Simulations and phantom evaluations of magnetic resonance electrical impedance tomography (MREIT) for breast cancer detection

Journal of Magnetic Resonance 230 (2013) 40–49

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Simulations and phantom evaluations of magnetic resonance electrical impedance tomography (MREIT) for breast cancer detection Rosalind J. Sadleir a,b, Saurav Z.K. Sajib a, Hyung Joong Kim a,⇑, Oh In Kwon c, Eung Je Woo a a

Department of Biomedical Engineering, Kyung Hee University, Yongin, Gyeonggi, Republic of Korea J. Crayton Pruitt Department of Biomedical Engineering, University of Florida, Gainesville, FL, USA c Department of Mathematics, Konkuk University, Seoul, Republic of Korea b

a r t i c l e

i n f o

Article history: Received 26 July 2012 Revised 22 January 2013 Available online 4 February 2013 Keywords: MREIT Breast cancer Conductivity image Magnetic flux density

a b s t r a c t MREIT is a new imaging modality that can be used to reconstruct high-resolution conductivity images of the human body. Since conductivity values of cancerous tissues in the breast are significantly higher than those of surrounding normal tissues, breast imaging using MREIT may provide a new noninvasive way of detecting early stage of cancer. In this paper, we present results of experimental and numerical simulation studies of breast MREIT. We built a realistic three-dimensional model of the human breast connected to a simplified model of the chest including the heart and evaluated the ability of MREIT to detect cancerous anomalies in a background material with similar electrical properties to breast tissue. We performed numerical simulations of various scenarios in breast MREIT including assessment of the effects of fat inclusions and effects related to noise levels, such as changing the amplitude of injected currents, effect of added noise and number of averages. Phantom results showed straightforward detection of cancerous anomalies in a background was possible with low currents and few averages. The simulation results showed it should be possible to detect a cancerous anomaly in the breast, while restricting the maximal current density in the heart below published levels for nerve excitation. Ó 2013 Elsevier Inc. All rights reserved.

1. Introduction Early diagnosis is the key to increasing breast cancer survival rates [1]. The standard diagnosis method, X-ray mammography, involves compression of the breast between two plates and acquisition of high resolution X-ray projection images [2]. However, it involves use of ionizing radiation. Furthermore, X-rays can only poorly differentiate soft tissues inside a dense breast [3]. The drawbacks of X-ray mammography stimulated developments of several new breast imaging methods including optical tomography, ultrasonic transmission tomography and contrast-enhanced MRI [3–5]. MRI is now widely used for screening in some populations at risk for breast cancer [6–8]. However, there still exists a need for methods that can both detect and characterize breast lesions. Several research groups have tested methods that investigated the electrical properties of breast tissues because studies have shown that cancerous tissues in the breast have much higher conductivity values than those of normal breast tissues [9–11]. Electrical impedance imaging approaches and experimental studies have been tested to determine their ability to detect a cancerous ⇑ Corresponding author. Address: Department of Biomedical Engineering, Kyung Hee University, 1 Seocheon Giheung, Yongin, Gyeonggi 446-701, South Korea. Fax: +82 31 201 2378. E-mail address: [email protected] (H.J. Kim). 1090-7807/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jmr.2013.01.009

anomaly in the breast. Cherepenin et al. [12] implemented electrical impedance tomography (EIT) of the breast using a probe incorporating a compact flat array of electrodes. Kerner et al. [13] proposed an EIT imaging method using circular arrays of electrodes around the breast, and Soni et al. [14] developed a breast EIT system using hemispherical electrode arrays. Kao et al. [15] and Choi et al. [16] placed two planar electrode arrays about the breast to perform EIT imaging of the breast coregistered with X-ray mammography. A projection imaging method denoted the ‘T-scan’ was clinically tested and commercially available (Siemens, Erlangen, Germany) as an adjunct to conventional mammography [17–19]. MR-based tissue property imaging has been tested before, and two recent in vivo studies using magnetic resonance electric properties tomography (MREPT) have been reported [20,21]. To date, all of these impedance imaging methods have not yet reached the stage of routine clinical uses, primarily due to limitations in spatial resolution, accuracy and reproducibility. Magnetic resonance electrical impedance tomography (MREIT) is a new bio-imaging method that can produce high-resolution conductivity images using an MRI scanner [19]. The method is based on the current density imaging MRI technique, in which the scanner is used to obtain images of internal magnetic flux density distributions induced by externally injected currents [22]. Numerous conductivity image reconstruction methods have been suggested to synthesize near MRI-resolution conductivity images

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from these data [23]. MREIT methods have been developed to the stage of obtaining in vivo data. For example Kim et al. [24] presented MREIT human leg imaging results, and other studies have involved imaging of the canine brain [25] and tumors [26]. Lee et al. [27] proposed an electrode configuration for breast MREIT. Lee noted that MREIT may potentially be useful for the diagnosis of breast cancer if the amount of injected current is restricted so as not to produce adverse effects, most importantly, on the heart tissue or nerve conduction system. MREIT may therefore be a useful adjunct to X-ray mammography and other breast cancer detection techniques if it can be found safe, and sufficiently sensitive and specific to cancerous changes. In this paper, we present a feasibility study of breast MREIT incorporating the latest technical developments in MREIT. We first describe experimental studies using a breast phantom to evaluate noise levels in measured magnetic flux density data collected by a clinical MRI scanner. We then present three-dimensional numerical simulation studies of a realistic breast model to establish whether a small anomaly in the breast can be distinguished from reconstructed conductivity images. We also estimate the current density in the heart region produced by currents injected through electrodes on the surface of the breast by connecting the breast model to a chest model that included the heart. Finally, we evaluate the practical feasibility of breast MREIT by considering its sensitivity to many imaging parameters; and suggest future experimental studies on animals and human subjects. As well as informing the feasibility of MREIT for imaging breast anomalies, the simulations and experiments performed here should form a good guide to other in vivo applications of MREIT.

2. Methods 2.1. Technical environment of breast MREIT We considered a three-dimensional model of the breast and chest shown in Fig. 1a. The model included an idealized pendant

breast-shaped object, attached to a simplified chest area that had an ellipsoidal inclusion representing the heart. We adopted the electrode configuration for breast MREIT suggested by Lee et al. [27]. Instead of using the small recessed electrodes proposed by Lee et al., we used four large flexible carbon–hydrogel electrodes denoted as e j for j = 1 and 2. Current pattern 1 first involved mea surement during current flow from eþ 1 to e1 , followed by a second measurement with these polarities reversed. An identical procedure was used to obtain data from current pattern 2. The electrode positions used were designed to produce a uniform current density distribution inside the breast. Each injected current produced a distribution of voltage uj satisfying the following Neumann boundary value problem:

r  ½rðrÞruj ðrÞ ¼ 0 in X;

rruj  n ¼ g j on @ X

ð1Þ

where r = (x, y, z) is a position vector, r is conductivity distribution within the breast in the three-dimensional model domain X, @ X is boundary of X, n is outward unit normal vector on @ X and gj is the Neumann boundary data due to the injected current Ij. The current density Jj inside X is given by

Jj ðrÞ ¼ rðrÞruj ðrÞ ¼ rðrÞ

  @uj @uj @uj ax þ ay þ az @x @y @z

ð2Þ

where ax, ay and az are unit vectors. From the Biot–Savart law, the zcomponent of the induced magnetic flux density, Bz,j caused by current flow is

l Bz;j ðrÞ ¼ 0 4p

Z X

h

i

rðr0 Þ ðx  x0 Þ @u@yj ðr0 Þ  ðy  y0 Þ @u@xj ðr0 Þ jr  r0 j3

dr

0

ð3Þ

We obtained Bz,j images using the current density imaging MRI technique [22], in which current injection is performed synchronous with a standard MR pulse sequence. The phase component of the MR images may then be straightforwardly converted to Bz images via the relation

Fig. 1. Three-dimensional model of the human breast including a simplified heart model and experimental setup for breast MREIT imaging. (a) Simulated three-dimensional breast and chest model, (b) finite element mesh created from (a), (c) conductivity distribution in simulated breast, showing 5-mm-diameter cancerous anomaly and large external electrodes, (d) oblique view and (e) configuration of the breast MREIT phantom, showing position of chicken and porcine muscle anomalies and (f) current injection methods used in phantom imaging.

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Bz ¼

R.J. Sadleir et al. / Journal of Magnetic Resonance 230 (2013) 40–49

/

c  Tc

ð4Þ

where / is (unwrapped) phase, Tc is the time per average for which current is injected, and c is the gyromagnetic ratio of hydrogen (42.576 MHz/T). The image reconstruction problem in breast MREIT is then to produce cross-sectional images of the conductivity distribution r inside the breast, using the relationship between the measured Bz,j data and the conductivity distribution r [23]. Reconstructions in this paper were performed using the CoReHA MREIT reconstruction package [28]. 2.2. Breast phantom imaging experiment We conducted breast phantom imaging experiments using a clinical 3T MRI scanner (Siemens Medical Solutions, Erlangen, Germany) with a 4-channel breast coil. We built an acrylic phantom of the chest (30  14  15 cm3) and breast (11 cm in diameter), shown in Fig. 1d. The phantom was filled with a saline solution having a conductivity of 0.12 S/m (0.3 g/l NaCl and 1 g/l CuSO4). Two different biological tissues: porcine muscle and chicken breast (about 3  2  3 cm3), were then suspended in the phantom on the strings, as shown in Fig. 1e. The conductivity values for each inclusion were measured with an impedance analyzer (SI1260A, AMETEK Inc., UK) using a four-electrode method and were found to be about 0.64 and 0.60 S/m, respectively. We attached four carbon–hydrogel electrodes (HUREV Co. Ltd., Korea) to the phantom using the electrode configuration shown in Fig. 1f. The conductivity of the hydrogel electrodes was approximately 0.17 S/m. The phantom was placed inside the bore of the 3T MRI scanner as the imaging plane shown in Fig. 1f. A custom-designed MREIT current source was used to generate magnetic flux density (Bz) data, using a 3 mA amplitude and current injection time, Tc, of 30 ms [19]. We then decreased injection current amplitude to 0.5 mA. After acquiring the first magnetic flux density data Bz,1 for I1, the second injection current I2 with the same amplitude and pulse width was injected through the other pair of electrodes to obtain the second data Bz,2. The multi-echo injection current nonlinear encoding (ICNE) pulse sequence [29] was used for MREIT imaging experiment. This sequence, which uses multiple refocusing pulses, was synchronized to alternating polarity injection currents. This approach maximizes the width of the injection current and minimizes the noise standard deviation of the measured Bz data. The imaging parameters used were TR/TE = 800/13, 25, 39 ms (3 echos), FOV = 180  180 mm2, slice thickness = 4 mm, number of averages N = 9, matrix size = 128  128 and number of slices = 7. The total scan time to obtain Bz by I1 and I2 was 40 min, which included three Dixon data sets with three read gradient shifts of (p, 0, +p) for the chemical shift artifact correction [30]. In the multi-echo ICNE pulse sequence, we therefore performed the chemical shift artifact correction three times separately for three echo signals. Further details of Bz,j data measurement are described in Minhas et al. [29,31] and Meng et al. [30]. 2.3. Noise estimation in breast MREIT Real Bz data is contaminated by noise, which is the primary limiting factor in detecting anomalies in reconstructed conductivity images. If the signal-to-noise ratio (SNR) is large enough that the noise distribution can be assumed Gaussian, we can express the noise standard deviation s in measured Bz data as

1 s ¼ pffiffiffi 2c  T c  WM

ð5Þ

where WM is the SNR of the MR magnitude image. WM was calculated from the magnitude part of MREIT data by taking the ratio

of MR signal intensity and noise in the imaged object and background [29,32,33]. We can estimate the noise level in measured Bz data (MREIT phase data) in phantom imaging experiments using Eq. (5). Consider MRI acquisition of a voxel with dimensions Dx, Dy, and Dz along x, y, and z directions respectively. Let Nx, Ny, and Nz be the number of k-space samples in each of these directions, with a total readout sampling duration of Ts = Nx  Dt, where Dt is the time for one readout sample. Assuming that a spin echo pulse sequence is used, the TR and TE dependence of MR magnitude is given by

  TE TR M ¼ 1  eT1 eT2

ð6Þ

where T1 and T2 are spin relaxation times. WM is given by the following relation [33]

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

WM ¼ M DxDyDz Nx Ny Nz DtNEX

ð7Þ

Substituting Eq. (7) into Eq. (5), we have

1 s ¼ pffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2cT c M DxDyDz Nx Ny Nz DtNEX

ð8Þ

We now compare two different MREIT experiments performed with the same total scan time and same current injection amplitude. If we denote the Bz noise standard deviation for each experiment to be s0 and s respectively, then, substituting (6) in (8), we have that s0 and s are related by

s¼

s0 TR

TE

  T c Dx Dy Dz 1e T1 e T2 TR TE T c0 Dx0 Dy0 Dz0  0  0 1e T10 e T20

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi NNx N y Nz Dt N 0 Nx0 N y0 N z0 Dt 0

ð9Þ

2.4. Numerical simulations of breast MREIT We discretized the model shown in Fig. 1a into a 3D finite element mesh comprising 319,753 tetrahedral and 44,263 triangular elements (Fig. 1b). The total number of degrees of freedom in the model was 2,985,532. The conductivity distributions modeled in numerical simulations are shown in Fig. 1c. We specified the conductivity values of tissues included in the model as follows: glandular tissue = 0.225 S/m, subcutaneous fatty tissue = 0.023 S/m, cancerous anomaly = 1.125 S/m, chest region = 0.219 S/m, and heart region was 0.348 S/m [34–36]. The cancerous anomalies were placed at multiple locations within the simulated breast, with the remainder of the breast tissue made up of subcutaneous fat and glandular tissue. We simulated electrode ports by attaching four electrodes to the breast model. The conductivity of the electrodes was set to be 0.17 S/m, the same as that measured for the hydrogel electrodes used in the phantom. Each electrode had dimensions of 70  50  2 mm3. Electrode locations are illustrated in the crosssection of the model shown in Fig. 1c. We solved for the two independent voltages, uj and corresponding current density distributions Jj for j = 1, 2, formed by injecting currents through each of the two port pairs using COMSOL (COMSOL Inc., Burlington MA, USA). The calculated current densities, Jj were then interpolated over a 145  145  140 mm3 domain with a grid size of 128  128  35. Eq. (3) was then used to calculate magnetic flux densities, Bz,j from J. Further details of the MREIT simulator can be found in [37]. We added Gaussian noise to the simulated data, with standard deviation values computed by using Eq. (9). Finally, the harmonic Bz algorithm implemented in CoReHA was used to perform multi-slice conductivity image reconstructions [19,23,28]. We assessed cases where we placed simple or complex form cancerous anomalies, with diameters of 10, 5 or 2.5 mm, with and without noise.

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One of the biggest problems in breast MR imaging is chemical shift in fat regions. This results in misalignments of pixels along the frequency encoding direction. We used a three-point Dixon’s technique, modified for MREIT [31,38], to remove chemical shift artifact in both MR magnitude and phase images. In a first step, we separated the MR image into water and fat images. Pixel misalignments were then corrected in the fat image. We then reduced fat-related artifact from both magnitude and phase data by adding the corrected fat image to the water image. Further details of the correction method are described in Meng et al. [30] and Minhas et al. [31]. 2.5. Estimation of current densities in heart tissue We used the Patterson chest model [39] to precisely model the effect of a similar current geometry as we used for MREIT on heart tissue. The Patterson model is a digital model (230  382  43 slice, 1.5  1.5  5 mm3 resolution) of the thorax containing indices specifying to 36 different tissue types. We used the model to create a tetrahedral quadratic electrostatic finite element model of the thorax following the method described in Sadleir et al. [40]. We chose to specify the model as comprised of (cortical) bone, blood, (isotropic) heart tissue, liver, spleen, kidney, cartilage and fat tissues. Conductivity values for these tissues were chosen with reference to Gabriel et al. [34,35] and Geddes et al. [41]. The Patterson model is of a male subject, but we believe that the results of these simulations represent similar order of magnitude results to those obtained from female subjects. We simulated placement of two electrodes (conductivity of 1 S/m) with an area of approximately 20 cm2 on the left breast as shown in Fig. 8a, and applied a current of 3 mA between them. This arrangement was shown to mimic the effect of placing electrodes of similar size on a female breast. 3. Results 3.1. Breast phantom images and noise estimation Fig. 2 shows acquired MR magnitude, magnetic flux density (Bz), and reconstructed conductivity images of the breast phantom,

43

respectively. Data for Fig. 2a–c were gathered at 3 mA amplitude and 30 ms current injection time. Fig. 2d shows reconstructed conductivity images of the breast phantom using 0.5, 0.7, 1.0 and 3.0 mA injection currents, respectively. Qualitative observations of the reconstructed conductivity images suggested that at least 1 mA should be injected to adequately recover the contrast of the anomalies included in the breast phantom. The primary limiting factor to detect anomalies in the conductivity image is noise in Bz images. To determine the feasibility of MREIT imaging of the human breast, we need to estimate the noise standard deviation s in Bz images of the human breast from the experimental values of s0 shown in Eq. (9). We found the SNR WM of acquired MR magnitude images in the background saline solution was about 1571. The corresponding noise level s in the Bz images was found to be 0.0561 nT using the noise estimation method described in Sadleir et al. [33]. We therefore set the value of s0 = to be 0.0561 nT with T10 and T20 value of 3000 and 1000 ms [42]. We set T1 and T2 of the breast tissue to be 1445 and 54 ms, respectively [43]. Assuming the same imaging parameters, the expected noise standard deviation s in Bz images of the human breast was computed to be 0.0598 nT using Eq. (9). Note that the absolute noise levels in Bz images did not change with different magnitudes of externally injected current. Rather, as current amplitude was decreased, magnitudes of Bz data decreased proportionally and this reduced data SNR and therefore reconstructed conductivity image quality. 3.2. Simulation results without added noise Fig. 3a–c shows plots of the computed voltage u2, the magnitude of current density |J2| and magnetic flux density Bz,2 for the injected current I2 without any anomaly present. Fig. 3e–g shows the differences in Du2, D|J2| and DBz,2 when a single cancerous anomaly with a 5 mm diameter was added (Fig. 3d). We saw that the anomaly perturbed the distributions of u2, |J2| and Bz,2 and note that the values of DBz,2 near the anomaly were greater than the noise level predicted in measured Bz,2 data for the case considered in Section 3.1 above. We found similar results for the first injection current I1. Fig. 3d and h represents the actual and reconstructed conductivity images of a simulated single anomaly.

Fig. 2. (a) MR magnitude image of the breast phantom containing chicken and porcine muscle and measured Bz,1 (b) and Bz,2 (c) images subject to the injection currents I1 and I2, respectively, at 3 mA amplitude and 30 ms injection time, (d–g) are reconstructed conductivity images using injected currents of 0.5, 0.7, 1.0 and 3.0 mA, respectively.

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We repeated the numerical simulations for the case of three different anomalies with diameters of 10, 5 and 2.5 mm respectively. Fig. 4a and b shows actual and conductivity images of multiple anomalies with a simple structure using the noise-free computed Bz,1 and Bz,2 data, reconstructed by the harmonic Bz algorithm [19,23,28]. Fig. 5a and b shows actual and conductivity images of multiple anomalies with complex structures. To realistically test the method, in the presence of non-uniform current density distributions and the possibility of current being shunted through the skin, some cancerous anomalies were enclosed by low-conductivity fatty tissue. Several ellipsoidal high-conductivity cancerous anomalies were also positioned at locations inside the glandular region. Without noise, the MREIT conductivity reconstruction method could qualitatively differentiate cancer-like anomalies with diameters larger than the pixel size of 1.2 mm.

Fig. 6a shows the results of chemical shift artifact correction in breast tissue. The uncorrected MR magnitude, magnetic flux density and reconstructed conductivity images in the top row of Fig. 6a show signal voids, overlap and spurious noise spikes due to the chemical shift. The corrected artifact-free images are shown in the bottom row of Fig. 6a. In the conductivity images (bottom right), the spurious noise spikes found without fat shift correction (top right) were significantly reduced after applying the chemical shift artifact correction. Fig. 6b shows determinant maps of breast with the three different electrode sizes. Since the determinant map includes the information of current pathways [27], the relatively homogeneous distribution in the left hand side of bottom row represents the advantage of applying a large electrode.

3.4. Comparison of DBz with noise level 3.3. Simulation results with added noise To better simulate an in vivo breast imaging experiment, we added Gaussian noise with standard deviation values of 0.1690, 0.0845 and 0.0598 nT to simulate noise-contaminated Bz data generated with averaging over N = 1, 4 and 8, sequences, respectively. These values were computed by using Eq. (9) with s0 = 0.0561 nT, the same as in the background saline region. Figs. 4c and 5c show reconstructed conductivity images of anomalies with 10, 5 and 2.5 mm diameters with added noise in both the simple and complex structure model, as the number of averages N was increased from 1 to 8 (top to bottom) and the amplitude of injected currents was increased from 0.5 to 3 mA (left to right). For any value of current amplitude, we can see that the image quality was improved as we increase the number of averages N to reduce the noise level in Bz data. We summarize standard deviations found in the reconstructed conductivity in Tables 1 and 2. For a fixed amount of noise in Bz data, (that is, for a given value of N) we could improve the image quality by increasing the current amplitude to produce Bz data with a larger dynamic range, that is, a higher SNR in measured Bz data. To remove chemical shift in fatty tissue, a correction method was introduced in both MR magnitude and phase images [30,31].

To detect an anomaly inside the breast, the change in measured Bz, due to the presence of an anomaly, DBz must be larger than the noise level s in measured Bz data. DBz values are influenced by injection current amplitude and anomaly size. We computed average values of DBz inside anomaly regions, and compared them with noise levels s, which in turn are determined by imaging parameters and tissue properties of T1 and T2 as shown in Eq. (9). Fig. 7a and b illustrates how the noise level s in measured Bz should change with pixel size Dx = Dy as the number of averages N, and the total current injection time Tc, are varied. In Fig. 7a, Tc was fixed at 30 ms. N was fixed at 8 in Fig. 7b. In both cases, the slice thickness Dz was 4 mm and the diameter of the anomaly was 5 mm with 400% conductivity contrast. In Fig. 7c, we show the noise level s with values of Tc = 30 ms, N = 8 and Dz = 4 mm. We compared the values of average DBz for different conductivity contrasts of 50% and 200%, and also for anomaly diameters of 5 and 10 mm, using 1 mA injection currents. The plots in Fig. 7 provide a useful guide to selection of parameters such as Dx, Dy, N and Tc, and injection current amplitudes required to produce Bz data that are capable of visualizing a certain anomaly in the presence of a particular estimated noise level. The plots in Fig. 7 may easily be scaled up or down to match different situations.

Fig. 3. Images of noise-free (a) voltage u2, (b) current density magnitude |J2| and (c) magnetic flux density Bz,2 for injected current I2 in a case without cancerous anomaly, (d) actual conductivity image showing a simulated single 5-mm-diameter anomaly. Panels (e–g) show difference images between the original cases and those found with a 5mm-diameter anomaly, Du2, D|J2| and DBz,2, respectively. (h) Reconstructed conductivity image of simulated anomaly.

R.J. Sadleir et al. / Journal of Magnetic Resonance 230 (2013) 40–49

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Fig. 4. (a) Actual and (b) reconstructed conductivity image of noise-free breast phantom containing 10, 5 and 2.5 mm diameter anomalies with a simple structure. (c) Reconstructed conductivity images of the phantom using different numbers of averages N, and current amplitudes. Simulated experimental noise was added and chemical shift artifact correction method applied in the conductivity images.

3.5. Current density estimation in the heart We examined the magnitude of the internal current density distribution caused by a 3 mA injection current, which was the largest amount used in our simulations. Results of simulations of current densities in heart tissue are shown overlaid on the tissue structure in Fig. 8b. The slice chosen contains the largest current density found inside the heart muscle, and it is clear that larger current densities are only present in the anterior epicardium. We found that the maximum current density inside the myocardium was around 0.49 A/m2. Median values were around 0.027 A/m2. We estimated the threshold of nerve stimulation to be 1.2 A/m2 at a distance of 1 mm from the tissue [44], and that the typical current density needed to induce fibrillation in the heart might be around 4 A/m2 [45]. Since the estimated maximum current density inside the heart region was below this threshold, we speculate that externally injected currents of 3 mA or lower should not stimulate the heart muscle, particularly in a female subject where current flow is further away from the heart. However, there is a small possibility that the externally injected current may disrupt the rate of action potential generation [46] and the simplified model and conductivity values used in our simulation study may have underestimated the maximum current density in the heart region.

4. Discussion Electromagnetic tissue property mapping is an emerging MRbased technique to derive non-invasive information concerning tissue properties, including electrical conductivity and permittivity [47]. Biological tissue includes conductive materials with

numerous ions and heterogeneous membrane structures, which are determining factors of tissue low-frequency electrical properties [48]. Several studies have reported that malignant tissue showed higher conductivities than normal tissue [9]. In addition, some studies have found significant differences in conductivity between normal and neoplastic tissues in many tumor models [49]. Therefore, MREIT conductivity imaging has the potential to provide unique and meaningful diagnostic information on the physiological and pathological conditions of breast tissues. Breast tissue contains distributed fat tissue. The chemical shift occurring in fat tissue results in misalignments of pixels along the frequency encoding direction in both MR magnitude and phase images [38]. Reconstructed conductivity images using such data suffer from artifacts originated from signal void at one side and overlap at the other [30,31,38]. Our results in Fig. 6a clearly show that the correction method effectively eliminates artifacts related with the chemical shift phenomenon in the conductivity images. Compared with the results in Lee et al. [27], the images in Figs. 4c and 6b show the importance of the electrode size and configuration. The use of two current injections through large and flexible electrodes covering most of the breast surface can produce a more uniform current density distribution inside the breast. Because the measured magnetic flux density Bz at a particular position is strongly influenced by the current density distribution there, use of uniform current density distributions inside the breast region may be an advantage in detecting an anomaly that may present anywhere in the breast. However, the electrode configuration we used also showed limitations, since it resulted in small current densities forming near the base and apex of the breast. This, in turn, should result in more relative noise in phase and Bz data gathered in these regions. In future work we may consider adding

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Fig. 5. (a) Actual and (b) reconstructed conductivity image of noise-free breast phantom containing 10, 5 and 2.5 mm diameter anomalies with a complex structure. Anomalies were surrounded by low-conductivity fatty tissue, and several high-conductivity cancerous ellipsoidal anomalies were positioned inside the glandular region. (c) Reconstructed conductivity images of the phantom using different numbers of averages N, and current amplitudes. Simulated experimental noise was added and the chemical shift artifact correction method was applied in the conductivity images.

Table 1 Measured standard deviation of conductivity values from Fig. 4c. ROI (region-of-interest) was located in both the glandular tissue and cancerous anomaly with a voxel size of 3  3  3 mm3 (Fig. 4a). Since CoReHA provides only contrast information of conductivity, we therefore measure the standard deviation of conductivity values as a quantitative criterion representing an improvement of conductivity image. Current (mA)

NEX Measured standard deviation of conductivity (mS/m) Glandular tissue (Region A)

0.5 0.7 1.0 3.0

Cancerous anomaly (Region B)

1 NEX

4 NEX

8 NEX

1 NEX

4 NEX

8 NEX

10.9 5.8 4.0 1.5

4.7 4.3 1.4 0.8

3.3 1.9 1.2 0.5

9.6 6.1 3.6 1.4

4.2 4.0 2.4 1.1

3.4 2.7 1.5 0.7

Table 2 Measured standard deviation in conductivity values from Figs. 4c and 5c. ROI (region-of-interest) was located in cancerous anomalies with a voxel size of 3  3  3 mm3 (Figs. 4a and 5a). We measured the standard deviation of conductivity to demonstrate the improvement of conductivity image according to the different numbers of averages N, and current amplitudes in both the simple and complex structured anomalies. Current (mA)

NEX Measured standard deviation of conductivity (mS/m) Anomaly 1

Anomaly 2

Anomaly 3

1 NEX

4 NEX

8 NEX

1 NEX

4 NEX

8 NEX

1 NEX

4 NEX

8 NEX

Simple structure

0.5 0.7 1.0 3.0

16.2 14.5 8.1 5.8

8.6 7.1 6.5 4.8

7.5 6.5 5.8 4.1

13.9 12.5 6.2 5.2

6.6 4.5 4.3 3.7

6.2 4.4 3.7 3.2

15.7 13.9 6.8 6.7

7.2 6.2 4.9 3.9

6.5 5.1 3.8 3.6

Complex structure

0.5 0.7 1.0 3.0

16.6 14.7 8.5 7.0

9.0 8.1 7.2 5.5

8.3 6.7 6.0 4.3

14.8 12.7 7.0 5.5

7.0 5.5 4.5 3.9

6.5 4.6 3.8 3.4

16.1 14.2 8.2 5.8

7.5 6.5 5.9 4.8

6.6 5.3 3.9 3.8

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Fig. 6. (a) Typical simulated MREIT images of the breast without and with chemical shift artifact correction. The top row shows simulated MR magnitude, Bz,1, and reconstructed conductivity images, respectively, without correction. The bottom row shows the corresponding simulated images after the correction method was applied. (b) Actual conductivity (top row) and determinant (bottom row) maps within the breast region using electrode sizes of 70  50  2, 30  50  2 and 15  15  2 mm3.

Fig. 7. Comparisons of calculated average DBz values caused by the simulated 5 mm anomaly with 400% conductivity contrast, and noise levels s found with a slice thickness Dz of 4 mm, showing (a) three different values of averages N at Tc = 30 ms; (b) three different values of total current injection time Tc at N = 8. Plot (c) shows noise level s with values of Tc = 30 ms, N = 8 and Dz = 4 mm. The values of average DBz compared for different simulated conductivity contrasts of 50% and 200%, and also for anomaly diameters of 5 and 10 mm, using 1 mA injection currents.

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Fig. 8. Geometry and results of current density simulations in the Patterson phantom for externally injected currents of 3 mA. (a) Electrode geometry shown on a transverse section of the model situated 10 cm below the shoulders. (b) Current density distribution (blue to red) shown in the anterior epicardium, overlaid on model conductivity distribution (gray scale). The image is of a slice containing voxel with largest current density, 14 cm below shoulders. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

electrodes on the subject’s back, and also on the apex of the breast to improve the overall uniformity of current density, Bz and thus image quality. The reconstructed conductivity images in Figs. 4c and 5c clearly illustrate the advantage of larger injection current amplitude and a larger number of averages at the expense of an increased scan time. The quality of conductivity images depends primarily on the noise level in the measured Bz image. The noise levels in Bz are closely related to the MR magnitude SNR and the injected current amplitude [32,33]. To reduce the imaging time while maintaining or improving image quality, approaches including improving pulse sequence (such as GRE, EPI, and SSFP), or k-space sampling strategies, and use of multi-channel RF coils may be required. If these approaches are combined, the imaging time may be reduced to clinically viable durations. Since the total scan time is not a critical limiting factor in this feasibility study of breast imaging, it is clear that the best results with the lowest risk of heart stimulation would be obtained using long scan times (many averages) and low currents. However, averaging cannot be used without limit to obtain signal [50]. Plots in Fig. 7a and b indicate that it should be possible to distinguish a cancerous anomaly of 5 mm diameter using injected currents of 0.5 mA amplitude at a pixel size greater than 2 mm, regardless of the number of average N and the total current injection time Tc. Plots in Fig. 7c show that conductivity images with pixel sizes of 3 or 4 mm may be used to detect an anomaly with 50% conductivity contrast and 5 mm diameter using 1 mA injection currents. Considering that cancerous tissues in the breast have conductivity contrasts much larger than 50%, it is probable that MREIT can distinguish an anomaly with a diameter than 5 mm diameter using 1 mA injection currents. Based on these experimental and numerical simulation results of breast MREIT, we suggest that at least 1 mA should be injected to correctly recover the contrast of the cancerous anomalies included in the breast tissue. Though we did not demonstrate plots representing other experimental scenarios, we may easily scale up and down the plots in Fig. 7 to simulate different conditions. However, this does not mean that MREIT imaging of the human breast can be performed using the same imaging setting as were used in the breast phantom experiment. Adjustment of imaging parameters such as TE, TR and NEX may be required to image the human breast in vivo. The estimated maximum current densities occurring within heart tissue when a 3 mA current was used were a large fraction of those cited as likely to cause depolarization. This is naturally a cause for concern, although our simulation conditions did not exactly mimic those that would be present in measurements on the female breast. There should therefore be more investigations about the effects of externally injected currents on the excitability of the heart in the context of MREIT.

5. Conclusions We have explored the feasibility of breast conductivity imaging using magnetic resonance electrical impedance tomography (MREIT) for the diagnosis of breast cancer. Simulation results indicate it is possible that a cancerous anomaly of less than 5 mm diameter may be detected by injecting less than 1 mA currents, while restricting the maximal current density inside the heart region below levels of nerve excitation. Based on the findings presented in this paper, we suggest breast MREIT imaging experiments using four large flexible uniform current density electrodes covering as much of the breast surface as possible. Extra electrodes may be attached on the back of the chest or the apex of the breast to improve the image quality in the base or apex region of the breast, respectively. Advanced breast MR imaging methods including multichannel high-sensitivity breast RF coils should be employed to minimize the noise level in measured magnetic flux density data and thus reduce the current needed to produce good conductivity resolution. Acknowledgment This work was supported by the National Research Foundation (NRF) of Korea grant funded by the Korean government (MEST) (No. 20100018275). References [1] S.G. Orel, M.D. Schnall, MR imaging of the breast for the detection, diagnosis, and staging of breast cancer, Radiology 220 (2001) 13–30. [2] J.H. Hipwell, C. Tanner, W.R. Crum, J.A. Schnabel, D.J. Hawkes, A new validation method for X-ray mammogram registration algorithms using a projection model of breast X-ray compression, IEEE Trans. Med. Imag. 26 (2007) 1190– 1200. [3] Q. Fang, S.A. Carp, J. Selb, G. Boverman, Q. Zhang, D.B. Kopans, R.H. Moore, E.L. Miller, D.H. Brooks, D.A. Boas, Combined optical imaging and mammography of the healthy breast: optical contrast derived from breast structure and compression, IEEE Trans. Med. Imag. 28 (2009) 30–42. [4] J. Jeong, T.S. Kim, D. Shin, M. Singh, V.Z. Marmarelis, Soft tissue differentiation using multi-band signatures of high resolution ultrasonic transmission tomography, IEEE Trans. Med. Imag. 24 (2005) 399–408. [5] C.K. Kuhl, P. Jost, N. Morakkabati, O. Zivanovic, H.H. Schild, J. Gieseke, Contrastenhanced MR imaging of the breast at 3.0 and 1.5 T in the same patient: initial experience, Radiology 239 (2006) 666–676. [6] E.A. Morris, L. Liberman, D.J. Ballon, M. Robson, A.F. Abramson, A. Heerdt, D.D. Dershaw, MRI of occult breast carcinoma in a high-risk population, Am. J. Radiol. 181 (2003) 619–626. [7] E. Warner, D.B. Plewes, R.S. Shumak, G.C. Catzavelos, L.S. Di Prospero, M.J. Yaffe, V. Goel, E. Ramsay, P.L. Chart, D.E. Cole, G.A. Taylor, M. Cultrara, T.H. Samuels, J.P. Murphy, J.M. Murphy, S.A. Narod, Comparison of breast magnetic resonance imaging, mammography and ultrasound for surveillance of women at high risk for hereditary breast cancer, J. Clin. Oncol. 19 (2004) 3524–3531. [8] M. Morrow, J. Waters, E. Morris, MRI for breast cancer screening, diagnosis, and treatment, Lancet 378 (2011) 1804–1811.

R.J. Sadleir et al. / Journal of Magnetic Resonance 230 (2013) 40–49 [9] A.J. Surowiec, S.S. Stuchly, J.R. Barr, A. Swarup, Dielectric properties of breast carcinoma and the surrounding tissues, IEEE Trans. Biomed. Eng. 35 (1988) 257–263. [10] J. Jossinet, M. Schmitt, A review of parameters for the bioelectrical characterization of breast tissue, Ann. N.Y. Acad. Sci. 873 (1999) 30–41. [11] J.E. Silva, J.P. Marques, J. Jossinet, Classification of breast tissue by electrical impedance spectroscopy, Med. Biol. Eng. Comput. 38 (2000) 26–30. [12] V. Cherepenin, A. Karpov, A. Korjenevsky, V. Kornienko, Y. Kultiasov, M. Ochapkin, O. Trochanova, J. Meister, Three-dimensional EIT imaging of breast tissues: system design and clinical testing, IEEE Trans. Med. Imag. 21 (2002) 662–667. [13] T.E. Kerner, K.D. Paulsen, A. Hartov, S.K. Soho, S.P. Poplack, Electrical impedance spectroscopy of the breast: clinical imaging results in 26 subjects, IEEE Trans. Med. Imag. 21 (2002) 638–645. [14] N.K. Soni, A. Hartov, C. Kogel, S.P. Poplack, K.D. Paulsen, Multi-frequency electrical impedance tomography of the breast: new clinical results, Physiol. Meas. 25 (2004) 301–314. [15] T. Kao, J.C. Newell, G.J. Saulinier, D. Isaacson, Distinguishability of inhomogeneities using planar electrode arrays and different patterns of applied excitation, Physiol. Meas. 24 (2003) 403–411. [16] M.H. Choi, T.J. Kao, D. Isaacson, G.J. Saulnier, J.C. Newell, A reconstruction algorithm for breast cancer imaging with electrical impedance tomography in mammography geometry, IEEE Trans. Biomed. Eng. 54 (2007) 700–710. [17] M. Assenheimer, O. Laver-Moskovitz, D. Malonek, D. Manor, U. Nahliel, R. Nitzan, A. Saad, The T-Scan technology: electrical impedance as a diagnostic tool for breast cancer detection, Physiol. Meas. 22 (2001) 1–8. [18] B. Scholz, Towards virtual electrical breast biopsy: space-frequency MUSIC for trans-admittance data, IEEE Trans. Med. Imag. 21 (2002) 588–595. [19] E.J. Woo, J.K. Seo, Magnetic resonance electrical impedance tomography (MREIT) for high-resolution conductivity imaging, Physiol. Meas. 29 (2008) R1–R26. [20] S.B. Bulumulla, I. Hancu, Breast permittivity imaging, in: Proceedings of the 20th Annual Meeting of the ISMRM, Melbourne, Australia, 2012, p. 2532. [21] U. Katscher, K. Djamshidi, T. Voigt, M. Ivancevic, H. Abe, G. Newstead, J. Keupp, Estimation of breast tumor conductivity using parabolic phase fitting, in: Proceedings of the 20th Annual Meeting of the ISMRM, Melbourne, Australia, 2012, p. 3482. [22] M.L.G. Joy, G.C. Scott, R.M. Henkelman, In vivo detection of applied electric currents by magnetic resonance imaging, Magn. Reson. Imag. 7 (1989) 89–94. [23] J.K. Seo, E.J. Woo, Magnetic resonance electrical impedance tomography (MREIT), SIAM Rev. 53 (2011) 40–68. [24] H.J. Kim, Y.T. Kim, A.S. Minhas, W.C. Jeong, E.J. Woo, J.K. Seo, O.J. Kwon, In vivo high-resolution conductivity imaging of the human leg using MREIT: the first human experiment, IEEE Trans. Med. Imag. 28 (2009) 1681–1687. [25] H.J. Kim, T.I. Oh, Y.T. Kim, B.I. Lee, E.J. Woo, J.K. Seo, S.Y. Lee, O. Kwon, C. Park, B.T. Kang, H.M. Park, In vivo electrical conductivity imaging of a canine brain using a 3 T MREIT system, Physiol. Meas. 29 (2008) 1145–1155. [26] L.T. Muftuler, M.J. Hamamura, O. Birgul, O. Nalciogul, In vivo MRI electrical impedance tomography (MREIT) of tumors, Technol. Cancer Res. Treat. 5 (2006) 381–387. [27] B.I. Lee, S.H. Oh, T.S. Kim, E.J. Woo, S.Y. Lee, O. Kwon, J.K. Seo, Basic setup for breast conductivity imaging using magnetic resonance electrical impedance tomography, Phys. Med. Biol. 51 (2006) 443–455. [28] K. Jeon, A.S. Minhas, Y.T. Kim, W.C. Jeong, H.J. Kim, B.T. Kang, H.M. Park, C.O. Lee, J.K. Seo, E.J. Woo, MREIT conductivity imaging of postmortem canine abdomen using CoReHA, Physiol. Meas. 30 (2009) 957–966. [29] A.S. Minhas, W.C. Jeong, Y.T. Kim, Y.Q. Han, H.J. Kim, E.J. Woo, Experimental performance evaluation of multi-echo ICNE pulse sequence in magnetic

[30]

[31] [32] [33]

[34] [35]

[36] [37]

[38]

[39]

[40]

[41]

[42]

[43]

[44] [45]

[46]

[47]

[48] [49]

[50]

49

resonance electrical impedance tomography, Magn. Reson. Med. 66 (2011) 957–965. Z.J. Meng, S.Z. Sajib, M. Chauhan, W.C. Jeong, Y.T. Kim, H.J. Kim, E.J. Woo, Improved conductivity image of human lower extremity using MREIT with chemical shift artifact correction, Biomed. Eng. Lett. 2 (2011) 62–68. A.S. Minhas, Y.T. Kim, W.C. Jeong, H.J. Kim, S.Y. Lee, E.J. Woo, Chemical shift artifact correction in MREIT, J. Biomed. Eng. Res. 30 (2009) 461–468. G.C. Scott, M.L.G. Joy, R.L. Armstrong, R.M. Henkelman, Sensitivity of magnetic resonance current density imaging, J. Magn. Reson. 97 (1992) 235–254. R.J. Sadleir, S. Grant, S.U. Zhang, B.I. Lee, H.C. Pyo, S.H. Oh, C. Park, E.J. Woo, S.Y. Lee, O. Kwon, J.K. Seo, Noise analysis in MREIT at 3 and 11 Tesla field strength, Physiol. Meas. 26 (2005) 875–884. C. Gabriel, S. Gabriel, E. Corthout, The dielectric properties of biological tissues: I. Literature survey, Phys. Med. Biol. 41 (1996) 2231–2249. S. Gabriel, R.W. Lau, C. Gabriel, The dielectric properties of biological tissues: II. Measurements in the frequency range 10 Hz to 20 GHz, Phys. Med. Biol. 41 (1996) 2251–2269. J. Jossinet, The impedivity of freshly excised human breast tissue, Physiol. Meas. 19 (1998) 61–75. A.S. Minhas, H.H. Kim, Z.J. Meng, Y.T. Kim, H.J. Kim, E.J. Woo, Threedimensional MREIT simulator of static bioelectromagnetism and MRI, Biomed. Eng. Lett. 1 (2011) 129–136. G.H. Glover, E. Schneider, Three-point Dixon technique for true water/fat decomposition with inhomogeneity correction, Magn. Reson. Med. 18 (1991) 371–383. F. Yang, P. Patterson, A simulation study on the effect of thoracic conductivity inhomogeneities on sensitivity distributions, Ann. Biomed. Eng. 36 (2008) 762–768. R.J. Sadleir, T.D. Vannorsdall, D.J. Schretlen, B. Gordon, Transcranial direct current stimulation (tDCS) in a realistic head model, Neuroimage 51 (2010) 1310–1318. L. Geddes, L.E. Baker, The specific resistance of biological materials: a compendium of data for the biomedical engineer and physiologist, Med. Biol. Eng. Comput. 5 (1967) 271–293. G.E. Gold, E. Han, J. Stainsby, G. Wright, J. Brittain, C. Beaulieu, Musculoskeletal MRI at 3.0 T: relaxation times and image contrast, Am. J. Roentgenol. 183 (2004) 343–351. R. Rakow-Penner, B. Daniel, H. Yu, A. Sawyer-Glover, G.H. Glover, Relaxation times of breast tissue at 1.5 T and 3 T measured using IDEAL, J. Magn. Reson. Imag. 23 (2006) 87–91. J.P. Reilly, Applied Bioelectricity, High-Voltage and High-Current Injuries, Springer-Verlag, New York, 1998. O.Z. Roy, J.R. Scott, G.C. Park, 60-Hz ventricular fibrillation and pump failure thresholds versus electrode area, IEEE Trans. Biomed. Eng. 23 (1976) 45–48. D.P. Purpura, J.P. McMurtry, Intracellular activities and evoked potential changes during polarization of motor cortex, J. Neurophysiol. 28 (1965) 166– 185. J.K. Seo, M. Kim, J. Lee, N. Choi, E.J. Woo, H.J. Kim, O.I. Kwon, D.H. Kim, Error analysis of non-constant admittivity for MR-based electric property imaging, IEEE Trans. Med. Imag. 31 (2012) 430–437. S. Grimnes, O.G. Martinsen, Bioimpedance and Bioelectricity Basics, Academic Press, London, 2000. D. Haemmerich, S.T. Staelin, J.Z. Tsai, S. Tungjitkusolmun, D.M. Mahvi, J.G. Webster, In vivo electrical conductivity of hepatic tumours, Physiol. Meas. 24 (2003) 251–260. O. Nalcioglu, Z.H. Cho, Limits to signal-to-noise improvement by FID averaging in NMR imaging, Phys. Med. Biol. 29 (1984) 969–978.