scholarly journals Forward Field Computation with OpenMEEG

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Alexandre Gramfort ◽  
Théodore Papadopoulo ◽  
Emmanuel Olivi ◽  
Maureen Clerc
Keyword(s):  
Inverse Problem ◽  
Electrical Impedance ◽  
Numerical Solutions ◽  
Physiological Modeling ◽  
Impedance Tomography ◽  
Piecewise Constant ◽  
The Core ◽  
Piecewise Constant Conductivity ◽  
Electric Potentials ◽  
Quasistatic Regime

To recover the sources giving rise to electro- and magnetoencephalography in individual measurements, realistic physiological modeling is required, and accurate numerical solutions must be computed. We present OpenMEEG, which solves the electromagnetic forward problem in the quasistatic regime, for head models with piecewise constant conductivity. The core of OpenMEEG consists of the symmetric Boundary Element Method, which is based on an extended Green Representation theorem. OpenMEEG is able to provide lead fields for four different electromagnetic forward problems: Electroencephalography (EEG), Magnetoencephalography (MEG), Electrical Impedance Tomography (EIT), and intracranial electric potentials (IPs). OpenMEEG is open source and multiplatform. It can be used from Python and Matlab in conjunction with toolboxes that solve the inverse problem; its integration within FieldTrip is operational since release 2.0.

Image Theory for Electrical Impedance Tomography

2011 ◽  
pp. 117-144
Author(s):  
P. D. Einziger ◽  
M. Dolgin
Keyword(s):  
Inverse Problem ◽  
Electrical Impedance Tomography ◽  
Electrical Impedance ◽  
Physical Phenomenon ◽  
Stable Solution ◽  
Least Square ◽  
Image Theory ◽  
Reconstruction Procedure ◽  
Impedance Tomography ◽  
Piecewise Constant Conductivity

Image reconstruction by electrical impedance tomography is, generally, an ill-posed nonlinear inverse problem. Regularization methods are widely used to ensure a stable solution. Herein, we present a novel electrical impedance tomography algorithm for reconstruction of layered biological tissues with piecewise continuous plane-stratified profiles. The algorithm is based on the reconstruction scheme for piecewise constant conductivity profiles, which utilizes Legendre expansion in conjunction with improved Prony method. This reconstruction procedure, which calculates both the locations and the conductivities, repetitively provides inhomogeneous depth discretization, (i.e., the depths grid is not equispaced). Incorporation of this specific inhomogeneous grid in the widely used mean least square reconstruction procedure results in a stable and accurate reconstruction, whereas, the commonly selected equispaced depth grid leads to unstable reconstruction. This observation establishes the main result of our investigation, highlighting the impact of physical phenomenon (image theory) on electrical impedance tomography, leading to a physically motivated stabilization of the inverse problem, (i.e., an inhomogeneous depth discretization renders an inherent regularization of the mean least square algorithm).

Shape and parameter reconstruction for the Robin transmission inverse problem

2016 ◽  
Vol 24 (6) ◽  
Author(s):  
Antoine Laurain ◽  
Houcine Meftahi
Keyword(s):  
Inverse Problem ◽  
Shape Optimization ◽  
Saddle Point Problem ◽  
Point Problem ◽  
Optimization Approach ◽  
Reconstruction Method ◽  
Piecewise Constant ◽  
Piecewise Constant Conductivity ◽  
Level Set Approach ◽  
Parameter Reconstruction

AbstractIn this paper we consider the inverse problem of simultaneously reconstructing the interface where the jump of the conductivity occurs and the Robin parameter for a transmission problem with piecewise constant conductivity and Robin-type transmission conditions on the interface. We propose a reconstruction method based on a shape optimization approach and compare the results obtained using two different types of shape functionals. The reformulation of the shape optimization problem as a suitable saddle point problem allows us to obtain the optimality conditions by using differentiability properties of the min-sup combined with a function space parameterization technique. The reconstruction is then performed by means of an iterative algorithm based on a conjugate shape gradient method combined with a level set approach. To conclude we give and discuss several numerical examples.

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