RICERCA ITALIANA     

Estimation of brain functional connectivity with advanced methodological procedures

Università degli Studi di Bologna

Abstract

In recent years, the concept of brain connectivity is viewed as central for the understanding of the organized behavior of cortical regions. Various definitions of brain connectivity have been proposed: among the others, functional connectivity is defined as the temporal correlation between spatially remote neurophysiological events. This definition is data-driven and does not require additional knowledge of the neural circuits involved. Several algorithms have been proposed to evaluate functional connectivity from high resolution EEG. However, the comparative performances of these methods under different conditions of signal to noise ration (SNR) as well as other computational factors (such as the signal's length) have been not addressed adequately. Moreover, what kind of information on connectivity can actually be extracted from EEG without ambiguity is still insufficiently known.
The methods for the assessment of cortical connectivity could be usefully tested in simulations, by using both mathematical models or real cultured neuronal populations. Aim of this project is to develop, test and apply advanced methods for estimation of brain functional connectivity.
The project will be articulated in four main activities:
i) To develop and test alternative models of neural populations, for signal generation. In the first phase of the project, the parameters of the models will be assigned to simulate the power spectral density of cortical activity in some region of interests (ROIs) during a cognitive task. This phase will terminate with the choice of the more suitable model. Subsequently (second phase), the existence of reliable functional connectivity patterns will be assumed among the ROIs, and their effect on power spectral density simulated. This activity will be important to reach a deeper understanding of the effect of various connectivity patterns on neuroimaging data (to be used in the activity 4) and to provide simulated data to test algorithms for functional connectivity evaluation (to be used in activity 2).
ii) To test the principal methods for evaluation of functional connectivity from scalp EEG data. The most used algorithms, or original algorithms developed during the project, will be firstly tested on data generated through known models (activity 1), in order to provide quantitative indications about their reliability and for the definition of precise hypothesis of applicability. The most efficient algorithms and parameters will be selected on the basis of the comparison between the obtained results and the imposed model generating the data.
iii) The previous methodologies, or similar ones, will be applied to the study of neural dynamics and connectivity in cultured populations of neurons. These methodologies will be used to test how the patterns of functional connectivity observed in neural populations change either during maturation of the neuronal culture, with or without external electrical and/or chemical stimulation; or as a consequence of activity-induced plastic changes. At the same time, the relationship between structural complexity and the observed collective neural dynamics will be expolored.
iv) The tools developed in the previous activities will be applied to data recorded during learning/motor tasks. A well defined experimental paradigm will be designed to elucidate the patterns of cortical connectivity subserving the activity of the primary and secondary motor areas. This study will use the estimators more useful under the particular conditions of signal to noise ratio and number of employed electrodes . Population models with time varying synapses will also be used to interpret the data.
The project will involve specialists in modeling neural population dynamics (BOLOGNA), in the analysis of real cultured populations (GENOVA), in the signal analysis processing (MILANO) and in the propagation and application of advanced EEG processing tools with realistic head volume conductors (ROME). <<<

Principal Investigator

Mauro URSINO Università degli Studi di BOLOGNA

Research Objectives

From the considerations described in the "International Scientific Background" (see that section) it seems clear that some methods have been proposed in literature for the assessment of functional connectivity in humans. However, few simulation studies have partially explained the validity of these methods, leaving the other untested. Then, there is a need to appropriately test the principal linear and non linear methods for the assessment of cortical connectivity. However, the test can be adequately performed only in a simulation setup, and the simulation setup has to be as realistic as possible, to return information about the behavior of the methods in the real case. Realistic simulation setup means an adequate description of the dynamics of the neural population at the microscopic scale, then integrate such activity at a mesoscopic scale for the generation of macroactivity detectable by EEG electrodes. For these reasons, the project will involve specialists in both modeling of neural population dynamics (BOLOGNA and GENOVA units), specialists in the signal analysis processing (MILANO unit) and specialists in the propagation and application of advanced EEG processing tools with realistic head volume conductors (ROME unit). All these research groups will work together to achieve the main objective of the research project, that is to validate advanced methods for evaluation of functional connectivity, both with reference to scalp EEG signals, and populations of cultured neurons.

The objective of the proposed research
The following main objectives will be pursued:

1) To implement different neural models for signal generation, with the use of state of art differential equations approaches, and to test their ability to mimic the cortical activities of several large patches of neuronsin different frequency bands . Fit these models to individual EEG data by using an automatic best-fitting procedure, in order to mimic the entire power spectrum density of cortical activity in some region of interests (ROI) during a cognitive task. Simulate the effect of various kinds of functional connectivity within the model. The final aim is to arrive at realistic models of cortical activities, which can be used to simulate EEG and to summarize data from different neuroimaging techniques.
2) To test and validate different algorithms for the determination of functional connectivity by using synthetic EEG signals obtained with the models developed above, with different level of superimposed noise and length of the simulated EEG signals. Compare the patterns of connectivity obtained with these algorithms with the imposed ones, by using opportune error functions and analyze with the Analysis of Variance the resulting influence of the number of electrodes, the SNR of the EEG data and the signal length. The objective is to quantify the virtues and limitations of the algorithms presently used, to select the most effective algorithms, and to understand which aspects of connectivity can actually be extracted from scalp EEG measurements. The final aim is to provide a set of reliable algorithms and parameters for a suitable and more precise functional description, characterization and quantification of the central nervous system (SNC) connectivity during the execution of motor and/or cognitive tasks.
3) To understand how development and/or activity affect functional connectivity and investigate the relationship between functional connectivity and the ability of neural populations to perform computations. This objective will be pursued on cultured neurons by developing models for simulating realistic populations of neurons, with a specified anatomical connectivity, and by estimating functional connectivity, and more global measures of structural complexity, from multi-site neural recordings (spike trains and/or LFPs) during either spontaneous or evoked activity.
4) To apply the functional connectivity techniques for high-resolution EEG, and the mathematical models developed and validated above, to the specific problem of identifying and monitoring the brain areas (and their functional connectivity) involved in some simple cognitive tasks (such as a simple movement of the limb).

Furthermore, the research consortium has well-defined questions to be tested within the objectives described above. In particular, the simulation models will try to advance the present status-of-the art as to the following points:
i) How can mathematical models of cortical populations fit the frequency content of real EEG data in individual ROIs during specific cognitive tasks?
ii) How can these models mimic dynamics of individual populations in vitro during spontaneous as well as evoked activity?
iii) What is the effect of a given pattern of connectivity on the frequency content and on synchronization among neural populations?
iv) What kind of information on connectivity can be extracted from information contained in scalp EEG signals? Can this information be retrieved without ambiguity?

Also in the area of the connectivity estimation algorithms, the research consortium has already well-defined questions to solve during the project development, listed in the following:
i) What is the influence of a variable SNR level imposed on the high resolution EEG data as well as the number of recording EEG electrodes on the accuracy of the connectivity estimation?
ii) What is the amount of data necessary to achieve a good accuracy of the estimation of connectivity between cortical areas?
iii) Are the connectivity estimators performances dependent on a particular frequency band analyzed?
iv) What is the relationship between network architecture (network complexity) and its computation capability (in information-theoretic sense).
v) How can development and/or activity affect functional connectivity? <<<

Timescale

24 months

National and international background

Brain activity relies on the complementary principles of modular and distributed information processing. The cerebral functions can be investigated by identifying functionally specialized neuronal clusters and the relationships among them. The brain is a synergy of functionally interacting sub-systems, each dedicated to specific functions. The acknowledgement of this viewpoint implies that differences in brain activation among experimental conditions or groups of subjects may derive in general by different neuronal dynamics, either the neuronal activity or the network connectivity. In other words, similarly activated regions may produce different responses due to variations in their functional connectivity
Over the last decade, the development of non-invasive brain imaging methods based on hemodynamic (functional Magnetic Resonance Imaging, fMRI), or electro-magnetic (high resolution EEG; magnetoencephalography, MEG) measurements has been providing a great knowledge on the cerebral areas activation underlying motor and/or cognitive tasks in humans. Nowadays, a main issue remains open of how these regions communicated to each other. In this regards, the concept of brain connectivity is viewed as central for the understanding of the organized behavior of cortical regions beyond the simple mapping of their activity (Lee et al., 2003, Horwitz, 2003). Various definitions of brain connectivity have been proposed along these years: neuroanatomical, functional and effective connectivity (Friston et al, 1993). Neuroanatomical connectivity concerns the plastic reorganization of neuronal networks that allows the brain to modify its performance after numerous repetitions of the same task. This mechanism is very slow and does not account for the flexibility actually characterizing the operating brain. Functional connectivity is defined as the temporal correlation between spatially remote neurophysiological events, while the effective connectivity is the influence that one neural system exerts over another (Friston et al., 1993). It is worth of note that effective connectivity needs a preliminary knowledge of the neural circuits involved, while the functional connectivity is data-driven and does not require such additional knowledge. Due to this fact, in the following review we will focus on the use of the functional connectivity methods to assess real pattern of brain connectivity

Methods for evaluation of functional connectivity
A considerable number of approaches has been proposed for the estimation of functional connectivity on EEG signals: linear techniques, as the cross-correlation or coherence (Gevins et al., 1989; Urbano et al., 1998); non linear techniques as the mutual information, mutual dimension, generalized synchronization and neural complexity (Inouye et al. 1995). The overall techniques can disclose the direct flow of information between scalp electrodes in the time domain, being the non linear more sensitive with respect to the linear techniques, although these latter require less computational demanding (Quian Quiroga et al., 2002).
The general concept that cortical and thalamo-cortical networks present widely distributed resonance frequencies over the brain surface, linked to some physical properties of the network itself (like coupling strengths, or architecture), has generated a growing interest on the use of frequency based approach to assess cortical connectivity. Indeed, it has been proved that important information in the EEG signals are often coded in the frequency and not in the time domain (reviewed in Pfurtscheller and da Silva, 1999). This has led to the search for frequency-specific interactions in MEG or EEG signals by analyzing the coherence between the activity of pairs of structures (Bressler, 1995; Gross et al., 2001, 2003). However, the coherence analysis has not a directional nature, i.e. it just examines whether a link exists between two neural structures. A further step in the coherence analysis was given by the introduction of the Directed Coherence, to examine the relation between a pair of data channels described by means of a bivariate autoregressive process (Saito and Harashima, 1981). The Directed Coherence can be seen as a decomposition of the ordinary coherence function into two directed coherences: one representing the feedforward and the other representing the feedback aspects of the interaction between two structures. This method, rather than just revealing mutual synchronicity, describes whether and how two structures are functionally connected.
The previous methods, however, have the principal limit of dealing with bivariate time series, thus not making use of the whole covariance structure for multivariate data. This would make the analysis of a set of multivariate data rather long and difficult, and even lead to erroneous results (Kaminski et al., 2001). Several approaches have been proposed in literature to estimate functional coupling in multivariate data sets. In these last decades, several multivariate spectral measurement called Directed Transfer Function (DTF) and Partial Directed Coherence (PDC) were proposed to determine the directional influences between any given pair of channels in a multivariate data set (Kamiski et al., 1991). These estimators characterize at the same time direction and spectral properties of the brain signals, and require only one multivariate autoregressive (MVAR) model to be estimated from all the EEG channel recordings. The DTF and PDC techniques have been demonstrated to rely on the key concept of Granger causality, according to which an observed time series x(n) causes another series y(n) if the knowledge of x(n)'s past significantly improves prediction of y(n); this relation between time series is not reciprocal, i.e. x(n) may cause y(n) without y(n) necessarily causing x(n). This lack of reciprocity allows the evaluation of the direction of information flow between structures. The DTF does not require an a priori formulation of a specific connectivity model to be tested, thus overcoming the principal shortcoming of another popular method for the estimation of cortical connectivity, i.e. the Structural Equation Modeling (SEM).
Dynamic causal modelling (DCM) has been specifically designed for functional images analysis (Friston et al., 2003). This approach supposes that neural activity in a region causes changes in neuronal activity in other regions via inter-regional connections and in its own activity via self-connections. These models are useful because they can work at the neuronal level, thus highlighting neuronal interactions not necessarily evident from hemodynamic measures, and they can work with arbitrarily complex connectivity patterns between regions; however, they are computationally demanding.

The methods for the assessment of the cortical connectivity could be usefully tested in simulations, by using both mathematical or real cultured neuronal populations. In the following, a brief review of the main studies using such populations is presented.

Simulation studies
Hence, the situation in literature is that there are several frequency methods for the estimation of the functional connectivity between signals, according to the Granger definition, but their comparative performances under different conditions of signal to noise ratio (SNR) as well as other computational factors (such for instance the signal's length) have been not addressed adequately. Of course, a simulation study is necessary in order to compare the performance of the studied estimators in the retrieval of the simulated cortical patterns. In particular, it is not clear which aspects of neural interactions are expressed in EEG signals, and which of them can be actually revealed by the estimation techniques delineated above. For this reason, the use of mathematical models and computer simulation techniques may be worthwhile to reach a deeper understanding of this information, to favor the conceptualization of knowledge, and the formulation of coherent and comprehensive theories. Furthermore, computer models can provide artificial data, which may be used as input to test the accuracy and reliability of proposed algorithms.
Various mathematical models have been proposed during the past decades to simulate neural signals. These models can be subdivided into two main classes: detailed models, which try to reproduce details of single neurons, or simplified models, in which neurons are reproduced at a population level (Whittington et al.,2000). The complexity of neural networks which generate EEG/MEG or functional imaging data makes the second approach more useful. Population models mimic the activity of entire neural groups, via the feedback arrangement of excitatory and inhibitory populations; this interaction induces rhythmic patterns similar to those observed in EEG recordings. These models may include Wilson-Cowan oscillators (Konig and Schillen,1991;Schillen and Konig,1991) or relaxation oscillators (Wang,1995;Wang and Terman,1997) which have been frequently employed to analyze synchronization among neural groups. More sophisticate neural mass-models of cortical columns, particularly useful to simulate realistic EEG signals, were developed by Lopes da Silva et al. (Lopes da Silva,1976) and by Freeman (Freeman,1978) in the mid seventies, and subsequently improved and extended by Jansen and De Rit (Jansen and Rit,1995) and Wendling et al. (Wendling et al.,2002).These models have been used to simulate alpha rhythms (Jansen and Rit,1995), dynamics in the olphactory cortex (Freeman,1987), or paradoxical epileptic discharges (Wendling et al.,2000;Wendling et al.,2002). However, just a few studies deals with the problem of simulation of the entire frequency content in a cortical region of interest (ROI), or with simulation of functional connectivity among different ROIs. Tagaments and Horwitz (Tagamets and Horwitz,1998;Tagamets and Horwitz,2000) presented a large-scale model based on Wilson-Cowan oscillators, to simulate working memory in a delayed match-to-sample task. The model aims at integrating electrophysiological and metabolic information. The synaptic activities in the model provide a match to experimental PET data. David and Friston (David and Friston,2003), analyzed the changes in power spectrum resulting from simple connectivity patterns among two ROIs, each simulated via a neural mass model of two parallel populations. This recent paper provides a first attempt to characterize how interactions among different ROIs are reflected in MEG/EEG oscillations, and represent a first step toward a theoretical analysis of indices for nonlinear coupling.
Furthermore, the previous simulation studies do not consider the biological structures interposed between the cortex and the scalp electrodes, namely skull, dura mater and the scalp (Kaminski and Blinowska, 1991, Kaminski et al., 2001). This approach has a main limitation related to the fact that, in the propagation of the potential from the cortex to the sensors, the different electrical conductivities of brain, skull and scalp strongly blurs the EEG potential distributions and makes the localization of the underlying cortical generators rather problematic.

Cultured neurons on microelectrode arrays
In the early 80's, advancements in micro-fabrication technologies enabled the introduction of a new generation of devices, Micro-Electrode Arrays (MEAs), which first allowed in-vivo (Gerstein & al 1982) and in-vitro (Gross & al 1982) multi-site, long-term recordings of the electrical activity of neuronal populations, thus enabling experimental investigation of their collective dynamics and computational properties. Cultures of dissociated neurons are particularly interesting in this respect, as they can be kept in healthy conditions for a long time (several months) and their morphological and physiological properties closely resemble those of the tissue of origin (Kriegstein & Dichter 1983, Banker &Waxman 1988). These preparations also display activity-dependent, path-specific synaptic modifications that closely resemble the long-term potentiation and depression phenomena found in acute preparations and in-vivo (Bi & Poo, 1999, Jimbo & al 1999).
Although, synaptic interconnections tend to grow randomly, the specific synaptic interconnections can be controlled, at least in part, by using the same microfabrication techniques. Therefore, at least to a certain extent, appropriate treatment of the substrate may induce a desired pattern of anatomical connectivity, and possibly a desired dynamic behavior. This would allow to experiment different anatomical structures. Populations of cultured neurons are highly connected. However, at least in organotypic cultures there are some indications that connectivity is not random but, instead, is distributed according to a power law (Beggs & Plenz 2003), a property that is referred as 'scale-free' connectivity; it implies that there is a small but finite number of nodes having broad "access" to most other regions, and those well-connected nodes are comparatively much more numerous than in a randomly connected network.
Neural activity can be modulated by appropriate electrical and/or chemical stimulation. (Shahaf and Maron, 2001) even managed to 'teach' cultured neurons to reproduce a desired, target population activity. In general, low frequency, sustained electrical stimulation locks the phase of periodic bursts to the applied stimuli (Maeda et al., 1995). Higher rates of stimulation induce a transition from synchronized bursting activity into a more sparse spiking behavior, more similar to in-vivo awake cortical dynamics (Wagenaar et al 2005).
It has been suggested that cultured neurons may be also relevant in investigating the structure and the emergence of distributed representations of sensorimotor informations in an intact brain. Along this direction, cultured neurons were connected to either a 'virtual', computer-simulated environment (De Marse et al 2000, 2001), or to a robotic body (Cozzi et al 2004). <<<