Multi-frequency Electrical Impedance Research Articles

Multi-Frequency Electrical Impedance Tomography System With Automatic Self-Calibration for Long-Term Monitoring

Electrical Impedance Tomography (EIT) is a safe medical imaging technology, requiring no ionizing or heating radiation, as opposed to most other imaging modalities. This has led to a clinical interest in its use for long-term monitoring, possibly at the bedside, for ventilation monitoring, bleeding detection, gastric emptying and epilepsy foci diagnosis. These long-term applications demand auto-calibration and high stability over long time periods. To address this need we have developed a new multi-frequency EIT system called the KHU Mark2.5 with automatic self-calibration and cooperation with other devices via a timing signal for synchronization with other medical instruments. The impedance measurement module (IMM) for flexible configuration as a key component includes an independent constant current source, an independent differential voltmeter, and a current source calibrator, which allows automatic self-calibration of the current source within each IMM. We installed a resistor phantom inside the KHU Mark2.5 EIT system for intra-channel and inter-channel calibrations of all voltmeters in multiple IMMs. We show the deterioration of performance of an EIT system over time and the improvement due to automatic self-calibration. The system is able to maintain SNR of 80 dB for frequencies up to 250 kHz and below 0.5% reciprocity error over continuous operation for 24 hours. Automatic calibration at least every 3 days is shown to maintain SNR above 75 dB and reciprocity error below 0.7% over 7 days at 1 kHz. A clear degradation in performance results with increasing time between automatic calibrations allowing the tailoring of calibration to suit the performance requirements of each application.

Multifrequency Electrical Impedance Tomography Using Spectral Constraints

Multifrequency electrical impedance tomography (MFEIT) exploits the dependence of tissue impedance on frequency to recover an image of conductivity. MFEIT could provide emergency diagnosis of pathologies such as acute stroke, brain injury and breast cancer. We present a method for performing MFEIT using spectral constraints. Boundary voltage data is employed directly to reconstruct the volume fraction distribution of component tissues using a nonlinear method. Given that the reconstructed parameter is frequency independent, this approach allows for the simultaneous use of all multifrequency data, thus reducing the degrees of freedom of the reconstruction problem. Furthermore, this method allows for the use of frequency difference data in a nonlinear reconstruction algorithm. Results from empirical phantom measurements suggest that our fraction reconstruction method points to a new direction for the development of multifrequency EIT algorithms in the case that the spectral constraints are known, and may provide a unifying framework for static EIT imaging.

Possibilities of electrical impedance tomography in gynecology

The paper describes results of comprehensive EIT diagnostics of mammary glands and cervix. The data were obtained from examinations of 170 patients by EIT system MEM (multi-frequency electrical impedance mammograph) and EIT system GIT (gynecological impedance tomograph). Mutual dependence is discussed.

Circuit modeling of the electrical impedance: II. Normal subjects and system reproducibility

Part I of this series showed that the five-element circuit model accurately mimics impedances measured using multi-frequency electrical impedance myography (MFEIM), focusing on changes brought on by disease. This paper addresses two requirements which must be met if the method is to qualify for clinical use. First, the extracted parameters must be reproducible over long time periods such as those involved in the treatment of muscular disease, and second, differences amongst normal subjects should be attributable to known differences in the properties of healthy muscle. It applies the method to five muscle groups in 62 healthy subjects, closely following the procedure used earlier for the diseased subjects. Test–retest comparisons show that parameters are reproducible at levels from 6 to 16% (depending on the parameter) over time spans of up to 267 days, levels far below the changes occurring in serious disease. Also, variations with age, gender and muscle location are found to be consistent with established expectations for healthy muscle tissue. We conclude that the combination of MFEIM measurements and five-element circuit analysis genuinely reflects properties of muscle and is reliable enough to recommend its use in following neuromuscular disease.

Circuit modeling of the electrical impedance: I. Neuromuscular disease

Multifrequency electrical impedance myography (MFEIM) in the 3–300 kHz range was applied to 68 subjects representing 19 different neuromuscular diseases, and the impedances analyzed using the 5-element circuit model. Depending on severity, the ‘cellular’ parameters r2, r3, 1/c1 and 1/c2 were found to be as much as 10- to 20-fold larger than for normal subjects (taking age and girth into account), but in almost every case the extracellular fluid parameter r1 was at most only marginally affected. Strong correlations are found between r2 and 1/c1, but in the case of ALS that breaks down when c1 (representing the muscle fiber membrane capacitance) falls below half the normal value. Also, c2 (tentatively associated with intracellular organelle membranes) was found to be the most sensitive to disease progress in ALS, about three times more so than the 50 kHz phase, already suggested for use in clinical drug testing. We conclude that following parameters obtained using the combined MFEIM/5-element circuit analysis scheme offer a reliable, non-invasive and objective way of characterizing muscle in neuromuscular disease or during clinical drug testing.

Asymptotic analysis of the membrane structure to sensitivity of frequency-difference electrical impedance tomography

There have been numerous studies using multi-frequency electrical impedance tomography to image frequency-dependent admittivity spectra of biological tissues. Considering the fundamental drawback of the static EIT in recovering the absolute admittivity image at a certain frequency, we will focus on a difference imaging method using a currently available EIT system. We are particularly interested in the frequency-difference EIT (fdEIT) in this paper since it may provide spectroscopic admittivity images without requiring a time-reference data. Noting that non-negligible susceptivity values of biological tissues are attributed to thin cell membranes, we analyze the role of the membrane in terms of the sensitivity of the complex voltage data in fdEIT. Such an analysis requires one to study the frequency-dependent behavior of a complex potential in the framework of the elliptic partial differential equation (PDE) with a frequency-dependent complex coefficient representing the admittivity. Due to complicated coupling between the real and imaginary parts of the complex potential, there is little study on the complex elliptic PDE. Although there exist several previous studies using spherical models which allow the potential to be represented as trigonometric series, these approaches are not apt for biological tissues. In this paper, we decouple the real and imaginary parts via a key asymptotic analysis and approximate the real part as a solution of a well-established elliptic PDE with a real coefficient whose value changes with frequency. This more general approach provides a quantitative analysis of the role of the thin membrane in forming a fdEIT image. We perform numerical simulations and phantom experiments on a two-dimensional imaging object containing an anomaly with a thin insulating membrane. The results provide better understanding of the role of the thin membrane in the sensitivity of a multi-frequency current–voltage data.

Comparison of frequency difference reconstruction algorithms for the detection of acute stroke using EIT in a realistic head-shaped tank

Imaging of acute stroke might be possible using multi-frequency electrical impedance tomography (MFEIT) but requires absolute or frequency difference imaging. Simple linear frequency difference reconstruction has been shown to be ineffective in imaging with a frequency-dependant background conductivity; this has been overcome with a weighted frequency difference approach with correction for the background but this has only been validated for a cylindrical and hemispherical tank. The feasibility of MFEIT for imaging of acute stroke in a realistic head geometry was examined by imaging a potato perturbation against a saline background and a carrot-saline frequency-dependant background conductivity, in a head-shaped tank with the UCLH Mk2.5 MFEIT system. Reconstruction was performed with time difference (TD), frequency difference (FD), FD adjacent (FDA), weighted FD (WFD) and weighted FDA (WFDA) linear algorithms. The perturbation in reconstructed images corresponded to the true position to <9.5% of image diameter with an image SNR of >5.4 for all algorithms in saline but only for TD, WFDA and WFD in the carrot-saline background. No reliable imaging was possible with FD and FDA. This indicates that the WFD approach is also effective for a realistic head geometry and supports its use for human imaging in the future.

A fully parallel multi-frequency EIT system with flexible electrode configuration: KHU Mark2

We report the development of a new multi-frequency electrical impedance tomography (EIT) system called the KHU Mark2. It is descended from the KHU Mark1 in terms of technical details such as digital waveform generation, Howland current source with multiple generalized impedance converters and digital phase-sensitive demodulators. New features include flexible electrode configurations to accommodate application-specific requirements, multiple independent current sources and voltmeters for fully parallel operations, improved data acquisition speeds for faster frame rates and compact mechanical design. Given an electrode configuration, we can design an analog backplane in such a way that both current injections and voltage measurements can be done without using any switch. The KHU Mark2 is based on an impedance measurement module (IMM) comprising a current source and a voltmeter. Using multiple IMMs, we can construct a multi-channel system with 16, 32 or 64 channels, for example. Adopting a pipeline structure, it has the maximum data acquisition speed of 100 scans s−1 with the potential to detect fast physiological changes during respiration and cardiac activity. Measuring both in-phase and quadrature components of trans-impedances at multiple frequencies simultaneously, the KHU Mark2 is apt at spectroscopic EIT imaging. In this paper, we describe its design, construction, calibration and performance evaluation. It has about 84 dB signal-to-noise ratio and 0.5% reciprocity error. Time-difference images of an admittivity phantom are presented showing spectroscopic admittivity images. Future application studies using the KHU Mark2 are briefly discussed.

Measuring the multi-frequency electrical impedance of the mouse gastrocnemius muscle using a tetrapolar technique

Electrical impedance methods can be used to evaluate and monitor neuromuscular disease states. Recently, we have applied tetrapolar surface electrical impedance methods to the gastrocnemius muscle of the rat for this purpose and substantial changes in the impedance parameters after sciatic nerve crush can be identified. In order to be able to study additional animal models of nerve and muscle disease, however, it would highly desirable to be able to perform such impedance measurements in the mouse. Yet the small size of the mouse presents a substantial technical challenge. In this study, we evaluate a basic approach for performing such measurements. A series of thin, stainless steel strip electrodes affixed to the gastrocnemius and interfaced via a separate connector to the Imp SFB7® (Impedimed, Inc), provided an effective means for obtaining impedance data in the 20-500 kHz range. After two weeks, test-retest reproducibility was good, with intra-class correlation coefficients as high 0.84 and variability as low as 12.86 ± 6.18% in the 15 mice studied. Using this approach, it may now be possible to study impedance changes in a variety of mouse models of neuromuscular disease, including amyotrophic lateral sclerosis, spinal muscular atrophy, muscular dystrophy and Charcot-Marie-Tooth disease.

A hybrid FEM model to simulate the electrical characteristics of biological tissues at the cellular level

Cancer screening is possible with multi-frequency electrical impedance tomography since specific impedance variations are observable as a function of frequency. Through genetic mutations, malignant cells have different cellular characteristics than benign cells and a different impedance signature as a function of frequency. The objective of this project is to develop a FEM model to simulate the electrical characteristics of benign and malignant cells at the cellular level. Traditional tetrahedral element meshing techniques were first considered but the narrowness of the extracellular space and thinness of cell membranes made it impractical since the number of FEM elements quickly reached values that were computationally unmanageable on a typical workstation. We are therefore proposing a hybrid FEM model which combines a standard tetrahedral element meshing technique with 2D surfaces to model the extracellular fluid and discrete electrical components to represent cell membranes. The proposed hybrid modelling approach was used to develop a 3D FEM model of the skin with cellular-level details that can be used to better understand how impedance measurements performed on the skin are affected by lesions as a function of frequency as well as cellular geometrical and electrical parameters.

A flexible low-cost, high-precision, single interface electrical impedance tomography system for breast cancer detection using FPGA

Typically, in multi-frequency Electrical Impedance Tomography (EIT) systems, a current is applied and the voltages developed across the subject are detected. However, due to the complexity of designing stable current sources, there has been mention in the literature of applying a voltage to the subject whilst measuring the consequent current flow. This paper presents a comparative study between the two techniques in a novel design suitable for the detection of breast cancers. The suggested instrument borrows the best features of both the injection of current and the application of voltage, circumventing their limitations. Furthermore, the system has a common patient-electrode interface for both methodologies, whilst the control of the system and the necessary signal processing is carried out in a field programmable gate array (FPGA). Through this novel system, wide-bandwidth, low-noise, as well as high-speed (frame rate) can be achieved.

The effect of subacute denervation on the electrical anisotropy of skeletal muscle: Implications for clinical diagnostic testing

Applied electrical current flows preferentially along rather than across muscle fibers, a characteristic called anisotropy. In this study, we investigate the alteration in muscle anisotropy after denervation. Eight adult male rats underwent sciatic nerve crush and the gastrocnemius was harvested from 1 to 2.5 weeks later. Muscle from 12 additional healthy rats was also obtained. Multifrequency electrical impedance measurements were made on the tissue and its conductivity and relative permittivity (i.e., its polarizability) calculated. Anisotropy of the tissue was determined by calculating conductivity and permittivity differences, subtracting transverse from longitudinal values. Muscle fiber and blood vessel quantification were also performed. The mean conductivity difference for sciatic crush animals was higher (p<0.05) than for the healthy animals across the frequency spectrum, due to a greater increase in longitudinal conductivity than in transverse conductivity. For example, at 10 kHz, the conductivity difference was 0.15S/m for healthy animals and 0.29 S/m for post-crush animals. Relative permittivity difference values, however, were similar between groups. There was a strong correlation of conductivity anisotropy to muscle fiber size but not to blood vessel area. Anisotropy of muscle conductivity increases markedly after subacute denervation injury. This alteration in anisotropy has direct relevance to the clinical application of electrical impedance myography. We also speculate that it may impact other forms of diagnostic testing, including needle electromyography and magnetic resonance imaging.

Comparison of a new integrated current source with the modified Howland circuit for EIT applications

Multi-frequency electrical impedance tomography (MF-EIT) systems require current sources that are accurate over a wide frequency range (1 MHz) and with large load impedance variations. The most commonly employed current source design in EIT systems is the modified Howland circuit (MHC). The MHC requires tight matching of resistors to achieve high output impedance and may suffer from instability over a wide frequency range in an integrated solution. In this paper, we introduce a new integrated current source design in CMOS technology and compare its performance with the MHC. The new integrated design has advantages over the MHC in terms of power consumption and area. The output current and the output impedance of both circuits were determined through simulations and measurements over the frequency range of 10 kHz to 1 MHz. For frequencies up to 1 MHz, the measured maximum variation of the output current for the integrated current source is 0.8% whereas for the MHC the corresponding value is 1.5%. Although the integrated current source has an output impedance greater than 1 MΩ up to 1 MHz in simulations, in practice, the impedance is greater than 160 kΩ up to 1 MHz due to the presence of stray capacitance.

A multi-frequency EIT system design based on telecommunication signal processors

A multi-frequency electrical impedance tomography system for cardiopulmonary monitoring has been designed with specialized digital signal processors developed primarily for the telecommunications sector. The system consists of two modules: a scan-head and a base-station. The scan-head, located close to the patient's torso, contains front-end circuits for measuring transfer impedance with a 16-electrode array. The base-station, placed at the bedside, comprises 16 direct digital synthesizers, 32 digital down-converters, digital circuits to control the data acquisition sequence and a USB-2.0 microcontroller. At every step of the scan sequence, the system simultaneously measures four complex variables at eight frequencies. These variables are the potential difference between the selected pair of sense electrodes, the currents applied by the source and sink electrodes, and the current flowing through the ground electrode. Frequencies are programmable from 10 kHz to 2 MHz with a resolution of 2 mHz. Characterization tests were performed with a precision mesh phantom connected to the scan-head. For a 5 Hz frame rate, the mean signal-to-noise ratio and accuracy are, respectively, 43 dB and 95.4% for eight frequencies logarithmically spaced from 70 to 950 kHz. In vitro and in vivo time-difference images have been reconstructed.

A DSP Based Multi-Frequency 3D Electrical Impedance Tomography System

This paper describes the design of a multi-frequency Electrical impedance tomography (EIT) system, which provides a flexible mechanism for addressing up to 48 electrodes for imaging conductivity and permittivity distributions. A waveform generator based on a digital signal processor is used to produce sinusoidal waveforms with the ability to select frequencies in the range of 0.1-125 kHz. A software based phase-sensitive demodulation technique is used to extract amplitudes and phases from the raw measurements. Signal averaging and automatic gain control are also implemented in voltage and phase measurements. System performance was validated using a Cardiff-Cole Phantom and a saline filled cylindrical tank. The signal-to-noise ratio (SNR) using saline tank was greater than 60 dB and the maximum reciprocity error less than 4% for most frequencies. The common-mode rejection ratio (CMRR) was nearly 60 dB at 50 kHz. Image reconstruction performance was assessed using data acquired through a range of frequencies. This EIT system offers image reconstruction of both conductivity and permittivity distributions in three dimensions. The imaging results are presented in time difference and frequency difference imaging.

BREAST IMAGING USING 3D ELECTRICAL IMPEDENCE TOMOGRAPHY

To determine the diagnostic efficiency of 3D Eletrical Impedance Tomography (EIT) compared to Mammography (MG) and Ultrasonography (USG) in imaging the breast. A group of 88 patients presenting with various breast complaints was examined using combined Mammography and Ultrasonography (MG & USG) or either of these modalities alone. The same patients were then examined using the 3D EIT imaging system "MEIK". The findings were then compared. The sensitivity of these modalities for this group of patients were later determined and statistically analysed. Of the total of 88 patients, 59 findings were "suspicious" by any of the 3 modalities alone or by their combination. EIT had a sensitivity of 77.8 % compared to MG with a sensitivity of 83.3 % and USG with a sensitivity of 94.4 % regarding cases of fibrocystic mastitis. For cases involving cysts, EIT had 100 % sensitivity which was the same as that for USG compared to MG with a sensitivity of only 81 %. Among cases of fibroadenoma, EIT had a sensitivity of just 68.8 % compared to MG with a sensitivity of 87.5 % and USG with a sensitivity of 75 %. Finally among cases of carcinoma, EIT had a sensitivity of 75 % compared to the sensitivity of 100 % of MG and USG in our group of patients. The study revealed that there was no overall significant difference in sensitivity between MG-USG (p = 0.219) and MG-EIT (p = 0.779) and USG-EIT (p = 0.169). However, in regard to identifying cysts there was significant difference in the sensitivity of MG compared to USG & EIT suggesting that EIT has a role in these cases. Electrical impedance could be used as an adjunct to Mammography and Ultrasonography for breast cancer detection. However, the differentiation of malignant from benign lesions based on impedance measurements needs further investigation. Multifrequency electrical impedance imaging appears the most promising for detecting breast malignancies but methodological improvements need to be made to realise its potential.

Dual-frequency electrical impedance mammography for the diagnosis of non-malignant breast disease

Electrical impedance tomography (EIT) enables one to determine and visualize non-invasively the spatial distribution of the electrical properties of the tissues inside the body, thus providing valuable diagnostic information. The electrical impedance mammography (EIM) system is a specialized EIT system for diagnostics and imaging of the breast. While breast cancer is the main target for any investigation conducted in this area, the diagnosis of non-cancerous diseases is also very important because it opens the way to improve the quality of life for many women and it may also reduce the incidence of breast cancer through effective treatment of mastopathy. This paper presents the main results of a comprehensive examination of 166 women using four methods: multifrequency electrical impedance mammography, ultrasonic investigation, x-ray mammography and puncture biopsy. The objective of the investigation is to estimate the usefulness of multifrequency electrical impedance mammography for diagnosing dyshormonal mammary gland diseases. The results demonstrate the advantages of the multifrequency EIM method. In particular, dual-frequency electrical impedance mammography in contrast with the single-frequency variant enables one not only to diagnose mastopathy, but also allows accurate detection of its cystless form based on observation of the absence of any difference between average conductivity in both phases of the menstrual cycle. Because the cystless form of mastopathy is associated with a higher risk of cancer development, this method allows identification of a higher risk group of patients for more frequent investigations.

Validation of a multi-frequency electrical impedance tomography (mfEIT) system KHU Mark1: impedance spectroscopy and time-difference imaging

Validation and interpretation of reconstructed images using a multi-frequency electrical impedance tomography (mfEIT) requires a conductivity phantom including imaging objects with known complex conductivity (σ + iωε) spectra. We describe imaging experiments using the recently developed mfEIT system called the KHU Mark1 with the frequency range of 10 Hz to 500 kHz. Using a bio-impedance spectroscopy (BIS) system, we first measured complex conductivity spectra of different imaging objects including saline, agar, polyacrylamide, TX151, animal hide gelatin, banana and cucumber. Based on an analysis of how conductivity and permittivity affect measured complex boundary voltages, we suggested a new complex version of a multi-frequency time-difference image reconstruction algorithm. Imaging experiments were conducted to produce time-difference images of the objects at multiple frequencies using the proposed algorithm. Images of a conductor (stainless steel) and an insulator (acrylic plastic) were used to set a common scale bar to display all images. Comparing reconstructed time-difference images at multiple frequencies with measured complex conductivity spectra, we found that they showed an overall similarity in terms of changes in complex conductivity values with respect to frequency. However, primarily due to the limitation of the difference imaging algorithm, we suggest that multi-frequency time-difference images must be interpreted in terms of relative contrast changes with respect to frequency. We propose further imaging studies using biological tissues of known complex conductivity spectra and using human subjects to find clinical applications of the mfEIT system.

Particle-phase distributions of pressure-driven flows of bidisperse suspensions

The phase distribution of a bimodal distribution of negatively buoyant particles in a low-Reynolds-number pressure-driven flow of a suspension in a horizontal pipe is measured using multi-frequency electrical impedance tomography (EIT). Suspensions of heavy silver-coated particles and slightly heavy PMMA particles exhibit different effective conductivities depending on the frequency of an applied electrical current. This difference allows the separate imaging of the phase distribution of each particle type and the composite suspension. At low flow rates the dense particles tend to distribute in the lower half of the pipe The particles are resuspended toward the centre as the flow rate is increased. The slightly heavy particles tend to accumulate closer to the centre of the pipe. The presence of the nearly neutrally buoyant particles enhances the resuspension of the heavy particles compared to that of a suspension of heavy particles alone at the same volume fraction. A suspension balance model is used to theoretically predict the distribution of particles in the flow assuming an ideal mixing rule for the particle partial pressures. The agreement between the predictions and the experimental observations is qualitatively correct and quantitatively fair.

Calibration methods for a multi-channel multi-frequency EIT system

Multi-channel multi-frequency electrical impedance tomography (EIT) systems require a careful calibration to minimize systematic errors. We describe novel calibration methods for the recently developed KHU Mark1 EIT system. Current source calibration includes maximization of output resistance and minimization of output capacitance using multiple generalized impedance converters. Phase and gain calibrations are used for voltmeters. Phase calibration nulls out the total system phase shift in measured voltage data. Gain calibrations are performed in two steps of intra- and inter-channel calibrations. Intra-channel calibration for each voltmeter compensates frequency dependence of its voltage gain and also discrepancy between design and actual gains. Inter-channel calibration compensates channel-dependent voltage gains of all voltmeters. Using the calibration methods described in this paper, we obtained 1 MΩ minimal output impedance of the current source in the frequency range 10 Hz–500 kHz. The reciprocity error was as small as 0.05% after intra- and inter-channel voltmeter calibrations. To demonstrate effects of calibration in reconstructed images, we used a homogenous phantom from which uniform images should be produced. Reconstructed time- and frequency-difference images using uncalibrated data showed spurious anomalies. By using calibrated data, standard deviations of time- and frequency-difference images of the homogenous phantom were reduced by about 40% and 90%, respectively.