Development of an anatomically realistic forward solver for thoracic electrical impedance tomography

Electrical impedance tomography (EIT) has the potential to provide a low cost and safe imaging modality for clinically monitoring patients being treated with mechanical ventilation. Variations in reconstruction algorithms at different clinical settings, however, make interpretation of regional ventilation across institutions difficult, presenting the need for a unified algorithm for thoracic EIT reconstruction. Development of such a consensual reconstruction algorithm necessitates a forward model capable of predicting surface impedance measurements as well as electric fields in the interior of the modeled thoracic volume. In this paper, we present an anatomically realistic forward solver for thoracic EIT that was built based on high resolution MR image data of a representative adult. Accuracy assessment of the developed forward solver in predicting surface impedance measurements by comparing the predicted and observed impedance measurements shows that the relative error is within the order of 5%, demonstrating the ability of the presented forward solver in generating high-fidelity surface thoracic impedance data for thoracic EIT algorithm development and evaluation

A Fast Algorithm for Parabolic PDE-based Inverse Problems Based on Laplace Transforms and Flexible Krylov Solvers

We consider the problem of estimating parameters in large-scale weakly nonlinear inverse problems for which the underlying governing equations is a linear, time-dependent, parabolic partial differential equation. A major challenge in solving these inverse problems using Newton-type methods is the computational cost associated with solving the forward problem and with repeated construction of the Jacobian, which represents the sensitivity of the measurements to the unknown parameters. Forming the Jacobian can be prohibitively expensive because it requires repeated solutions of the forward and adjoint time-dependent parabolic partial differential equations corresponding to multiple sources and receivers. We propose an efficient method based on a Laplace transform-based exponential time integrator combined with a flexible Krylov subspace approach to solve the resulting shifted systems of equations efficiently. Our proposed solver speeds up the computation of the forward and adjoint problems, thus yielding significant speedup in total inversion time. We consider an application from Transient Hydraulic Tomography (THT), which is an imaging technique to estimate hydraulic parameters related to the subsurface from pressure measurements obtained by a series of pumping tests. The algorithms discussed are applied to a synthetic example taken from THT to demonstrate the resulting computational gains of this proposed method

DassFlow v1.0: a variational data assimilation software for river flows

Dassflow is a computational software for river hydraulics (floods), especially designed for variational data assimilation. The forward model is based on the bidimensional shallow-water equations, solved by a finite volume method (HLLC approximate Riemann solver). It is written in Fortran 95. The adjoint code is generated by the automatic differentiation tool Tapenade. Thus, Dassflow software includes the forward solver, its adjoint code, the full optimization framework (based on the M1QN3 minimization routine) and benchmarks. The generation of new data assimilation twin experiments is easy. The software is interfaced with few pre and post-processors (mesh generators, GIS tools and visualization tools), which allows to treat real data