly conductive objects with conductivity perturbations are considered. The perturbations are realized by inserting a conducting body into a saline bath. Tubes or vessels filled with saline solutions of a different conductivity

from the bath conductivity are used to make perturbations. The purpose of using such conductivity phantoms is to assess the system’s performance when there are small conductivity perturbations from an object with a known boundary. The conductivity images in such cases can be obtained by linearizing the forward problem around an initial conductivity distribution and finding an estimate for the perturbation as discussed in Section II. The results of only a single experiment are presented here, as the images reconstructed for other perturbations provide similar characteristics. In this experiment, a 28 28 mm square vessel with a depth of 18 mm is filled with saline solution of conductivity 6.72 S/m and placed in a uniformly conductive bath (2.0 S/m). The container of the bath has a 10 cm 10 cm square shape and 18-mm depth. It it is considered as a 2-D phantom based on the discussion in Section II. The 17 17 measurement field profile is


(a)

(b)

(c) Fig. 7. Experiment result of square shaped phantom. (a) Field profile. (b) Conductivity distribution using magnetic vector potential. (c) Conductivity distribution using magnetic vector potential and scalar potential.

shown in Fig. 7(a). It is possible to distinguish the location of the object from the field profile, however, its actual size and geom-

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etry are not apparent. Fig. 7(b) shows the reconstructed conductivity image when the sensitivity matrix is calculated using the magnetic vector potential information only. It is now possible to identify the object’s square shape. Fig. 7(c) displays the conductivity perturbation when the sensitivity matrix is calculated using both the magnetic vector potential and the scalar potential distribution for a uniform conductivity profile. The reconstructed image is the result of only the first iteration. The square shape of the perturbation is again apparent. Notice that after the first iteration, it is possible to observe a superiority compared with the image in Fig. 7(b). However, an improvement may be expected after successive iterations. Since the sensitivity matrix (289 400) computation takes about 24 hours (Pentium II 500-MHz PC with 64 MB RAM) for a single iteration, a second iteration is not attempted. The reason for long computation time is explained in the following paragraph. In this study, the analytical method developed in [5] is not used in the sensitivity matrix calculations (and this yields an increase in the computation time). Instead, for each coil position, the forward problem is first solved for a homogeneous object then it is solved for the same object with a conductivity perturbation at one pixel. The difference of the measurements divided by the change in conductivity yields one entry of the sensitivity matrix. If the coil scans the image area at M M locations then the times for the uniform forward problem should be solved by object. If the image area has N N pixels, then for each coil times to obtain a position the forward problem is solved for solution for each pixel perturbation. Thus, the total number of . For forward problem solutions becomes and , this corresponds to approximately 115 889 forward problem calculations. Using the given computer configurations the total computation time becomes 24 hours. (Note that a single forward problem calculation takes about 1 s.) 3) Biological Tissues: The ultimate goal of the measurement system is to reconstruct the conductivity distribution of biological tissues from the field measurements. To understand the performance of the system for biological tissues, measurements are obtained for a piece of lamb chop [Fig. (8)] inserted in a uniform saline solution. The sensor is placed at a distance of 3 mm from the body. The measurement set 10 cm while is obtained by scanning an area of 10 cm collecting data at 102 102 locations. The picture of the lamb chop and the measured field profile are shown in Fig. 8(a) and (b), respectively. Similar to the other experiments, the field profile [Fig. 8(b)] roughly presents information about the size and location of the inhomogeneity in the saline solution. The conductivity images are also reconstructed, but since the actual conductivity distribution is not known exactly for biological tissues, they are not presented. More controllable experiments will be conducted using agar phantoms in future. V. CONCLUSION AND DISCUSSION In this paper, a low-frequency (11.6 kHz) data-acquisition system was designed and implemented for imaging conductivity of biological tissues via contactless measurements. The system has an SNR of 34 dB, a spatial resolution of 17 mm, and a sensitivity of 21.47 mV/(S/m). The average data-acquisition time

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Fig. 8.


Experiment result of a lamb chop. (a) Real object. (b) Field profile.

was calculated as 4.67 s mm . The images of different phantoms were found to be good representations of the actual conductivity distribution. The field profiles, obtained from biological tissues give information about the location and geometry of the object. The measurements are sensitive to the currents induced in a finite region near the sensor. The size and geometry of this region depends on the coil configuration, distance from sensor to conducting body, and the operating frequency. In this study, circular coils of 15-mm radius are used and sensor-body distance is usually chosen as 2–3 mm. The field profiles obtained from different conductivity phantoms are found to be rough representations of the conductivity distribution. Better representations can be obtained by decreasing sensor-body distance. Using smaller sensors and a lower operating frequency will confine the sensitive region of the sensor but also decrease the 3-D sensitivity. In this paper, the area under consideration is scanned using a single sensor. This increases the data-acquisition time considerably. The total data-acquisition time is affected by the number

of horizontal scans, the number of samples at each scan, and the number of measurements at each sample point. In order to reduce the acquisition time, a future development should be concentrated on linear or 2-D arrays. The measurement system is tuned to a single frequency in the experiments. However, a multifrequency system would be more informative especially for possible applications on biological tissues. This will bring new problems to be solved in the design of the data-acquisition system. In order to reconstruct the actual body geometry and conductivity distribution, the inverse problem must be solved. However, the relation between the magnetic measurements and the conductivity distribution is nonlinear. The nonlinearity originates from the scalar potential term in the electric field distribution. One way to estimate the solution is to linearize the forward problem around an initial conductivity distribution and update the conductivity distribution using a suitable algorithm by comparing the calculated fields with the measurements. For the solution of the linearized problem, different optimization algorithms can be employed. In this paper, least-squares solutions are obtained using the steepest-descent algorithm. Further iterations can be performed by linearizing the forward problem for successive conductivity updates. At each iteration of the inverse problem, the scalar potential distribution must be solved. In this paper, the FEM is used to solve the scalar potential distribution in two-dimensional and a 2-D algorithm is employed. However, the effects of applying a 2-D algorithm to an actual 3-D problem should be further explored using both simulated and experimental data. It is observed that even the 2-D algorithm is computationally expensive. In order to reduce the computation time, images were also reconstructed by neglecting the effects of the scalar potential term on the measurements. In that case, the relation between the measurements and conductivity distribution becomes linear. The least-squares solutions were obtained by imposing nonnegativity constraints. The results were found comparable to the first iteration images of the nonlinear problem. Since the scalar potential distribution is not solved, the images were obtained in a shorter time. This method may provide a quick initial estimate of the body distribution. Note that the phantoms employed in this paper are constructed using saline solution filled glass tubes, which isolates the inner conductivity from the external conductivity. Thus, they are not a good representation of the biological tissue distribution. In addition, using such phantoms is a disadvantage for the inverse problem solutions. Assuming an initially uniform conductivity distribution does not provide a good estimate for the actual conductivity distribution. These phantoms are preferred in the preliminary studies due to the following reasons: 1) it is easy to develop phantoms with different sizes and shapes; 2) the conductivity in a given geometry is uniform and can be changed easily by injecting a different saline solution inside; 3) vaporization is negligible; and 4) the saline solution can be kept clean. Thus, with the scanning system outlined above, these phantoms were used safely in the experiments which takes a long time. When a new system is developed with a shorter data-acquisition time, further experiments will be performed with agar phantoms. This will reveal the imaging


system performance and will give better results for the inverse problem solutions. In conclusion, the preliminary results of a promising new medical imaging modality were presented. This measurement methodology can provide necessary conductivity information for electromagnetic source imaging of the human brain. Moreover, this method can be applicable to obtain conductivity images of brain, breast, and lung. Other application areas should be further explored.

ACKNOWLEDGMENT The authors would like to thank T. Ahmad for his comments on the design of the experimental system, Dr. Y. Ziya ˙Ider for his criticisms, and R. J. Linnehan for reading the manuscript. They would also like to thank the anonymous reviewers for their constructive comments.

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[2] H. Griffiths, W. R. Stewart, and W. Gough, “Magnetic induction tomography. A measuring system for biological tissues,” Ann. N Y Acad. Sci., vol. 873, pp. 335–345, 1999. [3] A. Korjenevsky, V. Cherepenin, and S. Sapetsky, “Magnetic induction tomography: experimental realization,” Physiol. Meas., vol. 21, pp. 89–94, 2000. [4] N. G. Gençer and M. N. Tek, “Forward problem solution for electrical conductivity imaging via contactless measurements,” Phys. Med. Biol., vol. 44, pp. 927–940, Apr. 1999. , “Electrical conductivity imaging via contactless measurements,” [5] IEEE Trans. Med. Imag., vol. 18, pp. 617–627, July 1999. [6] A. Kaufman and G. Keller, Induction Logging. Amsterdam, The Netherlands: Elsevier, 1989. [7] P. Tarjan and R. McFee, “Electrodeless measurements of the effective resistivity of the human torso and head by magnetic induction,” IEEE Trans. Biomed. Eng., vol. BME–15, pp. 266–278, Oct. 1968. [8] J. Netz, E. Forner, and S. Haagemann, “Contactless impedance measurement by magnetic induction—a possible method for investigation of brain impedance,” Physiol. Meas., vol. 14, pp. 463–471, 1993. [9] H. Scharfetter, H. Lackner, and J. Rosell, “Magnetic induction tomography: hardware for multi-frequency measurements in biological tissues,” Physiol. Meas., vol. 22, pp. 131–146, 2001. [10] N. G. Gençer and M. N. Tek, “Imaging tissue conductivity via contactless measurements: a feasibility study,” TUBITAK Elektrik J., vol. 6, no. 3, pp. 183–200, 1998. [11] J. Tripp, “Physical concepts and mathematical models,” in Biomagnetism: An Interdisciplinary Approach, L. K. S. J. Williamson, G. L. Romani, and I. Modena, Eds, New York: Plenum, 1983, pp. 101–139. [12] M. S. Bazaraa, H. D. Sherali, and C. M. Shetty, Nonlinear Programming Theory and Algorithms. New York: Wiley, 1993. [13] J. Morucci and B. Rigaud, “Bioelectrical impedance techniques in medicines,” Crit. Rev. Biomed. Eng., vol. 24, pp. 467–597, 1996.