Combining Iterative Absolute EIT, Difference EIT and Control Theory to Optimise Mechanical Ventilation

We examine the combination of absolute and difference imaging to provide fast pseudo-absolute EIT reconstructions required for the recovery of local ventilation parameters. Parameters recovered from simulations are incorporated into an optimal control framework to demonstrate personalised optimisation of mechanical ventilation

Towards Efficient Iterative Absolute EIT

One factor limiting the use of absolute reconstructions in 3D lung EIT is the computational cost of iterative algorithms. We show how the programming experience of the Finite Element and Research Software Engineering communities can be applied to these algorithms, resulting in a speed up of reconstructions in EIDORS 3.8 [1]. We also outline a combination of absolute and difference imaging to provide fast pseudo-absolute imaging

Understanding the magnetic polarizability tensor

The aim of this paper is to provide new insights into the properties of the rank 2 polarizability tensor M̆ proposed by Ledger and Lionheart for describing the perturbation in the magnetic field caused by the presence of a conducting object in the eddy-current regime. In particular, we explore its connection with the magnetic polarizability tensor and the Pólya-Szegö tensor and how, by introducing new splittings of M̆, they form a family of rank 2 tensors for describing the response from different categories of conducting (permeable) objects. We include new bounds on the invariants of the Pólya-Szegö tensor and expressions for the low-frequency and high-conductivity limiting coefficients of M̆. We show, for the high-conductivity case (and for frequencies at the limit of the quasi-static approximation), that it is important to consider whether the object is simply or multiply connected but, for the low-frequency case, the coefficients are independent of the connectedness of the object. Furthermore, we explore the frequency response of the coefficients of M̆ for a range of simply and multiply connected objects

Validation of a finite-element solution for electrical impedance tomography in an anisotropic medium

Electrical impedance tomography is an imaging method, with which volumetric images of conductivity are produced by injecting electrical current and measuring boundary voltages. It has the potential to become a portable non-invasive medical imaging technique. Until now, implementations have neglected anisotropy even though human tissues such as bone, muscle and brain white matter are markedly anisotropic. We present a numerical solution using the finite-element method that has been modified for modelling anisotropic conductive media. It was validated in an anisotropic domain against an analytical solution in an isotropic medium after the isotropic domain was diffeomorphically transformed into an anisotropic one. Convergence of the finite element to the analytical solution was verified by showing that the finite-element error norm decreased linearly related to the finite-element size, as the mesh density increased, for the simplified case of Laplace's equation in a cubic domain with a Dirichlet boundary condition

Recovering the second moment of the strain distribution from neutron Bragg edge data

Point by point strain scanning is often used to map the residual stress (strain) in engineering materials and components. However, the gauge volume and hence spatial resolution is limited by the beam defining apertures and can be anisotropic for very low and high diffraction (scattering) angles. Alternatively, wavelength resolved neutron transmission imaging has a potential to retrieve information tomographically about residual strain induced within materials through measurement in transmission of Bragg edges - crystallographic fingerprints whose locations and shapes depend on microstructure and strain distribution. In such a case the spatial resolution is determined by the geometrical blurring of the measurement setup and the detector point spread function. Mathematically, reconstruction of strain tensor field is described by the longitudinal ray transform; this transform has a non-trivial null-space, making direct inversion impossible. A combination of the longitudinal ray transform with physical constraints was used to reconstruct strain tensor fields in convex objects. To relax physical constraints and generalise reconstruction, a recently introduced concept of histogram tomography can be employed. Histogram tomography relies on our ability to resolve the distribution of strain in the beam direction, as we discuss in the paper. More specifically, Bragg edge strain tomography requires extraction of the second moment (variance about zero) of the strain distribution which has not yet been demonstrated in practice. In this paper we verify experimentally that the second moment can be reliably measured for a previously well characterised aluminium ring and plug sample. We compare experimental measurements against numerical calculation and further support our conclusions by rigorous uncertainty quantification of the estimated mean and variance of the strain distribution