Simultaneous spatio-temporal matching pursuit decomposition of evoked brain responses in MEG.

We present a novel approach to the spatio-temporal decomposition of evoked brain responses in magnetoencephalography (MEG) aiming at a sparse representation of the underlying brain activity in terms of spatio-temporal atoms. Our approach is characterized by three attributes which constitute significant improvements with respect to existing approaches: (1) the spatial and temporal decomposition is addressed simultaneously rather than sequentially, with the benefit that source loci and corresponding waveforms can be unequivocally allocated to each other, and, hence, allow a plausible physiological interpretation of the parametrized data; (2) it is free from severe a priori assumptions about the solution space; (3) it comprises an optimization technique for the use of very large spatial and temporal subdirectories to greatly reduce the otherwise enormous computational cost by making use of the Cauchy-Schwarz inequality. We demonstrate the efficiency of the approach with simulations and real MEG data obtained from a subject exposed to a simple auditory stimulus.

Averaging auditory evoked magnetoencephalographic and electroencephalographic responses: a critical discussion.

In the analysis of data from magnetoencephalography (MEG) and electroencephalography (EEG), it is common practice to arithmetically average event-related magnetic fields (ERFs) or event-related electric potentials (ERPs) across single trials and subsequently across subjects to obtain the so-called grand mean. Comparisons of grand means, e.g. between conditions, are then often performed by subtraction. These operations, and their statistical evaluation with parametric tests such as ANOVA, tacitly rely on the assumption that the data follow the additive model, have a normal distribution, and have a homogeneous variance. This may be true for single trials, but these conditions are rarely met when ERFs/ERPs are compared between subjects, meaning that the additive model is seldom the correct model for computing grand mean waveforms. Here, we summarize some of our recent work and present new evidence, from auditory-evoked MEG and EEG results, that the non-normal distributions and the heteroscedasticity observed instead result because ERFs/ERPs follow a mixed model with additive and multiplicative components. For peak amplitudes, such as the auditory M100 and N100, the multiplicative component dominates. These findings emphasize that the common practice of simply subtracting arithmetic means of auditory-evoked ERFs or ERPs is problematic without prior adequate transformation of the data. Application of the area sinus hyperbolicus (asinh) transform to data following the mixed model transforms them into the requested additive model with its normal distribution and homogeneous variance. We therefore advise checking the data for compliance with the additive model and using the asinh transform if required.

Maximum-likelihood estimation of channel-dependent trial-to-trial variability of auditory evoked brain responses in MEG.

BACKGROUND: We propose a mathematical model for multichannel assessment of the trial-to-trial variability of auditory evoked brain responses in magnetoencephalography (MEG). METHODS: Following the work of de Munck et al., our approach is based on the maximum likelihood estimation and involves an approximation of the spatio-temporal covariance of the contaminating background noise by means of the Kronecker product of its spatial and temporal covariance matrices. Extending the work of de Munck et al., where the trial-to-trial variability of the responses was considered identical to all channels, we evaluate it for each individual channel. RESULTS: Simulations with two equivalent current dipoles (ECDs) with different trial-to-trial variability, one seeded in each of the auditory cortices, were used to study the applicability of the proposed methodology on the sensor level and revealed spatial selectivity of the trial-to-trial estimates. In addition, we simulated a scenario with neighboring ECDs, to show limitations of the method. We also present an illustrative example of the application of this methodology to real MEG data taken from an auditory experimental paradigm, where we found hemispheric lateralization of the habituation effect to multiple stimulus presentation. CONCLUSIONS: The proposed algorithm is capable of reconstructing lateralization effects of the trial-to-trial variability of evoked responses, i.e. when an ECD of only one hemisphere habituates, whereas the activity of the other hemisphere is not subject to habituation. Hence, it may be a useful tool in paradigms that assume lateralization effects, like, e.g., those involving language processing.

Optimising a computational model of human auditory cortex with an evolutionary algorithm.

We demonstrate how the structure of auditory cortex can be investigated by combining computational modelling with advanced optimisation methods. We optimise a well-established auditory cortex model by means of an evolutionary algorithm. The model describes auditory cortex in terms of multiple core, belt, and parabelt fields. The optimisation process finds the optimum connections between individual fields of auditory cortex so that the model is able to reproduce experimental magnetoencephalographic (MEG) data. In the current study, this data comprised the auditory event-related fields (ERFs) recorded from a human subject in an MEG experiment where the stimulus-onset interval between consecutive tones was varied. The quality of the match between synthesised and experimental waveforms was 98%. The results suggest that neural activity caused by feedback connections plays a particularly important role in shaping ERF morphology. Further, ERFs reflect activity of the entire auditory cortex, and response adaptation due to stimulus repetition emerges from a complete reorganisation of AC dynamics rather than a reduction of activity in discrete sources. Our findings constitute the first stage in establishing a new non-invasive method for uncovering the organisation of the human auditory cortex.

Application of modern tests for stationarity to single-trial MEG data: transferring powerful statistical tools from econometrics to neuroscience.

Stationarity is a crucial yet rarely questioned assumption in the analysis of time series of magneto- (MEG) or electroencephalography (EEG). One key drawback of the commonly used tests for stationarity of encephalographic time series is the fact that conclusions on stationarity are only indirectly inferred either from the Gaussianity (e.g. the Shapiro-Wilk test or Kolmogorov-Smirnov test) or the randomness of the time series and the absence of trend using very simple time-series models (e.g. the sign and trend tests by Bendat and Piersol). We present a novel approach to the analysis of the stationarity of MEG and EEG time series by applying modern statistical methods which were specifically developed in econometrics to verify the hypothesis that a time series is stationary. We report our findings of the application of three different tests of stationarity--the Kwiatkowski-Phillips-Schmidt-Schin (KPSS) test for trend or mean stationarity, the Phillips-Perron (PP) test for the presence of a unit root and the White test for homoscedasticity--on an illustrative set of MEG data. For five stimulation sessions, we found already for short epochs of duration of 250 and 500 ms that, although the majority of the studied epochs of single MEG trials were usually mean-stationary (KPSS test and PP test), they were classified as nonstationary due to their heteroscedasticity (White test). We also observed that the presence of external auditory stimulation did not significantly affect the findings regarding the stationarity of the data. We conclude that the combination of these tests allows a refined analysis of the stationarity of MEG and EEG time series.

Reducing the Number of MEG/EEG Trials Needed for the Estimation of Brain Evoked Responses: A Bootstrap Approach.

OBJECTIVE: A common problem in magnetoencephalographic (MEG) and electroencephalographic (EEG) experimental paradigms relying on the estimation of brain evoked responses is the lengthy time of the experiment, which stems from the need to acquire a large number of repeated recordings. Using a bootstrap approach, we aim at reliably reducing the number of these repeated trials. METHODS: To this end, we assessed five variants of non-parametric bootstrapping based on the classical signal-plus-noise model constituting the foundation of signal averaging in MEG/EEG. We explain which of these approaches should and which should not be used for the aforementioned purpose, and why. RESULTS: We present results for two advocated bootstrap variants applied to auditory MEG data. The ensuing trial-averaged magnetic fields served as input to the estimation of cortical source generators, with spatio-temporal matching pursuit as an example of an inverse solution technique. We propose, for a wide range of trial numbers, a general framework to evaluate the statistical properties of the parameter estimates for source locations and related time courses. CONCLUSION: The proposed bootstrap framework offers a systematic approach to reduce the number of trials required to estimate the evoked response. The general validity of our findings is neither bound to any particular type of MEG/EEG data nor to any specific source localization method. SIGNIFICANCE: Practical implications of this work relate to the optimization of acquisition time of MEG/EEG experiments, thus reducing stress for the subjects (especially for patients) and minimizing related artifacts.

A Fully Automated 3D In-Vivo Delineation and Shape Parameterization of the Human Lamina Cribrosa in Optical Coherence Tomography.

OBJECTIVE: A fully automated method for delineation of the lamina cribrosa in optical coherence tomography (OCT) is proposed. It assesses the three-dimensional (3D) shape of the lamina cribrosa in-vivo, based on a series of OCT B-scans. METHODS: The algorithm has several image processing steps and it is based on active contour detection performed along three orthogonal directions of the B-scan data cuboid. Further, the delineated 3D lamina cribrosa shape is parameterized with a fourth-order polynomial of two variables [Formula: see text] using the least-squares method. Datasets from a total of 255 subjects from three groups were analyzed: 92 primary open angle glaucoma patients, 77 glaucoma suspects, and 86 controls. RESULTS: Statistically significant differences were found in the coefficients of monomials xiyj, with both i and j even, between patients and controls and between suspects and controls. CONCLUSIONS: From the data obtained, it can be concluded that the mean shape parameterization of the lamina cribrosa of glaucoma suspects has similar appearance to that of glaucoma patients but it is markedly different from that of healthy controls. SIGNIFICANCE: The proposed algorithm enables automatically estimating, for the first time, the lamina cribrosa in 3D, further providing clinicians with a time-efficient discrimination tool supporting glaucoma diagnosis.

Can Kinect aid motor learning in sportsmen? A study for three standing techniques in judo.

Our objective was to examine how exercises with the second generation of the Microsoft Kinect sensor may aid in the process of motor learning in young judo practitioners. We addressed improvements in spatio-temporal accuracy during execution of three standing techniques in judo, in a simple paradigm designed to study short-term practice effects. Two groups of judokas, 12 athletes each-one aided with Kinect and our dedicated software vs a group of controls-were asked to mimic previously recorded master-level performances of the three techniques, established as benchmarks by a two times world champion in judo. In five training sessions, athletes of the aided group used a virtual-reality setup in which they trained with a virtual representation of the master displayed on a large screen with a simultaneous real-time visualisation of their own movements in the form of an avatar based on body joint localisation, as determined by Kinect, which also measured their performance. The control group used Kinect in the 1st and 5th session, which was necessary for the measurements that constituted the basis for subsequent statistical comparisons, whereas the 2nd, 3rd, and 4th session in this group was guided by a coach, without the use of the Kinect setup. In addition, athletes of the two groups had unrestricted access to a video recording of the master performing the three throws. We found statistically significant improvements (p < 0.05) in the accuracy of executing the three techniques between the 1st and the 5th training session for the aided group but not for the control group. We conclude that incorporating Kinect based exercises into a judo training programme may be a useful means to supporting motor learning, therefore enhancing training efficiency, and thus improving performance.

Effects of the task of categorizing FM direction on auditory evoked magnetic fields in the human auditory cortex.

We examined effects of the task of categorizing linear frequency-modulated (FM) sweeps into rising and falling on auditory evoked magnetic fields (AEFs) from the human auditory cortex, recorded by means of whole-head magnetoencephalography. AEFs in this task condition were compared with those in a passive condition where subjects had been asked to just passively listen to the same stimulus material. We found that the M100-peak latency was significantly shorter for the task condition than for the passive condition in the left but not in the right hemisphere. Furthermore, the M100-peak latency was significantly shorter in the right than in the left hemisphere for the passive and the task conditions. In contrast, the M100-peak amplitude did not differ significantly between conditions, nor between hemispheres. We also analyzed the activation strength derived from the integral of the absolute magnetic field over constant time windows between stimulus onset and 260 ms. We isolated an early, narrow time range between about 60 ms and 80 ms that showed larger values in the task condition, most prominently in the right hemisphere. These results add to other imaging and lesion studies which suggest a specific role of the right auditory cortex in identifying FM sweep direction and thus in categorizing FM sweeps into rising and falling.

Fully automated detection of lamina cribrosa in optical coherence tomography: Framework and illustrative examples.

We present an algorithm for automated detection of lamina cribrosa (LC) using optical coherence tomography scans. To the best of our knowledge, it is the first algorithm of this type, as previous attempts relied heavily on characteristic points marked a priori by a human expert and were hence semi-automated at best. First, we highlight the unwanted, yet unavoidable, influence of image rescaling necessary to provide the detection algorithm with real-world image proportions. Next, we simulate an LC phantom and test the influence of various combinations of the rescaling method and SNRs on the LC detection efficacy. Finally, we present some illustrative results from real-data analysis.

A maximum-likelihood estimator for trial-to-trial variations in noisy MEG/EEG data sets.

The standard procedure to determine the brain response from a multitrial evoked magnetoencephalography (MEG) or electroencephalography (EEG) data set is to average the individual trials of these data, time locked to the stimulus onset. When the brain responses vary from trial-to-trial this approach is false. In this paper, a maximum-likelihood estimator is derived for the case that the recorded data contain amplitude variations. The estimator accounts for spatially and temporally correlated background noise that is superimposed on the brain response. The model is applied to a series of 17 MEG data sets of normal subjects, obtained during median nerve stimulation. It appears that the amplitude of late component (30-120 ms) shows a systematic negative trend indicating a weakening response during stimulation time. For the early components (20-35 ms) no such a systematic effect was found. The model is furthermore applied on a MEG data set consisting of epileptic spikes of constant spatial distribution but varying polarity. For these data, the advantage of applying the model is that positive and negative spikes can be processed with a single model, thereby reducing the number of degrees of freedom and increasing the signal-to-noise ratio.

Variance stabilization for computing and comparing grand mean waveforms in MEG and EEG.

Grand means of time-varying signals (waveforms) across subjects in magnetoencephalography (MEG) and electroencephalography (EEG) are commonly computed as arithmetic averages and compared between conditions, for example, by subtraction. However, the prerequisite for these operations, homogeneity of the variance of the waveforms in time, and for most common parametric statistical tests also between conditions, is rarely met. We suggest that the heteroscedasticity observed instead results because waveforms may differ by factors and additive terms and follow a mixed model. We propose to apply the asinh-transformation to stabilize the variance in such cases. We demonstrate the homogeneous variance and the normal distributions of data achieved by this transformation using simulated waveforms, and we apply it to real MEG data and show its benefits. The asinh-transformation is thus an essential and useful processing step prior to computing and comparing grand mean waveforms in MEG and EEG.

The M100 component of evoked magnetic fields differs by scaling factors: implications for signal averaging.

MEG and EEG studies of event-related responses often involve comparisons of grand averages, requiring homogeneity of the variances. Here, we examine the possibility, implied by the nature of neural sources and the measuring principles involved, that the M100 component of auditory-evoked magnetic fields of different subjects, hemispheres, to different stimuli, and at different sensors differs by scaling factors. Such a multiplicative model predicts a linear increase in the standard deviation with the mean, and thus would have important implications for averaging and comparing such data. Our analyses, at the sensor and the source level, clearly show that the multiplicative model applies. We therefore propose geometric, rather than arithmetic, averaging of the M100 component across subjects and suggest a novel and superior normalization procedure. Our results question the justification of the common practice of subtracting arithmetic grand averages.

Single-trial evoked brain responses modeled by multivariate matching pursuit.

We present a new approach to the analysis of brain evoked electromagnetic potentials and fields. Multivariate version of the matching pursuit algorithm (MMP) performs an iterative, exhaustive search for waveforms, which optimally fit to signal structures, persistent in all the responses (trials) with the same time of occurrence, frequency, phase, and time width, but varying amplitude. The search is performed in a highly redundant time--frequency dictionary of Gabor functions, i.e., sines modulated by Gaussians. We present the feasibility of such a single-trial MMP analysis of the auditory M100 response, using an illustrative dataset acquired in a magnetoencephalographic (MEG) measurement with auditory stimulation with sinusoidal 1-kHz tones. We find that the morphology of the M100 estimate obtained from simple averaging of single trials can be very well explained by the average reconstruction with a few Gabor functions that parametrize those single trials. The M100 peak amplitude of single-trial reconstructions is observed to decrease with repetitions, which indicates habituation to the stimulus. This finding suggests that certain waveforms fitted by MMP could possibly be related to physiologically distinct components of evoked magnetic fields, which would allow tracing their dynamics on a single-trial level.