# Investigating the Impact of Local Manipulations on Spontaneous and Evoked Brain Complexity Indices: A Large-Scale Computational Model

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Model Simulations

#### 2.1.1. Structural Connectivity

#### 2.1.2. Neural Mass Model

_{NMDA}is the ratio of NMDA receptors to AMPA receptors, and a

_{xy}is the synaptic strength originating from population x (e.g., e, i, n, where e refers to the excitatory population, i to the inhibitory one, and n denotes a nonspecific input) to population y (e.g., e, i). The rate terms b and ϕ govern the time scales of Z and W, respectively. The term g

_{ion}is the maximum conductance (i.e., when all channels are open) of the corresponding ion species. The voltage-dependent fractions of open channels for a given ion is determined by m

_{ion}and is modeled by a sigmoidal shape function:

_{ion}is the mean threshold membrane potential of a given ion channel population, and δ

_{ion}is its standard deviation. The mean firing rates of the excitatory and inhibitory populations are determined by the voltage-dependent activation functions Q

_{V}and Q

_{Z}, respectively, modeled as:

_{max}and QZ

_{max}are the maximum firing rates of the excitatory and inhibitory populations, respectively. Their corresponding thresholds for action potential generation are given by the terms V

_{T}and Z

_{T}, with standard deviations δ

_{V}and δ

_{Z}, respectively. The network input to node k is given by:

_{kj}is the connection weight from node j to node k, τ is the input delay time, and G is the global coupling that scales the connection weights. The parameter C in Equation (1) ranges within [0, 1] and balances the strength of the self-connections against those of the rest of the network.

^{−7}) and an integration time step of 0.1 ms. A pre-processing step was performed to reduce the amount of data by temporally resampling the data to a resolution time of 1 ms (i.e., averaging over each 1 ms time step). In addition, the first 3 s of simulations were discarded (first 14 s in Hconn) to remove the initial transient activities in the model.

#### 2.1.3. Spontaneous Activity and Stimulation Protocol

#### 2.1.4. Local Manipulation Modeling

#### 2.1.5. Validation on a Larger Connectome (Hconn)

#### 2.2. Analysis of Network Simulations

#### 2.2.1. Firing Activity Analysis

_{ROI}) as the amount of spikes divided by the time window of observation.

_{ROI}values across nodes (either all nodes or, when specified, the ones of the intact or the manipulated hemisphere):

_{Δ}) as:

_{Δ}involved only the nodes not affected by the local manipulation (i.e., excluding the silenced nodes also in the control condition).

_{(t<0)}is the average IFR over the time prior to stimulation, and <ΔIFR(t)>

_{trials}is the average ΔIFR across trials.

_{i}, IFR

_{j}) is the covariance between two spontaneous IFR signals (IFR

_{i,}IFR

_{j}), and σ(IFR

_{i}), σ(IFR

_{j}) are the corresponding standard deviations of the IFR signals

#### 2.2.2. Network Analysis

_{BOLD}on the BOLD signal, a widely used approach in the literature with this model [39,50,51,56,57,58]. The BOLD signal was estimated from the model’s output following [39]. We used the nonlinear Balloon–Windkessel hemodynamic model [64], and the input to the model was the absolute value of the time derivative of the excitatory membrane potential within each node. All the hemodynamic parameters were taken from [64]. Lastly, the estimated BOLD signal was sampled every 2 s. The FC

_{BOLD}is defined as the Pearson correlation coefficient between each pair of BOLD signals. Then, similar to the SC analysis, we used the WD from the FC

_{IFR}and the FC

_{BOLD}to investigate the relationship between node centrality and complexity topographies. We also conducted the analysis by performing global signal regression (GSR) on the BOLD signal [51].

#### 2.2.3. Complexity Indices

- -
- Lempel–Ziv Complexity

- -
- Perturbational Complexity Index

^{LZ}is defined as the normalized CL of the evoked spatiotemporal patterns SS(x,t):

_{1}and (1 − p

_{1}) are the fraction of “1” (significant activity) and “0” (non-significant activity) in the binary matrix.

#### 2.2.4. Complexity Topographies

_{ROI}) for different conditions (local manipulations and control). The coefficient of determination (R

^{2}) for each node was then computed and mapped onto the brain topographies. Thus, LZc-R

^{2}and PCI-R

^{2}topographies were derived. Given the 12 stimulation sites for PCI, 12 topographies were generated, which were then averaged into a single PCI-<R

^{2}> topography.

#### 2.2.5. Statistical Analysis

^{2}, and R

^{2}

_{adjusted}to account for multiple regressors) and the p-value of the F-statistic. Additionally, we computed the slope coefficients of the regressors and their corresponding two-sided 95% confidence intervals (95% CI). For all statistical analyses, alpha = 0.05.

## 3. Results

#### 3.1. Spontaneous Activity

#### Impact of Local Node Silencing on Spontaneous Complexity Measures

_{Δ}) on the nodes within the manipulated hemisphere, the intact one, as well as in the entire model compared with the same nodes in the control condition (Figure 2a). This analysis revealed that the MFR decreased the most in the affected hemisphere (MFR

_{Δ}= −3.621 ± 1.629 Hz, mean across all manipulations ± SD) and to a lesser extent in the intact hemisphere (−1.431 ± 0.992 Hz).

_{IFR}, see methods) between nodes as a measure of the synchrony of network interactions. CC

_{IFR}was lower across local manipulations when compared to control (control: 0.067, average across manipulations: 0.061 ± 0.007; Figure 2d), which corresponds to a larger segregation of the network patterns. We found a negative correlation between LZc and CC

_{IFR}(r = −0.55, p = 0.009; Figure 2d).

_{IFR}) in shaping brain complexity, we performed a multivariate regression between MFR and CC

_{IFR}in explaining LZc across all conditions (Figure 2e). This model effectively captured the variance of LZc (R

^{2}= 0.98, R

^{2}

_{adjusted}= 0.98, p = 2 × 10

^{−16}). Confirming the results obtained with the univariate analyses, a positive relationship was found for LZc with respect to MFR (slope coefficient, β

_{MFR}= 0.0072, 95% CI [0.0066, 0.0078]), while CC

_{IFR}was found to be negatively correlated with LZc (β

_{CC}= −1.2, 95% CI [−1.3, −1.1]).

#### 3.2. Evoked Activity

#### 3.2.1. Local Node Silencing and PCI

_{Δ}) across stimuli (for each local manipulation p < 0.01, one sample t-test with Bonferroni–Holm correction; Figure 3a), albeit with a great variability depending on the specific stimulus-silencing pair (individual PCI values and statistical comparisons with respect to the control condition are reported in Figure S2).

#### 3.2.2. The Impact of Regional Silencing on PCI

_{ROI}) across all conditions (including the control condition and all local manipulations). Figure 4a shows the linear regressions for two representative ROIs (right posterior cingulate cortex; rCCp and right parahippocampal cortex; rPHC), corresponding to the ROIs showing the third highest and third lowest average correlations across stimuli, respectively. For each of the two ROIs, we show two representative stimulations delivered to the inferior parietal cortex (PCi; R

^{2}= 0.59, p = 5 × 10

^{−5}and R

^{2}= 0.02, p = 0.58) and the dorsolateral prefrontal cortex (PFCdl; R

^{2}= 0.23, p = 0.03 and R

^{2}= 0.01, p = 0.60). We found that PCI correlated well with MFR

_{ROI}(CCp) for most stimulations (F-statistic of R

^{2}, 11 with p < 0.05, one with p = 0.051), ranging from 0.19 to 0.59 (0.41 ± 0.14) (Figure 4b). On the other hand, MFR

_{ROI}(PHC) was always non-significantly correlated with PCI across the 12 stimulations (p > 0.05).

^{2}coefficients for each stimulation are presented topographically in Figure S5A, and the average topography across all stimulations is presented in Figure 4c. Interestingly, the three ROIs with the highest average R

^{2}across stimulations (i.e., CCr, <R

^{2}> = 0.51 ± 0.13; PCm, <R

^{2}> = 0.45 ± 0.14; CCp, <R

^{2}> = 0.41 ± 0.14) were located in the posterior cortex of the manipulated hemisphere. In addition, the ROIs with the three highest R

^{2}values across all stimulations were predominantly located in the posterior regions (~89%, Figure S5B,C).

^{2}values located in posterior regions of the manipulated hemisphere (Figure S4D).

#### 3.2.3. Assessing Regional Similarity between Spontaneous and Evoked Complexity Metrics

_{ROI}versus LZc (Figure S6A,B) and computed the similarity between the R

^{2}topography maps of these and the 12 R

^{2}PCI topographies for each stimulation (Figure 4d). We found that the correlations between PCI and LZ topographies were anti-correlated (−0.1 ± 0.23), though many correlations were not significant (5 out of 12). Similar results were obtained when restricting the analysis to either the intact or the manipulated hemisphere (−0.29 ± 0.11 and −0.19 ± 0.12, respectively).

#### 3.3. Assessing the Relationship between Complexity Measures and Graph Properties

^{2}-topographies derived from spontaneous (LZc) as well as perturbational complexity (PCI) measures and basic graph properties. To this aim, we correlated the weighted degree (WD) of each node (an index of network centrality calculated both on SC and FC) with the corresponding values of the complexity-R

^{2}topographies (Figure 5). The WD computed on the SC showed a weak, albeit significant, correlation with the PCI average-R

^{2}topography across the 12 stimulations (r = 0.34, p = 0.0026; Figure 5a). Conversely, we did not find a significant correlation with the LZc-R

^{2}topography (p = 0.063, Figure 5b). Similarly, we found a significant correlation between the WD computed on the SC and the PCI-R

^{2}topography applied to Hconn (r = 0.44, p = 2∙10

^{−49}; Figure S7A). Further, we found even more robust correlations between WD calculated on FC and the average PCI-R

^{2}topography (r = 0.6, p = 10

^{−8}, Figure 5c). Again, no significant relationship was found between WD and the LZc-R

^{2}topography (p = 0.5, Figure 5d). Similar results (Figure S7B–E) were obtained when using WD calculated on the FC derived from BOLD signals (FC

_{BOLD;}see Section 2).

## 4. Discussion

#### 4.1. Impact of Local Silencing on Complexity Measures: The Role of Global Activity Levels and Network Dynamics/Interactions

_{Δ}), with a large variability depending on the manipulated nodes (Figure 2a). A similar trend was also observed for spontaneous complexity quantified with LZc, indicating a correlation between LZc and the global activity levels (MFR; Figure 2c). However, LZc often remained unchanged or even increased as compared to the control condition (Figure 2b), suggesting that the observed effects of local silencing on LZc were not merely explained by changes in global activity levels. Crucially, local manipulations resulting in a reduction of functional connectivity (i.e., segregation of network interactions) as captured by the correlation of activity across nodes (CC

_{IFR}) tended to exhibit higher LZc values (Figure 2d). Thus, we tested the interplay between global activity levels (MFR) and network interactions (CC

_{IFR}) in sustaining complex dynamics (LZc) through a 3D linear model (Figure 2e). This model, rooted in simple network activity variables, effectively described LZc, corroborating (1) the role of an optimal global activity level in shaping spontaneous complexity values and (2) the negative relationship of LZc with respect to network interactions. Importantly, this result underscores a significant limitation of various complexity metrics based on spontaneous activity, such as LZc, as they assume a priori network integration [6] and yield high values in systems composed of independent/segregated elements [41]. Here, we confirm, in a whole-brain connectome endowed with neural mass models, previous studies illustrating an imbalance of LZc towards network segregation [44].

_{IFR}). This resulted in a less complex evoked response (as quantified by PCI; Figure 3b,c) despite increased LZc (Figure 2b). This result is also in line with several empirical findings across a variety of conditions where a disruption of effective connectivity across widespread brain networks results in a spatially constrained, short-lived EEG response to direct cortical stimulations with TMS and, in turn, in a significant reduction of PCI [17,18,25,67,68].

_{IFR}applied to PCI. In this case, compared to LZc, the 3D model does not describe PCI values across conditions resulting in a slope coefficient for CC

_{IFR}not significantly different from 0 for most stimulations (8 out of 12; Supplementary Results, Section S3).

#### 4.2. Regional Aspects of Complexity Indices: The Role of Posterior Regions

_{ROI}) displaying the highest correlations with PCI included the retrosplenial cingulate cortex, the medial parietal cortex (precuneus), and the posterior cingulate cortex. Similar findings, encompassing a similar set of posterior regions, were found for the Hconn model (Figure S4D). These results nicely complement recent empirical observations involving rats under ketamine anesthesia [72], which found a strong correlation between PCI and activity in posteromedial regions. This study demonstrated that deactivation of these posteromedial regions was associated with disruptions in long-lasting and widespread cortical interactions following electrical stimulation. Altogether, these findings suggest the central hub role of posterior regions for long-range communications in cortical networks. Consistently, we have observed a positive correlation (Figure 5 and Figure S7) between the weighted degree (a metric quantifying hub centrality), particularly when applied to functional connectivity estimates (Figure 5c,d and Figure S7B,C) and the PCI-R

^{2}topographies (but not for LZc-R

^{2}).

#### 4.3. Limitations and Future Directions

#### 4.4. Conclusions

## Supplementary Materials

^{2}topographies for each stimulation site confirm the importance of the posterior regions; Figure S6: Characterization of the LZc-R

^{2}topography; Figure S7: Network metrics of centrality correlate with complexity topographies.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**

**Whole-brain model for investigating brain complexity in silico.**(

**aI**) Each node of the whole-brain network is modelled by the Larter and Breakspear (LB) neural mass model (NMM), describing the interaction between excitatory (E) and inhibitory (I) neurons. The weights connecting the nodes are reported in the structural connectivity (SC) matrix. (

**aII**) The output of the model of a given node is the mean membrane potential of the excitatory population (green trace), and the timing of the spikes (red dots), detected with a hard threshold on the voltage, are then converted to an instantaneous firing rate (IFR) (black overlay trace). (

**b**) The working point of the model (i.e., set of model parameters) was obtained based on the spontaneous and evoked activity following three steps. First (

**bI**), the correlations between the spontaneous IFR traces were computed to estimate a functional connectivity (FC) matrix. Then, the similarity between the FC and SC matrices was assessed through the Pearson correlation coefficient. Second (

**bII**), by stimulating a node of the connectome (here rPCi), the propagation of activity in the network was quantified in terms of ΔIFR

_{SH}(ΔIFR averaged over the nodes of the stimulated hemisphere), and some representative trials of ΔIFR

_{SH}are reported. The evoked area is obtained as the integral after stimulation (red line, between 0 and 500 ms) of ΔIFR

_{SH}averaged across trials. Third (

**bIII**), the SC-FC correlation and the evoked area are reported for different global couplings (i.e., a scaling factor of the SC), and both metrics reached a peak at G = 4 (working point). The dashed blue lines and arrows illustrate the matches between the FC and the SC maps for different G values. The dashed green lines and arrows illustrate the evoked area by the stimulus. (

**cI**) We simulated control and local manipulation conditions. Local manipulations were implemented by silencing selected nodes. (

**cII**) To assess the impact of local node silencing on spontaneous complexity, we calculated Lempel–Ziv complexity (LZc) on ongoing network activity. Furthermore, we separately stimulated different connectome nodes under different local manipulations and calculated the Perturbational Complexity Index (PCI) to gauge the impact of local silencing on the evoked activity.

**Figure 2.**

**Impact of local manipulations on whole-brain spontaneous activity.**(

**a**) Mean firing rate difference (MFR

_{Δ}, see Methods) for each silencing condition of the manipulated hemisphere (green), the intact one (yellow), and overall nodes (black). Note that the ranking (i.e., ranked local manipulations, see Table 2) is based on the black curve. (

**b**) The Lempel–Ziv complexity (LZc) metric is reported versus the same ranked local manipulations. The red horizontal lines mark the average value of LZc in the control condition. Error bars represent one standard deviation and asterisks indicate a statistically significant difference from the control condition (* p < 0.05, ** p < 0.01, *** p < 0.001; Kruskal–Wallis and Dunn post hoc test with Benjamini–Hochberg correction). (

**c**) Linear regressions relating the mean firing rate of all nodes (MFR) to LZc (r = 0.69; p = 0.0005). (

**d**) Linear regression relating the averaged pairwise cross-correlation (CC

_{IFR}) to LZc (r = −0.55, p = 0.009). (

**e**) Multivariate regression of LZc with respect to the independent variables MFR and CC

_{IFR}(R

^{2}= 0.98, R

^{2}

_{adjusted}= 0.98, p = 2 × 10

^{−16}).

**Figure 3.**

**Impact of local manipulations on evoked activity.**(

**a**) Each box, corresponding to a local manipulation (ordered according to the ranking in Figure 2), displays the difference in PCI compared to the control (PCI

_{Δ}) for a given stimulation site (12 values per box, e.g., stimulation of rPCi: PCI

_{Δ}(local manipulation) = <PCI

_{local manipulation}> − <PCI

_{ctrl}>, where <…> indicates mean across resamples). For each local manipulation, p < 0.01 (one sample t-test against mean zero with Bonferroni–Holm correction). (

**b**) Spatiotemporal distribution of the areas with significant changes of their firing rate with respect to baseline activity following stimulation. Representative snapshots are reported at time t = 5 ms, t = 145 ms, t = 245 ms, t = 285 ms, t = 375 ms, and t = 485 ms in the control condition (top row), for the local manipulations L4 (middle row), and L17 (bottom row). (

**c**) Top: the temporal courses of the instantaneous firing rate (<ΔIFR>) are reported for all nodes and separately for the representative conditions: ctrl (grey), L4 (dark blue), and L17 (light blue). For each condition, the highest five <ΔIFR> (quantified as the total activity in the interval [0, 500] ms) of the non-stimulated hemisphere (orange traces) are also reported. The horizontal brown line indicates the mean baseline (defined as <ΔIFR(t)> averaged over the interval [−1000, 0] ms and over the latter highest five <ΔIFR(t)>). The vertical dotted black line marks the time of the stimulus, and the vertical continuous black lines are relative to the snapshots reported in panel b. Bottom: the corresponding sorted binary spatiotemporal matrices of significant activities highlight the impact of the local manipulations with respect to the control condition (the red line is the sum of significant activity over time). The Perturbational Complexity Index (PCI) decreases significantly (p < 0.00001, ANOVA and post hoc pairwise T test with Benjamini–Hochberg correction) in L4 and L17 compared with control (see Figure S2).

**Figure 4.**

**Topological aspects of perturbational complexity.**(

**a**) Linear regressions relating PCI to the spontaneous mean firing rate of the ROIs/nodes rCCp and rPHC for two representative stimulation sites (red boxes: rPCi; green boxes: rPFCdl). (

**b**) Boxplot of the R

^{2}relative to the PCI versus MFR

_{ROI}(rCCp) and PCI versus MFR

_{ROI}(rPHC) linear regressions for all stimulation sites. Note that the reduced plots of panel A are reported on the right of the boxplot to highlight the corresponding R

^{2}value. (

**c**) Brain topography of the average R

^{2}across stimulation sites (<R

^{2}>). For each ROI in the topography, the corresponding <R

^{2}> is derived as in panel (

**b**). (

**d**) Distributions of the Pearson correlation coefficients computed across the R

^{2}topography maps of LZc with PCI and separately for all ROIs (all), intact hemisphere ROIs (IH), and manipulated hemisphere ROIs (MH). Each square and X symbol is relative to a stimulation site, and X markers indicate nonsignificant p values (>0.05).

**Figure 5.**Graph properties and complexity topographies. (

**a**) The weighted degree (WD) of structural connectivity (SC) nodes correlated with the PCI-<R

^{2}> topography (r = 0.34, p = 0.0026) but (

**b**) not with the LZc-R

^{2}topography (p = 0.063). (

**c**) The WD of the nodes of the functional connectivity (FC

_{IFR}) correlated with the PCI- <R

^{2}> topography (r = 0.6, p = 10

^{−8}) but (

**d**) not with the LZc-R

^{2}topography (p = 0.5). Each point is representative of an ROI/node in the network. The regression lines are reported in red.

**Table 1.**

**Labels of the cortical nodes and their description in Dconn.**The stimulated nodes are reported in bold.

Label | Description |
---|---|

A1 | Primary auditory cortex |

A2 | Secondary auditory cortex |

Amyg | Amygdala |

CCa | Anterior cingulate cortex |

CCp | Posterior cingulate cortex |

CCr | Retrosplenial cingulate cortex |

CCs | Subgenual cingulate cortex |

FEF | Frontal eye field |

G | Gustatory area |

HC | Hippocampal cortex |

IA | Anterior insula |

IP | Posterior insula |

M1 | Primary motor area |

PCi | Inferior parietal cortex |

PCip | Cortex of intraparietal sulcus |

PCm | Medial parietal cortex (i.e. precuneus) |

PCs | Dorsal parietal cortex (superior parietal lobule) |

PFCcl | Centrolateral prefrontal cortex |

PFCdl | Dorsolateral prefrontal cortex |

PFCdm | Dorsomedial prefrontal cortex |

PFCm | Medial prefrontal cortex |

PFCorb | Orbitofrontal cortex |

PFCpol | Pole of prefrontal cortex |

PFCvl | Ventrolateral prefrontal cortex |

PHC | Parahippocampal cortex |

PMCdl | Dorsolateral premotor cortex |

PMCm | Medial premotor cortex (i.e. supplementary motor area) |

PMCvl | Ventrolateral premotor cortex |

S1 | Primary somatosensory cortex |

S2 | Secondary somatosensory cortex |

TCc | Central temporal cortex |

TCi | Inferior temporal cortex |

TCpol | Pole of temporal cortex |

TCs | Superior temporal cortex |

TCv | Ventral temporal cortex |

V1 | Primary visual cortex |

V2 | Secondary visual cortex |

**Table 2.**

**Local manipulation labels in the Dconn connectome.**The labels of the local manipulations and the corresponding nodes silenced in the Dconn connectome. The ranking is based on the MFR difference (from lowest to highest). Note that when a stimulus overlaps with a silenced node (in bold), the latter is replaced by a nearby node.

Local Manipulation Label | Nodes | Ranking (MFR_{Δ}) |
---|---|---|

L1 | PCip, PCs, PCm | 10 |

L2 | PFCcl, PFCdl, PMCvl | 7 |

L3 | TCc, TCs, TCi | 4 |

L4 | V2, V1, CCr | 18 |

L5 | CCs, PFCorb, Amyg | 19 |

L6 | CCa, CCp, CCr | 13 |

L7 | M1, S1, PMCdl | 5 |

L8 | PCm, PCip, CCp | 15 |

L9 | PFCdm, CCa, PFCm | 11 |

L10 | A1, A2, S2 | 16 |

L11 | Amyg, PHC, CCs | 17 |

L12 | HC, PHC, TCv | 2 |

L13 | PFCpol, PFCm, PFCdm | 9 |

L14 | PFCvl, G, PMCvl | 8 |

L15 | TCpol, Amyg, PFCorb | 20 |

L16 | CCa, PFCdm, PFCdl | 12 |

L17 | IP, TCs, S2 | 14 |

L18 | S1, M1, PCs | 3 |

L19 | PFCdl, CCa, PFCcl | 6 |

L20 | TCv, PHC, TCi | 1 |

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**MDPI and ACS Style**

Gaglioti, G.; Nieus, T.R.; Massimini, M.; Sarasso, S.
Investigating the Impact of Local Manipulations on Spontaneous and Evoked Brain Complexity Indices: A Large-Scale Computational Model. *Appl. Sci.* **2024**, *14*, 890.
https://doi.org/10.3390/app14020890

**AMA Style**

Gaglioti G, Nieus TR, Massimini M, Sarasso S.
Investigating the Impact of Local Manipulations on Spontaneous and Evoked Brain Complexity Indices: A Large-Scale Computational Model. *Applied Sciences*. 2024; 14(2):890.
https://doi.org/10.3390/app14020890

**Chicago/Turabian Style**

Gaglioti, Gianluca, Thierry Ralph Nieus, Marcello Massimini, and Simone Sarasso.
2024. "Investigating the Impact of Local Manipulations on Spontaneous and Evoked Brain Complexity Indices: A Large-Scale Computational Model" *Applied Sciences* 14, no. 2: 890.
https://doi.org/10.3390/app14020890