Help Privacy Policy Disclaimer
  Advanced SearchBrowse


  Boundary element fast multipole method for modeling electrical brain stimulation with voltage and current electrodes

Makarov, S. N., Golestanirad, L., Wartman, W. A., Nguyen, B. T., Noetscher, G. M., Ahveninen, J. P., et al. (2021). Boundary element fast multipole method for modeling electrical brain stimulation with voltage and current electrodes. Journal of Neural Engineering, 18(4): 0460d4. doi:10.1088/1741-2552/ac17d7.

Item is


show hide
Genre: Journal Article


show Files




Makarov, Sergey N.1, 2, Author
Golestanirad, Laleh3, Author
Wartman, William A.1, Author
Nguyen, Bach Thanh3, Author
Noetscher, Gregory M.1, Author
Ahveninen, Jyrki P.2, Author
Fujimoto, Kyoko4, Author
Weise, Konstantin5, Author           
Nummenmaa, Aapo R.2, Author
1Electrical and Computer Engineering Department, Worcester Polytechnic Institute, MA, USA, ou_persistent22              
2Athinoula A. Martinos Center for Biomedical Imaging, Charlestown, MA, USA, ou_persistent22              
3Department of Biomedical Engineering, Northwestern University, Chicago, MA, USA, ou_persistent22              
4Center for Devices and Radiological Health (CDRH), Silver Spring, MD, USA, ou_persistent22              
5Methods and Development Group Brain Networks, MPI for Human Cognitive and Brain Sciences, Max Planck Society, ou_2205650              


Free keywords: Boundary element method; Deep brain stimulation; Electroencephalography; Fast multipole method; Intracortical microstimulation; Numerical modeling; Transcranial electrical stimulation
 Abstract: Objective. To formulate, validate, and apply an alternative to the finite element method (FEM) high-resolution modeling technique for electrical brain stimulation-the boundary element fast multipole method (BEM-FMM). To include practical electrode models for both surface and embedded electrodes.Approach. Integral equations of the boundary element method in terms of surface charge density are combined with a general-purpose fast multipole method and are expanded for voltage, shunt, current, and floating electrodes. The solution of coupled and properly weighted/preconditioned integral equations is accompanied by enforcing global conservation laws: charge conservation law and Kirchhoff's current law.Main results.A sub-percent accuracy is reported as compared to the analytical solutions and simple validation geometries. Comparison to FEM considering realistic head models resulted in relative differences of the electric field magnitude in the range of 3%-6% or less. Quantities that contain higher order spatial derivatives, such as the activating function, are determined with a higher accuracy and a faster speed as compared to the FEM. The method can be easily combined with existing head modeling pipelines such as headreco or mri2mesh.Significance.The BEM-FMM does not rely on a volumetric mesh and is therefore particularly suitable for modeling some mesoscale problems with submillimeter (and possibly finer) resolution with high accuracy at moderate computational cost. Utilizing Helmholtz reciprocity principle makes it possible to expand the method to a solution of EEG forward problems with a very large number of cortical dipoles.


 Dates: 2021-08-19
 Publication Status: Published online
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: DOI: 10.1088/1741-2552/ac17d7
PMID: 34311449
 Degree: -



Legal Case


Project information

show hide
Project name : -
Grant ID : WE 59851/2
Funding program : -
Funding organization : Deutsche Forschungsgemeinschaft (DFG)
Project name : -
Grant ID : 1R01MH111829, R01DC016765
Funding program : -
Funding organization : National Institutes of Health (NIH)

Source 1

Title: Journal of Neural Engineering
Source Genre: Journal
Publ. Info: Bristol : Institute of Physics Publishing
Pages: - Volume / Issue: 18 (4) Sequence Number: 0460d4 Start / End Page: - Identifier: ISSN: 1741-2552
CoNE: https://pure.mpg.de/cone/journals/resource/17412552