A Simulation Study for Electrical Impedance Tomography

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tomography(EIT), magnetic induction tomography(MIT), ... computational model is a computer program, or network of ... Md. Ali Hossainis a student of the Department of Computer Science and ... 2012 IJCIT, ISSN 2078-5828 (PRINT), ISSN 2218-5224 (ONLINE), VOLUME 02, ISSUE 02, MANUSCRIPT CODE: 120110. 55.
COPYRIGHT © 2012 IJCIT, ISSN 2078-5828 (PRINT), ISSN 2218-5224 (ONLINE), VOLUME 02, ISSUE 02, MANUSCRIPT CODE: 120110

A Simulation Study for Electrical Impedance Tomography Md. Ahaduzzaman Khan, Dr. Ahsan-Ul-Ambia, Md. Ali Hossain, and Md. Robiul Hoque

particular system. Computer simulations have become a useful part of mathematical modeling of many natural systems in physics (computational physics), astrophysics, chemistry and biology, human systems in economics, physiology, psychology, social science, and engineering. Simulations can be used to explore and gain new insights into new technology, and to estimate the performance of systems too complex for analytical solutions. Simulation technique is widely used in the biomedical research for feasibility and performance analysis of new methods and devices. After conception and implementation of any new medical image processing algorithm, validation is an important step to ensure that the procedure fulfils all requirements at the initial design stage. Although the algorithm must be evaluated on real data, a comprehensive validation requires the additional use of simulated data since it is impossible to establish ground truth with in vivo data. Experiments with simulated data permit controlled evaluation over a wide range of conditions (e.g., different levels of noise, contrast, intensity artifacts, or geometric distortion). Such considerations have become increasingly important with the rapid growth of neuroimaging, i.e., computational analysis of brain structure and function using brain scanning methods such as positron emission tomography and magnetic resonance imaging. The popular biomedical imaging methods are X-ray computed tomography (CT) imaging, MRI, ultrasound imaging, and positron emission tomography (PET). Resolution of X-ray CT imaging is very good; but, it damages the tissue. Resolution of MRI is also good but it does not cause any tissue damage. In case of MRI , the instrument is very expensive and too large in size. Electrical impedance imaging is a method of reconstructing the internal impedance distribution of a human body based on the measurements at the surface. It has no biological hazard and allows long-term monitoring because it requires very small currents. One common method of electrical impedance imaging known as electrical impedance tomography(EIT) is promising, but it has the difficulty of attaching a large number of electrodes to the body surface [6]–[8]. Another method of electrical impedance imaging known as magnetic induction tomography(MIT) in which magnetic field is applied from an array of excitation coils to induce eddy currents in the body and the magnetic field from these currents is then detected using a separate set of sensing coils [9], [10]. In MIT, the measurement sensitivity at the center region is much less than that obtained in the peripheral regions. In the last decade, many studies have reported on MIT. The great advantage of MIT in contrast to EIT is the contactless operation [12]. However, the sensitivity of this

 Abstract—Electrical Impedance Tomography (EIT) is the technique to visualize spatial distribution of Electrical resistivity (or conductivity) inside the object, such as human body. Unlike MRI and CT, EIT uses diffusion of current to deduce conductivity distribution. Currents are produced by two ways: One is by applying electric field and another is by applying magnetic field from outside the body. The resulting electrical potentials are measured, and the process may be repeated for numerous different configurations of applied current. In this research, validity of a method of EIT is checked by simulation study. Main Principle of this method is to apply magnetic field to control the current distribution in the subject. The forward problem, that involves the modeling of the subject and mathematical calculation of resulting voltages from that model, is described in this work. A method based on Least Square Error Minimization technique is proposed for solution of the inverse problem. For various patterns of magnetic field, various voltages are found from which one dimensional conductances are calculated . Two dimensional images are made from one dimensional conductance distribution by inverse radon transform. Then reconstructed images are compared with simulated images. Index Terms—Biomedical imaging, electrical impedance tomography(EIT), magnetic induction tomography(MIT), simulation in biomedical imaging .

I. INTRODUCTION Biomedical Imaging is the science and the branch of medicine concerned with the development and use of imaging devices and techniques to obtain internal anatomic images and to provide biochemical and physiological analysis of tissues and organs. A computer simulation, a computer model, or a computational model is a computer program, or network of computers, that attempts to simulate an abstract model of a ● Md. Ahaduzzaman Khan is a student of the Department of Computer Science and Engineering, Islamic University, Kushtia-7003, Bangladesh. E-mail: [email protected] ● Dr. Ahsan-Ul-Ambia is serving in the Department of Computer Science and Engineering , Islamic , University, Kushtia-7003, Bangladesh. E-mail: [email protected] ● Md. Ali Hossain is a student of the Department of Computer Science and Engineering , Islamic University, Kushtia-7003, Bangladesh. E-mail: [email protected] ● Md. Robiul Hoque is serving in the Department of Computer Science and Engineering , Islamic University, Kushtia-7003,Bangladesh. E-mail: [email protected]

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method is not uniform over the measurement area [12]. Another difficulty encountered with this method is that the excitation field also induces a signal in the sensing coil, and the signal due to the eddy current in the material is normally much smaller in comparison [13]. In order to overcome this difficulty, various methods have been proposed [12], [14]. However, there still remain some significant drawbacks [14]. For example, using a planar gradiometer arrangement, a ghost object can be recognized in the reconstructed image [17]. In some cases, to reconstruct the image from measurement data, a weighted backprojection method has been proposed [18]. Unfortunately, the weights have been calculated only in the case of conducting perturbations in empty space, which is quite different from anatomical structures [15]. In this research, we have checked the validity of a method of EIT by simulation study using Matlab software. In that method, magnetic field is applied to control the current distribution in the body. In forward problem, the subject is modeled and resulting voltages due to the magnetic field is calculated from that model. Inverse problem is solved using Least Square Error Minimization(LSEM) method. For various patterns of magnetic field, various voltages are found from which one dimensional conductance distribution are calculated. From one dimensional conductivity distribution, two dimensional images are made by inverse radon transform. Then reconstructed images are compared with simulated images.

measurement part of the body. Eddy current is produced by an alternating magnetic field. The current distribution in the subject is changed by shifting the magnetic core. During this shifting, the output voltage is measured. This measured voltage is used to calculate the conductivity distribution in the measurement region. When the magnetic field is applied by placing magnetic cores at position i on the x-axis, an electromotive force is produced in each segment as shown in Fig. 4. The electromotive force produced in jth segment is proportional to the magnetic field intensity in the segment . We assume that the magnetic field intensity is uniform in the y and z directions in each segment. When the core position is at i, introducing a proportionality constant a, can be written as: =a

....................................(1)

where, is the average value of magnetic field pattern f(x) over the segment j. According to the superposition theorem the eddy current

through

is equal to the

sum of each eddy currents produced by each electromotive force separately and this can be written as: =

+

+…+

II. METHODOLOGY Where

Forward problem involves the calculation method of output voltages from known conductivity using the electrical model of the subject. Since, we can have a finite number of independent measurements, we cannot hope to obtain conductivity at every point in the interior of the subject. Thus, we have to make some approximations and to model our subject into an approximate resistor network. First step of forward problem is modeling of the subject. In most EIT and MIT researches the Finite Element method (FEM) was used as formulated by the Complete Electrode Model[7],[19]-[21]. In FEM subject is divided into a number of small elements and the conductivity of each element is considered to have a constant value. Boundary Element Method (BEM) and Finite Difference Method are used in some research [22][23]. In these methods the number of elements is much higher than the number of independent measurement, so that the system is under-determined [15]. A lumped-parameter model was used in [24] but the network used in this model was very complicated [6]. In this research, a simple parallel resistance model has been used for the calculation of measurement voltages in forward problem and also reconstruction in the inverse problem. For the calculation of the conductivity distribution, the measurement region is divided into n-segments as shown in Fig. 1, and is considered as a combination of n-conductances in parallel as shown in Fig. 2(a). Here, is the average conductance of the i-th segment. The resistance between each pair of segments is negligible and thus, the circuit is simplified, as shown in Fig. 2(b). Principle of this method is explained in Fig. 3. Two electrode bands are used at the top and the bottom of the

Hence, the voltage

across

can be written as:

Radious of the subject Radious of the embedded object gi width of each segment (w)

Vn Depth of subject and objects(d) Fig. 1. Segmentation of the subject.

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-----

----

----

-----

-----

-----

-----

- --- - -

-------

-------

-----

-------

----(x) i

----j

x n-1

Normaliz ed magnetic field intensity

----

----

-----

-----

(a)

-----

-------

----

X

(b) Fig. 4. Equivalent circuit with a magnetic field. Fig. 2. Equivalent circuit of measurement part

The left hand side of (3) can be rewritten as: = + +…+

Eddy current

Where, = Now (3) becomes:

Magnetic core Measurement area

+

+…+

=

This equation represents the relationship between the conductance of each segment and the voltage when the core position is located at i. The value of Gall/a is constant and can be determined by proper calibration. Now for each core position i=1 to n-1, we get following n-1 equations ,which can be written in matrix form as:

Measurement voltage (Vn)

(a)

Magnetic core

.

.

.

.

. .

.

.

.

Alternating magnetic field

Or in vector form

Measurement voltage( )

KG=M ………………….(4) Therefore, if we can solve this equation directly, we can estimate the conductance of each segment. However, due to the measurement errors in and the magnetic field, we cannot use a direct method for solving this equation. Instead, the least square error minimization (LSEM) method is employed and the 1-D conductance distribution of the body can be obtained. The steps of the LSEM method are as follows: 1) Assume initial conductance distribution. 2) Calculate the left-hand side of (4), i.e., KG. 3) Calculate square error using the formula …………………. (5) 4) Update the conductance value using the equation = (∂E/∂ ) …………………. (6) where η is a coefficient and it is called step size parameter. 5) Repeat steps 2–4 to minimize the error.

Direction of magnetic core movement (b) Fig. 3. Principle of of the method: (a) schematic view (b) top view

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By changing the direction of the measurements, we obtain the 1-D conductance distribution for each direction. From these distributions, we get the 2-D image of the conductivity distribution using the back projection algorithm. In the LSEM method, the square error (E) gradually decreases with increasing iterations, and converges as shown in Fig. 5 (for η =1.10). To decide the stopping criteria, we used the slope of this error-decreasing curve. After our observation of some pre-experimental results, we choose the criteria for stopping the iteration to be defined as:

y

x

Where is the sum of squared errors at the i-th iteration. In our simulation, we fixed j=51, k=1 and

Fig. 6. Image reconstruction from projection data

III. IMAGE RECONSTRUCTION In this research, we have reconstructed two-dimensional image from one-dimensional(1D) conductances using inverse Radon transform, which is depicted pictorially in Fig. 6 for angles 0°, 45°, and 90°. IV. SIMULATION RESULTS One Embedded Object Detection Fig. 7 to Fig. 15 are obtained for the condition: muscle’s resistivity(0.0002 Ω-m) within fat’s resistivity(0.0005 Ω-m). In these figures η is step size parameter and β is stopping criteria. For η=1.10, and β=0.009, 0.005, 0.001, one-dimentional(1D) curves are obtained as shown in Fig.7 to Fig. 9:

Fig. 7. Simulated and reconstructed 1D curves for η= 1.10 and β= 0.009

2

1.5 Sum of square errors

1

0.5

0 20

2000 200

2000

20000

Number of iterations

Fig. 5. Error Convergence of the LSEM process Fig. 8. Simulated and reconstructed 1D curves for η= 1.10 and β= 0.005

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Two Embedded Objects Detection The first row of Fig. 13 shows simulated images and second row shows reconstructed images for the condition: the radii of the embedded objects are r&r2= 5 mm and of the subject is R= 40 mm, η= 1.10, β= 0.001, resistivity of the subject is ρ1= 0.0005 Ω-m and of the embedded objects are ρ2&ρ3= 0.0002 Ω-m , the locations of the embedded objects in the 1st,2nd ,3rd ,and 4th columns are: (x1,y1) and (x2,y2)=[{(x1= -20,y1=20) and (x2= 20, y2= -20 )},{(x1=20,y1=20) and ( x2= -20,y2= -20)},{(x1=0 ,y1=0) and ( x2=30, y2=0)},and{(x1=0,y1=0) and (x2= -20,y2= 0 ) }], time to produce images of those columns are: T= 4,4,7, and 9 minutes. The images of Fig. 14 are obtained for the condition: the radii of the embedded objects are: r1&r2= 15 mm and of the subject is: R=40 mm, η= 1.10, β= 0.001, resistivity of the subject is ρ1= 0.0005 Ω-m and of the embedded objects are ρ2&ρ3= 0.0002 Ω-m, the locations of the embedded objects in the 1st,2nd ,and 3rd columns are: (x1,y1) and (x2,y2)=[{( x1=15,y1=15) and (x2= -15,y2= -15)},{(x1= -15,y1=15) and (x2=15,y2= -15)}, and{( x1=0,y1=0) and (x2= -15,y2=0)}], time to produce images of those columns are: T= 3,3, and 12 minutes. The images of 1st and 2nd columns of Fig. 15 are obtained by changing both radios and center positions of embedded objects. Images of 3rd and 4th columns of fig. 15 are obtained by keeping radios unchanged and by changing center position. In the 1st ,2nd ,3rd ,and 4th columns, radii of the embedded objects are :{(r1=9 mm, r2=13 mm), (r1=13 mm, r2=17 mm), (r1=17 mm, r2=13 mm), (r1=17mm, r2=13mm)}. In those columns, center positions of embedded objects are: (x1,y1) and (x2,y2)= [{(x1=15,y1=15),x2=-15,y2=-15)},{(x1=15,y1=15),(x2=-1 3,y2=-13)},{(x1=13,y1=13), (x2= -15,y2= -15)},{(x1= -13,y1=13 ), (x2= 15,y2= -15)}], time to produce images of those columns are: T= 3,4,1, and 3 minutes.

Fig. 9. Simulated and reconstructed 1D curves for η= 1.10 and β= 0.001.

For the condition: the value of radios of one embedded object is r=20 mm, it’s location is (x= -10, y= -10 ), η= 1.10, β= 0.001, for angles( 1D Fig. 10 and 2D Fig. 11 are obtained:

angles(

Fig. 10. Simulated and reconstructed 1D curves for r=20 mm, η= 1.10, β= 0.001, and ( x= -10, y= -10).

Fig. 11. (a) Simulated and (b) Reconstructed 2D images for angles( r= 20 mm, , η= 1.10, β= 0.001,and (x= -10,y= -10) .

The first row of Fig. 12 shows simulated images and second row shows equivalent reconstructed images. Here, radios of the embedded object is r= 5 mm and of the subject is R= 40 mm. Resistivity of the subject is ρ1=0.0005 Ω-m and of the embedded object is ρ2= 0.0002 Ω-m. The locations of the embedded objects in the 1st,2nd ,and 3rd columns are:{(x=0,y=0)}, {(x= -20,y= -20 )},and {(x=20,y= 20)}.

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Fig. 12 . Simulated and reconstructed 2D images when r= 5 mm ,R= 40 mm, η= 1.10, β= 0.001, the location of the embedded object in the 1st,2nd ,and 3rd columns are: (x,y)= {(x= 0,y= 0), (x= -20,y= -20),and (x= 20,y= 20)}.

Fig. 13. Simulated and reconstructed 2D images when r1& r2= 5 mm, R= 40 mm, η= 1.10, β= 0.001, the locations of the embedded objects in the 1st, 2nd , 3rd ,and 4th columns are: (x1,y1) and (x2,y2)= [{(x1= -20, y1=20) and (x2= 20, y2= -20 )},{(x1=20, y1=20) and (x2= -20, y2= -20)},{(x1=0,y1=0) and (x2=30,y2=0)},and{(x1=0,y1=0) and (x2= -20,y2=0)}].

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Fig. 14. Simulated and reconstructed 2D images when R= 40 mm, r1&r2=15 mm, P1= 0.0005 s/m, p2&p3= 0.0002 s/m, the locations of the embedded objects in the 1st,2nd,and3rd columns are : (x1,y1) and (x2,y2)= [{( x1= 15, y1=15) and ( x2= -15, y2= -15 )}, {(x1= -15,y1=15) and (x2=15,y2= -15)}, and{(x1=0,y1=0) and (x2= -15,y2=0)}], η= 1.10, β= 0.001.

Fig. 15. Simulated and reconstructed 2D images when radios of embedded objects are: {(r1=9 mm, r2=13 mm),( r1=13 mm, r2=17 mm),(r1=17 mm, r2=13 mm),( r1=17 mm, r2=13 mm)}, center positions of embedded objects are: (x1,y1) and (x2,y2)= [{(x1=15,y1=15),(x2= -15,y2= -15)},{(x1=15,y1=15),(x2= -13,y2= -13)},{(x1=13,y1=13), (x2= -15,y2= -15)},{(x1= -13,y1=13 ), (x2= 15,y2= -15)}], η= 1.10, β= 0.001.

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[18] H. Griffiths,W. R. Stewart, andW. Gough, “Magnetic induction tomography.A measurement system for biological tissues,” Ann. New York Acad.Sci., vol. 873, pp. 335–345, 1999. [19] T Murai and Y Kagawa, “Electrical Impedance Computed Tomography Based on Finite Element Model”, IEEE Trans. on Biomed. Eng., Vol. 32(2) March 1985. [20] P J Vauhkonen M Vauhkonen, T Savolainen, J.P Kaipio, “Three-dimensional electrical impedance tomography based on the complete electrode model”, IEEE Trans. on Biomed. Eng., Volume 46(9), pp 1150-1160, 1999. [21] K Hollaus, C Magele, R merwa and H Scharfetter,” Fast calculation of the sensitivity matrix in magnetic induction tomography by tetrahedral edge finite elements and the reciprocity theorem”, Physiol. Meas., Vol.25, pp. 159-168 2004. [22] J C de Munck, T J C Faes and R M Heethaar, “The Boundary element Method in the forward Problem of Electrical Impedance Tomography”, 19th Int. Conf. IEEE/EMBS 1997, Chicago, USA. [23] A Morris, H Griffiths and W Gough, “A numerical model for magnetic induction tomographic measurements in biological tissues”, Physiol. Meas., Vol.22, pp. 113-119, 2001. [24] K A Dines and R J Lytle, “Analysis of electrical conductivity imaging,” Geophysics, Vol. 46, pp. 1025-1036, 1981.

V. DISCUSSION AND CONCLUSION This method can give the image of the relative conductivity distribution not the absolute values of the conductivities. Simulation technique has been used for the performance, sensitivity and detectability analysis of the method. The resultant voltages were calculated using the simulation program. These calculated voltages data was then used as the input of the reconstruction program. The estimated absolute values of the conductivities were not as accurate as desired. However, the relative change in resistivity was clear in the reconstructed images. Images obtained by LSEM Method will not become accurate as simulated images. The edge of embedded object in reconstructed image is not clear. When embedded objects are overlapped, then, they are not clear in the reconstructed image. Fig. 9 to Fig. 15 are obtained for η= 1.10, and β= 0.001. For, η >1.10, and β > 0.001, images also produced, in that case, time required to produce image is low, but quality of image is poor. For, η< 1.10, and β< 0.001, images also produced, in that case, time required to produce image is high, but quality of image is unchanged. In this research, Noise that can be occurred in practical are not considered here. Thus, the experimental results may change in practical environment.

Md. Ahaduzzaman Khan was born in Faridpur, Bangladesh, on December 9,1987. He received the B.Sc. and M.Sc. degrees from the Department of Computer Science and Engineering, University of Islamic University, Kushtia, Bangladesh, in 2008 and 2009, respectively. His current research interests include biomedical imaging, biomedical signal and image processing, and bioinformatics. Mr. Khan is an Associate Member of the Bangladesh Computer Society. Dr. Ahsan-Ul-Ambia was born in Nawabgonj, Bangladesh. He received the B.Sc.,and M.Sc. degrees from the Department of Applied Physics and Electronics, University of Rajshahi, Rajshahi, Bangladesh, in 1996 , and 1998 respectively. He received the PhD degree from the Graduate School of Science and Technology, Dept. of Information Science and Technology, Shizuoka University,Japan, in September 2009 respectively. He was an Assistant Programmer in a private company .He is serving as an Associate Professor with the Department of Computer Science and Engineering (CSE), Islamic University, Kushtia. He joined at Islamic University in October 1999 after completion his M.Sc. degree. His current research interests include biomedical imaging, biomedical signal and image processing, and bioinformatics. He has several papers related to these areas published in national and international journals as well as in referred conference proceedings. Dr. Ambia is an Associate Member of the Bangladesh Computer Society and a member of the Institute of Electronics, Information and Communication Engineers, Japan.

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url: www.ijcit.org or www.ijcit.uap-bd.edu

Md. Ali Hossain was born in Manikganj, Bangladesh, on December 30, 1984. He received the B.Sc. and M.Sc. degrees from the Department of Computer Science and Engineering, University of Islamic University, Kushtia, Bangladesh, in 2008 and 2009, respectively. He is serving as an Lecturer with the Department of Computer Science and Engineering (CSE), Bangladesh University, Dhaka. His current research interests include biomedical imaging, biomedical signal and speech recognition and bioinformatics. Mr. Hossain is an Associate Member of the Bangladesh Computer Society and Executive Member of Islamic University Computer Association (IUCA). Md. Robiul Hoque has received B.Sc(Hon’s) and M.Sc. Degrees from the Dept.of Computer Science and Engineering, Islamic University, Kushtia, Bangladesh, in 2000 and 2001 respectively. He is serving as an Assistant Professor with the Department of Computer Science and Engineering (CSE), Islamic University, Kushtia. He joined at Islamic University in 2005, after completion his M.Sc. degree. His current research interests include Image processing; Optical Character Recognition; speech processing, analysis, synthesis and recognition; Natural language processing; Wireless Networking and Robotics.

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