EIT Reconstruction Algorithms for Respiratory Intensive Care

Electrical impedance tomography (EIT) is an emerging medical imaging technique that aims to reconstruct the internal conductivity distribution of a subject from electrical measurements obtained on the skin. In this thesis we explore the promising application of EIT to the respiratory monitoring of humans. We pay particular focus to the forward problem, highlighting the need to have an accurately known external boundary shape and electrode positions on a reconstruction model. A theoretical study of uniqueness results of EIT with an unknown external boundary shape is presented. A novel sensitivity study of the external boundary shape is presented as well as results from a reconstruction algorithm to account for errors in electrode position with simulated data in 3D. We also demonstrate results of a shape correction algorithm from a pilot study of lung EIT with data collected using the fEITER system, and MR images used to inform the external boundary shape of healthy subjects. After image co-registration of the resulting dynamic 3D EIT reconstruction images with the lung-segmented MR image, we outline a novel mutual information performance criterion to measure the quality of reconstructed images. We also outline the computation of the forward problem of the complete electrode model in 3D using high order polynomial finite elements and present convergence results in 2D for the continuum, point and complete electrode model. Our numerical study demonstrates that the convergence rate of the forward problem is independent of the polynomial approximation order for the complete electrode model and there is no global convergence for the point electrode model in the energy norm. Reconstructed conductivity images can be difficult to interpret at the bedside. Moreover clinicians would like clinically meaningful indices, such as regional lung compliance, to determine the pathologies of patients in real time. By modelling the respiratory system as a coupled time dependent system of simple mechanical functional units, we propose a novel methodology to couple mechanical ventilation and EIT. The mechanical properties of the lungs are estimated through an inverse coefficient problem on coupled ODEs, with the measurable data being the time series of pressure at airway opening and interior air volume data. We present results with simulated data as well as a discussion on extensions and limitations to the mechanical models. Finally we present a theoretical discussion of anisotropic EIT. It is well known that any diffeomorphism fixing points on the boundary gives rise to a conductivity with the same electrical measurements on the skin, generating a large class of conductivities that are electrically equivalent. We define novel classes of anisotropic media with constraints on their eigenspace: prescribed eigenvalues, prescribed orthogonal coordinates, prescribed eigenvectors, fibrous and layered conductivities. By drawing analogies with elasticity theory, we discuss how these constraints on the eigenspace restrict the set of diffeomorphisms fixing points on the boundary, and present two uniqueness results for anisotropic conductivities with prescribed eigenvalues and prescribed eigenvectors