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Analysis of response for magnetic induction tomography with internal source
Accepted Manuscript Analysis of Response for Magnetic Induction Tomography with Internal Source Yan Fu, Chao Tan, Feng Dong PII: DOI: Reference:
S0263-2241(15)00553-9 http://dx.doi.org/10.1016/j.measurement.2015.10.019 MEASUR 3631
To appear in:
Measurement
Received Date: Revised Date: Accepted Date:
20 December 2014 23 September 2015 9 October 2015
Please cite this article as: Y. Fu, C. Tan, F. Dong, Analysis of Response for Magnetic Induction Tomography with Internal Source, Measurement (2015), doi: http://dx.doi.org/10.1016/j.measurement.2015.10.019
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Analysis of Response for Magnetic Induction Tomography with Internal Source Yan Fu, Chao Tan* and Feng Dong Tianjin Key Laboratory of Process Measurement and Control, School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China *Tel & Fax: 86-22-27892055; Email: [email protected] Abstract: Magnetic induction tomography (MIT) can reconstruct the distribution of conductivity within the sensing field in a non-invasive and non-intrusive manner, thus receives wide attentions for its applications in industrial and biomedical detections. In some particular cases, internal signals exist in the sensing field that would affect the response of MIT. The information of the internal signals might aid the understanding of the condition of the process/object being measured. In order to understand the effects of internal sources upon the reconstruction accuracy and dynamic responses of MIT, the Izhikevich model is applied to generate different internal sources, and numerically simulated to study the responses of magnetic induction with the internal signals. The simulation results show that an internal signal causes a shifting of the object’s location in the reconstructed image, and the amplitude of the U-shape curve formed by the measurement of MIT receivers is helpful to recognize the internal sources of different signal pattern and number. Dynamic responses of the MIT to the point source model and the multi-point source model of different internal signal shapes are also numerically investigated. A modified independent component analysis (ICA) method is introduced to separate the internal signals from the measured signals. Simulation results show that the internal signals induced in MIT’s receivers can be separated by using ICA, and the kurtoses of the separated independent components are robust in identifying different internal sources. This work verifies that MIT could handle the coupling information detections, and the coupled signals could be separated effectively with ICA.
Keywords: Magnetic Induction Tomography; Internal Source; Signal Recognition; ICA; Feature Extraction
1 Introduction A non-contact and non-invasive detection method has potential applications in many fields. In a continuous industry process with high temperature or high pressure, a non-destructive detection method can monitor the process status and also measure the process parameters, for instance pipe health monitoring (Ma and Soleimani 2012). In biomedical applications, a non-destructive detection is valuable in physiological function research, for instance continuous monitoring on cardiac activities, gastric emptying and lung ventilation, lung or heart diseases diagnosis and others (Morucci et al 1996, Boone et al 1997, Frerichs 2000, Ren 2002). Comparing with the traditional detection method, electrical tomography has many benefits in the aforementioned situations, such as obtaining the general information of the object measured and reconstructing the image of a medium distribution. Electrical tomography can be divided into three kinds by sensing manners: contact measurement, incomplete contact measurement and contactless measurement. For the first two kinds, electrodes are in contact with the target to be tested, forming an electric circulation path in between electrodes, which produces coupling effects with the target and deteriorates measurement quality. Therefore, contactless sensor tomography has been given intensive attentions in practical applications, due to the advantages of no leakage current, non-invasion and low cost in measurement (Griffiths et al 1999). Magnetic induction tomography (MIT) is a typical noninvasive and contactless imaging method that reconstructs the interior electrical properties in the sensing field (Griffiths 2001, Korjenevsky et al 2000, Peyton et al 1996, Scharfetter et al 2008, Vauhkonen et al 2008, Watson et al 2008). MIT applies a time-varying exciting signal at the external of object space. An eddy current induced by the conductive target in the exciting magnetic field causes a secondary magnetic field which is detected by receivers placed around the region of interest. By sensing the response of a driving current or voltage that applied on the transmitter, MIT can reconstruct the physical properties (e.g. conductivity) distribution within the measuring section by using certain reconstruction algorithms (Soleimani et al 2006). It is a noninvasive imaging method with easy sensor installation but without ionization or radiation, which is favorable to biomedical detection comparing with nuclide or rays based methods.
For the industry applications of MIT, Peyton et al proposed a planar MIT system to detect defects in metal plates (Yin et al 2006). The axes of the sensitive coils were perpendicular to the test plane, rather than parallel. They conducted MIT simulations on horizontal level for conductivity detection, and concluded that MIT could apply to geophysics and marine engineering with further improvements/modifications. Later, they used MIT to inspect a two-phase metal liquid-gas two-phase flow on a continuous casting process. According to the oscillation patterns, it is possible to distinguish the argon gas injected into the single-phase flow (Terzjia et al 20011). For the biomedical detection with MIT, Al-Zeibak et al (1993) constructed an MIT system that collects multi-projection by mechanically rotating the detected object and reconstructed the distribution of the object space with the linear back projection algorithm. Korjenevsky et al (1997, 2000) developed a similar MIT system for biological tissue tomography. Watson et al (2003) found that the quality of reconstructed image mainly depends on the phase measurement accuracy, and proposed a new MIT system with a phase measurement accuracy of 0.01° at 10MHz operation frequency. In 2008, they designed a 16-channel MIT system to detect the medium with the conductivity lower than 10 S/m, and reconstructed an image of a human leg in vivo at a phase measurement accuracy of 17m° (Watson et al 2008). Merwa (2003) verified the feasibility of using MIT in cerebral oedema detection both by simulation and experiment, and found that a multi-frequency MIT would improve the detectability because of the sensitivity increases considerably at higher frequency. Gürsoy et al (2009, 2011) solved the problem of incorrectness in imaging caused by the movement of patients during data acquisition, through optimizing sensor structure and data processing system. Yasin (2014) used several approaches to improve the measurement accuracy and spatial resolution in hemorrhagic stroke detection by using MIT. The results showed that the selected approaches enhanced stroke visibility, lowered stroke detectability threshold from 15 ml to 5 ml, and improved the localization of phantom hemorrhages by combining the proposed approaches. Sun et al employed magnetic induction phase shift information in acute cerebral hemorrhage detection in rabbits, and reached a high sensitivity in bleeding detection ( Sun et al 2014, Jin et al 2014).
The research of MIT used to focusing on the design or optimization of sensor structure, data acquisition system and reconstruction algorithm, in order to improve the accuracy of measurements and finally the resolution of image reconstruction. Under some specific environments, the internal electricity signals may exist in the object space, such as in electrically charged fluid or in vivo biological tissues. This condition has not been considered in previously published studies. Sometimes, the internal signals reflect the status of the measured object. Take the biomedical detection as an example, electrocardio signals, myoelectric signals and electroencephalogram signals exist in different vivo tissues in human body, and they could reflect different health status of human body directly. The electroencephalogram signal could confirm the epilepsy and facilitate the diagnosis of hemorrhagic stroke in terms of its abnormal performance. If an internal source affected the resolution or precision of reconstructed image, measurements should be treated to remove or weaken such effects in MIT imaging. On the other hand, if MIT could obtain the distribution of conductivity and the location of the internal source in object space simultaneously, more useful information could be extracted to aid estimating the status of the target. Since neither similar topics nor the working mechanism of MIT in such detections have been reported so far, it is essential to understand the sensing field distribution of MIT and the interactions between MIT and internal source at first. In this paper, the Izhikevich model was adopted to simulate the varying internal sources. Considering the difficulty in quantitatively setting complex internal signals that can be detected by MIT in practical experiments, we conducted numerical simulations to analyze the detection of object with internal source based on MIT. Four distributions of internal source models were introduced, including the point source model, the multi-point source model, the line source model and the disc source model. In order to obtain the representative results, the point source model and multi-point source model are adopted in dynamic simulation analysis. Independent component analysis (ICA) is used to separate the internal signals from MIT observations, and to recognize them with different shapes and fluctuations by using high order statics of the separated independent components. According to the preliminary results, MIT has been verified feasible to
detect the object with internal sources and providing auxiliary information of detection conditions and electrical activities monitoring.
2 Theoretical foundation 2.1 Measurement principle Based on the electromagnetic induction principle, generalization of electromagnetic induction, law of total current, continuity of magnetic flux and Gauss’ law, MIT system could be presented by the macroscopic form of Maxwell’s equations as follows (Shang 1999, Assous et al 2000, Fu et al 2013):
D H J t B E t B 0 D ρ
where, H as magnetic density, E as electric field intensity, B as magnetic flux density, D
as electric displacement, J as current density, ρ as charge density. Equations (1) are under the assumption that the object material has linear and isotropic electrical and magnetic properties. Therefore, their constraint equations are as follows:
D εE J σE B μH
where, ε is the permittivity, σ is the conductivity and μ is permeability. According to equations (1) and (2), the electric field in object space could affect parameters in electric field and further change the measurements of MIT through the transmissions of electric field thus change the magnetic induction. Based on the above equations, the electromagnetic conversion is deduced as follow:
B μ H μ σE jωεE
where, μ is the relative magnetic permeability.
Define the curl of the magnetic vector potential A as magnetic flux density, which is
described as A B . According to the Coulomb standard condition, A 0 , equations (2)
turns into 2 A μ σE jωεE . With a further deduction, the electromagnetic field magnetic vector potential equation is expressed as follow:
( μ 1 A) jωσA
According to the theory of electromagnetic induction, varying magnetic field produces varying electric field. Thereby, a voltage signal is acquired through a receiving resistance when a varying electric current flows through the receiver. To bridge the output voltage of a practical
MIT system with the magnetic vector potential A in simulation, a relationship is deduced in (5).
dφ d (B S ) d ( A l) U n n njωl ( A1 A2 ) dt dt dt
where, A1 , A2 as the magnetic vector potential on the two endpoints of detecting coils. n and l represent the number of turns of receivers and the axial length along with pipeline respectively. represents the radian frequency. As shown in (5), given a pre-set excitation condition, resulted voltages in receivers are linearly proportional to the difference of magnetic vector potentials. Hence, the difference of magnetic vector potential reflects the change of the electromagnetic field distribution of MIT. 2.2 Independent component analysis As a method of blind source separation (BSS), independent component analysis (ICA) explores statically independent components and non-Gaussian factors from multi-dimensional or multivariate data. The development of ICA theory started in the early 1990s, when Jutten and
Herault (Jutten et al 1991) proposed the concept of ICA. ICA theory and algorithms developed rapidly and gradually extended to relative fields until the mid of 1990s.
Figure 1. Schematic diagram for ICA algorithm
Figure 1 demonstrates the calculation process of ICA. Assuming all the source signals are independent, a group of observations is expressed by a linear combination of statically independent variables. In addition, equation (6) and (7) describe Figure 1 as.
X Q X
Y W X W Q X
where, X is observation matrix, X is whiting matrix and Y is independent component. Whiting process in (6) reduces the complexity of problem. Therefore, ICA is essentially to optimize the separative matrix W through iterative estimations. The fix-point algorithm was used to estimate the separative matrix W (Hyvärinen et al 1997). Apply Newton iterative method to process the observation matrix, select negentropy maximization as objective function and separate one independent component for each process.
3
Effects of Internal Source in MIT Imaging
3.1 Simulation model description Build the simulation model according to an experimental device as shown in Figure 2. The experiment device used in this part referred to the mature sensor array design introduced by X
Ma. (Ma et al 2006, 2008) The center circular area of the model represents the object space that surrounded symmetrically by eight identical coils (coil 1 to coil 8). The simulation model is established by neglecting the thickness of pipe wall and simplifying each coil as a segment whose length equals to the diameter of the coil. In addition, set a shield layer at the external part of the sensor array in order to insulate the sensing field from the external noise. The shield layer is essential in MIT detection in which the measurements are very small compared to the direct coupling and other coupling mechanisms. However, the work is mainly to verify the effectiveness of internal sources detection and separation by using the magnetic induction method. The details of shield layer analyses is not included this time and more details of shield layer effects in MIT detection could refer to the reference (Wang et al 2011).
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(b)
Figure 2: MIT sensor array (a. diagram of practical sensor array, b. simplified simulation model) 3.2 MIT Imaging results The object space distribution is shown in Figure 3, an object at the center of the object space with a point source inside. The background conductivity and the target’s conductivity are 0.1S/m and 10S/m respectively, the electric current applied in the coil is 1.2A/m. The point source is a current source, which varies from 5mA to 100mA. The linear back projection algorithm reconstructed the image of the object.
Figure 3. Object space distribution for simulation model The sub-graphs in the first row of Figure 4 demonstrate the U-shape measured voltages of MIT in point source model detection when setting coil 1 as transmitter and others as receivers. With the intensity of internal signal in the target increasing, the of U-shape becomes more asymmetrical. Because the internal signal distorts the distribution of magnetic field in a way that the magnetic flux is enhanced at the position of internal signal. As demonstrated in Figure 4, the internal source obviously causes a location shift of the target in the reconstructed images that compared with the real location of target (dashed circle) in sensing field. This distortion directly corresponds to the asymmetry of U-shape measured voltages. The stronger the internal signal is, the more shifting of target in the reconstructed image. Sub-graphs (f) to (i) are the results for the multi-points model. The asymmetry of the U-shape measurement become more serious and the more shifting of target in the reconstructed image with same strength of internal source as the point source model.
Figure 4. Image reconstruction results of object with single-point internal source (a. without internal source, b.5mA, c. 10mA, d. 50mA, e.100mA) and multi-point internal source (f. 5mA, g. 10mA, h. 50mA, i.100mA)
3.3 Sensing field distribution for different internal source The internal sources have different types, therefore several internal sources of different types are used to simulate the MIT sensing field distribution with each internal source. Four different internal sources were introduced in the simulations: point source, multi-point source, disc source and line source. Different internal sources would change the intensity of magnetic field in different way, thus lead to the amplitude floating of measurements and the asymmetry of
U-shape curves at different level, and finally shift the position of target in the reconstructed image. Keept the background conductivity and the excitation currents in transmitter the same. The intensity of internal source for each simulation is 100 mA. Figure 5 illustrates the sensing field distributions of each simulation model for different internal sources, where the contour represents the electric field distribution and the arrow represents the magnetic field distribution. The magnetic fields of produced by the dipole of both the same direction and the different direction have been investigated. Figure 5 only gives an exemplary distribution contour of different models.
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(b)
(c)
(d)
Figure 5. Sensing field distribution, where the contour represents the electric field distribution and the arrow represents the magnetic field distribution (a. point source, b. multi-point source, c. disc source, d. line source)
Figure 6 shows the measurements from seven receivers at one excitation of each model in Figure 5. Considering the simulation without internal sources as a reference, measurements of different internal source models have obvious discrepancies, which can identify the internal sources. Disc source model has the largest measurements among these models. Then, multi-point source with the same electrical field direction has higher measurements with well symmetrical structure because of the increased intensity of the magnetic field. If the multi-point source has different direction, the asymmetry of U-shape curve is quite noticeable, because the different direction of magnetic fields produced by the two point sources leads an asymmetrical sensing field distribution. U-shape curves for one point source and line source are higher than the reference curve, which tells the existence of an internal source. Little discrepancy between these two U-shape curves makes them hardly to distinguish, because the 2-D simulation with same parameters configuration cause this phenomenon. Nevertheless, results in Figure 6 confirm that an internal source directly affects the sensing field distribution of MIT, and it is possible to recognize the type of internal sources through features extracted from the measured voltages.
Figure 6. Measurements comparisons between different internal source models
4 Dynamic simulation analysis for point source model Internal sources in different applications have distinct features, which could represent different intrinsic identities of detected object and reflect electrical activities. Therefore, if MIT
could induce different signals, then the internal signal can be separated from the observations of MIT. In order to simplify the simulation and obtain representative outcomes, the single point source model and the multi-point source model were employed in dynamic simulations. Apply Izhikevich model (Eugene 2003) as an example to generate different internal sources. The parameter settings of the excitation conditions are constant between models in static simulations. 4.1 Izhikevich model Izhikevich model came forward in 2003, which closely reflects the firing features of true biological neurons and possible to conduct the large-scale calculation in convenience. This model only composes of two equations and one nonlinear term, but can reproduce the rich behaviors of biological electrical activities, such as spiking, bursting and mixed mode firing patterns. The expression of Izhikevich neuron model is as follow:
dv 0.04v 2 5v 140 u I dt
du a(bv u ) dt
v c u u d
If v 30mV , then
where, v as neuron membrane voltage, u as recovery variable. Parameter a and b describe the time scale and sensitivity of u . c and d represent the after-spike reset values of
v and u , respectively. Change the combinations of (a, b, c, d) in equations (8) to (10) will reproduce different behaviors of biological electrical activities. 4.2 Simulation results for internal source without noise By adjusting the parameters of the Izhikevich model, eight different typical signals were simulated. Neocortical neurons in the mammalian brain can be classified into several types according to the pattern of spiking and bursting seen in intracellular recordings. According to Figure 7, regular spiking (RS), the most typical neurons in cortex, intrinsically bursting (IB), a
stereotypical burst of spikes followed by repetitive single spikes, and chattering (CH), stereotypical bursts of closely spaced spikes, represent the behaviors of all excitatory cortical cells. Fast spiking (FS) and low-threshold spiking (LTS) are common behaviors of inhibitory cortical cells. The main difference between FS and LTS is the noticeable spike frequency adaptation at the beginning of LTS. Behaviors of thalamo-cortical (TC) neurons have two types, depolarized and hyperpolarized membrane potential. Resonator (RZ) reproduces the damped and sustained subthreshold oscillations of neurons.
Figure 7. Simulation results based on Izhikevich model. (a) regular spiking (RS), (b) intrinsically bursting (IB), (c) chattering (CH), (d) fast spiking (FS), (e) low-threshold spiking (LTS), (f) thalamo-cortical for depolarization (TC), (g) thalamo-cortical for hyperpolarization (TC), (h) resonator (RZ) Apply the internal signal sources as shown in Figure 7 to the point source model (Figure5 (a)) respectively in MIT simulations. Set sinusoidal current signal as excitation signal in MIT, and the amplitude of the excitation signal and the background conductivity remain the same in static simulations. Since the model is symmetrical (Figure2 (a)), only the measurements when coil1 was transmitter and coil2 to coil8 were receivers were collected in the simulation. Figure 8 illustrates the time domain signals (response of coil2) for each internal source in Figure 7, along with the signal separation results with independent component analysis. Under the fixed simulation condition, all the receivers in MIT have the same response in signal morphology, while the only difference is the amplitudes of measurements from receivers as
shown in Figure 6. Thus, not all the measurements used in ICA are plotted in Figure8. The internal source is coupled in the measurements, hence, it is feasible to apply MIT in detecting the sensing field with internal sources. Considering the independence and amplitudes of measurements in MIT, employ measurements from coil2 and coil3 (Firgure2 (a)) as observations for ICA. Two independent components were separated from the measurements, which are the excitation signal (IC1) and the internal signal inside the object field (IC2). According to the principle of ICA, this method could reconstruct the morphology of signal components, rather than the amplitude and alignment permutation. Therefore, IC2 in Figure 8 (c) and (d) are reversed signals that compared with the chattering and fast spiking in Figure 7.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h) Figure 8. Simulation results and independent component analysis, measurement comes from coil2 (Figure2 (a)). IC1 represents excitation signal and IC2 represents internal source
The peculiar fluctuations of internal signals have correspondence with specific measurement conditions or status of target. Since kurtosis (K) reflects the fluctuation distribution of a signal, it can recognize internal sources of different shapes by calculating the kurtosis of IC2. As listed in Table 1, the kurtosis of separated signals with the data plotted in Figure7 can distinguish the varying internal signals, and ICA is effective to separate the components from the measurements at a high precision while maintaining features of them simultaneously. Table 1. Signal recognition for different internal sources Firing pattern
RS
IB
CH
FS
LTS
TC(f) TC(g)
RZ
K (reference)
28.48 21.26 8.10 11.79 14.41 43.06
16.06
61.35
K (IC2)
28.43 21.23 8.09 11.74 14.33 43.05
16.06
61.15
4.3 Simulation results for internal source with noise Noise is inevitable in practical detection, which could seriously deteriorate the purity of separated signal. In this part, a random noise is superimposed on the internal source signals in simulations to analyze its effects on MIT’s measurements and thus verify the effectiveness of ICA in signal separation. The intensity of the superimposed noise is the variance of the internal signal. Remain other simulation conditions the same in section 4.2. Generally, there are two methods to process the noisy signals. One is to regard the noise signal as an independent component and separate it independently with ICA. The other method is to consider the noise-contaminated signal as an independent component and apply denoising methods to filter out the noise. In this work, the wavelet-denoising method was applied in the latter way to process the independent component with noise. Comparing with the traditional denoising methods in frequency domain, the time-frequency domain based wavelet-denoising method could effectively remove the noise while keeping the details of original signal. Figure 9 illustrates the simulation results for the internal signals with noise. The last sub-graph in each figure illustrates the IC2 after wavelet denoising. Compare the kurtosis (K) of IC2 with the kurtosis of the original internal signals to investigate whether the combination of
ICA and wavelet-denoising method could properly deal with the noisy signals. To estimate the denoising effect, the energy ratio (Per) and standard deviation (Err) are calculated in Table 2, where IC2 denoise and IC2 in equations (11) and (12) represent the denoised independent component and the independent component with noise respectively.
Per norm(IC 2 denoise) / norm(IC 2)
Err norm(IC 2 denoise IC 2)
According to Table 2, the kurtoses of denoised signals are smaller than reference values. However, the errors between the kurtosis of denoised signal with the reference value are small enough to ignore in the internal sources recognition. Energy ratio (Per) in Table 2 indicates that more than 98% information in the independent components has been reserved after denoising. Based on the simulation results and feature extraction, wavelet-denoising method is feasible in eliminating the noise superimposed on internal signals, and kurtosis is an effective feature for signal recognition in such conditions.
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Figure 9. Simulation results and independent component analysis with denoising, measurement comes from the coil2 (Figure2 (a)), IC1 represents excitation signal, IC2 represents internal source and IC2 denoising represents the IC2 filter out noise Table 2. Signal recognition for internal sources with noise Firing pattern K (reference)
RS
IB
CH
FS
LTS
TC(f) TC(g)
RZ
28.48 21.26
8.10
11.79 14.41 43.06
16.06
61.35
K (denoising) 26.05 18.91
7.19
11.76 13.61 41.68
14.43
58.29
Per
0.990 0.988 0.989 0.995 0.990 0.993
0.985
0.986
Err
12.18 14.29 14.81
16.50
13.10
9.56
14.30 11.03
5 Dynamic simulations for multi-point source model In some cases, especially in biomedical detection, more than one type of internal sources exists in the detecting domain, and the measured data is affected by all the sources simultaneously. Therefore, simulation analysis for multi-point source model needs to be considered. The multi-point model in Figure 5(b) is selected and stimulated with three combinations of different signals into analysis: CH-FS, RS-IB and RS-TC(g). Because three models respectively represent the firing patterns in different cortical layers, firing patterns in the same cortical layer and similar firing patterns in different cortical layers. Therefore, they are the sufficient combinations to represent the typical signals to comprehensively investigate the influence of internal sources in this work. Figure 10 illustrates the signal separation results for multi-point source. The shapes of signals are different from direct observations, which are reproduced by the combination of CH and FS. As shown in Figure 10(a), three independent components are separated from the measurements. The excitation signal (IC1) is separated from measurements due to its large signal differences with the other two. IC2 and IC3 are not fully separated in the multi-point source model, but can be recognized by ignoring the uncompleted separation at several spikes. According to the features extracted in Table 3, although the separation of the CH-FS signal is incomplete, the
slight error in feature extraction has little effect on the signal recognition. The signal shape of RS has higher similarities with IB, and the shapes of the reproduced signals RS and TC(g) have partial similarities (Figure6 (a), Figure6 (g)). These similarities of signals bring difficulties in signal separation. Using the separation method for the single point model will deteriorate the separation of multi-point observations. Meanwhile, internal signals are hardly recognized with the kurtosis of signal. A modified method of signal separation is developed for RS-IB and RS-TC (g) as illustrated in Figure 11. This method conducts ICA separation on the measurements twice. For the first time, choose two different groups of observations and apply ICA respectively. After that, two groups of independent components are obtained and the excitation signal (IC11 and IC14) could be separated because of the apparent signal differences with each other. Select the other independent component in each group (IC12 and IC13) to form a new group of observations for the second independent component analysis. The superimposed internal signals could be separated after this step. Figure 10 (b) and (c) demonstrate different internal sources of similar shapes could be identified after separations. This method is possible to extend to the cases that more than two sources exist in one plane, and the modified data processing method is still effective. Figure 10 further validates the feasibility for MIT detecting the object with multiple internal sources. If generalize this modified ICA method into the detecting condition with more internal signals, more observations need to be obtained from receivers. Theoretically, increasing the number of coils as many as possible should receive more observations. MIT could not have too many coils on one layer due to the space limitation, coupling effect etc. A spherical sensor array or coils with multiple layers will provide more observations to improve the precision in signal recognition (Wei et al 2012).
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(c) Figure 10. Simulation results for multi-point source model, measurement comes from the receiver close to transmitter, IC1 represents excitation signal, and IC2 and IC3 represent internal sources ((a) CH-FS, (b) RS-IB, (c) RS-TC(g))
Figure 11. Flow chart of modified ICA (OB11, OB12 and OB13 come from the measurements of coil2 to coil4 in Figure 2; IC1, IC2 and IC3 correspond with them in Figure 10)
Table 3. Signal recognition for multi-point source model Firing pattern
RS
IB
CH
FS
TC(g)
K (reference)
28.48
21.26
8.10
11.79
16.06
K (CH-FS)
-
-
7.47
10.77
-
K (RS-IB)
30.10
19.32
-
-
-
K (RS-TC(g))
28.47
-
-
-
16.10
6 Internal source with small magnitude In some applications, the internal signal is small compared with the excitation signal in MIT detection, for instance untreated electroencephalogram signal is varying only from 10μV to 100μV while the excitation signal injected in a practical MIT device is 10V (Nunez 1981). Whether MIT still effective in such small signals detecting needs verifications. Therefore, new simulations were conducted by changing magnitudes of the internal signals at the same level of untreated electroencephalogram signals.
6.1 Simulations of point source model Select the point source model and keep the simulation settings as introduced in section5 except the amplitude of internal signal. As shown in Figure 12, the observations are hardly affected by the internal signals, so the observations of MIT could be directly applied in image reconstruction without complex data processing. The small internal signal is still detectable by MIT. After the data processing with ICA, the internal signals could be separated from observations. According to data listed in Table 4, kurtosis of IC2 is still effective in signal recognition for small internal signals detection of MIT.
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(h) Figure 12. Simulation results and independent component analysis, measurement comes from coil2 (Figure2 (a)), IC1 represents excitation signal and IC2 represents internal signal
Table 4. Signal recognition for different internal sources Firing pattern
RS
IB
CH
FS
LTS
TC(f) TC(g)
RZ
K (reference)
28.48 21.26 8.10 11.79 14.41 43.06
16.06
61.35
K (IC)
28.43 21.22 8.10 11.76 14.34 43.04
16.06
61.15
6.2 Simulations of multi-point source model Employ multi-point source model into simulations, and set the amplitude of internal signal was set one in a million of excitation signal. Although more internal sources locate in the sensing field, the observations are rarely affected, thus leading little distortions to conductivity distribution reconstruction. The modified independent component analysis method introduced in section 5 is applied here and the signal separation results are shown in Figure 13. The modified ICA can separate the small internal signals from observations. The magnitude of the internal signal affects the accuracy of separation as listed in Table 5. Compare Table 3 with Table 5, kurtosis shows an obvious error especially for the internal signals with partially similar morphology. Error is not big enough to affect the signal recognition.
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(c) Figure 13. Simulation results for dual dipole model, measurement comes from coil2 (Figure2 (a)), IC1 represents excitation signal, and IC2 and IC3 represent internal signals ((a) CH-FS, (b) RS-IB, (c) RS-TC(g))
Table 5. Signal recognition for dual dipole model Firing pattern
RS
IB
CH
FS
TC(g)
K (reference)
28.48
21.26
8.10
11.79
16.06
K (CH-FS)
-
-
7.47
10.77
-
K (RS-IB)
26.09
18.74
-
-
-
K (RS-TC(g))
27.97
-
-
-
15.74
7 Conclusions and outlook In some practical measurement, internal sources affect the sensing field distribution of MIT. If the internal signals are detected by MIT, more comprehensive information can be extracted to facilitate the diagnosis of target conditions and status in detection. An effective method is presented to weaken the effects of internal source in image reconstruction. Signals of different shapes were used as an example of internal sources to investigate the effectiveness of the proposed method. (1) The internal sources shift the reconstructed location of target in sensing field according to the reconstructed images by MIT measurements. The measurement amplitude of MIT has a large difference when an internal source signal exists in the detecting cross section, and the amplitudes of measurements directly relate to the strength and quantity of the internal sources. (2) The μV level internal sources can be induced by MIT receivers, and separated by using ICA in time domain (dynamic response). ICA is effective in separating the internal signal and the excitation signal from MIT observations. When two internal sources (multi-point source model) exist in the sensing field, the separation needs two steps: first the excitation signal and a mixed signal of the multi-point sources are separated by applying ICA to MIT observations; then the internal signal generated by each point can be separated from
the mixed signals by applying ICA again. The modified ICA improves separation of MIT observations and extracts multiple internal sources with high similarities. (3) Kurtosis of the separated internal signals presents high robustness in internal signal recognition. Although the denoising process causes information loss, signal recognition is hardly affected by using kurtosis as a feature. On the other hand, kurtosis also performs properly in multi-point model recognition, even though the two internal signals are similar in shape. MIT can handle the internal signals allowing more applications in industrial and biomedical detections. It is still a preliminary analysis and much more work is required to elaborate this issue in the future. A 3-D model will more closely simulate the real world and present more accurate estimates of the sensing field distribution than a 2-D model, and the simulated model needs experimental validations to provide more evidences to MIT applications in practical detection. Besides, whether the modified data separation method is possible to extend to the more complex internal source model needs further verification.
Acknowledgements The authors appreciate the support from National Natural Science Foundation of China (No. 61571321 & No. 61227006) and Science and Technology Innovation of Tianjin (No. 13TXSYJC40200).
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Korjenevsky A V, Cherepenin V and Sapetsky S 2000 Magnetic induction tomography: experimental realization Physiol. Meas. 21(1) 89-94 Ma L, Soleimani M 2012 Electromagnetic imaging for internal and external inspection of metallic pipes. Insight - Non-Destructive Testing and Condition Monitoring, 54(9) 4931495 Ma X, Peyton A J, Higson S R, Lyons A, and Dickinson S J 2006 Hardware and software design for an electromagnetic induction tomography (EMT) system for high contrast metal process applications Meas. Sci. Technol. 17(1) 111-118 Ma X, Peyton A J, Higson S R, and Drake P 2008 Development of multiple frequency electromagnetic induction systems for steel flow visualization Meas. Sci. Technol. 19(9) 094008 Merwa R, Hollaus K, Biró O and Scharfetter H 2004 Detection of brain oedema using magnetic induction tomography: a feasibility study of the likely sensitivity and detectability Physiol. Meas. 25(1) 347-354 Morucci J P and Rigaud B 1996 Bioelectrical impedance techniques in medicine. Part III: Impedance imaging. Third section: medical applications Crit. Rev. Biomed. Eng. 24(4-6) 655-677 Nunez P L., Katznelson R D 1981 Electric Field of the Brain: The Neurophysics of EEG. New York, Oxford: Oxford University Press, Peyton A J, Yu Z Z, Lyon G, Al-Zeibak S, Ferreira J, Velez J, Linhares F, Borges A R, Xiong H L, Saunders N H and Beck M S 1996 An overview of electromagnetic inductance tomography: description of three different systems Meas. Sci. Technol. 7(3) 261-271 Ren C S 2002 Medical electrical impedance technology and breast tumor measurement China Med. Device Inf. 624-627 Scharfetter H, Köstinger A and Issa S 2008 Hardware for quasi-single-shot multifrequency magnetic induction tomography (MIT): the Graz Mk2 system Physiol. Meas. 29(6) 431-443
Shang J S 1999 High-order compact-difference schemes for time-dependent Maxwell equations J. Comput. Phys. 153(2) 312-333 Soleimani M and Lionheart W R B 2006 Absolute conductivity reconstruction in magnetic induction tomography using a nonlinear method IEEE Trans. Med. Imag. 25(12) 1521-1530 Sun J, Jin G, Qin M X, Wan Z B, Wang J B, Wang C, Guo W Y, Xu L, Ning X, Xu J and Pu X J 2014 Detection of acute cerebral hemorrhage in rabbits by magnetic induction Br. J. Med. Biol. Res. 47(2) 144-150 Terzjia N, Yin W L, Gerbeth G, Stefani F, Timmel K, Wondrak T and Peyton A J 2011 Electromagnetic inspection of a two-phase flow of GaInSn and argon Flow Meas. Instrum 22(1) 10–16 Vauhkonen M, Hamsch M and Igney C H 2008 A measurement system and image reconstruction in magnetic induction tomography Physiol. Meas. 29(6) 445-454 Wang C, Zhang J Q, Li F W, Cui Z Q and Xu C J 2011 Design of a non-magnetic shielded and integrated electromagnetic tomography system. Meas. Sci. Technol. 22(10) 104007 Watson S, Williams R J, Gough W, Griffiths H, Rough W and Morris A 2003 Magnetic induction tomography: phase versus vector-voltmeter measurement technique Physiol. Meas. 24(2) 555-564 Watson S, Williams R J, Gough W and Griffiths H 2008 A magnetic induction tomography system for samples with conductivities below 10Sm-1 Meas. Sci. Technol. 19(4) 1-11 Wei H-Y, Ma L, Soleimani M 2012 Volumetric magnetic induction tomography. Meas. Sci. Technol. 23 0554015 Yasin M 2014 Imaging of hemorrhagic stroke in magnetic induction tomography: An in vitro study Int. J. Imaging Syst. Technol. 24(2) 161-166 Yin W L and Peyton A J 2006 A planar EMT system for the detection of faults on thin metallic plates Meas. Sci. Technol. 17(8):2130–2135.
S0263-2241(15)00553-9 http://dx.doi.org/10.1016/j.measurement.2015.10.019 MEASUR 3631
To appear in:
Measurement
Received Date: Revised Date: Accepted Date:
20 December 2014 23 September 2015 9 October 2015
Please cite this article as: Y. Fu, C. Tan, F. Dong, Analysis of Response for Magnetic Induction Tomography with Internal Source, Measurement (2015), doi: http://dx.doi.org/10.1016/j.measurement.2015.10.019
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Analysis of Response for Magnetic Induction Tomography with Internal Source Yan Fu, Chao Tan* and Feng Dong Tianjin Key Laboratory of Process Measurement and Control, School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China *Tel & Fax: 86-22-27892055; Email: [email protected] Abstract: Magnetic induction tomography (MIT) can reconstruct the distribution of conductivity within the sensing field in a non-invasive and non-intrusive manner, thus receives wide attentions for its applications in industrial and biomedical detections. In some particular cases, internal signals exist in the sensing field that would affect the response of MIT. The information of the internal signals might aid the understanding of the condition of the process/object being measured. In order to understand the effects of internal sources upon the reconstruction accuracy and dynamic responses of MIT, the Izhikevich model is applied to generate different internal sources, and numerically simulated to study the responses of magnetic induction with the internal signals. The simulation results show that an internal signal causes a shifting of the object’s location in the reconstructed image, and the amplitude of the U-shape curve formed by the measurement of MIT receivers is helpful to recognize the internal sources of different signal pattern and number. Dynamic responses of the MIT to the point source model and the multi-point source model of different internal signal shapes are also numerically investigated. A modified independent component analysis (ICA) method is introduced to separate the internal signals from the measured signals. Simulation results show that the internal signals induced in MIT’s receivers can be separated by using ICA, and the kurtoses of the separated independent components are robust in identifying different internal sources. This work verifies that MIT could handle the coupling information detections, and the coupled signals could be separated effectively with ICA.
Keywords: Magnetic Induction Tomography; Internal Source; Signal Recognition; ICA; Feature Extraction
1 Introduction A non-contact and non-invasive detection method has potential applications in many fields. In a continuous industry process with high temperature or high pressure, a non-destructive detection method can monitor the process status and also measure the process parameters, for instance pipe health monitoring (Ma and Soleimani 2012). In biomedical applications, a non-destructive detection is valuable in physiological function research, for instance continuous monitoring on cardiac activities, gastric emptying and lung ventilation, lung or heart diseases diagnosis and others (Morucci et al 1996, Boone et al 1997, Frerichs 2000, Ren 2002). Comparing with the traditional detection method, electrical tomography has many benefits in the aforementioned situations, such as obtaining the general information of the object measured and reconstructing the image of a medium distribution. Electrical tomography can be divided into three kinds by sensing manners: contact measurement, incomplete contact measurement and contactless measurement. For the first two kinds, electrodes are in contact with the target to be tested, forming an electric circulation path in between electrodes, which produces coupling effects with the target and deteriorates measurement quality. Therefore, contactless sensor tomography has been given intensive attentions in practical applications, due to the advantages of no leakage current, non-invasion and low cost in measurement (Griffiths et al 1999). Magnetic induction tomography (MIT) is a typical noninvasive and contactless imaging method that reconstructs the interior electrical properties in the sensing field (Griffiths 2001, Korjenevsky et al 2000, Peyton et al 1996, Scharfetter et al 2008, Vauhkonen et al 2008, Watson et al 2008). MIT applies a time-varying exciting signal at the external of object space. An eddy current induced by the conductive target in the exciting magnetic field causes a secondary magnetic field which is detected by receivers placed around the region of interest. By sensing the response of a driving current or voltage that applied on the transmitter, MIT can reconstruct the physical properties (e.g. conductivity) distribution within the measuring section by using certain reconstruction algorithms (Soleimani et al 2006). It is a noninvasive imaging method with easy sensor installation but without ionization or radiation, which is favorable to biomedical detection comparing with nuclide or rays based methods.
For the industry applications of MIT, Peyton et al proposed a planar MIT system to detect defects in metal plates (Yin et al 2006). The axes of the sensitive coils were perpendicular to the test plane, rather than parallel. They conducted MIT simulations on horizontal level for conductivity detection, and concluded that MIT could apply to geophysics and marine engineering with further improvements/modifications. Later, they used MIT to inspect a two-phase metal liquid-gas two-phase flow on a continuous casting process. According to the oscillation patterns, it is possible to distinguish the argon gas injected into the single-phase flow (Terzjia et al 20011). For the biomedical detection with MIT, Al-Zeibak et al (1993) constructed an MIT system that collects multi-projection by mechanically rotating the detected object and reconstructed the distribution of the object space with the linear back projection algorithm. Korjenevsky et al (1997, 2000) developed a similar MIT system for biological tissue tomography. Watson et al (2003) found that the quality of reconstructed image mainly depends on the phase measurement accuracy, and proposed a new MIT system with a phase measurement accuracy of 0.01° at 10MHz operation frequency. In 2008, they designed a 16-channel MIT system to detect the medium with the conductivity lower than 10 S/m, and reconstructed an image of a human leg in vivo at a phase measurement accuracy of 17m° (Watson et al 2008). Merwa (2003) verified the feasibility of using MIT in cerebral oedema detection both by simulation and experiment, and found that a multi-frequency MIT would improve the detectability because of the sensitivity increases considerably at higher frequency. Gürsoy et al (2009, 2011) solved the problem of incorrectness in imaging caused by the movement of patients during data acquisition, through optimizing sensor structure and data processing system. Yasin (2014) used several approaches to improve the measurement accuracy and spatial resolution in hemorrhagic stroke detection by using MIT. The results showed that the selected approaches enhanced stroke visibility, lowered stroke detectability threshold from 15 ml to 5 ml, and improved the localization of phantom hemorrhages by combining the proposed approaches. Sun et al employed magnetic induction phase shift information in acute cerebral hemorrhage detection in rabbits, and reached a high sensitivity in bleeding detection ( Sun et al 2014, Jin et al 2014).
The research of MIT used to focusing on the design or optimization of sensor structure, data acquisition system and reconstruction algorithm, in order to improve the accuracy of measurements and finally the resolution of image reconstruction. Under some specific environments, the internal electricity signals may exist in the object space, such as in electrically charged fluid or in vivo biological tissues. This condition has not been considered in previously published studies. Sometimes, the internal signals reflect the status of the measured object. Take the biomedical detection as an example, electrocardio signals, myoelectric signals and electroencephalogram signals exist in different vivo tissues in human body, and they could reflect different health status of human body directly. The electroencephalogram signal could confirm the epilepsy and facilitate the diagnosis of hemorrhagic stroke in terms of its abnormal performance. If an internal source affected the resolution or precision of reconstructed image, measurements should be treated to remove or weaken such effects in MIT imaging. On the other hand, if MIT could obtain the distribution of conductivity and the location of the internal source in object space simultaneously, more useful information could be extracted to aid estimating the status of the target. Since neither similar topics nor the working mechanism of MIT in such detections have been reported so far, it is essential to understand the sensing field distribution of MIT and the interactions between MIT and internal source at first. In this paper, the Izhikevich model was adopted to simulate the varying internal sources. Considering the difficulty in quantitatively setting complex internal signals that can be detected by MIT in practical experiments, we conducted numerical simulations to analyze the detection of object with internal source based on MIT. Four distributions of internal source models were introduced, including the point source model, the multi-point source model, the line source model and the disc source model. In order to obtain the representative results, the point source model and multi-point source model are adopted in dynamic simulation analysis. Independent component analysis (ICA) is used to separate the internal signals from MIT observations, and to recognize them with different shapes and fluctuations by using high order statics of the separated independent components. According to the preliminary results, MIT has been verified feasible to
detect the object with internal sources and providing auxiliary information of detection conditions and electrical activities monitoring.
2 Theoretical foundation 2.1 Measurement principle Based on the electromagnetic induction principle, generalization of electromagnetic induction, law of total current, continuity of magnetic flux and Gauss’ law, MIT system could be presented by the macroscopic form of Maxwell’s equations as follows (Shang 1999, Assous et al 2000, Fu et al 2013):
D H J t B E t B 0 D ρ
where, H as magnetic density, E as electric field intensity, B as magnetic flux density, D
as electric displacement, J as current density, ρ as charge density. Equations (1) are under the assumption that the object material has linear and isotropic electrical and magnetic properties. Therefore, their constraint equations are as follows:
D εE J σE B μH
where, ε is the permittivity, σ is the conductivity and μ is permeability. According to equations (1) and (2), the electric field in object space could affect parameters in electric field and further change the measurements of MIT through the transmissions of electric field thus change the magnetic induction. Based on the above equations, the electromagnetic conversion is deduced as follow:
B μ H μ σE jωεE
where, μ is the relative magnetic permeability.
Define the curl of the magnetic vector potential A as magnetic flux density, which is
described as A B . According to the Coulomb standard condition, A 0 , equations (2)
turns into 2 A μ σE jωεE . With a further deduction, the electromagnetic field magnetic vector potential equation is expressed as follow:
( μ 1 A) jωσA
According to the theory of electromagnetic induction, varying magnetic field produces varying electric field. Thereby, a voltage signal is acquired through a receiving resistance when a varying electric current flows through the receiver. To bridge the output voltage of a practical
MIT system with the magnetic vector potential A in simulation, a relationship is deduced in (5).
dφ d (B S ) d ( A l) U n n njωl ( A1 A2 ) dt dt dt
where, A1 , A2 as the magnetic vector potential on the two endpoints of detecting coils. n and l represent the number of turns of receivers and the axial length along with pipeline respectively. represents the radian frequency. As shown in (5), given a pre-set excitation condition, resulted voltages in receivers are linearly proportional to the difference of magnetic vector potentials. Hence, the difference of magnetic vector potential reflects the change of the electromagnetic field distribution of MIT. 2.2 Independent component analysis As a method of blind source separation (BSS), independent component analysis (ICA) explores statically independent components and non-Gaussian factors from multi-dimensional or multivariate data. The development of ICA theory started in the early 1990s, when Jutten and
Herault (Jutten et al 1991) proposed the concept of ICA. ICA theory and algorithms developed rapidly and gradually extended to relative fields until the mid of 1990s.
Figure 1. Schematic diagram for ICA algorithm
Figure 1 demonstrates the calculation process of ICA. Assuming all the source signals are independent, a group of observations is expressed by a linear combination of statically independent variables. In addition, equation (6) and (7) describe Figure 1 as.
X Q X
Y W X W Q X
where, X is observation matrix, X is whiting matrix and Y is independent component. Whiting process in (6) reduces the complexity of problem. Therefore, ICA is essentially to optimize the separative matrix W through iterative estimations. The fix-point algorithm was used to estimate the separative matrix W (Hyvärinen et al 1997). Apply Newton iterative method to process the observation matrix, select negentropy maximization as objective function and separate one independent component for each process.
3
Effects of Internal Source in MIT Imaging
3.1 Simulation model description Build the simulation model according to an experimental device as shown in Figure 2. The experiment device used in this part referred to the mature sensor array design introduced by X
Ma. (Ma et al 2006, 2008) The center circular area of the model represents the object space that surrounded symmetrically by eight identical coils (coil 1 to coil 8). The simulation model is established by neglecting the thickness of pipe wall and simplifying each coil as a segment whose length equals to the diameter of the coil. In addition, set a shield layer at the external part of the sensor array in order to insulate the sensing field from the external noise. The shield layer is essential in MIT detection in which the measurements are very small compared to the direct coupling and other coupling mechanisms. However, the work is mainly to verify the effectiveness of internal sources detection and separation by using the magnetic induction method. The details of shield layer analyses is not included this time and more details of shield layer effects in MIT detection could refer to the reference (Wang et al 2011).
(a)
(b)
Figure 2: MIT sensor array (a. diagram of practical sensor array, b. simplified simulation model) 3.2 MIT Imaging results The object space distribution is shown in Figure 3, an object at the center of the object space with a point source inside. The background conductivity and the target’s conductivity are 0.1S/m and 10S/m respectively, the electric current applied in the coil is 1.2A/m. The point source is a current source, which varies from 5mA to 100mA. The linear back projection algorithm reconstructed the image of the object.
Figure 3. Object space distribution for simulation model The sub-graphs in the first row of Figure 4 demonstrate the U-shape measured voltages of MIT in point source model detection when setting coil 1 as transmitter and others as receivers. With the intensity of internal signal in the target increasing, the of U-shape becomes more asymmetrical. Because the internal signal distorts the distribution of magnetic field in a way that the magnetic flux is enhanced at the position of internal signal. As demonstrated in Figure 4, the internal source obviously causes a location shift of the target in the reconstructed images that compared with the real location of target (dashed circle) in sensing field. This distortion directly corresponds to the asymmetry of U-shape measured voltages. The stronger the internal signal is, the more shifting of target in the reconstructed image. Sub-graphs (f) to (i) are the results for the multi-points model. The asymmetry of the U-shape measurement become more serious and the more shifting of target in the reconstructed image with same strength of internal source as the point source model.
Figure 4. Image reconstruction results of object with single-point internal source (a. without internal source, b.5mA, c. 10mA, d. 50mA, e.100mA) and multi-point internal source (f. 5mA, g. 10mA, h. 50mA, i.100mA)
3.3 Sensing field distribution for different internal source The internal sources have different types, therefore several internal sources of different types are used to simulate the MIT sensing field distribution with each internal source. Four different internal sources were introduced in the simulations: point source, multi-point source, disc source and line source. Different internal sources would change the intensity of magnetic field in different way, thus lead to the amplitude floating of measurements and the asymmetry of
U-shape curves at different level, and finally shift the position of target in the reconstructed image. Keept the background conductivity and the excitation currents in transmitter the same. The intensity of internal source for each simulation is 100 mA. Figure 5 illustrates the sensing field distributions of each simulation model for different internal sources, where the contour represents the electric field distribution and the arrow represents the magnetic field distribution. The magnetic fields of produced by the dipole of both the same direction and the different direction have been investigated. Figure 5 only gives an exemplary distribution contour of different models.
(a)
(b)
(c)
(d)
Figure 5. Sensing field distribution, where the contour represents the electric field distribution and the arrow represents the magnetic field distribution (a. point source, b. multi-point source, c. disc source, d. line source)
Figure 6 shows the measurements from seven receivers at one excitation of each model in Figure 5. Considering the simulation without internal sources as a reference, measurements of different internal source models have obvious discrepancies, which can identify the internal sources. Disc source model has the largest measurements among these models. Then, multi-point source with the same electrical field direction has higher measurements with well symmetrical structure because of the increased intensity of the magnetic field. If the multi-point source has different direction, the asymmetry of U-shape curve is quite noticeable, because the different direction of magnetic fields produced by the two point sources leads an asymmetrical sensing field distribution. U-shape curves for one point source and line source are higher than the reference curve, which tells the existence of an internal source. Little discrepancy between these two U-shape curves makes them hardly to distinguish, because the 2-D simulation with same parameters configuration cause this phenomenon. Nevertheless, results in Figure 6 confirm that an internal source directly affects the sensing field distribution of MIT, and it is possible to recognize the type of internal sources through features extracted from the measured voltages.
Figure 6. Measurements comparisons between different internal source models
4 Dynamic simulation analysis for point source model Internal sources in different applications have distinct features, which could represent different intrinsic identities of detected object and reflect electrical activities. Therefore, if MIT
could induce different signals, then the internal signal can be separated from the observations of MIT. In order to simplify the simulation and obtain representative outcomes, the single point source model and the multi-point source model were employed in dynamic simulations. Apply Izhikevich model (Eugene 2003) as an example to generate different internal sources. The parameter settings of the excitation conditions are constant between models in static simulations. 4.1 Izhikevich model Izhikevich model came forward in 2003, which closely reflects the firing features of true biological neurons and possible to conduct the large-scale calculation in convenience. This model only composes of two equations and one nonlinear term, but can reproduce the rich behaviors of biological electrical activities, such as spiking, bursting and mixed mode firing patterns. The expression of Izhikevich neuron model is as follow:
dv 0.04v 2 5v 140 u I dt
du a(bv u ) dt
v c u u d
If v 30mV , then
where, v as neuron membrane voltage, u as recovery variable. Parameter a and b describe the time scale and sensitivity of u . c and d represent the after-spike reset values of
v and u , respectively. Change the combinations of (a, b, c, d) in equations (8) to (10) will reproduce different behaviors of biological electrical activities. 4.2 Simulation results for internal source without noise By adjusting the parameters of the Izhikevich model, eight different typical signals were simulated. Neocortical neurons in the mammalian brain can be classified into several types according to the pattern of spiking and bursting seen in intracellular recordings. According to Figure 7, regular spiking (RS), the most typical neurons in cortex, intrinsically bursting (IB), a
stereotypical burst of spikes followed by repetitive single spikes, and chattering (CH), stereotypical bursts of closely spaced spikes, represent the behaviors of all excitatory cortical cells. Fast spiking (FS) and low-threshold spiking (LTS) are common behaviors of inhibitory cortical cells. The main difference between FS and LTS is the noticeable spike frequency adaptation at the beginning of LTS. Behaviors of thalamo-cortical (TC) neurons have two types, depolarized and hyperpolarized membrane potential. Resonator (RZ) reproduces the damped and sustained subthreshold oscillations of neurons.
Figure 7. Simulation results based on Izhikevich model. (a) regular spiking (RS), (b) intrinsically bursting (IB), (c) chattering (CH), (d) fast spiking (FS), (e) low-threshold spiking (LTS), (f) thalamo-cortical for depolarization (TC), (g) thalamo-cortical for hyperpolarization (TC), (h) resonator (RZ) Apply the internal signal sources as shown in Figure 7 to the point source model (Figure5 (a)) respectively in MIT simulations. Set sinusoidal current signal as excitation signal in MIT, and the amplitude of the excitation signal and the background conductivity remain the same in static simulations. Since the model is symmetrical (Figure2 (a)), only the measurements when coil1 was transmitter and coil2 to coil8 were receivers were collected in the simulation. Figure 8 illustrates the time domain signals (response of coil2) for each internal source in Figure 7, along with the signal separation results with independent component analysis. Under the fixed simulation condition, all the receivers in MIT have the same response in signal morphology, while the only difference is the amplitudes of measurements from receivers as
shown in Figure 6. Thus, not all the measurements used in ICA are plotted in Figure8. The internal source is coupled in the measurements, hence, it is feasible to apply MIT in detecting the sensing field with internal sources. Considering the independence and amplitudes of measurements in MIT, employ measurements from coil2 and coil3 (Firgure2 (a)) as observations for ICA. Two independent components were separated from the measurements, which are the excitation signal (IC1) and the internal signal inside the object field (IC2). According to the principle of ICA, this method could reconstruct the morphology of signal components, rather than the amplitude and alignment permutation. Therefore, IC2 in Figure 8 (c) and (d) are reversed signals that compared with the chattering and fast spiking in Figure 7.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h) Figure 8. Simulation results and independent component analysis, measurement comes from coil2 (Figure2 (a)). IC1 represents excitation signal and IC2 represents internal source
The peculiar fluctuations of internal signals have correspondence with specific measurement conditions or status of target. Since kurtosis (K) reflects the fluctuation distribution of a signal, it can recognize internal sources of different shapes by calculating the kurtosis of IC2. As listed in Table 1, the kurtosis of separated signals with the data plotted in Figure7 can distinguish the varying internal signals, and ICA is effective to separate the components from the measurements at a high precision while maintaining features of them simultaneously. Table 1. Signal recognition for different internal sources Firing pattern
RS
IB
CH
FS
LTS
TC(f) TC(g)
RZ
K (reference)
28.48 21.26 8.10 11.79 14.41 43.06
16.06
61.35
K (IC2)
28.43 21.23 8.09 11.74 14.33 43.05
16.06
61.15
4.3 Simulation results for internal source with noise Noise is inevitable in practical detection, which could seriously deteriorate the purity of separated signal. In this part, a random noise is superimposed on the internal source signals in simulations to analyze its effects on MIT’s measurements and thus verify the effectiveness of ICA in signal separation. The intensity of the superimposed noise is the variance of the internal signal. Remain other simulation conditions the same in section 4.2. Generally, there are two methods to process the noisy signals. One is to regard the noise signal as an independent component and separate it independently with ICA. The other method is to consider the noise-contaminated signal as an independent component and apply denoising methods to filter out the noise. In this work, the wavelet-denoising method was applied in the latter way to process the independent component with noise. Comparing with the traditional denoising methods in frequency domain, the time-frequency domain based wavelet-denoising method could effectively remove the noise while keeping the details of original signal. Figure 9 illustrates the simulation results for the internal signals with noise. The last sub-graph in each figure illustrates the IC2 after wavelet denoising. Compare the kurtosis (K) of IC2 with the kurtosis of the original internal signals to investigate whether the combination of
ICA and wavelet-denoising method could properly deal with the noisy signals. To estimate the denoising effect, the energy ratio (Per) and standard deviation (Err) are calculated in Table 2, where IC2 denoise and IC2 in equations (11) and (12) represent the denoised independent component and the independent component with noise respectively.
Per norm(IC 2 denoise) / norm(IC 2)
Err norm(IC 2 denoise IC 2)
According to Table 2, the kurtoses of denoised signals are smaller than reference values. However, the errors between the kurtosis of denoised signal with the reference value are small enough to ignore in the internal sources recognition. Energy ratio (Per) in Table 2 indicates that more than 98% information in the independent components has been reserved after denoising. Based on the simulation results and feature extraction, wavelet-denoising method is feasible in eliminating the noise superimposed on internal signals, and kurtosis is an effective feature for signal recognition in such conditions.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Figure 9. Simulation results and independent component analysis with denoising, measurement comes from the coil2 (Figure2 (a)), IC1 represents excitation signal, IC2 represents internal source and IC2 denoising represents the IC2 filter out noise Table 2. Signal recognition for internal sources with noise Firing pattern K (reference)
RS
IB
CH
FS
LTS
TC(f) TC(g)
RZ
28.48 21.26
8.10
11.79 14.41 43.06
16.06
61.35
K (denoising) 26.05 18.91
7.19
11.76 13.61 41.68
14.43
58.29
Per
0.990 0.988 0.989 0.995 0.990 0.993
0.985
0.986
Err
12.18 14.29 14.81
16.50
13.10
9.56
14.30 11.03
5 Dynamic simulations for multi-point source model In some cases, especially in biomedical detection, more than one type of internal sources exists in the detecting domain, and the measured data is affected by all the sources simultaneously. Therefore, simulation analysis for multi-point source model needs to be considered. The multi-point model in Figure 5(b) is selected and stimulated with three combinations of different signals into analysis: CH-FS, RS-IB and RS-TC(g). Because three models respectively represent the firing patterns in different cortical layers, firing patterns in the same cortical layer and similar firing patterns in different cortical layers. Therefore, they are the sufficient combinations to represent the typical signals to comprehensively investigate the influence of internal sources in this work. Figure 10 illustrates the signal separation results for multi-point source. The shapes of signals are different from direct observations, which are reproduced by the combination of CH and FS. As shown in Figure 10(a), three independent components are separated from the measurements. The excitation signal (IC1) is separated from measurements due to its large signal differences with the other two. IC2 and IC3 are not fully separated in the multi-point source model, but can be recognized by ignoring the uncompleted separation at several spikes. According to the features extracted in Table 3, although the separation of the CH-FS signal is incomplete, the
slight error in feature extraction has little effect on the signal recognition. The signal shape of RS has higher similarities with IB, and the shapes of the reproduced signals RS and TC(g) have partial similarities (Figure6 (a), Figure6 (g)). These similarities of signals bring difficulties in signal separation. Using the separation method for the single point model will deteriorate the separation of multi-point observations. Meanwhile, internal signals are hardly recognized with the kurtosis of signal. A modified method of signal separation is developed for RS-IB and RS-TC (g) as illustrated in Figure 11. This method conducts ICA separation on the measurements twice. For the first time, choose two different groups of observations and apply ICA respectively. After that, two groups of independent components are obtained and the excitation signal (IC11 and IC14) could be separated because of the apparent signal differences with each other. Select the other independent component in each group (IC12 and IC13) to form a new group of observations for the second independent component analysis. The superimposed internal signals could be separated after this step. Figure 10 (b) and (c) demonstrate different internal sources of similar shapes could be identified after separations. This method is possible to extend to the cases that more than two sources exist in one plane, and the modified data processing method is still effective. Figure 10 further validates the feasibility for MIT detecting the object with multiple internal sources. If generalize this modified ICA method into the detecting condition with more internal signals, more observations need to be obtained from receivers. Theoretically, increasing the number of coils as many as possible should receive more observations. MIT could not have too many coils on one layer due to the space limitation, coupling effect etc. A spherical sensor array or coils with multiple layers will provide more observations to improve the precision in signal recognition (Wei et al 2012).
(a)
(b)
(c) Figure 10. Simulation results for multi-point source model, measurement comes from the receiver close to transmitter, IC1 represents excitation signal, and IC2 and IC3 represent internal sources ((a) CH-FS, (b) RS-IB, (c) RS-TC(g))
Figure 11. Flow chart of modified ICA (OB11, OB12 and OB13 come from the measurements of coil2 to coil4 in Figure 2; IC1, IC2 and IC3 correspond with them in Figure 10)
Table 3. Signal recognition for multi-point source model Firing pattern
RS
IB
CH
FS
TC(g)
K (reference)
28.48
21.26
8.10
11.79
16.06
K (CH-FS)
-
-
7.47
10.77
-
K (RS-IB)
30.10
19.32
-
-
-
K (RS-TC(g))
28.47
-
-
-
16.10
6 Internal source with small magnitude In some applications, the internal signal is small compared with the excitation signal in MIT detection, for instance untreated electroencephalogram signal is varying only from 10μV to 100μV while the excitation signal injected in a practical MIT device is 10V (Nunez 1981). Whether MIT still effective in such small signals detecting needs verifications. Therefore, new simulations were conducted by changing magnitudes of the internal signals at the same level of untreated electroencephalogram signals.
6.1 Simulations of point source model Select the point source model and keep the simulation settings as introduced in section5 except the amplitude of internal signal. As shown in Figure 12, the observations are hardly affected by the internal signals, so the observations of MIT could be directly applied in image reconstruction without complex data processing. The small internal signal is still detectable by MIT. After the data processing with ICA, the internal signals could be separated from observations. According to data listed in Table 4, kurtosis of IC2 is still effective in signal recognition for small internal signals detection of MIT.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h) Figure 12. Simulation results and independent component analysis, measurement comes from coil2 (Figure2 (a)), IC1 represents excitation signal and IC2 represents internal signal
Table 4. Signal recognition for different internal sources Firing pattern
RS
IB
CH
FS
LTS
TC(f) TC(g)
RZ
K (reference)
28.48 21.26 8.10 11.79 14.41 43.06
16.06
61.35
K (IC)
28.43 21.22 8.10 11.76 14.34 43.04
16.06
61.15
6.2 Simulations of multi-point source model Employ multi-point source model into simulations, and set the amplitude of internal signal was set one in a million of excitation signal. Although more internal sources locate in the sensing field, the observations are rarely affected, thus leading little distortions to conductivity distribution reconstruction. The modified independent component analysis method introduced in section 5 is applied here and the signal separation results are shown in Figure 13. The modified ICA can separate the small internal signals from observations. The magnitude of the internal signal affects the accuracy of separation as listed in Table 5. Compare Table 3 with Table 5, kurtosis shows an obvious error especially for the internal signals with partially similar morphology. Error is not big enough to affect the signal recognition.
(a)
(b)
(c) Figure 13. Simulation results for dual dipole model, measurement comes from coil2 (Figure2 (a)), IC1 represents excitation signal, and IC2 and IC3 represent internal signals ((a) CH-FS, (b) RS-IB, (c) RS-TC(g))
Table 5. Signal recognition for dual dipole model Firing pattern
RS
IB
CH
FS
TC(g)
K (reference)
28.48
21.26
8.10
11.79
16.06
K (CH-FS)
-
-
7.47
10.77
-
K (RS-IB)
26.09
18.74
-
-
-
K (RS-TC(g))
27.97
-
-
-
15.74
7 Conclusions and outlook In some practical measurement, internal sources affect the sensing field distribution of MIT. If the internal signals are detected by MIT, more comprehensive information can be extracted to facilitate the diagnosis of target conditions and status in detection. An effective method is presented to weaken the effects of internal source in image reconstruction. Signals of different shapes were used as an example of internal sources to investigate the effectiveness of the proposed method. (1) The internal sources shift the reconstructed location of target in sensing field according to the reconstructed images by MIT measurements. The measurement amplitude of MIT has a large difference when an internal source signal exists in the detecting cross section, and the amplitudes of measurements directly relate to the strength and quantity of the internal sources. (2) The μV level internal sources can be induced by MIT receivers, and separated by using ICA in time domain (dynamic response). ICA is effective in separating the internal signal and the excitation signal from MIT observations. When two internal sources (multi-point source model) exist in the sensing field, the separation needs two steps: first the excitation signal and a mixed signal of the multi-point sources are separated by applying ICA to MIT observations; then the internal signal generated by each point can be separated from
the mixed signals by applying ICA again. The modified ICA improves separation of MIT observations and extracts multiple internal sources with high similarities. (3) Kurtosis of the separated internal signals presents high robustness in internal signal recognition. Although the denoising process causes information loss, signal recognition is hardly affected by using kurtosis as a feature. On the other hand, kurtosis also performs properly in multi-point model recognition, even though the two internal signals are similar in shape. MIT can handle the internal signals allowing more applications in industrial and biomedical detections. It is still a preliminary analysis and much more work is required to elaborate this issue in the future. A 3-D model will more closely simulate the real world and present more accurate estimates of the sensing field distribution than a 2-D model, and the simulated model needs experimental validations to provide more evidences to MIT applications in practical detection. Besides, whether the modified data separation method is possible to extend to the more complex internal source model needs further verification.
Acknowledgements The authors appreciate the support from National Natural Science Foundation of China (No. 61571321 & No. 61227006) and Science and Technology Innovation of Tianjin (No. 13TXSYJC40200).
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