Three-dimensional electrical impedance tomography

A fast time-difference inverse solver for 3D EIT with application to lung imaging

A class of sparse optimization techniques that require solely matrix-vector products, rather than an explicit access to the forward matrix and its transpose, has been paid much attention in the recent decade for dealing with large-scale inverse problems. This study tailors application of the so-called Gradient Projection for Sparse Reconstruction (GPSR) to large-scale time-difference three-dimensional electrical impedance tomography (3D EIT). 3D EIT typically suffers from the need for a large number of voxels to cover the whole domain, so its application to real-time imaging, for example monitoring of lung function, remains scarce since the large number of degrees of freedom of the problem extremely increases storage space and reconstruction time. This study shows the great potential of the GPSR for large-size time-difference 3D EIT. Further studies are needed to improve its accuracy for imaging small-size anomalies.

Imaging of acute respiratory distress syndrome

IMPORTANCE OF THE FIELD

Acute respiratory distress syndrome (ARDS) describes a relatively common and frequently lethal syndrome at the severe end of the spectrum of acute lung injury. Onset of symptoms is usually within 72 h of the inciting event and complicates a wide variety of clinical disorders, ranging from infection to trauma. It may be defined as resistant hypoxaemia in the clinical setting of one of the group of recognised causes, in association with bilateral pulmonary infiltrates and in the absence of left atrial hypertension. Accurate diagnosis and differentiation from other treatable conditions is crucial.

AREAS COVERED IN THIS REVIEW

This publication addresses the clinical and radiological features of ARDS, a review of the imaging technology with illustrations and differential diagnosis.

WHAT THE READER WILL GAIN

This paper will give insight into the strengths and weaknesses of imaging modalities used in the management of patients with ARDS.

TAKE HOME MESSAGE

Imaging plays a vital role in the assessment of acute respiratory syndromes. Computed tomography is much more sensitive compared with chest radiography, and relatively under-utilised. Other methods, such as bedside ultrasound and impedance tomography, may have roles to play in the future.

Imaging fast electrical activity in the brain with electrical impedance tomography

Imaging of neuronal depolarization in the brain is a major goal in neuroscience, but no technique currently exists that could image neural activity over milliseconds throughout the whole brain. Electrical impedance tomography (EIT) is an emerging medical imaging technique which can produce tomographic images of impedance changes with non-invasive surface electrodes. We report EIT imaging of impedance changes in rat somatosensory cerebral cortex with a resolution of 2ms and <200μm during evoked potentials using epicortical arrays with 30 electrodes. Images were validated with local field potential recordings and current source-sink density analysis. Our results demonstrate that EIT can image neural activity in a volume 7×5×2mm in somatosensory cerebral cortex with reduced invasiveness, greater resolution and imaging volume than other methods. Modeling indicates similar resolutions are feasible throughout the entire brain so this technique, uniquely, has the potential to image functional connectivity of cortical and subcortical structures.

Acoustic Source Analysis of Magnetoacoustic Tomography With Magnetic Induction for Conductivity Gradual-Varying Tissues

GOAL

As a multiphysics imaging approach, magnetoacoustic tomography with magnetic induction (MAT-MI) works on the physical mechanism of magnetic excitation, acoustic vibration, and transmission.

METHODS

Based on the theoretical analysis of the source vibration, numerical studies are conducted to simulate the pathological changes of tissues for a single-layer cylindrical conductivity gradual-varying model and estimate the strengths of sources inside the model.

RESULTS

The results suggest that the inner source is generated by the product of the conductivity and the curl of the induced electric intensity inside conductivity homogeneous medium, while the boundary source is produced by the cross product of the gradient of conductivity and the induced electric intensity at conductivity boundary.

CONCLUSION

For a biological tissue with low conductivity, the strength of boundary source is much higher than that of the inner source only when the size of conductivity transition zone is small. In this case, the tissue can be treated as a conductivity abrupt-varying model, ignoring the influence of inner source. Otherwise, the contributions of inner and boundary sources should be evaluated together quantitatively.

SIGNIFICANCE

This study provide basis for further study of precise image reconstruction of MAT-MI for pathological tissues.

Resolution Guarantees in Electrical Impedance Tomography

Electrical impedance tomography (EIT) uses current-voltage measurements on the surface of an imaging subject to detect conductivity changes or anomalies. EIT is a promising new technique with great potential in medical imaging and non-destructive testing. However, in many applications, EIT suffers from inconsistent reliability due to its enormous sensitivity to modeling and measurement errors. In this work, we show that it is principally possible to give rigorous resolution guarantees in EIT even in the presence of systematic and random measurement errors. We derive a constructive criterion to decide whether a desired resolution can be achieved in a given measurement setup. Our results cover the case where anomalies of a known minimal contrast in a subject with imprecisely known background conductivity are to be detected from noisy measurements on a number of electrodes with imprecisely known contact impedances. The considered settings are still idealized in the sense that the shape of the imaging subject has to be known and the allowable amount of uncertainty is rather low. Nevertheless, we believe that this may be a starting point to identify new applications and to design and optimize measurement setups in EIT.

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.

Sampling of finite elements for sparse recovery in large scale 3D electrical impedance tomography

This study proposes a method to improve performance of sparse recovery inverse solvers in 3D electrical impedance tomography (3D EIT), especially when the volume under study contains small-sized inclusions, e.g. 3D imaging of breast tumours. Initially, a quadratic regularized inverse solver is applied in a fast manner with a stopping threshold much greater than the optimum. Based on assuming a fixed level of sparsity for the conductivity field, finite elements are then sampled via applying a compressive sensing (CS) algorithm to the rough blurred estimation previously made by the quadratic solver. Finally, a sparse inverse solver is applied solely to the sampled finite elements, with the solution to the CS as its initial guess. The results show the great potential of the proposed CS-based sparse recovery in improving accuracy of sparse solution to the large-size 3D EIT.

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.

An instrumental electrode model for solving EIT forward problems

An instrumental electrode model (IEM) capable of describing the performance of electrical impedance tomography (EIT) systems in the MHz frequency range has been proposed. Compared with the commonly used Complete Electrode Model (CEM), which assumes ideal front-end interfaces, the proposed model considers the effects of non-ideal components in the front-end circuits. This introduces an extra boundary condition in the forward model and offers a more accurate modelling for EIT systems. We have demonstrated its performance using simple geometry structures and compared the results with the CEM and full Maxwell methods. The IEM can provide a significantly more accurate approximation than the CEM in the MHz frequency range, where the full Maxwell methods are favoured over the quasi-static approximation. The improved electrode model will facilitate the future characterization and front-end design of real-world EIT systems.

Gradient-based electrical properties tomography (gEPT): A robust method for mapping electrical properties of biological tissues in vivo using magnetic resonance imaging

PURPOSE

To develop high-resolution electrical properties tomography (EPT) methods and investigate a gradient-based EPT (gEPT) approach that aims to reconstruct the electrical properties (EP), including conductivity and permittivity, of an imaged sample from experimentally measured B1 maps with improved boundary reconstruction and robustness against measurement noise.

THEORY AND METHODS

Using a multichannel transmit/receive stripline head coil with acquired B1 maps for each coil element, and by assuming negligible Bz component compared to transverse B1 components, a theory describing the relationship between B1 field, EP value, and their spatial gradient has been proposed. The final EP images were obtained through spatial integration over the reconstructed EP gradient. Numerical simulation, physical phantom, and in vivo human experiments at 7 T have been conducted to evaluate the performance of the proposed method.

RESULTS

Reconstruction results were compared with target EP values in both simulations and phantom experiments. Human experimental results were compared with EP values in literature. Satisfactory agreement was observed with improved boundary reconstruction. Importantly, the proposed gEPT method proved to be more robust against noise when compared to previously described nongradient-based EPT approaches.

CONCLUSION

The proposed gEPT approach holds promises to improve EP mapping quality by recovering the boundary information and enhancing robustness against noise.

Single acquisition electrical property mapping based on relative coil sensitivities: A proof-of-concept demonstration

PURPOSE

All methods presented to date to map both conductivity and permittivity rely on multiple acquisitions to compute quantitatively the magnitude of radiofrequency transmit fields, B1+. In this work, we propose a method to compute both conductivity and permittivity based solely on relative receive coil sensitivities ( B1-) that can be obtained in one single measurement without the need to neither explicitly perform transmit/receive phase separation nor make assumptions regarding those phases.

THEORY AND METHODS

To demonstrate the validity and the noise sensitivity of our method we used electromagnetic finite differences simulations of a 16-channel transceiver array. To experimentally validate our methodology at 7 Tesla, multi compartment phantom data was acquired using a standard 32-channel receive coil system and two-dimensional (2D) and 3D gradient echo acquisition. The reconstructed electric properties were correlated to those measured using dielectric probes.

RESULTS

The method was demonstrated both in simulations and in phantom data with correlations to both the modeled and bench measurements being close to identity. The noise properties were modeled and understood.

CONCLUSION

The proposed methodology allows to quantitatively determine the electrical properties of a sample using any MR contrast, with the only constraint being the need to have 4 or more receive coils and high SNR. Magn Reson Med 74:185-195, 2015. © 2014 Wiley Periodicals, Inc.

On-chip detection of cellular activity

The use of on-chip cellular activity monitoring for biological/chemical sensing is promising for environmental, medical and pharmaceutical applications. The miniaturization revolution in microelectronics is harnessed to provide on-chip detection of cellular activity, opening new horizons for miniature, fast, low cost and portable screening and monitoring devices. In this chapter we survey different on-chip cellular activity detection technologies based on electrochemical, bio-impedance and optical detection. Both prokaryotic and eukaryotic cell-on-chip technologies are mentioned and reviewed.

Bioelectrical Impedance Methods for Noninvasive Health Monitoring: A Review

Under the alternating electrical excitation, biological tissues produce a complex electrical impedance which depends on tissue composition, structures, health status, and applied signal frequency, and hence the bioelectrical impedance methods can be utilized for noninvasive tissue characterization. As the impedance responses of these tissue parameters vary with frequencies of the applied signal, the impedance analysis conducted over a wide frequency band provides more information about the tissue interiors which help us to better understand the biological tissues anatomy, physiology, and pathology. Over past few decades, a number of impedance based noninvasive tissue characterization techniques such as bioelectrical impedance analysis (BIA), electrical impedance spectroscopy (EIS), electrical impedance plethysmography (IPG), impedance cardiography (ICG), and electrical impedance tomography (EIT) have been proposed and a lot of research works have been conducted on these methods for noninvasive tissue characterization and disease diagnosis. In this paper BIA, EIS, IPG, ICG, and EIT techniques and their applications in different fields have been reviewed and technical perspective of these impedance methods has been presented. The working principles, applications, merits, and demerits of these methods has been discussed in detail along with their other technical issues followed by present status and future trends.

A reconstruction algorithm of magnetoacoustic tomography with magnetic induction for an acoustically inhomogeneous tissue

Magnetoacoustic tomography with magnetic induction (MAT-MI) is a noninvasive electrical conductivity imaging approach that measures ultrasound wave induced by magnetic stimulation, for reconstructing the distribution of electrical impedance in a biological tissue. Existing reconstruction algorithms for MAT-MI are based on the assumption that the acoustic properties in the tissue are homogeneous. However, the tissue in most parts of human body has heterogeneous acoustic properties, which leads to potential distortion and blurring of small buried objects in the impedance images. In this study, we proposed a new algorithm for MAT-MI to image the impedance distribution in tissues with inhomogeneous acoustic speed distributions. With a computer head model constructed from MR images of a human subject, a series of numerical simulation experiments were conducted. The present results indicate that the inhomogeneous acoustic properties of tissues in terms of speed variation can be incorporated in MAT-MI imaging.

Magnetoacoustic tomography with magnetic induction for high-resolution bioimepedance imaging through vector source reconstruction under the static field of MRI magnet

PURPOSE

Magnetoacoustic tomography with magnetic induction (MAT-MI) is an imaging modality to reconstruct the electrical conductivity of biological tissue based on the acoustic measurements of Lorentz force induced tissue vibration. This study presents the feasibility of the authors' new MAT-MI system and vector source imaging algorithm to perform a complete reconstruction of the conductivity distribution of real biological tissues with ultrasound spatial resolution.

METHODS

In the present study, using ultrasound beamformation, imaging point spread functions are designed to reconstruct the induced vector source in the object which is used to estimate the object conductivity distribution. Both numerical studies and phantom experiments are performed to demonstrate the merits of the proposed method. Also, through the numerical simulations, the full width half maximum of the imaging point spread function is calculated to estimate of the spatial resolution. The tissue phantom experiments are performed with a MAT-MI imaging system in the static field of a 9.4 T magnetic resonance imaging magnet.

RESULTS

The image reconstruction through vector beamformation in the numerical and experimental studies gives a reliable estimate of the conductivity distribution in the object with a ∼ 1.5 mm spatial resolution corresponding to the imaging system frequency of 500 kHz ultrasound. In addition, the experiment results suggest that MAT-MI under high static magnetic field environment is able to reconstruct images of tissue-mimicking gel phantoms and real tissue samples with reliable conductivity contrast.

CONCLUSIONS

The results demonstrate that MAT-MI is able to image the electrical conductivity properties of biological tissues with better than 2 mm spatial resolution at 500 kHz, and the imaging with MAT-MI under a high static magnetic field environment is able to provide improved imaging contrast for biological tissue conductivity reconstruction.

Real-time 3D electrical impedance imaging for ventilation monitoring of the lung: Pilot study

We report an Electrical Impedance Tomography device capable of detecting gravity-induced regional ventilation changes in real-time without averaging or using a contrast medium. Changes in lung ventilation are demonstrated in right and left lateral decubitus position and compared to those seen in an upright and supine normal subject.

Compressed sampling for boundary measurements in three-dimensional electrical impedance tomography

Electrical impedance tomography (EIT) utilizes electrodes on a medium's surface to produce measured data from which the conductivity distribution inside the medium is estimated. For the cases that relocation of electrodes is impractical or no a priori assumptions can be made to optimize the electrodes placement, a large number of electrodes may be needed to cover all possible imaging volume. This may occur in dynamically varying conductivity distribution in 3D EIT. Three-dimensional EIT then requires inverting very large linear systems to calculate the conductivity field, which causes significant problems regarding storage space and reconstruction time in addition to that data acquisition for a large number of electrodes will reduce the achievable frame rate, which is considered as major advantage of EIT imaging. This study proposes an idea to reduce the reconstruction complexity based on the well-known compressed sampling theory. By applying the so-called model-based CoSaMP algorithm to large size data collected by a 256 channel system, the size of forward operator and data acquisition time is reduced to those of a 32 channel system, while accuracy of reconstruction is significantly improved. The results demonstrate great capability of compressed sampling for overriding the challenges arising in 3D EIT.

Intracranial electrical impedance tomography: a method of continuous monitoring in an animal model of head trauma

BACKGROUND

Electrical impedance tomography (EIT) is a method that can render continuous graphical cross-sectional images of the brain's electrical properties. Because these properties can be altered by variations in water content, shifts in sodium concentration, bleeding, and mass deformation, EIT has promise as a sensitive instrument for head injury monitoring to improve early recognition of deterioration and to observe the benefits of therapeutic intervention. This study presents a swine model of head injury used to determine the detection capabilities of an inexpensive bedside EIT monitoring system with a novel intracranial pressure (ICP)/EIT electrode combination sensor on induced intraparenchymal mass effect, intraparenchymal hemorrhage, and cessation of brain blood flow. Conductivity difference images are shown in conjunction with ICP data, confirming the effects.

METHODS

Eight domestic piglets (3-4 weeks of age, mean 10 kg), under general anesthesia, were subjected to 4 injuries: induced intraparenchymal mass effect using an inflated, and later, deflated 0.15-mL Fogarty catheter; hemorrhage by intraparenchymal injection of 1-mL arterial blood; and ischemia/infarction by euthanasia. EIT and ICP data were recorded 10 minutes before inducing the injury until 10 minutes after injury. Continuous EIT and ICP monitoring were facilitated by a ring of circumferentially disposed cranial Ag/AgCl electrodes and 1 intraparenchymal ICP/EIT sensor electrode combination. Data were recorded at 100 Hz. Two-dimensional tomographic conductivity difference (Δσ) images, rendered using data before and after an injury, were displayed in real time on an axial circular mesh. Regions of interest (ROI) within the images were automatically selected as the upper or lower 5% of conductivity data depending on the nature of the injury. Mean Δσ within the ROIs and background were statistically analyzed. ROI Δσ was compared with the background Δσ after an injury event using an unpaired, unequal variance t test. Conductivity change within an ROI after injury was likewise compared with the same ROI before the injury making use of unpaired t tests with unequal variance.

RESULTS

Eight animal subjects were studied, each undergoing 4 injury events including euthanasia. Changes in conductivity due to injury showed expected pathophysiologic effects in an ROI identified within the middle of the left hemisphere; this localization is reasonable given the actual site of injury (left hemisphere) and spatial warping associated with estimating a 3-dimensional conductivity distribution in 2-dimensional space. Results are shown as mean ± 1 SD. When averaged across all 8 animals, balloon inflation caused the mean Δσ within the ROI to shift by -11.4 ± 10.9 mS/m; balloon deflation by +9.4 ± 8.8 mS/m; blood injection by +19.5 ± 11.5 mS/m; death by -12.6 ± 13.2 mS/m. All induced injuries were detectable to statistical significance (P < 0.0001).

CONCLUSION

This study confirms that the bedside EIT system with ICP/EIT combination sensor can detect induced trauma. Such a technique may hold promise for further research in the monitoring and management of traumatically brain-injured individuals.

A local region of interest imaging method for electrical impedance tomography with internal electrodes

Electrical Impedance Tomography (EIT) is a very attractive functional imaging method despite the low sensitivity and resolution. The use of internal electrodes with the conventional reconstruction algorithms was not enough to enhance image resolution and accuracy in the region of interest (ROI). We propose a local ROI imaging method with internal electrodes developed from careful analysis of the sensitivity matrix that is designed to reduce the sensitivity of the voxels outside the local region and optimize the sensitivity of the voxel inside the local region. We perform numerical simulations and physical measurements to demonstrate the localized EIT imaging method. In preliminary results with multiple objects we show the benefits of using an internal electrode and the improved resolution due to the local ROI image reconstruction method. The sensitivity is further increased by allowing the surface electrodes to be unevenly spaced with a higher density of surface electrodes near the ROI. Also, we analyse how much the image quality is improved using several performance parameters for comparison. While these have not yet been studied in depth, it convincingly shows an improvement in local sensitivity in images obtained with an internal electrode in comparison to a standard reconstruction method.

Determining electrical properties based on B(1) fields measured in an MR scanner using a multi-channel transmit/receive coil: a general approach

Electrical properties tomography (EPT) is a recently developed noninvasive technology to image the electrical conductivity and permittivity of biological tissues at Larmor frequency in magnetic resonance scanners. The absolute phase of the complex radio-frequency magnetic field (B1) is necessary for electrical property calculation. However, due to the lack of practical methods to directly measure the absolute B1 phases, current EPT techniques have been achieved with B1 phase estimation based on certain assumptions on object anatomy, coil structure and/or electromagnetic wave behavior associated with the main magnetic field, limiting EPT from a larger variety of applications. In this study, using a multi-channel transmit/receive coil, the framework of a new general approach for EPT has been introduced, which is independent on the assumptions utilized in previous studies. Using a human head model with realistic geometry, a series of computer simulations at 7 T were conducted to evaluate the proposed method under different noise levels. Results showed that the proposed method can be used to reconstruct the conductivity and permittivity images with noticeable accuracy and stability. The feasibility of this approach was further evaluated in a phantom experiment at 7 T.

From complex B(1) mapping to local SAR estimation for human brain MR imaging using multi-channel transceiver coil at 7T

Elevated specific absorption rate (SAR) associated with increased main magnetic field strength remains a major safety concern in ultra-high-field (UHF) magnetic resonance imaging (MRI) applications. The calculation of local SAR requires the knowledge of the electric field induced by radio-frequency (RF) excitation, and the local electrical properties of tissues. Since electric field distribution cannot be directly mapped in conventional MR measurements, SAR estimation is usually performed using numerical model-based electromagnetic simulations which, however, are highly time consuming and cannot account for the specific anatomy and tissue properties of the subject undergoing a scan. In the present study, starting from the measurable RF magnetic fields (B1) in MRI, we conducted a series of mathematical deduction to estimate the local, voxel-wise and subject-specific SAR for each single coil element using a multi-channel transceiver array coil. We first evaluated the feasibility of this approach in numerical simulations including two different human head models. We further conducted experimental study in a physical phantom and in two human subjects at 7T using a multi-channel transceiver head coil. Accuracy of the results is discussed in the context of predicting local SAR in the human brain at UHF MRI using multi-channel RF transmission.

Volumetric electromagnetic phase-shift spectroscopy of brain edema and hematoma

Motivated by the need of poor and rural Mexico, where the population has limited access to advanced medical technology and services, we have developed a new paradigm for medical diagnostic based on the technology of “Volumetric Electromagnetic Phase Shift Spectroscopy” (VEPS), as an inexpensive partial substitute to medical imaging. VEPS, can detect changes in tissue properties inside the body through non-contact, multi-frequency electromagnetic measurements from the exterior of the body, and thereby provide rapid and inexpensive diagnostics in a way that is amenable for use in economically disadvantaged parts of the world. We describe the technology and report results from a limited pilot study with 46 healthy volunteers and eight patients with CT radiology confirmed brain edema and brain hematoma. Data analysis with a non-parametric statistical Mann-Whitney U test, shows that in the frequency range of from 26 MHz to 39 MHz, VEPS can distinguish non-invasively and without contact, with a statistical significance of p<0.05, between healthy subjects and those with a medical conditions in the brain. In the frequency range of between 153 MHz to 166 MHz it can distinguish with a statistical significance of p<0.05 between subjects with brain edema and those with a hematoma in the brain. A classifier build from measurements in these two frequency ranges can provide instantaneous diagnostic of the medical condition of the brain of a patient, from a single set of measurements. While this is a small-scale pilot study, it illustrates the potential of VEPS to change the paradigm of medical diagnostic of brain injury through a VEPS classifier-based technology. Obviously substantially larger-scale studies are needed to verify and expand on the findings in this small pilot study.

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.

Numerical study of magnetoacoustic signal generation with magnetic induction based on inhomogeneous conductivity anisotropy

Magnetoacoustic tomography with magnetic induction (MAT-MI) is a noninvasive imaging modality for generating electrical conductivity images of biological tissues with high spatial resolution. In this paper, we create a numerical model, including a permanent magnet, a coil, and a two-layer coaxial cylinder with anisotropic electrical conductivities, for the MAT-MI forward problem. We analyze the MAT-MI sources in two cases, on a thin conductive boundary layer and in a homogeneous medium, and then develop a feasible numerical approach to solve the MAT-MI sound source densities in the anisotropic conductive model based on finite element analysis of electromagnetic field. Using the numerical finite element method, we then investigate the magnetoacoustic effect of anisotropic conductivity under the inhomogeneous static magnetic field and inhomogeneous magnetic field, quantitatively compute the boundary source densities in the conductive model, and calculate the sound pressure. The anisotropic conductivity contributes to the distribution of the eddy current density, Lorentz force density, and acoustic signal. The proposed models and approaches provide a more realistic simulation environment for MAT-MI.

Reduction of the impact of multiple uncertain conductivity values on EEG dipole source analysis

It is well known that the uncertain knowledge of the conductivity values of the head tissues has an important impact upon the accuracy of the electroencephalogram source reconstruction. Assuming a certain value of the conductivity often leads to high reconstruction error values when solving the inverse problem. It is possible to quantify the impact of multiple uncertain conductivity values on the localization accuracy. We propose an approach that reduces the impact of these multiple uncertainties on the reconstruction accuracy of the dipole parameters. This paper elaborates the numerical method and shows results of localization accuracy in a five-shell spherical head model. Sensitivity analysis, when considering multiple layers in the head model, shows the different scales of the influence of the various uncertain conductivity values on the potential values. We propose a cost function that reduces the impact of multiple uncertainties of the conductivity value on the electroencephalogram dipole reconstruction and two strategies for selecting potential values on the basis of the sensitivity analysis. Numerical simulations, when considering multiple uncertainties in the model, provide results with higher reconstruction accuracy compared with the case where only a single uncertainty is taken into account.

Magnetoacoustic tomography with magnetic induction: bioimepedance reconstruction through vector source imaging

Magnetoacoustic tomography with magnetic induction (MAT-MI) is a technique proposed to reconstruct the conductivity distribution in biological tissue at ultrasound imaging resolution. A magnetic pulse is used to generate eddy currents in the object, which in the presence of a static magnetic field induces Lorentz force based acoustic waves in the medium. This time resolved acoustic waves are collected with ultrasound transducers and, in the present work, these are used to reconstruct the current source which gives rise to the MAT-MI acoustic signal using vector imaging point spread functions. The reconstructed source is then used to estimate the conductivity distribution of the object. Computer simulations and phantom experiments are performed to demonstrate conductivity reconstruction through vector source imaging in a circular scanning geometry with a limited bandwidth finite size piston transducer. The results demonstrate that the MAT-MI approach is capable of conductivity reconstruction in a physical setting.

Improving SAR estimations in MRI using subject-specific models

To monitor and strategically control energy deposition in magnetic resonance imaging (MRI), measured as a specific absorption rate (SAR), numerical methods using generic human models have been employed to estimate worst-case values. Radiofrequency (RF) sequences are therefore often designed conservatively with large safety margins, potentially hindering the full potential of high-field systems. To more accurately predict the patient SAR values, we propose the use of image registration techniques, in conjunction with high-resolution image and tissue libraries, to create patient-specific voxel models. To test this, a matching model from the archives was first selected. Its tissue information was then warped to the patient's coordinates by registering the high-resolution library image to the pilot scan of the patient. Results from studying the models' 1 g SAR distribution suggest that the developed patient model can predict regions of elevated SAR within the patient with remarkable accuracy. Additionally, this work also proposes a voxel analytical metric that can assist in the construction of a patient library and the selection of the matching model from the library for a patient. It is hoped that, by developing voxel models with high accuracy in patient-specific anatomy and positioning, the proposed method can accurately predict the safety margins for high-field human applications and, therefore maximize the safe use of RF sequence power in high-field MRI systems.

High density trans-admittance mammography development and preliminary phantom tests

Background

Malignant breast tumor tissue has a significantly different electrical impedance spectrum than surrounding normal tissues. This has led to the development of impedance imaging as a supplementary or alternative method to X-ray mammography for screening and assessment of breast cancers. However low spatial resolution and poor signal to noise ratio has limited the clinical application.

Methods

In order to improve spatial resolution we developed a trans-admittance mammography (TAM) system including an array of 60×60 current sensing electrodes. We adopted a similar setup to X-ray mammography where the breast is situated between two holding plates. The top plate is a large solid metal electrode for applying a sinusoidal voltage over a range of frequencies from 50 Hz to 500 kHz. The bottom plate has 3600 current sensing electrodes that are kept at the ground potential. Currents are generated from the top voltage-applying electrode and spread throughout the breast, entering the TAM system through the array of current sensing electrodes on the bottom plate. The TAM system measures the exit currents through 6 switching modules connected to 600 electrodes each. Each switching module is connected to 12 ammeter channels which are switched sequentially to 50 of the 600 electrodes each measurement time. Each ammeter channel is comprised of a current-to-voltage converter, a gain amplifier, filters, an analog to digital converter, and a digital phase sensitive demodulator.

Results

We found an average noise level of 38 nA, amplitude stability of less than 0.2%, crosstalk of better than -60 dB and 70 dB signal to noise ratio over all channels and operating frequencies. Images were obtained in time difference and frequency difference modes in a saline phantom.

Conclusion

We describe the design, construction, and calibration of a high density TAM system in detail. Successful high resolution time and frequency difference images showed regions of interest with the expected admittivity changes in the frequency spectrum.

Complex B1 mapping and electrical properties imaging of the human brain using a 16-channel transceiver coil at 7T

The electric properties of biological tissue provide important diagnostic information within radio and microwave frequencies, and also play an important role in specific absorption rate calculation which is a major safety concern at ultrahigh field. The recently proposed electrical properties tomography (EPT) technique aims to reconstruct electric properties in biological tissues based on B1 measurement. However, for individual coil element in multichannel transceiver coil which is increasingly utilized at ultrahigh field, current B1-mapping techniques could not provide adequate information (magnitude and absolute phase) of complex transmit and receive B1 which are essential for electrical properties tomography, electric field, and quantitative specific absorption rate assessment. In this study, using a 16-channel transceiver coil at 7T, based on hybrid B1-mapping techniques within the human brain, a complex B1-mapping method has been developed, and in vivo electric properties imaging of the human brain has been demonstrated by applying a logarithm-based inverse algorithm. Computer simulation studies as well as phantom and human experiments have been conducted at 7T. The average bias and standard deviation for reconstructed conductivity in vivo were 28% and 67%, and 10% and 43% for relative permittivity, respectively. The present results suggest the feasibility and reliability of proposed complex B1-mapping technique and electric properties reconstruction method.

Synchrotron-based dynamic computed tomography of tissue motion for regional lung function measurement

During breathing, lung inflation is a dynamic process involving a balance of mechanical factors, including trans-pulmonary pressure gradients, tissue compliance and airway resistance. Current techniques lack the capacity for dynamic measurement of ventilation in vivo at sufficient spatial and temporal resolution to allow the spatio-temporal patterns of ventilation to be precisely defined. As a result, little is known of the regional dynamics of lung inflation, in either health or disease. Using fast synchrotron-based imaging (up to 60 frames s(-1)), we have combined dynamic computed tomography (CT) with cross-correlation velocimetry to measure regional time constants and expansion within the mammalian lung in vivo. Additionally, our new technique provides estimation of the airflow distribution throughout the bronchial tree during the ventilation cycle. Measurements of lung expansion and airflow in mice and rabbit pups are shown to agree with independent measures. The ability to measure lung function at a regional level will provide invaluable information for studies into normal and pathological lung dynamics, and may provide new pathways for diagnosis of regional lung diseases. Although proof-of-concept data were acquired on a synchrotron, the methodology developed potentially lends itself to clinical CT scanning and therefore offers translational research opportunities.

Error analysis of nonconstant admittivity for MR-based electric property imaging

Magnetic resonance electrical property tomography (MREPT) is a new imaging modality to visualize a distribution of admittivity γ = σ+iωε inside the human body where σ and ε denote electrical conductivity and permittivity, respectively. Using B1 maps acquired by an magnetic resonance imaging scanner, it produces cross-sectional images of σ and ε at the Larmor frequency. Since current MREPT methods rely on an assumption of a locally homogeneous admittivity, there occurs a reconstruction error where this assumption fails. Rigorously analyzing the reconstruction error in MREPT, we showed that the error is fundamental and may cause technical difficulties in interpreting MREPT images of a general inhomogeneous object. We performed numerical simulations and phantom experiments to quantitatively support the error analysis. We compared the MREPT image reconstruction problem with that of magnetic resonance electrical impedance tomography (MREIT) to highlight distinct features of both methods to probe the same object in terms of its high- and low-frequency conductivity distributions, respectively. MREPT images showed large errors along boundaries where admittivity values changed whereas MREIT images showed no such boundary effects. Noting that MREIT makes use of the term neglected in MREPT, a novel MREPT admittivity image reconstruction method is proposed to deal with the boundary effects, which requires further investigation on the complex directional derivative in the real Euclidian space [Formula: see text].

Validation of weighted frequency-difference EIT using a three-dimensional hemisphere model and phantom

Frequency-difference (FD) electrical impedance tomography (EIT) using a weighted voltage difference has recently been proposed for imaging haemorrhagic stroke, abdominal bleeding and tumors. Although its feasibility was demonstrated through two-dimensional numerical simulations and phantom experiments, we should validate the method in three-dimensional imaging objects. At the same time, we need to investigate its robustness against geometrical modeling errors in boundary shapes and electrode positions. We performed a validation study of the weighted FD method through three-dimensional numerical simulations and phantom experiments. Adopting hemispherical models and phantoms whose admittivity distributions change with frequency, we investigated the performance of the method to detect an anomaly. We found that the simple FD method fails to detect the anomaly, whereas reconstructed images using the weighted FD method clearly visualize the anomaly. The weighted FD method is robust against modeling errors of boundary-shape deformations and displaced electrode positions. We also found that the method is capable of detecting an anomaly surrounded by a shell-shaped obstacle simulating the skull. We propose the weighted FD method for future studies of animal and human experiments.

Magnetoacoustic imaging of electrical conductivity of biological tissues at a spatial resolution better than 2 mm

Magnetoacoustic tomography with magnetic induction (MAT-MI) is an emerging approach for noninvasively imaging electrical impedance properties of biological tissues. The MAT-MI imaging system measures ultrasound waves generated by the Lorentz force, having been induced by magnetic stimulation, which is related to the electrical conductivity distribution in tissue samples. MAT-MI promises to provide fine spatial resolution for biological tissue imaging as compared to ultrasound resolution. In the present study, we first estimated the imaging spatial resolution by calculating the full width at half maximum (FWHM) of the system point spread function (PSF). The actual spatial resolution of our MAT-MI system was experimentally determined to be 1.51 mm by a parallel-line-source phantom with Rayleigh criterion. Reconstructed images made from tissue-mimicking gel phantoms, as well as animal tissue samples, were consistent with the morphological structures of the samples. The electrical conductivity value of the samples was determined directly by a calibrated four-electrode system. It has been demonstrated that MAT-MI is able to image the electrical impedance properties of biological tissues with better than 2 mm spatial resolution. These results suggest the potential of MAT-MI for application to early detection of small-size diseased tissues (e.g. small breast cancer).

Electrical impedance tomography measured at two thoracic levels can visualize the ventilation distribution changes at the bedside during a decremental positive end-expiratory lung pressure trial

Introduction

Computed tomography of the lung has shown that ventilation shifts from dependent to nondependent lung regions. In this study, we investigated whether, at the bedside, electrical impedance tomography (EIT) at the cranial and caudal thoracic levels can be used to visualize changes in ventilation distribution during a decremental positive end-expiratory pressure (PEEP) trial and the relation of these changes to global compliance in mechanically ventilated patients.

Methods

Ventilation distribution was calculated on the basis of EIT results from 12 mechanically ventilated patients after cardiac surgery at a cardiothoracic ICU. Measurements were taken at four PEEP levels (15, 10, 5 and 0 cm H₂O) at both the cranial and caudal lung levels, which were divided into four ventral-to-dorsal regions. Regional compliance was calculated using impedance and driving pressure data.

Results

We found that tidal impedance variation divided by tidal volume significantly decreased on caudal EIT slices, whereas this measurement increased on the cranial EIT slices. The dorsal-to-ventral impedance distribution, expressed according to the center of gravity index, decreased during the decremental PEEP trial at both EIT levels. Optimal regional compliance differed at different PEEP levels: 10 and 5 cm H₂O at the cranial level and 15 and 10 cm H₂O at the caudal level for the dependent and nondependent lung regions, respectively.

Conclusions

At the bedside, EIT measured at two thoracic levels showed different behavior between the caudal and cranial lung levels during a decremental PEEP trial. These results indicate that there is probably no single optimal PEEP level for all lung regions.

A novel method for recording neuronal depolarization with recording at 125-825 Hz: implications for imaging fast neural activity in the brain with electrical impedance tomography

Electrical impedance tomography (EIT) is a recently developed medical imaging method which has the potential to produce images of fast neuronal depolarization in the brain. Previous modelling suggested that applied current needed to be below 100 Hz but the signal-to-noise ratio (SNR) recorded with scalp electrodes during evoked responses was too low to permit imaging. A novel method in which contemporaneous evoked potentials are subtracted is presented with current applied at 225 Hz to cerebral cortex during evoked activity; although the signal is smaller than at DC by about 10×, the principal noise from the EEG is reduced by about 1000×, resulting in an improved SNR. It was validated with recording of compound action potentials in crab walking leg nerve where peak changes of -0.2% at 125 and 175 Hz tallied with biophysical modelling. In recording from rat cerebral cortex during somatosensory evoked responses, peak impedance decreases of -0.07 ± 0.006% (mean ± SE) with a SNR of >50 could be recorded at 225 Hz. This method provides a reproducible and artefact free means for recording resistance changes during neuronal activity which could form the basis for imaging fast neural activity in the brain.

Low-parametric induced current - magnetic resonance electrical impedance tomography for quantitative conductivity estimation of brain tissues using a priori information: a simulation study

Accurate estimation of the human head conductivity is important for the diagnosis and therapy of brain diseases. Induced Current - Magnetic Resonance Electrical Impedance Tomography (IC-MREIT) is a recently developed non-invasive technique for conductivity estimation. This paper presents a formulation where a low number of material parameters need to be estimated, starting from MR eddy-current field maps. We use a parameterized frequency dependent 4-Cole-Cole material model, an efficient independent impedance method for eddy-current calculations and a priori information through the use of voxel models. The proposed procedure circumvents the ill-posedness of traditional IC-MREIT and computational efficiency is obtained by using an efficient forward eddy-current solver.