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Objective: Pharmacokinetic and pharmacodynamic studies of topically applied drugs are commonly performed by sampling of interstitial fluid with dermal open flow microperfusion and subsequent analysis of the samples. However, the reliability of results from the measured concentration-time profile of the penetrating drug suffers from highly variable skin permeability to topically applied drugs that is mainly caused by inter- and intra-subject variations of the stratum corneum. Thus, statistically significant results can only be achieved by performing high numbers of experiments. To reduce the expenditures needed for such high experiment numbers we aimed to assess the correlation between skin permeability and skin impedance/skin admittance. Approach: We performed an ex vivo drug penetration study with human skin, based on the hypothesis that inter-subject variations of the respective concentration-time profiles can be correlated with variations of the passive electrical properties of the skin. Therefore, skin impedance and skin admittance were related to the skin permeability to the model drug Clobetasol-17-proprionate. Main results: The measured low frequency skin impedance and the skin admittance correlated linearly with the drug concentration-time profiles from dermal sampling. Significance: Skin permeability can be assessed by measuring the passive electrical properties of the skin, which enables correction of skin permeability variations. This allows reduction of experiment numbers in future pharmacokinetic and pharmacodynamic studies with human skin ex vivo and in vivo and leads to diminished study costs.

Magnetic induction tomography aims to reconstruct the electrical conductivity distribution of the human body using non-contact measurements. The potential of the method has been demonstrated by various simulation studies and a number of phantom experiments. These studies have all relied on models having isotropic distributions of conductivity, although the human body has a highly heterogeneous structure with partially anisotropic properties. Therefore, whether the conventional modeling approaches used so far are appropriate for clinical applications or not is still an open question. To investigate the problem, we performed a simulation study to investigate the feasibility of (1) imaging anisotropic perturbations within an isotropic medium and (2) imaging isotropic perturbations inside a partially anisotropic background. The first is the case for the imaging of anomalies that have anisotropic characteristics and the latter is the case e.g. in lung imaging where an anisotropic skeletal muscle tissue surrounds the lungs and the rib cage. An anisotropic solver based on the singular value decomposition was used to attain conductivity tensor images to be compared with the ones obtained from isotropic solvers. The results indicate the importance of anisotropic modeling in order to obtain satisfactory reconstructions, especially for the imaging of the anisotropic anomalies, and address the resolvability of the conductivity tensor components.

Magnetic induction tomography (MIT) attempts to obtain the distribution of passive electrical properties inside the body. Eddy currents are induced in the body using an array of transmitter coils and the magnetic fields of these currents are measured by receiver coils. In clinical usage, the relative position of the coils to the body can change during data acquisition because of the expected/unexpected movements of the patient. Especially in respiration monitoring these movements will inevitably cause artefacts in the reconstructed images. In this paper, this effect was investigated for both state and frequency differential variants of MIT. It was found that a slight shift of the body in the transverse plane causes spurious perturbations on the surface. In reconstructions, this artefact on the surface propagates towards the centre in an oscillatory manner. It was observed that the movement can corrupt all the valuable information in state differential MIT, while frequency differential MIT seems more robust against movement effects. A filtering strategy is offered in order to decrease the movement artefacts in the images. To this end, monitoring of the patient's movement during data acquisition is required.

The current paper proposes a new indicator for well-balanced dehydration of patients undergoing a haemodialysis. It is based on an estimator for the extra-cellular volume and the ultrafiltration rate. The extra-cellular fluid was computed from continuous tetrapolar bio-impedance measurements taken on the lower leg in a frequency range of several kilohertz up to 500 kHz. Finite element simulations on different leg models with anisotropic conductivities calculated with Cole models were carried out in order to incorporate the significant anisotropy of human tissue into the estimation process. The indicator was tested on measurement data gathered from 25 persons during 150 haemodialysis sessions. Its performance was determined by computing ROC curves. Results of the data analysis are reported.

The basic purpose of electrical impedance tomography (EIT) is the reconstruction of conductivity distributions. While multifrequency measurements are of common use, the majority of reconstructed images are still conductivity distributions from one single frequency. More interesting than conductivities at each frequency are electrical tissue parameters, which describe the frequency-dependent conductivity changes of tissue. These parameters give information about physiological or electrical properties of tissues. By using this spectral information, a classification of different tissue types is possible. To get a distribution of tissue parameters, usually a posterior fitting of a tissue model to the conductivity spectra obtained with classical reconstruction algorithms at various frequencies is used. In this work, a single-step reconstruction algorithm for differential imaging was developed for the direct estimation of Cole parameters. This method is termed differential parametric reconstruction. The Cole model was used as the underlying tissue model, where only the relative changes of the two conductivity parameters sigma(0) and sigma(infinity) were reconstructed and the other two parameters of the model which are less identifiable were set to constant values. The reconstruction algorithm was tested with simulated noisy datasets and real measurement data from EIT measurements on the human thorax. These measurements were taken from healthy subjects and from patients with a serious lung injury. The new method yields a good image quality and higher robustness against noise compared to conventional reconstruction methods.

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.

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.

Currently only ionizing or invasive methods are used in clinical applications for the monitoring of extracellular lung water. Alternatively a method called focused conductivity spectroscopy (FCS) is suggested, which aims at reconstructing a pulmonary edema index (PEIX) by measuring the electrical conductivity of the region of interest (ROI) at several frequencies. In contrast to electrical impedance tomography (EIT) a minimum number of strategically placed electrodes is used. The goals of this study were the analysis of the sensitivity for the PEIX, an estimate of the optimal electrode configuration and the determination of the required frequencies. In order to calculate the solution of the FCS forward problem a realistic 3D model of a human torso was developed containing both lungs, the heart, the liver and the thorax musculature. The bioelectrical properties for each compartment were described with appropriate tissue models which relate the conductivity spectra to physiological parameters. The PEIX was defined as the interstitial volume fraction of the alveolar septa. Furthermore the model includes 48 electrodes subdivided into three layers. The optimal electrode configuration was selected by minimizing the number of electrodes, among certain subsets of these electrodes. The analysis shows that eight to ten electrodes and six frequencies are theoretically sufficient to obtain a coefficient of variation.

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 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.

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.

A major drawback of electrical impedance tomography is the poor quality of the conductivity images, i.e., the low spatial resolution as well as large errors in the reconstructed conductivity values. The main reason is the necessity for regularization of the ill-conditioned inverse problem which results in excessive spatial low-pass filtering. A novel regularization method (SMORR (spectral modelling regularized reconstructor)) is proposed, which is based on the inclusion of spectral a priori information in the form of appropriate tissue models (e.g. Cole models). This approach reduces the ill-posedness of the inverse problem, when multifrequency data are available. An additional advantage is the direct reconstruction of the (physiological) tissue parameters of interest instead of the conductivities. SMORR was compared with posterior fitting of a Cole model to the conductivity spectra obtained with a classical iterative reconstruction scheme at various frequencies. SMORR performed significantly better than the reference method concerning robustness against noise in the data.

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.

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.

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 ofor = 20 dB at frequencies100 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.

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.

Magnetic induction tomography (MIT) has been suggested by several groups for the contact-less mapping of the passive electrical properties of tissues via AC magnetic fields in the frequency range between several tens of kHz and several tens of MHz. Multifrequency MIT as an analog to multifrequency EIT has been tried and first image reconstructions have been demonstrated with phantoms. MIT appears to yield comparable images to EIT but offers the advantage of being non-contacting. In the beta-dispersion range of most tissues the method is challenging because the signals are very small and buried in noise. In order to minimize drifts and systematic errors fast data acquisition is therefore pivotal. This paper presents a method for single-shot MIT which allows us to acquire the data for a multifrequency image with an analog bandwidth of 50 kHz-1.5 MHz which covers a good part of the beta-dispersion of many tissues. The transmit (TX) coils are simultaneously driven by individual power amplifiers with a multisinus pattern with up to 3 A(pp). The amplifiers are configured as current sources so as not to perturb the excitation fields by inappropriately terminated coils. The separation of the different TX channels after reception is achieved by splitting up the carrier frequencies into individual subcarriers with a narrow spacing of at most 300 Hz. In this way every TX coil is identifiable by its own subcarrier but the whole excitation band is contained within a few kHz. The real and imaginary parts of the received signals are extracted efficiently with FFT. The system noise and the sources for low-frequency perturbations are analyzed and characterized.

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.

Magnetic induction tomography (MIT) of biological tissue is used for the reconstruction of the complex conductivity distribution kappa 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.

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).

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.

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.