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Edited by: Joana Cabral, University of Minho, Portugal

Reviewed by: Kelly Shen, Rotman Research Institute (RRI), Canada; Changsong Zhou, Hong Kong Baptist University, Hong Kong

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

The structural connectivity of human brain allows the coexistence of segregated and integrated states of activity. Neuromodulatory systems facilitate the transition between these functional states and recent computational studies have shown how an interplay between the noradrenergic and cholinergic systems define these transitions. However, there is still much to be known about the interaction between the structural connectivity and the effect of neuromodulation, and to what extent the connectome facilitates dynamic transitions. In this work, we use a whole brain model, based on the Jasen and Rit equations plus a human structural connectivity matrix, to find out which structural features of the human connectome network define the optimal neuromodulatory effects. We simulated the effect of the noradrenergic system as changes in filter gain, and studied its effects related to the global-, local-, and meso-scale features of the connectome. At the global-scale, we found that the ability of the network of transiting through a variety of dynamical states is disrupted by randomization of the connection weights. By simulating neuromodulation of partial subsets of nodes, we found that transitions between integrated and segregated states are more easily achieved when targeting nodes with greater connection strengths—local feature—or belonging to the rich club—meso-scale feature. Overall, our findings clarify how the network spatial features, at different levels, interact with neuromodulation to facilitate the switching between segregated and integrated brain states and to sustain a richer brain dynamics.

The human brain generates a rich repertoire of spatiotemporal dynamics characterized by the

Neuroimaging recording techniques such as electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) allow the characterization of functional connectivity (FC) of the brain, from which the functional integration and segregation can be quantified using network theory tools (Bullmore and Sporns,

A plausible mechanism to facilitate—and regulate—transitions between different FC patterns are neuromodulatory systems. Neuromodulators do not directly excite neurons. Instead, they change their excitability and response to neurotransmitters, increasing or decreasing the probability of firing action potentials (Thiele and Bellgrove,

The noradrenergic system is involved in arousal when subjects engage in high-load cognitive tasks (Aston-Jones and Cohen, _{2} autoreceptors expressed on the varicosities. The overall result comprises an increase of the neuron responsivity above a threshold, and a decrease of the responsivity below this threshold. This is equivalent to increasing the slope of the input-output sigmoid function, also named filter gain, as proposed in Servan-Schreiber et al. (

In a recent article (Shine,

There is evidence about the importance of network properties of the human connectome (Cabral et al.,

To investigate this issue, we built a whole-brain model based on the Jansen and Rit equations (Jansen et al.,

We found that when we selectively neuromodulated the brain regions by the rich club (meso-scale property) or the high strength criteria (local-scale) the whole-brain network dynamics is most effectively modified. Additionally, we observed that surrogate connectomes reduced FC richness, compared with human SC, when neuromodulated. Overall, our findings clarify how the neuromodulation interacts with the anatomical network features at local-, meso-, and macro-scale levels in a whole-brain model to facilitate switching between segregated and integrated brain states.

To study the effect of neuromodulatory systems on the integrative/segregative capacities of the human connectome, we used a whole-brain model of brain activity (Coronel-Oliveros et al., _{4}, which we modified to _{4} = 0.5

Whole-brain neural mass model with neuromodulation. _{i} connect each population. The outputs are transformed from average pulse density to average postsynaptic membrane potential by an excitatory (inhibitory) impulse response function _{E}(_{I}(_{0} of their sigmoid function.

We modeled the influence of the noradrenergic system through the manipulation of the filter gain (Aston-Jones and Cohen, _{0} modifies the sigmoid function slope of pyramidal neurons, increasing their responsivity to relevant stimuli, decreasing the response to low amplitude stimuli, and boosting the signal-to-noise ratio.

First, we analyzed how neuromodulation depends on the connectivity pattern of the human connectome by using different randomized surrogate connectomes. We employed a degree- and strength-preserving randomization (DSPR), which randomizes the structural connectivity while preserving original degree and strength distributions (_{0} ∈ [0, 1] parameters. Here, the value of the parameters is equal for all the nodes, and we refer to this case as uniform neuromodulation. We computed the mean of the Kuramoto order parameter, also known as phase synchrony ^{w}, and the modularity, ^{w}, as measures of global phase synchronization, integration, and segregation, respectively. Global efficiency is a measure of integration defined as the inverse of the characteristic path length (Rubinov and Sporns, ^{w} represent an efficient coordination between all pairs of nodes in the network, a signature of integration. Modularity is a measure of segregation based on the detection of network communities, or modules (Rubinov and Sporns, ^{w} is associated with segregation and vice-versa.

Effects of network structure in neural synchronization and integration. From top to bottom: structural connectivity matrix, phase synchrony ^{w} (a measure of integration), and modularity ^{w} (measure of segregation), obtained in the model with different structural connectivities. ^{w} and ^{w} were calculated using the FC obtained from the corresponding fMRI BOLD-like traces.

^{w}, verifying a link between the fast dynamics of EEG and the slower one of fMRI-BOLD.

We repeated the same exploration using the DSPR surrogate connectome (_{0}, α) is reduced, and a spot of over-synchronized activity can be appreciated. Most importantly, the area of intermediate values of synchrony and integration is largely reduced, suggesting a reduction of dynamical richness. When the connectivity matrix is completely randomized (

The dramatic decrease in ^{w} in ^{w} should not be interpreted as a reduction of integration but a limitation of the hemodynamic model we employed in input simulations. Nevertheless, an over-synchronized regime of activity is a feature never found in the healthy brain (Miron-Shahar et al.,

Thus, in line with several previous reports (Cabral et al.,

In the following, we will study which local- or meso-scale organization features are determinant in the effect of neuromodulation of human connectome by evaluating the network behavior when changing the _{0} parameter in subsets of network nodes.

In this section, we investigate the impact on functional integration when an increasing number of nodes are neuromodulated. The order in which nodes are modulated is defined considering nodal measures obtained from the structural matrix _{0} ∈ [0.33, 1] and the number of nodes being neuromodulated in [0, 90] in steps of three. As before, we used the EEG-like and BOLD-like signals to extract synchrony, integration, and segregation.

A particular example of partial neuromodulation is shown with some detail in _{0}) parameter space is shown in ^{w} and modularity ^{w} in a uniform neuromodulation scenario (all nodes identical). _{0} = 0.33 (red dot in _{0} = 0.67 (blue dot in _{0} = 0.67 while the rest remain with _{0} = 0.33. As the number of nodes with _{0} = 0.67 increases, the FC matrices become more integrated (high ^{w} and low ^{w} values). Similarly, the FCD matrices change from incoherence (red FCD), to exhibit multi-stable behavior (FCD with yellow-green patches), and finally to show correlated FC patterns (blue FCD). In summary, the increment of the number of neuromodulated nodes increases phase synchrony, functional integration, and the time correlation of FCs captured by the FCD.

Partial noradrenergic neuromodulation. _{0}) parameter space showing phase synchrony ^{w}, and modularity ^{w}, for the Human connectome (same as in _{0} = 0.33; _{0} = 0.33 and 45 nodes have _{0} = 0.67; and _{0} = 0.67. In _{0} = 0.67.

_{0} with a target value in the [0.33, 1] interval and with the number of neuromodulated nodes ranging from 0 to 90. The order in which nodes are neuromodulated is either from low to high ^{w} raise markedly in both cases; the opposite can be observed for ^{w}. However, picking the nodes of high strength first (_{0} value of 0.67. There, the curves for the high to low _{0}. The results were also compared with a random selection of nodes for neuromodulation (green curves). As the blue curve is mainly below the green curve, neuromodulation of nodes with low

Incremental neuromodulation based on node strength. ^{w}, and modularity ^{w}, at different combinations of _{0} and number of neuromodulated nodes. Nodes were affected by neuromodulation according to their strength, from low to high. _{0} = 0.67 as target value. Blue curves for neuromodulation of nodes with low strength, orange the opposite, and green for a random ordering of the nodes. Shaded areas correspond to 95% confidence intervals, for 10 realizations.

We compared the results of sorting the nodes based on strength _{0} = 0.33 to a target _{0} = 0.67, when the nodes are ordered from low to high or high to low

Incremental neuromodulation based on nodal efficiency and clustering coefficient. ^{w}, and modularity ^{w} as a function of the number of neuromodulated nodes, for _{0} = 0.67 as target value. In

When comparing the results in ^{w} is unnoticeable, except in ^{w} when ordering the nodes from high to low

To summarize these results, we computed the difference between the area under the curve (AUC) for the high-to-low minus low-to-high (orange minus blue AUCs; ^{w}, and −Δ^{w} (note that the sign is inverted for visualization purposes), is lower for

Node strength, nodal efficiency and clustering coefficient are considered local-scale properties, i.e., they belong to each node. Several meso-scale network properties have been described as being determinant for network dynamic too, such as the rich club organization (Van Den Heuvel and Sporns, ^{w}(

Neuromodulation based on the rich club organization. ^{w} and modularity ^{w} when neuromodulating 24-node sets containing the rich club (blue), local nodes (green), or only feeders (orange). The results are shown as the difference with respect to a random subset of nodes of equal size (null case). The bottom row summarizes the area under the curve (AUC) for each metric and nodal category, averaged over the 10 realizations. Shaded areas correspond to 95% confidence intervals, and bar plots were built using the mean ± standard deviation. **

List of regions belonging (X) to the rich club, the _{3} category, and the 17 nodes with highest strength.

_{3} core |
|||
---|---|---|---|

Posterior cingulate gyrus (L, R) | X | X | X |

Precuneus (L, R) | X | X | X |

Calcarine fissure (L, R) | X | X | |

Cuncus (L, R) | X | ||

Cuneus (L, R) | X | X | |

Caudate nucleus (R) | X | ||

Hippocampus (L, R) | X | ||

Insula (L) | X | ||

Middle occipital gyrus (L) | X | X | |

Pallidum (L, R) | X | ||

Putamen (L, R) | X | X | |

Rolandic Operculum (L) | X | ||

Superior dorsal gyrus, dorsolateral (L, R) | X | ||

Superior frontal gyrus, orbital (L) | X | ||

Superior occipital gyrus (L, R) | X | ||

Superior frontal gyrus, medial (L) | X | X | |

Thalamus (L, R) | X |

As the analysis of the rich-club properties of the human SC defines sub-networks, instead of sorting the nodes, we chose a different approach than the neuromodulation of increasing subsets of nodes. Here, we simulated neuromodulation of a fixed-size subset of nodes, that included all nodes belonging to a certain category (rich club, feeders, or local). Because the categories differ in size, we complemented the rich club and local nodes with 7 and 11 nodes, respectively, selected randomly from the feeders. For the last one, we randomly chose 24 feeder nodes. Also, we had a null case, composed of 24 nodes randomly selected from the complete set of nodes. We repeated the random selection of nodes with 10 realizations, always using subsets of 24 nodes. The nodes started with a basal _{0} value of 0.33, and _{0} was swept up to 1 but only in the designated subset of nodes. For each _{0} increment, we measured ^{w}, and ^{w}. Then, we subtracted to each measurement the result of the null case. The results are shown in _{0}. Opposite results were observed for the subsets containing local nodes. Finally, neuromodulation of subsets containing only feeder nodes produce no difference compared to random selection of nodes. As a summary index, we calculated the AUC for each nodal category (^{w}) for the rich club respect to feeders and local, and higher (lower in the case of ^{w}) between feeders and local (

As previously shown, functional integration is also achieved by neuromodulation of highest strength nodes. To highlight the difference between the local and meso-scale approaches, we quantified the overlap between the rich club nodes and the 17 nodes with higher strength. We found that only 8 members of the rich club belong to the subset of 17 nodes with higher strength (

To explore a second meso-scale network organization, we performed a _{3} with 10 nodes (1.54 < _{2} with 56 nodes (1.48 < _{1} with 24 nodes (_{3} are nodes connected within them with highest strength, _{2} middle-strength nodes, and _{1} the nodes with the lowest strength. The _{3} subset comprises the brain regions shown in

Neuromodulation based on the _{3} (_{2} (_{1} (^{w} and modularity ^{w} when neuromodulating 24-node sets containing the _{3} nodes (blue), _{1} nodes (olive green), or only _{2} nodes (pink). _{1} and _{3} sets were complemented with random nodes from _{2} to obtain sets of 24. Results are shown as the difference with respect to a random subset of nodes of equal size (null case). The bottom row summarizes the area under the curve (AUC) for each metric and nodal category, averaged over the 10 random seeds. Shaded areas correspond to 95% confidence intervals, and bar plots were built using the mean ± standard deviation. ***

We simulated the neuromodulation in subsets of 24 nodes, containing either the _{3} or the _{1} category, and complementing _{3} with 14 random nodes from _{2} as done with the rich club. A third group was built with 24 nodes randomly selected from _{2}, and all groups were compared to a random selection of 24 nodes from the whole set. As shown in _{2} nodes for neuromodulation shows the largest effect in ^{w}, and Δ^{w}, compared with _{1} nodes (_{3} nodes (^{w} with

In this work, we sought to identify the relationship between structural features of the human connectome and the specific set of regions that, when neuromodulated in a biologically realistic whole-brain model, produce a significant increase in functional integration. We found that the global organization of the connectome sustains rich metastable and partially synchronized states, essential to the effects related to neuromodulation. At the meso- and local-scales, nodes belonging to the anatomical rich club, and those having high nodal strength, produce a marked increase in functional integration (and a decrease in segregation) when neuromodulated.

Our results show that the whole-brain model exhibits over-synchronized behavior when using surrogate connectomes, restricting the dynamic features of the model. This result is in the same line as other previous findings (Cabral et al., _{0}) parameter space, where simulations with randomized connectomes show either incoherent or over-synchronized activity. Using a whole-brain model to simulate and fit magnetoencephalography (MEG) resting-state recordings, Cabral et al. (

At the local level, the effects of neuromodulation strongly depend on the characteristics of the nodes in the human connectome. In our model, the nodes with high strength are the ones that better facilitate functional integration when neuromodulated. This result resonates with a recent work by Herzog et al. (_{2A} receptor density map, obtained by PET (Beliveau et al.,

Network hubs, or nodes belonging to the rich club or network's ignition core, can be critical elements for binding information of segregated brain regions, that is, to integrate information across brain areas (Griffa and Van den Heuvel,

Notably, neuromodulation of nodes belonging to the critical _{3} category are the nodes of the highest strength in the network; however, they cannot boost functional integration to the same extent as the rich club nodes.

Part of the brain regions we found in the rich club support high order brain functions. For example, frontoparietal regions play an important role in cognition, and are markedly activated when subjects engage in cognitive tasks (Cavanna,

The non-uniform expression of receptors across several brain areas suggests that the brain uses selective or partial neuromodulation. In this way, the effect of the noradrenergic system on filter gain may be modeled as proportional to adrenergic receptor expression. Experimentally, the optogenetic activation of the LC in mice increased average functional connectivity, which correlates with the expression of α_{2}, α_{1}, and β_{1} adrenergic receptors (Zerbi et al.,

Expression of some noradrenergic receptors genes in brain regions. Genes ADRA2A, ADRA2C, and ADRAB1 are related to noradrenergic receptors α_{2A}, α_{2C}, and β_{1}, respectively. The normalized expression was obtained from the Allen Human Brain Atlas using the AAL parcelation. Bar plots were built using the mean ± standard deviation. ***

It has been suggested that the effect of noradrenaline in functional connectivity is context-dependent (Shine et al.,

Our work considers an arbitrary basal value of _{0}. Despite this, we reported a clear effect of the selective noradrenergic neuromodulation on functional integration, that is, some brain regions have a greater impact in the noradrenaline-mediated effect on brain function. A further improvement to our approach constitutes the use of a different benchmark, e.g., fitting the model to reproduce the empirical FC in resting-state, and then apply a homogenoeus or selective neuromodulation. Furthermore, the addition of receptors maps may be considered, as commented above.

Overall, our results offer new insights into the key regions of the human brain that, when neuromodulated via the noradrenergic system, promote transitions to integrated functional states. Our results highlight the importance of the rich club and high-strength connections in producing changes related to neuromodulation. We hope that our theoretical framework inspires new research toward clinical applications or treatments of human brain disorders caused by or associated with changes in functional and structural brain connectivity.

We simulated neuronal activity using the Jansen and Rit neural mass model (Jansen et al.,

and for the inhibitory ones

The constants

with ζ_{max} as the maximum firing rate of the neuronal population, _{th} the half maximal response of the population, and ν their average PSP. Additionally, pyramidal neurons receive an external stimulus

The set of equations, for a node

where _{0}, _{1}, _{2} correspond to the outputs of the PSP blocks of the pyramidal neurons, and excitatory and inhibitory interneurons, respectively, and _{3} the long-range outputs of pyramidal neurons. The constants _{1}, _{2}, _{3}, and _{4} scale the connectivity between the neural populations (see _{0} and _{0}, are related to the outputs of pyramidal cells to both interneurons; the second pair, _{1} and _{1}, represent all the local excitatory inputs that the pyramidal neurons receive; _{2} and _{2} constitute the inhibitory contribution to pyramidal cells. An additional pair of equations (_{3} and _{3}) are introduced to represent long-range (inter-area) connections, as they target the apical dendrites of pyramidal neurons and thus their EPSP have a larger characteristic time constant. We used the original parameter values of Jansen and Rit (Jansen et al., _{4}: ζ_{max} = 5 s^{−1}, ν_{th} = 6 mV, _{0} = _{1} = _{2} = 0.56 mV^{−1}, ^{−1}, ^{−1}, _{1} = _{2} = 0.8_{3} = 0.25_{4} = 0.5_{4} from 0.25 C to 0.5 C allowed the model to sustain oscillations in a wider range of α values. The parameters

The input from brain areas

The average PSP of pyramidal neurons in region

The firing rates of pyramidal neurons ζ_{i}(_{i}, _{0}] were used to simulate the fMRI-BOLD signals.

The effect of the noradrenergic system was simulated controlling the parameter _{0} (filter gain;

_{0} was 0.33 for all nodes (_{0} in a subset of 24 nodes belonging to a particular category, and compared the results with the neuromodulation of a equal-length random subset of nodes.

Because the categories differ in the number of nodes, a fair comparison must considered subsets of equal size. To achieve that, we complemented the rich club with seven randomly selected feeder nodes, while the local nodes were complemented with 11 randomly selected feeders. Likewise, we complemented the _{3} category with 14 randomly selected _{2} nodes. From both the feeders and _{2} nodes we selected 24 nodes randomly. All subsets consisted on 24 nodes, were generated 10 times with different random seeds and the results averaged.

_{0}—node by node in increments of three, considering the metric from high to low and vice-versa (

Following Birn et al. (_{0} ∈ [0, 1], for the macro-scale scenario. In the local- and meso-scale scenarios, we swept _{0} ∈ [0.33, 1] for a susbset of nodes, considering a basal value of _{0} = 0.33 and a fixed α = 0.65. All the simulations were implemented in Python and the codes are freely available at:

We used the firing rates ζ_{i}(_{i}(_{i}, producing blood inflow _{i}, changes in the blood volume _{i} and deoxyhemoglobin content _{i}. The corresponding system of differential equations is

where τ_{s} = 0.65, τ_{f} = 0.41, τ_{v} = 0.98, τ_{q} = 0.98 represent the time constants for the signal decay, blood inflow, blood volume, and deoxyhemoglobin content, respectively. The stiffness constant (resistance of the veins to blood flow) is given by κ, and the resting-state oxygen extraction rate by _{0}. We used κ = 0.32 and _{0} = 0.4. The BOLD-like signal of node _{i}(_{i}(_{i}(

where _{0} = 0.04 represents the fraction of venous blood (deoxygenated) in resting-state, and _{1} = 2.77, _{2} = 0.2, _{3} = 0.5 are kinetic constants.

The system of differential equations (8) was solved using the Euler method with an integration step of 1 ms. The signals were band-pass filtered between 0.01 and 0.1 Hz with a 3rd order Bessel filter. These BOLD-like signals were used to build the functional connectivity (FC) matrices from which the subsequent analysis of functional network properties was performed.

To compare different Macro-scale features of the connectome we used four connectivity matrices (see _{ij} < 0.05, and 1 otherwise (Homogeneous,

We identified the nodes belonging to the “rich club” sub-network of the graph (Van Den Heuvel and Sporns,

where _{>K} is the sum of the weighted edges of the subgraph of nodes with a degree greater than _{>K} represent the total number of edges of the subgraph, and ^{w}(^{w}(

being

The core-periphery organization (Hagmann et al., _{1} with 24 nodes (_{2} with 56 nodes (1.48 < _{3} with 10 nodes (1.54 <

We employed three different metrics to characterize individual nodes. Node strength (weighted degree) was computed as

where _{ij} the weighted edge of the matrix

where

where

A node with a high

As a measure of global synchronization, we calculated the Kuramoto order parameter

where θ_{i}(_{N} denotes the average over all nodes, and 〈〉_{t} the average over time.

Functional Connectivity (FC) matrices were built from Pearson correlations of the entire BOLD-like time series. Instead of employing an absolute or proportional thresholding, we thresholded the FC matrices using Fourier transform (FT) surrogate data (Lancaster et al., ^{2} −

To reject the null hypothesis, we selected a

Integration was evaluated over the thresholded FC matrices. We employed the weighted version of the global efficiency (Latora and Marchiori,

being

Segregation was quantified using modularity ^{w}, a metric for the detection of the network's communities (Rubinov and Sporns,

where _{ij} is the weight of the link between the nodes ^{w} is the total number of weighted links of the network, _{i} (_{j}) the module of the node _{j}) the weighted degree (named also strength) of _{mi,mj} is equal to 1 when _{i} = _{j} (that is, when two nodes belongs to the same module), and 0 otherwise.

Because the Louvain's algorithm is stochastic, we employed the consensus-clustering algorithm (Lancichinetti and Fortunato, _{ij} ∈ [0, 1] indicates the proportion of partitions in which the pairs of nodes (

The FCD matrix captures the evolution of FC patterns and, consequently, the dynamical richness of the network (Hansen et al.,

To quantify the expression of some noradrenergic receptor genes in brain regions, we used the microarray expression data of the Allen Human Brain Atlas (Shen et al.,

The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found at:

CC-O, SC, RC, and PO contributed to conception and design of the study and wrote the manuscript. CC-O performed the simulations and statistical analysis. All authors contributed to manuscript revision, read, and approved the submitted version.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

We thank Gustavo Deco for kindly providing the anatomical connectivity matrix used in the model, and Vicente Medel for fruitful and critical discussions of the work.