Modelling of electromagnetic field distribution for optimising electrode configurations in liver MR-based electrical impedance tomography
The spherical anomaly of 30 mm diameter was included to evaluate the field distribution inside the liver. Further details of the simulation methods can be found in Sadleir et al. [4].
Tong In Oh, Munish Chauhan, Saurav Z.K. Sajib, Ji Eun Kim, Woo Chul Jeong, Hun Wi, Oh In Kwon, Eung Je Woo and Hyung Joong Kim In-vivo electromagnetic field distributions of biological systems can be imaged from the measured magnetic flux density of magnetic resonance-based electrical impedance tomography (MREIT), which was induced by the externally injected current through a pair of electrodes. Since the electromagnetic field is affected by the injected current and electrical conductivity of biological tissues, the electrode type and position are important factors for determining the voltage and current density distribution. Using a three-dimensional finite element model, the current pathway and electric field distribution to optimise the electrode configurations in liver MREIT are estimated.
Introduction: Magnetic resonance-based electrical impedance tomography (MREIT) is a new bioimaging modality capable of visualising cross-sectional current density and/or conductivity distribution inside an electrically conducting object [1]. Using a clinical magnetic resonance imaging scanner, MREIT measures the internal magnetic flux density generated by the externally injected current through a pair of electrodes [1]. It recovers the corresponding internal current density distribution from Ampere’s law. The electromagnetic field distribution of biological tissues is affected by the externally injected current and internal electrical conductivity. The electrode configurations are one of the critical factors for determining the electrical field distribution, which may provide clinically useful diagnostic information in electrical and thermal stimulations. For diagnostic as well as therapeutic purposes, an electrode can be attached to or inserted into the human body [2]. For example, an internal electrode in deep brain stimulation is intended to stimulate specific areas of the brain to treat neurological disease. In liver radio-frequency ablation (RFA), an alternating current of several hundreds of kilohertz is delivered through the RFA electrode to heat a target tissue. Several research groups have used an internal electrode to apply a high electrical field to deliver pharmaceutical agents and drugs into the cells directly [2, 3]. The electromagnetic field distribution of the liver is not well known due to the limitations of physical and physiological factors such as large imaging area, susceptibility effects, respiratory movements and motion artefacts. Since the signal intensity of current density is proportional to the measured magnetic flux density in MREIT imaging [1], by applying the optimal electrode configuration, the MREIT imaging has a potential to provide in-vivo high-resolution electromagnetic field distribution inside the liver. In the work reported in this Letter, we provided the simulation results of liver MREIT to evaluate the electromagnetic field distributions at three different electrode configurations. Using a three-dimensional (3D) realistic human abdomen model, we conducted and analysed a series of numerical simulations to evaluate its performance. The voltage, current density and magnetic flux density were imaged and compared for optimising the electrode configurations. Methods: A 3D abdomen finite element model was built using a reference CT dataset consisting of 180 axial plane slices (2 mm thickness) over a 500 × 400 mm field-of-view (FOV) with an image matrix size of 574 × 434 (Fig. 1a). The reference images were segmented into significant abdomen components (liver, kidney, spinal cord, skin, fat and muscle) and generated volumetric mesh using an image processing and meshing software (Figs. 1b and c). Conductivities used with the finite element model are shown in Table 1. Where possible, we chose the recently measured values that were gathered in situations close to in-vivo conditions. Three different electrode configurations representing the conventional, focused and internal injection current were located around the boundary or inside the liver region (Fig. 2). We used surface electrodes in both the conventional and focused injection, needle and surface electrodes in the internal injection. The electrode size was about 80 × 80 × 1 mm3 for the surface and 2 mm diameter for the needle electrode.
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Fig. 1 3D model of human abdomen for numerical simulation a Anatomical CT image of human abdomen b Segmentation of reference data into significant abdominal components c Lateral view of generated 3D model with external electrodes
Table 1: Electrical conductivities of abdominal components used in finite element model Component Conductivity (S/m) Component Conductivity (S/m) Liver 0.075 Muscle 0.266 Kidney 0.102 Fat 0.022 Spinal cord 0.028 Skin 0.001
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Fig. 2 Three different types of electrode configurations a Conventional b Focused current injection methods using surface electrodes c Internal injection using needle and surface electrode Arrow indicates single anomaly of 30 mm diameter
For the estimation of the electromagnetic field, we solved for the Laplace equation in our model. The induced voltage u in Ω satisfies the following boundary value problem with the Neumann boundary condition ∇.(s(r)∇u(r)) = 0 in V, − s∇u.n = j on ∂V
(1)
where σ(r) is the conductivity distribution within the abdomen ∂Ω, n is a vector normal to the surface, j is the surface current density and r = (x, y, z) is a position vector. The current density J is given by J(r) = −s(r)∇u(r) in V
(2)
The voltage solutions were computed on the abdominal domain, and then converted to magnetic flux density (Bz) values using the BiotSavart law m r − r′ J(r′ ) × dr′ (3) B(r) = 0 4p V |r − r′ |3 where μ0 = 4 × 10−7 Tm/A is the permeability of the free space. The MREIT technique uses the relationship between the measured Bz data and the current density J based on Ampere’s law J(r) =
1 ∇ × B(r) m0
(4)
To estimate the current density from the measured Bz data, we applied the projected current density method following the work of Park et al. [5]. The data with a 500 × 500 mm2 FOV, 128 × 128 matrix size, 1 mm slice thickness and 100 slices in total was simulated. Results: Fig. 3 shows the numerical simulation results of voltage (V), current density (J) and magnetic flux density (Bz) distributions in the abdominal region at three different electrode configurations. The calculation was performed with a single anomaly of 200% conductivity contrast inside the liver region. The current was vertically injected with a 3 mA of amplitude and duration of 30 ms. From the resulting current density images in Fig. 3b, the internal injection method showed significantly higher current density distribution near the anomaly than the other methods due to the high current flow around the electrode.
ELECTRONICS LETTERS 28th August 2014 Vol. 50 No. 18 pp. 1273–1275
When comparing the results from surface electrodes, the focused injection showed two times higher current density than the conventional injection. The calculated Bz of the internal injection also showed enhanced signal intensity among the electrode configurations. Fig. 4 shows the profile of current density distribution at three different electrode configurations. Using the projected current density method, we can successfully image the current density from the Bz data of MREIT. In the internal injection method, the extremely high current density value was observed in the anomaly. This primarily depends on the large amount of current flow around the electrode. [V]
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the diagnosis and treatment of various physiological conditions with weak electric currents, radio-frequency hyperthermia, electrocardiography and body composition [2, 3]. The human body consists of conductive materials with numerous ions and heterogeneous membrane structures. Recent MREIT techniques can provide high-resolution conductivity information of living tissues incorporating with a constant current source to an existing MR scanner. To reconstruct conductivity distribution, this technique uses the magnetic flux density (Bz) data induced by the externally injected current. Therefore, the quality of Bz is affected by the electromagnetic field distributions such as voltage and current density. When applying current MREIT techniques to human subjects, the prediction of the current pathway and electric field distribution is one of the research topics related to the evaluation of electrode configurations. In MREIT, electrodes are attached on the surface and/or inserted into the imaging object for injecting current. The quality of measured Bz data can be improved by the optimisation of electrode configurations. This can be done either by localising the current flow into the specific region-of-interest of the imaging area or by increasing the power efficiency through an optimised electrode position. Using a 3D finite element model of the abdomen, we provide numerical simulation results of electromagnetic field distributions from three possible electrode configurations in MREIT. Based on the magnetic flux density data, we can successfully image both the current density and electric field distribution of abdominal components. The strong current density signal in the internal injection method reveals enhanced magnetic flux density data. Providing a cross-sectional electromagnetic field distribution of biological systems, we expect that this kind of modelling study can provide prior information of tissues in situ to be utilised in-vivo human imaging.
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Fig. 3 Calculation of electromagnetic field distribution at three different electrode configurations a Cross-sectional voltage b Current density c Magnetic flux density Distributions were imaged using vertically injected current of 3 mA through pair of electrodes 0.8
Acknowledgment: This work was supported by the National Research Foundation (NRF) of Korea grant funded by the Korean government (MEST) (2011-0022779, 2012R1A1A2008477 and 2013R1A2A2A04016066). © The Institution of Engineering and Technology 2014 7 May 2014 doi: 10.1049/el.2014.1470 One or more of the Figures in this Letter are available in colour online. Tong In Oh, Munish Chauhan, Saurav Z.K. Sajib, Ji Eun Kim, Woo Chul Jeong, Hun Wi, Eung Je Woo and Hyung Joong Kim (Impedance Imaging Research Center and Department of Biomedical Engineering, Kyung Hee University, Yongin-si, Republic of Korea)
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E-mail:
[email protected] Oh In Kwon (Department of Mathematics, Konkuk University, Seoul, Republic of Korea)
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Fig. 4 Profiles of current density distribution at three different electrode configurations Anomaly with 200% conductivity contrast was located inside liver to evaluate electromagnetic field distribution by electrode type and position
Discussion and conclusions: Measurement of electrical current pathways through the body is important in the analysis of a wide range of biomedical applications such as functional electrical stimulation and
1 Woo, E.J., and Seo, J.K.: ‘Magnetic resonance electrical impedance tomography (MREIT) for high-resolution conductivity imaging’, Physiol. Meas., 2008, 29, pp. R1–26 2 Jeong, W.C., Sajib, S.Z.K., Kim, H.J., and Kwon, O.: ‘Focused current density imaging using internal electrode in magnetic resonance electrical impedance tomography (MREIT)’, IEEE Trans. Biomed. Eng., 2014, in press 3 Kranjc, M., Bajd, F., Sarsa, I., and Miklavcic, D.: ‘Magnetic resonance electrical impedance tomography for monitoring electric field distribution during tissue electroporation’, IEEE Trans. Med. Imaging, 2011, 30, pp. 1771–1778 4 Sadleir, R., Sajib, S.Z.K., Kim, H.J., Kwon, O., and Woo, E.J.: ‘Simulations and phantom evaluations of magnetic resonance electrical impedance tomography (MREIT) for breast cancer detection’, J. Magn. Reson., 2013, 230, pp. 40–49 5 Park, C., Lee, B.I., and Kwon, O.: ‘Analysis of recoverable current from one component of magnetic flux density in MREIT’, Phys. Med. Biol., 2007, 52, pp. 3001–3013
ELECTRONICS LETTERS 28th August 2014 Vol. 50 No. 18 pp. 1273–1275
