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Focused Current Density Imaging Using Internal Electrode in Magnetic Resonance Electrical Impedance Tomography (MREIT) Woo Chul Jeong, Saurav Z. K. Sajib, Hyung Joong Kim, and Oh In Kwon∗
Abstract—Magnetic resonance electrical impedance tomography (MREIT) is an imaging modality capable of visualizing crosssectional current density and/or conductivity distributions inside an electrically conducting object. It uses an MRI scanner to measure one component of the magnetic flux density induced by an externally injected current through a pair of surface electrodes. For the cases of deep brain stimulation (DBS), electroporation, and radio frequency (RF) ablation, internal electrodes can be used to improve the quality of the MREIT images. In this paper, we propose a new MREIT imaging method using internal electrodes to visualize a current density distribution within a local region around them. To evaluate its performance, we conducted and analyzed a series of numerical simulations and phantom imaging experiments. We compared the reconstructed current density images using the internal electrodes with the obtained using only the external electrodes. We found that the proposed method using the internal electrodes stably determines the current density in the focused region with better accuracy. Index Terms—Current density, internal electrode, magnetic flux density, magnetic resonance electrical impedance tomography (MREIT), MRI.
I. INTRODUCTION AGNETIC resonance electrical impedance tomography (MREIT) is a recently developed MR-based impedance imaging technique to provide cross-sectional images of the conductivity and/or current density distributions inside an electrically conducting imaging object [1]–[15]. When we inject current into the imaging object through a pair of surface electrodes, it induces an internal distribution of the magnetic flux density B = (Bx , By , Bz ). Using an MRI scanner with its main magnetic field aligned along the z direction, we can measure the z-component of B, Bz , in the form of a cross-sectional image. Since the measured data Bz is determined by the current density distribution and, therefore, by the conductivity distribution,
M
Manuscript received June 5, 2013; revised September 24, 2013, November 12, 2013, and January 16, 2014; accepted February 8, 2014. Date of publication February 21, 2014; date of current version June 14, 2014. This work was supported by the Konkuk University research support program and by the National Research Foundation of Korea (NRF) funded by the Korea government (MEST) under Grants 2012R1A1A2008477, 2013R1A2A2A04016066. Asterisk indicates corresponding author. W. C. Jeong, S. Z. K. Sajib, and H. J. Kim are with the Department of Biomedical Engineering, Kyung Hee University, Yongin-si 446-701, Korea (e-mail:
[email protected]). ∗ O. I. Kwon is with the Department of Mathematics, Konkuk University, Seoul 143-701, Korea (e-mail:
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TBME.2014.2306913
conductivity image reconstructions from the measured data are possible in MREIT. Recent studies of in vivo animal and human imaging experiments have showed successful reconstructions of cross-sectional conductivity images [16]–[18]. However, the measured Bz data is contaminated with noise and the noise level is inversely proportional to the signal-tonoise ratio (SNR) of the MR magnitude image and the duration of current injection. Using a constant current source and thin carbon-hydrogel surface electrodes with a large contact area, we have injected current synchronized with an MR pulse sequence [22]–[24]. One may adopt a pulse sequence such as the multiecho injection current nonlinear encoding (ME–ICNE) to minimize the noise level in the measured Bz data [19]–[24]. For a given amount of current amplitude, the quality of reconstructed images depends primarily on the noise level in the Bz data. The visualization of current density in the whole imaging region from the measured Bz by the externally injected current has been studied in Oh et al. [30]. Recently, the projected current density JP as the best approximation of the internal current density J from the measured Bz data was proposed by solving a two-dimensional Poisson’s equation with the Dirichlet condition determined by the relationship between the induced internal current density and the measured Bz data [31]. When we inject current through a pair of surface electrodes, it spreads all over the imaging object to produce a threedimensional distribution of the internal current density. This usually results in a poor SNR of the recovered conductivity and/or current density images due to weak Bz signals inside the imaging area. Since the quality of the measured Bz data depends on the MR magnitude image SNR and the duration of injection current, the measured Bz data becomes very noisy in the local region where MR signal void occurs. To compute the projected current density JP , it is required to solve Poisson’s equation with the Laplacian of the noisy Bz data as its source term. Therefore, excessive amount of noise in a defective region may affect other regions through the noise propagation process. For diagnostic as well as therapeutic purposes, electrodes can be inserted into the human body. For example, in electrical impedance tomography (EIT), a probe with multiple electrodes has been developed to inject currents and measure voltages inside the body for endo-tomography of an internal region of interest (ROI) [25]. In radio frequency (RF) ablation, an alternating current of several hundreds of kHz is delivered through an internal electrode to heat a target tissue [26]. Deep brain stimulation (DBS) electrodes are intended to stimulate specific areas of the brain to treat movement disorders including
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JEONG et al.: FOCUSED CURRENT DENSITY IMAGING USING INTERNAL ELECTRODE IN MREIT
essential tremor and Parkinson’s disease [27], [28]. One may also use an internal electrode to apply a high electric field for electroporation to deliver pharmaceutical agents and drugs directly into cells [29]. If such an internal electrode is available, we may use it as well to inject current for MREIT imaging. Then, the Bz signal in a local region near the internal electrode becomes stronger since it is highly dependent on the current density at the same position. In this paper, we focus on the recovery of the internal current density J in the ROI around the internal electrode using the enhanced Bz data. We propose a new method to recover the focused current density JF in a local region around the internal electrode. Using numerical simulation results, we validate the proposed algorithm to stably determine the current density in the ROI. We compare the reconstructed internal current densities with and without the use of the internal electrode. To verify the proposed method in a real experiment, we design a conductivity phantom and perform imaging experiments using an internal electrode at the center of the phantom. The Results of the phantom imaging experiments reflect the advantage of the proposed method over conventional methods to recover a focused current density JF in a local region around the internal electrode.
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Using the relation (2), the magnetic flux density Bz can be recovered as + M (r) 1 Bz (r) = arg , = 1, . . . , NE . (3) 2γTc M− (r) The noise standard deviation sdB z of the measured Bz satisfies sdB z (r) ∝
1 Tc ΥM (r)
(4)
where ΥM is the SNR of the th MR magnitude image [33], [34]. To reduce the noise level of Bz , the measured multiple values of Bz , = 1, . . . , NE , can be optimized as a weighted combina E by determining the appropriate tion Bz (r) = N =1 ω (r)Bz (r) E weighting factor ω (r) > 0 with N =1 ω (r) = 1 [21]. The optimal weighting factor ω (r) that reduces the noise level of Bz can be precisely described by Ψ (r) ω (r) = N E , =1 Ψ (r) −
= 1, . . . , NE
(5)
2 T c
where Ψ (r) := (Tc )2 e T 2 ( r ) and the T2 relaxation time are estimated using the multiple M± data, = 1, . . . , NE . B. Focused Current Density Recovery in Local Region
II. MATERIALS AND METHODS A. Magnetic Flux Density Measurement Let Ω be an electrically conducting cylindrical object with its boundary ∂Ω. Let Ω ⊂ Ω, = 1, . . . , Ns , denotes the th imaging slice of the cylindrical object Ω, where Ns is the number of imaging slices. The multiecho spin echo pulse sequence for MREIT receives NE multiple echoes by using a series of 180◦ RF pulses to obtain a train of echo signals at the echo times TE , = 1, . . . , NE . The th measured k-space data by injecting currents I ± can be expressed as S± (kx , ky ) = ρ (x, y)eiδ (x,y ) e±iγ B z (x,y )T c ei2π (k x x+k y y ) dxdy (1) Ω
where ρ is the th MR magnitude image, δ is the th systematic phase artifacts, γ = 26.75 × 107 rad/T · s is the gyromagnetic ratio of hydrogen, and Tc is the current pulse width for = 1, . . . , NE . The systematic phase artifacts are caused by a variety of factors such as the phase shift due to the main field inhomogeneity, the mismatch between the center of the data acquisition interval, RF pulse timing instabilities, additional gradient field, etc. The th MR magnitude image ρ can be precisely described as ρ (x, y) = M⊥ (0+ )e−T E /T 2 where M⊥ (0+ ) is the transverse magnetization after the RF pulse, T2 is the transverse relaxation time, and e−T E /T 2 denotes the exponential decay at the echo time TE [32]. The two-dimensional inverse Fourier transform provides the complex MR images M± as iδ (r) ±iγ B z (r)T c e . M± (r) = ρ (r)e
(2)
The MREIT technique utilizes the relation between the measured Bz data and the current density J based on Ampere’s law: 1 ∇ × B(r) (6) J(r) = μ0 where μ0 = 4π × 10−7 Tm/A is the magnetic permeability of free space. The quality of the measured Bz data is poor in a defective region, where the MR signal intensity is small or the duration of injection current is short as expressed in (4). In animal and human imaging experiments, this usually occurs in air-filled organs and the outer layers of bones. To recover the internal current density from the measured Bz data, we use the Biot–Savart law given by (y − y )Jx (r ) − (x − x )Jy (r ) μ0 Bz (r) = dr 4π Ω |r − r |3 + BzI (r),
r = (x, y, z) ∈ Ω
(7)
where BzI is the magnetic flux density due to the current I along the external wires. When we inject current through an internal electrode, there occurs a relatively high intensity of the current density in the local ROI R near the electrode. To recover the current density in R ⊂ Ω, we define a vector JF as ⎧ ∂u0 1 ∂Bzd F ⎪ J (r) − σ0 (r) (r) := ⎪ x ⎪ ⎪ μ0 ∂y ∂x ⎪ ⎪ ⎪ ⎨ ∂u0 1 ∂Bzd F (8) J (r) − σ0 (r) (r) := − y ⎪ μ ∂x ∂y ⎪ 0 ⎪ ⎪ ⎪ ⎪ ⎪ F ∂u0 ⎩ Jz (r) := −σ0 (r) ∂z
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where B d := Bz − Bz0 and B0 = (Bx0 , By0 , Bz0 ) represents the background magnetic flux density and the potential u0 is the voltage potential corresponding to the background conductivity σ0 . The estimated JF is divergence-free and the z-component of ∇ × JF satisfies ∂JyF ∂J F (r) − x (r) ∂x ∂y 2 1 ∂ Bz ∂ 2 Bz ∂ 2 Bz0 =− (r) + (r) + (r) . μ0 ∂x2 ∂y 2 ∂z 2
(9)
The projected current density JP , which is the best approximation of the current density J from the measured Bz data, can be expressed as an exact form [31]: JP (r) = J0 (r) + J∗ (r),
r ∈ Ω
(10)
where J0 is the background current density by the injected cur
∂β ∂β β := , − rent, J∗ := ∇⊥ xy ∂y ∂ x , 0 , and β(x, y) satisfies the following two-dimensional Poisson’s equation in the imaging region Ω ⊂ Ω: ⎧ 1 2 ⎨ ∇2xy β(r) = ∇ Bz (r) in Ω μ0 (11) ⎩ β(r) = 0 on ∂Ω . In the vector space V = {J = (Jx , Jy , Jz )|∇ · J(r) = 0, r ∈ Ω}, the estimated JP is a unique element up to a constant in V, which satisfies (∇ × JP ) · (0, 0, 1) = − μ10 ∇2 Bz in Ω and JP · n = J · n on ∂Ω [31], where n denotes the unit outward normal vector on ∂Ω . The difference JD between the projected current density JP and the directly calculated JF in (8) can be described as a twodimensional vector because the two vectors have the common z-component : JD (r) = (JxD (r), JyD (r)) JxF
(12) JyF .
where = − and = − Using the Helmholtz decomposition of the two-dimensional vector JD , we can decompose JD into a curl-free component and a divergencefree component as below JxD
JxP
JyD
JyP
JD (r) := ∇xy f (r) + ∇⊥ xy ψ(r) where ⎧ 2 ∇ f (r) = 0 ⎪ ⎨ xy
(13)
Fig. 1. Setup for the numerical simulation. (a) Three-dimensional model and (b) its finite element mesh. (c) Conductivity distribution at the center slice and (d) axial view of the simulation model. For the external electrode case, the current flows from ∂F1 to ∂F 1 , whereas for the internal electrode case, the current flows from ∂F1 to ∂F02 which is a part of the internal electrode. (e) Three-dimensional configuration of the internal electrode. (f) R denotes a region including the anomaly to measure the relative L 2 -error for the recovered current density J F .
z) z) difference of ( ∂ (B z∂ −B , − ∂ (B ∂z −B ) on the boundary ∂Ω and y x 0
0
z) the difference of ∂ (B∂zz−B in the imaging slice Ω . For the 2 cylindrical imaging object Ω, Ampere’s law (6) implies that the boundary condition on ∂Ω in (14) is small because Bz and Bz0 share the same injection current. The divergence-free ∂ 2 (B z −B z0 ) component ∇⊥ xy ψ in (15) depends on the variation of ∂z2 in Ω . When compared with the projected current density JP , the estimated JF has certain advantages. The estimated JF can be directly calculated by the simple differentiations of the measured Bz data without solving any partial differential equation. While the computation of JP requires a numerical solution of the Poisson’s equation in the whole imaging region Ω with the Laplacian of Bz as a source term, the calculated JF provides a recoverable current component in the chosen ROI, R ⊂ Ω , without being affected by the noise propagation from a defective region. 2
0
in Ω
∂B d 1 ∂Bzd ⎪ ⎩ ∇xy f (r) · n(r) = (r), − z (r) · n(r) on ∂Ω μ0 ∂y ∂x (14) and ⎧ 2 d ⎪ ⎨ ∇2 ψ(r) = − 1 ∂ Bz (r) in Ω xy μ0 ∂z 2 (15) ⎪ ⎩ ψ(r) = 0 on ∂Ω . Since the projected current density JP is the best approximation of J from the available Bz data, the recovered JF satisfying ∇ · JF = 0 may not be optimal due to the difference JD . However, the difference JD shows a reliable dependence on both the
C. Numerical Simulation We built a cylindrical model with a diameter of 110 mm and height of 140 mm using COMSOL (COMSOL Inc. USA) as shown in Fig. 1. We attached four electrodes around the middle surface of the model and placed one internal electrode at the center. Inside the model, we placed a cylindrical insulating barrier of 0.0001 Sm−1 and a conductive anomaly of 1.5 Sm−1 . The background saline had a conductivity of 1.0 Sm−1 . Figs. 1(a) and (b) show the model and its finite element mesh, respectively. The mesh consists of 990854 tetrahedral elements and 85 938 triangular elements on its surface. We solved the following elliptic equation with total 27 345 610 degrees of
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Fig. 2. Voltage distributions at the center slice for (a) the external electrode case and (e) the internal electrode case. The streamline superimposed on the voltage potential image shows the direction of current flow. (b) and (c) ((f) and (g)) The x and y components, respectively, of the true current density J for the external (internal) electrode case. B z images for (d) the external and (h) internal electrode cases.
freedom:
⎧ ∇ · (σ(r)∇u(r)) = 0 in Ω ⎪ ⎪ ⎨ −σ(r)∇u(r) · n = g(r) on ∂Ω ⎪ ⎪ ⎩ and ∂ Ω u(r, t) ds = 0
(16)
where σ denotes the described isotropic conductivity distribution, u is the voltage potential, and g is the Neumann boundary condition subject to the 5-mA injection current. We estimated the magnetic flux density Bz by using the Biot–Savart law in (7) with the computed current density J = −σ∇u. Figs. 1(d) and (e) show the axial view of the simulation model and the three-dimensional configuration of the internal electrode, respectively. Fig. 2(a) shows the internal current streamlines by the external injection current superimposed on the voltage potential image. Figs. 2(b) and (c) show the x and y components, respectively, of the simulated current density by the external current injection. The simulated Bz was shown in Fig. 2(d). Figs. 2(e–h) show the corresponding images for the case of internal injection current. The simulated current passed between the external electrode ∂F1 and ∂F02 which was a part of the internal electrode as shown in Fig. 1(e). In contrast, the conventional external current flows from ∂F1 to ∂F1 . D. Phantom Experiment We conducted a cylindrical acrylic phantom with a height of 140 mm and diameter of 110 mm to verify the proposed method in a real imaging experiment. An open-ended cylindrical insulating thin shell with 2-mm thickness was placed inside the phantom to create an obstacle to disturb the internal current flow. An anomaly with a diameter of 30 mm, made of agar gel (800 ml distilled water, 8 g NaCl, 1 g CuSO4 , and 15 g Agar), was also placed inside the phantom. The conductivity of the agar object was 1.5 Sm−1 . We placed an acrylic rod with a height of 140 mm and diameter of 10 mm at the center of the phantom. We constructed an internal electrode by wrapping the middle part of the rod with a sheet of carbon (HUREV Co. Ltd.,
Fig. 3. Setup for the phantom imaging experiment. (a) Image of the phantom showing the position of the agar object, acrylic insulation shell and the internal electrode. (b) Acrylic cylinder wrapped in a carbon electrode placed at the middle of the phantom for the internal electrode case. (c) Preparation of phantom inside the eight-channel RF head coil. (d) Schematic diagram of the multispinecho MREIT pulse sequence.
Korea). The phantom was subsequently filled with 1.0 Sm−1 saline (2 L of distilled water, 2 g CuSO4 , 7 g NaCl). Figs. 3(a–c) show the phantom design; (a) shows the positions of the agar object, the open-ended thin shell object, and the internal electrode, (b) depicts the internal electrode, and (c) shows the phantom inside the RF coil. We performed the imaging experiment using a 3 T MRI scanner (Philips Achieva 3.0 T) with a multi-channel RF coil (Philips, SENSE-Head-8ch). We collected two sets of k-space data by injecting currents; external injection current between the pair of surface electrodes from ∂F1 to ∂F1 and internal injection current from ∂F1 to the internal electrode ∂F02 . Using a custom-designed MREIT current source [23] synchronized with the ICNE multispin-echo pulse sequence [19], we injected a 5 mA current as shown in Fig. 3(d). The imaging parameters were as follows: repetition time (TR ) = 1500 ms, echo time (TE ) = 15 × ms, echo space (Es ) = 15 ms, slice thickness = 5 mm, number of echoes (NE ) = 8, field-of-view = 180 × 180 mm2 , imaging matrix = 128 × 128, number of excitation (NEX) = 10, and imaging time = 32 min. Fig. 4 shows the MR magnitude and the acquired Bz images by the external and internal injection currents. To obtain the Bz data, we combined multiple values of Bz for = 1, . . . , 8 by estimating the weighting factors ω in (5) to reduce the noise level of Bz . III. RESULTS A. Simulation Results In order to evaluate the performance of the proposed method, we assumed that the measured Bz data included white Gaussian noise with zero mean and standard deviation of sdB z . Since
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Fig. 4. (a) MR magnitude image of designed phantom. An ROI of 5 × 5 pixels is used to measure the noise level of B z and the recovered current density J F . Measured B z images for (b) the external current case and (c) the internal injection current case.
the noise standard deviation sdB z depends on the MR signal intensity, we added different amounts of noise. To differentiate the noisy Bz data, we used the following numerical differentiation procedure: ⎧ 1 ∂Bzi,j ⎪ ⎪ ((Bzi+1,j +1 − Bzi−1,j +1 ) = ⎪ ∂x ⎪ 8Δ ⎪ ⎪ ⎪ + 2(Bzi+1,j − Bzi−1,j ) ⎪ ⎪ ⎨ + (Bzi+1,j −1 − Bzi−1,j −1 )) (17) i,j 1 ∂Bz ⎪ i+1,j +1 i+1,j −1 ⎪ ((B = − B ) ⎪ z z ∂y ⎪ ⎪ 8Δ ⎪ i,j +1 i,j −1 ⎪ ⎪ + 2(B − B ) z z ⎪ ⎩ + (Bzi−1,j +1 − Bzi−1,j −1 )) where Δ denotes the pixel size of the image and Bzi,j is the value of Bz at the (i, j)th pixel. The level of the background region SNR was fixed at 100, 75, and 50 dB for three trials and the SNR at the target region of anomaly was set to two times higher than the level of the background noise. To generate a defective region, we added severe noise to the thin open-ended insulating shell. Fig. 5 shows the x and y components of the recovered current density JF obtained using (8). Due to the presence of the cylindrical insulating obstacle, most of the internal current was shunted around the ROI R [see Fig. 5(a)] for the case of external injection current. Since the estimated JF did not lead to propagation of noise effects to the surrounding region, the severe noise in the insulating shell did not affect the estimated current density JF in the region R. For the external injection current case with increased noise levels, the recovered current density was almost indistinguishable in R due to the relatively weak signal of Bz as shown in Fig. 5(a). However, for the internal electrode case the recovered current density JF in R was not affected by the noise in the insulating shell, and it provided a sufficient resolution to distinguish the anomaly. We calculated the relative L2 -error to compare the simulated noiseless current density J and the estimated current density JF in the region R. The relative L2 -error was defined by
J − JF F R ER (J ) := (18)
J R where · R denotes the discrete L2 -norm in the region R. Table I summarizes the relative L2 -error. For the external injection current case, the insulating shell mostly perturbed the transversal current flow in R. Since the relative L2 -error
Fig. 5. Comparison of the current densities J F at the center slice for different levels of background SNR. (a) and (b) The x and y components, respectively, of the current density J F . The upper and lower rows show the external and internal electrode cases, respectively. Columns from left to right represent the recovered current density at each level of the background SNR = ∞, 100, 75, and 50 dB. TABLE I RELATIVE L 2 -ERROR OF THE ESTIMATED CURRENT DENSITY IN THE LOCAL REGION R FOR DIFFERENT NOISE LEVELS IN B z
depended on the current flow in the z direction and the intensity of the current density, the relative L2 -error in R for the external injection current case was higher than that of the internal injection current case. B. Experimental Results For the background current density, we first solved the threedimensional harmonic equation assuming a background conductivity of σ0 = 1 Sm−1 . The upper and lower rows in Fig. 6 show the background current density and Bz0 images for the external and internal electrode cases, respectively. After evaluating the difference vector 0 ∂ (B z −B z0 ) z) , − , 0), we combined the vector with ( ∂ (B z∂ −B y ∂x the background current density using (8) to estimate the internal current density JF . Fig. 7 shows the x and y components of the recovered current density JF depending on the different number-of-excitation (NEX = 1, 3, 5) for the external case (upper row) and the internal case (lower row). From Fig. 7, as NEX increases, the recovered current density JF obtained by using the internal electrode showed a better resolution in the
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TABLE II INTENSITY OF THE RECOVERED CURRENT DENSITY IN THE LOCAL ROI OF 5 × 5 PIXELS DEPENDING ON THE NUMBER OF AVERAGES
Fig. 6. (a) and (b) [(d) and (e)] x and y components, respectively, of the homogeneous current density J 0 for the external (internal) electrode case. (c) and (f) The background B z0 images for the external and internal electrode cases, respectively.
Fig. 8. Recovered |J F | images with NEX = 5 for the external and internal electrode cases. (a) and (d) Color-coded streamlines superimposed on the current density image, which show the direction of current flow. (b) and (e) Recovered current density images. (c) and (f) Magnified current density images in the local region.
normal vector n was orthogonal to JF , provided a clear contrast as shown in Fig. 7. To investigate the effects of the injection current through the internal electrode, we selected a small ROI of 5 × 5 pixels within the region R shown in Fig. 4(a). Following the analysis of Sadlier et al. [34], the noise standard deviation of Bz , sdB z , satisfies the following relationship: sdB z =
Fig. 7. Comparison of the current densities J F at the center slice with different averages. (a) and (b) The x and y components, respectively, of the current density J F . The upper and lower rows depict the external and the internal electrode cases, respectively. Columns from left to right represent the recovered projected current density with NEX = 1, 3, and 5.
anomaly region than the case of external injection current. The internal current density J can be decomposed as J(r) = (J(r) · n(r))n(r) + (J(r) · τ (r))τ (r)for r ∈ ∂R (19) where n denotes the unit outward vector on ∂R and τ denotes the unit tangent vector on ∂R in the counterclockwise direction. The recovered JF near the edge of the anomaly, where the
sd∇2 B z 20/Δ4 + 6/Δ4z
(20)
where Δz represents the slice thickness. We denote sdE B z and I sdB z as the noise standard deviations of Bz for the external and internal electrode cases, respectively. We measured the intensity of the recovered current density JF and the noise standard deviation within the local ROI of 5 × 5 pixels and these values were listed in Table II. The noise standard deviation sdIB z with NEX = 1 (NEX = 3) was smaller than sdE B z with NEX = 3 (NEX = 5). This clearly indicates the advantage of the internal electrode in terms of the SNR in the ROI. F Moreover, the intensity of the recovered current density J obtained using the internal electrode was increased up to I 38% in the region R compared to the values of JF E obtained using the external electrodes. The upper and lower rows in Fig. 8 show the characteristics of the recovered current density JF for the external and internal electrode cases, respectively, with NEX = 5. In the first column,
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we note that the use of the internal electrode produced concentrated current flows in the anomaly region R whereas externally injected current spread over the whole domain. Figs. 8(b) and (e) show the intensity of the reconstructed current density by using the external and internal injection currents, respectively. Figs. 8(c) and (f) show the magnified views of JF in the region including R corresponding to Figs. 8(b) and (e), respectively. Due to the concentration of the current density in the ROI R, the enhanced current density in Fig. 8(f) using the internal electrode provided a clear contrast compared to the recovered current density using the external electrodes as shown in Fig. 8(c). IV. DISCUSSION From the measured magnetic flux density Bz data, the projected current density JP = J0 + J∗ in (10) is the best approximation of the current density by injecting current, which reflects the measured Bz and the injected current simultaneously. When the current is transversely injected into a cylindrical imaging object, the recovered projected current density JP stably approximates the true current density J depending on the z component of J − J0 . Unlike the conventional external electrode case, the current density J using the internal electrode was highly concentrated and rapidly changed around the internal electrode. The recovered current density JF in (8) instead of JP , which reduces noise propagation from defective regions to their surrounding regions, may include a relatively large difference compared to the JP corresponding to the transversally injected current through the external electrode. The recovered current density JF in the local region R ⊂ Ω in (8) can be applicable to any size of region and it can be used instead of JP by solving (11). In this paper, we focused on the recovery of current density in a local region around the internal electrode. If there is no defective area in the imaging region, the projected current density JP = J0 + J∗ can remove side artifacts BzI in (7) by the external lead wires because the harmonic term ∇2 Bz cancels the effect of BzI by taking ∇2 BzI (r) = 0 in the imaging region [39]. Magnetic resonance electrical impedance tomography (MREPT) is a technique that uses MR to derive noninvasive information of tissue properties including electrical conductivity and permittivity based on the B1 mapping technique without applying external current. MREIT and MREPT are electromagnetic tissue property mapping techniques that provide the electrical conductivity distribution of the human body at different frequency ranges. MREIT provides conductivity images in the low frequency range below 1 kHz, while MREPT provides conductivity images at the Larmor frequency. Since biological tissues exhibit frequency-dependent conductivity spectra, their values at different frequencies may provide valuable diagnostic information. To apply the MREIT technique to the recovery of current density in a local region, we focused on developing a local imaging technique. A typical MR imaging region in MREIT contains defective regions wherein the quality of Bz is very poor due
to low proton density and short transverse relaxation time. The noisy Bz data in the defective regions may severely degrade the reconstructed conductivity distribution in the whole imaging region. The current density imaging technique we have developed in a local region can avoid defective regions and visualize the internal conductivity within the local region around the internal electrode. The method enables the minimization of both the injection current and the imaging time while retaining or improving the image quality. Electrical stimulation techniques such as RF ablation, deep brain stimulation, electroporation, and endo-electrode usage in EIT for the treatment of various diseases utilize the internal electrode to enhance their clinical outcomes [25]–[29]. The internal current density distribution is influenced by several factors such as the shape and position of the internal electrode, imaging area, and conductivity distribution around the internal electrode. As a clinical application of the MREIT technique by optimizing the measured magnetic flux density signal using the internal electrode, each case requires appropriate approached considering its clinical situation. The proton resonance frequency (PRF) method is used to monitor RF ablation by detecting a temperature shift in the frequency. The method measures the temperature variation in tissues by subtracting the phase distributions before and after a temperature change [35]–[38]. In general, the PRF method typically uses spoiled gradient echo MR pulse sequences. Therefore, it suffers from magnetic field inhomogeneity artifacts, thereby resulting in inaccurate temperature imaging. Since there exists an approximatively linear relationship between tissue conductivity and temperature, the MREIT technique using the internal electrode can be utilized to measure the temperature variation by measuring the magnetic flux density Bz data by canceling out the background field inhomogeneity through interleaved acquisitions. The proposed method has the potential to visualize the internal current density and/or conductivity distribution corresponding to the temperature variation during RF ablation. As a restorative functional neurosurgical technique, DBS electrodes are implanted in what are assumed to be optimal sites inside the brain and the stimulator is turned on to stimulate areas near the targeted brain region. The MREIT technique, providing a continuous monitoring system showing the current density generated by DBS, can potentially be used to optimize the current density by changing the configuration of the active DBS contacts. Since the SNR of the measured magnetic flux density is inversely proportional to the intensity of MR magnitude and the duration of injected current, by combining the maximized duration of injection current using the ICNE-multiecho, we plan to develop an MR pulse sequence to maximize the quality of Bz in a local ROI and in dynamic MREIT imaging. V. CONCLUSION In this paper, we suggested a new method to visualize the internal current density within a local region around the internal electrode in MREIT imaging. The conventional MREIT
JEONG et al.: FOCUSED CURRENT DENSITY IMAGING USING INTERNAL ELECTRODE IN MREIT
technique suffers from poor SNR of the recovered conductivity and/or current density due to weak Bz signal by externally injected current. In combination with the use of the internal electrode, the MREIT technique can be applied to conventional clinical devices using the internal electrode and provide useful information regarding the electrical properties in a local region by enhancing the magnetic flux density. Results from numerical simulations and phantom imaging experiments demonstrated the feasibility of the proposed algorithm that stably determined and enhanced the current density in the local region. To test the proposed method, the reconstructed internal current density was compared to that obtained from the conventional method through a saline agar-gel phantom experiment. REFERENCES [1] Y. Z. Ider and O. Birgul, “Use of the magnetic field generated by the internal distribution of injected currents for Electrical Impedance Tomography (MR-EIT),” Elektrik, vol. 6, no. 3, pp. 215–225, 1998. [2] O. Kwon, E. J. Woo, J. R. Yoon, and J. K. Seo, “Magnetic resonance electrical impedance tomography (MREIT): Simulation study of J-substitution algorithm,” IEEE Trans. Biomed. Eng., vol. 48, pp. 160–167, Feb. 1998. [3] O. Birgul, B. M. Eyuboglu, and Y. Z. Ider, “Current constrained voltage scaled reconstruction (CCVSR) algorithm for MR-EIT and its performance with different probing current patterns,” Phys. Med. Biol., vol. 48, pp. 653–671, Mar. 2003. [4] B. I. Lee, S. H. Oh, E. J. Woo, S. Y. Lee, M. H. Cho, O. I. Kwon, J. K. Seo, J. Y. Lee, and W. S. Baek, “Static resistivity image of a cubic saline phantom in magnetic resonance electrical impedance tomography (MREIT),” Physiol. Meas., vol. 24, pp. 579–589, Apr. 2003. [5] Y. Z. Ider, S. Onart, and W. R. B. Lionheart, “Uniqueness and reconstruction in magnetic resonance-electrical impedance tomography (MR-EIT),” Physiol. Meas., vol. 24, pp. 591–604, Apr. 2003. [6] Y. Z. Ider and S. Onart, “Algebraic reconstruction for 3D MREIT using one component of magnetic flux density,” Physiol. Meas., vol. 25, pp. 281– 294, Feb. 2004. [7] M. L. G. Joy, “MR current density and conductivity imaging: The state of the art,” Proc. 26th Ann. Int. Conf. IEEE Eng. Med. Biol. Soc., San Francisco, CA, USA, Sep. 2004, pp. 5315–5319. [8] L. Muftuler, M. Hamamura, O. Birgul, and O. Nalcioglu, “Resolution and contrast in magnetic resonance electrical impedance tomography (MREIT) and its application to cancer imaging,” Tech. Cancer Res. Treat., vol. 3, pp. 599–609, Dec. 2004. [9] M. Ozdemir, B. M. Eyuboglu, and O. Ozbek, “Equipotential projectionbased magnetic resonance electrical impedance tomography and experimental realization,” Phys. Med. Biol., vol. 49, pp. 4765–4783, Oct. 2004. [10] J. K. Seo, H. C. Pyo, C. Park, O. I. Kwon, and E. J. Woo, “Image reconstruction of anisotropic conductivity tensor distribution in MREIT: Computer simulation study,” Phys. Med. Biol., vol. 49, pp. 4371–4382, Sep. 2004. [11] N. Gao, S. A. Zhu, and B. A. He, “New magnetic resonance electrical impedance tomography (MREIT) algorithm: The RSM–MREIT algorithm with applications to estimation of human head conductivity,” Phys. Med. Biol., vol. 51, pp. 3067–3083, May 2006. [12] O. Birgul, M. Hamamura, L. Muftuler, and O. Nalcioglu, “Contrast and spatial resolution in MREIT using low amplitude current,” Phys. Med. Biol., vol. 51, pp. 5035–5049, Sep. 2006. [13] M. J. Hamamura, L. Muftuler, O. Birgul, and O. Nalcioglu, “Measurement of ion diffusion using magnetic resonance electrical impedance tomography,” Phys. Med. Biol., vol. 51, pp. 2753–2762, May 2006. [14] M. J. Hamamura and L. Muftuler, “Fast imaging for magnetic resonance electrical impedance tomography,” Magn. Reson. Imaging., vol. 26, pp. 739–745, Jul. 2008. [15] S. Z. K. Sajib, H. J. Kim, O. I. Kwon, and E. J. Woo, “Regional absolute conductivity reconstruction using projected current density in MREIT,” Phys. Med. Biol., vol. 57, pp. 5841–5859, Sep. 2012. [16] H. J. Kim, Y. T. Kim, A. S. Minhas, W. C. Jeong, E. J. Woo, J. K. Seo, and O. J. Kwon, “In vivo high-resolution conductivity imaging of the human leg using MREIT: The first human experiment,” IEEE Trans. Med. Imag., vol. 28, no. 11, pp. 1681–1687, Nov. 2009.
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Woo Chul Jeong received the B.S. degrees in biomedical engineering from Konkuk University, Chungju, Korea, in 2007. He is currently working toward the Ph.D. degree in the Department of Biomedical Engineering, Kyung Hee University, Yongin, Korea. His research interests include magnetic resonance tissue property imaging and functional MRI.
Saurav Z. K. Sajib received the B.Sc. degrees in electrical and electronics engineering from Bangladesh University of Engineering and Technology, Dhaka, Bangladesh, in 2007. He is currently working toward the Ph.D. degree in the Department of Biomedical Engineering, Kyung Hee University, Yongin, Korea. His research interests include magnetic resonance electrical impedance tomography, diffusion MRI, and functional connectivity of brain.
Hyung Joong Kim received the B.S. degree in biomedical engineering from the Konkuk University, Chungju, Korea, in 1994, and the M.S. and Ph.D. degrees in radiology from the Chonnam National University Medical School, Gwangju, Korea, in 2000 and 2004, respectively. From 2004 to 2006, he completed a postdoctoral research fellowship at the Department of Radiology, Chonnam National University Hospital, where he continued his research in MRI technology development. Currently, he is a Research Professor of Impedance Imaging Research Center, Kyung Hee University, Yongin, Korea. His research interests include MREIT, functional MRI, MRS, and clinical application of MR techniques.
Oh In Kwon received the B.S., M.S., and Ph.D. degrees in mathematics from Seoul National University, Seoul, Korea, in 1988, 1990, and 1999, respectively. Currently, he is a Professor of mathematics at Konkuk University, Seoul, Korea. His research interests include magnetic resonance electrical impedance tomography, numerical analysis, and inverse problems.
