scholarly journals A hybrid boundary element-finite element method to solve the EEG forward problem

2021 ◽  
Author(s):  
Nasireh Dayarian ◽  
Reza Jafari ◽  
Ali Khadem
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element ◽  
Forward Problem ◽  
Head Model ◽  
Fem Modeling ◽  
Fe Method ◽  
Forward Problems ◽  
The Brain ◽  
Element Method

This article presents a hybrid boundary element-finite element (BE–FE) method to solve the EEG forward problem and take advantages of both the boundary element method (BEM) and finite element method (FEM). Although realistic EEG forward problems with heterogeneous and anisotropic regions can be solved by FEM accurately, the FEM modeling of the brain with dipolar sources may lead to singularity. In contrast, the BEM can solve EEG forward problems with isotropic tissue regions and dipolar sources using a suitable integral formulation. This work utilizes both FEM and BEM strengths attained by dividing the regions into some homogeneous BE regions with sources and some heterogeneous and anisotropic FE regions. Furthermore, the BEM is applied for modeling the brain, including dipole sources and the FEM for other head layers. To validate the proposed method, inhomogeneous isotropic/anisotropic three– and four–layer spherical head models are studied. Moreover, a four&-layer realistic head model is investigated. Results for six different dipole eccentricities and two different dipole orientations are computed using the BEM, FEM, and hybrid BE–FE method together with statistical analysis and the related error criteria are compared. The proposed method is a promising new approach for solving realistic EEG forward problems.

scholarly journals FEMfuns: A Volume Conduction Modeling Pipeline that Includes Resistive, Capacitive or Dispersive Tissue and Electrodes

2020 ◽  
Vol 18 (4) ◽  
pp. 569-580 ◽  
Author(s):  
M. Vermaas ◽  
M. C. Piastra ◽  
T. F. Oostendorp ◽  
N. F. Ramsey ◽  
P. H. E. Tiesinga
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Electrode Materials ◽  
Forward Problem ◽  
Head Model ◽  
Brain Computer Interfaces ◽  
Flexible Tool ◽  
Population Activity ◽  
Computer Interfaces ◽  
Element Method

Abstract Applications such as brain computer interfaces require recordings of relevant neuronal population activity with high precision, for example, with electrocorticography (ECoG) grids. In order to achieve this, both the placement of the electrode grid on the cortex and the electrode properties, such as the electrode size and material, need to be optimized. For this purpose, it is essential to have a reliable tool that is able to simulate the extracellular potential, i.e., to solve the so-called ECoG forward problem, and to incorporate the properties of the electrodes explicitly in the model. In this study, this need is addressed by introducing the first open-source pipeline, FEMfuns (finite element method for useful neuroscience simulations), that allows neuroscientists to solve the forward problem in a variety of different geometrical domains, including different types of source models and electrode properties, such as resistive and capacitive materials. FEMfuns is based on the finite element method (FEM) implemented in FEniCS and includes the geometry tessellation, several electrode-electrolyte implementations and adaptive refinement options. The code of the pipeline is available under the GNU General Public License version 3 at https://github.com/meronvermaas/FEMfuns. We tested our pipeline with several geometries and source configurations such as a dipolar source in a multi-layer sphere model and a five-compartment realistically-shaped head model. Furthermore, we describe the main scripts in the pipeline, illustrating its flexible and versatile use. Provided with a sufficiently fine tessellation, the numerical solution of the forward problem approximates the analytical solution. Furthermore, we show dispersive material and interface effects in line with previous literature. Our results indicate substantial capacitive and dispersive effects due to the electrode-electrolyte interface when using stimulating electrodes. The results demonstrate that the pipeline presented in this paper is an accurate and flexible tool to simulate signals generated on electrode grids by the spatiotemporal electrical activity patterns produced by sources and thereby allows the user to optimize grids for brain computer interfaces including exploration of alternative electrode materials/properties.

Postbuckling Analysis of Plates Under Combined Loads by a Mixed Finite Element and Boundary Element Method

1993 ◽  
Vol 115 (3) ◽  
pp. 262-267 ◽  
Author(s):  
J. Q. Ye
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Mixed Boundary ◽  
Mixed Finite Element ◽  
Plane Deformation ◽  
Thin Plates ◽  
Combined Loads ◽  
Element Method

The postbuckling behavior of thin plates under combined loads is studied in this paper by using a mixed boundary element and finite element method. The transverse and the in-plane deformation of the plates are analyzed by the boundary element method and the finite element method, respectively. Spline functions were used as the interpolation functions and shape functions in the solution of both methods. A quadratic rectangular spline element is adopted in the finite element procedure. Numerical results are given for typical problems to show the effectiveness of the proposed approach. The possibilities to extend the method developed in this paper to more complicated postbuckling problems are discussed in the concluding section.

Simulation of Axisymmetric Forming Processes, With Friction, Coupling Finite Elements and Boundary Elements

2006 ◽  
Author(s):  
Dominique Bigot ◽  
Hocine Kebir ◽  
Jean-Marc Roelandt
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element Method ◽  
Finite Elements ◽  
Boundary Element ◽  
Symmetric Part ◽  
Forming Process ◽  
Optimal Shapes ◽  
Numerical Software ◽  
Element Method

Nowadays, the simulation of forming processes is rather well integrated in the industrial numerical codes. However, to take into account the possible modifications of the tool during cycle of working, we develop dedicated numerical software. This one more particularly will allow the identification of the fatigue criteria of the tool. With the view to conceiving the optimal shapes of tool allowing increasing their lifespan while ensuring a quality required of the part thus manufactured. This latter uses coupling with friction finite element method — for modelling the axi-symmetric part — and boundary element method — for modelling the tool. For the validation, we modeled forming process.

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