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FwdEegSphereModel

Namespace: FWDLIB  ·  Library: Forward Library

Python equivalent

mne.make_sphere_model in MNE-Python.

#include <fwd/fwd_eeg_sphere_model.h>

class FWDLIB::FwdEegSphereModel

Implements FwdEegSphereModel (replaces fwdEegSphereModel / fwdEegSphereModelRec from MNE-C fwd_types.h).

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.

Public Methods​

FwdEegSphereModel()​

Constructs the Forward EEG Sphere Model.

FwdEegSphereModel(p_FwdEegSphereModel)​

Copy constructor.

Parameters:

  • p_FwdEegSphereModel : const FwdEegSphereModel & Forward EEG Sphere Model which should be copied.

~FwdEegSphereModel()​

Destroys the Electric Current Dipole description.

fwd_eeg_get_multi_sphere_model_coeff(n)​

fwd_multi_spherepot.c Get the model depended weighting factor for n

Parameters:

  • n : int coefficient to which the expansion shopuld be calculated.

Returns:

  • double — the weighting factor for n.

fwd_setup_eeg_sphere_model(rad, fit_berg_scherg, nfit)​

fwd_eeg_sphere_models.c

Setup the EEG sphere model calculations

Parameters:

  • rad.

  • fit_berg_scherg : bool If Fit Berg Scherg should be performed.

  • nfit.

Returns:

  • bool — True when setup was successful, false otherwise.

fwd_eeg_fit_berg_scherg(nterms, nfit, rv)​

Fit Berg-Scherg equivalent spherical model parameters (mu and lambda) by minimizing the difference between actual and approximated series expansions using simplex optimization.

On success, updates the internal mu and lambda member vectors.

Parameters:

  • nterms : int Number of terms in the series expansion.

  • nfit : int Number of equivalent dipoles to fit (must be >= 2).

  • rv : float & Relative variance of the final fit.

Returns:

  • bool — true if fitting succeeded, false otherwise. Number of layers.

nlayer()​

Static Methods​

fwd_create_eeg_sphere_model(name, nlayer, rads, sigmas)​

Create a new multi-layer EEG sphere model structure.

Sorts layers by radius and scales radii relative to the outermost layer.

Parameters:

  • name : const QString & Textual identifier for the model.

  • nlayer : int Number of concentric spherical layers.

  • rads : const Eigen::VectorXf & Radius values for each layer.

  • sigmas : const Eigen::VectorXf & Conductivity values for each layer.

Returns:

  • FwdEegSphereModel::UPtr — Pointer to the newly created sphere model.

setup_eeg_sphere_model(eeg_model_file, eeg_model_name, eeg_sphere_rad)​

Set up the desired sphere model for EEG.

Parameters:

  • eeg_model_file : const QString & Contains the model specifications.

  • eeg_model_name : QString Name of the model to use.

  • eeg_sphere_rad : float Outer surface radius.

Returns:

  • FwdEegSphereModel::UPtr — the setup eeg sphere model.

new_fit_user(nfit, nterms)​

Allocate and initialize a fitting workspace for Berg-Scherg parameter estimation.

Parameters:

  • nfit : int Number of equivalent dipoles to fit.

  • nterms : int Number of terms in the series expansion.

Returns:

  • fitUser — Pointer to the initialized fitting data structure.

next_legen(n, x, p0, p01, p1, p11)​

Compute the next Legendre polynomials of the first and second kind using a recursion formula.

Self-initializes for n = 0 and n = 1.

Parameters:

  • n : int Order of the Legendre polynomial.

  • x : double Evaluation point (cosine of the angle).

  • p0 : double & Legendre polynomial of the first kind.

  • p01 : double & Previous value of p0.

  • p1 : double & Legendre polynomial of the second kind.

  • p11 : double & Previous value of p1.

calc_pot_components(beta, cgamma, Vrp, Vtp, fn, nterms)​

Calculate the radial and tangential potential components for a dipole in a layered sphere model using a Legendre polynomial series expansion.

Parameters:

  • beta : double Ratio of dipole distance to field point distance.

  • cgamma : double Cosine of the angle between dipole and field point vectors.

  • Vrp : double & Radial component of the potential.

  • Vtp : double & Tangential component of the potential.

  • fn : const Eigen::VectorXd & Pre-computed expansion coefficients.

  • nterms : int Maximum number of terms in the series.

fwd_eeg_multi_spherepot(rd, Q, el, neeg, Vval, client)​

Compute EEG potentials at multiple electrodes for a current dipole in a multi-layer spherical head model.

Based on the formulas in Zhang (1995) and Mosher et al. (1996).

Parameters:

  • rd : const Eigen::Vector3f & Dipole position.

  • Q : const Eigen::Vector3f & Dipole moment.

  • el : const Eigen::Matrix< float, Eigen::Dynamic, 3, Eigen::RowMajor > & Electrode positions (neeg x 3).

  • neeg : int Number of electrodes.

  • Vval : Eigen::VectorXf & Computed potential values at each electrode.

  • client : *void ** Pointer to the FwdEegSphereModel.

Returns:

  • int — OK on success, FAIL otherwise.

fwd_eeg_multi_spherepot_coil1(rd, Q, els, Vval, client)​

Calculate EEG potentials at compound electrodes (coils) by summing weighted contributions from individual integration points.

Parameters:

  • rd : const Eigen::Vector3f & Dipole position.

  • Q : const Eigen::Vector3f & Dipole moment.

  • els : FwdCoilSet & Set of coils/electrodes.

  • Vval : Eigen::Ref< Eigen::VectorXf > Computed potentials (one per coil).

  • client : *void ** Pointer to the FwdEegSphereModel.

Returns:

  • int — OK on success, FAIL otherwise.

fwd_eeg_spherepot_vec(rd, el, neeg, Vval_vec, client)​

Compute the electric potentials in a set of electrodes in spherically Symmetric head model.

This routine calculates the fields for all dipole directions.

The code is based on the formulas presented in

J.C. Moscher, R.M. Leahy, and P.S. Lewis, Matrix Kernels for Modeling of EEG and MEG Data, Los Alamos Technical Report, LA-UR-96-1993, 1996.

This routine uses the acceleration with help of equivalent sources in the homogeneous sphere.

Parameters:

  • rd : const Eigen::Vector3f & Dipole position.

  • el : const Eigen::Matrix< float, Eigen::Dynamic, 3, Eigen::RowMajor > & Electrode positions.

  • neeg : int Number of electrodes.

  • Vval_vec : Eigen::MatrixXf & The potential values Vval_vec[0][k] potentials given by Q = (1.0,0.0,0.0) at electrode k; Vval_vec[1][k] potentials given by Q = (0.0,1.0,0.0) at electrode k; Vval_vec[2][k] potentials given by Q = (0.0,0.0,1.0) at electrode k.

Returns:

  • bool — true when successful.

fwd_eeg_spherepot_coil_vec(rd, els, Vval_vec, client)​

fwd_multi_spherepot.c

Calculate the EEG in the sphere model using the fwdCoilSet structure MEG channels are skipped

This routine uses the acceleration with help of equivalent sources in the homogeneous sphere.

Parameters:

  • rd : const Eigen::Vector3f & Dipole position.

  • els : FwdCoilSet & Electrode positions.

  • Vval_vec : Eigen::Ref< Eigen::MatrixXf > The potential values; Vval_vec[0][k] potentials given by Q = (1.0,0.0,0.0) at electrode k; Vval_vec[1][k] potentials given by Q = (0.0,1.0,0.0) at electrode k; Vval_vec[2][k] potentials given by Q = (0.0,0.0,1.0) at electrode k.

  • client.

Returns:

  • int — true when successful.

fwd_eeg_spherepot_grad_coil(rd, Q, coils, Vval, xgrad, ygrad, zgrad, client)​

Compute potentials and spatial gradients of the potential field at coils using finite differences.

Parameters:

  • rd : const Eigen::Vector3f & Dipole position.

  • Q : const Eigen::Vector3f & Dipole moment.

  • coils : FwdCoilSet & Set of coils/electrodes.

  • Vval : Eigen::Ref< Eigen::VectorXf > Computed potentials (one per coil).

  • xgrad : Eigen::Ref< Eigen::VectorXf > Gradient with respect to x dipole coordinate.

  • ygrad : Eigen::Ref< Eigen::VectorXf > Gradient with respect to y dipole coordinate.

  • zgrad : Eigen::Ref< Eigen::VectorXf > Gradient with respect to z dipole coordinate.

  • client : *void ** Pointer to the FwdEegSphereModel.

Returns:

  • int — OK on success, FAIL otherwise.

fwd_eeg_spherepot(rd, Q, el, neeg, Vval, client)​

fwd_multi_spherepot.c

This routine calculates the potentials for a specific dipole direction

This routine uses the acceleration with help of equivalent sources in the homogeneous sphere.

Parameters:

  • rd : const Eigen::Vector3f & Dipole position.

  • Q : const Eigen::Vector3f & Dipole moment.

  • el : const Eigen::Matrix< float, Eigen::Dynamic, 3, Eigen::RowMajor > & Electrode positions.

  • neeg : int Number of electrodes.

  • Vval : Eigen::VectorXf & The potential values.

  • client.

Returns:

  • int — true when successful.

fwd_eeg_spherepot_coil(rd, Q, els, Vval, client)​

fwd_multi_spherepot.c

Calculate the EEG in the sphere model using the megCoil structure MEG channels are skipped

Parameters:

  • rd : const Eigen::Vector3f & Dipole position.

  • Q : const Eigen::Vector3f & Dipole moment.

  • els : FwdCoilSet & Electrode positions.

  • Vval : Eigen::Ref< Eigen::VectorXf > The potential values.

  • client.

Returns:

  • int — true when successful.

compose_linear_fitting_data(mu, u)​

Build the data matrix and target vector for the linear part of the Berg-Scherg parameter fit.

Parameters:

  • mu : const Eigen::VectorXd & Distance multipliers for the equivalent dipoles.

  • u : fitUser Fitting workspace (M and y are populated on output).

compute_linear_parameters(mu, lambda, u)​

Solve for the optimal lambda (dipole magnitude) parameters given fixed mu values using SVD.

Returns the relative variance goodness-of-fit metric.

Parameters:

  • mu : const Eigen::VectorXd & Distance multipliers for the equivalent dipoles.

  • lambda : Eigen::VectorXd & Computed dipole magnitudes.

  • u : fitUser Fitting workspace.

Returns:

  • double — Relative variance (0 = perfect fit, 1 = no fit).

one_step(mu, user_data)​

Objective function for the simplex optimizer: evaluate the residual sum of squares for a given set of mu values.

Parameters:

  • mu : const Eigen::VectorXd & Distance multipliers to evaluate.

  • user_data : *const void ** Pointer to the fitUser workspace.

Returns:

  • double — Sum of squared residuals; 1.0 if any mu exceeds +/-1.

Authors of this file​