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.

Fast calculation of the sensitivity matrix in magnetic induction tomography by tetrahedral edge finite elements and the reciprocity theorem

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.

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 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.

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.

Direct estimation of Cole parameters in multifrequency EIT using a regularized Gauss-Newton 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.

Fluid volume changes and LBNP response after simulated weightlessness with varied oral sodium supply

There is evidence on body fluid volume effects of head-down tilt bed rest and altered oral sodium supply, but the combined impact of both has not been investigated in detail. We therefore studied circulatory adaptation to 8 days -6 degrees head down bed rest (HDBR) with different levels (-140 to -430 mM/d) of oral sodium load (SL). We expected decreased extracellular volume and increased aldosterone and PRA levels with low sodium load, and hypothesized that these effects get exaggerated with additional HDBR, also influencing lower body suction (LBNP) responses. Variations in sodium status seem to influence plasma but not interstitial volume, confirming recent results of another group who used different experimental conditions.

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.

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.

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.

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.

Kinetics of the metal cations magnesium, calcium, copper, zinc, strontium, barium, and lead in chronic hemodialysis patients

BACKGROUND

Dialysis patients are at risk of developing trace element imbalances. To further elucidate the origin of these potential trace element imbalances, plasma and dialysis fluids concentrations of the elements barium (Ba), calcium (Ca), copper (Cu), lead (Pb), magnesium (Mg), strontium (Sr) and zinc (Zn) of seven maintenance dialysis patients were investigated.

PATIENTS AND METHODS

In each hemodialysis session 10 to 15 samples of each, whole blood and dialysis liquid before and after passing the artificial kidney were collected. Concentrations of elements were determined by inductively coupled plasma mass spectrometry following strict quality control schemes to guarantee the accuracy and precision of the results.

RESULTS

Plasma concentrations of Cu and Zn continuously increased during hemodialysis. Plasma Cu remained within the reference range for healthy adults, whereas plasma Zn was always at or below the reference range in our patients. The behavior of Ca and Sr exhibited extraordinarily strong similarities both in plasma and dialysis liquids, although concentrations of Sr are approximately 2000 times lower. Plasma Ca and Sr were at or above the upper level of the reference range. Plasma Mg concentrations decreased during clinical treatment, but were at the end of dialysis still more than 50% higher than the high end of the reference range. Although concentrations of Ba in dialysis fluids were approximately 10 times lower than in plasma, plasma Ba concentrations (approximately 23 microg/l) were significantly elevated compared to plasma Ba of healthy adults. Initial concentrations of Pb in plasma (0.74 microg/l) were increased by approximately 15% during the clinical treatment and were always higher than the high limit of the reference range. Dialysis liquids had approximately the same Pb concentrations (0.5 to 1.3 microg/l) as found in the plasma of our patients but with higher concentrations at the inlet of the dialyzer.

CONCLUSION

This study could give an insight into the kinetics of trace element concentrations during dialysis, the clinical relevance of which needs to be further elucidated.

Exchange of alkali trace elements in hemodialysis Patients: a comparison with Na(+) and K(+)

BACKGROUND

In the past, nephrologists have been troubled by electrolyte disturbances and consequently focused their attention on the importance of maintaining the concentrations of electrolytes within the normal range. However, information about the potential role of trace elements in chronic renal failure is scarce.

METHODS

During hemodialysis sessions, the concentrations of the five alkali metal cations lithium (Li), sodium (Na), potassium (K), rubidium (Rb), and cesium (Cs) have been determined in plasma and dialysis fluids of chronic hemodialysis patients by inductively coupled plasma mass spectrometry (Li, Rb, Cs) and by ion-sensitive electrodes (Na, K). Strict quality control schemes were applied to all analytical procedures to ensure accuracy and precision of the results.

RESULTS

The plasma concentrations of the elements Li, Cs, Rb, and K distinctly decreased to 29, 50, 69, and 71%, respectively, of their initial values during hemodialysis. Simultaneously, the concentrations of these elements in dialysis fluids at the outlet of the dialyzer increased approximately 13-fold for Rb, 11-fold for Li, 3-fold for Cs, and 2-fold for K as compared with the inlet values. The concentrations of Na in plasma and dialysis fluids were almost identical and did not change during hemodialysis.

CONCLUSIONS

Li, Rb, and Cs were depleted in hemodialysis patients, although the plasma concentrations of these trace elements still remained within the reference ranges for healthy adults. Consequently, further studies are needed to elucidate the clinical importance and long-term effects of these trace element imbalances - for example, CNS disturbances associated with diminished concentrations of Rb - in hemodialysis patients.

Inductively coupled wideband transceiver for bioimpedance spectroscopy (IBIS)

Most measurement devices for bioimpedance spectroscopy are coupled to the measured object (tissue) via electrodes. At frequencies > 500 kHz, they suffer from artifacts due to stray capacitances between electrode leads as well as between the ground and object. The noninvasive measurement of the brain conductivity is hardly possible with surface electrodes. These disadvantages can be obviated by inductive coupling. The aim of this work was the development of a wideband transceiver for inductive impedance spectroscopy. In order to define its specifications, a feasibility study has been carried out with a simulation model for three different coil systems above a homogeneous conducting plate. According to simulation results, all systems render it possible to resolve conductivity changes down to 10(-3) (omega m)-1 at frequencies > 50 kHz. The transceiver electronics must then provide a resolution of > or = 1 microV and an excitation current of up to 1 A. The realized receiver matches these specifications with an S/N ratio of 22 dB at 1 microV in the frequency range of 50 kHz to 5 MHz.

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.

Effect of postural changes on the reliability of volume estimations from bioimpedance spectroscopy data

Bioimpedance spectroscopy (BIS) has been suggested for the assessment of fluid shifts between intracellular (ICV) and extracellular volume (ECV) during dialysis. The electrical tissue parameters are estimated by fitting a Cole-Cole model to the impedance data. Those parameters are used for the calculation of ICV and ECV with a fluid distribution model (FDM). We investigated whether postural changes cause artifacts in the volume data measured with a commercial BIS system. This is of importance at the beginning of dialysis, when the patient lies down for treatment. Volume estimations were performed during tilt table experiments with 11 healthy volunteers. Impedance spectra (5 to 500 kHz) were recorded for the total body as well as for body segments (leg and arm) during three phases: (1) 30 minutes resting in a supine position after standing; (2) 30 minutes 70 degrees head up tilt; and (3) a 30-minute resting period in a supine position. ECV and ICV were estimated with a commercially utilized FDM which is based on Hanai's mixture theory. A monoexponential function was fitted to the data for extracting the time constants and the extrapolated steady state values of the volume changes. The ECV and ICV data changed significantly during all three periods, that is, a steady state could not be reached within 30 minutes. During phase 1 the ECV decreased by 1.8 +/- 0.7%, in the tilt phase it increased by 3.8 +/- 1.1%, and in phase 3 it decreased again by 2.9 +/- 1%. The ICV increased by 3.6 +/- 2.4% during phase 1 and decreased by 6.8 +/- 5.1% during tilting; in phase 3 it increased by 4.6 +/- 1.7%. The time constants were 36.4 +/- 12.7 minutes (ECV) and 10.8 +/- 5.4 minutes (ICV) during phase 3. Segmental measurements revealed that the legs contribute significantly to the measured volume changes. The absolute volume changes in ICV and ECV differed significantly in all phases, and the same was found for the time constants during phases 1 and 3. From this discrepancy it is concluded that the measured volume changes are artifacts that are caused by extracellular fluid redistribution. Furthermore, it appears unlikely that the measured fluid shifts actually occur between ECV and ICV in the absence of osmotic changes in the body fluids. The validity of the method for a reliable assessment of volume changes during dialysis appears questionable, as dialysis-induced volume changes lie in the same range as the orthostatically-induced spurious volume changes.

Influence of ionic shifts during dialysis on volume estimations with multifrequency impedance analysis

During dialysis the ion concentrations in many body fluids change significantly. The influence of these changes on the accuracy of volume measurements with bioimpedance spectroscopy is investigated by the following procedure: Plasma ion concentrations and impedance spectra (5-500 kHz) are measured during six standard haemodialyses. Intracellular ion concentrations are estimated using a multi-compartment model. Intra- (ICV) and extracellular (ECV) volumes are calculated using a fluid distribution model (FDM) based on Hanai's mixture theory. The input variables of the FDM are intra- and extracellular resistance data that have been fitted from impedance spectra with a Cole-Cole model. Resistivity changes (RCs) due to concentration changes of Na+, K+, Cl-, HCO3- and unspecified intracellular ions are estimated. The FDM is corrected for the RCs. Corrected ICVs and ECVs are calculated and compared with uncorrected values. The range of relative RCs between the start and end of the dialyses is -3.2% to 1.4% in the ECV and -3.7% to 1.7% in the ICV. From the RCs, volume estimation errors of -1.0% to 1.9% (ECV) and -1.2% to 2.1% (ICV) relative to the initial values have been calculated. At the end of dialysis, the percentage of the error with respect to the volume change is < 15% for the ECV but > 20% for the ICV. Consequently, a correction of the FDM for RCs is necessary to obtain more reliable ICV data.

Dynamical control of the dialysis process. Part II: An improved algorithm for the solution of a tracking problem

An efficient algorithm for the optimization of process parameters during dialysis has been developed. By solving a tracking-problem for prescribed time courses of distinguished variables, it is possible to compute optimal concentrations of electrolytes in dialysate as well as an optimal rate of ultrafiltration. These variables are indirectly influencing the status of the patient and can be directly modelled. They are describing the important exchange processes between blood and dialysate as well as between the different distribution spaces within the patient during dialysis. Their time courses are determined by an individually identifiable patient model. The tracking problem was treated as a dynamic optimization problem, and a continuous descent procedure which is usually employed for solving unconstrained static optimization problems has been adapted in such a manner that it is applicable for the solution of this problem. The used method is characterized by its simple mode of application, short solution time and moderate storage need. Especially in cases of contradictional requirements for desired time courses of model outputs the used optimization method performs well.

Dynamical control of the dialysis process. Part I: Structural considerations and first mathematical approach

Individual optimization of the dialysis process requires the (open-loop or closed-loop) control of many different variables, e.g. plasma ion concentrations, acid base state, volemic state and hemodynamic quantities. For this purpose a general concept for multiple-input-multiple-output (MIMO) control of the dialysis process is presented. The controlled variables have been differentiated into variables which can be modeled mechanistically (primary controlled variables, PCVs) and (hemodynamic) variables for which no mechanistic model has been developed up to now (secondary controlled variables, SCVs). Accordingly the controller is decomposed into two stages. Stage 1 contains an expert system which links the PCVs to the SCVs and provides the generation of optimal profiles for the PCVs with respect to maximum hemodynamic stability of the patient. Stage 2 is a tracking controller for the PCVs. An algorithm for the multidimensional tracking problem at stage 2 has been developed. It can be used for open-loop and future closed-loop control. The algorithm has been tested for 4 controlled (plasma Na+, plasma K+, plasma volume and ratio between intra- and extracellular volume) and 3 control variables (dialysate Na+, dialysate K+, ultrafiltration rate) up to now. It renders possible the exact tracking of the prescribed trajectories as long as all points are reachable under consideration of all physical and physiological boundary conditions. If they are not, appropriate weighting of the conflicting optimization goals must be applied. An extension towards more than 4 controlled variables is possible on principle. Main advantages of the method are its mathematical simplicity and the applicability of standard optimization subroutines.