Med Biol Eng Comput (2015) 53:589–597 DOI 10.1007/s11517-015-1274-y
ORIGINAL ARTICLE
Evaluation of measurement and stimulation patterns in open electrical impedance tomography with scanning electrode Jinzhen Liu1 · Hui Xiong1 · Ling Lin2 · Gang Li2
Received: 26 September 2013 / Accepted: 3 March 2015 / Published online: 13 March 2015 © International Federation for Medical and Biological Engineering 2015
Abstract The reconstruction quality in electrical impedance tomography is limited by the current injection amplitude, the injection and measurement patterns, and the measurement accuracy as well as the number and placement of electrodes. This paper dedicates to increase the number of independent voltage measurements by scanning electrode (SE), and design an optimal measurement and stimulation pattern for open electrical impedance tomography (OEIT). Firstly, several measurement patterns are, performed in OEIT, aiming to evaluate the right number of the measurement points for the imaged target in a certain depth. The results indicate that the image quality gets higher with the number of measurement point increased to some extent. Thus, it can guide the optimum design for the electrode system in OEIT. Secondly, through the numerical calculation and salt water tank experiment, in contrast to adjacent current injection pattern, cross-current-injection pattern achieves better reconstruction with higher imaging quality and penetration depth, and is more robust against data noise in deep domain. Lastly, the experiments also indicate that
* Jinzhen Liu [email protected] Hui Xiong [email protected] Ling Lin [email protected] Gang Li [email protected] 1
School of Electrical Engineering and Automation, Tianjin Polytechnic University, Tianjin, People’s Republic of China
2
State Key Laboratory of Precision Measurement Technology and Instruments, Tianjin University, Tianjin, People’s Republic of China
the electrode contact area affects the reconstruction quality and investigation depth. Therefore, OEIT with SE can improve the application in clinic, such as the detection and monitoring of vascular, breast, and pulmonary diseases. Keywords Open electrical impedance tomography · Scanning electrode · Cross current injection mode · Adjacent current injection mode
1 Introduction Electrical impedance tomography (EIT) is particularly promising because of its functional imaging, non-invasion, and medical imaging monitoring, which has been gradually developed in recent decades. It is characterized to reflect the structure and function of the internal organs and tissues by imaging the distribution of conductivity from measurement of the surface potential [7]. Static and dynamic EIT methods are performed according to the applications, particularly attractive in many important applications such as the detecting and monitoring about pulmonary function, breast, and brain diseases, and many industrial applications such as the fields of process tomography, nondestructive testing, geological studies, and archaeology [2]. According to the imaging domain model, EIT can be divided into enclosed EIT and open EIT (OEIT), which is referred to as EIT on unbounded domain in geophysical prospecting [10]. In enclosed EIT, the uncertain electrode position and inconsistent imaging domain shape result in low image quality and resolution. However, OEIT can alleviate these such as position error, ringing and movement artifacts, and make EIT more suitable for clinical application. In order to overcome the uncertainty of electrode position in the enclosed EIT, Mueller et al. [11] began
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to use fixed electrode array to detect the target in shallow domain but the whole measured domain. Huang et al. [8] rotated the electrode pairs attached on a phantom tank to scan around the boundary of the imaging object, which can enhance the reconstruction quality by increasing the electrode number. However, the reported scanned image is restricted to the application in uniformly cylindrical phantom tank. At present He et al. [6] and Zhang et al. [20] in Chongqing University have developed a system for OEIT with only eight fixed electrodes, and have applied it into the breast disease detection and monitoring as well as preliminary clinical applications. However, the imaging system obtains low imaging quality. The reconstruction quality of EIT is determined by the current injection amplitude, the current injection and voltage measurement patterns, and the measurement accuracy, as well as the number and placement of electrode [16]. In practice, firstly, the number of electrode and current injection is limited, resulting in the information obtained from the boundary electrode that is not enough to determine the internal impedance distribution, so it suffers from a high degree of nonlinearity and severe ill-posedness [19]. Secondly, EIT itself exhibits ill-posed problem that boundary voltage is only sensitive to the impedance change near the electrode but to the impedance change in the center or deep domain [4]. Most importantly, when the current is injected into the imaging domain, the electric field distribution will be changed by the traditional electrode fixed to the surface of the measured domain [18]. Moreover, current will be bypassed by the adjacent electrode but injected into the interior domain [12]. Therefore, in order to reduce ill-posedness in inverse problem, this paper researches on the OEIT using a scanning mechanism with SE, which can increase the number of independent measurement only by two measurement electrodes, reduce the complexity of the measurement system and the mutual influence among the traditional fixed electrode, and improve imaging quality. In EIT, the current injection patterns consist of adjacent, diagonal, trigonometric and adaptation. Avis and Barber [3] have put forward trigonometric pattern with 90° phase difference between two injection electrodes. Kolehmainen et al. [9] carried out the simulations both with adjacent and with trigonometric current patterns, and it seems that the adjacent pattern is more tolerant of errors than the trigonometric pattern. Adler et al. [1] analyzed various choices of stimulation and measurement patterns and obtained the result that the traditional (and still most common) adjacent stimulation and measurement patterns have by far the poorest performance in comparison with trigonometric pattern. Nasehi et al. [17] evaluated different current injection and measurement patterns with both external and internal electrodes and showed that the trigonometric injection patterns had better performance and improved pixel intensity of the
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small conductivity changes. The results of these papers are not comparable with each other because there are no common parameters among these papers with the perturbation only in one fixed location. In this study, we firstly proposed the novel open electrical impedance imaging mode with scanning electrode and presented the system composition and reconstruction principle. Secondly, based on the OEIT with SE, we evaluated the effect of the number of measurement point on the reconstruction quality, and the effect of cross and adjacent current injection patterns on the reconstruction quality in two-dimensional domain. Lastly, we performed the salt water tank experiment to verify the feasibility and availability of the OEIT with SE, evaluate the impact of the electrode contact area on the reconstruction quality and investigation depth, and evaluate the cross and adjacent current injection patterns.
2 Methods 2.1 Mathematical model for OEIT Compared to the enclosed EIT, the OEIT converts closed domain model into a simple open domain model as shown in Fig. 1, which is more practical than the enclosed EIT. Firstly the open domain mode makes the EIT flexibly apply to various kinds of domain shapes. Thanks to the relative regular domain boundary, the electrode array or SE is easy to be placed. Therefore, in our study we dedicate our research to the OEIT with SE in superficial layer, making EIT more portable. OEIT is a boundary value problem with an incomplete electromagnetic domain boundary constraint condition [15]. However, the mathematical model of enclosed EIT can also be applied to OEIT. It is assumed to be a virtual field problem by solving a certain sensitive field instead of the whole electromagnetic field. In theory, EIT is the solution of forward problem and inverse problem in lowfrequency current field. When solving the EIT problem, we
Fig. 1 Two domain models with electrodes in the boundary, a the closed domain model, b the open domain model
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only consider the electric field effect and ignore the magnetic field effect because of the low permeability of biological tissue. Based on the current field with low frequency and low permittivity, from the mathematical point of view, the research field is considered as the quasi-static field. And it is assumed that there is no current source in the sensitive field, so according to Maxwell equation, the potential distribution ϕ and the conductivity distribution σ meet the elliptic partial differential equation in the electric field [5]: ∇ · −σ (x, y)∇ϕ(x, y) = 0 (x, y) ∈ Ω (1a) Without considering the surface contact impedance, the Dirichlet and Neumann boundary conditions [14] for the model shown in Fig. 1b can be stated as follows:
ϕ(x, y) = f (x, y) σ (x, y)
(x, y) ∈ ∂Ω
∂ϕ(x, y) = j(x, y) (x, y) ∈ ∂Ω ∂ n�
(1b) (1c)
where n is the unit outward normal vector to the boundary ∂Ω, f is the measured electrode potential and j is the current density at the current injecting electrodes. Dirichlet conditions are assumed under electrodes, while Neumann conditions on the remaining part of the boundary. For each electrode, the flux of the current density through the contact surface must equal the injected current ∂ϕ(x, y) dS = Il l = 1 . . . L ′ σ (x, y) (2) ∂ n� ∂Ωl
where l is the electrode number, Il is the injected current at the electrode l, S is the surface of the electrode. Underneath the inter-electrode gaps no current should flow, and the following condition is applied:
∂ϕ =0 ∂ n�
on ∂Ω {∂Ω1 ∪ · · · ∪ ∂ΩL′ }
F(σ ) =
1 1 [v(σ ) − v0 ]T [v(σ ) − v0 ] + α(σ − σ0 )T R(σ − σ0 ) 2 2
(4) where v(σ) is the voltage vector obtained by solving the forward problem, v0 is the measurement voltage vector, T is the transpose matrix, α is the regularization parameter and R is the identity matrix. In practical implementation, the optimization problem (4) is solved iteratively by the Gauss–Newton method, and the updated electrical conductivity distribution is expressed as follows:
δσ = −(J T J + αR)−1 [J T (v(σ ) − v0 ) + α(σ − σ0 )]
(5)
where J is the Jacobian matrix. 2.3 The scanning platform and measurement patterns In this paper, a four-terminal measurement protocol consisting of a bipolar push–pull current injection and a differential voltage measurement is performed to obtain the boundary voltages. The schematic diagram for OEIT with SE is shown in Fig. 2. The current produced by module 7 is injected into domain 9 by electrode 1 and flowed from electrode 2. The electrode 2 is driven by the mechanical skid platform 5 and scans along the domain boundary to carry out multiple current injections. Then after each current injection, the resulting voltages from the adjacent electrodes 3 and 4 which are driven by mechanical skid platform 10 are recorded by the signal acquisition device 6. Lastly the recorded boundary voltages are transmitted to the computer for reconstruction. Therefore, the electrode scanning pattern is promising to increase the number of boundary voltage in the limited measurement area and avoid the influence of electrode on electric field distribution.
(3)
where ∂ΩL′ is the boundary underneath electrode L′. The forward problem of EIT refers to determine the potentials in the domain by solving the boundary value problem in (1) with the known boundary conditions and conductivity distribution. The inverse problem is the solution of the conductivity distribution with known boundary conditions and electrical potential distribution. 2.2 The inverse method The reconstruction for OEIT is in terms of a traditional nonlinear, least squares Gauss–Newton–Raphson approach [13] with Tikhonov style regularization. Regularization techniques are commonly adopted to stabilize the inversion to solve the ill-posed problem. The cost function is
Fig. 2 Schematic diagram for OEIT with SE, (1, 2) current injection electrodes, (3, 4) voltage measurement electrodes, (5) mechanical skid platform for current injection, (6) signal acquisition device, (7) current source, (8) computer, (9) imaging target, (10) mechanical skid platform
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Fig. 3 Block diagram of current injection and voltage measurement patterns, a crosscurrent-injection pattern, b adjacent current injection pattern
We firstly evaluate the effect of the number of boundary voltage collected by SE on image quality. Secondly, because the current injection mode will affect the ill-posed condition of inverse problem, we also perform the research on the effect of adjacent and cross-current-injection patterns on the imaging quality and robustness. The block diagram of current injection and voltage measurement patterns are shown in Fig. 3. The cross-current-injection pattern refers to that the current is injected into two measurement points with different interval that is gradually increased, which can make the current distribution more uniform. In the cross injection strategy, the current is injected into measurement point 1 that is fixed and firstly flowed from measurement point 2, and the resulting adjacent voltages are collected. Secondly the current is injected into measurement point 1 and flowed from measurement point 3, and the resulting voltages between other adjacent measurement points are measured. Then the constant current is injected into measurement point 1 and flowed from other cross measurement points, in turn the voltages between other adjacent measurement points are measured. Thus, we can obtain (n − 2) × (n − 3) boundary voltages, where n is the number of measurement point. In the adjacent injection strategy, the current is firstly injected into measurement point 1 and flowed from measurement point 2, and the resulting voltages from the remaining adjacent measurement points are collected. Then the constant current is injected into other adjacent measurement points, and similarly the voltages between other adjacent measurement points are measured. Thus we can also obtain (n − 2) × (n − 3) boundary voltages.
Fig. 4 Measurement system for OEIT, a the experiment setup, b the schematic diagram
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2.4 Simulation and experimental protocols In this study, the imaging domain is 175 mm in width and 75 mm in length. The fine mesh with 4290 triangulation elements and 2247 nodes is for the forward solution, and the coarse mesh with 1080 triangulation elements and 592 nodes is for the inverse solution. The conductivity will affect the reconstruction quality, but the conductivity difference will not affect the performance comparison. For comparison, in the simulations, we choose the conductivities of the inclusion and background according to the common study. In the phantom modes shown in Fig. 5a, the conductivity of inclusion is 2 S/m and the background conductivity is 1 S/m. In the phantom mode with two inclusions shown in Fig. 7, the conductivity of the inclusion on the right is 8 S/m, the low conductivity of inclusion on the left is 1 S/m, and the background conductivity is 4 S/m. The synthetic data are created using the forward model based on the simulation software Matlab with the injection current of 5 mA and the frequency of 1 kHz. In the salt water tank experiment, the small electrode can be seen as the point electrode with the diameter of 1 mm. The diameter of the big electrode is 5 mm. We use ten metal big electrodes placed on the side of the domain boundary for injecting current. The middle 14 boundary voltages are collected by the scanning electrode with the diameter of 1 mm driven by the displacement table. The increase in injection current amplitude strengthens the electric field intensity in the imaging area. Thus the signal-tonoise ratio of the boundary voltage can be improved, which can improve the electrical impedance imaging quality.
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Fig. 5 Reconstruction images in the depth of 5, 20, and 35 mm using 8, 16, 20, 24, 28, and 32 measurement points. a Original phantom models, b reconstruction images with the inclusion in the depth of 5 mm, c reconstruction images with the inclusion in the depth of 20 mm, d reconstruction images with the inclusion in the depth of 35 mm
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However, the current amplitude should be smaller than 5 mA considering safety. The height of the domain is 95 mm, the length is 225 mm, the interval of the two current injection electrodes is 5 mm, and the interval of the boundary voltage is 5 mm. The injection current is 1 mA with the frequency of 1 kHz. Figure 4a, b shows the actual measurement system and the schematic diagram for OEIT, including the displacement table, the current injection electrodes, the scanning electrode, the current source, and the salt water tank. We use the Labview software to control the motor, collect the boundary voltages, process the signal, and store the image information. The total scanning time for measuring 128 boundary voltages is 8.4 min. In our study, correlation coefficient is employed to evaluate imaging accuracy, which is calculated as follow: n (ˆgi − g¯ˆ )(gi − g¯ ) a = i=1 (6) n gi − g¯ˆ )2 ni=1 (gi − g¯ )2 i=1 (ˆ where α is correlation coefficient, gˆ is reconstruction electrical conductivity and g is initial electrical conductivity. Furthermore, g¯ˆ and g¯ are the average value of gˆ and g, respectively. The reconstruction image is close to the real image when the value of α is bigger.
3 Results 3.1 The simulation results 3.1.1 The effect of the number of measurement point on the reconstruction quality By increasing the number of measurement point, we can obtain more independence boundary voltage, so the study about 8, 16, 20, 24, 28, and 32 equally interval measurement points are, respectively, performed to explore the
Fig. 6 Comparison of correlation coefficients for the reconstructions
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effect of the number of measurement point on image quality in the domain shown in Fig. 3a. Figure 5a shows the conductivity distributions for the inclusion in the depth of 5, 10, 15, 20, 25, 30, 35, 40, and 45 mm. Figure 5b–d shows the reconstructions for the inclusion in the depth of 5, 20, and 35 mm using 8, 16, 20, 24, 28, and 32 measurement points. Figure 5 illustrates that the reconstruction images are so terrible using eight measurement points that we cannot distinguish the size, shape, and position of the inclusion. In the depth of 5 mm, the imaging quality is better than that in the depth of 20 and 35 mm, which produces more image artifacts. Figure 6 shows the reconstruction correlation coefficients for the results of the inclusion in the depth of 5, 10, 15, 20, 25, 30, 35, 40, and 45 mm, respectively, using 8, 16, 20, 24, 28, 32 measurement points. 3.1.2 The effect of current injection pattern on the reconstruction quality In this study, the adjacent and cross-current-injection patterns using 32 measurement points are chosen to evaluate the effect of current injection pattern on the reconstruction quality in the phantom mode with two inclusions. Figure 7a, b shows the reconstructions, respectively, by the cross and adjacent current injection patterns with the inclusions in the depth of 15, 25, 35, and 55 mm. In order to test the robustness to noise about the two current injection patterns, 50- and 40-dB Gaussian noise is added to the synthetic data, respectively, with the inclusions in the depth of 15, 25, 35, and 45 mm. Figure 7c, d shows the reconstructions by cross and adjacent current injection patterns with the noise level of 50 dB. Figure 7e, f shows the reconstructions by cross and adjacent current injection patterns with the noise level of 40 dB. We also compare the correlation coefficients that are shown in Table 1. 3.2 The salt water tank experiment results In order to evaluate the adjacent and cross-current-injection patterns, as well as the impact of the electrode contact area on the reconstruction quality and investigation depth, we perform the salt water tank experiment. Although the big electrode has its inherent advantages, the big area of the electrode will inevitably cause the potentials under the electrode equal and affect the electric field distribution inside the domain. This problem still exhibits even with the composite electrode. Obviously, in the reconstruction calculation, the electrode area should be considered. The needle electrode with small area and the cylinder electrode with big area are, respectively, used as the current injection electrode. Then, we discuss the impact of the electrode contact area on the reconstruction quality and investigation
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Fig. 7 a, b Reconstructions by the cross and adjacent current injection patterns. c, d Reconstructions by the cross and adjacent current injection patterns with 50-dB noise. e, f Reconstructions by the cross and adjacent current injection patterns with 40-dB noise
Table 1 Comparison of the correlation coefficient for the results of Fig. 7 Without noise
15 mm
25 mm
35 mm
55 mm
Cross Adjacent
0.8984 0.8985
0.7773 0.7593
0.6429 0.6456
0.4197 0.1753
With 50 dB noise
15 mm
25 mm
35 mm
45 mm
Cross Adjacent
0.6695 0.7424
0.4155 0.4250
0.3038 0.1814
0.1799 0.0871
With 40 dB noise
15 mm
25 mm
35 mm
45 mm
Cross
0.5846
0.3620
0.2273
0.1002
Adjacent
0.6629
0.3319
0.1423
0.0314
depth by the cross-current-injection pattern and the adjacent voltage measurement pattern to verify the availability of the scanning electrode.
Figure 8a shows the boundary voltage distributions, respectively, using the big and small metal electrodes as the current injection electrodes in the simulation calculation. From Fig. 8a, we can see that the boundary voltages by the big electrode are higher than those by the small electrode. The results of the salt water tank measurement are shown in Fig. 8b. In the reconstruction test, we place the organic glass rod in the salt water tank in the depth of 5 and 20 mm and use the designed collection system to obtain the boundary voltages. The diameter of the organic glass rod is 8 mm. The reconstructed images by the big and small electrodes are shown in Fig. 9. From the measurement, we can also conclude that the measured boundary voltage quality by cross-currentinjection pattern is higher than that by the adjacent current injection pattern. However, because of the low signal-tonoise ratio of the measured data by the adjacent current injection pattern, the reconstruction is hardly performed. Figure 8b shows the boundary voltages measured by the
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Fig. 8 Boundary voltage distributions u1 and u2 are, respectively, using the big and small metal electrodes as the current injection electrodes, a in the simulation calculation, b in the salt water tank experiment
cross-current-injection pattern with the noise level above 60 dB. Therefore, the salt water tank experiment indicates that the cross-current-injection pattern is more suitable for OEIT.
4 Discussion and conclusion Compared with the traditional enclosed EIT, OEIT with SE overcomes the restriction of imaging domain and the number of fixed electrode, but reconstruction imaging quality is still the bottleneck that limits the EIT for further development. In order to improve the imaging quality, this paper Fig. 9 Reconstructions by the electrodes with different contact area for the current injection, when the organic glass rod is place in the depth of 5 and 20 mm. a The reconstructions by the big electrodes, b the reconstructions by the small electrodes
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proposed an OEIT pattern with SE. And we performed the optimization design for the voltage measurement pattern and current injection pattern to obtain the optimum reconstruction. The correlation coefficients for Fig. 5 reflect the effect of measurement point and the depth of inclusion on the reconstructions. To summarize, from Figs. 5 and 6, we can conclude that, when the inclusion in a certain depth, the reconstruction quality rises as the number of measurement points is increased, and this effect is largest for target in the bottom. This may be explained by the expanded independent measurement voltages that are measured by SE. The number of independent measurement voltage can reduce the ill-posed condition of inverse problem. But increasing the measurement point requires the hardware system to improve measurement accuracy and enlarge the measurement dynamic range. Figure 6 illustrates that the imaging quality is increased slightly when the measurement points are increased to a certain extent. According to this result and priori position knowledge in actual measurement, the high-quality reconstruction will be product with optimal measurement point. We suggest that it is important to evaluate the number of measurement point, the current amplitude, and the measurement accuracy as well as the depth of target according the prior knowledge in OEIT. Figure 7a, b and Table 1 illustrate that the reconstruction quality and correlation coefficient have a few difference in the depth of 15, 25, and 35 mm by the two current injection patterns. However, in the depth of 55 mm, the reconstruction image by the adjacent current injection pattern contains bigger imaging artifact, and the correlation coefficient is lower by 0.2442 in comparison with the cross-current-injection pattern. The results indicate that the cross-current-injection pattern achieves better reconstructions with higher imaging quality and penetration depth. This may be explained that the commonly used adjacent current injection pattern makes the current to distribute in the superficial layer of the image domain, so the current density in the center of domain is relatively small. While the cross-current-injection pattern is able to make the
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current distribution of internal domain more uniform and increase the current penetration depth. From Fig. 7c–f, we observe that the adjacent current injection pattern obtains better reconstruction quality in the depth of 15 mm, but in the depth of 35 mm and 45 mm the cross-current-injection pattern achieves higher reconstruction quality and correlation coefficient. In Fig. 8b, the voltage differences between the big and small electrodes are less than the results of the simulation calculation. The reason mainly is that the contact area of the big electrode can influence the electric field distribution. From the previous analysis, the electrode contact area of big electrode will force the potentials under the electrode into equal potential, which can cause the boundary voltages smaller in actual measurement than in the theoretical calculation, which is consistent with the theoretical analysis [18]. From Fig. 9 we can conclude the electrode contact area will affect the reconstruction quality of OEIT. The results also illustrate that the scanning electrode with small contact area improves the resolution of the traditional EIT with fixed electrode and promotes the development of EIT. Because of the open domain model in reconstruction, the OEIT improves the applicability of EIT, which can be applied in the study of superficial body surface conductivity character, such as the detection of abdomen, lungs, and breast diseases. In the salt water tank experiment, the total scanning time for measuring 128 boundary voltages is 8.4 min. In future study, we will reduce the scanning time to increase the real-time capability of reconstruction. The electrode error is the main source of the measurement error. In the experiment, we found that the driver chip fever will cause unstable job of the displacement platform. Therefore, firstly, we should improve the stability of the displacement platform. Then, in order to guarantee the measurement conditions and contact impedance as consistent as possible, the pressure sensor should be added to the measurement electrode in future study.
References 1. Adler A, Pascal OG, Yasheng M (2011) Adjacent stimulation and measurement patterns considered harmful. Physiol Meas 32(7):731–744 2. Adler A, Amato MB, Arnold JH (2012) Whither lung EIT: Where are we, where do we want to go and what do we need to get there? Physiol Meas 33(5):679–694 3. Avis NJ, and Barber DC (1992) Adjacent or polar drive?: image reconstruction implications in electrical impedance tomography
597 systems employing filtered back projection In: Proceedings of IEEE engineering in medicine and biology society. 1689–1690 4. Borsic A, Graham BM, Adler A, Lionheart WRB (2010) In vivo impedance imaging with total variation regularization. IEEE Trans Med Imaging 29(1):44–54 5. Chung ET, Chan TF, Tai XC (2005) Electrical impedance tomography using level set representation and total variational regularization. J Comput Phys 205(1):357–372 9. He W, Li, B and He CH (2010) Open electrical impedance tomography: computer simulation and system realization. In: International Conference on life system modeling and simulation 97:163–170 6. Holder D (2005) Electrical impedance tomography: methods, history and applications. Institute of physics Publishing, Bristol 7. Huang CN, Yu FM, Chung HY (2008) The scanning data collection strategy for enhancing the quality of electrical impedance tomography. IEEE T Instrum Meas 57(6):1193–1198 8. Kolehmainen V, Vauhkoneny M, Karjalainen PA, Kaipio JP (1997) Assessment of errors in static electrical impedance tomography with adjacent and trigonometric current patterns. Physiol Meas 18(4):289–303 10. Michael L, Peter M, Michael P (2003) Tikhonov regularization for electrical impedance tomography on unbounded domains. Inverse Prob 19(3):585–610 11. Mueller J, Isaacson D, Newell J (1999) A reconstruction algorithm for electrical impedance tomography data collected on rectangular electrode arrays. IEEE Trans Biomed Eng 46(11):1379–1386 12. Murphy SC, Chin RKY, York TA (2008) Design of an impellermounted electrode array for EIT imaging. Meas Sci Technol 19(9):094009 1–12 13. Rao LY, He RJ, Wang YH, Yan WL, Bai J, Ye DJ (1999) An efficient improvement of modified Newton-Raphson algorithm for Electrical Impedance Tomography. IEEE T Magn 35(3):1562–1565 14. Somersalo E, Cheney M, Isaacson D (1992) Existence and uniqueness for electrode models for electric current computed tomography SIAM. J Appl Math 52(4):1023–1040 15. Syed H, Borsic A, Hartov A, Halter RJ (2012) Anatomically accurate hard priors for transrectal electrical impedance tomography (TREIT) of the prostate. Physiol Meas 33(5):719–738 16. Tang MX, Wang W, Wheeler J, McCormick M, Dong XZ (2002) The number of electrodes and basis functions in EIT image reconstruction. Physiol Meas 23(1):129–140 17. Tehrani JN, Oh TI, Jin C, Thiagalingam A, McEwan A (2012) Evaluation of different stimulation and measurement patterns based on internal electrode: application in cardiac impedance tomography. Comput Biol Med 42(11):1122–1132 18. Wang HX, Wang C, Yin WL (2001) Optimum design of the structure of the electrode for a medical EIT system. Meas Sci Technol 12(8):1020–1023 19. Wang Q, Wang HX, Zhang RH, Wang JH, Zheng Y (2012) Image reconstruction based on L1 regularization and projection methods for electrical impedance tomography. Rev Sci Instrum 83(10):104707 1–11 20. Zhang XJ, Chen MY, He W (2010) Modeling and simulation of open electrical impedance tomography. In: 14th International symposium on applied electromagnetics and mechanics 33:713–20
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ORIGINAL ARTICLE
Evaluation of measurement and stimulation patterns in open electrical impedance tomography with scanning electrode Jinzhen Liu1 · Hui Xiong1 · Ling Lin2 · Gang Li2
Received: 26 September 2013 / Accepted: 3 March 2015 / Published online: 13 March 2015 © International Federation for Medical and Biological Engineering 2015
Abstract The reconstruction quality in electrical impedance tomography is limited by the current injection amplitude, the injection and measurement patterns, and the measurement accuracy as well as the number and placement of electrodes. This paper dedicates to increase the number of independent voltage measurements by scanning electrode (SE), and design an optimal measurement and stimulation pattern for open electrical impedance tomography (OEIT). Firstly, several measurement patterns are, performed in OEIT, aiming to evaluate the right number of the measurement points for the imaged target in a certain depth. The results indicate that the image quality gets higher with the number of measurement point increased to some extent. Thus, it can guide the optimum design for the electrode system in OEIT. Secondly, through the numerical calculation and salt water tank experiment, in contrast to adjacent current injection pattern, cross-current-injection pattern achieves better reconstruction with higher imaging quality and penetration depth, and is more robust against data noise in deep domain. Lastly, the experiments also indicate that
* Jinzhen Liu [email protected] Hui Xiong [email protected] Ling Lin [email protected] Gang Li [email protected] 1
School of Electrical Engineering and Automation, Tianjin Polytechnic University, Tianjin, People’s Republic of China
2
State Key Laboratory of Precision Measurement Technology and Instruments, Tianjin University, Tianjin, People’s Republic of China
the electrode contact area affects the reconstruction quality and investigation depth. Therefore, OEIT with SE can improve the application in clinic, such as the detection and monitoring of vascular, breast, and pulmonary diseases. Keywords Open electrical impedance tomography · Scanning electrode · Cross current injection mode · Adjacent current injection mode
1 Introduction Electrical impedance tomography (EIT) is particularly promising because of its functional imaging, non-invasion, and medical imaging monitoring, which has been gradually developed in recent decades. It is characterized to reflect the structure and function of the internal organs and tissues by imaging the distribution of conductivity from measurement of the surface potential [7]. Static and dynamic EIT methods are performed according to the applications, particularly attractive in many important applications such as the detecting and monitoring about pulmonary function, breast, and brain diseases, and many industrial applications such as the fields of process tomography, nondestructive testing, geological studies, and archaeology [2]. According to the imaging domain model, EIT can be divided into enclosed EIT and open EIT (OEIT), which is referred to as EIT on unbounded domain in geophysical prospecting [10]. In enclosed EIT, the uncertain electrode position and inconsistent imaging domain shape result in low image quality and resolution. However, OEIT can alleviate these such as position error, ringing and movement artifacts, and make EIT more suitable for clinical application. In order to overcome the uncertainty of electrode position in the enclosed EIT, Mueller et al. [11] began
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to use fixed electrode array to detect the target in shallow domain but the whole measured domain. Huang et al. [8] rotated the electrode pairs attached on a phantom tank to scan around the boundary of the imaging object, which can enhance the reconstruction quality by increasing the electrode number. However, the reported scanned image is restricted to the application in uniformly cylindrical phantom tank. At present He et al. [6] and Zhang et al. [20] in Chongqing University have developed a system for OEIT with only eight fixed electrodes, and have applied it into the breast disease detection and monitoring as well as preliminary clinical applications. However, the imaging system obtains low imaging quality. The reconstruction quality of EIT is determined by the current injection amplitude, the current injection and voltage measurement patterns, and the measurement accuracy, as well as the number and placement of electrode [16]. In practice, firstly, the number of electrode and current injection is limited, resulting in the information obtained from the boundary electrode that is not enough to determine the internal impedance distribution, so it suffers from a high degree of nonlinearity and severe ill-posedness [19]. Secondly, EIT itself exhibits ill-posed problem that boundary voltage is only sensitive to the impedance change near the electrode but to the impedance change in the center or deep domain [4]. Most importantly, when the current is injected into the imaging domain, the electric field distribution will be changed by the traditional electrode fixed to the surface of the measured domain [18]. Moreover, current will be bypassed by the adjacent electrode but injected into the interior domain [12]. Therefore, in order to reduce ill-posedness in inverse problem, this paper researches on the OEIT using a scanning mechanism with SE, which can increase the number of independent measurement only by two measurement electrodes, reduce the complexity of the measurement system and the mutual influence among the traditional fixed electrode, and improve imaging quality. In EIT, the current injection patterns consist of adjacent, diagonal, trigonometric and adaptation. Avis and Barber [3] have put forward trigonometric pattern with 90° phase difference between two injection electrodes. Kolehmainen et al. [9] carried out the simulations both with adjacent and with trigonometric current patterns, and it seems that the adjacent pattern is more tolerant of errors than the trigonometric pattern. Adler et al. [1] analyzed various choices of stimulation and measurement patterns and obtained the result that the traditional (and still most common) adjacent stimulation and measurement patterns have by far the poorest performance in comparison with trigonometric pattern. Nasehi et al. [17] evaluated different current injection and measurement patterns with both external and internal electrodes and showed that the trigonometric injection patterns had better performance and improved pixel intensity of the
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small conductivity changes. The results of these papers are not comparable with each other because there are no common parameters among these papers with the perturbation only in one fixed location. In this study, we firstly proposed the novel open electrical impedance imaging mode with scanning electrode and presented the system composition and reconstruction principle. Secondly, based on the OEIT with SE, we evaluated the effect of the number of measurement point on the reconstruction quality, and the effect of cross and adjacent current injection patterns on the reconstruction quality in two-dimensional domain. Lastly, we performed the salt water tank experiment to verify the feasibility and availability of the OEIT with SE, evaluate the impact of the electrode contact area on the reconstruction quality and investigation depth, and evaluate the cross and adjacent current injection patterns.
2 Methods 2.1 Mathematical model for OEIT Compared to the enclosed EIT, the OEIT converts closed domain model into a simple open domain model as shown in Fig. 1, which is more practical than the enclosed EIT. Firstly the open domain mode makes the EIT flexibly apply to various kinds of domain shapes. Thanks to the relative regular domain boundary, the electrode array or SE is easy to be placed. Therefore, in our study we dedicate our research to the OEIT with SE in superficial layer, making EIT more portable. OEIT is a boundary value problem with an incomplete electromagnetic domain boundary constraint condition [15]. However, the mathematical model of enclosed EIT can also be applied to OEIT. It is assumed to be a virtual field problem by solving a certain sensitive field instead of the whole electromagnetic field. In theory, EIT is the solution of forward problem and inverse problem in lowfrequency current field. When solving the EIT problem, we
Fig. 1 Two domain models with electrodes in the boundary, a the closed domain model, b the open domain model
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only consider the electric field effect and ignore the magnetic field effect because of the low permeability of biological tissue. Based on the current field with low frequency and low permittivity, from the mathematical point of view, the research field is considered as the quasi-static field. And it is assumed that there is no current source in the sensitive field, so according to Maxwell equation, the potential distribution ϕ and the conductivity distribution σ meet the elliptic partial differential equation in the electric field [5]: ∇ · −σ (x, y)∇ϕ(x, y) = 0 (x, y) ∈ Ω (1a) Without considering the surface contact impedance, the Dirichlet and Neumann boundary conditions [14] for the model shown in Fig. 1b can be stated as follows:
ϕ(x, y) = f (x, y) σ (x, y)
(x, y) ∈ ∂Ω
∂ϕ(x, y) = j(x, y) (x, y) ∈ ∂Ω ∂ n�
(1b) (1c)
where n is the unit outward normal vector to the boundary ∂Ω, f is the measured electrode potential and j is the current density at the current injecting electrodes. Dirichlet conditions are assumed under electrodes, while Neumann conditions on the remaining part of the boundary. For each electrode, the flux of the current density through the contact surface must equal the injected current ∂ϕ(x, y) dS = Il l = 1 . . . L ′ σ (x, y) (2) ∂ n� ∂Ωl
where l is the electrode number, Il is the injected current at the electrode l, S is the surface of the electrode. Underneath the inter-electrode gaps no current should flow, and the following condition is applied:
∂ϕ =0 ∂ n�
on ∂Ω {∂Ω1 ∪ · · · ∪ ∂ΩL′ }
F(σ ) =
1 1 [v(σ ) − v0 ]T [v(σ ) − v0 ] + α(σ − σ0 )T R(σ − σ0 ) 2 2
(4) where v(σ) is the voltage vector obtained by solving the forward problem, v0 is the measurement voltage vector, T is the transpose matrix, α is the regularization parameter and R is the identity matrix. In practical implementation, the optimization problem (4) is solved iteratively by the Gauss–Newton method, and the updated electrical conductivity distribution is expressed as follows:
δσ = −(J T J + αR)−1 [J T (v(σ ) − v0 ) + α(σ − σ0 )]
(5)
where J is the Jacobian matrix. 2.3 The scanning platform and measurement patterns In this paper, a four-terminal measurement protocol consisting of a bipolar push–pull current injection and a differential voltage measurement is performed to obtain the boundary voltages. The schematic diagram for OEIT with SE is shown in Fig. 2. The current produced by module 7 is injected into domain 9 by electrode 1 and flowed from electrode 2. The electrode 2 is driven by the mechanical skid platform 5 and scans along the domain boundary to carry out multiple current injections. Then after each current injection, the resulting voltages from the adjacent electrodes 3 and 4 which are driven by mechanical skid platform 10 are recorded by the signal acquisition device 6. Lastly the recorded boundary voltages are transmitted to the computer for reconstruction. Therefore, the electrode scanning pattern is promising to increase the number of boundary voltage in the limited measurement area and avoid the influence of electrode on electric field distribution.
(3)
where ∂ΩL′ is the boundary underneath electrode L′. The forward problem of EIT refers to determine the potentials in the domain by solving the boundary value problem in (1) with the known boundary conditions and conductivity distribution. The inverse problem is the solution of the conductivity distribution with known boundary conditions and electrical potential distribution. 2.2 The inverse method The reconstruction for OEIT is in terms of a traditional nonlinear, least squares Gauss–Newton–Raphson approach [13] with Tikhonov style regularization. Regularization techniques are commonly adopted to stabilize the inversion to solve the ill-posed problem. The cost function is
Fig. 2 Schematic diagram for OEIT with SE, (1, 2) current injection electrodes, (3, 4) voltage measurement electrodes, (5) mechanical skid platform for current injection, (6) signal acquisition device, (7) current source, (8) computer, (9) imaging target, (10) mechanical skid platform
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Fig. 3 Block diagram of current injection and voltage measurement patterns, a crosscurrent-injection pattern, b adjacent current injection pattern
We firstly evaluate the effect of the number of boundary voltage collected by SE on image quality. Secondly, because the current injection mode will affect the ill-posed condition of inverse problem, we also perform the research on the effect of adjacent and cross-current-injection patterns on the imaging quality and robustness. The block diagram of current injection and voltage measurement patterns are shown in Fig. 3. The cross-current-injection pattern refers to that the current is injected into two measurement points with different interval that is gradually increased, which can make the current distribution more uniform. In the cross injection strategy, the current is injected into measurement point 1 that is fixed and firstly flowed from measurement point 2, and the resulting adjacent voltages are collected. Secondly the current is injected into measurement point 1 and flowed from measurement point 3, and the resulting voltages between other adjacent measurement points are measured. Then the constant current is injected into measurement point 1 and flowed from other cross measurement points, in turn the voltages between other adjacent measurement points are measured. Thus, we can obtain (n − 2) × (n − 3) boundary voltages, where n is the number of measurement point. In the adjacent injection strategy, the current is firstly injected into measurement point 1 and flowed from measurement point 2, and the resulting voltages from the remaining adjacent measurement points are collected. Then the constant current is injected into other adjacent measurement points, and similarly the voltages between other adjacent measurement points are measured. Thus we can also obtain (n − 2) × (n − 3) boundary voltages.
Fig. 4 Measurement system for OEIT, a the experiment setup, b the schematic diagram
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2.4 Simulation and experimental protocols In this study, the imaging domain is 175 mm in width and 75 mm in length. The fine mesh with 4290 triangulation elements and 2247 nodes is for the forward solution, and the coarse mesh with 1080 triangulation elements and 592 nodes is for the inverse solution. The conductivity will affect the reconstruction quality, but the conductivity difference will not affect the performance comparison. For comparison, in the simulations, we choose the conductivities of the inclusion and background according to the common study. In the phantom modes shown in Fig. 5a, the conductivity of inclusion is 2 S/m and the background conductivity is 1 S/m. In the phantom mode with two inclusions shown in Fig. 7, the conductivity of the inclusion on the right is 8 S/m, the low conductivity of inclusion on the left is 1 S/m, and the background conductivity is 4 S/m. The synthetic data are created using the forward model based on the simulation software Matlab with the injection current of 5 mA and the frequency of 1 kHz. In the salt water tank experiment, the small electrode can be seen as the point electrode with the diameter of 1 mm. The diameter of the big electrode is 5 mm. We use ten metal big electrodes placed on the side of the domain boundary for injecting current. The middle 14 boundary voltages are collected by the scanning electrode with the diameter of 1 mm driven by the displacement table. The increase in injection current amplitude strengthens the electric field intensity in the imaging area. Thus the signal-tonoise ratio of the boundary voltage can be improved, which can improve the electrical impedance imaging quality.
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Fig. 5 Reconstruction images in the depth of 5, 20, and 35 mm using 8, 16, 20, 24, 28, and 32 measurement points. a Original phantom models, b reconstruction images with the inclusion in the depth of 5 mm, c reconstruction images with the inclusion in the depth of 20 mm, d reconstruction images with the inclusion in the depth of 35 mm
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However, the current amplitude should be smaller than 5 mA considering safety. The height of the domain is 95 mm, the length is 225 mm, the interval of the two current injection electrodes is 5 mm, and the interval of the boundary voltage is 5 mm. The injection current is 1 mA with the frequency of 1 kHz. Figure 4a, b shows the actual measurement system and the schematic diagram for OEIT, including the displacement table, the current injection electrodes, the scanning electrode, the current source, and the salt water tank. We use the Labview software to control the motor, collect the boundary voltages, process the signal, and store the image information. The total scanning time for measuring 128 boundary voltages is 8.4 min. In our study, correlation coefficient is employed to evaluate imaging accuracy, which is calculated as follow: n (ˆgi − g¯ˆ )(gi − g¯ ) a = i=1 (6) n gi − g¯ˆ )2 ni=1 (gi − g¯ )2 i=1 (ˆ where α is correlation coefficient, gˆ is reconstruction electrical conductivity and g is initial electrical conductivity. Furthermore, g¯ˆ and g¯ are the average value of gˆ and g, respectively. The reconstruction image is close to the real image when the value of α is bigger.
3 Results 3.1 The simulation results 3.1.1 The effect of the number of measurement point on the reconstruction quality By increasing the number of measurement point, we can obtain more independence boundary voltage, so the study about 8, 16, 20, 24, 28, and 32 equally interval measurement points are, respectively, performed to explore the
Fig. 6 Comparison of correlation coefficients for the reconstructions
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effect of the number of measurement point on image quality in the domain shown in Fig. 3a. Figure 5a shows the conductivity distributions for the inclusion in the depth of 5, 10, 15, 20, 25, 30, 35, 40, and 45 mm. Figure 5b–d shows the reconstructions for the inclusion in the depth of 5, 20, and 35 mm using 8, 16, 20, 24, 28, and 32 measurement points. Figure 5 illustrates that the reconstruction images are so terrible using eight measurement points that we cannot distinguish the size, shape, and position of the inclusion. In the depth of 5 mm, the imaging quality is better than that in the depth of 20 and 35 mm, which produces more image artifacts. Figure 6 shows the reconstruction correlation coefficients for the results of the inclusion in the depth of 5, 10, 15, 20, 25, 30, 35, 40, and 45 mm, respectively, using 8, 16, 20, 24, 28, 32 measurement points. 3.1.2 The effect of current injection pattern on the reconstruction quality In this study, the adjacent and cross-current-injection patterns using 32 measurement points are chosen to evaluate the effect of current injection pattern on the reconstruction quality in the phantom mode with two inclusions. Figure 7a, b shows the reconstructions, respectively, by the cross and adjacent current injection patterns with the inclusions in the depth of 15, 25, 35, and 55 mm. In order to test the robustness to noise about the two current injection patterns, 50- and 40-dB Gaussian noise is added to the synthetic data, respectively, with the inclusions in the depth of 15, 25, 35, and 45 mm. Figure 7c, d shows the reconstructions by cross and adjacent current injection patterns with the noise level of 50 dB. Figure 7e, f shows the reconstructions by cross and adjacent current injection patterns with the noise level of 40 dB. We also compare the correlation coefficients that are shown in Table 1. 3.2 The salt water tank experiment results In order to evaluate the adjacent and cross-current-injection patterns, as well as the impact of the electrode contact area on the reconstruction quality and investigation depth, we perform the salt water tank experiment. Although the big electrode has its inherent advantages, the big area of the electrode will inevitably cause the potentials under the electrode equal and affect the electric field distribution inside the domain. This problem still exhibits even with the composite electrode. Obviously, in the reconstruction calculation, the electrode area should be considered. The needle electrode with small area and the cylinder electrode with big area are, respectively, used as the current injection electrode. Then, we discuss the impact of the electrode contact area on the reconstruction quality and investigation
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Fig. 7 a, b Reconstructions by the cross and adjacent current injection patterns. c, d Reconstructions by the cross and adjacent current injection patterns with 50-dB noise. e, f Reconstructions by the cross and adjacent current injection patterns with 40-dB noise
Table 1 Comparison of the correlation coefficient for the results of Fig. 7 Without noise
15 mm
25 mm
35 mm
55 mm
Cross Adjacent
0.8984 0.8985
0.7773 0.7593
0.6429 0.6456
0.4197 0.1753
With 50 dB noise
15 mm
25 mm
35 mm
45 mm
Cross Adjacent
0.6695 0.7424
0.4155 0.4250
0.3038 0.1814
0.1799 0.0871
With 40 dB noise
15 mm
25 mm
35 mm
45 mm
Cross
0.5846
0.3620
0.2273
0.1002
Adjacent
0.6629
0.3319
0.1423
0.0314
depth by the cross-current-injection pattern and the adjacent voltage measurement pattern to verify the availability of the scanning electrode.
Figure 8a shows the boundary voltage distributions, respectively, using the big and small metal electrodes as the current injection electrodes in the simulation calculation. From Fig. 8a, we can see that the boundary voltages by the big electrode are higher than those by the small electrode. The results of the salt water tank measurement are shown in Fig. 8b. In the reconstruction test, we place the organic glass rod in the salt water tank in the depth of 5 and 20 mm and use the designed collection system to obtain the boundary voltages. The diameter of the organic glass rod is 8 mm. The reconstructed images by the big and small electrodes are shown in Fig. 9. From the measurement, we can also conclude that the measured boundary voltage quality by cross-currentinjection pattern is higher than that by the adjacent current injection pattern. However, because of the low signal-tonoise ratio of the measured data by the adjacent current injection pattern, the reconstruction is hardly performed. Figure 8b shows the boundary voltages measured by the
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Fig. 8 Boundary voltage distributions u1 and u2 are, respectively, using the big and small metal electrodes as the current injection electrodes, a in the simulation calculation, b in the salt water tank experiment
cross-current-injection pattern with the noise level above 60 dB. Therefore, the salt water tank experiment indicates that the cross-current-injection pattern is more suitable for OEIT.
4 Discussion and conclusion Compared with the traditional enclosed EIT, OEIT with SE overcomes the restriction of imaging domain and the number of fixed electrode, but reconstruction imaging quality is still the bottleneck that limits the EIT for further development. In order to improve the imaging quality, this paper Fig. 9 Reconstructions by the electrodes with different contact area for the current injection, when the organic glass rod is place in the depth of 5 and 20 mm. a The reconstructions by the big electrodes, b the reconstructions by the small electrodes
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proposed an OEIT pattern with SE. And we performed the optimization design for the voltage measurement pattern and current injection pattern to obtain the optimum reconstruction. The correlation coefficients for Fig. 5 reflect the effect of measurement point and the depth of inclusion on the reconstructions. To summarize, from Figs. 5 and 6, we can conclude that, when the inclusion in a certain depth, the reconstruction quality rises as the number of measurement points is increased, and this effect is largest for target in the bottom. This may be explained by the expanded independent measurement voltages that are measured by SE. The number of independent measurement voltage can reduce the ill-posed condition of inverse problem. But increasing the measurement point requires the hardware system to improve measurement accuracy and enlarge the measurement dynamic range. Figure 6 illustrates that the imaging quality is increased slightly when the measurement points are increased to a certain extent. According to this result and priori position knowledge in actual measurement, the high-quality reconstruction will be product with optimal measurement point. We suggest that it is important to evaluate the number of measurement point, the current amplitude, and the measurement accuracy as well as the depth of target according the prior knowledge in OEIT. Figure 7a, b and Table 1 illustrate that the reconstruction quality and correlation coefficient have a few difference in the depth of 15, 25, and 35 mm by the two current injection patterns. However, in the depth of 55 mm, the reconstruction image by the adjacent current injection pattern contains bigger imaging artifact, and the correlation coefficient is lower by 0.2442 in comparison with the cross-current-injection pattern. The results indicate that the cross-current-injection pattern achieves better reconstructions with higher imaging quality and penetration depth. This may be explained that the commonly used adjacent current injection pattern makes the current to distribute in the superficial layer of the image domain, so the current density in the center of domain is relatively small. While the cross-current-injection pattern is able to make the
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current distribution of internal domain more uniform and increase the current penetration depth. From Fig. 7c–f, we observe that the adjacent current injection pattern obtains better reconstruction quality in the depth of 15 mm, but in the depth of 35 mm and 45 mm the cross-current-injection pattern achieves higher reconstruction quality and correlation coefficient. In Fig. 8b, the voltage differences between the big and small electrodes are less than the results of the simulation calculation. The reason mainly is that the contact area of the big electrode can influence the electric field distribution. From the previous analysis, the electrode contact area of big electrode will force the potentials under the electrode into equal potential, which can cause the boundary voltages smaller in actual measurement than in the theoretical calculation, which is consistent with the theoretical analysis [18]. From Fig. 9 we can conclude the electrode contact area will affect the reconstruction quality of OEIT. The results also illustrate that the scanning electrode with small contact area improves the resolution of the traditional EIT with fixed electrode and promotes the development of EIT. Because of the open domain model in reconstruction, the OEIT improves the applicability of EIT, which can be applied in the study of superficial body surface conductivity character, such as the detection of abdomen, lungs, and breast diseases. In the salt water tank experiment, the total scanning time for measuring 128 boundary voltages is 8.4 min. In future study, we will reduce the scanning time to increase the real-time capability of reconstruction. The electrode error is the main source of the measurement error. In the experiment, we found that the driver chip fever will cause unstable job of the displacement platform. Therefore, firstly, we should improve the stability of the displacement platform. Then, in order to guarantee the measurement conditions and contact impedance as consistent as possible, the pressure sensor should be added to the measurement electrode in future study.
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