- Research
- Open Access
Reconstruction of dual-frequency conductivity by optimization of phase map in MREIT and MREPT
- Oh In Kwon^{1},
- Woo Chul Jeong^{2},
- Saurav Z K Sajib^{2},
- Hyung Joong Kim^{2},
- Eung Je Woo^{2} and
- Tong In Oh^{2}Email author
https://doi.org/10.1186/1475-925X-13-24
© Kwon et al.; licensee BioMed Central Ltd. 2014
- Received: 12 November 2013
- Accepted: 25 February 2014
- Published: 8 March 2014
Abstract
Background
The spectroscopic conductivity distribution of tissue can help to explain physiological and pathological status. Dual frequency conductivity imaging by combining Magnetic Resonance Electrical Property Tomography (MREPT) and Magnetic Resonance Electrical Impedance Tomography (MREIT) has been recently proposed. MREIT can provide internal conductivity distributions at low frequency (below 1 kHz) induced by an external injecting current. While MREPT can provide conductivity at the Larmor frequency related to the strength of the magnetic field. Despite this potential to describe the membrane properties using spectral information, MREPT and MREIT techniques currently suffer from weak signals and noise amplification as they both reply on differentiation of measured phase data.
Methods
We proposed a method to optimize the measured phase signal by finding weighting factors according to the echo signal for MREPT and MREIT using the ICNE (Injected current nonlinear encoding) multi-echo pulse sequence. Our target weights are chosen to minimize the measured noise. The noise standard deviations were precisely analyzed for the optimally weighted magnetic flux density and the phase term of the positive-rotating magnetic field. To enhance the quality of dual-frequency conductivity images, we applied the denoising method based on the reaction-diffusion equation with the estimated noise standard deviations. A real experiment was performed with a hollow cylindrical object made of thin insulating film with holes to control the apparent conductivity using ion mobility and an agarose gel cylinder wrapped in an insulating film without holes to show different spectroscopic conductivities.
Results
The ability to image different conductivity characteristics in MREPT and MREIT from a single MR scan was shown by including the two objects with different spectroscopic conductivities. Using the six echo signals, we computed the optimized weighting factors for each echo. The qualities of conductivity images for MREPT and MREIT were improved by optimization of the phase map. The proposed method effectively reduced the random noise artifacts for both MREIT and MREPT.
Conclusion
We enhanced the dual conductivity images using the optimally weighted magnetic flux density and the phase term of positive-rotating magnetic field based on the analysis of the noise standard deviations and applying the optimization and denoising methods.
Keywords
- MRI
- MREIT
- MREPT
- Conductivity
- Magnetic flux density
- Optimization
Background
The conductivity spectra of biological tissues can provide diagnostic medical information from the estimation of physiological and pathological conditions of in-vivo and ex-vivo tissue. However it is difficult to produce high resolution conductivity images inside the human body [1, 2]. The conventional conductivity imaging methods have limited spatial resolution and sensitivity inherited from the ill-posed nature of the problem [3]. In order to achieve sensitive conductivity images with high resolution, electric impedance imaging techniques based on a magnetic resonance imaging (MRI) have been propsed. These include magnetic resonance electrical impedance tomography (MREIT) and magnetic resonance electrical property tomography (MREPT) which are under active investigation [4–17]. Both methods use the internal magnetic field information obtained from the phase data of MRI scanner to reconstruct the internal conductivity image.
MREPT can provide the electrical conductivity information at the Larmor frequency by measuring the phase of positive rotating field due to the applied B _{1} field. It does not require application of external current and therefore directly recovers the conductivity distribution by taking the derivative of the measured phase signals twice. MREIT needs a pair of electrodes to inject current into an imaging object during MRI scan for measuring a magnetic flux density induced by the external injecting current. The MREIT technique used only the z-component of magnetic flux density, B _{ z }, of B=(B _{ x },B _{ y },B _{ z }) to reconstruct the cross-sectional apparent conductivity image at a lower frequency range (below 1 kHz) [18–22]. The phase difference approach with an interleaved encoding scheme was adopted to cancel the systematic artifacts accumulated in phase signals and also reduce the random noise artifacts. Recently, a simultaneous conductivity imaging technique using a combination of MREPT and MREIT was proposed to provide the dual-frequency conductivities of tissue from a common MR scan [23]. MREPT using B _{1}-mapping technique visualizes the conductivity and permittivity distributions at the Larmor frequency and MREIT recovers the apparent conductivity distribution when injecting low-frequency external current through the attached electrodes. Since the biological tissues show the frequency dependent conductivity property [1, 2], the simultaneous dual-frequency conductivity imaging using a single MR scan is beneficial to provide distinct electrical features of tissues quantitatively.
Both conductivity imaging techniques use the phase signals of measured MR data. MREIT and MREPT commonly suffer from weak signals and noise amplification by using the derivative of the measured signal. The noise level of B _{ z } in MREIT is inversely proportional to the signal-to-noise ratio (Υ^{ j }) of the MR magnitude image and the current injection pulse width. Because of the small amount of injection current and the poor quality of measured B _{ z } change due to the injected current, it is difficult to perform in vivo human experiments using a conventional MR pulse sequence. To enhance the magnetic flux density due to the injected current in MREIT, the injected current nonlinear encoding (ICNE) method was introduced. This extended the duration of injecting current until the end of a readout gradient, and improved the signal by using a multi-echo train MR pulse sequence [24–26]. MREPT also suffers from low sensitivity due to the inherently poor signal to noise ratio and noise sensitive characteristics as it also needs the derivative of measured data, is very sensitive to the measured noise.
In this paper, we adopt a multiple spin echo MREIT pulse sequence based on the ICNE scheme to measure multiple phase data for MREIT and MREPT images. The acquired multiple phase data can be decomposed to the phase term reflecting the magnetic flux density signal induced by the injected current and the other phase term of positive rotating field due to the applied B _{1} field. We analyze the noise level of the two decomposed phase terms and minimize the measured random noise artifacts by applying the optimal combination of multiple phase terms. Also, we apply a denoising technique to the optimized magnetic flux density for MREIT and to the phase signal for MREPT in order to improve the quality of the reconstructed conductivity images. We prepared a conductivity phantom consisted of two different kinds of anomalies to show the difference of MREIT and MREPT. A phantom experiment is conducted to validate that the proposed method is able to improve the qualities of reconstructed dual-frequency conductivity images compared to the results of using conventional MREIT and MREPT reconstruction algorithms.
Methods
Governing equation
where the current J and the electric field intensity E satisfy the relation J=κ E by Ohm’s law.
where n is the outward normal vector on the surface ∂ Ω and g is the current density on the surface.
ICNE multi-echo pulse sequence and multiple phase data
where ${M}_{\mathit{\text{xy}},j}^{\alpha}\left(\mathbf{r}\right)={M}_{\mathit{\text{xy}}}^{\alpha}\left(\mathbf{r}\right){e}^{-{T}_{{E}_{j}}/{T}_{2}\left(\mathbf{r}\right)}$ is the j-th transverse magnetization at a flip angle α, δ _{ ε } is the systematic phase artifact, γ is the gyromagnetic ratio of hydrogen, T _{2} is the transverse relaxation time, and ${T}_{{c}^{\phantom{\rule{0.3em}{0ex}}j}}$ is the j-th duration of the injecting current.
Optimal combination of multiple ${B}_{{z}^{\phantom{\rule{0.3em}{0ex}}j}}$
where ${\Psi}_{j}\left(\mathbf{r}\right):={T}_{{c}^{\phantom{\rule{0.3em}{0ex}}j}}^{2}\left|{\zeta}_{j}^{\pm}\right(\mathbf{r}){|}^{2}$.
where ${\mathcal{N}}_{{M}_{\mathit{\text{xy}}}}$ denotes the noise level of magnitude image.
Optimal combination of multiple φ j+
where ${\Phi}_{j}\left(\mathbf{r}\right):=\left|{\zeta}_{j}^{\pm}\right(\mathbf{r}){|}^{2}$.
Considering only random noise effects, the optimal weighting factor χ _{ j }(r) reduces the noise level, depending on the echo number and T _{2}-decay rate at each imaging pixel.
Denoising method using the estimated ${\mathit{\text{sd}}}_{{B}_{z}^{\xi}}$ and ${\mathit{\text{sd}}}_{{\phi}^{+,\chi}}$
A denoising technique is applied to gradients of the optimized magnetic flux density for MREIT image and the optimized phase signal for MREPT image since the reconstruction procedures only require the differentiated measured data. Also, it is advantageous to denoise $\nabla {B}_{z}^{\xi}$ and ∇φ^{+,χ } because the measured magnetic flux density of ${B}_{z}^{\xi}$ and the phase of H^{+} are inherently continuous without conventional edge information.
Here, the initial state f denotes each component of the optimized magnetic flux density $\nabla {B}_{z}^{\xi}$ or the phase signal ∇φ^{+,χ }, which is to be denoised. The time dependent solution v(r,t) is the denoised image of the initial state image f.
where ς _{ ε } is a small parameter to guarantee the positive sign of |∇v(r,t)|+ς _{ ε }. For the magnetic flux density ${B}_{z}^{\xi}$, the diffusion function ψ can be selected similarly.
The quality of magnetic flux density signal in MREIT depends on the magnitude intensity and width of injected current simultaneously, while the quality of phase signal in MREPT only depends on the magnitude intensity. Therefore, there are common effects due to the decay of the magnitude intensity in MREPT and MREIT processing. There are also different effects caused by externally injecting current in MREIT. These occur when we calculate each of the optimal weighting factors and the noise standard deviation in the optimal combination of multiple phase and magnetic flux density images. The proposed optimization method uses the decay rate of magnitude intensities to determine the weighting factors in MREIT and MREPT, which relate with the T _{2} values. However, the determined weighting factors in 16 and 20 only include the measured magnitude intensity at each echo time ${T}_{{E}_{j}},\phantom{\rule{0.3em}{0ex}}j=1,\cdots \phantom{\rule{0.3em}{0ex}},{N}_{E}$. The proposed method therefore does not need estimates T _{2} values to optimize the multiple phase signals.
Phantom design and experimental setup
Two different objects were positioned inside phantom. The left one was a thin hollow cylindrical object with the diameter of 4 cm using an insulating thin film of 0.4 mm thickness. We punched four holes which had 2 mm diameter with equally spaced around the circumference. Because we filled the same saline of 0.2 Sm^{−1} inside and outside of the hollow cylindrical object with holes, the apparent electrical conductivities inside and outside of object were determined by the movement of ions through the holes [31]. The right cylindrical object with the diameter of 3 cm was made of an agarose gel (1 g/L CuSO_{4}, 2.1 g/L NaCl, 15 g/L Agar) to generate different conductivity, spin density and T _{2}-decay compared with the background saline. The conductivity of agarose gel was 1.10 Sm^{−1}. It was wrapped in a thin insulating film without holes.
A transversal injecting current of 10 mA was introduced into the phantom via a pair of recessed carbon hydrogel electrodes attached at the middle of the phantom. Figure 2(c) shows the magnitude image at the middle slice. We used the ICNE multi-echo MR pulse sequence by injecting current of alternating polarity synchronized with the multiple refocusing pulses as shown in Figure 1.
Imaging parameters in a 3T MRI scanner (Achieva, Philips) with birdcage transmit-receive (Tx/Rx) RF head coil were as follows: repetition time T _{ R }=1200 ms, data acquisition time width T _{ s }=3.584 ms, echo-spacing ${T}_{{E}_{\mathit{\text{sp}}}}=15$ ms, total number of echo N _{ E }=6 and number of averaging = 4. The reconstructed image matrix was 128×128, with a FOV of 180×180 mm^{2}, 5 mm slice thickness. Total scanning time for both vertical and horizontal injection currents was 20 minutes with an interleaved phase encoding acquisition.
Results
Weighting factor values for MREPT inside ( ${\mathcal{R}}_{\mathit{\text{in}}}$ ) and outside ( ${\mathcal{R}}_{\mathit{\text{out}}}$ ) the agarose anomaly
N _{ E } =1 | N _{ E } =2 | N _{ E } =3 | N _{ E } =4 | N _{ E } =5 | N _{ E } =6 | |
---|---|---|---|---|---|---|
${\mathcal{R}}_{\mathit{\text{out}}}$ | 0.2030 | 0.2046 | 0.1737 | 0.1570 | 0.1385 | 0.1232 |
${\mathcal{R}}_{\mathit{\text{in}}}$ | 0.4926 | 0.2830 | 0.1215 | 0.0617 | 0.0268 | 0.0143 |
Weighting factor values for MREIT inside ( ${\mathcal{R}}_{\mathit{in}}$ ) and outside ( ${\mathcal{R}}_{\mathit{out}}$ ) the agarose anomaly
N _{ E } =1 | N _{ E } =2 | N _{ E } =3 | N _{ E } =4 | N _{ E } =5 | N _{ E } =6 | |
---|---|---|---|---|---|---|
${\mathcal{R}}_{\mathit{\text{out}}}$ | 0.0238 | 0.0734 | 0.1269 | 0.1936 | 0.2585 | 0.3239 |
${\mathcal{R}}_{\mathit{\text{in}}}$ | 0.1404 | 0.2466 | 0.2158 | 0.1849 | 0.1214 | 0.0910 |
Discussion
MREPT and MREIT used an internal magnetic flux density information from a phase imaging can provide conductivity images with high resolution compared to the conventional electrical impedance imaging techniques. Moreover, the interleaved measurement technique with alternating injected current polarity based on a multi-spin-echo pulse sequence, enables simultaneous dual conductivity images. From a single MR scan, we could obtain the low-frequency conductivity images by subtracting and the high-frequency conductivity images by adding the measured phase terms. Despite their advantages and usefulness, MREPT and MREIT techniques commonly suffer from noise amplifications in phase imaging. The proposed method used a ICNE multi-echo pulse sequence based on a spin echo pulse sequence in order to suppress the background field inhomogeneity. This also influenced to the reconstructed high-frequency conductivity using the MREPT technique. Even though the estimated weighting factors for MREIT and MREPT optimally reduce the random noise artifacts, non-uniform noise artifacts from various sources can severely deteriorate the reconstructed conductivity distributions. To be a clinical device used practically, it is important to develop noise reduction techniques taking into account the physical properties and experimental environments of MREIT and MREPT.
The designed phantom consists of two different kinds of anomalies to show the frequency dependent conductivity information. The stable apparent conductivity contrast of hollow cylindrical object made of thin insulating transparency film was only controlled by ion mobility through holes on the film wall. It excluded other effects caused by any ion concentration gradient. Therefore, MREIT images could only present the hollow cylindrical object with holes when comparing the phase terms${\mathcal{P}}^{+}$and${\mathcal{P}}^{-}$in 10. The apparent conductivity of the region inside cylinder was a non-zero conductivity value because the externally injected current entered the anomaly through the holes. In MREPT, the reconstructed high-frequency conductivity was same inside and outside of the anomaly since the measured phase of H^{+}only reflected the material conductivities inside and outside of the cylindrical film. Another agarose gel cylinder wrapped in an insulating film without holes shows different conductivity characteristics in MREPT and MREIT. Due to the short T _{2}-decay relaxation time of agarose gel, the noise levels of${\mathit{\text{sd}}}_{{\phi}^{+,\chi}}$and${\mathit{\text{sd}}}_{{B}_{z}^{\xi}}$were relatively severe compared to those in the other regions. The noise level of each${\mathit{\text{sd}}}_{{\phi}_{j}^{+}}$was strictly increasing with respect to the echo number depending on the T _{2}-decay rate, whereas those of${\mathit{\text{sd}}}_{{B}_{{z}^{\phantom{\rule{0.3em}{0ex}}j}}}$had different characteristics depending on${T}_{{c}^{\phantom{\rule{0.3em}{0ex}}j}}$and the T _{2}-decay rate simultaneously.
MREIT provides the conductivity distribution at a low frequency, whereas MREPT produces the conductivity at the Larmor frequency of 128 MHz at 3 T. The cell membranes consisted of the phospholipid bilayer with embedded proteins behave as a capacitor or insulating film. It shows a complicated pattern of conductivity depending on the measured frequencies. For the biological tissues, the membranes restrict the flow of current of low frequency. MREIT images reflect the membrane properties quantitatively and MREIT has a potential to visualize the anisotropic conductivity tensor map. On the other hand, the membranes become transparent at high frequency and provide a relatively degraded sensitivity in the conductivity image. MREPT may provide different conductivity characteristics compared to MREIT results. Based on the previous studies related to the complex conductivity spectra measured at multiple frequencies within the range of 10 Hz to several kHz, spectroscopic complex conductivity distribution can contribute to explain the physiological and pathological status of internal tissues [33]. The dual-frequency conductivity imaging by combination of MREPT and MREIT is an advanced technique to show different information in spite of displaying two extreme cases at low and the Larmor frequencies. It is meaningful to develop a method to produce multi-frequency conductivity image spectra with high spatial resolution and sensitivity using MR scanner within the range of DC to the Larmor frequency since significantly distinguishable signal changes in biological tissues depending on the applied frequency range.
We have a plan to support the clinically applicable combined conductivity imaging method based on MR techniques. We may apply this method to detect the destroyed cell membrane or the modification of cell or tissue structure due to necrosis or apoptosis initiated by inflammatory response inside the body. Since RF ablation and cryoablation for cancer treatments are accompanied by the destruction of cell membranes, it will be a good method to diagnose ablated lesions based on physiological status of tissue to improve the safety and predict the local recurrence after ablation.
Conclusions
Cross-sectional conductivity imaging methods for high spatial resolution and sensitivity inside the human body has been actively investigated. MREIT and MREPT techniques show different electrical properties at low frequency (below 1 kHz) as MREIT uses an externally injecting current while MREPT uses the Larmor frequency of an MRI scanner. Recently, the dual-frequency conductivity imaging from a single MR scan simultaneously was proposed based on combination of MREPT and MREIT. Even though it produces conductivity spectral information, MREPT and MREIT have commonly suffered from weak signals and noise amplification since the procedures to reconstruct the conductivity in MREIT and MREPT need to differentiate the measured phase signals. We suggested the optimization method to find weighting factors according to echo signals for MREPT and MREIT using the ICNE multi-echo pulse sequence, which minimized the noise artifacts in the measured phase data. The noise standard deviations were precisely analyzed for the optimally weighted magnetic flux density and the phase term of positive-rotating magnetic field. We applied the denoising method based on the reaction-diffusion equation with the estimated noise standard deviations to enhance the quality of dual-frequency conductivity images. A real phantom experiment was performed to validate the proposed method using common measured data to reconstruct the dual-frequency conductivity distributions for MREPT and MREIT.
Declarations
Acknowledgements
This paper was supported by Konkuk University in 2013.
Authors’ Affiliations
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