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.

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 system's 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.

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.

Abstract-Magnetic induction tomography (MIT) is a lowresolution 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 GaussNewton 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.

Magnetic induction tomography of biological tissue is used to reconstruct the changes in the complex conductivity distribution by measuring the perturbation of an alternating primary magnetic field. To facilitate the sensitivity analysis and the solution of the inverse problem a fast calculation of the sensitivity matrix, i.e. the Jacobian matrix, which maps the changes of the conductivity distribution onto the changes of the voltage induced in a receiver coil, is needed. The use of finite differences to determine the entries of the sensitivity matrix does not represent a feasible solution because of the high computational costs of the basic eddy current problem. Therefore, the reciprocity theorem was exploited. The basic eddy current problem was simulated by the finite element method using symmetric tetrahedral edge elements of second order. To test the method various simulations were carried out and discussed.

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Magnetic induction tomography (MIT) of biological tissue is used for the reconstruction of the complex conductivity distribution κ inside the object under investigation. It is based on the perturbation of an alternating magnetic field caused by the object and can be used in all applications of electrical impedance tomography (EIT) such as functional lung monitoring and assessment of tissue fluids. In contrast to EIT, MIT does not require electrodes and magnetic fields can also penetrate non-conducting barriers such as the skull. As in EIT, the reconstruction of absolute conductivity values is very difficult because of the method's sensitivity to numerical errors and noise. To overcome this problem, image reconstruction in EIT is often done differentially. Analogously, this concept has been adopted for MIT. Two different methods for differential imaging are applicable. The first one is state-differential, for example when the conductivity change between inspiration and expiration in the lung regions is being detected. The second one is frequency-differential, which is of high interest in motionless organs like the brain, where a state-differential method cannot be applied. An equation for frequency-differential MIT was derived taking into consideration the frequency dependence of the sensitivity matrix. This formula is valid if we can assume that only small conductivity changes occur. In this way, the non-linear inverse problem of MIT can be approximated by a linear one (depending only on the frequency), similar to in EIT. Keeping this limitation in mind, the conductivity changes between one or more reference frequencies and several measurement frequencies were reconstructed, yielding normalized conductivity spectra. Due to the differential character of the method, these spectra do not provide absolute conductivities but preserve the shape of the spectrum. The validity of the method was tested with artificial data generated with a spherical perturbation within a conducting cylinder as well as for real measurement data. The measurement data were obtained from a potato immersed in saline. The resulting spectra were compared with reference measurements and the preservation of the shape of the spectra was analyzed.

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