The Forward Problem of Electrocardiography

2011 ◽  
pp. 247-298
Author(s):  
Rob MacLeod ◽  
Martin Buist
Keyword(s):  
Forward Problem

scholarly journals Solving the magnetocardiography forward problem in a realistic three-dimensional heart-torso model

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Zhenghui Hu ◽  
Kaikai Ye ◽  
Mingzhu Bai ◽  
Zekuan Yang ◽  
Qiang Lin
Keyword(s):  
Three Dimensional ◽  
Forward Problem ◽  
Torso Model

Framework for Flaw Detection: Application to Dynamic Crack Detection in Flat Membranes

2008 ◽  
Author(s):  
Daniel Rabinovich ◽  
Dan Givoli ◽  
Shmuel Vigdergauz
Keyword(s):  
Inverse Problem ◽  
Crack Detection ◽  
Flexible Structures ◽  
Flaw Detection ◽  
Forward Problem ◽  
Dynamic Crack ◽  
Computational Framework ◽  
Time Harmonic ◽  
Present Context ◽  
Flat Membranes

A computational framework is developed for the detection of flaws in flexible structures. The framework is based on posing the detection problem as an inverse problem, which requires the solution of many forward problems. Each forward problem is associated with a known flaw; an appropriate cost functional evaluates the quality of each candidate flaw based on the solution of the corresponding forward problem. On the higher level, the inverse problem is solved by a global optimization algorithm. The performance of the computational framework is evaluated by considering the detectability of various types of flaws. In the present context detectability is defined by introducing a measure of the distance between the sought flaw and trial flaws in the space of the parameters characterizing the configuration of the flaw. The framework is applied to crack detection in flat membranes subjected to time-harmonic and transient excitations. The detectability of cracks is compared for these two cases.

Mathematical models and numerical methods for the forward problem in cardiac electrophysiology

2002 ◽  
Vol 5 (4) ◽  
pp. 215-239 ◽  
Author(s):  
G.T. Lines ◽  
M.L. Buist ◽  
P. Grottum ◽  
A.J. Pullan ◽  
J. Sundnes ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Mathematical Models ◽  
Cardiac Electrophysiology ◽  
Forward Problem

scholarly journals Adjoint Numerical Method for a Multiphysical Inverse Problem of Two-Phase Well Testing in Petroleum Reservoirs

2021 ◽  
Vol 2090 (1) ◽  
pp. 012139
Author(s):  
OA Shishkina ◽  
I M Indrupskiy
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Objective Function ◽  
Petroleum Reservoirs ◽  
Forward Problem ◽  
Adjoint Equations ◽  
Well Testing ◽  
Adjoint Methods ◽  
Two Phase ◽  
Gradient Calculation

Abstract Inverse problem solution is an integral part of data interpretation for well testing in petroleum reservoirs. In case of two-phase well tests with water injection, forward problem is based on the multiphase flow model in porous media and solved numerically. The inverse problem is based on a misfit or likelihood objective function. Adjoint methods have proved robust and efficient for gradient calculation of the objective function in this type of problems. However, if time-lapse electrical resistivity measurements during the well test are included in the objective function, both the forward and inverse problems become multiphysical, and straightforward application of the adjoint method is problematic. In this paper we present a novel adjoint algorithm for the inverse problems considered. It takes into account the structure of cross dependencies between flow and electrical equations and variables, as well as specifics of the equations (mixed parabolic-hyperbolic for flow and elliptic for electricity), numerical discretizations and grids, and measurements in the inverse problem. Decomposition is proposed for the adjoint problem which makes possible step-wise solution of the electric adjoint equations, like in the forward problem, after which a cross-term is computed and added to the right-hand side of the flow adjoint equations at this timestep. The overall procedure provides accurate gradient calculation for the multiphysical objective function while preserving robustness and efficiency of the adjoint methods. Example cases of the adjoint gradient calculation are presented and compared to straightforward difference-based gradient calculation in terms of accuracy and efficiency.

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