Optimum Design of the Structure of Electrode for Medical EIT System

Transcription

1 Optimum Design of the Structure of Electrode for Medical EIT System Huaxiang Wang Chao Wang Automation School Automation School Tianjin University Tianjin University Tianjin, P.R. China 372 Tianjin, P.R. China INTRODUCTION In medical electrical impedance tomography (MEIT) system, wide electrodes which cover 8% - 9% of the peripheral area were usually used[1,2]. Compared with the narrow electrode, this wide electrode can provide more uniform current distribution in the domain of interest and has low electrode-skin contact impedance, which is a benefit to increasing system sensitivity. However, the highly conductive electrode material on the surface of the body provides an effective short circuit for the injection current and coerces the contact surface underneath the electrode to be changed into an equal potential. This reduces the current density at the interior of the body and affects the distribution of the sensitive field, and will finally result in the reduction of the system sensitivity. Fig. 1: Medical Electrical Impedance Tomography system with the compound electrode array Fig. 1 shows an array of 32 electrodes around the object to be imaged. The compound electrode uses the outer electrode as a current electrode and the inner electrode as a voltage electrode. Its current electrode is much larger than its voltage electrode. So the voltage electrode can be equivalent a point electrode. However, the outer current electrode coerces equally the contact surface underneath the electrode to be changed into an equal potential. Therefore, it is necessary to optimize the structure size of the compound electrode. 2 FINITE ELEMENT MODEL WITH THE CONDITION OF COERCIVE EQUIPOTENTIAL NODES In general, for a low frequency of current being applied to the object, e.g. less than 1kHz, the sensitive field may be approximated to be quasistatic. If only the resistivity distribution is considered in this study, the electrical potential φ satisfies, 1

2 ( σ φ) = 1 For the homogenous resistivity distribution case, σ is a constant, then each point in the sensitive field can be simplified and written as follows 2 φ = 2 Corresponding to the Laplace equation (2), the finite element model is [ K ] [ φ ] = [ B] Where [K] is the coefficient matrix, [φ] 3 is the potential of all over dissection nodes, and [B] includes the boundary conditions. Assume that N is the sum of all dissection nodes. There are J groups of the coercive equipotential nodes, which form J sets, namely EQU{ ( i J, i N). These elements in each set exist in the form of serial number of equipotential nodes in the set. There exist M elements in each set, in which the minimal element is min_equ{. Firstly, collating the columns becomes K l = K,min_ equ{ Where l = 1, 2,, N. l, j 4 After collating Columns, Klj l = 1 2 N j EQU{-{min_equ{} i J are deleted, and move the reminder columns forward and complement those null columns deleted. Then, collate rows K B min_ equ{, l min_ equ{ = = B K j j, l Where l = 1 2 N -J (M-1). 5 6 After collating rows, Kjl ( l = 1 2 N -J (M-1), j EQU{-{min_equ{} i J ) and Bj ( j EQU{-{min_equ{} i J ) are deleted, and move the reminder rows forward and complement those null rows deleted. After collating columns and rows, (4) becomes as follows [ K] = [ B] 1 ( M 1) [ φ] 1 So each node potential in the sensitive field is obtained by solving the system of equations. 7 3 THE INFLUENCE OF THE measuring ELECTRODE ON THE DISTRIBUTION OF THE SENSITIVE FIELD In the same excitation conditions, the influence of the compound electrode width on the sensitive field is analyzed, as shown in Fig. 2. Fig. 2(a) represents the equipotential line distribution in which the coercive equipotential nodes are left out of account. The Fig. 2(b), (c), (d), (e), (f) takes four groups of existing coercive equipotential node 2

3 (a) (b) (c) (d) (e) (f) Fig. 2: The equipotential line distribution of the measuring electrode for different width conditions into account, and the number of equipotential nodes in each group is two, three, four, five, and six nodes respectively. From Fig.2 it is obvious that the deviation of equipotential line is more and more serious with the increase in the number of equipotential nodes. At the same time, it indicates that if two coercive equipotential nodes exist in a group, the deviation of equipotential lines exhibits neighboring compound electrodes, and the equipotential lines of the center domain of the sensitive field are only slightly affected. As the number of the coercive equipotential nodes increases, the domain affected by coercive equipotential nodes is enlarged gradually. When the number of the coercive equipotential nodes increases up to six, the equipotential line distribution of the entire sensitive field is almost changed. 4 OPTIMUM DESIGN OF THE ELECTRODE COVERING RATIO The detection sensitivity ( K ) is chosen as the optimum objective function[4]. The parameter K is defined as follows 3

4 V V 1 V K = 8 σ1 σ σ The meaning of the formula (8) is that when the conductivity in a region of the sensitive field changes from to σ, the detection voltage changes from V to V 1, then parameter K σ 1 characterizes the sensitivity of the electrode to the conductivity change in the field. Based on the FEM model, the optimum parameter K can be obtained by using simulation method for different electrode covering ratios ( i.e. the ratio of the sum of electrode array width to the circumference of the cross section ) and different excitation strategy, i.e. the adjacent and the opposite excitation. The simulation result of having eight-electrode EIT system is shown in Fig. 3 and Fig. 4. Normalizing Parameter Center EdgeNear EdgeFar Average Electrode Covering Ratio(%) Fig. 3: optimum parameter K for Opposite excitation strategy Normalizing Parameter Center EdgeNear EdgeMiddle EdgeFar Average Electrode Covering Ratio Fig. 4: optimum parameter K for Adjacent excitation strategy In addition, note that the change trend of the optimum parameter K to the covering ratio is different in different regions of the sensitivity field. In our design, the means of the optimum parameters in different regions is chosen as a criteria. For the opposite excitation strategy, when the electrode covering ratio reaches 28.6%, a higher sensitivity is achieved both in the center and in the boundary of the sensitive field. For the adjacent excitation strategy, the best electrode covering ratio is 57.1%. Summarizing the two types of excitation strategies, when the electrode covering is 57.1%, the effectiveness is best. REFERENCES [1] Hua P., Woo E. J., Webster J. G.. Using Compound Electrode in Electrical Impedance Tomograohy. IEEE 4

5 Tran. on Biom. Eng., 1993, 4(1): [2] Hua P., Woo E. J., Webster J. G., et al. Finite Element Modeling of Electrode-Skin Contact Impedance in Electrical Impedance Tomography. IEEE Tran. on Biom. Eng., 1993, 4(4): [3] Woo E. J., Hua P., Webster J. G., et al. Skin Impedance Measurement using Simple and Compound Electrode. Med. & Biol. Eng. & Comp., 1992, 3 (1): [4] Wang Huaxiang, Yin Wuliang, Yang W Q, et al. Optimum Design of Segmented Capacitance Sensing Array for Multi-phase Imterface Measurement. Meas. Sci. Technol., 1996, 7: