16 International Conference on Electrical Engineering and Automation (ICEEA 16) ISBN: 978-1-6595-47-3 Electrical Impedance Tomography Based on Vibration Excitation in Magnetic Resonance System Shi-qiang LI 1, Guo-qiang LIU 1,,*, Xue-gang XIN 3 and Xin-li WANG 1 1 Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing 119, China University of the Chinese Academy of Sciences, Beijing 149, China 3 Biomedical Engineering Department, Southern Medical University, Guang Zhou 51515, China *Corresponding author Keywords: Electrical impedance tomography, Magnetic resonance, Magneto-acoustic-electrical tomography, Motional-electrical tomography. Abstract. Because of low resolution, Electrical Impedance Tomography (EIT) had been criticized by the experts and scholars. Although the resolution of the Magnetic Resonance Electrical Impedance Tomography (MREIT) which is combined EIT with Magnetic Resonance Imaging (MRI) technology and the resolution of the Magneto-Acoustic-Electrical Tomography (MAET) which is combined EIT with ultrasonic technology are improved, there are still existing problems, which are the electrode RF shielding in MREIT, the difficulty of further improving resolution in MAET. Combining the technologies of MRI and MAET for mutual advantage, this paper proposed a new method of Magnetic Resonance Motional-Electrical Tomography (MRMET) based on the principle of MAET. The software Comsol and Matlab were used to establish a two-dimensional simulation model, and the forward problem and inverse problem of MRMET were researched on the simulation works. The simulation results could reflect the conductivity distribution inside the simulation model, and MRMET could solve the problems of the EIT combination technologies. Introduction Through the detections to the electrical characteristics of human tissue, Electrical Impedance Tomography (EIT) could explore the structure and function of the human body and achieve the early diagnosis to the diseases such as cancer. Because of the only measurement of body surface electric potential value, the large variation of the boundary shape and conductivity, and the low sensitivity to internal conductivity, the solving problem of EIT becomes serious illness and low resolution [1,,3]. In order to giving full play to the advantages of EIT functional imaging, scholars used the methods of combining EIT with other detection means to increase the amount of information and improve the resolution. There were two kinds of typical approaches: one is the combination of EIT and Magnetic Resonance Imaging (MRI) techniques, such as Magnetic Resonance Electrical Impedance Tomography (MREIT) [4] ; another one is a combination of EIT and ultrasound technology, such as Magneto Acoustic Tomography (MAT) and Magneto-Acoustic-Electrical Tomography (MAET) [5,6]. The combination technologies could effectively overcome the serious illness of the EIT inverse problem and the low resolution problem, but also brought new problems, which are the RF shielding effect in the strong magnetic field when the electrode excitation is used in MREIT; the poor anti-noise performance of imaging algorithm in MREIT [7,8] ; the difficulty of further improving resolutions in MAT and MAET which are affected by the factors such as the number of probe [9]. Otherwise, the combination technologies couldn t completely solve the problem of EIT, such as: the influence of the contact resistance between the electrode and skin when the electrode excitation or the electrode detection are used in MREIT and MAET, the injection current divergence when the electrode excitation is used in MREIT, the current shielding caused by organizations such as skull, and so on. All of these are challenges to the practical using of EIT combination technologies.
Aiming at the defects of the existing technologies, this paper combined the technologies of MRI and MAET for mutual advantages, and proposed a new method of Magnetic Resonance Motional-Electrical Tomography (MRMET). Based on the principle of MAET, MRMET uses a vibration acoustic excitation, and the current is generated by magnetic acoustic effect in research object. MRMET uses the MRI equipment to detect the intensity of the magnetic field of the fault plane of the object, and reconstructs the electrical conductivity distribution imaging. This method not only inherits the characteristics of EIT's functional imaging of electrical conductivity detection, but also inherits the advantages of MAET's non-contact excitation and MRI's high sensitivity and resolution. It also solves the problems of the EIT combination technologies. Analysis of MRMET Principle Principle of MRMET The principle of MRMET is that when a beam of vibration acoustic injects to the object which is placed in a static magnetic field of MRI system, the particles of the object vibrate with the transmission of the sound waves; the moving particles in the static magnetic field are affected by Lorenz force, and the electric field and current in the organization are forming while the charge separation occurs; the current produces a magnetic field component which is parallel to the direction of the static magnetic field, and the phase of the magnetic resonance echo signal will be influenced by this magnetic field component; the phase difference can be captured by the phase code of the MRI system. Using this phase difference, the magnetic field component can be solved, and then the conductivity distribution inside the object can be gotten by using Ampere's law. The block diagram of the principle is shown in Figure 1. Figure 1. The block diagram of the MRMET principle. Compared with the traditional impedance imaging methods like EIT, MREIT, and MAET, MRMET has unique advantages. The specific implementation technology comparison is shown in table 1. Driving Source Detection Device Table 1. The comparison of Several electrical impedance imaging methods. EIT MREIT MAET MRMET Ultrasound Probe, Static Vibration Acoustic Feeder, Magnet Static Magnet (Contact Measurement) Excitation Signal Injection Current MRI (Non Contact Measurement) Injection Current Direct: MRI echo signal phase Detection Signal Boundary Voltage Indirect: The magnetic field intensity of fault plane (Contact Measurement) Ultrasound, Static Magnet Boundary Voltage MRI (Non Contact Measurement) Vibration Acoustic Direct: MRI echo signal phase Indirect: The magnetic field intensity of fault plane Imaging Area D fault plane D fault plane D fault plane D fault plane Resolution low High Relatively High High
Compared with the traditional impedance imaging technique, MRMET has the following advantages: 1) The particles in the object generate the effect of MAET with the vibration acoustic and MRI main magnetic field, and the current distribution occurs on the fault plane, then the magnetic field which is generated by the current superposes to the main magnetic field of MRI. By detecting the MRI echo signal phase, high resolution of the magnetic field intensity on the fault plane can be obtained. Compared with the EIT which only gets the boundary voltage, MRMET can get more information, not only avoid the effect of electrode, but also greatly improve the imaging resolution. ) Compared with the MREIT, MRMET can avoid the effect of electrode RF shielding from the driving source. No matter how the distribution of injection vibration acoustic to the object and the distribution of particle vibration velocity(v) in the imaging body, according to the left-handed rule, the direction of the current source(j'=σ*v B) is perpendicular to the direction of the static magnetic field(b, assuming z direction). This means that the MRMET source J'only has the components of x and y direction, no z direction component. This has brought great benefits in the excitation for partly avoiding the divergence problem caused by electrode injection current. 3) The resolution of MAET depends on the acoustic frequency, acoustic probe number, and the acoustic focal region size. Compared with MAET, the resolution of MRMET is higher than MAET because its resolution depends on the resolution of MRI equipment. The Electromagnetic Field Problem in MRMET In the research of MRMET, considering the research object as ideal fluid, vibration velocity of the particles in the object doesn t change with space. The interaction of the vibration wave and static magnetic field induces charge separation and produces Coulomb field and excitation electric field, then generates a magnetic field which superposes to the main magnetic field of MRI to influence the phase of MRI echo signal. In order to improve the detection value, we need the MRMET excitation source as a low frequency signal, to ensure that the current keep constant direction during the time of MRI RF pulse sequence. Because low conductivity of the research object, the generating induction field is very small, and it can be neglected. The electromagnetic field equations, which meeting the condition that a research object placed in the MRI static magnetic field and excitated by the vibration acoustic are: E H =J= E+ ( v B ) (1.1-1.4) D= B= where, v B is the particle vibration velocity, is the magnetic induction intensity of MRI main v B magnetic field, is the vibration acoustic excitation source, E is the Coulomb field generated under the excitation of vibration, H and B respectively is magnetic field intensity and magnetic induction intensity generated by current source, is the internal conductivity distribution of the research object, is the electric charge density. In quasi-static conditions, we introduce the scalar potential( u ), have: E= u. Ohm's law in the detection area is to meet: ' J = E+ E u vb According to the current continuity theorem: J (1.5), we can get the electric field equation: ( u )= [ ( vb )] (in ) (1.6)
The boundary conditions for the electric field: u vb n n (1.7) where, is the research area, is the boundary of the research area. The formulas (1.6) and (1.7) are the electromagnetic field equations of MRMET. In the course of the study for the electromagnetic field forward problem, the conductivity distribution, particle vibration velocities v and MRI main magnetic field B have been known. According to the electromagnetic field equations of MRMET, the scalar potential u can be solved. The current density J and magnetic induction intensity B in research object also can be calculated according to Ohm's Law(formula 1.5) and Biot-Savart Law (formula 1.8). B d 3 4 J R R (1.8) is the medium permeability in the formula. In the course of the study for the electromagnetic field inverse problem, generating by current source, the magnetic induction intensity component B z, the direction of which is the same with MRI main magnetic field direction, has been known, and the particle vibration velocities v and the MRI main field B have also been known. We need to solve the conductivity distribution of the research object. Method: Iterative solution using scalar potential u. The curl of the formula (1.) is: H = [ E+ ( vb)] [ u vb] (1.9) Put the vector identities H = ( H) H and formula (1.4) into formula (1.9), we can get: H = u B v v B (1.1) Assuming the z direction as MRI main magnetic field direction, we can get the z direction of the formula (1.1), there is: Hz Hz u u v v x y ( vb x ) ( vb y ) B x y y x x y x y (1.11) where, H z is the z direction component of the magnetic field intensity generated by current source. v v x and y is the particle vibration velocities of x and y direction respectively, B is the magnetic induction intensity of MRI main magnetic field. Using the formula (1.11), the methods can get the conductivity distribution, and it used the two order derivative of the magnetic field intensity, so the algorithm has a higher requirement to the measurement accuracy of the magnetic induction intensity, and its anti-jamming performance is poor. Simulation Research on MRMET Using the simulation software of COMSOL Multiphysics to simulate and analysis the electromagnetic field of MRMET, the -dimensional simulation model (a) and are shown in Figure.
(a) Figure. The -dimensional simulation model of MRMET. In Figure, the model size is *, the conductivity of the blue region is set to 1 S/m. In model (a), the conductivity of a radius of.3 red circle, which has a center coordinates (,), is 1 S/m. In model, the conductivity of a radius of.4 red circle, which has a center coordinates (.4,.4), is 1 S/m. The main field intensity of MRI system is 1 T, and its direction is perpendicular to the -dimensional model, which is set to z direction. The applied acoustic vibration excitation in a cycle is shown in figure 3. Figure 3. The acoustic vibration excitation in a cycle in the models. The acoustic vibration excitation in model (a) is the same with model. Along x direction, the acoustic vibration velocity is: vx sin( t), and the vibration frequency is 1kHz. Along x direction, the acoustic vibration velocity is: vx. According to the formula (1.6) and (1.7), the distribution of the scalar potential inside the simulation models are calculated as shown in figure 4. Where, model (a) is in the time of.6 ms, and model is in the time of.5 ms. (a) Figure 4. Distribution of the scalar potential inside the simulation model.
Using the formula (1.8), the magnetic induction intensity component, which direction is the same with MRI main magnetic field direction, can be solved by the current density distribution from the COMSOL output. The calculated magnetic induction intensity component in the z direction is shown in figure 5. Here, the time points of the computation are consistent with the time points of the above scalar potentials. Because the limit of the computer matrix operation ability, the output data numbers from COMSOL are 4 * 4. Bz x 1-18 Bz x 1-18.8.6.4. 6 4.8.6.4. 1.5 1.5 -. -.4 -.6 -.8 - -4-6 -. -.4 -.6 -.8 -.5-1 -1.5 -.5.5-8 -.5.5 - (a) Figure 5. Z direction component of magnetic induction intensity in simulation model. We use the data Bz calculated by Biot-Savart Law as the measurement data of the MRI equipment. The conductivity reconstruction algorithm of simulation model is the method mentioned in the previous section. The reconstructed results of conductivity distribution are shown in figure 6. Here, the time points of the computation are consistent with the time points of the above scalar potentials. 3 sigma -.8 -.6 5.8.6 -.4 -..4. 15 15..4 1 -. -.4 1.6.8 5 -.6 -.8 5 -.8 -.6 -.4 -...4.6.8 -.8 -.6 -.4 -...4.6.8 (a) Figure 6. The reconstructed conductivity distribution of simulation models. From the reconstruction results, the algorithm can realize the reconstruction of conductivity imaging. Because of the needing for two order derivative of the magnetic induction intensity, the algorithm causes weak anti-noise performance. Here, we only studied the feasibility of the MRMET method, without considering the recognition of the algorithm itself to the conductivity and the resolution of the image reconstruction. In future work, we also need to make some improvements to the algorithm, and enhance the calculation accuracy. Discussion This paper proposed a new method of MRMET combined the technologies of MRI and MAET for mutual advantages. The combination of MRI main magnetic field magnet and vibration acoustic are used to excitation in MRMET. Compared with EIT, the effect of electrode can be avoided in MRMET, and the more information can be gotten, so the MRMET can greatly improve the imaging resolution
in theory; compared with the MREIT, the effect of electrode RF shielding can be avoided in MRMET, and the distribution of the excitation source is perpendicular to the direction of MRI main magnetic field, partly avoid the divergence problem caused by electrode injection current; meanwhile, the resolution of MRMET depends on the resolution of MRI equipment, and it's higher than MAET in theory. According to the common excitations of Coulomb field and excitation electric field(generated by vibration wave and MRI main magnetic field) in MRMET, this paper proposed a new conductivity reconstruction algorithm, and validated the feasibility of MRMET using the simulation method. But this work for MRMET is still in the exploratory stage, without considering the vibration acoustic effect on MRI system and MRI system impact MRMET. In the future works, the in-depth study is needed to the specific implementation form, affecting factors, inversion algorithm in MRMET. Acknowledgement This work was supported by the National Natural Science Foundation of China under Grant Nos. 5137164, 511374 and 51677181. References [1] Mark J. Hamamura, L. Tugan Muftuler. Fast imaging for magnetic resonance electrical impedance tomography [J]. Magnetic Resonance Imaging. 8, 6: 739-745. [] Jian-Bo Li, Chi Tang, Meng Dai, et al. A New Head Phantom With Realistic Shape and Spatially Varying Skull Resistivity Distribution, IEEE Trans. Biomed. Eng., vol. 61, no., February 14, pp. 54-63. [3] Marco Guermandi, Roberto Cardu, et al. Active IC for EEG and Electrical Impedance Tomography With Continuous Monitoring of Contact Impedance, IEEE Trans. Biomed. Eng., vol. 9, no. 1, February 15, pp. 1-33. [4] H.J. Kim, W.C. Jeong, S.Z.K. Sajib, M. Kim, O.I. Kwon, E.J. Woo, and D.H. Kim, Simultaneous imaging of dual-frequency electrical conductivity using a combination of MREIT and MREPT, Magn. Reson. Med., vol. 71, pp. -8, 14. [5] Xin Huang, Fundamental Investigations on Magnetoacoustics Tomography with Current Injection [D], Institute of Electrical Engineering of the Chinese Academy of Sciences, 13. [6] Liang Guo, Guo-qiang Liu, Hui Xia, Jing Chen, Forward Procedure of Magneto-Acousto-Electric Signal in Radial Stratified Medium of Conductivity for Logging Models, Chin. Phys. Lett. Vol. 3, No. 1 (13), 1433-1167. [7] T.I. Oh, Munish Chauhan, et al. Modelling of electromagnetic field distribution for optimizing electrode configurations in liver MR-based electrical impedance tomography, Electronics Letters, 14.8, 5(18), pp. 173 175. [8] J.K. Seo, E.J. Woo, Electrical Tissue Property Imaging at Low Frequency Using MREIT, IEEE Transaction on Biomedical Engineering, 14, 61(5), pp: 139-1399. [9] Liang Guo, Guo Qiang Liu, Hui Xia, Conductivity Reconstruction Algorithms and Numerical Simulations for Magneto-Acousto-Electrical Tomography with Piston Transducer in Scan Mode, Chin. Phys. B, vol. 3, no.1, 14.