Neural Plasticity

Volume 2018, Article ID 6815040, 11 pages

https://doi.org/10.1155/2018/6815040

## Anticorrelations between Active Brain Regions: An Agent-Based Model Simulation Study

Correspondence should be addressed to Fabrizio Parente; ti.1amorinu@etnerap.oizirbaf

Received 5 July 2017; Revised 19 December 2017; Accepted 9 January 2018; Published 19 March 2018

Academic Editor: Stuart C. Mangel

Copyright © 2018 Fabrizio Parente and Alfredo Colosimo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Anticorrelations among brain areas observed in fMRI acquisitions under resting state are not endowed with a well-defined set of characters. Some evidence points to a possible physiological role for them, and simulation models showed that it is appropriate to explore such an issue. A large-scale brain representation was considered, implementing an agent-based brain-inspired model (ABBM) incorporating the SER (susceptible-excited-refractory) cyclic mechanism of state change. The experimental data used for validation included 30 selected functional images of healthy controls from the 1000 Functional Connectomes Classic collection. To study how different fractions of positive and negative connectivities could modulate the model efficiency, the correlation coefficient was systematically used to check the goodness-of-fit of empirical data by simulations under different combinations of parameters. The results show that a small fraction of positive connectivity is necessary to match at best the empirical data. Similarly, a goodness-of-fit improvement was observed upon addition of negative links to an initial pattern of only-positive connections, indicating a significant information intrinsic to negative links. As a general conclusion, anticorrelations showed that it is crucial to improve the performance of our simulation and, since these cannot be assimilated to noise, should be always considered in order to refine any brain functional model.

#### 1. Introduction

The not-well-defined nature of negative correlations stimulated several authors to study the persistence of significant negative correlations by means of fMRI-specific correction methods and to propose a possible physiological role for them [1–4]. In this regard, however, a clear mechanism about how negative interactions are related to the positive ones is not available as yet. A rewarding approach to the problem would be the simulation of brain activity, which opens the door to mechanistic models amenable to validation by empirical data.

Different models have been proposed [5] to approximate the collective activity of neurons such as the conductance-based biophysical model [6–8] or the FitzHugh-Nagumo model [9, 10], by the mean-field [11] or mass action [12] formalisms. fMRI produces data at a mesoscopic level while brain activities are inspected at a much larger scale than that of single neurons. This implies that we have to imagine how the behavior of single functional units, of major importance for the current understanding of brain’s activities, may influence the observations at a higher hierarchical level [13].

In order to reproduce the brain resting state from fMRI acquisitions, the long-range myelinated fiber connections by diffusion imaging, or the folded cortical surface by high resolution imaging [14–17], have been used as a background for the interactions between brain areas. Such interactions have been simulated using the Kuramoto model [18], the Ising model [19], and some discrete-time dynamical models [20, 21]. In the last case [20, 21], a stochastic cellular automaton approach was used by two well-established brain computational models, the susceptible-excited-refractory (SER) [22] model and the FitzHugh-Nagumo model [9].

An alternative approach to the large-scale brain modeling is to simulate the brain activity using the functional connectivity map itself as a background. In such a context, Joyce et al. [23] realized an agent-based brain-inspired model (ABBM) using both positive and negative values of functional connectivity. In general, an agent-based model (ABM) includes a set of agents whose reciprocal interactions are defined by a set of rules depending upon the system at hand. These models can exhibit emergent behavior as described by Wolfram [24].

Here we develop a model using an ABM model and a biologically plausible SER model, which should account for both positive and negative interactions between large-scale brain areas. Different levels of functional connectivity in the background modulate the goodness-of-fit of simulations, and we focus, in particular, on the fraction of negative links to test their role in the organization of structured networks.

#### 2. Materials and Methods

##### 2.1. Data Collection

The sample is composed of 30 selected functional images of healthy controls from the Beijing Zang dataset (180 subject) in the 1000 Functional Connectomes Classic collection (http://fcon_1000.projects.nitrc.org/indi/retro/BeijingEnhanced.html). Resting data were obtained using a 3.0 T Siemens scanner at the Imaging Center for Brain Research, Beijing Normal University. For each subject, a total of 240 volumes of EPI images were obtained axially (repetition time, 2000 ms; echo time, 30 ms; slices, 33; thickness, 3 mm; gap, 0.6 mm; field of view, 200 × 200 mm^{2}; resolution, 64 × 64; flip angle, 90°). For the anatomical images, a T1-weighted sagittal three-dimensional magnetization prepared rapid gradient echo (MPRAGE) sequence was acquired, covering the entire brain: 128 slices, TR = 2530 ms, TE = 3.39 ms, slice thickness = 1.33 mm, flip angle = 7°, inversion time = 1100 ms, FOV = 256 × 256 mm, and in-plane resolution = 256 × 192.

##### 2.2. Data Preprocessing

The first 10 scans of each subject were removed, and the remaining functional images were analyzed according to the procedures fully described elsewhere [25]. The SPM8 (Statistical Parametric Mapping) (Wellcome Department of Cognitive Neurology, London, UK) toolbox and the Functional Connectivity (CONN) toolbox were used in the preprocessing of data on a MATLAB R2010b platform.

The images from each subject were divided into 105 ROIs without brainstem and cerebellum (see Figure 1) through the MRI Atlas of the Human Brain, Harvard Medical School [26], and from each ROI, the time series was extracted. An average correlation matrix for each subject was calculated for all possible couples of the 105 ROIs considering both correlation signs and was used as an (individual) connectivity matrix. Thus, the global, mean matrix to be used as a background for the brain simulation was reckoned according to the following overall procedure:
(1)For each subject, the activation time series of 105 ROIs extracted from 240 functional images (see Data Collection) were coupled and correlated in all possible combinations, producing an individual connectivity matrix. Then, a global average concerning the whole group of subjects is obtained by averaging the 30 individual matrices, as schematized in Figure 2(a).(2)For both positive and negative interactions, in the above average matrix, a series of 20 binary and thresholded matrices are constructed, taking fractions of the highest absolute correlation values in the range from 0% to 100% at 5% steps: this represents the *network density* (cost). Thus, 20 binary matrices of increasing cost are derived, having an unbalanced amount of total positive and negative links (total positive correlations 70%, total negative correlations 30%). We call this type of threshold *absolute-values-proportional-threshold.* A graphical overview of the procedure is reported in Figure 2(b).(3)A further set of binary and thresholded matrices is calculated in order to distinguish the most significant correlation value for each sign: 15 matrices from the 0%–70% cost (maximum fraction of positive links), containing only positive values, and 7 matrices from the 0%–30% cost (maximum fraction of negative links), containing only negative values. Thus, we have different amounts of positive and negative correlations for the same fraction of total links. We call this type of threshold *signed-values-proportional-threshold*.(4)Finally, all the combinations of positive and negative matrices for different thresholds are joined, producing matrices having different amounts of positive and negative correlations.