Robust imaging using electrical impedance tomography: review of current tools

Electrical impedance tomography (EIT) is a medical imaging technique with many advantages and great potential for development in the coming years. Currently, some limitations of EIT are related to the ill-posed nature of the problem. These limitations are translated on a practical level by a lack of genericity of the developed tools. In this paper, the main robust data acquisition and processing tools for EIT proposed in the scientific literature are presented. Their relevance and potential to improve the robustness of EIT are analysed, in order to conclude on the feasibility of a robust EIT tool capable of providing resistivity or difference of resistivity mapping in a wide range of applications. In particular, it is shown that certain measurement acquisition tools and algorithms, such as faulty electrode detection algorithm or particular electrode designs, can ensure the quality of the acquisition in many circumstances. Many algorithms, aiming at processing acquired data, are also described and allow to overcome certain difficulties such as an error in the knowledge of the position of the boundaries or the poor conditioning of the inverse problem. They have a strong potential to faithfully reconstruct a quality image in the presence of disturbances such as noise or boundary modelling error.

Cancer detection through Electrical Impedance Tomography and optimal control theory: theoretical and computational analysis

The Inverse Electrical Impedance Tomography (EIT) problem on recovering electrical conductivity tensor and potential in the body based on the measurement of the boundary voltages on the $ m $ electrodes for a given electrode current is analyzed. A PDE constrained optimal control framework in Besov space is developed, where the electrical conductivity tensor and boundary voltages are control parameters, and the cost functional is the norm difference of the boundary electrode current from the given current pattern and boundary electrode voltages from the measurements. The novelty of the control-theoretic model is its adaptation to the clinical situation when additional "voltage-to-current" measurements can increase the size of the input data from $ m $ up to $ m! $ while keeping the size of the unknown parameters fixed. The existence of the optimal control and Fréchet differentiability in the Besov space along with optimality condition is proved. Numerical analysis of the simulated model example in the 2D case demonstrates that by increasing the number of input boundary electrode currents from $ m $ to $ m^2 $ through additional "voltage-to-current" measurements the resolution of the electrical conductivity of the body identified via gradient method in Besov space framework is significantly improved.

Incorporating a Spatial Prior into Nonlinear D-Bar EIT Imaging for Complex Admittivities

Electrical Impedance Tomography (EIT) aims to recover the internal conductivity and permittivity distributions of a body from electrical measurements taken on electrodes on the surface of the body. The reconstruction task is a severely ill-posed nonlinear inverse problem that is highly sensitive to measurement noise and modeling errors. Regularized D-bar methods have shown great promise in producing noise-robust algorithms by employing a low-pass filtering of nonlinear (nonphysical) Fourier transform data specific to the EIT problem. Including prior data with the approximate locations of major organ boundaries in the scattering transform provides a means of extending the radius of the low-pass filter to include higher frequency components in the reconstruction, in particular, features that are known with high confidence. This information is additionally included in the system of D-bar equations with an independent regularization parameter from that of the extended scattering transform. In this paper, this approach is used in the 2-D D-bar method for admittivity (conductivity as well as permittivity) EIT imaging. Noise-robust reconstructions are presented for simulated EIT data on chest-shaped phantoms with a simulated pneumothorax and pleural effusion. No assumption of the pathology is used in the construction of the prior, yet the method still produces significant enhancements of the underlying pathology (pneumothorax or pleural effusion) even in the presence of strong noise.

Mutual information as a measure of image quality for 3D dynamic lung imaging with EIT

We report on a pilot study of dynamic lung electrical impedance tomography (EIT) at the University of Manchester. Low-noise EIT data at 100 frames per second were obtained from healthy male subjects during controlled breathing, followed by magnetic resonance imaging (MRI) subsequently used for spatial validation of the EIT reconstruction. The torso surface in the MR image and electrode positions obtained using MRI fiducial markers informed the construction of a 3D finite element model extruded along the caudal-distal axis of the subject. Small changes in the boundary that occur during respiration were accounted for by incorporating the sensitivity with respect to boundary shape into a robust temporal difference reconstruction algorithm. EIT and MRI images were co-registered using the open source medical imaging software, 3D Slicer. A quantitative comparison of quality of different EIT reconstructions was achieved through calculation of the mutual information with a lung-segmented MR image. EIT reconstructions using a linear shape correction algorithm reduced boundary image artefacts, yielding better contrast of the lungs, and had 10% greater mutual information compared with a standard linear EIT reconstruction.