Noninvasive imaging of bioimpedance distribution by means of current reconstruction magnetic resonance electrical impedance tomography

Low frequency conductivity reconstruction based on a single current injection via MREIT

Conventional magnetic resonance electrical impedance tomography (MREIT) reconstruction methods require administration of two linearly independent currents via at least two electrode pairs. This requires long scanning times and inhibits coordination of MREIT measurements with electrical neuromodulation strategies. We sought to develop an isotropic conductivity reconstruction algorithm in MREIT based on a single current injection, both to decrease scanning time by a factor of two and enable MREIT measurements to be conveniently adapted to general transcranial- or implanted-electrode neurostimulation protocols. In this work, we propose and demonstrate an iterative algorithm that extends previously published MREIT work using two-current administration approaches. The proposed algorithm is a single-current adaptation of the harmonic B _z algorithm. Forward modeling of electric potentials is used to capture changes of conductivity along current directions that would normally be invisible using data from a single-current administration. Computational and experimental results show that the reconstruction algorithm is capable of reconstructing isotropic conductivity images that agree well in terms of L ² error and structural similarity with exact conductivity distributions or two-current-based MREIT reconstructions. We conclude that it is possible to reconstruct high quality electrical conductivity images using MREIT techniques and one current injection only.

Gradient-based magnetic resonance electrical properties imaging of brain tissues

Electrical properties tomography (EPT) holds promise for noninvasively mapping at high spatial resolution the electrical conductivity and permittivity of biological tissues in vivo using a magnetic resonance imaging (MRI) scanner. In the present study, we have developed a novel gradient-based EPT approach with greatly improved tissue boundary reconstruction and largely elevated robustness against measurement noise compared to existing techniques. Using a 7 Tesla MRI system, we report, for the first time, high-quality in vivo human brain electrical property images with refined structural details, which can potentially merit clinical diagnosis (such as cancer detection) and high-field MRI applications (quantification of local specific absorption rate) in the future.

Magnetic-resonance-based electrical properties tomography: a review

Frequency-dependent electrical properties (EPs; conductivity and permittivity) of biological tissues provide important diagnostic information (e.g., tumor characterization), and also play an important role in quantifying radiofrequency (RF) coil induced specific absorption rate (SAR), which is a major safety concern in high- and ultrahigh-field magnetic resonance imaging (MRI) applications. Cross-sectional imaging of EPs has been pursued for decades. Recently introduced electrical properties tomography (EPT) approaches utilize the measurable RF magnetic field induced by the RF coil in an MRI system to quantitatively reconstruct the EP distribution in vivo and noninvasively with a spatial resolution of a few millimeters or less. This paper reviews the EPT approach from its basic theory in electromagnetism to the state-of-the-art research outcomes. Emphasizing on the imaging reconstruction methods rather than experimentation techniques, we review the developed imaging algorithms, validation results in physical phantoms and biological tissues, as well as their applications in in vivo tumor detection and subject-specific SAR prediction. Challenges for future research are also discussed.

A feasibility study of magnetic resonance electrical impedance tomography for prostate cancer detection

Magnetic resonance electrical impedance tomography (MREIT) is an imaging technique that reconstructs the conductivity distribution inside the subject using magnetic flux density or current density measurements acquired by a magnetic resonance imaging system. Since the primary prostate cancer diagnostic method, prostate biopsy, has limited accuracy in cancer diagnosis and malignant tissues have shown significantly different electrical properties from normal or benign tissues, MREIT has potential application in prostate cancer detection. The feasibility of utilizing MREIT in detecting prostate cancer was evaluated via a series of well-designed computer simulations in the present study. MREIT techniques with three different electrode configurations (external, trans-rectal, and trans-urethral electrode arrays) and two different reconstruction algorithms (J-substitution algorithm and harmonic Bz algorithm) were successfully developed. The performance of different MREIT techniques were evaluated and compared based on the imaging accuracy of the reconstructed conductivity distribution in the prostate. Without the presence of noise, the external MREIT achieves a better imaging accuracy than the two endo-MREIT (trans-rectal and trans-urethral) techniques, while the trans-urethral MREIT achieves the best imaging accuracy in noisy environments. We also found that the J-substitution reconstruction algorithm consistently offered better imaging accuracy than the harmonic Bz algorithm. When Gaussian distributed random noise with a standard deviation of 0.25 nT was added, the relative errors (RE) between the reconstructed and target conductivity distributions inside the prostate were observed to be 14.18% and 17.35% by the trans-urethral MREIT with the J-substitution and harmonic Bz algorithms respectively. The lower REs of 9.64% and 11.17% were achieved respectively when the standard deviation of noise was reduced to 0.05 nT. The simulation results demonstrate the feasibility of applying MREIT for prostate cancer detection.

Acoustic dipole radiation based electrical impedance contrast imaging approach of magnetoacoustic tomography with magnetic induction

PURPOSE

Different from the theory of acoustic monopole spherical radiation, the acoustic dipole radiation based theory introduces the radiation pattern of Lorentz force induced dipole sources to describe the principle of magnetoacoustic tomography with magnetic induction (MAT-MI). Although two-dimensional (2D) simulations have been studied for cylindrical phantom models, layer effects of the dipole sources within the entire object along the z direction still need to be investigated to evaluate the performance of MAT-MI for different geometric specifications. The purpose of this work is further verifying the validity and generality of acoustic dipole radiation based theory for MAT-MI with two new models in different shapes, dimensions, and conductivities.

METHODS

Based on the theory of acoustic dipole radiation, the principles of MAT-MI were analyzed with derived analytic formulae. 2D and 3D numerical studies for two new models of aluminum foil and cooked egg were conducted to simulate acoustic pressures and corresponding waveforms, and 2D images of the scanned layers were reconstructed with the simplified back projection algorithm for the waveforms collected around the models. The spatial resolution for conductivity boundary differentiation was also analyzed with different foil thickness. For comparison, two experimental measurements were conducted for a cylindrical aluminum foil phantom and a shell-peeled cooked egg. The collected waveforms and the reconstructed images of the scanned layers were achieved to verify the validation of the acoustic dipole radiation based theory for MAT-MI.

RESULTS

Despite the difference between the 2D and 3D simulated pressures, good consistence of the collected waveforms proves that wave clusters are generated by the abrupt pressure changes with bipolar vibration phases, representing the opposite polarities of the conductivity changes along the measurement direction. The configuration of the scanned layer can be reconstructed in terms of shape and size, and the conductivity boundaries are displayed in stripes with different contrast and bipolar intensities. Layer effects are demonstrated to have little influence on the collected waveforms and the reconstructed images of the scanned layers for the two new models. The experimental results have good agreements with numerical simulations, and the reconstructed 2D images provide conductivity configurations in the scanned layers of the aluminum foil and the egg models.

CONCLUSIONS

It can be concluded that the acoustic pressure of MAT-MI is produced by the divergence of the induced Lorentz force, and the collected waveforms comprise wave clusters with bipolar vibration phases and different amplitudes, providing the information of conductivity boundaries in the scanned layer. With the simplified back projection algorithm for diffraction sources, collected waveforms can be used to reconstruct 2D conductivity contrast image and the conductivity configuration in the scanned layer can be obtained in terms of shape and size in stripes with the spatial resolution of the acoustic wavelength. The favorable results further verify the validity and generality of the acoustic dipole radiation based theory and suggest the feasibility of MAT-MI as an effective electrical impedance contrast imaging approach for medical imaging.

Three-dimensional noninvasive ultrasound Joule heat tomography based on the acousto-electric effect using unipolar pulses: a simulation study

Electrical properties of biological tissues are highly sensitive to their physiological and pathological status. Thus it is of importance to image electrical properties of biological tissues. However, spatial resolution of conventional electrical impedance tomography (EIT) is generally poor. Recently, hybrid imaging modalities combining electric conductivity contrast and ultrasonic resolution based on the acousto-electric effect has attracted considerable attention. In this study, we propose a novel three-dimensional (3D) noninvasive ultrasound Joule heat tomography (UJHT) approach based on the acousto-electric effect using unipolar ultrasound pulses. As the Joule heat density distribution is highly dependent on the conductivity distribution, an accurate and high-resolution mapping of the Joule heat density distribution is expected to give important information that is closely related to the conductivity contrast. The advantages of the proposed ultrasound Joule heat tomography using unipolar pulses include its simple inverse solution, better performance than UJHT using common bipolar pulses and its independence of a priori knowledge of the conductivity distribution of the imaging object. Computer simulation results show that using the proposed method, it is feasible to perform a high spatial resolution Joule heat imaging in an inhomogeneous conductive media. Application of this technique on tumor scanning is also investigated by a series of computer simulations.

A 3-D reconstruction solution to current density imaging based on acoustoelectric effect by deconvolution: a simulation study

Hybrid imaging modality combining ultrasound scanning and electrical current density imaging through the acoustoelectric (AE) effect may potentially provide solutions to imaging electrical activities and properties of biological tissues with high spatial resolution. In this study, a 3-D reconstruction solution to ultrasound current source density imaging (UCSDI) by means of Wiener deconvolution is proposed and evaluated through computer simulations. As compared to previous 2-D UCSDI problem, in a 3-D volume conductor with broadly distributed current density field, the AE signal becomes a 3-D convolution between the electric field and the acoustic field, and effective 3-D reconstruction algorithm has not been developed so far. In the proposed method, a 3-D ultrasound scanning is performed while the corresponding AE signals are collected from multiple electrode pairs attached on the surface of the imaging object. From the collected AE signals, the acoustic field and electric field were first decoupled by Wiener deconvolution. Then, the current density distribution was reconstructed by inverse projection. Our simulations using artificial current fields in homogeneous phantoms suggest that the proposed method is feasible and robust against noise. It is also shown that using the proposed method, it is feasible to reconstruct 3-D current density distribution in an inhomogeneous conductive medium.

Ramp-preserving denoising for conductivity image reconstruction in magnetic resonance electrical impedance tomography

In magnetic resonance electrical impedance tomography, among several conductivity image reconstruction algorithms, the harmonic B(z) algorithm has been successfully applied to B(z) data from phantoms and animals. The algorithm is, however, sensitive to measurement noise in B(z) data. Especially, in in vivo animal and human experiments where injection current amplitudes are limited within a few milliampere at most, measured B(z) data tend to have a low SNR. In addition, magnetic resonance (MR) signal void in outer layers of bones and gas-filled organs, for example, produces salt-pepper noise in the MR phase and, consequently, B(z) images. The B(z) images typically present areas of sloped transitions, which can be assimilated to ramps. Conductivity contrasts change ramp slopes in B(z) images and it is critical to preserve positions of those ramps to correctly recover edges in conductivity images. In this paper, we propose a ramp-preserving denoising method utilizing a structure tensor. Using an eigenvalue analysis, we identified local regions of salt-pepper noise. Outside the identified local regions, we applied an anisotropic smoothing to reduce noise while preserving their ramp structures. Inside the local regions of salt-pepper noise, we used an isotropic smoothing. After validating the proposed denoising method through numerical simulations, we applied it to in vivo animal imaging experiments. Both numerical simulation and experimental results show significant improvements in the quality of reconstructed conductivity images.

3D current source density imaging based on the acoustoelectric effect: a simulation study using unipolar pulses

It is of importance to image electrical activity and properties of biological tissues. Recently hybrid imaging modality combing ultrasound scanning and source imaging through the acoustoelectric (AE) effect has generated considerable interest. Such modality has the potential to provide high spatial resolution current density imaging by utilizing the pressure-induced AE resistivity change confined at the ultrasound focus. In this study, we investigate a novel three-dimensional (3D) ultrasound current source density imaging approach using unipolar ultrasound pulses. Utilizing specially designed unipolar ultrasound pulses and by combining AE signals associated to the local resistivity changes at the focusing point, we are able to reconstruct the 3D current density distribution with the boundary voltage measurements obtained while performing a 3D ultrasound scan. We have shown in computer simulation that using the present method it is feasible to image with high spatial resolution an arbitrary 3D current density distribution in an inhomogeneous conductive media.

Integration of the denoising, inpainting and local harmonic B(z) algorithm for MREIT imaging of intact animals

Conductivity imaging based on the current-injection MRI technique has been developed in magnetic resonance electrical impedance tomography. Current injected through a pair of surface electrodes induces a magnetic flux density distribution inside an imaging object, which results in additional magnetic field inhomogeneity. We can extract phase changes related to the current injection and obtain an image of the induced magnetic flux density. Without rotating the object inside the bore, we can measure only one component B(z) of the magnetic flux density B = (B(x), B(y), B(z)). Based on a relation between the internal conductivity distribution and B(z) data subject to multiple current injections, one may reconstruct cross-sectional conductivity images. As the image reconstruction algorithm, we have been using the harmonic B(z) algorithm in numerous experimental studies. Performing conductivity imaging of intact animal and human subjects, we found technical difficulties that originated from the MR signal void phenomena in the local regions of bones, lungs and gas-filled tubular organs. Measured B(z) data inside such a problematic region contain an excessive amount of noise that deteriorates the conductivity image quality. In order to alleviate this technical problem, we applied hybrid methods incorporating ramp-preserving denoising, harmonic inpainting with isotropic diffusion and ROI imaging using the local harmonic B(z) algorithm. These methods allow us to produce conductivity images of intact animals with best achievable quality. We suggest guidelines to choose a hybrid method depending on the overall noise level and existence of distinct problematic regions of MR signal void.

In vivo high-resolution conductivity imaging of the human leg using MREIT: the first human experiment

We present the first in vivo cross-sectional conductivity image of the human leg with 1.7 mm pixel size using the magnetic resonance electrical impedance tomography (MREIT) technique. After a review of its experimental protocol by an Institutional Review Board (IRB), we performed MREIT imaging experiments of four human subjects using a 3 T MRI scanner. Adopting thin and flexible carbon-hydrogel electrodes with a large surface area and good contact, we could inject as much as 9 mA current in a form of 15 ms pulse into the leg without producing a painful sensation and motion artifact. Sequentially injecting two imaging currents in two different directions, we collected induced magnetic flux density data inside the leg. Scaled conductivity images reconstructed by using the single-step harmonic B(z) algorithm well distinguished different parts of the subcutaneous adipose tissue, muscle, crural fascia, intermuscular septum and bone inside the leg. We could observe spurious noise spikes in the outer layer of the bone primarily due to the MR signal void phenomenon there. Around the fat, the chemical shift of about two pixels occurred obscuring the boundary of the fat region. Future work should include a fat correction method incorporated in the MREIT pulse sequence and improvements in radio-frequency coils and image reconstruction algorithms. Further human imaging experiments are planned and being conducted to produce conductivity images from different parts of the human body.

Induced current magnetic resonance electrical impedance tomography of brain tissues based on the J-substitution algorithm: a simulation study

We have investigated induced current magnetic resonance electrical impedance tomography (IC-MREIT) by means of computer simulations. The J-substitution algorithm was implemented to solve the IC-MREIT reconstruction problem. By providing physical insight into the charge accumulating on the interfaces, the convergence characteristics of the reconstruction algorithm were analyzed. The simulation results conducted on different objects were well correlated with the proposed theoretical analysis. The feasibility of IC-MREIT to reconstruct the conductivity distribution of head-brain tissues was also examined in computer simulations using a multi-compartment realistic head model. The present simulation results suggest that IC-MREIT may have the potential to become a useful conductivity imaging technique.

Solving the forward problem of magnetoacoustic tomography with magnetic induction by means of the finite element method

Magnetoacoustic tomography with magnetic induction (MAT-MI) is a recently proposed imaging modality to image the electrical impedance of biological tissue. It combines the good contrast of electrical impedance tomography with the high spatial resolution of sonography. In this paper, a three-dimensional MAT-MI forward problem was investigated using the finite element method (FEM). The corresponding FEM formulae describing the forward problem are introduced. In the finite element analysis, magnetic induction in an object with conductivity values close to biological tissues was first carried out. The stimulating magnetic field was simulated as that generated from a three-dimensional coil. The corresponding acoustic source and field were then simulated. Computer simulation studies were conducted using both concentric and eccentric spherical conductivity models with different geometric specifications. In addition, the grid size for finite element analysis was evaluated for the model calibration and evaluation of the corresponding acoustic field.