t. This paper surveys some of the work our group has done in electrical impedance tomography.

Electrical Impedance Tomography

A new method for the ablation of undesirable tissue such as cells of a cancerous or non-cancerous tumor is disclosed. It involves the placement of electrodes into or near the vicinity of the undesirable tissue through the application of electrical pulses causing irreversible electroporation of the cells throughout the entire area of the undesirable tissue. The electric pulses irreversibly permeate the cell membranes, thereby invoking cell death. The irreversibly permeabilized cells are left in situ and are removed by the body immune system. The amount of tissue ablation achievable through the use of irreversible electroporation without inducing thermal damage is considerable.

Tissue ablation with irreversible electroporation

The following experiment is considered. To a body of given conductivity, a number of electrodes are attached, through which current is sent. On the same electrodes, the resulting voltages are measured. This experiment can be described by a number of mathematical models [K.-S. Cheng et al., IEEE Transactions on Biomedical Engineering, 36 (1989), pp. 918–924]. These models are discussed and their predictions compared with experiment. In particular, a model is exhibited that is capable of predicting the experimentally measured voltages to within 0.1 percent. For this model, existence and uniqueness of the associated electrical potential is proved.

Existence and uniqueness for electrode models for electric current computed tomography

EIDORS is an open source software suite for image reconstruction in electrical impedance tomography and diffuse optical tomography, designed to facilitate collaboration, testing and new research in these fields. This paper describes recent work to redesign the software structure in order to simplify its use and provide a uniform interface, permitting easier modification and customization. We describe the key features of this software, followed by examples of its use. One general issue with inverse problem software is the difficulty of correctly implementing algorithms and the consequent ease with which subtle numerical bugs can be inadvertently introduced. EIDORS helps with this issue, by allowing sharing and reuse of well-documented and debugged software. On the other hand, since EIDORS is designed to facilitate use by non-specialists, its use may inadvertently result in such numerical errors. In order to address this issue, we develop a list of ways in which such errors with inverse problems (which we refer to as 'cheats') may occur. Our hope is that such an overview may assist authors of software to avoid such implementation issues.

/pdf/uses-and-abuses-of-eidors-an-extensible-software-base-for-2wfh5gpw2q.pdf

Uses and abuses of EIDORS: an extensible software base for EIT

We review theoretical and numerical studies of the inverse problem of electrical impedance tomography which seeks the electrical conductivity and permittivity inside a body, given simultaneous measurements of electrical currents and potentials at the boundary.

/pdf/electrical-impedance-tomography-3po2ct3t0v.pdf

Electrical impedance 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. >

Electrode models for electric current computed tomography

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. >

/pdf/act3-a-high-speed-high-precision-electrical-impedance-19ie483iyr.pdf

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

An electric current tomograph

In electric current computed tomography, patterns of currents or voltages are applied to electrodes on the surface of a body and the resulting voltages or currents are measured. A reconstruction and display of an approximation to the impedance inside the body is then made based on these external measurements.It is shown how the problems of choosing current patterns, electrode size and number can be studied in terms of the spectral properties of certain pseudodifferential operators.The proofs given here are simpler and more general than those in [ IEEE Trans. Medical Imaging, 5 (1986), pp. 91–95] and [Clin. Phys. Physiol. Meas. Suppl. A, (1987), pp. 39–46].

Electric current computed tomography eigenvalues

The authors introduce a definition of 'best' currents to apply to an electrode array on the surface of a body in order to distinguish between the conductivity inside the body and a conjectured conductivity. Using these 'best' currents, they illustrate with a simple example the general fact that a single current applied between a pair of electrodes loses its ability to distinguish between different conductivities as the size of the region over which the current is applied goes to zero. They next introduce approximations to the best currents on systems having L electrodes, and calculate the ability of these systems to distinguish between conductivities as L goes to infinity and the electrode size goes to zero. It is concluded with a simple example that illustrates a process for producing the 'best' currents without a previous knowledge of what is inside the body.

https://iopscience.iop.org/article/10.1088/0143-0815/8/4A/005/pdf

D.G. Gisser

Papers

Electrode models for electric current computed tomography

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

An electric current tomograph

Electric current computed tomography eigenvalues

Current topics in impedance imaging