Model misspecification detection by means of multiple generator errors, using the observed potential map

EEG source imaging

OBJECTIVE

Electroencephalography (EEG) is an important tool for studying the temporal dynamics of the human brain's large-scale neuronal circuits. However, most EEG applications fail to capitalize on all of the data's available information, particularly that concerning the location of active sources in the brain. Localizing the sources of a given scalp measurement is only achieved by solving the so-called inverse problem. By introducing reasonable a priori constraints, the inverse problem can be solved and the most probable sources in the brain at every moment in time can be accurately localized.

METHODS AND RESULTS

Here, we review the different EEG source localization procedures applied during the last two decades. Additionally, we detail the importance of those procedures preceding and following source estimation that are intimately linked to a successful, reliable result. We discuss (1) the number and positioning of electrodes, (2) the varieties of inverse solution models and algorithms, (3) the integration of EEG source estimations with MRI data, (4) the integration of time and frequency in source imaging, and (5) the statistical analysis of inverse solution results.

CONCLUSIONS AND SIGNIFICANCE

We show that modern EEG source imaging simultaneously details the temporal and spatial dimensions of brain activity, making it an important and affordable tool to study the properties of cerebral, neural networks in cognitive and clinical neurosciences.

Noninvasive identification of human central sulcus: a comparison of gyral morphology, functional MRI, dipole localization, and direct cortical mapping

The locations of the human primary hand cortical somatosensory and motor areas were estimated using structural and functional MRI, scalp-recorded somatosensory-evoked potential dipole localization, expert judgments based on cortical anatomy, and direct cortical stimulation and recording studies. The within-subject reliability of localization (across 3 separate days) was studied for eight normal subjects. Intraoperative validation was obtained from five neurosurgical patients. The mean discrepancy between the different noninvasive functional imaging methods ranged from 6 to 26 mm. Quantitative comparison of the noninvasive methods with direct intraoperative stimulation and recording studies did not reveal a significant mean difference in accuracy. However, the expert judgments of the location of the sensory hand areas were significantly more variable (maximum error, 39 mm) than the dipole or functional MRI techniques. It is concluded that because expert judgments are less reliable for identifying the cortical hand area, consideration of the findings of noninvasive functional MRI and dipole localization studies is desirable for preoperative surgical planning.

The usefulness of the Laplacian in principal component analysis and dipole source localization

Evoked potentials are difficult to analyze because multiple sources are active simultaneously. Principal component analysis and dipole localization are two techniques that have been used to disentangle overlapping sources. Both of these techniques have problems. Principal component analysis suffers from a rotation ambiguity. Dipole localization suffers from biases when the model used to derive the sources from the scalp potentials is misspecified. Using computer simulations we demonstrate that by applying both of these techniques to the Laplacian of the voltages rather than to the raw voltages the problems associated with the two techniques are reduced. Computer programs for the analyses are presented in an Appendix.

The Duffing oscillator: a model for the dynamics of the neuronal groups comprising the transient evoked potential

Thirty years ago Zeeman conjectured that the dynamics of the EEG might be modeled by the "equation of motion" of a Duffing oscillator, a pendulum with a nonlinear, cubic, restoring force. In this study the idea is extended to the evoked potential (EP). A transient sensory EP reflects activity from several neuronal groups, pools of neurons that fire in synchrony, with voltage-time curves that overlap appreciably. When the dynamics of each neuronal group is modeled by a Duffing oscillator, multi-electrode transient VEPs are well predicted. Predictions based on Duffing oscillator dynamics are substantially better than those based on the assumption that each neuronal group follows a simpler exponentially damped sinusoid or a function that simulates a post-synaptic potential. The component voltage-time curves are reasonably consistent over 7 subjects, suggesting sequential activation of neuronal groups with delays of several tens of milliseconds between them. The scalp topographies of the components suggest their origins in the occipital cortex.

Multiple-generator errors are unavoidable under model misspecification

Model misspecification poses a major problem for dipole source localization (DSL) because it causes insidious multiple-generator errors (MulGenErrs) to occur in the fitted dipole parameters. This paper describes how and why this occurs, based upon simple algebraic considerations. MulGenErrs must occur, to some degree, in any DSL analysis of real data because there is model misspecification and mathematically the equations used for the simultaneously active generators must be of a different form than the equations for each generator active alone.

A fast method to compute surface potentials generated by dipoles within multilayer anisotropic spheres

Berg and Scherg's fast computation method is extended to multilayer anisotropic spheres. The Berg parameters can be dependent upon a dipole radial parameter or not, depending on the actual sphere conductivities and the layer the dipole is within. To find the Berg parameters, no specific electrode locations are required. Berg and Scherg's method is generally applicable whenever de Munck and Peters's addition-subtraction method can be used.

DSL and MUSIC under model misspecification and noise-conditions

The concepts of both the traditional DSL (Dipole Source Localization) and MUSIC (MUltiple SIgnal Classification) are explained using simple vectors. DSL and MUSIC differ in the way the weighting functions are found. In both DSL and MUSIC, the fitted generator magnitudes are found by projecting the recorded potential map onto the fitted weighting functions, and the model transfers the weighting functions into generator locations/orientations. Both DSL and MUSIC will cause errors in the fitted dipole parameters when there is model misspecification, noise, or both. Therefore, an accurate head model is essential for either method to give reliable results.