Multi-frequency Electrical Impedance Tomography Research Articles

Factorization Method and Its Physical Justification in Frequency-Difference Electrical Impedance Tomography

Time-difference electrical impedance tomography (tdEIT) requires two data sets measured at two different times. The difference between them is utilized to produce images of time-dependent changes in a complex conductivity distribution inside the human body. Frequency-difference EIT (fdEIT) was proposed to image frequency-dependent changes of a complex conductivity distribution. It has potential applications in tumor and stroke imaging since it can visualize an anomaly without requiring any time-reference data obtained in the absence of an anomaly. In this paper, we provide a rigorous analysis for the detectability of an anomaly based on a constructive and quantitative physical correlation between a measured fdEIT data set and an anomaly. From this, we propose a new noniterative frequency-difference anomaly detection method called the factorization method (FM) and elaborate its physical justification. To demonstrate its practical applicability, we performed fdEIT phantom imaging experiments using a multifrequency EIT system. Applying the FM to measured frequency-difference boundary voltage data sets, we could quantitatively evaluate indicator functions inside the imaging domain, of which values at each position reveal presence or absence of an anomaly. We found that the FM successfully localizes anomalies inside an imaging domain with a frequency-dependent complex conductivity distribution. We propose the new FM as an anomaly detection algorithm in fdEIT for potential applications in tumor and stroke imaging.

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.

Weighted frequency-difference EIT measurement of hemisphere phantom

We have proposed a new frequency difference method using a weighted voltage difference (WFD-EIT) between two frequencies [1, 2]. Previous studies demonstrated its feasibility through numerical experiments and two-dimensional phantom experiments. In this study, we validate the WFD-EIT algorithm on a three-dimensional hemisphere phantom using a multi-frequency EIT system KHU Mark1. We built the hemisphere phantom with 17 stainless-steel electrodes on its inner surface. We filled the phantom with a biological material having a frequency-dependent admittivity such as carrot pieces mixed in saline. Using boundary voltage data from the deformed phantom, we reconstructed weighted frequency difference images on the computational model domain with a hemisphere shape. We discuss comparative reconstruction performance results including time difference (TD), simple frequency difference (FD), and weighted frequency difference (WFD). Animal and human head imaging experiments with the weighted frequency-difference EIT method are under investigation.

Development of a prototype micro-EIT system using three sets of 15×8 array electrodes

We developed a new microscopic electrical impedance tomography (micro-EIT) system to visualize admittivity distributions within a miniature hexahedral container, where we place small biological samples with a background solution or gel. Each of two facing sides (left and right) of the container is fully covered by a solid metal electrode. We inject current between them, thereby producing a uniform parallel current flow along the longitudinal direction inside the container. Each of three sides at the bottom, front and back is equipped with a 15×8 array of voltage-sensing electrodes. Switching modules are located underneath the container so that we can measure voltage between any neighbouring pair of electrodes. Three switching modules are connected to a 16-channel multi-frequency EIT system to collect induced voltage data from the three sets of 15x8 array electrodes subject to the single fixed current injection. Voltage data set from 360 voltage-sensing electrodes on three sides are utilized to produce cross-sectional images of the admittivity distribution. We describe the design and construction of the new micro-EIT system. Our future work should include development of a customized image reconstruction algorithm for the micro-EIT system and experimental validation.

Performance evaluation of KHU Mark2 parallel multi-frequency EIT system

We describe a new parallel multi-frequency EIT system, KHU Mark2. It is based on the impedance measurement module (IMM), which comprises a single-ended constant current source and a voltmeter. Each IMM has an FPGA for its independent operations including current injection at multiple frequencies, voltage amplification, ADC, digital phase-sensitive demodulation and intra-networking with a main controller of the system. The main controller is based on a DSP and an isolated USB for its connection to a PC. There is an FPGA-based intranet controller, which arbitrates data exchanges between the DSP and multiple IMMs. Unlike its precursor, KHU Mark1, it is a true parallel system with no switching for both current injection and voltage sensing. The small size of the IMM results in a much reduced dimension of a multi-channel system. The KHU Mark2 can be assembled in any channels between 1 and 64. Depending on a chosen application, we custom design an analog backplane that interfaces multiple IMMs with electrodes. Special care was given to the system calibration to maximize its performance in frequency-difference EIT imaging as well as time-difference. Flexibility is the key improvement factor compared with the KHU Mark1. The new system can accommodate any current injection and voltage sensing protocol including the optimal injection current pattern. Reduced size and new internal architecture significantly improved mechanical as well as electrical stability of the system.

Human interface design using Button-type PEDOT electrode array in EIT

Animal and human experiments using a multi-channel EIT system requires a cumbersome procedure to attach multiple electrodes. We have to ensure good contact of all electrodes and manage many lead wires during experiments. The problem becomes more severe as we increase the number of electrodes. These may limit the applicability of the imaging method in practice. Noting this technical difficulty, there have been a few trials to design human interface means such as electrode belts, helmets or rings. In this study, we developed an electrode belt for long-term monitoring of human lung ventilation. The belt includes 16 embossed electrodes which make good contact with the skin. The electrode is made by conductive polymer and metallic thread. Soft cushion and wide contact area minimize uncomfortable sensation and reduce contact impedances. The electrodes are attached to an elastic fabric belt at equal spacing. We describe details of its design and fabrication. Using the electrode belt and recently developed multi-frequency EIT system KHU Mark2, we show time-difference chest images of three human subjects during normal breathing cycles.

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 comparison study of electrodes for neonate electrical impedance tomography

Electrical impedance tomography (EIT) is an imaging technique that has the potential to be used for studying neonate lung function. The properties of the electrodes are very important in multi-frequency EIT (MFEIT) systems, particularly for neonates, as the skin cannot be abraded to reduce contact impedance. In this work, the impedance of various clinical electrodes as a function of frequency is investigated to identify the optimum electrode type for this application. Six different types of self-adhesive electrodes commonly used in general and neonatal cardiology have been investigated. These electrodes are Ag/AgCl electrodes from the Ambu® Cardiology Blue sensors range (BR, NF and BRS), Kendall (KittyCat™ and ARBO®) and Philips 13953D electrodes. In addition, a textile electrode without gel from Textronics was tested on two subjects to allow comparison with the hydrogel-based electrodes. Two- and four-electrode measurements were made to determine the electrode-interface and tissue impedances, respectively. The measurements were made on the back of the forearm of six healthy adult volunteers without skin preparation with 2.5 cm electrode spacing. Impedance measurements were carried out using a Solartron SI 1260 impedance/gain-phase analyser with a frequency range from 10 Hz to 1 MHz. For the electrode-interface impedance, the average magnitude decreased with frequency, with an average value of 5 kΩ at 10 kHz and 337 Ω at 1 MHz; for the tissue impedance, the respective values were 987 Ω and 29 Ω. Overall, the Ambu BRS, Kendall ARBO® and Textronics textile electrodes gave the lowest electrode contact impedance at 1 MHz. Based on the results of the two-electrode measurements, simple RC models for the Ambu BRS and Kendall-ARBO and Textronics textile electrodes have been derived for MFEIT applications.

Multi-frequency time-difference complex conductivity imaging of canine and human lungs using the KHU Mark1 EIT system

We evaluated the performance of the lately developed electrical impedance tomography (EIT) system KHU Mark1 through time-difference imaging experiments of canine and human lungs. We derived a multi-frequency time-difference EIT (mftdEIT) image reconstruction algorithm based on the concept of the equivalent homogeneous complex conductivity. Imaging experiments were carried out at three different frequencies of 10, 50 and 100 kHz with three different postures of right lateral, sitting (or prone) and left lateral positions. For three normal canine subjects, we controlled the ventilation using a ventilator at three tidal volumes of 100, 150 and 200 ml. Three human subjects were asked to breath spontaneously at a normal tidal volume. Real- and imaginary-part images of the canine and human lungs were reconstructed at three frequencies and three postures. Images showed different stages of breathing cycles and we could interpret them based on the understanding of the proposed mftdEIT image reconstruction algorithm. Time series of images were further analyzed by using the functional EIT (fEIT) method. Images of human subjects showed the gravity effect on air distribution in two lungs. In the canine subjects, the morphological change seems to dominate the gravity effect. We could also observe that two different types of ventilation should have affected the results. The KHU Mark1 EIT system is expected to provide reliable mftdEIT images of the human lungs. In terms of the image reconstruction algorithm, it would be worthwhile including the effects of three-dimensional current flows inside the human thorax. We suggest clinical trials of the KHU Mark1 for pulmonary applications.

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.

Robust Linearized Image Reconstruction for Multifrequency EIT of the Breast

Electrical impedance tomography (EIT) is a developing imaging modality that is beginning to show promise for detecting and characterizing tumors in the breast. At Rensselaer Polytechnic Institute, we have developed a combined EIT-tomosynthesis system that allows for the coregistered and simultaneous analysis of the breast using EIT and X-ray imaging. A significant challenge in EIT is the design of computationally efficient image reconstruction algorithms which are robust to various forms of model mismatch. Specifically, we have implemented a scaling procedure that is robust to the presence of a thin highly-resistive layer of skin at the boundary of the breast and we have developed an algorithm to detect and exclude from the image reconstruction electrodes that are in poor contact with the breast. In our initial clinical studies, it has been difficult to ensure that all electrodes make adequate contact with the breast, and thus procedures for the use of data sets containing poorly contacting electrodes are particularly important. We also present a novel, efficient method to compute the Jacobian matrix for our linearized image reconstruction algorithm by reducing the computation of the sensitivity for each voxel to a quadratic form. Initial clinical results are presented, showing the potential of our algorithms to detect and localize breast tumors.

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.

On-electrode autonomous current generator for multi-frequency EIT

The paper presents an autonomous programmable current generator module for multi-frequency EIT systems. The module incorporates all stages from the sine wave generation with frequency and amplitude tuning, D/A converter and filter, a high output resistance voltage-to-current converter to the associated digital communication and control. The paper presents in depth the original digital quadrature signal generator and the output current generator with a high resistance. The other main blocks of the design use current practice specifications, since recent technological solutions proposed in the literature were found appropriate. The proposed signal generator circuit, characterized by a very low complexity, is analyzed in its capacity to produce multiple accurate signals up to 1 MHz in frequency. The precision output current source uses a modified current conveyor of type CCII with a high output resistance and low distortion. The output current frequency spectrum and linearity parameters obtained in the simulations are also described. The simulation results indicate a good linearity and high output resistance with an acceptable output voltage swing. The calculated performance parameters are validated with simulations, and future work for the prototype fabrication of the IC is outlined.

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.

A review of errors in multi-frequency EIT instrumentation

Multi-frequency electrical impedance tomography (MFEIT) was proposed over 10 years ago as a potential spectroscopic impedance imaging method. At least seven systems have been developed for imaging the lung, heart, breast and brain, yet none has yet achieved clinical acceptance. While the absolute impedance varies considerably between different tissues, the changes in the spectrum due to physiological changes are expected to be quite small, especially when measured through a volume. This places substantial requirements on the MFEIT instrumentation to maintain a flat system frequency response over a broad frequency range (dc–MHz). In this work, the EIT measurement problem is described from a multi-frequency perspective. Solutions to the common problems are considered from recent MFEIT systems, and the debate over four-terminal or two-terminal (multiple source) architecture is revisited. An analysis of the sources of MFEIT errors identifies the major sources of error as stray capacitance and common-mode voltages which lead to a load dependence in the frequency response of MFEIT systems. A system that employs active electrodes appears to be the most able to cope with these errors (Li et al 1996). A distributed system with digitization at the electrode is suggested as a next step in MFEIT system development.

Multi-frequency EIT system with radially symmetric architecture: KHU Mark1

We describe the development of a multi-frequency electrical impedance tomography (EIT) system (KHU Mark1) with a single balanced current source and multiple voltmeters. It was primarily designed for imaging brain function with a flexible strategy for addressing electrodes and a frequency range from 10 Hz–500 kHz. The maximal number of voltmeters is 64, and all of them can simultaneously acquire and demodulate voltage signals. Each voltmeter measures a differential voltage between a pair of electrodes. All voltmeters are configured in a radially symmetric architecture in order to optimize the routing of wires and minimize cross-talk. We adopted several techniques from existing EIT systems including digital waveform generation, a Howland current generator with a generalized impedance converter (GIC), digital phase-sensitive demodulation and tri-axial cables. New features of the KHU Mark1 system include multiple GIC circuits to maximize the output impedance of the current source at multiple frequencies. The voltmeter employs contact impedance measurements, data overflow detection, spike noise rejection, automatic gain control and programmable data averaging. The KHU Mark1 system measures both in-phase and quadrature components of trans-impedances. By using a script file describing an operating mode, the system setup can be easily changed. The performance of the developed multi-frequency EIT system was evaluated in terms of a common-mode rejection ratio, signal-to-noise ratio, linearity error and reciprocity error. Time-difference and frequency-difference images of a saline phantom with a banana object are presented showing a frequency-dependent complex conductivity of the banana. Future design of a more innovative system is suggested including miniaturization and wireless techniques.

Identification of a suitable current waveform for acute stroke imaging

MFEIT (multi-frequency electrical impedance tomography) has the potential to provide a portable non-invasive neuroimaging method ideal for use in acute stroke. Skin perception has not previously occurred in MFEIT with injected frequencies above 2 kHz, but use in brain imaging requires applied current below 100 Hz, which could stimulate cutaneous nerve endings. The purpose of this work was to find the most suitable current pattern that could be employed in MFEIT measurements in the adult head with the UCLH Mk2.5 system, which applies currents from 20 Hz–1.6 MHz. Single frequency current waveforms of 0.28 mA peak-to-peak at 20 Hz–80 Hz were applied to the forearms of three volunteers; although the skin was abraded, none of these were perceived, which agrees with similar studies in the literature. When a full frequency pattern at 20 Hz–1.6 MHz was applied to the forearm or head in four healthy subjects, with the same current amplitude of 0.28 mA for each component, an unpleasant tingling sensation was perceived, due to summation of the applied currents. The sensation was reduced or abolished by attenuation or removal of frequencies below 100 Hz; the optimal compromise was a pattern with absence of 40 Hz, and with 80 and 20 Hz respectively reduced to 75% and 50%.