... | ... | @@ -2,7 +2,7 @@ There are different approaches how to handle the source term that appears in the |
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When solving the EEG/MEG forward problems using DUNEuro, the source model parameters are passed in a nested configuration structure **source_model** when applying the transfer matrix or solving directly.
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An overview of the different parameters is given below.
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A short description of the supported source models and an overview of the different required parameters is given below.
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# Partial Integration
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Direct application of the distributional derivative of the dipolar source term to the test function. The resulting right hand side will have as many non-zero entries as the element containing the dipole has associated degrees of freedom (e.g. nodes for linear basis functions). For tetrahedral meshes, the partial integration approach is constant within each element.
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... | ... | @@ -11,6 +11,10 @@ For a mathematical description see, e.g.: |
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Bauer M, Pursiainen S, Vorwerk J, Kostler H, Wolters CH. Comparison Study for Whitney (Raviart-Thomas)-Type Source Models in Finite-Element-Method-Based EEG Forward Modeling. IEEE Trans Biomed Eng. 2015 Nov;62(11):2648-56. [https://doi.org/10.1109/TBME.2015.2439282](https://doi.org/10.1109/TBME.2015.2439282)
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This source model does not require additional parameters, only the type needs to be specified:
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- **'type' : 'partial_integration'**
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The type in the source_model configuration is specified as PI
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# St. Venant
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The idea of the approach following St. Venant is to replace the dipolar source by a distribution of electrical monopoles which best reproduces the source moment.
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... | ... | @@ -25,6 +29,31 @@ For a detailed description, please see: |
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Miinalainen, T, Rezaei, A, Us, D, Nüßing, A, Engwer, C, Wolters, CH & Pursiainen, S 2019, 'A realistic, accurate and fast source modeling approach for the EEG forward problem', NeuroImage, vol. 184, no. 1, pp. 56-67. [https://doi.org/10.1016/j.neuroimage.2018.08.054](https://doi.org/10.1016/j.neuroimage.2018.08.054)
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A list of parameters passed to DUNEuro when using this approach:
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- **'type' : 'venant'**
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The type in the source_model configuration is specified as St. Venant
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- **'numberOfMoments' : 'int'**
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- **'numberOfMoments' : 'int'**
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- **'numberOfMoments' : 'int'**
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- **'numberOfMoments' : 'int'**
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- **'numberOfMoments' : 'int'**
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- **'numberOfMoments' : 'int'**
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- **'numberOfMoments' : 'int'**
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'numberOfMoments' : int
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'weightingExponent' : int
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'relaxationFactor' : double
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'mixedMoments' : int
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'referenceLength' : int
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'relaxationFactor' : int
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'initialization' : {'single_element', 'closest_vertex'}
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'weightingExponent' : int
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'restrict' : bool
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# Subtraction
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The subtraction approach relies on the assumption that there exists a small area around the dipole location, where the conductivity is constant. As a result, the potential and the conductivity can be split into two contributions, a singularity contribution and a correction part: $`u = u_\infty + u_{corr}`$, and $`\sigma = \sigma_\infty + \sigma_{corr}`$.
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While $`u_\infty`$ can be computed analytically, the insertion of the above decomposition into the EEG forward problem results in a Poisson equation for the correction potential with a right hand side $`- \nabla \cdot (\sigma_{corr} \nabla u_\infty)`$ and inhomogeneous Neumann boundary conditions.
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