Forward model#

This module may be employed to calculate the forward model for the source reconstruction.

src_rec.fwd_mdl.compute(cort_mdl, coreg, rec_meta_info, bem_model, _mag_factor=1e-07)#

Calculates the forward model according to Mosher et al, 1999.

Parameters:

  • cort_mdl (finnpy.src_rec.cort_mdl.Cort_mdl) –

    Container populated with the following items:

    lh_vertnumpy.ndarray, shape(lh_vtx_cnt, 3)

    White matter surface model vertices (left hemisphere).

    lh_facesnumpy.ndarray, shape(lh_face_cnt, 3)

    White matter surface model faces (left hemisphere).

    rh_vertnumpy.ndarray, shape(rh_vtx_cnt, 3)

    White matter surface model vertices (right hemisphere).

    rh_facesnumpy.ndarray, shape(rh_face_cnt, 3)

    White matter surface model faces (right hemisphere).

    lh_sphere_vertnumpy.ndarray, shape(lh_sphere_vtx_cnt, 3)

    Spherical freesurfer head model vertices (left hemisphere).

    rh_sphere_vertnumpy.ndarray, shape(rh_sphere_vtx_cnt, 3)

    Spherical freesurfer head model vertices (right hemisphere).

  • coreg (finnpy.src_rec.coreg.Coreg) –

    Container class, populed with the following items:

    rotors : numpy.ndarray, shape(9,) Sequence of rotors defining rotation (3), translation (3) and scaling (3).

    mri_to_meg_trs : numpy.ndarray, shape(4, 4) Full affine transformation matrix (MRI -> MEG) mri_to_meg_tr : numpy.ndarray, shape(4, 4) Rigid affine transformation matrix (MRI -> MEG) mri_to_meg_rs : numpy.ndarray, shape(4, 4) Rotation & scaling only affine transformation matrix (MRI -> MEG) mri_to_meg_r : numpy.ndarray, shape(4, 4) Rotation only affine transformation matrix (MRI -> MEG)

    meg_to_mri_trs : numpy.ndarray, shape(4, 4) Full affine transformation matrix (MEG -> MRI) meg_to_mri_tr : numpy.ndarray, shape(4, 4) Rigid affine transformation matrix (MEG -> MRI) meg_to_mri_rs : numpy.ndarray, shape(4, 4) Rotation & scaling only affine transformation matrix (MEG -> MRI) meg_to_mri_r : numpy.ndarray, shape(4, 4) Rotation only affine transformation matrix (MEG -> MRI)

  • rec_meta_info (mne.io.read_info) – MEG scan meta info, obtailable via mne.io.read_info

  • bem_mdl (finnpy.src_rec.bem_mdl.BEM_mdl) –

    Container class, populed with the following items:

    vertnumpy.ndarray, shape(scaled_vtx_cnt, 3)

    Remaining Vertices of a skin/skull model vertices.

    facesnumpy.ndarray, shape(scaled_face_cnt, 3)

    Remaining Vertices of a skin/skull model faces.

    faces_normalnumpy.ndarray, shape(scaled_face_cnt, 3)

    Normals of the individual remaining inner skull faces.

    faces_areanumpy.ndarray, shape(scaled_face_cnt)

    Surface area of the remaining faces.

    bem_solutionnumpy.ndarray, shape(scaled_vtx_cnt, scaled_vtx_cnt)

    BEM solution (preliminary step for the calculation of the forward model).

Returns:

fwd_sol – Forward model, projecting from sen into src space.

Return type:

Var_type, shape(meg_ch_cnt, valid_vtx_cnt * 3)

src_rec.fwd_mdl.restrict(cort_mdl, fwd_sol, coreg)#

Transforms a fwd model into surface orientation (orthogonal to the respective surface cluster; allowing for cortically constrained inverse modeling) and shrinks it by making closeby channels project to the same destination. This is different from a ‘default’ 3D transformation.

Parameters:

  • cort_mdl (finnpy.src_rec.cort_mdl.Cort_mdl) –

    Container populated with the following items:

    lh_vertnumpy.ndarray, shape(lh_vtx_cnt, 3)

    White matter surface model vertices (left hemisphere).

    lh_facesnumpy.ndarray, shape(lh_face_cnt, 3)

    White matter surface model faces (left hemisphere).

    lh_valid_vertnumpy.ndarray, shape(lh_vtx_cnt,)

    Valid flags for white matter surface model vertices (left hemisphere).

    rh_vertnumpy.ndarray, shape(rh_vtx_cnt, 3)

    White matter surface model vertices (right hemisphere).

    rh_facesnumpy.ndarray, shape(rh_face_cnt, 3)

    White matter surface model faces (right hemisphere).

    lh_valid_vertnumpy.ndarray, shape(rh_vtx_cnt,)

    Valid flags for white matter surface model vertices (right hemisphere).

    octa_model_vertnumpy.ndarray, shape(octa_mdl_vtx_cnt, 3)

    Octamodel vertices (left hemisphere).

    octa_model_facesnumpy.ndarray, shape(octa_mdl_face_cnt, 3)

    Octamodel faces (right hemisphere).

  • fwd_sol (numpy.ndarray, shape(meg_ch_cnt, valid_vtx_cnt * 3)) – Forward solution with default orientation.

  • coreg (finnpy.src_rec.coreg.Coreg) –

    Container class, populed with the following items:

    rotors : numpy.ndarray, shape(9,) Sequence of rotors defining rotation (3), translation (3) and scaling (3).

    mri_to_meg_trs : numpy.ndarray, shape(4, 4) Full affine transformation matrix (MRI -> MEG) mri_to_meg_tr : numpy.ndarray, shape(4, 4) Rigid affine transformation matrix (MRI -> MEG) mri_to_meg_rs : numpy.ndarray, shape(4, 4) Rotation & scaling only affine transformation matrix (MRI -> MEG) mri_to_meg_r : numpy.ndarray, shape(4, 4) Rotation only affine transformation matrix (MRI -> MEG)

    meg_to_mri_trs : numpy.ndarray, shape(4, 4) Full affine transformation matrix (MEG -> MRI) meg_to_mri_tr : numpy.ndarray, shape(4, 4) Rigid affine transformation matrix (MEG -> MRI) meg_to_mri_rs : numpy.ndarray, shape(4, 4) Rotation & scaling only affine transformation matrix (MEG -> MRI) meg_to_mri_r : numpy.ndarray, shape(4, 4) Rotation only affine transformation matrix (MEG -> MRI)

Returns:

fwd_sol * rot – Transformed surface model.

Return type:

numpy.ndarray, shape(meg_ch_cnt, valid_vtx_cnt)

src_rec.fwd_mdl._get_meg_coil_info(rec_meta_info, coreg)#

Accumulates spatial information on MEG sensor position.

Parameters:

  • rec_meta_info (mne.io.read_info) – MEG scan meta info, obtailable via mne.io.read_info

  • coreg (finnpy.src_rec.coreg.Coreg) –

    Container class, populed with the following items:

    rotors : numpy.ndarray, shape(9,) Sequence of rotors defining rotation (3), translation (3) and scaling (3).

    mri_to_meg_trs : numpy.ndarray, shape(4, 4) Full affine transformation matrix (MRI -> MEG) mri_to_meg_tr : numpy.ndarray, shape(4, 4) Rigid affine transformation matrix (MRI -> MEG) mri_to_meg_rs : numpy.ndarray, shape(4, 4) Rotation & scaling only affine transformation matrix (MRI -> MEG) mri_to_meg_r : numpy.ndarray, shape(4, 4) Rotation only affine transformation matrix (MRI -> MEG)

    meg_to_mri_trs : numpy.ndarray, shape(4, 4) Full affine transformation matrix (MEG -> MRI) meg_to_mri_tr : numpy.ndarray, shape(4, 4) Rigid affine transformation matrix (MEG -> MRI) meg_to_mri_rs : numpy.ndarray, shape(4, 4) Rotation & scaling only affine transformation matrix (MEG -> MRI) meg_to_mri_r : numpy.ndarray, shape(4, 4) Rotation only affine transformation matrix (MEG -> MRI)

Returns:

  • rmags (numpy.ndarray, shape(meg_ch_integration_pt_cnt, 3)) – 3D positions of MEG coil integration points (MEG space).

  • cosmags (numpy.ndarray, shape(meg_ch_integration_pt_cnt, 3)) – Direction of the MEG coil integration points (MEG space).

  • rmags_mri (numpy.ndarray, shape(meg_ch_integration_pt_cnt, 3)) – 3D positions of MEG coil integration points (MRI space).

  • cosmags_mri (numpy.ndarray, shape(meg_ch_integration_pt_cnt, 3)) – Direction of the MEG coil integration points (MRI space).

  • ws (Var_type, shape(meg_ch_integration_pt_cnt,)) – Weights for MEG coil integration points.

  • meg_ch_indices (Var_type, shape(meg_ch_integration_pt_cnt,)) – Indices of MEG channels.

  • meg_ch_cnt (integer) – Number of MEG channels.

src_rec.fwd_mdl._get_meg_coil_positions(rec_meta_info, meg_to_mri_trans)#

Gets MEG coil spatial information, such as coils’ individual integration points (rmag), their directions (cosmag), and weights for these integration points.

Parameters:

  • rec_meta_info (mne.io.read_info) – MEG scan meta info, obtailable via mne.io.read_info

  • meg_to_mri_trans (numpy.ndarray, shape(4, 4)) – Transformation from MEG to MRI space.

Returns:

meg_chs – MEG channel specific information.

Return type:

dict, (‘coil_type’, ‘rmag’, ‘cosmag’, ‘w’, ‘ch_trans’, ‘rmag_mri’, ‘cosmag_mri’)

src_rec.fwd_mdl._comp_src_sen_contrib(bem_model, rmags_mri, cosmags_mri, ws, meg_ch_indices, meg_ch_cnt, conductivity=(0.3,))#

Calculates the contribution of each current source (BEM normals) towards to each MEG sensor. Based on Mosher, 1999, formula #3 µ/(4*pi)(normals x tau)/norm³ … extended with additional weights for MEG coil direction, MEG coil weight Integration simplified as multiplication with surface area, see “Multiple Interface Brain and Head Models for EEG: A Surface Charge Approach”, Solis and Papandreou-Suppappola

Parameters:

  • bem_mdl (finnpy.src_rec.bem_mdl.BEM_mdl) –

    Container class, populed with the following items:

    vertnumpy.ndarray, shape(scaled_vtx_cnt, 3)

    Remaining Vertices of a skin/skull model vertices.

    facesnumpy.ndarray, shape(scaled_face_cnt, 3)

    Remaining Vertices of a skin/skull model faces.

    faces_normalnumpy.ndarray, shape(scaled_face_cnt, 3)

    Normals of the individual remaining inner skull faces.

    faces_areanumpy.ndarray, shape(scaled_face_cnt)

    Surface area of the remaining faces.

    bem_solutionnumpy.ndarray, shape(scaled_vtx_cnt, scaled_vtx_cnt)

    BEM solution (preliminary step for the calculation of the forward model).

  • rmags_mri (numpy.ndarray, shape(meg_ch_integration_pt_cnt, 3)) – 3D positions of MEG coil integration points (MRI space).

  • cosmags_mri (numpy.ndarray, shape(meg_ch_integration_pt_cnt, 3)) – Direction of the MEG coil integration points (MRI space).

  • ws (Var_type, shape(meg_ch_integration_pt_cnt,)) – Weights for MEG coil integration points.

  • meg_ch_indices (Var_type, shape(meg_ch_integration_pt_cnt,)) – Indices of MEG channels.

  • meg_ch_cnt (integer) – Number of MEG channels.

Returns:

  • src_sen_contrib (numpy.ndarray,)

  • Contribution of each current source towards each sensor.

src_rec.fwd_mdl._calc_magnetic_fields(white_vertices_mri, reduced_in_skull_vert, meg_to_mri_r, pre_fwd_solution)#

Computes infinite medium potentials.

Parameters:

  • white_vertices_mri (numpy.ndarray, shape(valid_white_vtx_cnt, 3)) – White matter vertices.

  • reduced_in_skull_vert (numpy.ndarray, shape(reduced_in_skull_vtx_cnt, 3)) – Inner skull model vertices.

  • meg_to_mri_trans (numpy.ndarray, shape(4, 4)) – Transformatio matrix from the coregistration.

  • pre_fwd_solution (numpy.ndarray, shape(meg_ch_cnt, reduced_in_skull_vtx_cnt)) – Fwd solution precursor.

Returns:

fwd_sol – Forward solution with infinite medium potentials.

Return type:

numpy.ndarray, shape(valid_white_vtx_cnt * 3, meg_ch_cnt)

src_rec.fwd_mdl._add_current_distribution(fwd_sol, white_vertices, meg_ch_cnt, rmags, cosmags, ws, meg_ch_indices)#

Adds current distribution to the MEG forward solution.

Parameters:

  • fwd_sol (numpy.ndarray, shape(number_of_valid_vertices * 3, meg_ch_cnt)) – Previously calcualted (preliminary) forward solution.

  • white_vertices (numpy.ndarray, shape(number_of_valid_vertices, 3)) – Valid white matter vertices.

  • meg_ch_infos (list of dictionaries, ('coil_type', 'rmag', 'cosmag', 'w', 'ch_trans', 'rmag_mri', 'cosmag_mri')) – MEG recording meta into.

  • rmags (numpy.ndarray, shape(meg_ch_integration_pt_cnt, 3)) – 3D positions of MEG coil integration points (MEG space).

  • cosmags (numpy.ndarray, shape(meg_ch_integration_pt_cnt, 3)) – Direction of the MEG coil integration points (MEG space).

  • ws (Var_type, shape(meg_ch_integration_pt_cnt,)) – Weights for MEG coil integration points.

  • meg_ch_indices (Var_type, shape(meg_ch_integration_pt_cnt,)) – Indices of MEG channels.

Returns:

fwd_sol – Forward solution with current distribution.

Return type:

numpy.ndarray, shape(number_of_valid_vertices * 3, meg_ch_cnt)

src_rec.fwd_mdl._calc_bem_fields(vortex, rmags, cosmags)#

Calculates the magnetic field at a vortex from all MEG sensors.

Parameters:

  • vortex (numpy.ndarray, shape(3,)) – Position of the vortex

  • rmags (numpy.ndarray, shape(meg_chs_integration_pt_cnt, 3)) – 3D positions of MEG coil integration points (MEG space)

  • cosmags (numpy.ndarray, shape(meg_chs_integration_pt_cnt, 3)) – Direction of the MEG coil integration points (MEG space)

Returns:

fields – The magnetic field of all MEG sensors at a vortex.

Return type:

numpy.ndarray, shape(1, 3, meg_chs_integration_pt_cnt)

src_rec.fwd_mdl._calc_acc_hem_normals(white_vert, white_faces)#

Generatoes vertex normals from accumulated face normals. See https://en.wikipedia.org/wiki/Vertex_normal.

Parameters:

  • white_vert (numpy.ndarray, shape(vert_cnt, 3)) – MRI model vertices.

  • white_faces (numpy.ndarray, shape(face_cnt, 3)) – MRI model faces.

Returns:

acc_normals – Array of surface normals for the input faces/vertices.

Return type:

numpy.ndarray, shape(vert_cnt, 3)

src_rec.fwd_mdl._find_vertex_clusters(white_vert, valid_vert, white_faces)#

Identifies which input vertices (white_vert) are presented by which valid vortex.

Parameters:

  • white_vert (numpy.ndarray, shape(lh_vert_cnt, 3)) – MRI model vertices.

  • valid_vert (numpy.ndarray, shape(lh_vert_cnt,)) – Valid/supporting vertices.

  • white_faces (numpy.ndarray, shape(lh_face_cnt, 3)) – MRI model faces.

Returns:

  • cluster_grp (list, len(n,)) – Transformed surface model.

  • cluster_indices (list, len(n,)) – Transformed surface model.

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