Jonathan C. Newell

Electrical Impedance Tomography

Electrical impedance tomography (EIT) is an imaging modality that estimates the electrical properties at the interior of an object from measurements made on its surface. Typically, currents are injected into the object through electrodes placed on its surface, and the resulting electrode voltages are measured. An appropriate set of current patterns, with each pattern specifying the value of the current for each electrode, is applied to the object, and a reconstruction algorithm uses knowledge of the applied current patterns and the measured electrode voltages to solve the inverse problem, computing the electrical conductivity and permittivity distributions in the object. This article focuses on the type of EIT called adaptive current tomography (ACT) in which currents are applied simultaneously to all the electrodes. A number of current patterns are applied, where each pattern defines the current for each electrode, and the subsequent electrode voltages are measured to generate the data required for image reconstruction. A ring of electrodes may be placed in a single plane around the object, to define a two-dimensional problem, or in several layers of such rings, to define a three-dimensional problem. The reconstruction problem is described and two algorithms are discussed, a one-step, two-dimensional (2-D) Newton-Raphson algorithm and a one-step, full three-dimensional (3-D) reconstructor. Results from experimental data are presented which illustrate the performance of the algorithms.

Electrode models for electric current computed tomography

A mathematical model for the physical properties of electrodes suitable for use in electric current computed tomography is discussed. The model includes the effects of discretization, shunt, and contact impedance. The complete model was validated by experiment. Bath resistivities of 284.0, 139.7, 62.3, and 29.5 Omega -cm were studied. Values of effective contact impedance used in the numerical approximations were 58.0, 35.0, 15.0, and 7.5 Omega -cm/sup 2/, respectively. Agreement between the calculated and experimentally measured values was excellent throughout the range of bath conductivities studied. It is desirable in electrical impedance imaging systems to model the observed voltages to the same precision as they are measured in order to be able to make the highest-resolution reconstructions of the internal conductivity that the measurement precision allows. The complete electrode model, which includes the effects of discretization of the current pattern, the shunt effect due to the highly conductive electrode material, and the effect of an effective contact impedance, allows calculation of the voltages due to any current pattern applied to a homogeneous resistivity field.<<ETX>>

NOSER: An algorithm for solving the inverse conductivity problem

The inverse conductivity problem is the mathematical problem that must be solved in order for electrical impedance tomography systems to be able to make images. Here we show how this inverse conductivity problem is related to a number of other inverse problem. We then explain the workings of an algorithm that we have used to make images from electrical impedance data measured on the boundary of a circle in two dimensions. This algorithm is based on the method of least squares. It takes one step of a Newtons method, using a constant conductivity as an initial guess. Most of the calculations can therefore be done analytically. The resulting code is named NOSER, for Newtons One‐Step Error Reconstructor. It provides a reconstruction with 496 degrees of freedom. The code does not reproduce the conductivity accurately (unless it differs very little from a constant), but it yields useful images. This is illustrated by images reconstructed from numerical and experimental data, including data from a human chest.

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

Presents the design, implementation, and performance of Rensselaers 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.<<ETX>>

An electric current tomograph

A description is given of an instrument designed to acquire data for the construction of images of internal body structures based on measurements of electrical impedance made from a set of electrodes applied around the periphery of the body. The instrument applies currents at 15 kHz in any desired pattern to 32 electrodes and measures the resulting voltage at each electrode. The construction of a test phantom is also described and the results of initial studies showing the distinguishability of targets of differing sizes and conductivities placed in the phantom are reported. The system is able to distinguish the presence of 9-mm-diameter insulators or conductors placed in the center of a 30-cm-diameter circular tank of salt water. This system is capable of implementing an adaptive process of produce the best currents to distinguish the unknown conductivity from a homogeneous conductivity.<<ETX>>

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.

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 impedance tomography to detect tumors in the human breast. The algorithm is based on linearizing the conductivity about a constant value. Here, the authors 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.

Reconstructions of chest phantoms by the D-bar method for electrical impedance tomography

The problem this paper addresses is how to use the two-dimensional D-bar method for electrical impedance tomography with experimental data collected on finitely many electrodes covering a portion of the boundary of a body. This requires an approximation of the Dirichlet-to-Neumann, or voltage-to-current density map, defined on the entire boundary of the region, from a finite number of matrix elements of the current-to-voltage map. Reconstructions from experimental data collected on a saline filled tank containing agar heart and lung phantoms are presented, and the results are compared to reconstructions by the NOSER algorithm on the same data.

Influence of hematocrit on cardiopulmonary function after acute hemorrhage.

The ‘optimal’ hematocrit to which patients should be resuscitated after shock and trauma is controversial. To test the hypothesis that sufficient oxygen delivery can be provided at a lower hematocrit without impairing oxygen consumption or hemodynamic function, 25 patients were prospectively studied

Failure of red blood cell transfusion to increase oxygen transport or mixed venous PO2 in injured patients.

Post-trauma patients have an oxygen consumption which is proportional to oxygen delivery, suggesting that tissue oxygen consumption is limited by diffusion. Transfusion of packed red blood cells (RBC), which increases the oxygen-carrying capacity of blood, would be expected to increase mixed venous PO2, thereby improving tissue oxygenation. However, the low P50 of stored blood may increase the affinity of hemoglobin for oxygen and reduce oxygen consumption. To evaluate the net effect of these mechanisms, we studied hemodynamic and oxygen transport parameters before and after RBC transfusion in eight critically ill patients. Mixed venous O2 content was measured directly by fuel cell O2 analyzer, and standard P50 was calculated. Following transfusion of one unit of packed RBC which increased mean hemoglobin from 9.2 +/- 0.3 gm/dl to 10.1 +/- 0.3 gm/dl (p less than 0.01), there were no changes in oxygen delivery (490 +/- 80 ml/min/m2), oxygen consumption (210 +/- 30 ml/min/m2), or mixed venous PO/ (37 +/- 2 Torr). Cardiac index (4.1 +/- 0.71 L/min) decreased by 0.4 L/min/m2 (p less than 0.05). Standard P50 decreased by 4.2 +/- 2.4 Torr following transfusion of two units of RBC (p less than 0.05). Red blood cell transfusion thus failed to increase oxygen consumption in these patients, despite an increase in oxygen content. Thus, RBC transfusion may not improve tissue oxygenation.