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. 2010 Sep 6:9:45.
doi: 10.1186/1475-925X-9-45.

OpenMEEG: opensource software for quasistatic bioelectromagnetics

Alexandre Gramfort  1 , Théodore Papadopoulo, Emmanuel Olivi, Maureen Clerc
Affiliations

OpenMEEG: opensource software for quasistatic bioelectromagnetics

Alexandre Gramfort et al. Biomed Eng Online. .

Abstract

Background: Interpreting and controlling bioelectromagnetic phenomena require realistic physiological models and accurate numerical solvers. A semi-realistic model often used in practise is the piecewise constant conductivity model, for which only the interfaces have to be meshed. This simplified model makes it possible to use Boundary Element Methods. Unfortunately, most Boundary Element solutions are confronted with accuracy issues when the conductivity ratio between neighboring tissues is high, as for instance the scalp/skull conductivity ratio in electro-encephalography. To overcome this difficulty, we proposed a new method called the symmetric BEM, which is implemented in the OpenMEEG software. The aim of this paper is to present OpenMEEG, both from the theoretical and the practical point of view, and to compare its performances with other competing software packages.

Methods: We have run a benchmark study in the field of electro- and magneto-encephalography, in order to compare the accuracy of OpenMEEG with other freely distributed forward solvers. We considered spherical models, for which analytical solutions exist, and we designed randomized meshes to assess the variability of the accuracy. Two measures were used to characterize the accuracy. the Relative Difference Measure and the Magnitude ratio. The comparisons were run, either with a constant number of mesh nodes, or a constant number of unknowns across methods. Computing times were also compared.

Results: We observed more pronounced differences in accuracy in electroencephalography than in magnetoencephalography. The methods could be classified in three categories: the linear collocation methods, that run very fast but with low accuracy, the linear collocation methods with isolated skull approach for which the accuracy is improved, and OpenMEEG that clearly outperforms the others. As far as speed is concerned, OpenMEEG is on par with the other methods for a constant number of unknowns, and is hence faster for a prescribed accuracy level.

Conclusions: This study clearly shows that OpenMEEG represents the state of the art for forward computations. Moreover, our software development strategies have made it handy to use and to integrate with other packages. The bioelectromagnetic research community should therefore be able to benefit from OpenMEEG with a limited development effort.

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Figures

Figure 1
Figure 1
Models for Boundary Elements Methods. Boundary Elements are well-suited for piecewise constant isotropic conductivity models. OpenMEEG handles nested regions (left), and could in principle be extended to more general, disjoint regions (right) as presented in [8].
Figure 2
Figure 2
Head model made of 3 nested regular sphere meshes and 5 dipoles. Head model made of 3 nested regular sphere meshes with 5 dipoles close to the inner layer.
Figure 3
Figure 3
Accuracy comparison of the different BEM solvers for EEG. Forward EEG: accuracy comparison of different BEM solvers with three-layers sphere head models. We observe that the Symmetric BEM outperforms the other methods in term of precision.
Figure 4
Figure 4
Accuracy comparison for EEG using random meshes with fixed number of vertices. Forward EEG: RDM and MAG boxplots obtained on 100 random 3-layers sphere models. Each layer contains 600 or 800 random vertices.
Figure 5
Figure 5
Accuracy comparison for EEG using random meshes and fixed number of unknowns. Forward EEG: RDM and MAG boxplots obtained on 100 random 3-layers sphere models. Each forward solution is obtained taking as constraint that the number of unknowns that is estimated is the same for all BEM solvers. Results are presented for 1500 and 3000 unknowns.
Figure 6
Figure 6
Accuracy comparison for MEG using random meshes with fixed number of vertices and non-radial magnetometers. Forward MEG: RDM and MAG boxplots obtained on 100 random sphere models (1 and 3-layers) using non-radial magnetometers. Each layer contains 600 or 800 random vertices.
Figure 7
Figure 7
Accuracy comparison for MEG using random meshes with fixed number of vertices and radial magnetometers. Forward MEG: RDM and MAG boxplots obtained on 100 random sphere models (1 and 3-layers) using radial magnetometers. Each layer contains 600 or 800 random vertices.
Figure 8
Figure 8
Computation times of the different BEM solvers for EEG. Forward EEG: computation times for the different solvers as a function of the number of vertices per layer or the number of unknowns.
Figure 9
Figure 9
Pipelines for computing lead fields with OpenMEEG. Diagram for the low level pipeline for computing MEG and EEG leadfields (a.k.a., gain matrices) using OpenMEEG. To facilitate the understanding of this diagram one can give an example. An EEG gain matrix is obtained with the om_gain command using with option -EEG taking as input an inverted head matrix, an EEG sensors matrix and a source matrix. The source matrix can be obtained using om_assemble taking as input a head model (geometry and conductivities) and a source descriptionfile (option -dsm when using isolated dipoles). The inverted head matrix is obtained using om_minverser from a head matrix which is obtained using om_assemble and the option -HM from a head model (geometry and conductivities).
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