Use of 3-D magnetic resonance electrical impedance tomography in detecting human cerebral stroke: a simulation study

Use of 3-D magnetic resonance electrical impedance tomography in detecting human cerebral stroke: a simulation study 1 first-author †E-mail:gaonuo@jnnc.com; binhe@umn.edu †E-mail:gaonuo@jnnc.com; binhe@umn.edu gaonuo@jnnc.com 1 2 †E-mail:gaonuo@jnnc.com; binhe@umn.edu †E-mail:gaonuo@jnnc.com; binhe@umn.edu gaonuo@jnnc.com School of Electrical Engineering, Zhejiang University, Hangzhou 310027, China School of Electrical Engineering, Zhejiang University, Hangzhou 310027, China Department of Biomedical Engineering, University of Minnesota, MN, USA Department of Biomedical Engineering, University of Minnesota, MN, USA We have developed a new three dimensional (3-D) conductivity imaging approach and have used it to detect human brain conductivity changes corresponding to acute cerebral stroke. The proposed Magnetic Resonance Electrical Impedance Tomography (MREIT) approach is based on the J-Substitution algorithm and is expanded to imaging 3-D subject conductivity distribution changes. Computer simulation studies have been conducted to evaluate the present MREIT imaging approach. Simulations of both types of cerebral stroke, hemorrhagic stroke and ischemic stroke, were performed on a four-sphere head model. Simulation results showed that the correlation coefficient (CC) and relative error (RE) between target and estimated conductivity distributions were 0.9245±0.0068 and 8.9997%±0.0084%, for hemorrhagic stroke, and 0.6748±0.0197 and 8.8986%±0.0089%, for ischemic stroke, when the SNR (signal-to-noise radio) of added GWN (Gaussian White Noise) was 40. The convergence characteristic was also evaluated according to the changes of CC and RE with different iteration numbers. The CC increases and RE decreases monotonously with the increasing number of iterations. The present simulation results show the feasibility of the proposed 3-D MREIT approach in hemorrhagic and ischemic stroke detection and suggest that the method may become a useful alternative in clinical diagnosis of acute cerebral stroke in humans. Magnetic Resonance Electrical Impedance Tomography Conductivity Acute cerebral stroke Hemorrhagic stroke Ischemic stroke Current density imaging INTRODUCTION 1 Magnetic Resonance Electrical Impedance Tomography (MREIT) is a new imaging technique combining traditional Electrical Impedance Tomography (EIT) and Current Density Imaging (CDI) for determining conductivity distribution inside a subject (Khang et al., 2002 2002 ; Kwon et al., 2002 2002 ). In MREIT, a current is injected into the subject through a pair of surface electrodes. The induced magnetic flux density inside the subject can be measured through a Magnetic Resonance Imaging (MRI) scanner (Pešikan et al., 1990 1990 ; Scott et al., 1991 1991 ; İder and Muftuler, 1997 1997 ; Eyüboğlu et al., 1998 1998 ) and the current density distribution can be calculated according to Ampere’s law. Then the conductivity distribution images can be obtained through the relationship between the conductivity and the current density or the magnetic flux density (Birgül and İder, 1996 1996 ; İder and Birgül, 1998 1998 ; Khang et al., 2002 2002 ; Kwon et al., 2002 2002 ). MREIT has been used for imaging absolute conductivity distribution and the results are encouraging (Khang et al., 2002 2002 ; Kwon et al., 2002 2002 ; Gao et al., 2004 2004 ). In the present study, we use the MREIT technique to detect human brain conductivity changes. It is well known that brain activity under some physiological phenomena will cause local and temporal conductivity changes within human brain tissue (Boone et al., 1997 1997 ). Classical examples are the visual and auditory stimulations, migraines, strokes and epilepsy (Boone et al., 1994 1994 ; Holder et al., 1999 1999 ; Sadleir and Fox, 2001 2001 ; Towers et al., 2000 2000 ). Although the effects of these conditions vary in their magnitude and duration, each one tends to affect a particular area of the brain. This paper focuses on the brain conductivity changes due to acute cerebral strokes. In the present study, we consider both types of acute cerebral stroke: ischemia and haemorrhage. Ischemia occurs when blood flow is reduced, e.g., due to a clogged artery. The most common technique for imaging stroke is MRI. However, while conventional MRI shows infracted (dead) tissue many hours after the onset of a stroke, it cannot readily detect ischemic tissue in the acute time window (i.e., within three hours), within which the tissue may be rescued by drug intervention. Ischemic tissue is characterized by abnormally high impedance which occurs because of cell swelling that reduces the extracellular space and increases the bulk tissue impedance as much as 50% (Hansen and Olsen, 1989 1989 ; Holder, 1992 1992 ). The present work was motivated in part by the recognition that the reconstruction accuracy of MREIT is much better than that of traditional EIT and therefore we hypothesize that it may provide the sensitivity needed to detect conductivity changes caused by ischemia. A related problem is hemorrhagic stroke, which occurs when blood fills the extracellular space or displaces brain tissue entirely. While far fewer patients have hemorrhagic stroke, it is much more likely to result in death. Ironically, the primary drug used to treat cerebral ischemia (t-PA) carries a 6% chance of causing brain hemorrhage (Albers et al., 1998 1998 ). Since the conductivity of blood ( σ k =0.61 s/m) (Geddes and Baker, 1967 1967 ) is approximately three times that of the brain, it seems reasonable to hypothesize that MREIT may be able to detect hemorrhagic stroke as well. MREIT for the head is obviously handicapped by the low skull conductivity, since much of the current is shunted through the scalp and does not enter the brain compartment. Nevertheless, the reconstruction accuracy of MREIT is the same through the imaging space and the inner part of it will not blur, which will occur in traditional EIT (Khang et al., 2002 2002 ; Kwon et al., 2002 2002 ). In the present work, we conducted computer simulations to investigate how well can MREIT detect ischemic and hemorrhagic strokes in humans. Three aspects of the present approach have direct bearing on the results. First, we assume that head geometry is known, since this data can be obtained from the MRI scanner. Second, we assume the current density distribution is known and this can be obtained through CDI. Third, to focus on the changes in brain conductivity which might occur in stroke, we fix the conductivity of the outer head tissues [scalp, skull and cerebrospinal fluid (CSF)] to their base values. METHODS 1 Overview of the MREIT approach 2 The whole procedure of the proposed MREIT reconstruction approach is illustrated in Fig. 1 1 . A three-dimensional (3-D) head model was constructed based on structure MRI scans. In the present study, to demonstrate the feasibility of this MREIT approach, a simple four-sphere head model (Burger and Milaan, 1943 1943 ; Geddes and Baker, 1967 1967 ; Baumann et al., 1997 1997 ) was used and we assumed uniform and isotropic conductivity for each sphere. A current presumably of 100 μA was assumed to be injected into the human head through a pair of surface electrodes. A current under this limit is considered to be safe for human and would not elicit neural activity (Clay and Ferree, 2002 2002 ). The induced magnetic flux density can be measured by an MRI scanner and the current density distribution can be obtained. The present MREIT algorithm needs not only the current density distribution but also voltage differences between the two injection electrodes (Khang et al., 2002 2002 ; Kwon et al., 2002 2002 ; İder et al., 2003 2003 ). In the present simulation study, the “measured” current density and voltage differences were simulated (Given the target conductivity distribution, through solving the forward problem, we can get the target current density and voltage differences. Different signal-to-noise ratio (SNR) Gaussian White Noise (GWN) was added to the target current density and voltage differences to simulate the “measured” noise-contaminated current density and voltage differences). To assure the uniqueness of the results, three currents were assumed to be injected into the 3-D human head from three vertical directions (Khang et al., 2002 2002 ; Kwon et al., 2002 2002 ; İder et al., 2003 2003 ) to obtain three “measured” current densities and voltage differences. The conductivity distribution is estimated by minimizing the differences between the “measured” and calculated current densities and voltage differences. In the present study, we used an iterative algorithm called J-Substitution algorithm to update the conductivity change distribution. J-Substitution algorithm has been used to reconstruct 2-D subject absolute conductivity image (Khang et al., 2002 2002 ; Kwon et al., 2002 2002 ). Here, we extended it to reconstruct 3-D subject conductivity image and used it to detect human brain conductivity changes. To our knowledge, J-Substitution algorithm had not been applied previously for detecting human head conductivity changes. In practical reconstruction procedure, since the target conductivity changes are unknown, we stop the iterative procedure when the difference of the two estimated conductivity changes is less than the allowable error. The mathematical model of the stopping criterion can be represented as follows: ‖ σ i +1 − σ i ‖ < ε where σ i +1 represents the reconstructed conductivity distribution of the brain at the ( i +1)th iteration and σ i for the i th iteration. ‖·‖ is the Euclidian norm and ε is the allowable error. The selection of ε will affect the reconstruction accuracy and the convergence rate of the MREIT algorithm. The smaller the ε is, the higher the reconstruction accuracy is and the slower the convergence is. Forward solver 2 Low frequency ( f < 10 kHz) current injected into the scalp creates quasistatic electric fields, which may be computed using techniques from electrostatics. For a good approximation, the electric and magnetic fields are decoupled and the local impedance is real. With these simplifications, electric current in the conductive media is governed by Poisson’s equation for the electric potential U ( r ) subject to Neumann boundary conditions: $$\nabla [\sigma (r)\nabla U(r)] = 0,{\text{ }}r \in \Omega$$ $$\sigma (\partial U/\partial n) = \left\{ \begin{gathered}J{\text{ for positive current electrode}} \\- J{\text{ for negative current electrode}} \\0{\text{ elsewhere}} \\\end{gathered} \right.$$ where U ( r ) is the electric potential distribution, σ ( r ) the conductivity distribution and Ω the subject to be imaged. Analytical solutions for complex conductivity distribution are not available for the Neumann boundary value problem (NBVP) given by Eq.( 2 2 ) and Eq.( 3 3 ). Finite element method (FEM) was used to solve this NBVP. In the present study, we used ANSYS 8.1, a general-purpose finite element analytical software for the finite element modeling and analytical procedure. After obtaining the electric potential distribution U ( r ), the electric field $$\overrightarrow E$$ and current density distribution $$\overrightarrow J$$ can be calculated as: $$\overrightarrow E = - \nabla U$$ $$\overrightarrow J = \sigma \overrightarrow E$$ Iterative reconstruction algorithm 2 Through solving the above forward problem, given a conductivity distribution σ , we can get a current density distribution J , and if the conductivity distribution is equal to the target conductivity σ * , then the current density must be equal to the “measured” current density J * . According to the relationship between current density $$\overrightarrow J$$ and electric field $$\overrightarrow E$$ , we define the objective function as: f ( σ )=‖| J * |− σ ·| E |‖ Since σ is a scalar, we used the magnitude of the current density and electric field. | J * | is the magnitude of “measured” current density and | E | is the magnitude of the calculated electric field when the conductivity is σ . Minimizing the above objective function, we can get the update formula: σ =| J * |/| E | To assure the uniqueness of the solution, the voltage differences between the injection electrodes must be added into the above update formula (Khang et al., 2002 2002 ; Kwon et al., 2002 2002 ; İder et al., 2003 2003 ): $$\sigma = (|J^* |/|E|) \times (V_\sigma /V_{\sigma ^* } )$$ where V σ is the calculated voltage difference when the conductivity is σ and V σ * is the “measured” voltage difference. Simulation protocols 2 As mentioned above, we used a four-sphere head model and assumed uniform and isotropic conductivity for each sphere. The four spheres are brain, cerebrospinal fluid (CSF), skull and scalp, each characterized by a scalar conductivity σ and an outer radii r . The four spheres have outer radii (conductivities) of 8 cm (0.25 s/m) for the brain, 8.2 cm (1.79 s/m) for the CSF, 8.7 cm (0.018 s/m) for the skull and 9.2 cm (0.44 s/m) for the scalp (Burger and Milaan, 1943 1943 ; Geddes and Baker, 1967 1967 ; Baumann et al., 1997 1997 ). The parameters of the four-sphere head model are listed in Table 1 1 . Fig. 2 2 shows the finite element (FE) mesh used for the simulations. It includes 35429 nodes and 25411 triangular elements. Brain CSF Skull Scalp r (cm) 8.0 8.2 8.7 9.2 σ (s/m) 0.25 1.79 0.018 0.44 To mimic the conductivity changes related to ischemic and hemorrhagic strokes, we used three focal anomalies that were located at three different locations. The three anomalies are numbered in order of decreasing depth. The first anomaly was in the center of the brain and the other two were shifted 3 cm in the brain radially along the x axis. Eighty-eight percents of ischemic and hemorrhagic strokes are of medium size (10–50 cm 3 ) (Reimann et al., 2000 2000 ). In the present simulation, we set the volume of the three anomalies to be about 50 cm 3 , which is about 2.3% of the brain. Anomaly 1 is comprised of 295 finite elements, anomaly 2 has 299 finite elements, and anomaly 3 consisted of 357 finite elements. The locations and volumes of the three anomalies are shown in Fig. 3 3 . We assume that ischemic tissue may be characterized by a contiguous region with its conductivity equal to 50% of that of the brain: σ i =0.125 s/m (Holder, 1992 1992 ). We also assume that a hemorrhage may be characterized by a contiguous region with conductivity equal to that of blood: σ h =0.61 s/m (Geddes and Baker, 1967 1967 ). This assumes that blood completely displaces brain tissue, which is most common. It probably does not apply to the case where blood replaces only the extracellular fluid, which would tend to decrease the bulk tissue conductivity, since blood has lower conductivity than that of extracellular fluid. To study the noise tolerance of the proposed algorithm, different SNR GWNs were added to the target current density to simulate the “measured” noise contaminated J * . The SNRs of GWN were infinite, 80, 60, 40, 20 and 10. In the present study, the correlation coefficient (CC) and the relative error (RE) were used to quantitatively assess the performance of the MREIT reconstruction approach. The CC and RE between the target and estimated conductivity distribution are defined as follows: $$CC[\sigma (n),\sigma ^* (n)] = \frac{{\sum\limits_{n = 1}^N {\sigma (n) \cdot \sigma ^* (n)} }}{{\left[ {\sum\limits_{n = 1}^N {\sigma ^2 (n)} } \right]^{1/2} \cdot \left[ {\sum\limits_{n = 1}^N {\sigma ^{*2} (n)} } \right]^{1/2} }}$$ RE (%)=(║ σ * − σ ║/║ σ * ║)×100% where σ * is the target conductivity distribution and σ the estimated conductivity distribution. In this study, we calculated CC and RE only within the brain region because we fixed the conductivity of the outer head tissues [scalp, skull and CSF] to their base values during our reconstruction procedure, so it is meaningless to calculate CC and RE for outer head tissues. RESULTS 1 Reconstructed conductivity changes correspond to hemorrhagic stroke 2 The performance of this MREIT technique was tested by “simulated” hemorrhagic stroke with six noise levels. The three anomaly conductivities increase from brain conductivity ( σ b =2.5 s/m) to blood conductivity ( σ h =0.61 s/m). In each situation, different SNR of GWN was added to the target current density to simulate the “measured” current density. The simulation results are listed in Table 2 2 . 2 Anomaly 2 CC / RE 6 SNR of added GWN Infinite 80 60 40 20 10 2 1 CC 0.9999 0.9795 0.9545 0.9193 0.8859 0.8314 RE (%) 0.1155 4.3830 6.6921 8.9906 11.3496 13.9800 2 2 CC 0.9999 0.9791 0.9543 0.9220 0.8823 0.8308 RE (%) 0.0929 4.4224 6.7187 9.0012 11.4580 14.0732 2 3 CC 0.9999 0.9816 0.9603 0.9322 0.8930 0.8528 RE (%) 0.0638 4.4479 6.6809 9.0072 11.5436 13.9800 2 Average CC 0.9999±0.0000 0.9801±0.0013 0.9564±0.0034 0.9245±0.0068 0.8871±0.0054 0.8383±0.0125 RE (%) 0.0907±0.0259 4.4178±0.0327 6.6972±0.0194 8.9997±0.0084 11.4504±0.0972 14.0111±0.0538 The listed results in Table 2 2 show that the MREIT technique can detect the conductivity changes correspond to hemorrhagic stroke clearly. When there is no added GWN, all the CCs are nearly 1 and all the REs are less than 0.12% for the three anomalies. When the SNR of added GWN is 10, the CCs are all above 0.8 and REs are all less than 15%. Averaging all the three anomalies, the CC is 0.8383±0.0125 and the RE is 14.0111%±0.0538% when the SNR of the added GWN is 10. These promising results demonstrate the excellent detection ability of the proposed MREIT technique. In Table 2 2 we also can see that when the SNRs of added GWN are the same, CC and RE change little among these three anomalies. This phenomenon shows that the spatial resolution of this technique is not affected by the location. This is quite different compared with traditional EIT technique. Traditional EIT’s spatial resolution for the inner part is much lower than that of the outer part. Fig. 4 4 depicts the section map of the estimated results. In order to display the conductivity changes clearly, when we plot the section map, we set the conductivities of outer head tissues [scalp, CSF, skull] to be the same as the brain conductivity (they were all fixed to their base value when we conducted the simulation study). In Fig. 4 4 , the left column corresponds to anomaly 1, the middle column corresponds to anomaly 2 and the right column corresponds to anomaly 3. The first row is the target conductivity distribution and the second to fifth rows correspond to the estimated results when the SNRs of added GWN are infinite, 80, 40 and 10, respectively. Fig. 4 4 shows that these three anomalies can be detected clearly by this MREIT technique even with high noise disturbance. This MREIT technique captures well the target conductivity distribution. Fig. 5 5 illustrates the CC values between target and estimated conductivity under different noise levels. Fig. 5 5 indicates that with the increase of noise, the CC decreases monotonously. When the SNR of added GWN is 10, the CC is 0.8383±0.0125, which illuminates that a good estimation of the hemorrhagic stroke can be obtained with high noise disturbance. Reconstructed conductivity distribution for ischemic stroke 2 The performance of the MREIT imaging approach was also evaluated by simulating ischemic stroke. All the simulation situations were the same as that of the hemorrhagic stroke except the magnitude of the conductivity changes. In ischemic stroke, we assume three anomaly conductivities to be 0.125 s/m, 50% of the brain. The magnitude of conductivity changes is much smaller than that of hemorrhagic stroke, so it is more difficult to detect ischemic stroke. Fig. 6 6 shows the reconstructed results for ischemic stroke, with the same display format as in Fig. 4 4 . The CC and RE for ischemic stroke are listed in Table 3 3 , with the same format of Table 2 2 . Averaging all three anomalies, the CC for the six noise levels are 0.9999±0.0000, 0.8786±0.0109, 0.7746±0.0173, 0.6748±0.0197, 0.5828±0.0230 and 0.5109±0.0175. The averaged RE with six noise levels are 0.0161%±0.0094%, 4.4144%±0.0091%, 6.6619%±0.0053%, 8.8986%±0.0089%, 11.4250%±0.0273% and 13.9051%±0.0100%. The promising results suggest the feasibility of the proposed MREIT technique in imaging human brain conductivity changes for ischemic stroke. 2 Anomaly 2 CC / RE 6 SNR of added GWN Infinite 80 60 40 20 10 2 1 CC 0.9999 0.8711 0.7646 0.6672 0.5695 0.4989 RE (%) 0.0245 4.4232 6.6649 8.9073 11.4407 13.9163 2 2 CC 0.9999 0.8735 0.7646 0.6601 0.5695 0.5029 RE (%) 0.0179 4.4148 6.6649 8.8989 11.4407 13.8972 2 3 CC 0.9999 0.8911 0.7945 0.6972 0.6093 0.5310 RE (%) 0.0060 4.4051 6.6558 8.8895 11.3935 13.9017 2 Average CC 0.9999±0.0000 0.8786±0.0109 0.7746±0.0173 0.6748±0.0197 0.5828±0.0230 0.5109±0.0175 RE (%) 0.0161±0.0094 4.4144±0.0091 6.6619±0.0053 8.8986±0.0089 11.4250±0.0273 13.9051±0.0100 Convergence of the MREIT technique 2 In order to evaluate the convergence of the proposed MREIT technique, we study the changes of CC and RE. Fig. 7 7 depicts the changes of CC for different iteration numbers for the hemorrhagic situation of anomaly 1. Fig. 8 8 depicts the changes of RE for the same situation as Fig. 7 7 . Both Figs. 7 7 and 8 8 include six curves corresponding to six noise levels. In Fig. 7 7 , all six curves are monotonously increasing and in Fig. 8 8 , all curves are monotonously decreasing, suggesting good convergence characteristics of this technique. Similar trends were also observed for other two anomalies of hemorrhagic situation and three anomalies of ischemic situation. DISCUSSION 1 In the present study, we have developed a new 3-D MREIT approach for noninvasive human brain conductivity change imaging. The proposed approach is based on the J-Substitution algorithm (Khang et al., 2002 2002 ; Kwon et al., 2002 2002 ) and is extended to 3-D subject conductivity imaging. To our knowledge, this is the first time that this approach is used to detect human brain conductivity changes. The present study suggests that one can noninvasively estimate the location, size and magnitude of hemorrhagic and ischemic strokes with high accuracy and spatial resolution. For hemorrhagic situation, averaging three anomalies, the CC and RE between the target and estimated conductivity distribution were 0.9245±0.0068 and 8.9997%±0.0084%, when the SNR of added GWN was 40. For ischemic situation, averaging three anomalies, the CC and RE were 0.6748±0.0197 and 8.8986%±0.0089%, when the SNR of added GWN is 40. The present simulation results demonstrate the excellent performance of the proposed 3-D MREIT approach for imaging human brain conductivity changes. Note that a four-sphere head model with isotropic nature was used in this study to represent the human head. A more sophisticated head model, e.g. real geometry head model with anisotropy nature, will enhance the accuracy and resolution of this approach. These works will be done in our future study. 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Physiol Meas , 2000 . 21 119 - 124 . . 3D simulation of EIT for monitoring impedance variations within the human head 10.1631/jzus.2005.B0438 Project supported partly by the National Science Foundation (No. BES-0411898) and the National Institues of Health (No. R01 EB00178), USA 2004-11-21 2005-01-21 2005-04-10 2022-01-05 Copyright © 2005, Journal of Zhejiang University Science 2005 Journal of Zhejiang University-SCIENCE B (Biomedicine and Biotechnology) 05 6B