Coding of saliency by ensemble bursting in the amygdala of primates.

Salient parts of a visual scene attract longer and earlier fixations of the eyes. Saliency is driven by bottom-up (image dependent) factors and top-down factors such as behavioral relevance, goals, and expertise. It is currently assumed that a saliency map defining eye fixation priorities is stored in neural structures that remain to be determined. Lesion studies support a role for the amygdala in detecting saliency. Here we show that neurons in the amygdala of primates fire differentially when the eyes approach to or fixate behaviorally relevant parts of visual scenes. Ensemble bursting in the amygdala accurately predicts main fixations during the free-viewing of natural images. However, fixation prediction is significantly better for faces-where a bottom-up computational saliency model fails-compared to unfamiliar objects and landscapes. On this basis we propose the amygdala as a locus for a saliency map and ensemble bursting as a saliency coding mechanism.

Non-stationary distributed source approximation: an alternative to improve localization procedures.

Localization of the generators of the scalp measured electrical activity is particularly difficult when a large number of brain regions are simultaneously active. In this study, we describe an approach to automatically isolate scalp potential maps, which are simple enough to expect reasonable results after applying a distributed source localization procedure. The isolation technique is based on the time-frequency decomposition of the scalp-measured data by means of a time-frequency representation. The basic rationale behind the approach is that neural generators synchronize during short time periods over given frequency bands for the codification of information and its transmission. Consequently potential patterns specific for certain time-frequency pairs should be simpler than those appearing at single times but for all frequencies. The method generalizes the FFT approximation to the case of distributed source models with non-stationary time behavior. In summary, the non-stationary distributed source approximation aims to facilitate the localization of distributed source patterns acting at specific time and frequencies for non-stationary data such as epileptic seizures and single trial event related potentials. The merits of this approach are illustrated here in the analysis of synthetic data as well as in the localization of the epileptogenic area at seizure onset in patients. It is shown that time and frequency at seizure onset can be precisely detected in the time-frequency domain and those localization results are stable over seizures. The results suggest that the method could also be applied to localize generators in single trial evoked responses or spontaneous activity.

Noninvasive localization of electromagnetic epileptic activity. I. Method descriptions and simulations.

This paper considers the solution of the bioelectromagnetic inverse problem with particular emphasis on focal compact sources that are likely to arise in epileptic data. Two linear inverse methods are proposed and evaluated in simulations. The first method belongs to the class of distributed inverse solutions, capable of dealing with multiple simultaneously active sources. This solution is based on a Local Auto Regressive Average (LAURA) model. Since no assumption is made about the number of activated sources, this approach can be applied to data with multiple sources. The second method, EPIFOCUS, assumes that there is only a single focal source. However, in contrast to the single dipole model, it allows the source to have a spatial extent beyond a single point and avoids the non-linear optimization process required by dipole fitting. The performance of both methods is evaluated with synthetic data in noisy and noise free conditions. The simulation results demonstrate that LAURA and EPIFOCUS increase the number of sources retrieved with zero dipole localization error and produce lower maximum error and lower average error compared to Minimum Norm, Weighted Minimum Norm and Minimum Laplacian (LORETA). The results show that EPIFOCUS is a robust and powerful tool to localize focal sources. Alternatives to localize data generated by multiple sources are discussed. A companion paper (Lantz et al. 2001, this issue) illustrates the application of LAURA and EPIFOCUS to the analysis of interictal data in epileptic patients.

Noninvasive localization of electromagnetic epileptic activity. II. Demonstration of sublobar accuracy in patients with simultaneous surface and depth recordings.

Seven patients with complex partial epileptic seizures undergoing invasive video/EEG-monitoring were investigated with a combination of 10 subdural strip electrode contacts (subtemporal + lateral temporal), and 22 extracranial recording sites. In each patient spikes with different intracranial distributions were identified, and for those with similar distributions the extracranial activity was averaged. A new inverse solution method called EPIFOCUS (Grave et al. 2001, this issue) was used to reconstruct the sources of both single and averaged spikes in a standard 3D-MRI, and a statistical analysis was performed in order to demonstrate location differences between spikes with different intracranial distributions. The results revealed significantly more anterior and ventral source locations for subtemporal compared to lateral temporal spikes. Within the subtemporal group, medial spikes had more mesial and dorsal locations compared to lateral ones. In the lateral temporal group, more anterior and ventral locations were obtained for anterior compared to posterior spikes. The results demonstrate the applicability of EPIFOCUS in the localization of sources in the temporal lobe with sublobar accuracy. This possibility may become important in the future, for instance in identifying cases where amygdalo-hippocampectomy or other limited temporal lobe resections may replace the standard en bloc resections.

Measuring the complexity of time series: an application to neurophysiological signals.

Measures of signal complexity can be used to distinguish neurophysiological activation from noise in those neuroimaging techniques where we record variations of brain activity with time, e.g., fMRI, EEG, ERP. In this paper we explore a recently developed approach to calculate a quantitative measure of deterministic signal complexity and information content: The Renyi number. The Renyi number is by definition an entropy, i.e., a classically used measure of disorder in physical systems, and is calculated in this paper over the basis of the time frequency representation (TFRs) of the measured signals. When calculated in this form, the Renyi entropy (RE) indirectly characterizes the complexity of a signal by providing an approximate counting of the number of separated elementary atoms that compose the time series in the time frequency plane. In this sense, this measure conforms closely to our visual notion of complexity since low complexity values are obtained for signals formed by a small number of "components". The most remarkable properties of this measure are twofold: 1) It does not rely on assumptions about the time series such as stationarity or gaussianity and 2) No model of the neural process under study is required, e.g., no hemodynamic response model for fMRI. The method is illustrated in this paper using fMRI, intracranial ERPs and intracranial potentials estimated from scalp recorded ERPs through an inverse solution (ELECTRA). The main theoretical and practical drawbacks of this measure, especially its dependence of the selected TFR, are discussed. Also the capability of this approach to produce, with less restrictive hypothesis, results comparable to those obtained with more standard methods but is emphasized.

Imaging the electrical activity of the brain: ELECTRA.

The construction of a tomography of neuronal sources is limited by a lack of information. A possible way around this problem is to change the biophysical model that underlies the statement of the inverse problem, i.e., searching for magnitudes that can be better determined from the available data. In this report, we describe a mathematical characterization of the type of currents that are actually able to produce the scalp-recorded EEG. Considering this characterization, we reformulate the bioelectric inverse problem. This approach, called ELECTRA, yields some advantages over the classical formulation in terms of the current density vector: (1) the number of unknowns can be reduced, which is equivalent to increasing the number of independent measurements, (2) the constraints used to reformulate the problem are undeniable since they do not imply any hypothesis about brain function but are instead based on the character of the measurements, and (3) existing experimental evidence suggests that the proposed source model characterizes the type of currents that arise in excitable tissues. We conclude that if the latter fact proves to be true for brain tissues, then no additional information is added to the inverse problem by using a more general source model than the one proposed here. Images obtained using this method for synthetic data, as well as early and middle components of human visual evoked responses to checkerboard stimuli, are presented to illustrate the characteristics of the reconstructed maps and their interpretation.

Backus and Gilbert method for vector fields.

This report describes the theory of Backus and Gilbert with special emphasis for the case of vector fields as required for the solution of the electromagnetic inverse problem. A description of the method is presented with the detailed mathematical derivation of the coefficients that determine the solution for the retrieval of vector fields. Such derivation, to our knowledge, has never been reported in the literature. We also identify some crucial points that can (and had) lead to misuse of this solution and describe some disadvantages of this theory for the case of vector fields suggesting some alternatives to deal with them.

A critical analysis of linear inverse solutions to the neuroelectromagnetic inverse problem.

This paper explores the possibilities of using linear inverse solutions to reconstruct arbitrary current distributions within the human brain. We formally prove that due to the underdetermined character of the problem, the only class of measurable current distributions that can be totally retrieved are those of minimal norm. The reconstruction of smooth or averaged versions of the currents is also explored. A solution that explicitly attempts to reconstruct averages of the current is proposed and compared with the minimum norm and the minimum Laplacian solution. In contrast to the majority of previous analysis carried out in the field, in the comparisons, we avoid the use of measures designed for the case of dipolar sources. To allow for the evaluation of distributed solutions in the case of arbitrary current distributions we use the concept of resolution kernels. Two summarizing measures, source identifiability and source visibility, are proposed and applied to the comparison. From this study can be concluded: 1) linear inverse solutions are unable to produce adequate estimates of arbitrary current distributions at many brain sites and 2) averages or smooth solutions are better than the minimum norm solution estimating the position of single point sources. However, they systematically underestimate their amplitude or strength especially for the deeper brain areas. Based on these result, it appears unlikely that a three-dimensional (3-D) tomography of the brain electromagnetic activity can be based on linear reconstruction methods without the use of a significant amount of a priori information.

Linear inverse solutions with optimal resolution kernels applied to electromagnetic tomography.

This paper discusses the construction of inverse solutions with optimal resolution kernels and applications of them in the reconstruction of the generators of the EEG/MEG. On the basis of the framework proposed by Backus and Gilbert [1967], we show how a family of well-known solutions ranging from the minimum norm method to the generalized Wiener estimator can be derived. It is shown that these solutions have optimal properties in some well-defined sense since they are obtained by optimizing either the resolution kernels and/or the variances of the estimates. New proposals for the optimization of resolution are made. In particular, a method termed "weighted resolution optimization" (WROP) is introduced that deals with the difficulties inherent to the method of Backus and Gilbert [1967], from both a conceptual and a numerical point of view. One-dimensional simulations are presented to illustrate the concept and the interpretation of resolution kernels. Three-dimensional simulations shed light on the resolution properties of some linear inverse solutions when applied to the biomagnetic inverse problem. The simulations suggest that a reliable three-dimensional electromagnetic tomography based on linear inverse solutions cannot be constructed, unless significant a priori information is included. The relationship between the resolution kernels and a definition of spatial resolution is emphasized. Special consideration is given to the use of resolution kernels to assess the properties of linear inverse solutions as well as for the design of inverse solutions with optimal resolution kernels.

Some limitations of spatio temporal source models.

The spatio temporal source model (STSM) interprets the successive scalp topographies of an electrophysiological event as the summed activity of a few fixed generators. This modeling methodology is expected to provide a unique solution for a fixed number of sources. Because in general there is no "a priori" available physiological information, independent criteria need to be applied for determining the correct number of sources (Ns). This study illustrates theoretically as well as in simulations, that the existence of a unique solution can only be claimed when Ns is known a priori. Since most of the methods proposed for estimate Ns are not accurate as illustrated here, STSM may result in unpredictable non-physiological solutions. Basic modeling aspects and additional factors affecting reliability of STSM such as those related to the optimization process associated to the source parameter search are discussed. Some of the possible inverse solutions are illustrated in our simulations. Our main conclusion is the need to improve STSM before claims about neural generator localization can be accepted. We will also discuss, how attempts to apply STSM to clinical data, apparently supporting their reliability, are plagued with incorrect assumptions and do not justify the expectancy aroused about such models. We discuss some ways for improving STSM and the need to develop measures to evaluate their reliability, independent of the physiological plausibility of the solutions obtained. Finally we propose two mathematical measures that can be incorporated to the optimization process to contribute to the evaluation of its performance.

Single dipole localization: some numerical aspects and a practical rejection criterion for the fitted parameters.

There have been a number of attempts in the last years to localize the generators of brain electromagnetic activity, considering one current dipole as the source model. Single Dipole Localization (SDL) requires the selection of an optimization algorithm (OA). General aspects related with the selection, implementation and evaluation of some of the OA employed for SDL are discussed in this paper. Specifically the performance of two algorithms, those of Hooke-Jeeves and Levenberg-Marquardt, are tested by simulations. Suggestions for including restrictions to the dipole position and comments about some commonly used measures of the goodness of fit are given. Examples of erroneous implementations of these algorithms are also illustrated. A simple graphic rejection criterion, which can be easily used by inexperienced researchers, is introduced and tested in noisy and noise free simulations.