Parametric modelling for electrical impedance spectroscopy system

The Research Progress of Electrical Impedance Tomography for Lung Monitoring

Medical imaging can intuitively show people the internal structure, morphological information, and organ functions of the organism, which is one of the most important inspection methods in clinical medical diagnosis. Currently used medical imaging methods can only be applied to some diagnostic occasions after qualitative lesions have been generated, and the general imaging technology is usually accompanied by radiation and other conditions. However, electrical impedance tomography has the advantages of being noninvasive and non-radiative. EIT (Electrical Impedance Tomography) is also widely used in the early diagnosis and treatment of some diseases because of these advantages. At present, EIT is relatively mature and more and more image reconstruction algorithms are used to improve imaging resolution. Hardware technology is also developing rapidly, and the accuracy of data collection and processing is continuously improving. In terms of clinical application, EIT has also been used for pathological treatment of lungs, the brain, and the bladder. In the future, EIT has a good application prospect in the medical field, which can meet the needs of real-time, long-term monitoring and early diagnosis. Aiming at the application of EIT in the treatment of lung pathology, this article reviews the research progress of EIT, image reconstruction algorithms, hardware system design, and clinical applications used in the treatment of lung diseases. Through the research and introduction of several core components of EIT technology, it clarifies the characteristics of EIT system complexity and its solutions, provides research ideas for subsequent research, and once again verifies the broad development prospects of EIT technology in the future.

A novel method for estimating the fractional Cole impedance model using single-frequency DC-biased sinusoidal excitation

OBJECTIVE

The Cole model is a widely used fractional circuit model in electrical bioimpedance applications for evaluating the content and status of biological tissues and fluids. Existing methods for estimating the Cole impedance parameters are often based on multi-frequency data obtained from stepped-sine measurements fitted using a complex non-linear least square (CNLS) algorithm. Newly emerged numerical methods from the magnitude of electrical bio-impedance data-only do not need CNLS fitting, but they still require multi-frequency stepped-sine data. This study proposes a novel approach to estimating the Cole impedance parameters that combines a numerical and time-domain fitting method based on a single-frequency DC-biased sinusoidal current excitation.

APPROACH

First, the transient and steady-state voltage response along with the current excitation are acquired in electrical bio-impedance measurement. From the sampled data, a numerical method is applied to provide the initial estimation of the Cole impedance parameters, which are then used in a time-domain iterative fitting algorithm.

RESULTS

The accuracy of the algorithm proposed is tested with noisy electrical bio-impedance simulations. The maximum relative error of the estimated Cole impedance parameters is 1% considering 2% (34 dB) additive Gaussian noise. Experimental measurements performed on a 2R-1C circuit and some fruit samples show a mean difference less than 1% and 5% respectively compared to the Cole impedance parameters estimated from a commercial electrical bio-impedance analyzer performing stepped-sine measurements and CNLS fitting.

SIGNIFICANCE

This is the first method that allows estimating the Cole impedance parameters from single-frequency electrical bio-impedance data. The approach presented could find broad use in many applications, including single-frequency body impedance analysis.

Numerical estimation of Fricke-Morse impedance model parameters using single-frequency sinusoidal excitation

OBJECTIVE

The Fricke-Morse impedance model is widely used in bioelectrical impedance analysis (BIA), which is usually fitted by multi-frequency electrical impedance data. Here, we propose a novel numerical method for estimating the model parameters using single-frequency sinusoidal excitation.

APPROACH

A single-frequency sinusoidal signal is used as the current excitation, from which the initial transient, the steady-state and the ending transient voltage responses along with the current excitation are recorded. The model parameters can be then estimated with numerical calculations from the acquired signals.

MAIN RESULTS

Simulation and experimental measurements are verified on a 2R1C circuit by using a 50 kHz sinusoidal current excitation. The results show that the maximum relative errors of the estimated model parameters are  <1% in simulation with 2% noise and  <2% in experimental measurement.

SIGNIFICANCE

The proposed method could extend the applications of wideband BIA by using single-frequency excitation, rather than multi-frequency excitation as is done today.

Nonparametric dynamical model of cardiorespiratory responses at the onset and offset of treadmill exercises

This paper applies a nonparametric modelling method with kernel-based regularization to estimate the carbon dioxide production during jogging exercises. The kernel selection and regularization strategies have been discussed; several commonly used kernels are compared regarding the goodness-of-fit, sensitivity, and stability. Based on that, the most appropriate kernel is then selected for the construction of the regularization term. Both the onset and offset of the jogging exercises are investigated. We compare the identified nonparametric models, which include both impulse response models and step response models for the two periods, as well as the relationship between oxygen consumption and carbon dioxide production. The result statistically indicates that the steady-state gain of the carbon dioxide production in the onset of exercise is bigger than that in the offset while the response time of both onset and offset are similar. Compared with oxygen consumption, the response speed of carbon dioxide production is slightly slower in both onset and offset period while its steady-state gains are similar for both periods. The effectiveness of the kernel-based method for the dynamic modelling of cardiorespiratory response to exercise is also well demonstrated. Graphical Abstract Comparison between VO₂ and VCO₂ during onset and offset of exercise.

Influence of electrode mismatch on Cole parameter estimation from total right side electrical bioimpedance spectroscopy measurements

Applications based on measurements of Electrical Bioimpedance (EBI) spectroscopy analysis, like assessment of body composition, have proliferated in the past years. Currently Body Composition Assessment (BCA) based in Bioimpedance Spectroscopy (BIS) analysis relays on an accurate estimation of the Cole parameters R(0) and R(∞). A recent study by Bogonez-Franco et al. has proposed electrode mismatch as source of remarkable artefacts in BIS measurements. Using Total Right Side BIS measurements from the aforementioned study, this work has focused on the influence of electrode mismatch on the estimation of R(0) and R(∞) using the Non-Linear Least Square curve fitting technique on the modulus of the impedance. The results show that electrode mismatch on the voltage sensing electrodes produces an overestimation of the impedance spectrum leading to a wrong estimation of the parameters R(0) and R(∞), and consequently obtaining values around 4% larger that the values obtained from BIS without electrode mismatch. The specific key factors behind electrode mismatch or its influence on the analysis of single and spectroscopy measurements have not been investigated yet, no compensation or correction technique is available to overcome the deviation produced on the EBI measurement. Since textile-enabled EBI applications using dry textrodes, i.e. textile electrodes with dry skin-electrode interfaces and potentially large values of electrode polarization impedance are more prone to produce electrode mismatch, the lack of a correction or compensation technique might hinder the proliferation of textile-enabled EBI applications for personalized healthcare monitoring.

Some early results related to electrical impedance of normal and abnormal gastric tissue

Gastric cancer is the fourth most common cancer and most patients with gastric cancer are being diagnosed in advanced stages of the disease so they do not gain any survival chance from conventional surgical, chemotherapeutic or radiotherapeutic methods. These are relatively high cost procedures in terms of both time and money. This study considers the introduction of a novel minimally invasive diagnostic technique which shows the relationship between histopathology and the electrical impedance spectrum in the human stomach. In this study, 4 electrode technique was used to differentiate tissues from each other using Tabriz Mark 1 electrical impedance system (30 different frequencies in the range of 2 kHz to 1 MHz). A total of 97 points from 45 patients were studied in terms of their biopsy reports matching to the electrical impedance measurements (in vivo). After impedance measurements and applying calibration factors, a non-parametric statistical technique, the Kruskal-Wallis test was used to evaluate the difference among the groups. According to the calculation of respective data using this spectroscopy system, the resistivity of the normal group was higher than that of the benign group, and the resistivity of these groups were higher than that of the malignant group at frequencies between 470 kHz and 1 MHz (P < 0.05). In these frequencies, the impedivity of the dysplastic tissue was significantly lower than that of the other groups (P < 0.05). Also, Cole equation fitting procedure was used to generate a scatter plot of the malignant and benign points: it shows in general, benign points had higher values of R than the malignant points. Therefore, electrical impedance spectroscopy can be a useful technique to characterize the stomach tissue.

Two-dimensional impedance imaging of cell migration and epithelial stratification

We present a miniaturized impedance imaging system, developed for 2D imaging of cell and tissue culture. The system is based on 16 microelectrodes (5 microm x 4 mm). An equivalent circuit for four-point (tetrapolar) impedance spectra was developed and validated. The system uses an Agilent 4294A impedance analyser combined with a front-end amplifier for the impedance measurements. Human epithelial stem cells (YF 29) were grown on the device surface. Cell migration speeds of 300 nm min(-1) following a "scratch" wound closure assay could be established. Using a commercial software developed for geophysical prospecting, we could generate impedance tomography images at 10 kHz revealing cell migration, increase of epithelial thickness and changes in tissue resistivity over a time course of several days.

Accuracy of an optically isolated tetra-polar impedance measurement system

Accurate electrical transfer impedance measurement at the high frequencies (> 1 MHz) required to characterise blood and intracellular structures is very difficult, owing to stray capacitances between lead wires. To solve this problem, an optically isolated measurement system has been developed using a phase-locked-loop technique for synchronisation between current injection (drive) and voltage measurement (receive) circuits. The synchronisation error between drive and receive circuits was less than 1 ns. The accuracy and reproducibility of the developed system was examined using a tissue equivalent Cole model consisting of two resistors and one capacitor. The absolute value Z and phase shift theta in impedance of the Cole model was measured at 1.25 MHz by both an LCR meter and the isolated measurement system. The difference between the values measured by the isolated measurement system and those measured by the LCR meter was less than 0.27omega (2.9%) in Z and 0.79 degree in theta. The standard deviation was less than 0.09 omega in Z and 0.60 degree in theta.

Cole equation modelling to measurements made using an impulse driven transfer impedance system

Electrical impedance measurements are used to obtain information about a subject, tissue sample or tissue model under test. There are several ways of obtaining these impedance data and thereafter analysing the data to obtain relevant parameters. This paper shows how a completely isolated drive and receive system using current pulses, as opposed to sine waves, achieves good fitted results with resistor-capacitor Cole phantoms.

Algorithms for parametric images in MEIT systems

In this work we show the algorithms developed to extract the Cole parameters from multi-frequency EIT. With these parameters it is possible to obtain information about various different tissues and their pathologies. The algorithms developed obtain the Cole-model parameters from the real and imaginary parts of impedance, or using only the real part, without problems of convergence. A study of the influence of noise is performed with simulations. We find a correct solution in all cases with signal to noise ratio in the data higher than 40 dB. Finally, we show parametric images of the human abdomen obtained with these algorithms.

A comparison of neonatal and adult lung impedances derived from EIT images

An objective method of extracting respiratory data from lung images is presented, together with a technique for automatically generating regions of interest delineating the anterior and posterior regions of the lungs. The method is used to extract data on the change in lung impedance with frequency, and on calculated Cole parameters, from 19 normal neonates (gestational age 32 to 42 weeks) and 8 normal adults (age 21 to 82 years). A comparison of the impedance properties of neonatal and adult lungs was made. The variation of lung impedance with frequency in neonates, as derived from EIT images, is significantly different from that found for adults. The implications for a model of the electrical impedance of lung tissue are discussed.

Selection of measurement frequencies for optimal extraction of tissue impedance model parameters

The results are presented of a study performed to determine the measurement frequencies that provide optimal extraction of tissue impedance model parameters from in vivo measured electrical impedance spectra. Measurement frequency sets that are logarithmic and quasi-linear, and frequency sets that produce angularly equidistant points on the Nyquist loci are used to test the parametric fitting algorithm that calculates R0, R infinity, alpha and tau tissue parameters from complex impedance spectra. Simulated data, calculated in the presence of < or = 5% measurement noise, and in vivo experiments indicate that the quality of the fitted parameters depends upon the selection of measurement frequencies. The results show that, if measurements are performed with a system that has a realistic measurement bandwidth, then, for the best estimation of: R0, the measurement frequencies should include the decade from 100 Hz-1 kHz; R infinity, the algorithm should not include frequencies under 1 kHz; alpha and tau, the measurement frequencies should be equidistantly spaced on the Nyquist locus.

Real-time extraction of tissue impedance model parameters for electrical impedance spectrometer

This paper presents a new algorithm for real-time extraction of tissue electrical impedance model parameters from in vivo electrical impedance spectroscopic measurements. This algorithm was developed as a part of a system for muscle tissue ischemia measurements using electrical impedance spectroscopy. An iterative least square fitting method, biased with a priori knowledge of the impedance model was developed. It simultaneously uses both the real and imaginary impedance spectra to calculate tissue parameters R0, R infinity, alpha and tau. The algorithm was tested with simulated data, and during real-time in vivo ischemia experiments. Experimental results were achieved with standard deviations of sigma R0 = 0.80%, sigma R infinity = 0.84%, sigma alpha = 0.72%, and sigma tau = 1.26%. On a Pentium II based PC, the algorithm converges to within 0.1% of the results in 17 ms. The results show that the algorithm possesses excellent parameter extraction capabilities, repeatability, speed and noise rejection.

In vivo and in situ ischemic tissue characterization using electrical impedance spectroscopy

The investigation of processes of ischemia in different organ tissues is very important for the development of methods of protection and preservation during surgical procedures. Electrical impedance spectroscopy was used to distinguish between different tissues and their degree of ischemia. We describe mathematical methods used to adjust experimental data to Cole-Cole models for one-circle and two-circle impedance loci and a study of the main parameters for representing the behavior of ischemia in time. In vivo and in situ postmortem measurements of different tissues from pigs are shown in the 100 Hz to 1 MHz range. The Cole parameters that best characterize the ischemia are R0 and fc.

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.

Extraction of electrical characteristics from pixels of multifrequency EIT images

Computer modelling has shown that electrical characteristics of individual pixels may be extracted from within multiple-frequency electrical impedance tomography (MFEIT) images formed using a reference data set obtained from a purely resistive, homogeneous medium. In some applications it is desirable to extract the electrical characteristics of individual pixels from images where a purely resistive, homogeneous reference data set is not available. One such application of the technique of MFEIT is to allow the acquisition of in vivo images using reference data sets obtained from a non-homogeneous medium with a reactive component. However, the reactive component of the reference data set introduces difficulties with the extraction of the true electrical characteristics from the image pixels. This study was a preliminary investigation of a technique to extract electrical parameters from multifrequency images when the reference data set has a reactive component. Unlike the situation in which a homogeneous, resistive data set is available, it is not possible to obtain the impedance and phase information directly from the image pixel values of the MFEIT images data set, as the phase of the reactive reference is not known. The method reported here to extract the electrical characteristics (the Cole-Cole plot) initially assumes that this phase angle is zero. With this assumption, an impedance spectrum can be directly extracted from the image set. To obtain the true Cole-Cole plot a correction must be applied to account for the inherent rotation of the extracted impedance spectrum about the origin, which is a result of the assumption. This work shows that the angle of rotation associated with the reactive component of the reference data set may be determined using a priori knowledge of the distribution of frequencies of the Cole-Cole plot. Using this angle of rotation, the true Cole-Cole plot can be obtained from the impedance spectrum extracted from the MFEIT image data set. The method was investigated using simulated data, both with and without noise, and also for image data obtained in vitro. The in vitro studies involved 32 logarithmically spaced frequencies from 4 kHz up to 1 MHz and demonstrated that differences between the true characteristics and those of the impedance spectrum were reduced significantly after application of the correction technique. The differences between the extracted parameters and the true values prior to correction were in the range from 16% to 70%. Following application of the correction technique the differences were reduced to less than 5%. The parameters obtained from the Cole-Cole plot may be useful as a characterization of the nature and health of the imaged tissues.