Electrical Impedance Tomography (EIT) is an imaging technology based on the electrical characteristics of biological tissue, allowing the reconstruction of the impedance distribution in a transversal section of an object, based on the peripheral voltage profile, resulting from the successive application of drive currents in a number of determined positions. Since the major problems in Electrical Impedance Imaging are encountered in the solution of the inverse problem, i.e. to find a unique 2- or 3-dimensional impedance distribution, given a vector of measured boundary voltages, the most straightforward and most promising application of ANN's will be situated in this domain.Despite the combinatorial explosion that can be observed in the number of reconstruction strategies described in various publications last years, the majority of them is still facing, in more or less degree of severity, two of the basic shortcomings inherited from the earlier reconstruction techniques : noise susceptibility and prolonged calculation times. Observing these facts, it was a small step to the idea of introducing Neural Network strategies to help overcome these problems. The massive parallelism and connectionism of these networks is reflected both in their innate ability to learn in a generalized fashion, contributing to a considerable degree of noise immunity, and their almost instantaneous respons, once they passed the learning process, tackling virtually all time related constraints and opening the doors to high speed real-time imaging. The type of network organization considered in this application, is the so called Spin Glass based neural network or Hopfield network. These symmetrical, fully connected networks, are despite their almost simplistic topology, backed by one of the most extensive mathematical and physical theories in the NN community, partially explaining their intriguing behaviour. John Hopfield's main contribution consisted of the development of an explicit formalization, describing the isomorphism between Spin Glass Systems in physics and these symmetrical networks. As a direct result, it was straightforward to define a measure describing the state of the system, called the computational energy, very closely related to the concept of energy in Spin Glasses. The evolution of the network state can be visualized as an evolution along trajectories on an energy surface, starting from an initial state proceeding towards a local or global energy minimum.Considering the nature of the measurement results in EIT, a very high degree of variability may be expected, due to the large number of noncontrollable and often obscure influence parameters. This characteristic will prevent a fundamental analysis of the learning performance. In an initial phase, much more informative conclusions may be drawn, when the training set or peripheral voltage profile is not derived from in vivo measurements or in vitro experiments, but mathematically synthesized from a geometric description combined with an impedance description, using a simulator or forward solver. Noise influence and errors due to measurement artifacts may be added in a controlled fashion, to analyze system performance under conditions approximating those of real measurements.The simulator uses a finite differences approximation method (FDM) for solving the set of nonlinear partial difference equations, describing the forward solution. The 2-D or 3-D continuous impedance distribution will be modelled by a 2- or 3-dimensional discretized resistivity mesh. Taking into account the very large number of simulations required to train adequately the networks, and given the excessive number of calculations in 3-D simulations, optimization is a necessity. If these optimized techniques still appear to be unacceptable slow on the Sparc Station 1+, an implementation of this algorithm on the CRAY XMP/4 supercomputer of the shared computing center of the VUB-ULB in Brussels, is considered.
Truyen, B 1991, Spin glass model based neural networks for applications in EIT. in Proceedings Neural Networks in Biomedical Engineering. Vrije Universiteit Brussel, Brussels, Belgium, Neural Networks in Biomedical Engineering, Brussels, Belgium, 19/07/91.
Truyen, B. (1991). Spin glass model based neural networks for applications in EIT. In Proceedings Neural Networks in Biomedical Engineering Vrije Universiteit Brussel.
@inproceedings{64bc6022dc93490d9c5f928c47f5e278,
title = "Spin glass model based neural networks for applications in EIT",
abstract = "Electrical Impedance Tomography (EIT) is an imaging technology based on the electrical characteristics of biological tissue, allowing the reconstruction of the impedance distribution in a transversal section of an object, based on the peripheral voltage profile, resulting from the successive application of drive currents in a number of determined positions. Since the major problems in Electrical Impedance Imaging are encountered in the solution of the inverse problem, i.e. to find a unique 2- or 3-dimensional impedance distribution, given a vector of measured boundary voltages, the most straightforward and most promising application of ANN's will be situated in this domain.Despite the combinatorial explosion that can be observed in the number of reconstruction strategies described in various publications last years, the majority of them is still facing, in more or less degree of severity, two of the basic shortcomings inherited from the earlier reconstruction techniques : noise susceptibility and prolonged calculation times. Observing these facts, it was a small step to the idea of introducing Neural Network strategies to help overcome these problems. The massive parallelism and connectionism of these networks is reflected both in their innate ability to learn in a generalized fashion, contributing to a considerable degree of noise immunity, and their almost instantaneous respons, once they passed the learning process, tackling virtually all time related constraints and opening the doors to high speed real-time imaging. The type of network organization considered in this application, is the so called Spin Glass based neural network or Hopfield network. These symmetrical, fully connected networks, are despite their almost simplistic topology, backed by one of the most extensive mathematical and physical theories in the NN community, partially explaining their intriguing behaviour. John Hopfield's main contribution consisted of the development of an explicit formalization, describing the isomorphism between Spin Glass Systems in physics and these symmetrical networks. As a direct result, it was straightforward to define a measure describing the state of the system, called the computational energy, very closely related to the concept of energy in Spin Glasses. The evolution of the network state can be visualized as an evolution along trajectories on an energy surface, starting from an initial state proceeding towards a local or global energy minimum.Considering the nature of the measurement results in EIT, a very high degree of variability may be expected, due to the large number of noncontrollable and often obscure influence parameters. This characteristic will prevent a fundamental analysis of the learning performance. In an initial phase, much more informative conclusions may be drawn, when the training set or peripheral voltage profile is not derived from in vivo measurements or in vitro experiments, but mathematically synthesized from a geometric description combined with an impedance description, using a simulator or forward solver. Noise influence and errors due to measurement artifacts may be added in a controlled fashion, to analyze system performance under conditions approximating those of real measurements.The simulator uses a finite differences approximation method (FDM) for solving the set of nonlinear partial difference equations, describing the forward solution. The 2-D or 3-D continuous impedance distribution will be modelled by a 2- or 3-dimensional discretized resistivity mesh. Taking into account the very large number of simulations required to train adequately the networks, and given the excessive number of calculations in 3-D simulations, optimization is a necessity. If these optimized techniques still appear to be unacceptable slow on the Sparc Station 1+, an implementation of this algorithm on the CRAY XMP/4 supercomputer of the shared computing center of the VUB-ULB in Brussels, is considered.",
author = "Bart Truyen",
year = "1991",
language = "English",
booktitle = "Proceedings Neural Networks in Biomedical Engineering",
publisher = "Vrije Universiteit Brussel",
note = "Neural Networks in Biomedical Engineering ; Conference date: 19-07-1991 Through 19-07-1991",
}