Unraveling Interconnected Minds: Investigating the Impact of Brain Stimulation on Networked Cortical Regions

Aims

Brain stimulation targets multiple or single cortical regions that leads to higher or lower brain activity. However, the regions of the brain have linkages through fiber tracts that lead to potentially indirect effect on other, non targeted regions.

The hypothesis of this project is to test how stimulation in one region of the brain affects other regions over time.

Objectives

Specific: A short survey reviewing the brain connectivity studies’ literature

Measurable: It will be encompassing all forms of dynamic and static connectivity whether effective, functional, or anatomical.

Achievable: the last decade has demonstrated ever rising number of studies dedicated to effective or functional connectivity, majorly from the experiments of functional neuroimaging.

Realistic: the resting state conditions have turned out to be a dominant experimental paradigm. There have also been several resting networks and amongst them the important default mode network is identified. Graphical models are the representations of the convenient vehicle in formalizing the findings of the experiment and to quantitatively and closely characterize the several networks identified. Underlying the anatomical networks’ abstract concepts, the connectome, which are investigable also by the functional imaging techniques.

Timely: To organize the survey, first, some recently conducted reviews and studies about the functional connectivity’s experimental studies are reported. It illustrates certain prototypical studies in the field, and is not meant to be comprehensive. Next, collection of computational methods that deals with functional connectivity takes place along with a few illustrative applications. A short survey follows on effective connectivity with some recent studies.

Proposed Research Context

Developing a model of connection between brain regions based on anatomical literature

The brain’s functional organization is characterized by integration and segregation of processed information. In modern neuroscience, a central paradigm is that functional and anatomical connections between the regions of the brain are organization in a way to ensure that processing of information is close to optimality. The synchronized activity, between the distant regions of the brain as well as locally, provides functional interaction. Thus, brain networks comprised of functionally connected although spatially distributed regions processing information. The analysis of brain connectivity rests on three different although related connectivity forms (Sporns, 2010).

1. Anatomical connectivity (AC), also known as structural connectivity, which through synaptic contacts forms the connectome (Sporns et al., 2005) amongst the fiber tracks or neighboring neurons that connects neuron pools in the regions of the brain which are spatially distant. In the brain, the fiber tracks of the whole set is known as the white matter. The anatomical connections on short time scales (min, sec) are quite stable and persistent, where there can be spans substantial plasticity observed for longer time spans.

2. Functional connectivity (FC) can be defined as neuronal activation patterns’ temporal dependency of anatomically separated regions of the brain. It is reflective of statistical dependencies between the distant and distinct regions of the neuronal populations’ information processing. Therefore, it is fundamentally a statistical concept relying of statistical measures such as spectral coherence, covariance, correlation, and phase locking. Statistical dependencies have high level of dependencies and are subject to fluctuations on multiple time scales that range from milliseconds to seconds.

3. Effective connectivity (EC) describes exertion of influence of one neuronal system on another. This way it reflects the casual interactions among the areas of the activated brain. It combines effective and structural connectivity to a wiring diagram and within a neuronal network reflecting directional effects. There can be inferring of casualty from network perturbations or TSA (time series analysis). Techniques on the basis of network perturbations usually have the need as input with structural information, while Granger causality like TSA-based techniques may be considered model free.

The last two concept’s synthesis of connectivity primarily applied to and deducible from the modalities of functional neuroimaging, is provided by Friston (1994). The effective and functional connectivity may originate, for instance, from multielectrode array recordings. Both have the reference of abstract concepts which to anatomical connectivity has no immediate connection and which mediates physically such correlations. In the recent years, however, efforts were made in bridging gap between connectivity analyses of these types, mainly put forward by the likes of diffusion tensor imaging (DTI) techniques allowing in the process to track fibers for the functional correlations’ neuronal basis.

Background Research

Horwitz (2003) questioned the effective and functional connectivity concepts. His argument centered on these notions derivable from various functional imaging modalities such as PET (positron emission tomography) or fMRI (functional magnetic resonance imaging). The connectivity concept designates the interaction’s strength, whether indirect or direct, between various areas of brain where the information is processed locally. However, effective and functional connectivity are derivable from the computed quantities on different temporal and spatial scales with the use of definitions and employment of various algorithms.

So long it is not understood as to how such abstract concepts are related to the structural connectivity underlying, to compare across studies must be taken with caution. However, it is noticeable the existence large amount of evidences that both concepts are derivable from the same imaging modality (Friston, 1994).

The studies of connectivity analysis created the complex brain network notion that has the characteristics of information processing’s densely connected nodes which in anatomical space are distant and connected sparsely through connections of long range between various brain regions that are functionally interacting. These network topologies have the reflection of two basic principles that underlies the processing of information in the brain: functional integration and functional segregation. Such network topologies experimental evidences primarily emanates from neuroimaging techniques (SPECT, PET, fMRI, MEG, and EEG) and neuroanatomical methods.

Between the distinct regions of brain, signal transmission requires connecting fiber tracts, and thereby it forms the human connectome’s structural basis. The magnetic resonance imaging which is diffusion weighted and its variant known as DTI (diffusion tensor imaging) represents the fiber tracking’s most promising approaches (Johansen-Berg and Rushworth, 2009). The water molecules’ diffusive motion are mapped by the former in the tissues that returns back per voxel a single gray value only, while the diffusive motion’s direction is also considered by the latter, and therefore symmetric diffusion tensor’s second-order is determined instead. However, this method’s one serious limitation is the low spatial resolution. The 3D-PLI (3D polarized light imaging) overcomes the latter, and here 3-dimensional course of fibers are traceable down to 100 μm with a spatial resolution. Therefore, the provision of 3D-PLI is with an independent evaluation pertaining to the obtained results with DTI.

There can be quantifiable brain connectivity in connectivity matrix with the help of neighborhood relations’ encoding, whose columns and rows have the corresponding brain regions. The mapping of this representation is lent to a graphical model with the provision of means for quantifying various connectome’s topological aspects. The graphical models are representative of versatility of mathematical framework for the pair wise relations’ generic study between the interacting regions of brain. In the recent years, there is witnessing of studies’ exponential growth in relation to graph theory’s application in unraveling characteristic features of effective, functional, and structural connectivity from neuroimaging investigations (Bullmore and Bassett, 2011). The discovery that is most striking reveals the complex brain networks’ small world properties shared with a number of complex systems. The topology of a small world allows high degree of efficiency at various temporal and spatial scales with a lowly energy and wiring cost. The recent discoveries like this may be indicative of the connectome being only one example of complex system of a more general universality class observable in nature (Fornito et al., 2010).

Proposed approach

Consideration of the functional brain connectivity’s prototypical studies has led to the functional neuroimaging in the time of resting state conditions is particularly interesting that the spontaneous activity of the brain is explored. The latter has indicated its organization to reproducible activity patterns. Therefore, the structure is displayed reflecting the architecture of the underlying brain and is the carrier of brain pathology marker. The modern neuroscience view is that such coherent activity’s large-scale structure is the reflection of the brain’s modularity properties connectivity graphs. To learn such models involve two primary challenges.

I. Modelling the full connectivity of brain has difficulty to estimate problem having to face the dimensionality curse.

II. Between subjects, variability coupled with functional signals’ variability between experimental trials, makes it challenging the usage of multiple data sets.

To concern functional brain connectivity studies’ computational methods, there has been identification of two broad classes, such as supervised methods or knowledge based methods, as well as unsupervised or exploratory methods which are a data driven method. The latter is sub-divisible into clustering techniques and decomposition method (Li et al., 2009).

Project Plan

The prior knowledge afforded by the supervised methods about the temporal and spatial activation pattern involved, along with the model for the process of data generation. Generally specific cognitive tasks are employed by the methods that are supposed to be performed by the volunteers. However, in the recent years, they have been subject to application to the resting state conditions. They are usable widely as their straightforward interpretation and easy implementation. The methods of knowledge-based data analysis select some ROI (regions of interest) as seeds and the generation of the human brain’s connectivity map by the determination of whether there is functional connectivity of the other regions to these seeds as per the predefined metrics. A convenient method of defining a metric such as that is on the basis of CCA (cross-correlation analysis) between the seed region’s BOLD time courses and any other region of the brain under consideration. The measurement of correlation is by Pearson correlation coefficient ρ qs as given below.

Here,

A predefined time lag is denoted τ

The neuronal activity’s variance is denoted by σ in the seed region i = s or query region i = q

is the fluctuation’s covariance in neuronal activity of the seed and query regions respectively. The assumption of the functional connectivity is in case ρ qs > ρ 0 exceeds the threshold predefined ρ 0. Given that HRF (hemodynamic response function) rather quickly returns to zero in shorter time than a minute is the correlation needed for the exploration for delays of a limited number and thereby reducing the method’s computational load. CCA, in practice, is performed at zero lag. This seemingly has justification if the times of the signal propagation are less compared to the involved experimental method’s temporal resolution. To average the courses of the pixel time in the seed region does elimination of the noise contributions. Moreover, the employment of the spatial smoothing is by the application of Gaussian filtering.

Data driven computational methods

Exploratory techniques of data analysis are mainly clustering and decomposition techniques representing international methods not relying on the prior knowledge. Therefore, they could show in the data unexpected correlations. These methods have reliance on the assumptions that the organization of the brain has been in functional networks of finite set. EMF (Exploratory matrix factorization) techniques do addressing of the problems of the blind source separation by the extraction of distinct components from the observations with the properties that are predefined from constraints of only a minimal set. The data driven methods of such can have consideration of the most suitability for the resting state of the exploration of the studies, beneath others, with the so called DMN (default mode networks). The techniques based on decomposition such as ICA (independent component analysis), PCA (principal component analysis), SVD (singular value decomposition), and tensor factorization and nonnegative matrix (NTF/NMF) have the consideration of any observation as underlying features’ linear superposition. The latter should be considered to be capturing the information’s essence buried in the functional images. Therefore, they have the consideration of having feature generating techniques. The features subjected for extraction is not known and different features yield different methods, and thereby exposing the relevant information in a rather transparent way to the analyzer. PCA and SVD do transformation of the functional images that orthogonal, uncorrelated eigen images result.

The PCA de-correlation dependencies is of second order only, while ICA have tried de-correlating the dependencies of all higher order as well, and therefore produce statistically independent features. However, in practice, the third and the fourth order only does correlation and de-correlation to the maximum extent. In spite of minimum assumptions at the outset, the techniques such as ICA suffer from the reliable and robust techniques for the estimation of the unknown number of the embedded independent components. The selection techniques of model order like MDL (minimum description length), BIC (Bayes information criterion), AIC (Akaike information criterion), and so forth is for mostly overestimating the number of components. An added difficulty is measuring the extracted components being extracted reliably, particularly in higher dimensions where the independence’s most reliable indicator as the mutual information is hard to estimate. The separation of blind source, in fact, has the presumption of the existence of the sought after sources along with their number, while EMF have tried in decomposing the observations of any given set into independent components. Therefore, independence of certain degree is achievable when there is application of EMF technique. A third concern in that respect is about independence as there is no clarity as why the existence of neuronal activity distribution network in the brain takes place. Therefore, other paradigms such as DCA (dependent component analysis) has been allowing dependencies in the component groups, which however, have the independence of other groups which may be attractive to the community of functional imaging. The uncorrelatedness or independence entails sparseness, the techniques of EMF is drawn towards yielding sparse components rather than the ones that are independent (Daubechies et al., 2009). Although the extraction and existence, with the techniques of EMF, the component networks that are meaningful of neuronal activity in relation to the important steps of information processing in the brain are debatable artifact removal and denoising that is achievable with such techniques in a reliable manner. Therefore, the techniques of EMF are employable also as properly done in preprocessing methods for even later processing with the use of seed based procedures. As the EMF techniques ignore the extracted components’ natural ordering, to identify corresponding components across the volunteers’ groups is debatable and subject to methodological development. There are many approaches extended to encompass template matching (Seeley et al., 2009), individual data set’s temporal concatenation registered from some subject groups (Habas et al., 2009), dual, which is spatial and after that temporal, data sets of regression of group level (Filippini et al., 2009), and group level data sets’ back reconstruction individually decomposed with ICA (Calhoun et al., 2001). Nonetheless, majority of these approaches have the entailment of template matching at some stage of the analysis that have been strongly rendering their outcome depending on the template’s quality established earlier.

To consider EMF as an unsupervised tool of data analysis and the extracted component number as the model of unconstrained parameter, the categorization of these techniques as the methods of clustering which supervise the data set’s unsupervised partitioning, according to the predefined non-metric or metric similarity measure (Weissmuller et al., 2010). With respect to EMF, the projection of observations in the system of new basis generated for the data set’s new representation and according to the size, these projections are grouped. Other techniques of clustering employable in the functional imaging include spectral clustering, partitional clustering, and hierarchical clustering accompanied often by bagging, bootstrapping, gaussian mixturemodels, and multidimensional scaling (van den Heuvel et al., 2008a). Hierarchical clustering, either divisive or agglomerative, may achieve clusters of any predefined number, where it can be decided upon with the appropriate number of clusters after the process of partitioning. Alongside the partitional clustering, the fixing of the number of clusters must be done before the commencement of clustering. The number of clusters, typically, is subject to optimization by the minimization of intracluster variance in obtaining the homogeneous clusters in accordance with the problem-dependent and appropriate homogeneity measures. Initially the spectral clustering performs the Kirchhoff matrix’s eigendecomposition of the graph underlying and followed by the data clusters based on the resulting eigenvectors (van den Heuvel et al., 2008b). Like the EMF techniques, all clustering algorithms’ drawback is the cluster’s unknown number to which the decomposition of the data set is natural. In the recent years, the proposal of the probabilistic methods has been for overcoming this omnipresent model-order selection problem (Cemgil, 2009) that proposes techniques called ARD (automatic relevance detection).

In close relation to the clustering are the problems of classification, particularly when functional connectivity in comparison between some states of disease and their normal counterparts. The comparison of the latter is particularly interesting when under resting state conditions the images are acquired. With the presentation of the specific stimuli, the multivoxel pattern analysis is being known as brain reading (Haynes and Rees, 2006). Such multivariate approaches’ essential prerequisite is a reliable and robust feature stage of extraction when generated with appropriate features, a subset usable for the purposes of classification in identifying the brain’s specific mental states. The training is needed for all classifiers with the pattern of pre-classified activity. The following testing is inclusive cross validation with the provision of the generalization ability measures in terms of accuracy, selectivity, and specificity of the employed classifier. Measures such as ROC (receiver-operating characteristics) curves and AUC and other related curves are usually usable in measuring the classifier’s performance. The most frequently employed classifiers are LDA (Fisher discriminant analysis), RF (random forests) like tree classifiers or nonlinear Kernel machines or SVM (linear support vector). Usually, any classifier’s success rests upon the appropriateness or quality of the features given with for the performing the discrimination task.

With properly given features, high accuracy is achieved often with simple linear classifiers, while the improper features ensures failure in achieving good results even by the most sophisticated classifiers. Application of the SVMs, a technique known as RFE-SVM (recursive feature elimination) (Guyon and Elisseeff, 2003) is applicable for finding the feature’s most discriminate subset for the problem’s classification at hand. A similar goals is achievable with the Gini index computing (Breiman, 2001) of an RF classifier providing for each feature with a key measure relative to the considered discrimination task.

References

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