Absolute electrical impedance tomography (aEIT) guided ventilation therapy in critical care patients: simulations and future trends

Thoracic electrical impedance tomography (EIT) is a noninvasive, radiation-free monitoring technique whose aim is to reconstruct a cross-sectional image of the internal spatial distribution of conductivity from electrical measurements made by injecting small alternating currents via an electrode array placed on the surface of the thorax. The purpose of this paper is to discuss the fundamentals of EIT and demonstrate the principles of mechanical ventilation, lung recruitment, and EIT imaging on a comprehensive physiological model, which combines a model of respiratory mechanics, a model of the human lung absolute resistivity as a function of air content, and a 2-D finite-element mesh of the thorax to simulate EIT image reconstruction during mechanical ventilation. The overall model gives a good understanding of respiratory physiology and EIT monitoring techniques in mechanically ventilated patients. The model proposed here was able to reproduce consistent images of ventilation distribution in simulated acutely injured and collapsed lung conditions. A new advisory system architecture integrating a previously developed data-driven physiological model for continuous and noninvasive predictions of blood gas parameters with the regional lung function data/information generated from absolute EIT (aEIT) is proposed for monitoring and ventilator therapy management of critical care patients

Nonlinear Inversion from Partial EIT Data: Computational Experiments

Electrical impedance tomography (EIT) is a non-invasive imaging method in which an unknown physical body is probed with electric currents applied on the boundary, and the internal conductivity distribution is recovered from the measured boundary voltage data. The reconstruction task is a nonlinear and ill-posed inverse problem, whose solution calls for special regularized algorithms, such as D-bar methods which are based on complex geometrical optics solutions (CGOs). In many applications of EIT, such as monitoring the heart and lungs of unconscious intensive care patients or locating the focus of an epileptic seizure, data acquisition on the entire boundary of the body is impractical, restricting the boundary area available for EIT measurements. An extension of the D-bar method to the case when data is collected only on a subset of the boundary is studied by computational simulation. The approach is based on solving a boundary integral equation for the traces of the CGOs using localized basis functions (Haar wavelets). The numerical evidence suggests that the D-bar method can be applied to partial-boundary data in dimension two and that the traces of the partial data CGOs approximate the full data CGO solutions on the available portion of the boundary, for the necessary small $k$ frequencies.Comment: 24 pages, 12 figure

A multiscattering series for impedance tomography in layered media

We introduce an inversion algorithm for tomographic images of layered media. The algorithm is based on a multiscattering series expansion of the Green function that, unlike the Born series, converges unconditionally. Our inversion algorithm obtains images of the medium that improves iteratively as we use more and more terms in the multiscattering series. We present the derivation of the multiscattering series, formulate the inversion algorithm and demonstrate its performance through numerical experiments

Discrete mathematical models for electrical impedance tomography

Electrical Impedance Tomography (EIT) is a non-invasive, portable and low-cost medical imaging technique. Different current patterns are injected to the surface of a conductive body and the corresponding voltages are measured also on the boundary. These mea-surements are the data used to infer the interior conductivity distribution of the object. However, it is well known that the reconstruction process is extremely ill-posed due to the low sensitivity of the boundary voltages to changes in the interior conductivity distribution. The reconstructed images also suffer from poor spatial resolution. In tomographic systems, the spatial resolution is related to the number of applied current patterns and to the number and positions of electrodes which are placed at the surface of the object under examination. Two mammographic sensors were recently developed at the University of Mainz in collaboration with Oxford Brookes University. These prototypes consist of a planar sensing head of circular geometry with twelve large outer (active) electrodes arranged on a ring of radius 4.4cm where the external currents are injected and a set of, respectively thirty six and fifty four point-like high-impedance inner (passive) electrodes arranged in a hexagonal pattern where the induced voltages are measured. Two 2D reconstruction methods were proposed for these devices, one based on resistor network models and another one which uses an integral equation formulation. The novelty of the device and hence of these imaging techniques consists exactly in the distinct use of active and passive electrodes. The 2D images of the conductivity distribution of the interior tissue of the breast provide only information about the existence and location of the tumour. In this thesis different circular designs for the sensing head of this EIT device were analysed. The 2D resistor network approach was adapted to the different data collection geometries and the sensitivity of the reconstructions with respect to errors in the simulate data were investigated before any modifications to the original design were made. A novel 3D reconstruction algorithm was also developed for a simpler geometry of the sensing head which consisted of a rectangular array of thirty six electrodes (twenty active+ sixteen passive). This electrode configuration as well as the proposed imaging technique are intended to be used for breast cancer detection. The algorithm is based on linearizing the conductivity about a constant value and allows real-time reconstructions. The perfor-mance of the algorithm was tested on numerically simulated data and small inclusions with conductivities three or four times the background lying beneath the data collection surface were successfully detected. The results were fairly stable with respect to the noise level in the data and displayed very good spatial resolution in the plane of electrodes

A Hybrid Segmentation and D-bar Method for Electrical Impedance Tomography

The Regularized D-bar method for Electrical Impedance Tomography provides a rigorous mathematical approach for solving the full nonlinear inverse problem directly, i.e. without iterations. It is based on a low-pass filtering in the (nonlinear) frequency domain. However, the resulting D-bar reconstructions are inherently smoothed leading to a loss of edge distinction. In this paper, a novel approach that combines the rigor of the D-bar approach with the edge-preserving nature of Total Variation regularization is presented. The method also includes a data-driven contrast adjustment technique guided by the key functions (CGO solutions) of the D-bar method. The new TV-Enhanced D-bar Method produces reconstructions with sharper edges and improved contrast while still solving the full nonlinear problem. This is achieved by using the TV-induced edges to increase the truncation radius of the scattering data in the nonlinear frequency domain thereby increasing the radius of the low pass filter. The algorithm is tested on numerically simulated noisy EIT data and demonstrates significant improvements in edge preservation and contrast which can be highly valuable for absolute EIT imaging

Multilevel Double Loop Monte Carlo and Stochastic Collocation Methods with Importance Sampling for Bayesian Optimal Experimental Design

An optimal experimental set-up maximizes the value of data for statistical inferences and predictions. The efficiency of strategies for finding optimal experimental set-ups is particularly important for experiments that are time-consuming or expensive to perform. For instance, in the situation when the experiments are modeled by Partial Differential Equations (PDEs), multilevel methods have been proven to dramatically reduce the computational complexity of their single-level counterparts when estimating expected values. For a setting where PDEs can model experiments, we propose two multilevel methods for estimating a popular design criterion known as the expected information gain in simulation-based Bayesian optimal experimental design. The expected information gain criterion is of a nested expectation form, and only a handful of multilevel methods have been proposed for problems of such form. We propose a Multilevel Double Loop Monte Carlo (MLDLMC), which is a multilevel strategy with Double Loop Monte Carlo (DLMC), and a Multilevel Double Loop Stochastic Collocation (MLDLSC), which performs a high-dimensional integration by deterministic quadrature on sparse grids. For both methods, the Laplace approximation is used for importance sampling that significantly reduces the computational work of estimating inner expectations. The optimal values of the method parameters are determined by minimizing the average computational work, subject to satisfying the desired error tolerance. The computational efficiencies of the methods are demonstrated by estimating the expected information gain for Bayesian inference of the fiber orientation in composite laminate materials from an electrical impedance tomography experiment. MLDLSC performs better than MLDLMC when the regularity of the quantity of interest, with respect to the additive noise and the unknown parameters, can be exploited