Hermann Scharfetter

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.

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) /spl sigma/, /spl epsiv/, and /spl 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 /spl sigma/) of the measured complex field much less than the real part (mainly related to /spl epsiv/ and /spl 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.

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.

Detection of brain oedema using magnetic induction tomography: a feasibility study of the likely sensitivity and detectability

The detection and continuous monitoring of brain oedema is of particular interest in clinical applications because existing methods (invasive measurement of the intracranial pressure) may cause considerable distress for the patients. A new non-invasive method for continuous monitoring of an oedema promises the use of multi-frequency magnetic induction tomography (MIT). MIT is an imaging method for reconstructing the changes of the conductivity deltakappa in a target object. The sensitivity of a single MIT-channel to a spherical oedematous region was analysed with a realistic model of the human brain. The model considers the cerebrospinal fluid around the brain, the grey matter, the white matter, the ventricle system and an oedema (spherical perturbation). Sensitivity maps were generated for different sizes and positions of the oedema when using a coaxial coil system. The maps show minimum sensitivity along the coil axis, and increasing values when moving the perturbation towards the brain surface. Parallel to the coil axis, however, the sensitivity does not vary significantly. When assuming a standard deviation of 10(-7) for the relative voltage change due to the systems noise, a centrally placed oedema with a conductivity contrast of 2 with respect to the background and a radius of 20 mm can be detected at 100 kHz. At higher frequencies the sensitivity increases considerably, thus suggesting the capability of multi-frequency MIT to detect cerebral oedema.

A model of artefacts produced by stray capacitance during whole body or segmental bioimpedance spectroscopy

We have developed a novel model for the simulation of artefacts which are produced by stray capacitance during bioimpedance spectroscopy. We focused on whole body and segmental measurements in the frequency range 5-1000 kHz. The current source was assumed to by asymmetric with respect to ground as is the case for many commercial devices. We considered the following stray pathways: 1, cable capacitance; 2, capacitance between neighbouring electrode leads; 3. capacitance between different body segments and earth; 4, capacitance between signal ground of the device and earth. According to our results the pathways 3 and 4 cause a significant spurious dispersion in the measured impedance spectra at frequencies > 500 kHz. During segmental measurements the spectra have been found to be sensitive to an interchange of the electrode cable pairs. The sensitivity was also observed in vivo and is due to asymmetry of the potential distribution along the segment with respect to earth. In contrast to previously published approaches, our model renders possible the simulation of this effect. However, it is unable to fully explain the deviations of in vivo measured impedance spectra from a single Cole circle. We postulate that the remaining deviations are due to a physiologically caused superposition of two dispersions from two different tissues.

Assessing abdominal fatness with local bioimpedance analysis: basics and experimental findings.

OBJECTIVE: Abdominal fat is of major importance in terms of body fat distribution but is poorly reflected in conventional body impedance measurements. We developed a new technique for assessing the abdominal subcutaneous fat layer thickness (SFL) with single-frequency determination of the electrical impedance across the waist (SAI).SUBJECTS AND MEASUREMENTS: The method uses a tetrapolar arrangement of surface electrodes which are placed symmetrically to the umbilicus in a plane perpendicular to the body axis. Twenty-four test subjects (12 male, 12 female) underwent SAI and abdominal magnetic resonance imaging (MRI). The SFL below the sensing electrodes was determined from MRI and correlated with the SAI data at four different frequencies (5, 20, 50 and 204 kHz).RESULTS: A highly significant linear correlation (r2=0.99) between SFL and SAI over a wide range of the abdominal SFL was found. Separate regression models for female and male subjects did not differ significantly, except at 50 kHz.CONCLUSION: SAI represents a good predictor of the SFL and provides an excellent tool for the assessment of central obesity.International Journal of Obesity (2001) 25, 502–511

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

We evaluated analytically and experimentally the performance of a planar gradiometer as a sensing element in a system for magnetic induction tomography. A system using an excitation coil and a planar gradiometer was compared against a system with two coils. We constructed one excitation coil, two different sensing elements and a high-resolution phase detector. The first sensor was a PCB square spiral coil with seven turns. The second sensor was a PCB planar gradiometer with two opposite square spirals of seven turns, with a distance between centres of 8 cm. Theoretical sensitivity maps were derived from basic equations and compared with experimental data obtained at 150 kHz. The experimental sensitivity maps were obtained measuring the perturbation produced by a brass sphere of 12 mm in empty space. The advantage of using a gradiometer is that it can be adjusted to give a minimum signal for homogeneous objects, while increasing the sensitivity to local perturbations of the conductivity. Results show that a system using a planar gradiometer as detector has less demanding requirements for the electronic system than a system using simple coils.

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.

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.

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 amplifiers 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).