Abstract


    The main objective of this Ph.D. Thesis is the study of functional brain connectivity in vivo combining functional magnetic resonance imaging with electrical brain microstimulation in experimental animals.
    This Ph.D. Thesis is part of a multidisciplinary team result of close collaboration between the Center for Biomaterials and Tissue Engineering of Universitat Politècnica de València and the Neuroscience Institute of Alicante of the National Research Council in Spain–Universidad Miguel Hernández.
    The study of functional connectivity is of great interest in current basic neurobiology and a fundamental part of pre-clinical research of psychiatric illness. Indeed, it is the mechanism on which are based two of the basic principles of neurobiology: functional specialization and integration. The nervous system implements a highly distributed processing of information, with specialized modules on specific aspects of processing that are combined together in an integral form. For example, the multisensorial experience of a daily episode is experienced as a single (or integrated) perception. In this context, the efficient connectivity between functional modules, or functional connectivity, is an indispensable requirement. In order to be efficient, this connectivity must adapt to the needs of the system in an enviroment –the medium in which the body develops– which is in continuous change. Therefore, the functional configuration is a dynamic characteristic determined by synaptic plasticity mechanisms, adaptation and modulation, defining the flow of information in the system. The great similarity between some brain models (such as monkeys or rats) and the human brain, makes conclusions drawn from animal experiments relatively easy to extrapolate.
    The analysis methods for studying functional connectivity presented here have been applied to the specific case of functional magnetic resonance imaging of rat brains that are stimulated electrically. In order to detect brain networks that are functionally connected, cerebral hemodynamical signal correlation techniques have been used as indicators of connectivity, either from the standard analysis of the cross-correlation or from multivariate measures for detecting patterns of variance/covariance. 
    The first six chapters of the doctoral dissertation introduce the theoretical and knowledge foundations that enable the design and development of all those methods that are presented as tools for our study of functional connectivity. In this first part of the Doctoral Thesis the following key concepts are shown:

1. That modern neuroscience is postulated on the basis of neuron doctrine—a theory that describes the human brain as a system composed of billions of discrete elements specialized in very precise operations (called neurons), that are connected (via a small electrochemical connections called synapses) with other elements or similar neurons forming small-world networks that respond specifically against certain stimuli families.

2. That one of the most efficient ways to study the functional connectivity, nowadays, is through functional magnetic resonance imaging (or fMRI) and the general linear model, which allows the construction of statistical parametric maps that locate the brain regions involved in a cognitive task or specific sensory perception. The statistical parametric maps were constructed based on the Fick principle and the blood-oxygen-level-dependent signal or BOLD, which predicts with a high degree of confidence the underlying neural activity [1].

3. That constructing statistical parametric maps to reveal the global neuronal activity in an effective way involves a set of operations prior to parametric analysis, such as: pre-processing of functional images, modeling of serial correlations or global standardization—which prevents the masking of the segregated functional responses.

4. That functional connectivity is a statistical concept whereby it is intended to quantify the mutual information between the time series of neurophysiological events, and that one of the best indicators (or markers) of the functional connectivity is the correlation between BOLD-fMRI signals of one or more voxels that (normally) are separated anatomically. In this sense, the assumption connectivity/correlation enables multiple measurement techniques ranging from the simplest (such as classical analysis of cross-correlation) to much more sophisticated. Among the latter are very popular those multivariate techniques which are based on the principal components or coordinates decomposition such as singular value decomposition (or SVD) and unsupervised classification or clustering.

    Once exposed the principles and basic methodological tools for the study of functional connectivity, Chapter 7 presents the experimental procedures allowing to acquire the magnetic resonance imaging of experimental rat brains. In the various experiments functional imaging is combined with the implantation of one (or two) microstimulation electrodes that enable the elicitation of controlled neuronal activations [2]. All rats were subjected to a strict surgical protocol that allows an accurate placement of stimulation electrodes in a predetermined and well-known coordinates (which is a fundamental fact in the design of our analysis methods, allowing to reach and discuss many of the results that we present).
    A very important complement (indispensable in most of our analysis) corresponds to an anatomical atlas designed specifically for the anatomical reference space of our data. The way we design the rat brain atlas is presented in a separate chapter in the methods (vid. Chapter 8—Síntesis de atlas tridimensionales para el estudio de la conectividad en cerebros de rata) as the design methodology presented here was conceived to be applied generically to the synthesis of atlases for different reference spaces instead of that we assume as own.
    For the rest, we deal with the study of connectivity from two well differentiated development perspectives, which are based on two orthogonal but complementary paradigms of analysis (as they both assume the correlation as a marker of neuronal connectivity):

- The first group of methods measure the functional connectivity in the traditional way, e.g.: based on analysis of the cross-correlation between time series representing isolated voxels or groups of them. The use of our multifunctional brain atlas together with an iterative process that calculates the cross-correlation between all averaged fMRI-BOLD signals for all active regions/tags of a parametric statistical map allows the calculation of some square matrices that reveal in vivo and dynamically the weight of the connections that identify a functional state. Since electrical stimulation of a same brain nucleus should show the same pattern of synaptic modulation (accepting the possible experimental error and the variance in the functional response of each subject), the matrices we calculate (which we call connectivity fingerprints) support the development of subject classification techniques based on their specific functional states, and therefore, the groups of subjects reveal patterns of neural activation (or underlying functional connectivity) recognizable (and therefore characteristic) among subjects of the analyzed population (vid. Chapter 9—Huellas de conectividad y análisis de grupos).

- The second development track in our study of functional connectivity in the rat brain has to do with a multivariate vision of fMRI data through its singular value decomposition. In particular, we perform the multidimensional data analysis combining SVD and a clustering process. First, we perform a SVD projection of BOLD-fMRI time series known as functional space—a metric system in which the distance between any two voxels is related to the degree of connectivity between them. Secondly, by virtue of the abstraction connectivity/distance, we submit the functional space to a process of unsupervised classification, procedure by which we can identify, as members of the same cluster, those voxels which are functionally connected to one another, therefore, with an averaged functional response which is representative of the system. Since two voxels that are close in the functional space could be anatomically segregated, we use functional space clusters to construct multiparametric  functional connectivity maps allowing to express the functional response of the global neuronal effects as a sum of several hemodynamic modes (vid. Capítulo 10—Sistemas funcionales).

    Finally, it should be mentioned that all analysis methodologies designed functional connectivity in this Doctoral Thesis have been transcribed in dozens of functions that, along with the multifunctional atlas of the rat brain we designed specifically for our data, allows us to (as results):

1. Create a software of own elaboration for the analysis of functional magnetic resonance imaging in rat brains that are stimulated electrically. Such software (which we call SPMrat) use some features of the MATLAB package known as (SPM8, www.fil.ion.ucl.ac.uk/spm/software/spm8/) and allows a very simple (through dialogues of question/answer, friendly invoking functions and graphical interfaces) a comprehensive and automatic analysis of functional images for studying functional connectivity from image preprocessing, the analysis of groups of subjects by means of the connectivity fingerprints classification or the extraction of functional systems from the mean shift analysis over the functional connectivity metric system.

2. Synthesize some matrix structures representing the neural activity that dynamically reveal the anatomical substrate associable to a specific set of established connections (together with their functional weights), uniquely identifying each individual subject from the induced fMRI activity.

3. Design a functional connectivity pattern classifier (e.g., the matrix representations of the previous section or connectivity fingerprints) that (in turn) allows the identification of the different functional states that may result among several subjects to whom one or more electrical stimulation paradigms are applied.

4. Implement an unsupervised classification procedure using the mean shift algorithm which is able to extract the modes of that statistical distribution that represents the connection of the above-voxels represented in certain functional space and thus, the definition of identifiable clusters or functional systems both spatially (from binary membership masks) and temporally (from the mean BOLD-fMRI signals).

5. Develop some multiparametric maps allowing to express the integrated functional response into a sum of partial functional responses, mainly from dispersive characterization of hemodynamic response functions according to the mean shift decomposition from the previous step.

    Based on these results, we can derive the following biomedical conclusions:

- Connectivity fingerprints allows to predict the position of stimulation electrodes and the stimulation parameters used to generate functional responses. This suggests that transfering these techniques to the clinical world, and specifically to the practice of deep brain stimulation, can be very beneficial. For example, it can confirm the correct placement of the electrode and otherwise modify its positioning to optimize the clinical outcome—vid. chapters 12, 13 and/or 15.

- Mean shift algorithm allows the decomposition of the integrated functional response in various partial responses that identify groups of voxels that are functionally connected to each other, so we can: 

- Draw conclusions regarding functional responses causality or systematic delay [3] (according to the principle of the initial rest of linear time-invariant systems).

- Study effective connectivity from the use of two or more electrodes whose evoked stimulation responses are interfered asymmetrically.

- Create some analytical maps that allow us to isolate anatomically those functionally connected macroscopic systems to allow, for example, to differentiate direct and indirect responses (or monosynaptic vs. polysynaptic) or the study of the problem associated with negative BOLD responses—vid. Chapter 14.