Estimating a regional ventilation-perfusion index.

This is a methods paper, where an approximation to the local ventilation-perfusion ratio is derived. This approximation, called the ventilation-perfusion index since it is not exactly the physiological ventilation-perfusion ratio, is calculated using conductivity reconstructions obtained using electrical impedance tomography. Since computation of the ventilation-perfusion index only requires knowledge of the internal conductivity, any conductivity reconstruction method may be used. The method is explained and results are presented using conductivities obtained from two EIT systems, one using an iterative method and the other a linearization method.

Calderón's method on an elliptical domain.

One possible application for electrical impedance tomography is in medical imaging where lung and heart function may be monitored. One drawback of current algorithms is that they are implemented for use in a circular domain, but a human thorax is more elliptical than circular. In this paper, a reconstruction algorithm based on the work of Calderón (1980 Seminar on Numerical Analysis and its Applications to Continuum Physics (Rio de Janeiro) pp 65-75) on the inverse conductivity problem is derived for an elliptical domain. It is explained how this reconstruction algorithm uses a transformed Dirichlet-to-Neumann map. Experimental results from an elliptical tank are given to show how correct domain modelling reduces the artefacts produced by this version of Calderón's reconstruction algorithm.

An electrical impedance spectroscopy system for breast cancer detection.

This paper describes Rensselaer's ACT 4 electrical impedance tomography system which has been developed for breast cancer detection. ACT 4 acquires electrical impedance data at a set of discrete frequencies in the range from 3.33 kHz to 1 MHz and can support up to 72 electrodes. The instrument applies either voltages or currents to all the electrodes simultaneously and measures the resulting currents and/or voltages. Radiolucent electrode arrays are applied to the compression plates of an x-ray mammography system for collecting impedance data in register with x-ray images. The analog front-end electronics are supported with a distributed digital system, including a computer, Digital Signal Processors (DSPs) and Field-Programmable Gate Arrays (FPGAs). A Microsoft Visual C/C++ -based user interface controls the system operation. The overall system architecture is presented as well as performance results.

Reconstructions of conductive and insulating targets using the D-bar method on an elliptical domain.

The D-bar algorithm based on A Nachman's 2D global uniqueness proof for the inverse conductivity problem (Nachman 1996 Ann. Math. 143 71-96) is implemented on an elliptical domain. The scattering transform is computed on an ellipse and the complete electrode model (CEM) for the forward problem is computed with the finite element method (FEM) in order to obtain static conductivity reconstructions of conductive and insulating targets in a saline-filled tank. It is demonstrated that the spatial artifacts in the image are significantly reduced when the domain is properly modeled in the reconstruction, as opposed to being modeled as a disk.

A compensated radiolucent electrode array for combined EIT and mammography.

Electrical impedance tomography (EIT), a non-invasive technique used to image the electrical conductivity and permittivity within a body from measurements taken on the body's surface, could be used as an indicator for breast cancer. Because of the low spatial resolution of EIT, combining it with other modalities may enhance its utility. X-ray mammography, the standard screening technique for breast cancer, is the first choice for that other modality. Here, we describe a radiolucent electrode array that can be attached to the compression plates of a mammography unit enabling EIT and mammography data to be taken simultaneously and in register. The radiolucent electrode array is made by depositing thin layers of metal on a plastic substrate. The structure of the array is presented along with data showing its x-ray absorbance and electrical properties. The data show that the electrode array has satisfactory radiolucency and sufficiently low resistance.

A 3D reconstruction algorithm for EIT using a handheld probe for breast cancer detection.

A 3D reconstruction algorithm for electrical impedance tomography is presented for determining the distribution of electrical properties inside the body, given electrical measurements made on the surface. A linearized reconstruction algorithm using planar electrode arrays in a handheld probe geometry developed by Mueller et al (1999 IEEE Trans. Biomed. Eng. 46 1379-86) has been refined and extended in this paper. This algorithm is based on linearizing the conductivity about a constant value. We have extended the distance below the electrodes at which a target can be imaged by using a combination of two regularization schemes and a weighted mesh. An appropriate combination of Tikhonov and NOSER regularization produces satisfactory static images of a 2 cm cube placed 2 cm below the array, and difference images of a 1 cm cube 4 cm away from the array. The weighted mesh allows use of fixed regularization parameters for all depths of the target.

Reducing boundary effects in static EIT imaging.

Electrical impedance tomography (EIT) is a non-invasive technique used to image the electrical conductivity and permittivity within a body from measurements taken on the body's surface. High-quality static images are required for many medical imaging applications. Forming such images usually requires an accurate way to calculate the expected voltages on the surface resulting from the application of known currents to that surface. This is described as the forward problem. This paper introduces a new method to improve static images by using an improved forward solution which estimates a different conductivity value for each applied current pattern. This method, creating an automatically adjusting forward solution, can improve the sensitivity of static images under many EIT imaging applications. It does so by reducing the boundary effects caused by electrodes and any layered structures near them such as skin. The drawback of this method is that circularly symmetric structures of interest may be suppressed or eliminated from the images. The performance of this method is illustrated in a 2D circular phantom with simulation data from both a FEM model and experimental data.

Imaging cardiac activity by the D-bar method for electrical impedance tomography.

A practical D-bar algorithm for reconstructing conductivity changes from EIT data taken on electrodes in a 2D geometry is described. The algorithm is based on the global uniqueness proof of Nachman (1996 Ann. Math. 143 71-96) for the 2D inverse conductivity problem. Results are shown for reconstructions from data collected on electrodes placed around the circumference of a human chest to reconstruct a 2D cross-section of the torso. The images show changes in conductivity during a cardiac cycle.

Distinguishability of inhomogeneities using planar electrode arrays and different patterns of applied excitation.

Electrical impedance tomography (EIT) is a non-invasive technique used to image the electrical conductivity and permittivity within a body from measurements taken on the body surface. Four methods are being investigated for breast cancer diagnosis by EIT today: Single voltage source, single current source and multiple current sources with a fixed pre-determined 'canonical' pattern of currents and an adaptively determined 'optimal' pattern of currents. To determine which of these four methods might yield the best distinguishability using planar electrode arrays for breast cancer detection, we placed electrode arrays on a saline tank and used each excitation pattern to detect a conducting target placed at the centre of a flat electrode array in two geometries: mammography geometry and single probe geometry. The result was that the multiple current sources method had higher distinguishability than either the SCS or the SVS method. In both these electrode geometries, the optimal current pattern had higher distinguishability than the other patterns at all distances.

Current source design for electrical impedance tomography.

Questions regarding the feasibility of using electrical impedance tomography (EIT) to detect breast cancer may be answered by building a sufficiently precise multiple frequency EIT instrument. Current sources are desirable for this application, yet no current source designs have been reported that have the required precision at the multiple frequencies needed. We have designed an EIT current source using an enhanced Howland topology in parallel with a generalized impedance converter (GIC). This combination allows for nearly independent adjustment of output resistance and output capacitance, resulting in simulated output impedances in excess of 2 Gohms between 100 Hz and 1 MHz. In this paper, the theoretical operation of this current source is explained, and experimental results demonstrate the feasibility of creating a high precision, multiple frequency, capacitance compensated current source for EIT applications.

Phasic three-dimensional impedance imaging of cardiac activity.

Electrical impedance images were made using the ACT 3 instrument, which applies currents simultaneously to 32 electrodes and measures the resulting voltages on those same electrodes. A reconstruction algorithm was written for a three-dimensional cylinder having electrodes in two or four layers, using current patterns that pass current among different planes of electrodes, as well as within each plane. We have previously reported useful vertical resolution by the use of added layers of electrodes. The aim of the present study was to demonstrate that physiologically useful information can be obtained by examining cephalo-caudal differences in three-dimensional images. Phasic changes throughout the cardiac cycle are seen to be markedly different at the heart compared to lung region, both above and beside it. We formed hydrogel electrodes each 3 cm tall and 7 cm wide and applied them to the thorax of an upright human subject in four horizontal rows; each row contained eight electrodes. During breath-holding, cardiac activity was seen in all layers. With systole, conductivity in the anterior of the lowest layers decreased, but not in the upper layer. In the upper layers, conductivity increased with systole in many regions. These observations are consistent with the opposite changes in blood volume of the heart and lungs and the locations of these organs. This paper demonstrates the feasibility of producing and displaying physiologically interpretable three-dimensional images of the chest in real time.

Reconstruction of conductivity changes due to ventilation and perfusion from EIT data collected on a rectangular electrode array.

In this paper we demonstrate that conductivity changes caused by ventilation and perfusion in a human subject can be reconstructed from electrical impedance tomography data collected on a rectangular array of electrodes placed on a subject's chest. Currents are applied on the electrodes and the resulting voltages on the electrodes are measured. A 3D reconstruction algorithm is used to reconstruct the conductivity distribution in the region beneath the array. Time traces of the reconstructed conductivity distribution demonstrate the detected changes in conductivity due to ventilation and perfusion.

Real-time three-dimensional electrical impedance imaging.

Electrical impedance tomography is a technology for producing images of internal body structures based upon electrical measurements made from electrodes on the body surface. Typically a single plane of electrodes is used, seeking to reconstruct a cross section of the body. Yet the majority of image reconstruction algorithms ignore the three-dimensional (3D) characteristics of the current flow in the body. Actually, a substantial amount of current flows out of the electrode plane, creating distortions in the resulting images. This paper describes a reconstruction algorithm, ToDLeR, for solving a linearized 3D inverse problem in impedance imaging. The algorithm models the body as a homogeneous cylinder and accounts for the 3D current flow in the body by analytically solving for the current flow from one or more layers of electrodes on the surface of the cylinder. The algorithm was implemented on the ACT3 real-time imaging system and data were collected from a 3D test phantom using one, two and four layers of electrodes. By using multiple planes of electrodes, improved accuracy in any particular electrode plane was obtained, with decreased sensitivity to out-of-plane objects. A cylindrical target located vertically more than 8 cm below a single layer of 16 electrodes, and positioned radially midway between the centre and the boundary, produced an image that had 35% of the value obtained when the target was in the electrode plane. By adding an additional layer of 16 electrodes below the first electrode plane, and using 3D current patterns, this artefact was reduced to less than 10% of the peak value. We conclude that the 3D algorithm, used with multiple planes of electrodes, reduces the distortions from out-of-plane structures in the body.

A reconstruction algorithm for electrical impedance tomography data collected on rectangular electrode arrays.

A three-dimensional reconstruction algorithm in electrical impedance imaging is presented for determining the conductivity distribution beneath the surface of a medium, given surface voltage data measured on a rectangular array of electrodes. Such an electrode configuration may be desirable for using electrical impedence tomography to detect tumors in the human breast. The algorithm is based on linearizing the conductivity about a constant value. Here, we describe a simple implementation of the algorithm on a four-electrode--by-four-electrode array and the reconstructions obtained from numerical and experimental tank data. The results demonstrate significantly better spatial resolution in the plane of the electrodes than with respect to depth.

An iterative Newton-Raphson method to solve the inverse admittivity problem.

By applying electrical currents to the exterior of a body using electrodes and measuring the voltages developed on these electrodes, it is possible to reconstruct the electrical properties inside the body. This technique is known as electrical impedance tomography. The problem is nonlinear and ill conditioned meaning that a large perturbation in the electrical properties far away from the electrodes produces a small voltage change on the boundary of the body. This paper describes an iterative reconstruction algorithm that yields approximate solutions of the inverse admittivity problem in two dimensions. By performing multiple iterations, errors in the conductivity and permittivity reconstructions that result from a linearized solution to the problem are decreased. A finite-element forward-solver, which predicts voltages on the boundary of the body given knowledge of the applied current on the boundary and the electrical properties within the body, is required at each step of the reconstruction algorithm. Reconstructions generated from numerical data are presented that demonstrate the capabilities of this algorithm.

Effect of electrode size on impedance images of two- and three-dimensional objects.

The sensitivity of an impedance imaging system to small cylindrical inhomogeneities in two-dimensional (2-D) and three-dimensional (3-D) saline tanks was studied for different height electrodes and different height targets. Experimental results were compared with analytical models. Inhomogeneities in the 3-D tank having limited vertical extent were detected by electrodes of vertical size comparable to that of the inhomogeneity. Taller electrodes had increased sensitivity to short targets to only a limited extent. When the electrode height was more than twice that of the target, sensitivity decreased or remained the same with further increases in electrode height. The system was less sensitive to inhomogeneities in the 3-D tank than to those in the 2-D tank. The distinguishability of conductors was greater than that of insulators in the 3-D tank, and the opposite was true in the 2-D tank, consistent with an analytical result.

Electrical impedance tomography of complex conductivity distributions with noncircular boundary.

Electrical impedance tomography (EIT) uses low-frequency current and voltage measurements made on the boundary of a body to compute the conductivity distribution within the body. Since the permittivity distribution inside the body also contributes significantly to the measured voltages, the present reconstruction algorithm images complex conductivity distributions. A finite element model (FEM) is used to solve the forward problem, using a 6017-node mesh for a piecewise-linear potential distribution. The finite element solution using this mesh is compared with the analytical solution for a homogeneous field and a maximum error of 0.05% is observed in the voltage distribution. The boundary element method (BEM) is also used to generate the voltage data for inhomogeneous conductivity distributions inside regions with noncircular boundaries. An iterative reconstruction algorithm is described for approximating both the conductivity and permittivity distributions from this data. The results for an off-centered inhomogeneity showed a 35% improvement in contrast from that seen with only one iteration, for both the conductivity and the permittivity values. It is also shown that a significant improvement in images results from accurately modeling a noncircular boundary. Both static and difference images are distorted by assuming a circular boundary and the amount of distortion increases significantly as the boundary shape becomes more elliptical. For a homogeneous field in an elliptical body with axis ratio of 0.73, an image reconstructed assuming the boundary to be circular has an artifact at the center of the image with an error of 20%. This error increased to 37% when the axis ratio was 0.64. A reconstruction algorithm which used a mesh with the same axis ratio as the elliptical boundary reduced the error in the conductivity values to within 0.5% of the actual values.

Assessment of acute pulmonary edema in dogs by electrical impedance imaging.

Acute pulmonary edema was assessed quantitatively in 12 experiments on six anesthetized dogs. Thirty-two copper foil electrodes were placed around each animal's thorax at the level of the third intercostal space. A real-time electrical impedance tomograph was used to form images of the electrical admittivity of the thorax in and near the plane of these electrodes. The lungs were identified by studying the change in admittivity associated with inspiration. Mean admittivity in these lung regions was assessed at 40-min intervals for the next 3-6 hours. In six control experiments, each having a duration of 200 min, the initial admittivity of the lung regions was 102 +/- 16(SD) mS/m. Lung admittivity usually increased during the first 80 min, and then remained within 2 mS/m of its value at 80 min for the remaining 120 min. In six experiments with pulmonary edema, an initial period of change followed by stability was observed. When stability had been attained, 0.07 ml/kg of oleic acid was injected slowly into a central venous site. Five animals received oleic acid, the sixth received a sham injection of saline. In the five receiving oleic acid, lung admittivity rose steadily for the remainder of the experiment. The increase in lung admittivity in these five animals was between 4 and 16 mS/m. In the sham injected experiment, the lung admittivity changed by 1 mS/m. We conclude that impedance imaging can provide semiquantitative assessment of the development of acute pulmonary edema.

A real-time electrical impedance tomograph.

Electrical properties of tissues in the human body can be imaged using a technology known as Electrical Impedance Tomography. In this modality, sinusoidal electrical currents are applied to the body using electrodes attached to the skin, and voltages that are developed on the electrodes are measured. Using these data, a reconstruction algorithm computes the conductivity and permittivity distributions within the body. This paper describes the reconstruction algorithm, image display algorithm, and hardware of a real-time Electrical Impedance Tomograph known as the Real-Time Imaging System. The reconstruction algorithm, executed by a commercially available coprocessor board that resides in a 386-based personal computer, is a modification of the Newton's One Step Error Reconstructor (NOSER) that minimizes algorithm execution time by precomputing many quantities. The image display algorithm, also executed by the coprocessor board, maps the output of the reconstruction algorithm into an image which is displayed using a video graphics board. The architecture of the system and execution times of algorithms implemented by the system are discussed. Using the continuous data acquisition mode of the Real-Time Imaging System, data from the thorax of a normal human subject were collected. Admittivity changes in the chest, as a result of respiration and the cardiac cycle, are presented. Data that were collected from the leg of a normal subject are shown which demonstrate capabilities of the triggered data acquisition mode of the system, allowing data acquisition synchronization with an electrocardiogram.

ACT3: a high-speed, high-precision electrical impedance tomograph.

This paper presents the design, implementation, and performance of Rensselaer's third-generation Adaptive Current Tomograph, ACT3. This system uses 32 current sources and 32 phase-sensitive voltmeters to make a 32-electrode system that is capable of applying arbitrary spatial patterns of current. The instrumentation provides 16 b precision on both the current values and the real and reactive voltage readings and can collect the data for a single image in 133 ms. Additionally, the instrument is able to automatically calibrate its voltmeters and current sources and adjust the current source output impedance under computer control. The major system components are discussed in detail and performance results are given. Images obtained using stationary agar targets and a moving pendulum in a phantom as well as in vivo resistivity profiles showing human respiration are shown.