MEG & EEG » Statistical Analysis

Evaluation of inverse methods

The MEG and EEG literature encompasses a wide variety of reconstruction and localization methodologies. It is important to evaluate the relative performance of these methods under different experimental settings such as the number, location and time series of neural sources. Furthermore, several methods require fine tuning of parameters, for example the Tikhonov regularization parameter in current density reconstruction, or the subspace correlation threshold for the MUSIC algorithm. Adjusting these parameters affects the sensitivity and specificity of each method. We illustrate the use of the Receiver Operating Characteristic (ROC) curve to study the trade-off between sensitivity and specificity and to compared different inverse methods.

Figure: ROC methods produce a plot of the variation in True Positive Fraction (TPF) vs. False Positive Fraction (FPF) as a function of some decision threshold. The area under the curve is a good measure of the performance of each method.

Figure: Sample detection map. Blue represents true brain activity; red represents detected brain activity. There are many approaches of defining the TPF and the FPF, based on the possible overlap of these regions and the size of the intersection.

Confidence / Statistical Significance

In addition to evaluating the relative performance of different methods, it is also important to establish some degree of confidence in the results of real data analysis. Dipole scanning methods often produce unstable solutions and the reproducibility of the reconstructed dipoles is not guaranteed. Consequently, it is important to quantify the accuracy of the dipole locations and time series. Conversely, imaging methods are hugely underdetermined, resulting in low resolution localization maps; interpretation is further confounded by the presence of additive noise exhibiting a highly nonuniform spatial correlation. In this case, we need a mechanism to decide which features in the data are indicative of true activation versus those that are noise artifacts. While parametric models can be assumed as the basis for developing statistical tests, nonparametric resampling methods such as the bootstrap and permutation methods are well suited to analysis of MEG and EEG data. Event related studies typically involve multiple repetitions which can be treated as a set of identically distributed and independent realizations from which we can resample.

We estimate the confidence of a dipole localization (see modeling) by using the nonparametric bootstrap, a method for assessing accuracy of an estimator by sampling with replacement from a set of independent trials. By repeating this process and estimating parameters from each bootstrap resample, we can learn the approximate distribution of the estimator.

Figure: Bootstrap results from an MEG somatosensory study involving delivery of electrical pulses to the fingers of both hands of a healthy subject; (left) locations from original data of the strongest dipole source for each of the four digits demonstrating somatotopic mapping in the sensory cortex; (middle) scatter distribution of bootstrapped dipoles, color coded for each digit; (right) Confidence ellipsoids constructed with principal axes along the eigenvectors of the cluster covariances; axes of length equal to two times the standard deviation along each principal axis represent an 87% confidence region for a Gaussian distribution.

Detection of Regions of Significant Activation in Cortical Maps

In contrast to dipole localization, where the number of spatial parameters is far fewer than the number of detectors, cortically constrained maps typically contain far more surface elements than detectors. This overparameterization leads to high spatial correlation in the maps and presents difficulties in determining a suitable threshold for detecting statistically significant activation. Applying a simple Bonferroni correction and testing at each surface element will lead to a very conservative threshold. Conversely, an unacceptably high false positive rate may arise if no correction is made for multiple hypothesis testing. The standard approach to this problem is to control the Familywise Error Rate (FWER), i.e. the chance of any false positives under the null hypothesis (type 1 error). Parametric random field methods and non-parametric permutation methods address this problem by estimating familywise-corrected thresholds.

Figure: Examples of significant activation maps for permutation and random field methods for two simulated sources on the right and left somatosensory area; (a) Permutation method controlling spatiotemporal FWER and using unsmoothed current densities, (b) Permutation method controlling spatial FWER and using unsmoothed current densities, (c) Permutation method controlling spatial FWER and using smoothed current densities, (d) RF method controlling spatial FWER and using smoothed current densities. Smoothing is optional for permutation tests, but necessary for RFs to avoid conservative thresholds.

Imaging oscillatory activity in MEG using time-frequency analysis and permutation tests

In event-related MEG studies, the standard technique for noise reduction involves averaging over stimulus-locked responses. However this also removes higher frequency components in the data that are not phase locked to the stimulus. To overcome this problem, we combine time-frequency analysis of individual epochs with minimum norm imaging to produce dynamic cortical images in multiple frequency bands. To detect statistically significant differences between two conditions, such as post-stimulus vs. baseline, we use a permutation test. By learning the null distribution of maximum signal power in each band across the cortex, we can then determine a threshold that controls the familywise error rate, i.e. the probability of one or more false positive detections across the entire cortex. Applying this test to each frequency band produces a set of cortical images showing significant event-related activity in each band of interest.

Figure: Time-varying frequency components of a source on the frontal lobe; we notice desynchronization in the β band 250-600ms after stimulus. The Morlet wavelet is a Gaussian-windowed complex sinusoid with the real part shown in blue, and the imaginary part in red.

Figure: Significant maps at the upper betta frequency band (20-30Hz) for a high density MEG data of a visual study. The maps show decreased power in what is considered to be a network for deploying attention: dorsolateral prefrontal, inferior parietal, lateral and ventral temporal areas. There is a larger decrease contralateral to the direction of attention (i.e. right hemi., for cue-left field).

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