fwd_eeg_sphere_model.h File Reference

Multi-shell spherical head model with Berg-Scherg equivalent-source approximation for fast EEG forward computation. More...

#include "fwd_global.h"
#include "fwd_eeg_sphere_layer.h"
#include "fwd_coil_set.h"
#include <Eigen/Core>
#include <QDebug>
#include <memory>
#include <vector>

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Classes
struct	FWDLIB::fitUserRec
	Workspace for the linear least-squares fit of Berg-Scherg parameters in the EEG sphere model (SVD matrices, residuals, weights). More...
class	FWDLIB::FwdEegSphereModel
	Multi-shell concentric-sphere head model holding the Berg-Scherg equivalent-source parameters that accelerate the de Munck Legendre series for EEG, plus the Sarvas closed-form coefficients used for the spherically-symmetric MEG forward solution. More...

Namespaces
namespace	FWDLIB
	Forward modelling — BEM solver, spherical models, sensor/coil definitions and the lead-field assembly that links current dipoles to MEG/EEG sensor readings.

Typedefs
using	FWDLIB::fitUser = fitUserRec*

Detailed Description

Multi-shell spherical head model with Berg-Scherg equivalent-source approximation for fast EEG forward computation.

SPDX-License-Identifier: BSD-3-Clause Copyright (c) 2017-2026 MNE-CPP Authors

Author

Christoph Dinh chris.nosp@m.toph.nosp@m..dinh.nosp@m.@mne.nosp@m.-cpp..nosp@m.org; Lorenz Esch loren.nosp@m.z.es.nosp@m.ch@tu.nosp@m.-ilm.nosp@m.enau..nosp@m.de; Juan GPC jgarc.nosp@m.iapr.nosp@m.ieto@.nosp@m.mgh..nosp@m.harva.nosp@m.rd.e.nosp@m.du; Gabriel Motta gabri.nosp@m.elbe.nosp@m.nmott.nosp@m.a@gm.nosp@m.ail.c.nosp@m.om

Since

0.1.0

Date

March 2017

For EEG, the exact potential of a current dipole in a layered sphere is a Legendre series whose convergence slows dramatically as the dipole approaches the inner-skull boundary, making the analytic solution expensive at realistic source eccentricities. Berg & Scherg (1994) showed that the series can be reproduced to four-digit accuracy by replacing it with a small set (typically 3) of equivalent dipoles inside a single homogeneous sphere, whose magnitudes and radial positions are obtained once per model via a non-linear least-squares fit. FwdEegSphereModel stores both the concentric layers and the fitted Berg-Scherg parameters mu / lambda so subsequent dipole evaluations cost only a few image-charge contributions.

For MEG, the Sarvas (1987) closed-form expression — also implemented here — gives the analytic magnetic field of a dipole in a spherically symmetric conductor with no series at all, because the radial conductivity profile drops out of the Biot-Savart line integral.

Refactored from MNE-C fwd_eeg_sphere_model.c / fwd_types.h (fwdEegSphereModelRec); the embedded fitUserRec carries the SVD workspace of the Berg-Scherg fit.

Definition in file fwd_eeg_sphere_model.h.