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Dynamic Statistical Parametric Mapping

Solver ID: dSPM

Usage

from invert import Solver

# fwd = ...    (mne.Forward object)
# evoked = ... (mne.Evoked object)

solver = Solver("dSPM")
solver.make_inverse_operator(fwd)
stc = solver.apply_inverse_operator(evoked)
stc.plot()

Overview

Noise-normalized minimum-norm inverse (MNE) that yields statistical maps by scaling the MNE estimate with an estimate of its variance.

References

  1. Dale, A. M., Liu, A. K., Fischl, B. R., Buckner, R. L., Belliveau, J. W., Lewine, J. D., & Halgren, E. (2000). Dynamic statistical parametric mapping: combining fMRI and MEG for high-resolution imaging of cortical activity. Neuron, 26(1), 55–67.

API Reference

Bases: BaseSolver

Class for the Dynamic Statistical Parametric Mapping (dSPM) inverse solution [1,2]. The formulas provided by [3] were used for implementation.

References

[1] Dale, A. M., Liu, A. K., Fischl, B. R., Buckner, R. L., Belliveau, J. W., Lewine, J. D., & Halgren, E. (2000). Dynamic statistical parametric mapping: combining fMRI and MEG for high-resolution imaging of cortical activity. neuron, 26(1), 55-67.

[2] Dale, A. M., Fischl, B., & Sereno, M. I. (1999). Cortical surface-based analysis: I. Segmentation and surface reconstruction. Neuroimage, 9(2), 179-194.

[3] Grech, R., Cassar, T., Muscat, J., Camilleri, K. P., Fabri, S. G., Zervakis, M., ... & Vanrumste, B. (2008). Review on solving the inverse problem in EEG source analysis. Journal of neuroengineering and rehabilitation, 5(1), 1-33.

Source code in invert/solvers/minimum_norm/dspm.py 
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class SolverDSPM(BaseSolver):
    """Class for the Dynamic Statistical Parametric Mapping (dSPM) inverse
        solution [1,2].  The formulas provided by [3] were used for
        implementation.

    References
    ----------
    [1] Dale, A. M., Liu, A. K., Fischl, B. R., Buckner, R. L., Belliveau, J.
    W., Lewine, J. D., & Halgren, E. (2000). Dynamic statistical parametric
    mapping: combining fMRI and MEG for high-resolution imaging of cortical
    activity. neuron, 26(1), 55-67.

    [2] Dale, A. M., Fischl, B., & Sereno, M. I. (1999). Cortical surface-based
    analysis: I. Segmentation and surface reconstruction. Neuroimage, 9(2),
    179-194.

    [3] Grech, R., Cassar, T., Muscat, J., Camilleri, K. P., Fabri, S. G.,
    Zervakis, M., ... & Vanrumste, B. (2008). Review on solving the inverse
    problem in EEG source analysis. Journal of neuroengineering and
    rehabilitation, 5(1), 1-33.
    """

    meta = SolverMeta(
        acronym="dSPM",
        full_name="Dynamic Statistical Parametric Mapping",
        category="Minimum Norm",
        description=(
            "Noise-normalized minimum-norm inverse (MNE) that yields statistical "
            "maps by scaling the MNE estimate with an estimate of its variance."
        ),
        references=[
            "Dale, A. M., Liu, A. K., Fischl, B. R., Buckner, R. L., Belliveau, J. W., Lewine, J. D., & Halgren, E. (2000). Dynamic statistical parametric mapping: combining fMRI and MEG for high-resolution imaging of cortical activity. Neuron, 26(1), 55–67.",
        ],
    )

    def __init__(self, name="Dynamic Statistical Parametric Mapping", **kwargs):
        self.name = name
        kwargs.setdefault("use_depth_weighting", True)
        kwargs.setdefault("depth_weighting", 0.1)
        return super().__init__(**kwargs)

    def make_inverse_operator(
        self,
        forward,
        *args,
        alpha="auto",
        noise_cov=None,
        source_cov=None,
        verbose=0,
        **kwargs,
    ):
        """Calculate inverse operator.

        Parameters
        ----------
        forward : mne.Forward
            The mne-python Forward model instance.
        alpha : float
            The regularization parameter.
        noise_cov : numpy.ndarray
            The noise covariance matrix (channels x channels).
        source_cov : numpy.ndarray
            The source covariance matrix (dipoles x dipoles). This can be used if
            prior information, e.g., from fMRI images, is available.

        Return
        ------
        self : object returns itself for convenience
        """
        super().make_inverse_operator(forward, *args, alpha=alpha, **kwargs)
        n_chans, n_dipoles = self.leadfield.shape

        if noise_cov is None:
            noise_cov = np.identity(n_chans)
        if source_cov is None:
            source_cov = np.identity(n_dipoles)

        inverse_operators = []
        leadfield_source_cov = source_cov @ self.leadfield.T
        LLS = self.leadfield @ leadfield_source_cov
        if alpha == "auto":
            r_grid = np.asarray(self.r_values, dtype=float)
        else:
            r_grid = np.asarray([float(alpha)], dtype=float)
        max_eig_LLS = float(np.linalg.svd(LLS, compute_uv=False).max())
        max_eig_noise = float(np.linalg.svd(noise_cov, compute_uv=False).max())
        scale = max_eig_LLS / max(max_eig_noise, 1e-15)
        self.alphas = list(r_grid * scale)

        for alpha in self.alphas:
            K = leadfield_source_cov @ self.robust_inverse(LLS + alpha * noise_cov)
            W_dSPM = np.diag(np.sqrt(1 / np.diagonal(K @ noise_cov @ K.T)))
            inverse_operator = W_dSPM @ K
            inverse_operators.append(inverse_operator)

        self.inverse_operators = [
            InverseOperator(inverse_operator, self.name)
            for inverse_operator in inverse_operators
        ]
        return self

__init__ 

__init__(
    name="Dynamic Statistical Parametric Mapping", **kwargs
)
Source code in invert/solvers/minimum_norm/dspm.py 
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def __init__(self, name="Dynamic Statistical Parametric Mapping", **kwargs):
    self.name = name
    kwargs.setdefault("use_depth_weighting", True)
    kwargs.setdefault("depth_weighting", 0.1)
    return super().__init__(**kwargs)

make_inverse_operator 

make_inverse_operator(
    forward,
    *args,
    alpha="auto",
    noise_cov=None,
    source_cov=None,
    verbose=0,
    **kwargs,
)

Calculate inverse operator.

Parameters:

Name Type Description Default
forward Forward

The mne-python Forward model instance.

 required
alpha float

The regularization parameter.

 'auto'
noise_cov ndarray

The noise covariance matrix (channels x channels).

 None
source_cov ndarray

The source covariance matrix (dipoles x dipoles). This can be used if prior information, e.g., from fMRI images, is available.

 None
Return

self : object returns itself for convenience

Source code in invert/solvers/minimum_norm/dspm.py 
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def make_inverse_operator(
    self,
    forward,
    *args,
    alpha="auto",
    noise_cov=None,
    source_cov=None,
    verbose=0,
    **kwargs,
):
    """Calculate inverse operator.

    Parameters
    ----------
    forward : mne.Forward
        The mne-python Forward model instance.
    alpha : float
        The regularization parameter.
    noise_cov : numpy.ndarray
        The noise covariance matrix (channels x channels).
    source_cov : numpy.ndarray
        The source covariance matrix (dipoles x dipoles). This can be used if
        prior information, e.g., from fMRI images, is available.

    Return
    ------
    self : object returns itself for convenience
    """
    super().make_inverse_operator(forward, *args, alpha=alpha, **kwargs)
    n_chans, n_dipoles = self.leadfield.shape

    if noise_cov is None:
        noise_cov = np.identity(n_chans)
    if source_cov is None:
        source_cov = np.identity(n_dipoles)

    inverse_operators = []
    leadfield_source_cov = source_cov @ self.leadfield.T
    LLS = self.leadfield @ leadfield_source_cov
    if alpha == "auto":
        r_grid = np.asarray(self.r_values, dtype=float)
    else:
        r_grid = np.asarray([float(alpha)], dtype=float)
    max_eig_LLS = float(np.linalg.svd(LLS, compute_uv=False).max())
    max_eig_noise = float(np.linalg.svd(noise_cov, compute_uv=False).max())
    scale = max_eig_LLS / max(max_eig_noise, 1e-15)
    self.alphas = list(r_grid * scale)

    for alpha in self.alphas:
        K = leadfield_source_cov @ self.robust_inverse(LLS + alpha * noise_cov)
        W_dSPM = np.diag(np.sqrt(1 / np.diagonal(K @ noise_cov @ K.T)))
        inverse_operator = W_dSPM @ K
        inverse_operators.append(inverse_operator)

    self.inverse_operators = [
        InverseOperator(inverse_operator, self.name)
        for inverse_operator in inverse_operators
    ]
    return self