Sensitivity maps and system requirements for magnetic induction tomography using a planar gradiometer

Multi-Frequency Electromagnetic Tomography for Acute Stroke Detection Using Frequency-Constrained Sparse Bayesian Learning

Imaging the bio-impedance distribution of the brain can provide initial diagnosis of acute stroke. This paper presents a compact and non-radiative tomographic modality, i.e. multi-frequency Electromagnetic Tomography (mfEMT), for the initial diagnosis of acute stroke. The mfEMT system consists of 12 channels of gradiometer coils with adjustable sensitivity and excitation frequency. To solve the image reconstruction problem of mfEMT, we propose an enhanced Frequency-Constrained Sparse Bayesian Learning (FC-SBL) to simultaneously reconstruct the conductivity distribution at all frequencies. Based on the Multiple Measurement Vector (MMV) model in the Sparse Bayesian Learning (SBL) framework, FC-SBL can recover the underlying distribution pattern of conductivity among multiple images by exploiting the frequency constraint information. A realistic 3D head model was established to simulate stroke detection scenarios, showing the capability of mfEMT to penetrate the highly resistive skull and improved image quality with FC-SBL. Both simulations and experiments showed that the proposed FC-SBL method is robust to noisy data for image reconstruction problems of mfEMT compared to the single measurement vector model, which is promising to detect acute strokes in the brain region with enhanced spatial resolution and in a baseline-free manner.

A noninvasive flexible conformal sensor for accurate real-time monitoring of local cerebral edema based on electromagnetic induction

Cerebral edema (CE) is a non-specific pathological swelling of the brain secondary to any type of neurological injury. The real-time monitoring of focal CE mostly found in early stage is of great significance to reduce mortality and disability. Magnetic Induction Phase Shift (MIPS) is expected to achieve non-invasive continuous monitoring of CE. However, most existing MIPS sensors are made of hard materials which makes it difficult to accurately retrieve CE information. In this article, we designed a conformal two-coil structure and a single-coil structure, and studied their sensitivity map using finite element method (FEM). After that, the conformal MIPS sensor that is preferable for local CE monitoring was fabricated by flexible printed circuit (FPC). Next, physical experiments were conducted to investigate its performance on different levels of simulated CE solution volume, measurement distance, and bending. Subsequently, 14 rabbits were chosen to establish CE model and another three rabbits were selected as controls. The 24-hour MIPS real-time monitoring experiments was carried out to verify that the feasibility. Results showed a gentler attenuation trend of the conformal two-coil structure, compared with the single-coil structure. In addition, the novel flexible conformal MIPS sensor has a characteristic of being robust to bending according to the physical experiments. The results of animal experiments showed that the sensor can be used for CE monitoring. It can be concluded that this flexible conformal MIPS sensor is desirable for local focusing measurement of CE and subsequent multidimensional information extraction for predicting model. Also, it enables a much more comfortable environment for long-time bedside monitoring.

Technologies for magnetic induction tomography sensors and image reconstruction in medical assisted diagnosis: A review

Magnetic induction tomography (MIT) is a non-invasive and non-contact imaging technology, which can be used in medical diagnosis by reconstructing the electrical distribution of biological tissues. Unlike other large medical imaging equipment, the device of MIT is with small size and low cost. The theoretical basis of MIT is by measuring the phase difference of magnetic flux density generated around the imaging objects, analyzing the eddy current distribution, and then using the reconstruction algorithms to obtain the electrical characteristic distribution of the object. This review introduces the development of imaging systems and the reconstruction algorithms of MIT as a medical assisted diagnostic technology, including the optimal design of the sensors, the excitation methods of the system, the calculation methods of the eddy current, and the improved methods of different reconstruction algorithms.

Sparse defects detection and 3D imaging base on electromagnetic tomography and total variation algorithm

Metal products are widely used in the industrial field. However, internal defects such as holes, dents, and scratches are prone to occur due to factors such as processing, production equipment failure, and poor working conditions. Electromagnetic tomography (EMT) is an effective method for defects imaging. Nevertheless, metal defects are prone to be small and sparsely distributed on the surface or inside so that image reconstruction for metal defects based on EMT is still challenging. In this paper, the sparse regularization method is used for a mathematical model of EMT reconstruction in order to improve the image quality. According to the relationship between the detection depth and the excitation frequency, three-dimensional reconstructed images are used for the surface and internal defects of the metal parts. Both simulations and experiments are carried out to verify the effectiveness of the method.

Screening and Biosensor-Based Approaches for Lung Cancer Detection

Early diagnosis of lung cancer helps to reduce the cancer death rate significantly. Over the years, investigators worldwide have extensively investigated many screening modalities for lung cancer detection, including computerized tomography, chest X-ray, positron emission tomography, sputum cytology, magnetic resonance imaging and biopsy. However, these techniques are not suitable for patients with other pathologies. Developing a rapid and sensitive technique for early diagnosis of lung cancer is urgently needed. Biosensor-based techniques have been recently recommended as a rapid and cost-effective tool for early diagnosis of lung tumor markers. This paper reviews the recent development in screening and biosensor-based techniques for early lung cancer detection.

Magnetic induction spectroscopy (MIS)-probe design for cervical tissue measurements

OBJECTIVE

Gradiometers have the advantage of increasing measuring sensitivity, which is particularly useful in magnetic induction spectroscopy (MIS) for bio-impedance measurements. Traditional gradiometers use a pair of field sensing coils equally distant and on opposite sides of a drive coil, which provides high immunity to interference. In this paper, a ferrite-cored coaxial gradiometer probe of 29 mm diameter has been developed for measuring the impedance spectra of cervical tissues in vivo.

APPROACH

It consists of a ferrite rod with outer ferrite confinement screening in order to eliminate the signals from surrounding tissue. The magnetic screening efficiency was compared with an air-cored gradiometer probe. For both gradiometer probes, a drive coil and two sensing coils were wound on a borosilicate glass former aligned coaxially with two sensing coils equidistant from the drive coil. The signal sensitivity of those two MIS gradiometers has been measured using saline samples with a conductivity range between 0.1 and 1.1 S m^-1. Finite element methods using COMSOL Multiphysics have been used to simulate the distribution of sensitivity to conductivity over the face of each probe and with depth.

MAIN RESULTS

The ferrite-cored probe has a sensitivity confined to the volume defined by the gap between the ferrite core and outer tube of ferrite while the air-cored probe without any magnetic shielding had a wide sensitivity over the face and the side of the probe. Four saline samples and one of distilled water with conductivities from 0.1 to 1.1 S m^-1 have been used to make conductivity measurements at frequencies of 50 kHz, 100 kHz, and 300 kHz. The measurement accuracy of the air-cored MIS probe was 0.09 S m^-1 at 50 kHz, improving to 0.05 S m^-1 at 300 kHz. For the ferrite-cored MIS probe, the measurement accuracy was 0.28 S m^-1 at 50 kHz, improving to 0.04 S m^-1 at 300 kHz.

SIGNIFICANCE

In vivo measurements on human hand have been performed using both types of gradiometers and the conductivity is consistent with reported data.

Advancements in transmitters and sensors for biological tissue imaging in magnetic induction tomography

Magnetic Induction Tomography (MIT), which is also known as Electromagnetic Tomography (EMT) or Mutual Inductance Tomography, is among the imaging modalities of interest to many researchers around the world. This noninvasive modality applies an electromagnetic field and is sensitive to all three passive electromagnetic properties of a material that are conductivity, permittivity and permeability. MIT is categorized under the passive imaging family with an electrodeless technique through the use of excitation coils to induce an electromagnetic field in the material, which is then measured at the receiving side by sensors. The aim of this review is to discuss the challenges of the MIT technique and summarize the recent advancements in the transmitters and sensors, with a focus on applications in biological tissue imaging. It is hoped that this review will provide some valuable information on the MIT for those who have interest in this modality. The need of this knowledge may speed up the process of adopted of MIT as a medical imaging technology.

Extraction of single-trial cortical beta oscillatory activities in EEG signals using empirical mode decomposition

Background

Brain oscillatory activities are stochastic and non-linearly dynamic, due to their non-phase-locked nature and inter-trial variability. Non-phase-locked rhythmic signals can vary from trial-to-trial dependent upon variations in a subject's performance and state, which may be linked to fluctuations in expectation, attention, arousal, and task strategy. Therefore, a method that permits the extraction of the oscillatory signal on a single-trial basis is important for the study of subtle brain dynamics, which can be used as probes to study neurophysiology in normal brain and pathophysiology in the diseased.

Methods

This paper presents an empirical mode decomposition (EMD)-based spatiotemporal approach to extract neural oscillatory activities from multi-channel electroencephalograph (EEG) data. The efficacy of this approach manifests in extracting single-trial post-movement beta activities when performing a right index-finger lifting task. In each single trial, an EEG epoch recorded at the channel of interest (CI) was first separated into a number of intrinsic mode functions (IMFs). Sensorimotor-related oscillatory activities were reconstructed from sensorimotor-related IMFs chosen by a spatial map matching process. Post-movement beta activities were acquired by band-pass filtering the sensorimotor-related oscillatory activities within a trial-specific beta band. Signal envelopes of post-movement beta activities were detected using amplitude modulation (AM) method to obtain post-movement beta event-related synchronization (PM-bERS). The maximum amplitude in the PM-bERS within the post-movement period was subtracted by the mean amplitude of the reference period to find the single-trial beta rebound (BR).

Results

The results showed single-trial BRs computed by the current method were significantly higher than those obtained from conventional average method (P < 0.01; matched-pair Wilcoxon test). The proposed method provides high signal-to-noise ratio (SNR) through an EMD-based decomposition and reconstruction process, which enables event-related oscillatory activities to be examined on a single-trial basis.

Conclusions

The EMD-based method is effective for artefact removal and extracting reliable neural features of non-phase-locked oscillatory activities in multi-channel EEG data. The high extraction rate of the proposed method enables the trial-by-trial variability of oscillatory activities can be examined, which provide a possibility for future profound study of subtle brain dynamics.

Single-trial analysis of cortical oscillatory activities during voluntary movements using empirical mode decomposition (EMD)-based spatiotemporal approach

This study presents a method based on empirical mode decomposition (EMD) and a spatial template-based matching approach to extract sensorimotor oscillatory activities from multi-channel magnetoencephalographic (MEG) measurements during right index finger lifting. The longitudinal gradiometer of the sensor unit which presents most prominent SEF was selected on which each single-trial recording was decomposed into a set of intrinsic mode functions (IMFs). The correlation between each IMF of the selected channel and raw data on other channels were created and represented as a spatial map. The sensorimotor-related IMFs with corresponding correlational spatial map exhibiting large values on primary sensorimotor area (SMI) were selected via spatial-template matching process. Trial-specific alpha and beta bands were determined in sensorimotor-related oscillatory activities using a two-spectrum comparison between the spectra obtained from baseline period (-4 to -3 s) and movement-onset period (-0.5 to 0.5 s). Sensorimotor-related oscillatory activities were filtered within the trial-specific frequency bands to resolve task-related oscillatory activities. Results demonstrated that the optimal phase and amplitude information were preserved not only for alpha suppression (event-related desynchronization) and beta rebound (event-related synchronization) but also for profound analysis of subtle dynamics across trials. The retention of high SNR in the extracted oscillatory activities allow various methods of source estimation that can be applied to study the intricate brain dynamics of motor control mechanisms. The present study enables the possibility of investigating cortical pathophysiology of movement disorder on a trial-by-trial basis which also permits an effective alternative for participants or patients who can not endure lengthy procedures or are incapable of sustaining long experiments.

Sensitivity of a single coil electromagnetic sensor for non-contact monitoring of breathing

We design and analyse a flexible non-contact electromagnetic sensor for monitoring breathing. This paper presents the sensor design and the theoretical model for the expected sensitivity from which we optimize design components. The primary application of this device is in non-invasive sleep monitoring and it has the potential to be useful for detection of both adult and infant apnea. The conductivity changes of the lungs during breathing are monitored by inducing eddy currents within them. The sensor consists of a small coil that acts as both a transmitter and a receiver. The theoretical sensitivity of the sensor to breathing changes is calculated and corresponds within the assumptions of the model to the measured results.

Magnetic induction tomography: evaluation of the point spread function and analysis of resolution and image distortion

Magnetic induction tomography (MIT) is a low-resolution imaging modality used for reconstructing the changes of the passive electrical properties in a target object. For an imaging system, it is very important to give forecasts about the image quality. Both the maximum resolution and the correctness of the location of the inhomogeneities are of major interest. Furthermore, the smallest object which can be detected for a certain noise level is a criterion for the diagnostic value of an image. The properties of an MIT image are dependent on the position inside the object, the conductivity distribution and of course on the location and the number of excitation coils and receiving coils. Quantitative statements cannot be made in general but it is feasible to predict the image quality for a selected problem. For electrical impedance tomography (EIT), the theoretical limits of image quality have been studied carefully and a comprehensive analysis for MIT is necessary. Thus, a simplified analysis on resolution, dimensions and location of an inhomogeneity was carried out by means of an evaluation of the point spread function (PSF). In analogy to EIT the PSF depends strongly on the location, showing the broadest distribution in the centre of the object. Increasing the amount of regularization according to increasing measurement noise, the PSF broadens and its centre is shifted towards the borders of the object. The resolution is indirectly proportional to the width of the PSF and increases when moving from the centre towards the border of the object and decreases with increasing noise.

Absolute conductivity reconstruction in magnetic induction tomography using a nonlinear method

Magnetic induction tomography (MIT) attempts to image the electrical and magnetic characteristics of a target using impedance measurement data from pairs of excitation and detection coils. This inverse eddy current problem is nonlinear and also severely ill posed so regularization is required for a stable solution. A regularized Gauss-Newton algorithm has been implemented as a nonlinear, iterative inverse solver. In this algorithm, one needs to solve the forward problem and recalculate the Jacobian matrix for each iteration. The forward problem has been solved using an edge based finite element method for magnetic vector potential A and electrical scalar potential V, a so called A, A - V formulation. A theoretical study of the general inverse eddy current problem and a derivation, paying special attention to the boundary conditions, of an adjoint field formula for the Jacobian is given. This efficient formula calculates the change in measured induced voltage due to a small perturbation of the conductivity in a region. This has the advantage that it involves only the inner product of the electric fields when two different coils are excited, and these are convenient computationally. This paper also shows that the sensitivity maps change significantly when the conductivity distribution changes, demonstrating the necessity for a nonlinear reconstruction algorithm. The performance of the inverse solver has been examined and results presented from simulated data with added noise.

Single-step 3-d image reconstruction in magnetic induction tomography: theoretical limits of spatial resolution and contrast to noise ratio

Magnetic induction tomography (MIT) is a low-resolution imaging modality for reconstructing the changes of the complex conductivity in an object. MIT is based on determining the perturbation of an alternating magnetic field, which is coupled from several excitation coils to the object. The conductivity distribution is reconstructed from the corresponding voltage changes induced in several receiver coils. Potential medical applications comprise the continuous, non-invasive monitoring of tissue alterations which are reflected in the change of the conductivity, e.g. edema, ventilation disorders, wound healing and ischemic processes. MIT requires the solution of an ill-posed inverse eddy current problem. A linearized version of this problem was solved for 16 excitation coils and 32 receiver coils with a model of two spherical perturbations within a cylindrical phantom. The method was tested with simulated measurement data. Images were reconstructed with a regularized single-step Gauss-Newton approach. Theoretical limits for spatial resolution and contrast/noise ratio were calculated and compared with the empirical results from a Monte-Carlo study. The conductivity perturbations inside a homogeneous cylinder were localized for a SNR between 44 and 64 dB. The results prove the feasibility of difference imaging with MIT and give some quantitative data on the limitations of the method.

A multifrequency magnetic induction tomography system using planar gradiometers: data collection and calibration

We developed a 14-channel multifrequency magnetic induction tomography system (MF-MIT) for biomedical applications. The excitation field is produced by a single coil and 14 planar gradiometers are used for signal detection. The object under measurement was rotated (16 steps per turn) to obtain a full data set for image reconstruction. We make measurements at frequencies from 50 kHz to 1 MHz using a single frequency excitation signal or a multifrequency signal containing several frequencies in this range. We used two acquisition boards giving a total of eight synchronous channels at a sample rate of 5 MS s(-1) per channel. The real and imaginary parts of DeltaB/B(0) were calculated using coherent demodulation at all injected frequencies. Calibration, averaging and drift cancellation techniques were used before image reconstruction. A plastic tank filled with saline (D = 19 cm) and with conductive and/or paramagnetic perturbations was measured for calibration and test purposes. We used a FEM model and an eddy current solver to evaluate the experimental results and to reconstruct the images. Measured equivalent input noise voltage for each channel was 2 nV Hz(-1/2). Using coherent demodulation, with an integration time of 20 ms, the measured STD for the magnitude was 7 nV(rms) (close to the theoretical value only taking into account the amplifier's thermal noise). For long acquisition times the drift in the signal produced a bigger effect than the input noise (typical STD was 10 nV with a maximum of 35 nV at one channel) but this effect was reduced using a drift cancellation technique based on averaging. We were able to image a 2 S m(-1) agar sphere (D = 4 cm) inside the tank filled with saline of 1 S m(-1).

Vector projection of biomagnetic fields

Biomagnetic measurements are increasingly popular as functional imaging techniques for the non-invasive assessment of electrically active tissue. Although most currently available magnetometers utilise only one component of the vector magnetic field, some studies have suggested the possibility of obtaining additional information from recordings of the full magnetic field vector. Three projection techniques were applied to different biomagnetic signals for analysis of the three orthogonal components of the vector magnetic field. Vector magnetic fields obtained from fetal cardiac activity were projected into evenly spaced directions around a unit sphere. The vector magnetic field recorded from multiple intestinal current sources with independent temporal frequencies was then projected. Finally, an external reference signal from an invasive electrode was used to project the recorded vector magnetic fields due to gastric electrical activity. In each case, it was found that the information obtained by examination of the projected magnetic field vectors gave superior clinical insight to that obtained by analysis of any single magnetic field component.

Solution of the inverse problem of magnetic induction tomography (MIT)

Magnetic induction tomography (MIT) of biological tissue is used to reconstruct the changes in the complex conductivity distribution inside an object under investigation. The measurement principle is based on determining the perturbation DeltaB of a primary alternating magnetic field B0, which is coupled from an array of excitation coils to the object under investigation. The corresponding voltages DeltaV and V0 induced in a receiver coil carry the information about the passive electrical properties (i.e. conductivity, permittivity and permeability). The reconstruction of the conductivity distribution requires the solution of a 3D inverse eddy current problem. As in EIT the inverse problem is ill-posed and on this account some regularization scheme has to be applied. We developed an inverse solver based on the Gauss-Newton-one-step method for differential imaging, and we implemented and tested four different regularization schemes: the first and second approaches employ a classical smoothness criterion using the unit matrix and a differential matrix of first order as the regularization matrix. The third method is based on variance uniformization, and the fourth method is based on the truncated singular value decomposition. Reconstructions were carried out with synthetic measurement data generated with a spherical perturbation at different locations within a conducting cylinder. Data were generated on a different mesh and 1% random noise was added. The model contained 16 excitation coils and 32 receiver coils which could be combined pairwise to give 16 planar gradiometers. With 32 receiver coils all regularization methods yield fairly good 3D-images of the modelled changes of the conductivity distribution, and prove the feasibility of difference imaging with MIT. The reconstructed perturbations appear at the right location, and their size is in the expected range. With 16 planar gradiometers an additional spurious feature appears mirrored with respect to the median plane with negative sign. This demonstrates that a symmetrical arrangement with one ring of planar gradiometers cannot distinguish between a positive conductivity change at the true location and a negative conductivity change at the mirrored location.

A comparison of sensors for minimizing the primary signal in planar-array magnetic induction tomography

In magnetic induction tomography reducing the influence of the primary excitation field on the sensors can provide a significant improvement in SNR and/or allow the operating frequency to be reduced. For the purposes of imaging, it would be valuable if all, or a useful subset, of the detection coils could be rendered insensitive to the primary field for any excitation coil activated. Suitable schemes which have been previously suggested include the use of axial gradiometers and coil-orientation methods (Bx sensors). This paper examines the relative performance of each method through computer simulation of the sensitivity profiles produced by a single sensor, and comparison of reconstructed images produced by sensor arrays. A finite-difference model was used to determine the sensitivity profiles obtained with each type of sensor arrangement. The modelled volume was a cuboid of dimensions 50 cmx50 cmx12 cm with a uniform conductivity of 1 S m-1. The excitation coils were of 5 cm diameter and the detection coils of 5 mm diameter. The Bx sensors provided greater sensitivity than the axial gradiometers at all depths, other than on the surface layer of the volume. Images produced using a single-planar array were found to contain distortion which was reduced by the addition of a second array.

A new type of gradiometer for the receiving circuit of magnetic induction tomography (MIT)

Magnetic induction tomography (MIT) is a low-resolution imaging modality which aims at the three-dimensional (3D) reconstruction of the electrical conductivity in objects from alternating magnetic fields. In MIT systems the magnetic field perturbations to be detected are very small when compared to the excitation field (ppm range). The voltage which is induced by the excitation field in the receiver coils must be suppressed for providing sufficient dynamic range. In the past, two very efficient strategies were proposed: adjusted planar gradiometers (PGRAD) and the orientation of a receiver coil with respect to the excitation coil such that the net magnetic flow is zero (zero flow coil, ZFC). In contrast to the PGRAD no voltage is induced in the ZFC by the main field. This is advantageous because two comparatively high voltages in the two gradiometer coils can never be subtracted perfectly, thus leaving a residual voltage which is prone to drift. However, a disadvantage of the ZFC is the higher susceptibility to interferences from far RF sources. In contrast, in the gradiometer such interferences are cancelled to a high degree. We developed a new type of gradiometer (zero flow gradiometer, ZFGRAD) which combines the advantages of ZFC and PGRAD. All three systems were compared with respect to sensitivity and perturbation to signal ratio (PSR) defined as the ratio of the signal change due to a magnetic perturbation field at the carrier frequency and the signal change due to shifting a metallic sphere between two test points. The spatial sensitivity of the three systems was found to be very similar. The PSR of the ZFGRAD was more than 12 times lower than that of the ZFC. Finally, the feasibility of image reconstruction with two arrays of eight excitation coils and eight ZFGRAD, respectively, was shown with a single-step Gauss-Newton reconstructor and simulated measurement data generated for a cylindrical tank with a spherical perturbation. The resulting images show a clear, bright feature at the correct position of the sphere and are comparable to those with PGRAD arrays.

Planar gradiometer for magnetic induction tomography (MIT): theoretical and experimental sensitivity maps for a low-contrast phantom

Planar gradiometers (PGRAD) have particular advantages compared to solenoid receiver coils in magnetic induction tomography (MIT) for biological objects. A careful analysis of the sensitivity maps has to be carried out for perturbations within conducting objects in order to understand the performance of a PGRAD system and the corresponding implications for the inverse problem of MIT. We calculated and measured sensitivity maps for a single MIT-channel and a cylindrical tank (diameter 200 mm) with a spherical perturbation (diameter 50 mm) and with conductivities in the physiological range (0.4-0.8 S m(-1)). The excitation coil (EXC) was a solenoid (diameter 100 mm) with its axis perpendicular to the cylinder axis. As receiver a PGRAD was used. Calculations were carried out with a finite element model comparing the PGRAD and a solenoid receiver coil with its axis perpendicular to the excitation coil axis (SC90). The measured and simulated sensitivity maps agree satisfactorily within the limits of unavoidable systematic errors. In PGRAD the sensitivity is zero on the coil axis, exhibiting two local extrema near the receiver and a strong increase of the sensitivity with the distance from the coil axis. In SC90 the sensitivity map is morphologically very similar to that of the PGRAD. The maps are completely different from those known in EIT and may thus cause different implications for the inverse problem. The SC90 can, in principle, replace the mechanically and electrically more complicated PGRAD, however, the immunity to far sources of electromagnetic interference is worse, thus requiring magnetic shielding of the system.

Measurement of liver iron overload by magnetic induction using a planar gradiometer: preliminary human results

The measurement of hepatic iron overload is of particular interest in cases of hereditary hemochromatosis or in patients subject to periodic blood transfusion. The measurement of plasma ferritin provides an indirect estimate but the usefulness of this method is limited by many common clinical conditions (inflammation, infection, etc). Liver biopsy provides the most quantitative direct measurement of iron content in the liver but the risk of the procedure limits its acceptability. This work studies the feasibility of a magnetic induction (MI) low-cost system to measure liver iron overload. The excitation magnetic field (B0, frequency: 28 kHz) was produced by a coil, the perturbation produced by the object (deltaB) was detected using a planar gradiometer. We measured ten patients and seven volunteers in supine and prone positions. Each subject was moved in a plane parallel to the gradiometer several times to estimate measurement repeatability. The real and imaginary parts of deltaB/B0 were measured. Plastic tanks filled with water, saline and ferric solutions were measured for calibration purposes. We used a finite element model to evaluate the experimental results. To estimate the iron content we used the ratio between the maximum values for real and imaginary parts of deltaB/B0 and the area formed by the Nyquist plot divided by the maximum imaginary part. Measurements in humans showed that the contribution of the permittivity is stronger than the contribution of the permeability produced by iron stores in the liver. Defined iron estimators show a limited correlation with expected iron content in patients (R < or = 0.56). A more precise control of geometry and position of the subjects and measurements at multiple frequencies would improve the method.

ICA-based spatiotemporal approach for single-trial analysis of postmovement MEG beta synchronization⋆

The extraction of event-related oscillatory neuromagnetic activities from single-trial measurement is challenging due to the non-phase-locked nature and variability from trial to trial. The present study presents a method based on independent component analysis (ICA) and the use of a template-based correlation approach to extract Rolandic beta rhythm from magnetoencephalographic (MEG) measurements of right finger lifting. A single trial recording was decomposed into a set of coupled temporal independent components and corresponding spatial maps using ICA and the reactive beta frequency band for each trial identified using a two-spectrum comparison between the postmovement interval and a reference period. Task-related components survived dual criteria of high correlation with both the temporal and the spatial templates with an acceptance rate of about 80%. Phase and amplitude information for noise-free MEG beta activities were preserved not only for optimal calculation of beta rebound (event-related synchronization) but also for profound penetration into subtle dynamics across trials. Given the high signal-to-noise ratio (SNR) of this method, various methods of source estimation were used on reconstructed single-trial data and the source loci coherently anchored in the vicinity of the primary motor area. This method promises the possibility of a window into the intricate brain dynamics of motor control mechanisms and the cortical pathophysiology of movement disorder on a trial-by-trial basis.

Biological tissue characterization by magnetic induction spectroscopy (MIS): requirements and limitations

Magnetic induction spectroscopy (MIS) aims at the contactless measurement of the passive electrical properties (PEP) sigma, epsilon, and mu of biological tissues via magnetic fields at multiple frequencies. Whereas previous publications focus on either the conductive or the magnetic aspect of inductive measurements, this article provides a synthesis of both concepts by discussing two different applications with the same measurement system: 1) monitoring of brain edema and 2) the estimation of hepatic iron stores in certain pathologies. We derived the equations to estimate the sensitivity of MIS as a function of the PEP of biological objects. The system requirements and possible systematic errors are analyzed for a MIS-channel using a planar gradiometer (PGRAD) as detector. We studied 4 important error sources: 1) moving conductors near the PGRAD; 2) thermal drifts of the PGRAD-parameters; 3) lateral displacements of the PGRAD; and 4) phase drifts in the receiver. All errors were compared with the desirable resolution. All errors affect the detected imaginary part (mainly related to sigma) of the measured complex field much less than the real part (mainly related to epsilon and mu). Hence, the presented technique renders possible the resolution of (patho-) physiological changes of the electrical conductivity when applying highly resolving hardware and elaborate signal processing. Changes of the magnetic permeability and permittivity in biological tissues are more complicated to deal with and may require chopping techniques, e.g., periodic movement of the object.

Numerical solution of the general 3D eddy current problem for magnetic induction tomography (spectroscopy)

Magnetic induction tomography (MIT) is used for reconstructing the changes of the conductivity in a target object using alternating magnetic fields. Applications include, for example, the non-invasive monitoring of oedema in the human brain. A powerful software package has been developed which makes it possible to generate a finite element (FE) model of complex structures and to calculate the eddy currents in the object under investigation. To validate our software a model of a previously published experimental arrangement was generated. The model consists of a coaxial coil system and a conducting sphere which is moved perpendicular to the coil axis (a) in an empty space and (b) in a saline-filled cylindrical tank. The agreement of the measured and simulated data is very good when taking into consideration the systematic measurement errors in case (b). Thus the applicability of the simulation algorithm for two-compartment systems has been demonstrated even in the case of low conductivities and weak contrast. This can be considered an important step towards the solution of the inverse problem of MIT.

Sensitivity maps for low-contrast perturbations within conducting background in magnetic induction tomography

Magnetic induction tomography (MIT) is a contactless method for mapping the electrical conductivity of tissue by measuring the perturbation of an alternating magnetic field with appropriate receiver coils. Reconstruction algorithms so far suggested for biomedical applications are based on weighted backprojection, hence requiring tube-shaped zones of sensitivity between excitation coils and receiving coils, the sensitivity being essentially zero outside this 'projection beam'. This condition is met for conducting perturbations in empty space and for some special configurations of insulators in saline. In biological structures, however, perturbations with low conductivity contrast are embedded into a bulk conductor. The respective sensitivity distribution was investigated and quantified theoretically and experimentally by displacing a conducting (agar, 8 S m(-1)) and an insulating sphere within a saline tank (4 S m(-1)). In contrast to the case in the empty space the sensitivity is not confined to a tube but even increases outside the 'projection beam'. The difference can be explained by the interaction of bulk currents with the perturbing object. This effect invalidates backprojection and hence the solution of the complete inverse eddy-current problem is suggested.

Magnetic induction tomography: hardware for multi-frequency measurements in biological tissues

Magnetic induction tomography (MIT) is a contactless method for mapping the electrical conductivity of tissue. MIT is based on the perturbation of an alternating magnetic field by a conducting object. The perturbation is detected by a voltage change in a receivercoil. At physiologically interesting frequencies (10 kHz-10 MHz) and conductivities (< 2 S m(-1)) the lower limit for the relative voltage change (signal/carrier ratio = SCR) to be resolved is 10(-7)-10(-10). A new MIT hardware has been developed consisting of a coil system with planar gradiometers and a high-resolution phase detector (PD). The gradiometer together with the PD resolves an SCR of 2.5 x 10(-5) (SNR = 20 dB at 150 kHz, acquisition speed: 100 ms). The system operates between 20 and 370 kHz with the possibility of extending the range up to 1 MHz. The feasibility of measuring conductivity spectra in the beta-dispersion range of biological tissues is experimentally demonstrated. An improvement of the resolution towards SCR = 10(-7) with an SNR of > or = 20 dB at frequencies > 100 kHz is possible. On-line spectroscopy of tissue conductivity with low spatial resolution appears feasible, thus enabling applications such as non-invasive monitoring of brain oedema.