# Workshop on Stroke classification and monitoring using Electrical Impedance Tomography

## Department of Mathematics and Statistics, University of Helsinki

### 25-26 April 2018

 Stefan Björkman, University of Helsinki, Finland. Title: Presentation of the Saari unit of Department of Production Animal Medicine Bachir Dekdouk, Tampere University of Technology, Finland. Title: Understanding Stroke Manifestations and Project Outlook for EIT Imaging Abstract: For the last two decades, interests of EIT community in stroke detection, led the commonly known causes of stroke generally described as either blockage or leakage of blood flow into the brain to formulate the problem as merely the formation of single local volumes with relatively shortage or excess of blood respectively, which can be detected by an increase or decrease in the transcranial impedances. Thus, this mis-representation of the pathology has been passed on over literature and was blindly adopted by engineers and mathematicians in designing imaging and classification algorithms for stroke types based on a quite inaccurate problem setting. In this presentation, based on a throughout literature review, major stroke types and related progressive pathophysiological processes are described in attempt to highlight the interior tissue dielectric property changes starting from the acute phase, which need to be taken into account in EIT. Possible applications for EIT to help aid the existing imaging modalities in stroke detection/management are outlined. Finally, the work progress done so far is described and required data inputs necessary for fulfilling project objectives are highlighted. Andreas Hauptmann, University College London, UK. Title: Deep Learning for image reconstruction - Deep D-Bar Abstract: In this talk I will give an introduction to Deep Learning for image reconstruction with a special focus on Electrical Impedance tomography (EIT) and the D-bar algorithm. Specifically, D-bar methods are based on a rigorous mathematical analysis and provide robust direct reconstructions by using a low-pass filtering of the associated nonlinear Fourier data. Similarly to low-pass filtering of linear Fourier data, only using low frequencies in the image recovery process results in blurred images lacking sharp features such as clear organ boundaries. Convolutional Neural Networks provide a powerful framework for post-processing such convolved direct reconstructions. The networks are trained on simulated examples and then applied to experimental data without the need to perform an additional transfer training. Results for absolute EIT images are presented using experimental EIT data from the ACT4 and KIT4 EIT systems. Additionally to accompany the workshop theme, we will present some preliminary studies with a stroke phantom on reconstruction and classification using Deep Learning. Sarah Hamilton, Marquette University, USA. Title: Robust Recovery of Admittivities for 2D Real-time Absolute/Difference EIT Abstract: The recovery of absolute (or static) EIT images is a notoriously challenging problem. Optimization based methods are strive to minimize the error between the measured data and data simulated by solving the forward conductivity problem (e.g., via FEM) for a guess conductivity. The optimization is highly sensitive to errors in domain modeling (shape, electrode locations, contact impedances) and modeling of system/environmental noise. Although many of these modeling errors can be overcome for tank data, imaging of live or moving subjects is another story. Here we explore how D-bar methods can robustly recover a conductivity/admittivity even when incorrect boundary shapes and electrode locations are used. We focus on a specific D-bar method which requires no $\Lambda_1$ data for absolute imaging completely removing the need to simulate any data and thus the need for a finely tuned forward model. Various ways of including a priori information are discussed, in particular how the D-bar methods can be combined with Convolutional Neural Networks (CNNs) to sharpen blurry D-bar images without ever needing to simulate the current/voltage data or electrode locations. Possible extensions to partial boundary data and 3D are discussed. Antti Hannukainen, Aalto University, Finland. Title: Parametric model of human head Nuutti Hyvönen, Aalto University, Finland. Title: Generalized linearization in electrical impedance tomography Abstract: Electrical impedance tomography aims at reconstructing the interior electrical conductivity from surface measurements of currents and voltages. As the current-voltage pairs depend nonlinearly on the conductivity, impedance tomography leads to a nonlinear inverse problem. Often, the forward problem is linearized with respect to the conductivity and the resulting linear inverse problem is regarded as a subproblem in an iterative algorithm or as a simple reconstruction method as such. We compare this basic linearization approach to linearizations with respect to the resistivity or the logarithm of the conductivity. It is numerically demonstrated that the conductivity linearization often results in compromised accuracy. Inspired by these observations, we present and analyze a new linearization technique which is based on the logarithm of the Neumann-to-Dirichlet operator. The method is directly applicable to discrete settings, including the complete electrode model. We also consider Frechet derivatives of the logarithmic operators. Numerical examples indicate that the proposed method is an accurate way of linearizing the problem of electrical impedance tomography. Matti Lassas, University of Helsinki, Finland. Title: Inverse problems for hyperbolic equations and artificial point sources Abstract: We consider uniqueness results for inverse problems for hyperbolic equations. Our aim is to determine the Riemannian metric, associated to travel times of waves, inside a domain from the observations done on the boundary. The inverse problems on Riemannian manifolds ar not generally uniquely solvable: A change of coordinates changes the equation but does not change the boundary data. To prove uniqueness results, one may consider properties that are invariant in diffeomorphisms and aim to reconstruct those uniquely. For example, there is an underlying manifold structure that can be uniquely determined. Thus the inverse problem in a subset of the Euclidean space can solved in two steps. The first one is to reformulate the problem in terms of manifolds and to reconstruct the underlying manifold structure. The second step is to find an embedding of the constructed manifold to the Euclidean space. In the talk we focus to the reconstruction of the invariant manifold structure. We consider solutions of hyperbolic inverse problems that are based on focusing of waves. For linear equations we consider a time reversal iteration where one focuses waves in an unknown medium. For non-linear equations we consider the artificial point source method that applies the non-linear interaction of spherical waves or distorted plane waves to create points sources inside the medium. The new feature of the artificial point source method is that it utilizes the non-linearity as a tool in imaging. The above methods reduce the inverse boundary value problems to passive imaging problems where one observes waves coming from the point sources that are inside the medium, and these problems are solved using geometric methods. Matteo Santacesaria, University of Helsinki, Finland. Title: Calderón's Inverse Problem with a Finite Number of Measurements Abstract: In this talk I will discuss how ideas from applied harmonic analysis, in particular sampling theory and compressed sensing (CS), may be applied to inverse problems in PDEs. The focus will be on inverse boundary value problems for the conductivity and the Schrodinger equations, and I will give uniqueness and stability results, both in the linearized and in the nonlinear case. These results make use of a recent general theory of infinite-dimensional CS for deterministic and non-isometric operators, which will be briefly surveyed. This is joint work with Giovanni S. Alberti (University of Genoa). Tuomo Savolainen, University of Eastern Finland, Finland. Title: Design of the injection and measurement front end, system parameters and the user interface. Daniel Strbian, HUCH, Finland. Title: Types of brain haemorrhages, current treatment optionsand challenges in monitoring of the intracerebral haemorrhage Jussi Toivanen, University of Eastern Finland, Finland. Title: Reconstruction of conductivity in multi-frequency EIT Abstract: In multi-frequency EIT, a series of measurements are performed with different current frequencies. Because conductivity is a function of frequency, the estimation process gives a set of conductivity images. The conductivity values in these images are not equal, but the images are usually structurally similar. This structural similarity can be exploited in the estimation process by estimating the conductivities simultaneously whilst utilizing specific priors. Some examples of these priors are the joint total variation prior, the parallel level sets prior, and priors based on either the second difference or the structural similarity index.