Magnetic Induction Tomography Modeling in Biological Tissue Imaging Using Two-Port Network Technique

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1 Sensors & Transducers, Vol. 50, Issue 3, March 03, pp. -9 Sensors & Transducers 03 by IFSA Magnetic Induction Tomography Modeling in Biological Tissue Imaging Using Two-Port Network Technique Muhammad Saiful Badri MANSOR, Mohd. Fahjumi JUMAAH, ulkarnay AKARIA, Ruzairi ABDUL RAHIM, Nor Muzakkir NOR AYOB, Khairul Hamimah ABBAS, 3 Siti arina MOHD MUJI, Sazali YAACOB, Herlina ABDUL RAHIM, Leow PEI LING Process Tomography Research Group (PROTOM-i), Faculty of Electrical Engineering, Uniersiti Teknologi Malaysia, 830 Skudai, Johor Bahru, Johor, Malaysia Tel: Biomedical Electronic Engineering Department, School of Mechatronic Engineering, Uniersiti Malaysia Perlis, 0600 Arau, Perlis, Malaysia 3 Department of Computer Engineering, Faculty of Electrical and Electronic Engineering, Uniersiti Tun Hussein Onn Malaysia, Batu Pahat, Johor, Malaysia msbadri3@lie.utm.my, zulkarnay@unimap.edu.my, ruzairi@fke.utm.my Receied: February 03 /Accepted: 9 March 03 /Published: 9 March 03 Abstract: Magnetic Induction Tomography (MIT) is a non-inasie and non-intrusie imaging technique which interested in passie electrical properties of a material that are permittiity, permeability and conductiity. MIT applies sinusoidal electromagnetic field generated by excitation coil. The electromagnetic signal propagates and then penetrates the material located in the region of interest (ROI). The eddy currents are induced within the material itself due to its conductiity property. These eddy currents generate secondary fields and then are measured at the receier by the sensors. Secondary magnetic field carries the information of the electrical properties inside the material, thus it is ery important in reconstructing the image of the material through the use of image reconstruction algorithm. This paper is intended to discuss the modeling of Magnetic Induction tomography (MIT) in biological tissue imaging using two-port network technique hence deeloped the sensitiity maps which is ital in image reconstruction algorithm. Copyright 03 IFSA. Keywords: Magnetic induction tomography, Passie electrical properties, Biological tissue, Sensitiity maps, Two-port network.. Introduction Magnetic Induction Tomography (MIT) is a noninasie and non-intrusie technique. It is categorized as passie imaging modality. Besides MIT, are Electrical Impedance Tomography (EIT), Electrical Capacitance Tomography (ECT) and Magnetostatic Permeability Tomography (MPT) [] are in the same passie imaging family. EIT and ECT modalities use electrodes in their applications, the Article number P_64

2 Sensors & Transducers, Vol. 50, Issue 3, March 03, pp. -9 electrodes hae to be contacted with the body; while MIT and MPT are electrode less, thus proide opportunity to aoid ill-defined electrode-skin interface problems [, 3, 4]. MIT is interested in all passie three electrical properties of materials, which are conductiity ( ), permittiity (ε) and permeability (). In biomedical imaging, MIT is famously reported as focused to image the changes k of complex electrical conductiity k j distribution [5], since conductiity is always dominant in biological tissue compared to permittiity and permeability [6, 7] especially in dispersion range (0 khz 0 MHz) [8]. Howeer, different to metallic object, the alue of conductiity in biological tissue is relatiely ery small [9]. Reconstruction of complex conductiity distribution cannot be done without an image reconstruction algorithm which needs sensitiity maps in producing images[0], hence clear and accurate image needs a practical image reconstruction algorithm []. Most of tomographic images were deried from back projection algorithm and in order to derie this algorithm which results in the solution to the inerse problem, the forward problem must be soled first. The forward problem determines the theoretical output of each of the sensors when the sensing area is considered to be two-dimensional. The forward problem can be soled by using the analytical solution of sensitiity maps which produces the sensitiity matrices []. Sensitiity calculation can be done through seeral techniques that are based on finite element method (FEM) [8, 3, 4], analytically [8, 5] and experimentally [6]. Simulation on the forward model is initially done to ensure that correct fundamentals of process tomography technique hae been implemented specifically in image reconstruction [7]. This paper discusses the modeling of MIT system using two-port network technique which inoles reciprocity theorem, sensitiity maps and image reconstruction algorithm.. Fundamentals of Physics in MIT MIT inole the application of electromagnetic field (primary field), B 0 generated at the excitation coil. This primary field interacts with the tissue located in the ROI, and this tissue, depends on its conductiity alue produces its own field known as secondary field, B or eddy current field [8] as shown in Fig.. Secondary field which has the characteristic information of the tissue is detected by the measurement sensors at the receiing side [9, 0]. These measured data undergoes signal conditioning circuit for noise remoal before being used as the input to the image reconstruction algorithm for image reconstruction process. Fig.. Fundamental principal of MIT modality. All interactions between electromagnetic fields and biological tissues follow the Maxwell s rules [0,, ]. Equation () is Faraday s law which stated that, electric field, E [V m - ] is induced in a medium when time arying magnetic field density; B [Wb m - ] with frequency, ω [rad s - ] is applied. E jb () In scalar potential and ector potential terms, electric field, E can be presented as E ja () where [V] and A [Wb m - ] are scalar potential and ector potential respectiely [3]. Vector potential A can be represented as ector potential due to primary field, A 0 and ector potential due to secondary field, A [4, 5]. o A I o 4 dl r o J c A dv 4 r, (3) (4) where dl [m] is the element of the coil, r is the distance between the coil length element and the point Ao is calculated, I [A] is the sinusoidal current amplitude in the excitation coil, J c [A m - ] and dv [m 3 ] are the olume element of the material. Ampere s law as in equation (5) explained on the relation between the induced conduction current density, J c and displacement current, D [C m - ] with the magnetic field, H [A m - ] in the existing of electric field, E. H ( j ) E E je J c jd (5) 3

Sensors & Transducers, Vol. 50, Issue 3, March 03, pp. -9 In biological tissue (where ), displacement current is normally neglected due to ery small alue compared to conduction current [5, 6].

3 Sensors & Transducers, Vol. 50, Issue 3, March 03, pp. -9 In biological tissue (where ), displacement current is normally neglected due to ery small alue compared to conduction current [5, 6]. The induced current, J c in the material, in turn, produced secondary magnetic field, B and is gien by: B A (6) At the measurement side of the MIT system, the receiers detect both primary field, B 0 and secondary field, B. Howeer since this system had implemented receier positioning arrangement technique in such that, it is insensitie to the primary field, thus it is assumed that the signal measured at the receiers are only due to the secondary field, B [3]. The induced oltage, [V ] in the receier due to this secondary field, B can be calculated through Lenz s law [7] by integrating magnetic field oer the receier coil surfaces, ds [m ]. 3. Hardware Model j B ds (7) In this experiment, a noel TRI-COIL sensor jig design as in Fig. had been used. consist of three slots of 4cm 4cm 4cm in size. There are three layers of slots in the jig design where each slot is located with transmitter in transmitter panels whereas sensors are located in the receier panels. The purpose of these slots are for minimizing the interference from the other coils in the jig system which may affected the measurements through introduction of errors in the measured signals. In this paper the modeling and image reconstruction algorithm are only focused on the single layer measurement basis for the sake of simplicity in the modeling itself. 4. Two-Port Network Modeling In MIT modeling based on the application in biological tissue, seeral assumptions are made. The assumptions are neglecting of wae propagation delay effect at low frequency [, 7, 4], skin depth of the electromagnetic field in the material is larger than the dimensions of the sample [8, 4, 8], homogeneous and isotropic model of tissue conductiity [6, 4, 9] and the tissue is not magnetizable, where relatie permeability, r [7, 30]. Linear two-port network model as in Fig. 3 is among the technique used in MIT modeling. The reciprocity theorem [8, 9, 3] is applied in its implementation. There are seeral parameter models can be used in describing two-port network; Impedance (), Admittance (Y), Transmission (a), Hybrid (h) and Inerse Hybrid (g). Howeer this paper only focused on Impedance () model, which a general expression can be deried with ports and are fed by a current I and I respectiely. It is assumed that port represents excitation coil while port is the receiing coil of an MIT system. (a) (b) Fig. 3. Two-port network model. The general equation of model is (c) Fig.. A noel TRI-COIL sensor jig design: a) Isotropic iew; b) Top iew and c) Single panel iew. This design which consists of 8 panels of transmitters and 8 panels of receiers, arranged alternately in equidistance between each in circular manner. These panels are made of aluminum and where [ ]= [ I ] [ ] (8) I I 0 I (9) 4

4 Sensors & Transducers, Vol. 50, Issue 3, March 03, pp. -9 (0) I0 I () I 0 I () I0 I Both and are local impedance of the port and port respectiely, while and are transfer impedance; between the two ports (port and port ) is the interest in this modeling technique. Based on the reciprocity theorem, and are same since both of them representing the same portion of biological tissue under inestigation as explained in Fig. 4. ke EdV j H H dv (4) E and Hare electric field and magnetic field respectiely when I is fed to port, while E and H are electric field and magnetic field respectiely when I is fed to port. If permeability is constant, the second term is anished and changes for a small oxel will be proportional to only the complex conductiity change and the scalar products of the electric field ke EdV ke E (5) In MIT system, by definition the transfer impedance, [8, 9] is gien by, (6) I exc [V] is the secondary signal measured at where the receier coil. In relation to that, the sensitiity, S in bio-impedance is usually defined based on Geselowitz theorem [6, 8, 30] which is Fig. 4. Interaction of primary field excited from excitation coil #7 (Ex7) on the small portion of object and the receied secondary field by receier coil #5 (R5). Primary field excited at coil#7 with ( Ex7, Iex7 ) interacts with biological tissue with impedance, and secondary field generated by this tissue then is measured at detected at receier coil#5 with the alue I (, Rx5 Rx5 ( Rx5, I Rx5 ). Based on reciprocity theorem, if Rx5 ), excited a field on the same tissue, then the receied signal at Ex7 will be (, Ex7 ex7 ). This can be represented as ( Ex7, I ex7 ) ( Rx5, I rx5) (3) Through this theorem, it is assumed that the transfer impedance change, of the two-port network system is due to a small change k of complex conductiity ( k j ) and permeability, of the passie electrical properties (PEP) in the space filled with the electromagnetic field [30]. The transfer impedance change, of a two-port network system is due to changes of complex conductiity and/or permeability and is gien as I Insert (5) into (7) S (7) k S E E (8) For a conductie spherical oxel inside a homogeneous magnetic field B, eddy currents (J) and, consequently the electric field (E = J/κ) will be parallel to the sphere surface [8], therefore: Hence E E B B (9) S kb B, (0) k depends only on the perturbation characteristics. Hence sensitiity maps normalization [9] is gien by S S( x, y ) i i norm ( x, () wi where w i is the area or olume of the i th element. In this small scale system, 64 sensitiity maps hae been generated due to 64 possible interactions between 8 excitation coils and 8 receier coils. Examples of sensitiity maps for excitation coil # (Ex) are shown in Fig. 5 and sensitiity maps normalization is in Fig. 6. 5

5 Sensors & Transducers, Vol. 50, Issue 3, March 03, pp. -9 (a) (b) (c) (d) (e) (f) (g) (h) Fig. 5. Sensitiity maps of excitation coil (Ex) with receiers (Rx). a) Ex Rx, b) Ex Rx, c) Ex Rx3, d) Ex Rx4, e) Ex Rx5, f) Ex Rx6, g) Ex Rx7 and h) Ex Rx8. 6

Sensors & Transducers, Vol. 50, Issue 3, March 03, pp. -9 SIMULATED SAMPLE RECONSTRUCTED IMAGES (a) Sample. Fig. 6. Sensitiity maps normalization pattern. 5. Image Reconstruction Algorithm Image reconstruction algorithm is the heart in any tomography modality since it conerts the captured data at the sensor into an image.

In this paper, Linear Back Projection (LBP) had been implemented in the image reconstructions process due to its simplicity and its fast in processing [6].

equals to dimension of sensitiity maps; S Tx, Rx is the signal loss amplitude of receier Rx-th for projection Tx-th in unit of olt and M Tx, Rx ( x, is the normalized sensitiity matrices for the iew

This forward problem is soled through the use of 64 generated sensitiity maps. The reconstructed images in Fig.

This may due to inadequate linear algorithm in reconstructing the nonlinear behaior of the magnetic interaction in the ROI.

6 Sensors & Transducers, Vol. 50, Issue 3, March 03, pp. -9 SIMULATED SAMPLE RECONSTRUCTED IMAGES (a) Sample. Fig. 6. Sensitiity maps normalization pattern. 5. Image Reconstruction Algorithm Image reconstruction algorithm is the heart in any tomography modality since it conerts the captured data at the sensor into an image. There are seeral types of tomographic image reconstruction algorithm; howeer it depends on the types of tomography and the application itself. In this paper, Linear Back Projection (LBP) had been implemented in the image reconstructions process due to its simplicity and its fast in processing [6]. In mathematical term LBP can be represented as 8 Tx0 8 V ( x, S X M Tx, Rx( x, () LBP Rx0 Tx, Rx where, V LBP ( x, is the oltage distribution obtained using LBP algorithm in n n matrix, where n equals to dimension of sensitiity maps; S Tx, Rx is the signal loss amplitude of receier Rx-th for projection Tx-th in unit of olt and M Tx, Rx ( x, is the normalized sensitiity matrices for the iew of Tx-Rx. 6. Results and Discussion Based on this algorithm, reconstructed images of three simulated samples are shown in Fig. 7. This forward problem is soled through the use of 64 generated sensitiity maps. The reconstructed images in Fig. 7 show that the system is sensitie to the location of the perturbations; howeer in term of size and shape, it is out of accuracy. This may due to inadequate linear algorithm in reconstructing the nonlinear behaior of the magnetic interaction in the ROI. Upgrading on the algorithm is crucial in enhancing the accuracy in both location and size of the perturbation. The pixel threshold alue related algorithm may proide the solution to this problem. (b) Sample. (c) Sample 3. Fig. 7. Three simulated samples and its reconstructed images using Linear Back Projection Technique (LBP) algorithm. 7. Conclusions Two-port network modeling technique of MIT system has been presented and through this technique 64 sensitiity maps of this MIT system hae been generated. Based on the reconstructed images, it is found that two-port network is capable in soling the forward problem of an MIT system. Howeer further inestigations are needed in increasing the quality of the images through implementation of more promising image reconstruction algorithm in soling nonlinear phenomena within the ROI. Acknowledgements This work was supported in part by the Malaysian Goernment under Science Fund Grant SF0889. The authors also gratefully acknowledge the helpful comments and suggestions of the reiewers, which hae improed the presentation. 7

7 Sensors & Transducers, Vol. 50, Issue 3, March 03, pp. -9 References []. Soleimani, M. Computational aspects of low frequency electrical and electromagnetic tomography-a reiew Study, International Journal of Numerical Analysis and Modelling, 008, 5, 3, pp []. akaria,., Rahim, R. A., Mansor, M. S. B, Yaacob, S., Muzakkir, N., Muji, S.. M., Rahiman, M. H. F., Aman, S. M. K. S., Adancements in transmitters and sensors for biological tissue imaging in magnetic induction tomography, Sensors,, 6, 0, pp [3]. Babushkin, A. K., Bugae, A. S., Vartano, A. V., Korzheneskii, A. V., Sapetskii, S. A., Tuikin T. S., Cheperenin, V. A. Deeloping methods and instruments of electromagnetic tomography for studying the human brain and cognitie functions, Bulletin of the Russian Academy of Sciences: Physics, 75,, 0, pp [4]. Watson, S. A highly phase-stable differential detector amplifier for magnetic induction tomography. Physiological measurement, 3, 7, 0, pp [5]. Merwa, R., Hollaus, K., Scharfetter, H. 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Scharfetter, H., Casañas, R., Rosell, J.

8 Sensors & Transducers, Vol. 50, Issue 3, March 03, pp. -9 [9]. Scharfetter, H., Rauchenzauner, S., Merwa, R., Biró, O., Hollaus, K., Planar gradiometer for magnetic induction tomography (MIT): Theoretical and experimental sensitiity maps for a low-contrast phantom, Physiological Measurement, 5,, 004, pp [30]. Scharfetter, H., Casañas, R., Rosell, J., Biological tissue characterization by magnetic induction spectroscopy (MIS): requirements and limitations, IEEE Transactions on Biomedical Engineering, 50, 7, 003, pp [3]. Gürsoy, D., Scharfetter, H., Anisotropic conductiity tensor imaging using magnetic induction tomography, Physiological Measurement, 3, 8, 00, pp Copyright, International Frequency Sensor Association (IFSA). All rights resered. ( 9

Forward Problem in 3D Magnetic Induction Tomography (MIT)

Forward Problem in 3D Magnetic Induction Tomography (MIT) Manuchehr Soleimani 1, William R B Lionheart 1, Claudia H Riedel 2 and Olaf Dössel 2 1 Department of Mathematics, UMIST, Manchester, UK, Email: