A dual-frequency applied potential tomography technique: computer simulations

Bioimpedance analysis as a tool for hemodynamic monitoring: overview, methods and challenges

Recent advances in hemodynamic monitoring have seen the advent of non-invasive methods which offer ease of application and improve patient comfort. Bioimpedance Analysis or BIA is one of the currently employed non-invasive techniques for hemodynamic monitoring. Impedance Cardiography (ICG), one of the implementations of BIA, is widely used as a non-invasive procedure for estimating hemodynamic parameters such as stroke volume (SV) and cardiac output (CO). Even though BIA is not a new diagnostic technique, it has failed to gain consensus as a reliable measure of hemodynamic parameters. Several devices have emerged for estimating CO using ICG which are based on evolving methodologies and techniques to calculate SV. However, the calculations are generally dependent on the electrode configurations (whole body, segmental or localised) as well as the accuracy of different techniques in tracking blood flow changes. Blood volume changes, concentration of red blood cells, pulsatile velocity profile and ambient temperature contribute to the overall conductivity of blood and hence its impedance response during flow. There is a growing interest in investigating limbs for localised BIA to estimate hemodynamic parameters such as pulse wave velocity. As such, this paper summarises the current state of hemodynamic monitoring through BIA in terms of different configurations and devices in the market. The conductivity of blood flow has been emphasized with contributions from both volume and velocity changes during flow. Recommendations for using BIA in hemodynamic monitoring have been mentioned highlighting the suitable range of frequencies (1 kHz-1 MHz) as well as safety considerations for a BIA setup. Finally, current challenges in using BIA such as geometry assumption and inaccuracies have been discussed while mentioning potential advantages of a multi-frequency analysis to cover all the major contributors to blood's impedance response during flow.

A Review on Electrical Impedance Tomography Spectroscopy

Electrical Impedance Tomography Spectroscopy (EITS) enables the reconstruction of material distributions inside an object based on the frequency-dependent characteristics of different substances. In this paper, we present a review of EITS focusing on physical principles of the technology, sensor geometries, existing measurement systems, reconstruction algorithms, and image representation methods. In addition, a novel imaging method is proposed which could fill some of the gaps found in the literature. As an example of an application, EITS of ice and water mixtures is used.

Detection of admittivity anomaly on high-contrast heterogeneous backgrounds using frequency difference EIT

This paper describes a multiple background subtraction method in frequency difference electrical impedance tomography (fdEIT) to detect an admittivity anomaly from a high-contrast background conductivity distribution. The proposed method expands the use of the conventional weighted frequency difference EIT method, which has been used limitedly to detect admittivity anomalies in a roughly homogeneous background. The proposed method can be viewed as multiple weighted difference imaging in fdEIT. Although the spatial resolutions of the output images by fdEIT are very low due to the inherent ill-posedness, numerical simulations and phantom experiments of the proposed method demonstrate its feasibility to detect anomalies. It has potential application in stroke detection in a head model, which is highly heterogeneous due to the skull.

Breast EIT using a new projected image reconstruction method with multi-frequency measurements

We propose a new method to produce admittivity images of the breast for the diagnosis of breast cancer using electrical impedance tomography(EIT). Considering the anatomical structure of the breast, we designed an electrode configuration where current-injection and voltage-sensing electrodes are separated in such a way that internal current pathways are approximately along the tangential direction of an array of voltage-sensing electrodes. Unlike conventional EIT imaging methods where the number of injected currents is maximized to increase the total amount of measured data, current is injected only twice between two pairs of current-injection electrodes attached along the circumferential side of the breast. For each current injection, the induced voltages are measured from the front surface of the breast using as many voltage-sensing electrodes as possible. Although this electrode configurational lows us to measure induced voltages only on the front surface of the breast,they are more sensitive to an anomaly inside the breast since such an injected current tends to produce a more uniform internal current density distribution. Furthermore, the sensitivity of a measured boundary voltage between two equipotential lines on the front surface of the breast is improved since those equipotential lines are perpendicular to the primary direction of internal current streamlines. One should note that this novel data collection method is different from those of other frontal plane techniques such as the x-ray projection and T-scan imaging methods because we do not get any data on the plane that is perpendicular to the current flow. To reconstruct admittivity images using two measured voltage data sets, a new projected image reconstruction algorithm is developed. Numerical simulations demonstrate the frequency-difference EIT imaging of the breast. The results show that the new method is promising to accurately detect and localize small anomalies inside the breast.

Validation of weighted frequency-difference EIT using a three-dimensional hemisphere model and phantom

Frequency-difference (FD) electrical impedance tomography (EIT) using a weighted voltage difference has recently been proposed for imaging haemorrhagic stroke, abdominal bleeding and tumors. Although its feasibility was demonstrated through two-dimensional numerical simulations and phantom experiments, we should validate the method in three-dimensional imaging objects. At the same time, we need to investigate its robustness against geometrical modeling errors in boundary shapes and electrode positions. We performed a validation study of the weighted FD method through three-dimensional numerical simulations and phantom experiments. Adopting hemispherical models and phantoms whose admittivity distributions change with frequency, we investigated the performance of the method to detect an anomaly. We found that the simple FD method fails to detect the anomaly, whereas reconstructed images using the weighted FD method clearly visualize the anomaly. The weighted FD method is robust against modeling errors of boundary-shape deformations and displaced electrode positions. We also found that the method is capable of detecting an anomaly surrounded by a shell-shaped obstacle simulating the skull. We propose the weighted FD method for future studies of animal and human experiments.

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 method for modelling and optimizing an electrical impedance tomography system

Electrical impedance tomography (EIT) image reconstruction is an ill-posed problem requiring maximum measurement precision. Recent EIT systems claim 60 to 80 dB precision. Achieving higher values is hard in practice since measurements must be performed at relatively high frequency, on a living subject, while using components whose tolerance is usually higher than 0.1%. To circumvent this difficulty, a method for modelling the electronic circuits of an EIT system was developed in order to optimize the circuits and incorporate the model in the reconstruction algorithms. The proposed approach is based on a matrix method for solving electrical circuits and has been applied to the scan-head which contains the front-end electronic circuits of our system. The method is used to simulate the system characteristic curves which are then optimized with the Levenberg-Marquardt method to find optimal component values. A scan-head was built with the new component values and its simulated performance curves were compared with network analyser measurements. As a result of the optimization, the impedance at the operating frequency was increased to minimize the effects of variations in skin/electrode contact impedance. The transconductance and gain frequency responses were also reshaped to reduce noise sensitivity and unintended signal modulation. Integrating the model in the reconstruction algorithms should further improve overall performance of an EIT system.

A multichannel continuously selectable multifrequency electrical impedance spectroscopy measurement system

There is increasing evidence that alterations in the electrical property spectrum of tissues below 10 MHz is diagnostic for tissue pathology and/or pathophysiology. Yet, the complexity associated with constructing a high-fidelity multichannel, multifrequency data acquisition instrument has limited widespread development of spectroscopic electrical impedance imaging concepts. To contribute to the relatively sparse experience with multichannel spectroscopy systems this paper reports on the design, realization and evaluation of a prototype 32-channel instrument. The salient features of the system include a continuously selectable driving frequency up to 1 MHz, either voltage or current source modes of operation and simultaneous measurement of both voltage and current on each channel in either of these driving configurations. Comparisons of performance with recently reported fixed-frequency systems is favorable. Volts dc (VDC) signal-to-noise ratios of 75-80 dB are achieved and the noise floor for ac signals is near 100 dB below the signal strength of interest at 10 kHz and 60 dB down at 1 MHz. The added benefit of being able to record multispectral information on source and sense signal amplitudes and phases has also been realized. Phase-sensitive detection schemes and multiperiod undersampling techniques have been deployed to ensure measurement fidelity over the full bandwidth of system operation.

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.

Multi-frequency static imaging in electrical impedance tomography: Part 1. Instrumentation requirements

Static images of the human body using electrical impedance tomography techniques can be obtained by measuring at two or more different frequencies. The frequencies used depend on the application, and their selection depends on the frequency behaviour of the impedance for the target tissue. An analysis using available data and theoretical models for tissue impedance yields the expected impedance and boundary voltage changes, therefore setting the measurement instrument specifications. The instrument errors produced by different sources are analysed, and, from this analysis it is possible to determine the feasibility of building the instrument, the limit values for some parameters (or components) and indications on the most suitable design of critical parts. This analysis also shows what kinds of error can be expected in the reconstructed images. It is concluded that it is possible to build an instrument with limited errors, allowing static images to be obtained. An instrument has been built that meets some of the design requirements and fails in others because of technological problems. In vivo images obtained with this instrument will be presented in Part 2 of this work.

Electrical impedance tomography: a review of current literature

Electrical impedance tomography (EIT) is a relatively new imaging technique that has been developed during the past decade. The electrical properties of tissues are imaged by injecting small currents and measuring the resultant voltages. These voltages are then converted into a tomographic image using a reconstructing algorithm. The method has no known hazards and is relatively inexpensive. There are many possible clinical applications of this technique but apart from gastric emptying, most are still at the research stage as there are various technical and practical problems to be overcome. This paper describes the basic principles of EIT and reviews the English literature to try to assess its potential in clinical imaging.

A broadband system for multifrequency static imaging in electrical impedance tomography

A widely accepted method for static imaging in electrical impedance tomography (EIT) is to measure at two frequencies. The choice of measurement frequencies is application-dependent because some different tissues cannot be distinguished when using two fixed frequencies. We have developed a system that generates signals from 8-10(3) kHz and applies two of these signals simultaneously to the body through a broadband current mirror. Great care has been taken in the design of the current injection multiplexer in order to keep the current source output capacitance as low as possible. Furthermore design of the layout of the patient interface board, in order to reduce feedthrough capacitances, also needs great care. Other parameters for driving and detection sections have been designed according to our results from FEM and circuit simulations including skin and electrode effects. Simulations using FEM with available tissue impedance data and preliminary measurements in a discrete phantom show that static imaging is possible for both the real and imaginary parts of the impedance.

Two-frequency impedance plethysmograph: real and imaginary parts

A four-channel impedance plethysmograph has been designed. Impedance signals are obtained at two frequencies by measuring both real and imaginary parts. Particular attention has been paid to the sine wave generation circuits that provide system versatility. The required phase-sensitive demodulation is achieved by means of analogue multiplexers. Results show that there are significant variations in the thoracic equivalent capacitance related to respiration and that there is an increased sensitivity to cardiac activity at low frequencies.

A dual-frequency electrical impedance tomography system

An electrical impedance tomography (EIT) system has been constructed, operating at two frequencies, 40.96 and 81.92 kHz, for investigating the practicability of the dual-frequency imaging method discussed theoretically in a previous paper. For testing the system, a phantom with a frequency-dependent electrical conductivity was designed. The properties of the phantom can be adjusted to match the frequency dependence observed in a given type of tissue. Dual-frequency images were obtained from a phantom simulating liver and also from 200 g of porcine liver in a saline tank. Prior to image reconstruction, it was necessary to apply a correction to the data to cancel the effects of stray capacitance within the electronics.

A phantom for electrical impedance tomography

A method has been developed for constructing phantoms for electrical impedance tomography (EIT). A mesh of resistors is soldered to pins in a matrix board and forms a physical realisation of a finite element numerical model. To simulate different body tissues, changes in the apparent electrical conductivity and permittivity can be introduced at a particular location within the phantom by shunting the resistors in the mesh with additional resistors and capacitors. The phantom was used to test an EIT system employing phase-sensitive detection to separate the real and imaginary parts of the peripheral electric potentials. From the measurements images of conductivity and permittivity were reconstructed using an algorithm developed recently. The phantom has good mechanical strength and is electrically stable. The design could easily be reproduced and distributed to other centres developing similar EIT systems to enable testing on a common basis.

Aspects of instrumentation design for impedance imaging

This paper takes the circuit for a general purpose impedance imaging data measurement system and analyses the importance of several components. For high accuracy it is shown that stray capacitances in the input circuitry are the major problem although the use of a phase sensitive demodulator can minimise this problem. It is shown that harmonic distortion in the constant current generator can cause errors which are, however, reduced if a linear multiplying demodulator is used rather than a switching demodulator.

A fast approximation for the calculation of potential distributions in electrical impedance tomography

A number of proposed electrical impedance tomography reconstruction algorithms rely on the assumption that the pattern of potentials produced in an unknown conductivity distribution will be similar to that produced in a uniformly conducting object of the same external dimensions. This potential distribution can be calculated from Laplace's equation. A fast approximation to the solution of Laplace's equation is formulated and tested against experimental and computer generated data. Whilst it does not fully converge to the solution, the approximation is shown to be an improvement over the assumption of semi-infinite boundary conditions and to be very much faster than conventional numerical methods.

The importance of phase measurement in electrical impedance tomography

A method is described for reconstructing images of electrical conductivity and relative permittivity in electrical impedance tomography (applied potential tomography). The method relies on measurement of both the amplitude and the phase of the surface electric potential profile. The principle is demonstrated using a computer model to simulate measurements. The reconstructed images, referenced to homogeneous saline, agree qualitatively with the values of conductivity and permittivity used in the computer model. In addition, by displaying the imaginary part of the logarithm of the complex electrical conductivity, certain tissues, e.g. liver and kidney, are emphasised on the image. When the same parameter is displayed for simulated dual-frequency measurements, in which 150 kHz values are referenced against 100 kHz, liver and pancreas are emphasised. These results suggest the possibility of distinguishing between different types of soft tissue more effectively than if only signal amplitudes are measured. The phase changes in the simulated signals, on which the formation of such images depends, have a mean value of 13.3 degrees for the saline-referenced simulation but only 1.6 degrees for the dual-frequency simulation requiring accurate measurement in practice.