We have proposed a new method of image reconstruction in EIT (Electrical Impedance

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Impedance tomography using internal current density distribution measured by nuclear magnetic resonance Eung Je Woo, Soo Yeol Lee, Chi Woong Mun Kon Kuk University, Department of Biomedical

1 Impedance tomography using internal current density distribution measured by nuclear magnetic resonance Eung Je Woo, Soo Yeol Lee, Chi Woong Mun Kon Kuk University, Department of Biomedical Engineering 322 Danwol-Dong, Choongju, Choongbuk, KOREA * Asan Institute for Life Sciences, NMR Lab Poongnapdong, Songpagu, Seoul, Korea, ABSTRACT We have proposed a new method of image reconstruction in EIT (Electrical Impedance Tomography). In EIT, we usually use boundary current and voltage measurements to provide the information about the spatial distribution of electrical impedance or resistivity. One of the major problems in EIT has been the inaccessibility of internal voltage or current data in finding the internal impedance values. The new method uses internal current density data measured by NMR imaging technique. By knowing the internal current density, we can improve the accuracy of the impedance images. Keywords : electrical impedance tomography, internal current density, image reconstruction, NMR, FEM 1. INTRODUCTION Dynamic and static imaging of the electric impedance in the human body has been tried for more than 10 years and now is called the electrical impedance tomography 1 In EIT, we use boundary current and voltage measurements to provide the information about the spatial distribution of electrical impedance or resistivity. Clinical applications include the estimation of cardiac parameters, cerebral hemodynamics, plethysmography, pulmonary ventilation, stomach emptying, and so on. It can also be used for the planning of therapies in which external electric currents are injected to the human body such as cardiac defibrillation and pacing. However, the inherent insensitivity of boundary measurements to the impedance of deep tissues and the nonlinearity of current flows have been major problems in achieving useful images. In this paper, we present a new modality of EIT by using NMR. The electric current density in the human body can be measured using conventional NMR imaging machine.2 Since the electric current produces the magnetic field, it has effects on the phase of NMR images. In experiments, 4.7 Tesla NMR imaging machine with 30cm clear bore has been used. For phantom study, a cylindrically shaped phantom with two small cylindrically shaped insulating objects was constructed. In the experiment, conventional spin echo imaging technique was used to reduce the experimental phase errors. Between 90 excitation RF pulse and 180 refocussing RF pulse, a positive current pulse was injected via two electrodes and between 180 refocussing RF pulse and data acquisition period, a negative current pulse with the same magnitude and duration was injected. After gathering full set of NMR signals, two-dimensional NMR images were reconstructed by Fourier transforms. Since the phase of each pixel in the NMR image is proportional to the magnetic field strength, the spatial O /94/$6.OO SPIE Vol / 377

2 distribution of the magnetic field strength can be calculated. Then, by solving Maxwell equation, the current density distribution can be found. We constructed a computer model of the phantom using the finite element method. The model provides the computed current density distribution due to the same current excitation. We implemented an image reconstruction algorithm based on the sensitivity matrix. The algorithm changes the conductivity distribution of the model using the measured and computed current density distribution data. In this paper, we present the reconstructed two-dimensional conductivity images by computer simulation technique. Reconstruction of the conductivity images of the phantom or human body requires more accurate measurements of current density and larger finite element model. In this paper, we tried the conductivity imaging by considering only the real part of the electrical impedance and the reconstructed image is presented as resistivity image since it is more popular in EIT The effect of current in NMR imaging 2. NMR IMAGING In the conventional nuclear magnetic resonance(nmr) imaging, the NIMR signal is radiated from nuclear spins lying in the uniform magnetic field. The uniform magnetic field is usually produced by superconductive magnet. In addition to the uniform magnetic field, gradient magnetic fields are applied in pulsed forms to resolve the spatial information. After demodulating the NMR signal, the signal can be written by S(t, t, t) = J p(x, y, z) exp [ j'y(xgt + ygt + zgt)] dxdydz (1) where S(t, t, t) is the NMR signal expressed in three-dimensional data acquisition axes t,, t, and. p(x, y, z) is the nuclear spin density function and y is the gyromagnetic ratio. G, Gy, and G are the gradient field strengths in x-, y- and z-direction, respectively, and spin relaxation effects are neglected. By three-dimensional Fourier transforming the signal, the spin density image can be reconstructed. If the NMR imaging is performed while injecting the electric current into the object, the NMR signal will be perturbed by the induced magnetic field. Since the induced magnetic field is superimposed on the main uniform magnetic field B0, the spin density image p'(x, y, z) obtained with current injection is given by p'(x, y, z) = p(x, y, z) exp [jy f B(x, y, z, t)dt] (2) 0 where B(x, y, z, t) is the magnetic field induced by the injection current, and T is the duration of the current pulse. Therefore, the current has effects on the phase of the reconstructed image. If the magnitude of the current is constant during the injection period, the induced magnetic field becomes also constant, and Eq. (2) can be simplified as p'(x, y, z) = p(x, y, z) exp [jyb(x, y, z)t]. (3) Therefore by measuring the phase in each pixel of the reconstructed image, the induced magnetic filed strength in that pixel can be calculated. 378 ISPIE Vol. 2299

2.2. Phantom We constructed a phantom shown in Fig. 1. At the top and bottom side of the cylindrically shaped phantom, we placed copper electrodes to inject currents into the phantom.

3 2.2. Phantom We constructed a phantom shown in Fig. 1. At the top and bottom side of the cylindrically shaped phantom, we placed copper electrodes to inject currents into the phantom. The width and length of the copper electrodes were 2 mm and 70 mm, respectively. Inside the phantom, two regions A and B were electrically isolated by acryl tubes. The region A was confined by a acryl tube with the inner diameter of 70mm and the length of 70mm. The region B was confined by acryl tubes with the inner diameter of 26mm, the length of 70mm, and the thickness of 4mm. The region A and B were filled with 0.2 mm MnCl2 solution with addition of the salt to control the conductivity of the solution NMR imaging sequence and experiments The NMR imaging pulse sequence shown in Fig. 2 has been used in the experiment. The pulse sequence is the conventional spin echo imaging pulse sequence with the addition of current pulses. For doubling phase shifts, two current pulses separated by it RF pulse were applied in a bipolar form. Since the it RF pulse compensates the effects of main magnetic field non-uniformity, the phase shift in the reconstructed image depends only on the current pulse. In experiments, NMR imaging was performed with a 4.7T NMR imaging machine with a 30cm clear bore. The potential difference between two electrodes was 1OV during the period of current injection. The 256 x 256 images in Fig. 3 were obtained with the TE(echo time) of 4Oms and the T of 2Oms and we also obtained other images not shown in this paper with the TE of 8Oms and the T of 5Oms. Fig. 3(a) is the real part and (b) is the imaginary part of the image. 3. COMPUTATION OF INTERNAL CURRENT DENSITY We computed the magnitude of the real and imaginary image shown in Fig. 3. By applying a simple thresholding technique to the magnitude image, we extracted the portion of the image only within the circular phantom. We computed the phase value of all pixels within the phantom. The phase image is shown in Fig. 4(a). Since the tan1 function returns a value between it and it, the phase image contains several discontinuities. We compensated these phase wrapping phenomena when we computed the current density Ȯnce we found the phase shift in the image due to the injection current pulse, the phase shift is proportional to the magnetic flus density produced by the injection current. Therefor, we can compute the current density by J=VxB/ji0 (4) When we computed the curl of the phase image, we applied a local phase unwrapping algorithm. Fig. 4(b) shows the image of the magnitude of the internal current density vectors obtained from real and imaginary images in Fig. 3. As shown in Fig. 4(b), we can see that the changes in current density are larger near electrodes and current flows through region with low electrical impedance Forward problem 4. RESISTIVITY IMAGE RECONSTRUCTION SPIE Vol / 379

4 We developed a finite element model of the phantom shown in Fig. 5(a). We used a finite element mesh generation program developed by Woo for Eff.3 We applied the boundary condition to electrode 1 and 2 and electrode 2 is taken as the reference for node voltages. We constructed several models with different number of elements. After we setup the admittance matrix for the model, we computed node voltages. Then, we computed current density vector of the i-th element J1 by where is the conductivity, E1 is the electric field intensity, Vij (j = 1, 2, 3 for triangular element) are node voltages of the i-th element. We assumed each element is homogeneous and isotropic. By taking the magnitude of each current density vector, we obtained the image of the computed current density distribution for homogeneous model with resistivity of 1OO-cm as shown in Fig. 5(b) Inverse problem Now the inverse problem is to find a conductivity distribution of the computer model which produces the same current density distribution measured by the NMR imaging technique. We can formulate the inverse problem as follows: MincIy) (6) (5) where J(4:Y) is the computed current density distribution of a finite element model with a conductivity distribution and j 4) is the measured current density distribution of an object with conductivity distribution Many different algorithms are possible to find a solution of Eq. (6) and (7). In EIT using boundary voltage and current measurements, several different algorithms have been proposed including backprojection, perturbation, Newton-Raphson algorithm, and so on.' In this paper, we implemented an algorithm based on the sensitivity matrix S of the current density to the conductivity value of each element. The ij-th element of the sensitivity matrix is computed from the model with as follows: (7) (8) where AJ1 is a change of current density of the i-th element due to the change of the conductivity of the j- th element (t). Reconstruction of conductivity image is an iterative process where we begin with an arbitrary initial conductivity distribution of the model. The process in the k-th iteration can be summarized as follows: Step 1: compute all for Jk Step 2: solve S &i = J( for LYk Step 3: check the direction of Aak Step 4: k+1 = cyk + &k 380/SP1EVo!. 2299

5 4.3. Computer simulation Step 5: compute 1(ak+1) We used a smaller model shown in Fig. 6 in the computer simulation to reduce the computation time. We placed an object with resistivity value of 3OO-cm at the center of the finite element model. By solving the forward problem for this model, we prepared a current density distribution data. This internal current density distribution was used as measured data in Eq. (7) for the solution of inverse problem. Now, the inverse problem can be stated as the problem of finding the resistivity distribution of the model starting from the model with homogeneous initial resistivity distribution. Fig. 7(a) and (b) shows the true resistivity image and the reconstructed image after 30 iterations, respectively. We can see that the object at the center is correctly found. However, we can also observe errors in the reconstructed resistivity values especially at the region where current density changes rapidly. 5. DISCUSSION We have proposed a new resistivity image reconstruction algorithm using the internal current density data measured by NMR imaging technique. Even though the measured current density data by NMR imaging technique and the result of the computer simulation of the inverse problem show the feasibility of the new method, we could not yet obtain accurate resistivity images of the phantom. Since the 256 x 256 NMR image includes the square area enclosing the phantom or subject, one of the problems is to accurately extract the region of image only within the phantom or subject. However, simple thresholding technique used in this paper is not good enough to accomplish this. The images shown in Fig. 4 contain some unnecessary pixels and the values of those pixels become sources of errors in current density data. Therefore, some image processing techniques such as the edge detection algorithm should be utilized. Another problem is in unwrapping the phase of the NMR image. Since the changes in current density must be finite, the phase of the NMR image should be continuous. However, since the tan1 function returns a value between it and it, we need to more carefully unwrap the computed phase using the fact that phase should be continuous. The conductivity image reconstruction algorithm proposed in this paper needs to be improved in several ways. The characteristics of the sensitivity matrix should be further studied. And a more sophisticated algorithm in finding the conductivity update should be derived. Larger finite element model with each element derived from each pixel of the NMR image should be used for maximal spatial resolution. More efficient resistivity image reconstruction algorithm might also be possible without using the minimization technique which requires a large amount of computation time. 6. CONCLUSION The impedance images reconstructed so far have poor spatial resolution and many limitations in clinical application mainly due to the inaccessibility of internal data and the inherent insensitivity of the boundary measurements to the impedance of deep tissues. The method presented in this paper utilizes the internal current distribution data measured from the NMR image. Even though this method requiring the NMR machine loose some advantages of EIT such as the simplicity and portability, it can be used in various ways together with NMR imaging. Further studies are required in the accurate computation of current density data and more efficient resistivity image reconstruction algorithm. Also, we must extend the two-dimensional study to the threedimensional one since the current flows in three-dimension. SPIEVo!. 2299/381

6 After we improve the method of computing the internal current density data, we plan to apply the current image reconstruction algorithm to reconstruct the resistivity images of the two-dimensional phantom. It will be also possible to use both boundary voltage and current data and internal current density data to improve the accuracy and spatial resolution of the impedance image. 7. REFERENCES 1. J. G. Webster, ed., Electrical Impedance Tomography, Adam Huger, Bristol, C. Scott, M. L. 0. Joy, R. L. Armstrong, and R. M. Henkelman, "RF current density imaging in homogeneous media," Mag. Resonance in Medicine, Vol. 28, pp , E. J. Woo, Finite Element Method and Image Reconstruction Algorithms in Electrical Impedance Tomography, PhD Thesis, University of Wisconsin-Madison, Department of Electrical and Computer Engineering, Copper electrode Figure 1. Phantom used in the experiments. 382 / SP1E Vol. 2299

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8 (a) (b) Figure 4. (a) Phase image ( it it) and (b) image of the magnitude of current density vectors. (a) Figure 5. (a) Finite element model of the phantom. (b) Computed current density distribution using the FEM for homogeneous resistivity distribution of 1OO-cm. (b) 384 / SPIE Vol. 2299

9 Figure 6. Finite element model used for the computer simulation of the inverse problem. (a) Figure 7. (a) True resistivity image with 3OO -cm object at the center. (b) Reconstructed resistivity image using the sensitivity matrix method. (b) SPIE Vol / 385

Dual modality electrical impedance and ultrasound reflection tomography to improve image quality

Dual modality electrical impedance and ultrasound reflection tomography to improve image quality K. Ain 1,4, D. Kurniadi 2, S. Suprijanto 2, O. Santoso 3 1. Physics Department - Airlangga University, Surabaya,