Joint multi-field T1 quantification for fast field-cycling MRI

Purpose

Recent developments in hardware design enable the use of fast field‐cycling (FFC) techniques in MRI to exploit the different relaxation rates at very low field strength, achieving novel contrast. The method opens new avenues for in vivo characterizations of pathologies but at the expense of longer acquisition times. To mitigate this, we propose a model‐based reconstruction method that fully exploits the high information redundancy offered by FFC methods.

Methods

The proposed model‐based approach uses joint spatial information from all fields by means of a Frobenius ‐ total generalized variation regularization. The algorithm was tested on brain stroke images, both simulated and acquired from FFC patients scans using an FFC spin echo sequences. The results are compared to three non‐linear least squares fits with progressively increasing complexity.

Results

The proposed method shows excellent abilities to remove noise while maintaining sharp image features with large signal‐to‐noise ratio gains at low‐field images, clearly outperforming the reference approach. Especially patient data show huge improvements in visual appearance over all fields.

Conclusion

The proposed reconstruction technique largely improves FFC image quality, further pushing this new technology toward clinical standards.

High-Field Detection of Biomarkers with Fast Field-Cycling MRI: The Example of Zinc Sensing

Many smart magnetic resonance imaging (MRI) probes provide response to a biomarker based on modulation of their rotational correlation time. The magnitude of such MRI signal changes is highly dependent on the magnetic field and the response decreases dramatically at high fields (>2 T). To overcome the loss of efficiency of responsive probes at high field, with fast-field cycling magnetic resonance imaging (FFC-MRI) we exploit field-dependent information rather than the absolute difference in the relaxation rate measured in the absence and in the presence of the biomarker at a given imaging field. We report here the application of fast field-cycling techniques combined with the use of a molecular probe for the detection of Zn2+ to achieve 166 % MRI signal enhancement at 3 T, whereas the same agent provides no detectable response using conventional MRI. This approach can be generalized to any biomarker provided the detection is based on variation of the rotational motion of the probe.

Multi-quantum quadrupole relaxation enhancement effects in 209Bi compounds

¹H spin-lattice nuclear magnetic resonance relaxation experiments have been performed for triphenylbismuth dichloride (C₁₈H₁₅BiCl₂) and phenylbismuth dichloride (C₆H₅BiCl₂) in powder. The frequency range of 20-128 MHz has been covered. Due to ¹H-²⁰⁹Bi dipole-dipole interactions, a rich set of pronounced Quadrupole Relaxation Enhancement (QRE) peaks (quadrupole peaks) has been observed. The QRE patterns for both compounds have been explained in terms of single- and double-quantum transitions of the participating nuclei. The analysis has revealed a complex, quantum-mechanical mechanism of the QRE effects. The mechanism goes far beyond the simple explanation of the existence of three quadrupole peaks for ¹⁴N reported in literature. The analysis has been supported by nuclear quadrupole resonance results that independently provided the ²⁰⁹Bi quadrupole parameters (amplitude of the quadrupole coupling constant and asymmetry parameter).

Model - free approach to quadrupole spin relaxation in solid 209Bi-aryl compounds

Nuclear Quadrupole Resonance (NQR) experiments were performed for deuterated and non-deuterated triphenylbismuth (BiPh3) to inquire into 209Bi relaxation mechanisms. The studies are motivated by the idea of exploiting Quadrupole Relaxation Enhancement (QRE) as a novel contrast mechanism for Magnetic Resonance Imaging. From this perspective relaxation features of nuclei possessing quadrupole moment (quadrupole nuclei) are of primary importance for the contrast effect. Spin-spin relaxation rates associated with the NQR lines were described in terms of the Redfield relaxation theory assuming that the relaxation is caused by fluctuations of the electric field gradient tensor at the position of the quadrupole nucleus that are described by an exponential correlation function. The description referred to as a model-free approach is an analogy of the description used for paramagnetic contrast agents. It was demonstrated that for the deuterated compound this approach captures the essential features of 209Bi relaxation, but it should not be applied for non-deuterated compounds as dipolar interactions between neighbouring protons and the quadrupole nucleus considerably contribute to the relaxation of the last one. Thus, the relaxation scenario for species containing quadrupole nuclei is fundamentally different than for paramagnetic contrast agents and this fact has to be taken into account when predicting contrast effects based on QRE.

R1 dispersion contrast at high field with fast field-cycling MRI

Contrast agents with a strong R₁ dispersion have been shown to be effective in generating target-specific contrast in MRI. The utilization of this R₁ field dependence requires the adaptation of an MRI scanner for fast field-cycling (FFC). Here, we present the first implementation and validation of FFC-MRI at a clinical field strength of 3 T. A field-cycling range of ±100 mT around the nominal B₀ field was realized by inserting an additional insert coil into an otherwise conventional MRI system. System validation was successfully performed with selected iron oxide magnetic nanoparticles and comparison to FFC-NMR relaxometry measurements. Furthermore, we show proof-of-principle R₁ dispersion imaging and demonstrate the capability of generating R₁ dispersion contrast at high field with suppressed background signal. With the presented ready-to-use hardware setup it is possible to investigate MRI contrast agents with a strong R₁ dispersion at a field strength of 3 T.

209Bi quadrupole relaxation enhancement in solids as a step towards new contrast mechanisms in magnetic resonance imaging

²⁰⁹Bi containing species have the potential to become novel contrast agents for MRI.

A cryostatic, fast scanning, wideband NQR spectrometer for the VHF range

In the search for a novel MRI contrast agent which relies on T₁ shortening due to quadrupolar interaction between Bi nuclei and protons, a fast scanning wideband system for zero-field nuclear quadrupole resonance (NQR) spectroscopy is required. Established NQR probeheads with motor-driven tune/match stages are usually bulky and slow, which can be prohibitive if it comes to Bi compounds with low SNR (excessive averaging) and long quadrupolar T₁ times. Moreover many experiments yield better results at low temperatures such as 77 K (liquid nitrogen, LN) thus requiring easy to use cryo-probeheads. In this paper we present electronically tuned wideband probeheads for bands in the frequency range 20-120 MHz which can be immersed in LN and which enable very fast explorative scans over the whole range. To this end we apply an interleaved subspectrum sampling strategy (ISS) which relies on the electronic tuning capability. The superiority of the new concept is demonstrated with an experimental scan of triphenylbismuth from 24 to 116 MHz, both at room temperature and in LN. Especially for the first transition which exhibits extremely long T₁ times (64 ms) the and low signal the new approach allows an acceleration factor by more than 100 when compared to classical methods.

Detection and Elimination of Signal Errors Due to Unintentional Movements in Biomedical Magnetic Induction Tomography Spectroscopy (MITS)

In biomedical MITS, slight unintentional movements of the patient during measurement can contaminate the aimed images to a great extent. This study deals with measurement optimization in biomedical MITS through the detection of these unpredictable movements during measurement and the elimination of the resulting movement artefacts in the images to be reconstructed after measurement. The proposed detection and elimination (D&E) methodology requires marking the surface of the object under investigation with specific electromagnetically perturbing markers during multi-frame measurements. In addition to the active marker concept already published, a new much simpler passive marker concept is presented. Besides the biological signal caused by the object, the markers will perturb the primary magnetic field inducing their own signals. The markers' signals will be used for the detection of any unwanted object movements and the signal frames corrupted thereby. The corrupted signal frames will be then excluded from image reconstruction in order to prevent any movement artefacts from being imaged with the object. In order to assess the feasibility of the developed D&E technique, different experiments followed by image reconstruction and quantitative analysis were performed. Hereof, target movements were provoked during multifrequency, multiframe measurements in the β-dispersion frequency range on a saline phantom of physiological conductivity. The phantom was marked during measurement with either a small single-turn coil, an active marker, or a small soft-ferrite plate, a passive marker. After measurement, the erroneous phantom signals were corrected according to the suggested D&E strategy, and images of the phantom before and after correction were reconstructed. The corrected signals and images were then compared to the erroneous ones on the one hand, and to other true ones gained from reference measurements wherein no target movements were provoked on the other hand. The obtained qualitative and quantitative measurement and image reconstruction results showed that the erroneous phantom signals could be accurately corrected, and the movement artefacts could be totally eliminated, verifying the applicability of the novel D&E technique in measurement optimization in biomedical MITS and supporting the proposed aspects.

Assessment of skin permeability to topically applied drugs by skin impedance and admittance

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.

An electronically tuned wideband probehead for NQR spectroscopy in the VHF range

Nuclear quadrupole resonance spectroscopy is an analytical method which allows to characterize materials which contain quadrupolar nuclei, i.e. nuclei with spin ⩾1. The measurement technology is similar to that of NMR except that no static magnetic field is necessary. In contrast to NMR, however, it is frequently necessary to scan spectra with a very large bandwidth with a span of several tens of % of the central frequency so as to localize unknown peaks. Standard NMR probeheads which are typically constructed as resonators must be tuned and matched to comparatively narrow bands and must thus be re-tuned and re-matched very frequently when scanning over a whole NQR spectrum. At low frequencies up to few MHz dedicated circuits without the need for tuning and matching have been developed, but many quadrupole nuclei have transitions in the VHF range between several tens of MHz up to several hundreds of MHz. Currently available commercial NQR probeheads employ stepper motors for setting mechanically tuneable capacitors in standard NMR resonators. These yield high quality factors (Q) and thus high SNR but are relatively large and clumsy and do not allow for fast frequency sweeps. This article presents a new concept for a NQR probehead which combines a previously published no-tune no-match wideband concept for the transmit (TX) pulse with an electronically tuneable receive (RX) part employing varactor diodes. The prototype coil provides a TX frequency range of 57MHz with a center frequency of 97.5MHz with a return loss of ⩽-15dB. During RX the resonator is tuned and matched automatically to the right frequency via control voltages which are read out from a previously generated lookup table, thus providing high SNR. The control voltages which bias the varactors settle very fast and allow for hopping to the next frequency point in the spectrum within less than 100μs. Experiments with a test sample of ZnBr2 proved the feasibility of the method.

A deterministic approach to the adapted optode placement for illumination of highly scattering tissue

A novel approach is presented for computing optode placements that are adapted to specific geometries and tissue characteristics, e.g., in optical tomography and photodynamic cancer therapy. The method is based on optimal control techniques together with a sparsity-promoting penalty that favors pointwise solutions, yielding both locations and magnitudes of light sources. In contrast to current discrete approaches, the need for specifying an initial set of candidate configurations as well as the exponential increase in complexity with the number of optodes are avoided. This is demonstrated with computational examples from photodynamic therapy.

High-performance image reconstruction in fluorescence tomography on desktop computers and graphics hardware

Image reconstruction in fluorescence optical tomography is a three-dimensional nonlinear ill-posed problem governed by a system of partial differential equations. In this paper we demonstrate that a combination of state of the art numerical algorithms and a careful hardware optimized implementation allows to solve this large-scale inverse problem in a few seconds on standard desktop PCs with modern graphics hardware. In particular, we present methods to solve not only the forward but also the non-linear inverse problem by massively parallel programming on graphics processors. A comparison of optimized CPU and GPU implementations shows that the reconstruction can be accelerated by factors of about 15 through the use of the graphics hardware without compromising the accuracy in the reconstructed images.

Phase synchronization of hemodynamic variables and respiration during mental challenge

We studied the synchronization of heart rate, blood pressure and respiration in the sympathetic and parasympathetic branches of the autonomic nervous system during a cancellation test of attention and during mental arithmetic tasks. The synchronization was quantified by the index γ, which has been adopted from the analysis of weakly coupled chaotic oscillators. We analyzed in twenty healthy women the continuous signals partitioned in low (LF, 0.04-0.15 Hz) and high (HF, 0.15-0.40 Hz) frequencies to investigate whether or not respiration is a main determinant of cardiovascular synchronization. We used surrogate data analysis to distinguish between causal relationships from those that occur by chance. The LF-components of R-R interval and blood pressure showed no synchronization with respiration, whereas synchronization between blood pressure and R-R interval exceeded that occurring by chance (p < .001). Although heart rate, blood pressure and respiratory frequency increased from rest to mental challenge, no effect of mental challenge on the synchronization of the LF-components was seen. The HF-components showed significant synchronization for all variables (p < .001). During mental challenge, synchronization between respiration and R-R interval, respiration and systolic blood pressure (SBP), as well as R-R interval and SBP decreased (p < .01), whereas under resting conditions, respiration was one of the dominant mechanisms determining heart rate variability and systolic blood pressure fluctuations. We conclude that the observed decrease of synchronization during mental challenge is not only driven by the increase in respiratory frequency but that 'top down' intervention by the control system at higher levels may play an additional role.

Anisotropic conductivity tensor imaging using magnetic induction tomography

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.

Total variation regularization for nonlinear fluorescence tomography with an augmented Lagrangian splitting approach

Fluorescence tomography is an imaging modality that seeks to reconstruct the distribution of fluorescent dyes inside a highly scattering sample from light measurements on the boundary. Using common inversion methods with L(2) penalties typically leads to smooth reconstructions, which degrades the obtainable resolution. The use of total variation (TV) regularization for the inverse model is investigated. To solve the inverse problem efficiently, an augmented Lagrange method is utilized that allows separating the Gauss-Newton minimization from the TV minimization. Results on noisy simulation data provide evidence that the reconstructed inclusions are much better localized and that their half-width measure decreases by at least 25% compared to ordinary L(2) reconstructions.

Nonlinear inversion schemes for fluorescence optical tomography

Fluorescence optical tomography is a non-invasive imaging modality that employs the absorption and re-emission of light by fluorescent dyes. The aim is to reconstruct the fluorophore distribution in a body from measurements of light intensities at the boundary. Due to the diffusive nature of light propagation in tissue, fluorescence tomography is a nonlinear and severely ill-posed problem, and some sort of regularization is required for a stable solution. In this paper we investigate reconstruction methods based on Tikhonov regularization with nonlinear penalty terms, namely total-variation regularization and a levelset-type method using a nonlinear parameterization of the unknown function. Moreover, we use the full threedimensional nonlinear forward model, which arises from the governing system of partial differential equations. We discuss the numerical realization of the regularization schemes by Newtontype iterations, present some details of the discretization by finite element methods, and outline the efficient implementation of sensitivity systems via adjoint methods. As we will demonstrate in numerical tests, the proposed nonlinear methods provide better reconstructions than standard methods based on linearized forward models and linear penalty terms. We will additionally illustrate, that the careful discretization of the methods derived on the continuous level allows to obtain reliable, mesh independent reconstruction algorithms.

Effects of Stimuli on Cardiovascular Reactivity Occurring at Regular Intervals During Mental Stress

Studies examining the direct effects of stimuli needed to perform mental stress tasks such as instructor commands at regular intervals during the mental task are limited to date. Because of the comprehensive effects of different stimuli, we studied the effect of short instructor commands occurring at regular intervals on the behavior of the cardiovascular system during two different types of tasks. Continuous beat-to-beat heart rate and blood pressure, respiration, thoracic impedance, skin conductance, and peripheral temperature were measured in 20 healthy females during a cancellation test of attention (stimuli interval of 20 s) and during mental arithmetic tasks (stimuli interval of 120 s). The transient effects of the stimuli on measures in the time domain as well as the effects of stimulus intervals on measures in the frequency domain (using spectral analysis) were examined. Instructor commands caused increases in several cardiovascular variables and in skin conductance. SBP (systolic blood pressure) and DBP (diastolic blood pressure) showed a significant stimulus response only during the mental arithmetic tasks. An effect of instructor commands at regular intervals was seen in the spectral analysis at 0.05 Hz (cancellation test of attention) and 1/120 Hz (mental arithmetic), according to the stimulus intervals of 20 s and 120 s used in these tasks. The findings suggest that even simple instructor commands given during high mental task load had a strong impact and can considerably influence measures of cardiovascular reactivity. The effects of paced stimuli should be considered when interpreting cardiovascular responses to task conditions with constant stimulus intervals.

Adaptation and focusing of optode configurations for fluorescence optical tomography by experimental design methods

Fluorescence tomography excites a fluorophore inside a sample by light sources on the surface. From boundary measurements of the fluorescent light, the distribution of the fluorophore is reconstructed. The optode placement determines the quality of the reconstructions in terms of, e.g., resolution and contrast-to-noise ratio. We address the adaptation of the measurement setup. The redundancy of the measurements is chosen as a quality criterion for the optodes and is computed from the Jacobian of the mathematical formulation of light propagation. The algorithm finds a subset with minimum redundancy in the measurements from a feasible pool of optodes. This allows biasing the design in order to favor reconstruction results inside a given region. Two different variations of the algorithm, based on geometric and arithmetic averaging, are compared. Both deliver similar optode configurations. The arithmetic averaging is slightly more stable, whereas the geometric averaging approach shows a better conditioning of the sensitivity matrix and mathematically corresponds more closely with entropy optimization. Adapted illumination and detector patterns are presented for an initial set of 96 optodes placed on a cylinder with focusing on different regions. Examples for the attenuation of fluorophore signals from regions outside the focus are given.

Reconstruction artefacts in magnetic induction tomography due to patient's movement during data acquisition

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.

Optimum receiver array design for magnetic induction tomography

Magnetic induction tomography (MIT) is an imaging modality that aims at mapping the distribution of the electrical conductivity inside the body. Eddy currents are induced in the body by magnetic induction and the resulting fields are measured by an array of receiver coils. In MIT, the location of the receivers affects the quality of the image reconstruction. In this paper, a fast deterministic algorithm was applied to obtain optimum receiver array designs for a given specific excitation. The design strategy is based on the iterative exclusion of receiver locations, which yield poor conductivity information, from the space spanning all possible locations until a feasible design is reached. The applicability of "regionally focused" MIT designs that increase the image resolution at a particular region was demonstrated. Currently used design geometries and the corresponding reconstructed images were compared to the images obtained by optimized designs. The eigenvalue analysis of the Hessian matrix showed that the algorithm tends to maintain identical conductivity information content sensed by the receivers. Although the method does not guarantee finding the optimum design globally, the results demonstrate the practical usability of this algorithm in MIT experimental designs.

Magnetic induction tomography: comparison of the image quality using different types of receivers

Magnetic induction tomography is used to image the electrical properties inside a region of interest. The systems differ in the construction of the receiver channels which can be composed of coils or gradiometers. We will compare and discuss the image quality subject to two different types of receivers, different arrangements for the exciters and receivers and different signal-to-noise ratios. In order to evaluate the image quality, the point-spread function (PSF) was determined which is used for the calculation of the resolution and the correctness of the location of a perturbation. The results show that the PSF depends on (a) the location inside the object, (b) the type of receivers and (c) the configuration used, especially the location of the receiving and excitation channels. According to this, the local resolution is changed and has the maximum near the border of the object and decreases towards the centre of the object. In addition, the evaluation of the PSF shows a dislocation with respect to the underlying point-source position.

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.

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.

Reconstruction of the shape of conductivity spectra using differential multi-frequency magnetic induction tomography

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.

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).

Solution of the inverse problem of magnetic induction tomography (MIT) with multiple objects: analysis of detectability and statistical properties with respect to the reconstructed conducting region

Magnetic induction tomography (MIT) is a technique to image the passive electrical properties (i.e. conductivity, permittivity, permeability) of biological tissues. The inverse eddy current problem is nonlinear and ill-posed, thus a Gauss-Newton one-step method in combination with four different regularization schemes is used to obtain stable solutions. Simulations with 16 excitation coils, 32 receiving coils and different spherical perturbations inside a homogeneous cylinder were computed. In order to compare the statistical properties of the reconstructed results a Monte Carlo study with a SNR of 40 dB and 20 dB was carried out. Simulated conductivity perturbations inside a homogeneous cylinder can be localized and resolved and the results prove the feasibility of difference imaging with MIT.

Direct reconstruction of tissue parameters from differential multifrequency EITin vivo

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.

Fat and Hydration Monitoring by Abdominal Bioimpedance Analysis: Data Interpretation by Hierarchical Electrical Modeling

In a previous publication, it was demonstrated that the abdominal subcutaneous fat layer thickness (SFL) is strongly correlated with the abdominal electrical impedance when measured with a transversal tetrapolar electrode arrangement. This article addresses the following questions: 1) To which extent do different abdominal compartments contribute to the impedance? 2) How does the hydration state of tissues affect the data? 3) Can hydration and fat content be assessed independently? For simulating the measured data a hierarchical electrical model was built. The abdomen was subdivided into three compartments (subcutaneous fat, muscle, mesentery). The true anatomical structure of the compartment boundaries was modeled using finite-element modeling (FEM). Each compartment is described by an electrical tissue model parameterized in physiological terms. Assuming the same percent change of the fat fraction in the mesentery and the SFL the model predicts a change of 1,24 omega/mm change of the SFL compared to 1,1 omega/mm measured. 42% of the change stem from the SFL, 56% from the mesentery and 2% from changes of fat within the muscle compartment. A 1% increase of the extracellular water in the muscle is not discernible from a 1% decrease of the SFL. The measured data reflect not only the SFL but also the visceral fat. The tetrapolar electrode arrangement allows the measurement of the abdominal fat content only if the hydration remains constant.

Bioelectrical impedance analysis-part II: utilization in clinical practice

BIA is easy, non-invasive, relatively inexpensive and can be performed in almost any subject because it is portable. Part II of these ESPEN guidelines reports results for fat-free mass (FFM), body fat (BF), body cell mass (BCM), total body water (TBW), extracellular water (ECW) and intracellular water (ICW) from various studies in healthy and ill subjects. The data suggests that BIA works well in healthy subjects and in patients with stable water and electrolytes balance with a validated BIA equation that is appropriate with regard to age, sex and race. Clinical use of BIA in subjects at extremes of BMI ranges or with abnormal hydration cannot be recommended for routine assessment of patients until further validation has proven for BIA algorithm to be accurate in such conditions. Multi-frequency- and segmental-BIA may have advantages over single-frequency BIA in these conditions, but further validation is necessary. Longitudinal follow-up of body composition by BIA is possible in subjects with BMI 16-34 kg/m(2) without abnormal hydration, but must be interpreted with caution. Further validation of BIA is necessary to understand the mechanisms for the changes observed in acute illness, altered fat/lean mass ratios, extreme heights and body shape abnormalities.

Bioelectrical impedance analysis--part I: review of principles and methods

The use of bioelectrical impedance analysis (BIA) is widespread both in healthy subjects and patients, but suffers from a lack of standardized method and quality control procedures. BIA allows the determination of the fat-free mass (FFM) and total body water (TBW) in subjects without significant fluid and electrolyte abnormalities, when using appropriate population, age or pathology-specific BIA equations and established procedures. Published BIA equations validated against a reference method in a sufficiently large number of subjects are presented and ranked according to the standard error of the estimate. The determination of changes in body cell mass (BCM), extra cellular (ECW) and intra cellular water (ICW) requires further research using a valid model that guarantees that ECW changes do not corrupt the ICW. The use of segmental-BIA, multifrequency BIA, or bioelectrical spectroscopy in altered hydration states also requires further research. ESPEN guidelines for the clinical use of BIA measurements are described in a paper to appear soon in Clinical Nutrition.

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 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.

Monitoring of lung edema using focused impedance spectroscopy: a feasibility study

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.

Sodium intake does not influence bioimpedance-derived extracellular volume loss in head-down rest

INTRODUCTION

There is disagreement regarding the impact of dietary sodium on alterations in extracellular volume during head-down bed rest (HDBR). The primary purpose of this study was to assess the effects of salt intake on extracellular volume (ECV) during HDBR.

METHODS

We performed whole-body bioimpedance spectroscopy with controlled sodium intake during 4 d of ambulation and 8 d of -6 degrees HDBR in 10 normotensive men. Each subject performed an initial 12-d familiarization run with moderate sodium (246 +/- 12 mmol x L(-1) x d(-1) excreted) during which no measurements were made. They then participated in treatment runs involving low sodium (LS: 143 +/- 10 mmol x L(-1) x d(-1) Na+ excreted) and high sodium (HS: 434 +/- 17 mmol x L(-1) x d(-1) Na+ excreted). The different treatments were separated by > or =1 mo and the order of LS and HS was balanced among the subjects. These treatments were based on controlled food and drink supplies as prepared by a dietitian. We monitored sodium output and measured aldosterone, plasma renin activity (PRA), and vasopressin. Bioimpedance was measured every second day in supine position using tetrapolar electrodes.

RESULTS

Based on exponential data fitting, we calculated an ECV decrease of 0.79 +/- 0.32 L (-5.8%; p = 0.018) in LS, and 1.21 +/- 0.31 L (-4.0%; p = 0.002) in HS during HDBR. LS and HS were not different (p > 0.1); 4 d pre-HDBR sodium adjustment produced a fall in ECV in the LS group only (-3.7%, p = 0.023). Hormone levels were not changed by HDBR. Plasma aldosterone was lower in HS (69 +/- 7 pg x ml(-1)) than in LS (180 +/- 24 pg x ml(-1)).

DISCUSSION

Our bioimpedance data confirm that low sodium intake decreases ECV in ambulatory conditions and indicate that 8 d of HDBR produce a loss of ECV of about 5% (p < 0.05). The loss did not seem to be influenced by sodium intake between approximately 3 and approximately 10 g x d(-1).