Cheryl J. Aine

Multi-start downhill simplex method for spatio-temporal source localization in magnetoencephalography

A multi-start downhill simplex method is examined as a global minimization technique for fitting multidipole, spatio-temporal magnetoencephalography (MEG) data. This procedure has been performed on both simulated and empirical human visual data, known to exhibit complex field patterns due to multiple sources. Unlike some other non-linear fitting techniques the multi-start downhill simplex method does not require users to provide initial guesses for the dipole parameters, hence the fitting procedure is less time-consuming, more objective, and user-friendly. In addition, this method offers more than one adequate solution thus providing a range of uncertainty for the estimated parameters. The Multi-start downhill simplex method is used to fit the non-linear dipole spatial parameters, while the linear temporal parameters are fit using a separate linear fitting procedure. Singular value decomposition (SVD) is also used in order to improve the procedure for determining the adequate number of modeled dipoles.

Temporal dynamics of visual-evoked neuromagnetic sources: Effects of stimulus parameters and selective attention

Results are reviewed from several neuromagnetic studies which characterize the temporal dynamics of neural sources contributing to the visual evoked response and effects of attention on these sources. Different types of pattern-onset stimuli (< or = 2 degrees) were presented sequentially to a number of field locations in the right visual field. Multiple dipole models were applied to a sequence of instantaneous field distributions constructed at 10 ms intervals. Best-fitting source parameters were superimposed on Magnetic Resonance images (MRI) of each subject to identify the anatomical structure(s) giving rise to the surface patterns. At least three sources, presumably corresponding to different visual areas, were routinely identified from 80-150 ms following the onset of visual stimulation. This observation was consistent across subjects and studies. The temporal sequence and strength of activation of these sources, however, were dependent upon the specific stimulus parameters used to evoke the response (e.g., eccentricity) and on the relevance of the stimulus to the subject. In addition, our results provide evidence for the recurrence of activity in striate and extrastriate regions, following the initial cycle of responses.

Monte Carlo analysis of localization errors in magnetoencephalography

In magnetoencephalography (MEG), the magnetic fields created by electrical activity in the brain are measured on the surface of the skull. To determine the location of the activity, the measured field is fit to a parameterized source generator model by minimizing chi-square. In the case of a current dipole model, the parameters computed by the fitting procedure are the location and orientation of the dipole. For current dipoles and other nonlinear source models, the fit is performed by an iterative least squares procedure such as the Levenberg-Marquardt algorithm (Press 1986). Once the fit has been computed, analysis of the resulting value of chi-square can determine whether the assumed source model is adequate to account for the measurements. If the source model is adequate, then the effect of measurement error on the fitted model parameters must be analyzed.

Spatio-Temporal Modeling of Neuromagnetic Data: I. Multi-Source Location Versus Time-Course Estimation Accuracy

Numerical simulations were conducted to examine multi‐source spatio‐temporal resolution for neuromagnetic field distributions “measured” by a large sensor array (i.e., 135). spatio‐temporal field distributions were generated by a series of two‐dipole and three‐dipole configurations in which source locations, orientations, and temporal dynamics of individual sources were systematically varied to represent classes of cases of interest for neuromagnetic studies. The specific goals of our numerical simulations were to examine multi‐source resolution and parameter estimation accuracy as a function of 1) specific multi‐source configurations; 2) different time courses, i.e., degree of temporal correlation; 3) measurement noise; 4) spatio‐temporal modeling strategy (i.e., sequential fitting of instantaneous field distributions, two‐step spatio‐temporal modeling); 5) source modeling assumptions associated with model order; and 6) effects of initial modeling assumptions (i.e., starting points for the nonlinear minimization procedure derived by MUltiple SIgnal Classification (MUSIC), sequential instantaneous fitting, and arbitrary selections). The ability to determine the number of active sources by different approaches is compared, and the consequences on the accuracy of estimated solutions for simulated data are discussed. In all cases, model adequacy was assessed using reduced chi‐square as a measure of goodness‐of‐fit. The present simulations demonstrate that location estimation was more robust and accurate compared to the estimation of temporal dynamics of individual sources. Implications for spatio‐temporal modeling of neuromagnetic empirical data are suggested. Hum. Brain Mapping 5:139–153, 1997.

Frequency-Following and Connectivity of Different Visual Areas in Response to Contrast-Reversal Stimulation

The sensitivity of visual areas to different temporal frequencies, as well as the functional connections between these areas, was examined using magnetoencephalography (MEG). Alternating circular sinusoids (0, 3.1, 8.7 and 14 Hz) were presented to foveal and peripheral locations in the visual field to target ventral and dorsal stream structures, respectively. It was hypothesized that higher temporal frequencies would preferentially activate dorsal stream structures. To determine the effect of frequency on the cortical response we analyzed the late time interval (220–770 ms) using a multi-dipole spatio-temporal analysis approach to provide source locations and timecourses for each condition. As an exploratory aspect, we performed cross-correlation analysis on the source timecourses to determine which sources responded similarly within conditions. Contrary to predictions, dorsal stream areas were not activated more frequently during high temporal frequency stimulation. However, across cortical sources the frequency-following response showed a difference, with significantly higher power at the second harmonic for the 3.1 and 8.7 Hz stimulation and at the first and second harmonics for the 14 Hz stimulation with this pattern seen robustly in area V1. Cross-correlations of the source timecourses showed that both low- and high-order visual areas, including dorsal and ventral stream areas, were significantly correlated in the late time interval. The results imply that frequency information is transferred to higher-order visual areas without translation. Despite the less complex waveforms seen in the late interval of time, the cross-correlation results show that visual, temporal and parietal cortical areas are intricately involved in late-interval visual processing.

Nonlinear analysis of biological systems using short M-sequences and sparse-stimulation techniques

The m-sequence pseudorandom signal has been shown to be a more effective probing signal than traditional Gaussian white noise for studying nonlinear biological systems using cross-correlation techniques. The effectiveness is evidenced by the high signal-to-noise (S/N) ratio and speed of data acquisition. However, the “anomalies” that occur in the estimations of the cross-correlations represent an obstacle that prevents m-sequences from being more widely used for studying nonlinear systems. The sparse-stimulation method for measuring system kernels can help alleviate estimation errors caused by anomalies. In this paper, a “padded sparse-stimulation” method is evaluated, a modification of the “inserted sparse-stimulation” technique introduced by Sutter, along with a short m-sequence as a probing signal. Computer simulations show that both the “padded” and “inserted” methods can effectively eliminate the anomalies in the calculation of the second-order kernel, even when short m-sequences were used (length of 1023 for a binary m-sequence, and 728 for a ternary m-sequence). Preliminary experimental data from neuromagnetic studies of the human visual system are also presented, demonstrating that the system kernels can be measured with high signal-to-noise (S/N) ratios using short m-sequences.

Spatial/Temporal Resolution of Multiple Sources: Paths of Activation in Human Visual Cortex

We have employed neuromagnetic mapping techniques to characterize neural responses evoked by sinusoidal gratings presented at various locations in the visual field. A primary goal of this work has been to localize the neurophysiological processes which underlie response components empirically defined in previous event-related potential (ERP) studies. Our analyses have focused on temporal as well as spatial tracking of sources because the combination permits more powerful inferences concerning the number and location of active neural sources (1–4).

Identification of Multiple Sources in Transient Visual Evoked Neuromagnetic Responses

Neuromagnetic measurements and associated modeling procedures must be capable of resolving multiple sources in order to localize and accurately characterize generators of visual evoked activity. Okada (1984) has estimated that a field pattern generated by two dipoles can be distinguished from that generated by a single dipole provided that the separation between the sources is greater than 1–2 cm, but there have been few attempts at modeling neurally generated field patterns with multiple, simultaneously active dipoles. The expanse of man’s occipital cortex is estimated to be 150–250 cm2 and invasive experiments with cats and monkeys suggest that this region most likely includes several discrete visual areas (e.g., Van Essen, 1985). It thus seems plausible that visual stimuli evoke activity from multiple discrete populations of neurons within visual cortical areas and that the application of appropriate modeling procedures to visually evoked neuromagnetic field data will resolve these populations.

Spatio-temporal modeling of neuromagnetic data: II. Multi-source resolvability of a MUSIC-based location estimator

A MUItiple SIgnal Classification‐based (MUSIC) approach for neuromagnetic multi‐source localization (Mosher et al. [1992] (IEEE Trans Med Eng BME‐39:541–557) was evaluated through numerical simulations and by applying it to visually evoked neuromagnetic responses. A series of two‐dipole and three‐dipole spatio‐temporal data were generated to examine effects of 1) source configurations, 2) temporal correlations, 3) noise, and 4) subspace dimensionality assumptions on the number of MUSIC metric maxima, their amplitudes, and how the resulting metric maxima locations relate to the actual source locations. In its present form, i.e., using simple one‐dipole scanning over an assumed source subspace, MUSIC resulted either in 1) peaks sufficiently close to 1, but fewer than the actual number of sources which affected location estimation accuracy, or 2) the peaks were too low to qualify as source locations. Our simulations indicate difficulties in defining threshold values as to which peak values are close enough to 1 while avoiding significant type II errors (i.e., accepting peaks which should not be interpreted as source locations). Modifications to the MUSIC approach are necessary in order for the method to be considered of practical value for reliably localizing multiple neuromagnetic sources in empirical cases in which a high degree of temporal correlation between sources is likely (e.g., visual data). Hum. Brain Mapping 5:154–167, 1997.

A Modality-Specific Neuromagnetic P3

Several studies indicate that in cases of psychopathology and alcoholism the amplitude and/or latency of endogenous, scalp-recorded P3 potentials elicited by rare events are abnormal (e.g., Roth et al., 1980; Polich, 1984). The P3 complex may normally be a valuable index of cognitive processing (see Donchin and Coles, 1988) and identification of the neural generator(s) of this response would thus provide valuable insight into both normal and abnormal information processes.