A Software Toolkit for TMS Electric-Field Modeling with Boundary Element Fast Multipole Method: An Efficient MATLAB Implementation

AbstractBackgroundTranscranial magnetic stimulation (TMS) is currently the only non-invasive neurostimulation modality that enables painless and safe supra-threshold stimulation by employing electromagnetic induction to efficiently penetrate the skull. Accurate, fast, and high resolution modeling of the electric fields (E-fields) may significantly improve individualized targeting and dosing of TMS and therefore enhance the efficiency of existing clinical protocols as well as help establish new application domains.ObjectiveTo present and disseminate our TMS modeling software toolkit, including several new algorithmic developments, and to apply this software to realistic TMS modeling scenarios given a high-resolution model of the human head including cortical geometry and an accurate coil model.MethodThe recently developed charge-based boundary element fast multipole method (BEM-FMM) is employed as an alternative to the 1st order finite element method (FEM) most commonly used today. The BEM-FMM approach provides high accuracy and unconstrained field resolution close to and across cortical interfaces. Here, the previously proposed BEM-FMM algorithm has been improved in several novel ways.Results and ConclusionsThe improvements resulted in a threefold increase in computational speed while maintaining the same solution accuracy. The computational code based on the MATLAB® platform is made available to all interested researchers, along with a coil model repository and examples to create custom coils, head model repository, and supporting documentation. The presented software toolkit may be useful for post-hoc analyses of navigated TMS data using high-resolution subject-specific head models as well as accurate and fast modeling for the purposes of TMS coil/hardware development.

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Solving High-Resolution Forward Problems for Extra- and Intracranial Neurophysiological Recordings Using Boundary Element Fast Multipole Method

10.1101/567933 ◽

2019 ◽

Author(s):

Sergey N Makarov ◽

Matti Hämäläinen ◽

Yoshio Okada ◽

Gregory M Noetscher ◽

Jyrki Ahveninen ◽

...

Keyword(s):

High Resolution ◽

Boundary Element ◽

Fast Multipole Method ◽

Field Potential ◽

Head Model ◽

Practical Case ◽

Source Modeling ◽

Fast Multipole ◽

Forward Solution ◽

Multipole Method

AbstractWe present a general numerical approach for solving the forward problem in high-resolution. This approach can be employed in the analysis of noninvasive electroencephalography (EEG) and magnetoencephalography (MEG) as well as invasive electrocorticography (ECoG), stereoencephalography (sEEG), and local field potential (LFP) recordings. The underlying algorithm is our recently developed boundary element fast multipole method (BEM-FMM) that simulates anatomically realistic head models with unprecedented numerical accuracy and speed. This is achieved by utilizing the adjoint double layer formulation and zeroth-order basis functions in conjunction with the FMM acceleration. We present the mathematical formalism in detail and validate the method by applying it to the canonical multilayer sphere problem. The numerical error of BEM-FMM is 2-10 times lower while the computational speed is 1.5–20 times faster than those of the standard first-order FEM. We present four practical case studies: (i) evaluation of the effect of a detailed head model on the accuracy of EEG/MEG forward solution; (ii) demonstration of the ability to accurately calculate the electric potential and the magnetic field in the immediate vicinity of the sources and conductivity boundaries; (iii) computation of the field of a spatially extended cortical equivalent dipole layer; and (iv) taking into account the effect a fontanel for infant EEG source modeling and comparison of the results with a commercially available FEM. In all cases, BEM-FMM provided versatile, fast, and accurate high-resolution modeling of the electromagnetic field and has the potential of becoming a standard tool for modeling both extracranial and intracranial electrophysiological signals.

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A software toolkit for TMS electric-field modeling with boundary element fast multipole method: an efficient MATLAB implementation

Journal of Neural Engineering ◽

10.1088/1741-2552/ab85b3 ◽

2020 ◽

Vol 17 (4) ◽

pp. 046023 ◽

Cited By ~ 4

Author(s):

Sergey N Makarov ◽

William A Wartman ◽

Mohammad Daneshzand ◽

Kyoko Fujimoto ◽

Tommi Raij ◽

...

Keyword(s):

Electric Field ◽

Boundary Element ◽

Fast Multipole Method ◽

Fast Multipole ◽

Software Toolkit ◽

Field Modeling ◽

Multipole Method ◽

Matlab Implementation

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Multiscale Modeling of EEG/MEG Response of a Compact Cluster of Tightly Spaced Pyramidal Neocortical Neurons

Brain and Human Body Modeling 2020 ◽

10.1007/978-3-030-45623-8_11 ◽

2020 ◽

pp. 195-211

Author(s):

Sergey N. Makarov ◽

Jyrki Ahveninen ◽

Matti Hämäläinen ◽

Yoshio Okada ◽

Gregory M. Noetscher ◽

...

Keyword(s):

High Resolution ◽

Boundary Element ◽

Multiscale Modeling ◽

Cluster Size ◽

Fast Multipole Method ◽

Head Model ◽

Current Dipole ◽

Neocortical Neurons ◽

Dipole Sources ◽

Compact Cluster

AbstractIn this study, the boundary element fast multipole method or BEM-FMM is applied to model compact clusters of tightly spaced pyramidal neocortical neurons firing simultaneously and coupled with a high-resolution macroscopic head model. The algorithm is capable of processing a very large number of surface-based unknowns along with a virtually unlimited number of elementary microscopic current dipole sources distributed within the neuronal arbor.The realistic cluster size may be as large as 10,000 individual neurons, while the overall computation times do not exceed several minutes on a standard server. Using this approach, we attempt to establish how well the conventional lumped-dipole model used in electroencephalography/magnetoencephalography (EEG/MEG) analysis approximates a compact cluster of realistic neurons situated either in a gyrus (EEG response dominance) or in a sulcus (MEG response dominance).

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Application of the fast multipole method to the 2D finite element‐boundary element analysis of electromechanical devices

COMPEL The International Journal for Computation and Mathematics in Electrical and Electronic Engineering ◽

10.1108/03321640310475100 ◽

2003 ◽

Vol 22 (3) ◽

pp. 659-673 ◽

Cited By ~ 3

Author(s):

R.V. Sabariego ◽

J. Gyselinck ◽

C. Geuzaine ◽

P. Dular ◽

W. Legros

Keyword(s):

Finite Element ◽

Boundary Element ◽

Fast Multipole Method ◽

Fast Multipole ◽

Element Analysis ◽

Multipole Method ◽

Boundary Element Analysis ◽

Electromechanical Devices ◽

Element Boundary

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Acceleration of isogeometric boundary element analysis through a black-box fast multipole method

Engineering Analysis with Boundary Elements ◽

10.1016/j.enganabound.2016.03.004 ◽

2016 ◽

Vol 66 ◽

pp. 168-182 ◽

Cited By ~ 22

Author(s):

R.N. Simpson ◽

Z. Liu

Keyword(s):

Boundary Element ◽

Fast Multipole Method ◽

Black Box ◽

Fast Multipole ◽

Element Analysis ◽

Multipole Method ◽

Boundary Element Analysis

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Application of the inverse fast multipole method as a preconditioner in a 3D Helmholtz boundary element method

Journal of Computational Physics ◽

10.1016/j.jcp.2017.04.016 ◽

2017 ◽

Vol 341 ◽

pp. 406-428 ◽

Cited By ~ 7

Author(s):

Toru Takahashi ◽

Pieter Coulier ◽

Eric Darve

Keyword(s):

Boundary Element Method ◽

Boundary Element ◽

Fast Multipole Method ◽

Fast Multipole ◽

Multipole Method ◽

Element Method

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A fast multipole method accelerated adaptive background cell-based domain integration method for evaluation of domain integrals in 3D boundary element method

Engineering Analysis with Boundary Elements ◽

10.1016/j.enganabound.2016.03.002 ◽

2016 ◽

Vol 67 ◽

pp. 1-12 ◽

Cited By ~ 11

Author(s):

Wei Zhou ◽

Qiao Wang ◽

Yonggang Cheng ◽

Gang Ma

Keyword(s):

Boundary Element Method ◽

Boundary Element ◽

Integration Method ◽

Fast Multipole Method ◽

Fast Multipole ◽

Multipole Method ◽

Domain Integration ◽

Element Method

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Profiling General-Purpose Fast Multipole Method (FMM) Using Human Head Topology

Brain and Human Body Modeling 2020 ◽

10.1007/978-3-030-45623-8_21 ◽

2020 ◽

pp. 347-381

Author(s):

Dung Ngoc Pham

Keyword(s):

Fast Multipole Method ◽

Human Head ◽

General Purpose ◽

Test Cases ◽

Fast Multipole ◽

Helmholtz Equations ◽

Modeling Methods ◽

Wide Range ◽

Multipole Method ◽

Test Objects

AbstractIn this study, we characterize the performance of the fast multipole method (FMM) in solving the Laplace and Helmholtz equations. We use the FMM library developed by the group of Dr. L. Greengard. This version of the FMM algorithm is multilayer with no priori limit on the number of levels of the FMM tree, although, after about thirty levels, there may be floating point issues. A collection of high-resolution human head models is used as test objects. We perform a detailed analysis of the runtime and memory consumption of the FMM in a wide range of frequencies, problem sizes, and precisions required. Although we focus on two-manifold test cases, the results are generalizable to other topologies as well. The tests are conducted on both Windows and Linux platforms. The results obtained in this study can serve as a general benchmark for the performance of FMM. It can also be employed to pre-estimate the efficiency of numerical modeling methods (e.g., the boundary element method) accelerated by FMM.

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