The authors have declared that no competing interests exist.
Conceived and designed the experiments: CJS. Performed the experiments: WDH KM. Analyzed the data: WDH KM. Contributed reagents/materials/analysis tools: CJS. Wrote the paper: WDH. Helped drafting the manuscript: KM ECWvS PS CJS.
Brain connectivity studies have revealed that highly connected ‘hub’ regions are particularly vulnerable to Alzheimer pathology: they show marked amyloid-β deposition at an early stage. Recently, excessive local neuronal activity has been shown to increase amyloid deposition. In this study we use a computational model to test the hypothesis that hub regions possess the highest level of activity and that hub vulnerability in Alzheimer's disease is due to this feature. Cortical brain regions were modeled as neural masses, each describing the average activity (spike density and spectral power) of a large number of interconnected excitatory and inhibitory neurons. The large-scale network consisted of 78 neural masses, connected according to a human DTI-based cortical topology. Spike density and spectral power were positively correlated with structural and functional node degrees, confirming the high activity of hub regions, also offering a possible explanation for high resting state Default Mode Network activity. ‘Activity dependent degeneration’ (ADD) was simulated by lowering synaptic strength as a function of the spike density of the main excitatory neurons, and compared to random degeneration. Resulting structural and functional network changes were assessed with graph theoretical analysis. Effects of ADD included oscillatory slowing, loss of spectral power and long-range synchronization, hub vulnerability, and disrupted functional network topology. Observed transient increases in spike density and functional connectivity match reports in Mild Cognitive Impairment (MCI) patients, and may not be compensatory but pathological. In conclusion, the assumption of excessive neuronal activity leading to degeneration provides a possible explanation for hub vulnerability in Alzheimer's disease, supported by the observed relation between connectivity and activity and the reproduction of several neurophysiologic hallmarks. The insight that neuronal activity might play a causal role in Alzheimer's disease can have implications for early detection and interventional strategies.
An intriguing recent observation is that deposition of the amyloid-β protein, one of the hallmarks of Alzheimer's disease, mainly occurs in brain regions that are highly connected to other regions. To test the hypothesis that these ‘hub’ regions are more vulnerable due to a higher neuronal activity level, we examined the relation between brain connectivity and activity in a computational model of the human brain. Furthermore, we simulated progressive damage to brain regions based on their level of activity, and investigated its effect on the structure and dynamics of the remaining brain network. We show that brain hub regions are indeed the most active ones, and that by damaging networks according to regional activity levels, we can reproduce not only hub vulnerability but a range of phenomena encountered in actual neurophysiological data of Alzheimer patients as well: loss and slowing of brain activity in Alzheimer, loss of synchronization between areas, and similar changes in functional network organization. The results of this study suggest that excessive, connectivity dependent neuronal activity plays a role in the development of Alzheimer, and that the further investigation of factors regulating regional brain activity might help detect, elucidate and counter the disease mechanism.
Like many other complex networks, the human brain contains parts that are better connected to the rest than others: ‘hub’ regions. Evidence is increasing that a collection of brain hub regions forms a ‘structural core’ or ‘connectivity backbone’ that facilitates cognitive processing
The prevailing amyloid-cascade hypothesis of AD states that interstitial amyloid-beta proteins exert a toxic effect on surrounding neurons and synapses, thereby disturbing their function and eventually causing dementia
To test this hypothesis, a model is required that incorporates both large-scale connectivity as well as (micro-scale) neuronal activity. The macroscopic level is needed to provide a realistic structural human brain topology, including hub regions. Topological maps are well within reach nowadays, since an increasing amount of imaging data describing the human
Structural (anatomical) connectivity and functional (dynamical) connectivity are strongly related, but not always in a straightforward way
In short, by simulating neuronal dynamics on a network that is modeled on a realistic human cortical connectivity structure we explore the relation between large-scale connectivity and neuronal activity in normal and abnormal conditions. In the present study we use this approach to a) establish that cortical hub regions,
To assess whether the most highly connected cortical regions also showed the highest levels of neuronal activity, we plotted spike density and total power for all regions against the structural degree of nodes (
A: Six bins with ascending mean structural degrees are plotted against their average spike density and total power values. Nodes in the ‘very high’ degree bin were defined as hubs. Coupling strength (S) between neural masses was set to 1.5. Error bars indicate standard deviation within each bin. B: Similar plots as in the left panel, but for every region individually, and for three different coupling strengths S (see
Since activity level might also be influenced by a nodes functional role rather than its structural connectivity status, we performed comparisons between structural and functional degree (sum of all weighted
Cortical region |
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20 | 0.034 | ±0.004 | 435 | 420 |
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19 | 0.034 | ±0.003 | 426 | 408 |
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17 | 0.033 | ±0.004 | 428 | 447 |
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13 | 0.035 | ±0.004 | 395 | 228 |
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13 | 0.035 | ±0.004 | 408 | 296 |
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13 | 0.034 | ±0.004 | 404 | 275 |
|
13 | 0.032 | ±0.005 | 410 | 342 |
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13 | 0.032 | ±0.005 | 412 | 352 |
|
13 | 0.031 | ±0.005 | 403 | 312 |
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12 | 0.032 | ±0.004 | 403 | 203 |
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12 | 0.032 | ±0.005 | 395 | 226 |
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12 | 0.031 | ±0.004 | 404 | 285 |
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12 | 0.03 | ±0.004 | 398 | 278 |
Postcentral Gyrus L | 11 | 0.033 | ±0.004 | 396 | 227 |
Superior Frontal Gyrus, dorsal L | 11 | 0.032 | ±0.005 | 396 | 242 |
Postcentral Gyrus R | 11 | 0.031 | ±0.004 | 395 | 261 |
Superior Frontal Gyrus, dorsal R | 11 | 0.03 | ±0.005 | 396 | 234 |
Superior Temporal Gyrus R | 10 | 0.034 | ±0.004 | 397 | 127 |
Supplementary motor area R | 10 | 0.034 | ±0.005 | 398 | 188 |
Cuneus R | 10 | 0.034 | ±0.004 | 398 | 276 |
Superior Occipital Gyrus.L | 10 | 0.027 | ±0.004 | 398 | 264 |
Insula L | 9 | 0.035 | ±0.006 | 395 | 143 |
Inferior Temporal Gyrus L | 9 | 0.033 | ±0.004 | 395 | 184 |
Lingual Gyrus L | 9 | 0.033 | ±0.005 | 398 | 205 |
Supplementary motor area L | 9 | 0.032 | ±0.005 | 397 | 131 |
Supramarginal Gyrus R | 9 | 0.032 | ±0.005 | 393 | 175 |
Angular gyrus R | 9 | 0.03 | ±0.006 | 391 | 200 |
Middle Temporal Gyrus R | 9 | 0.03 | ±0.005 | 393 | 177 |
Fusiform Gyrus L | 9 | 0.03 | ±0.005 | 395 | 167 |
Superior Parietal Gyrus R | 9 | 0.029 | ±0.005 | 393 | 207 |
Middle Frontal Gyrus, R | 9 | 0.029 | ±0.004 | 400 | 61 |
Inferior Frontal Gyrus, orbital part L | 9 | 0.028 | ±0.006 | 398 | 130 |
Anterior Cingulate and paracingulate Gyri L | 9 | 0.028 | ±0.006 | 395 | 140 |
Cuneus L | 9 | 0.028 | ±0.004 | 397 | 86 |
Superior Frontal Gyrus, medial orbital R | 8 | 0.033 | ±0.004 | 393 | 109 |
Angular gyrus L | 8 | 0.032 | ±0.005 | 392 | 232 |
Superior Parietal Gyrus L | 8 | 0.03 | ±0.004 | 395 | 163 |
Inferior Frontal Gyrus, opercular part.R | 8 | 0.029 | ±0.006 | 400 | 64 |
Superior Frontal Gyrus, orbital part L | 8 | 0.028 | ±0.005 | 395 | 122 |
Superior Temporal Gyrus L | 8 | 0.028 | ±0.004 | 402 | 74 |
Middle Frontal Gyrus L | 8 | 0.028 | ±0.005 | 394 | 123 |
Temporal Pole: middle temporal gyrus R | 8 | 0.026 | ±0.005 | 396 | 113 |
Paracentral Lobule L | 8 | 0.026 | ±0.005 | 399 | 101 |
Anterior Cingulate and paracingulate gyri R | 8 | 0.026 | ±0.004 | 394 | 143 |
Fusiform Gyrus R | 8 | 0.024 | ±0.005 | 394 | 145 |
Superior Frontal Gyrus, medial orbital L | 7 | 0.032 | ±0.003 | 390 | 120 |
Median Cingulate and paracingulate gyri R | 7 | 0.031 | ±0.005 | 402 | 69 |
Inferior Occipital Gyrus L | 7 | 0.03 | ±0.005 | 397 | 127 |
Paracentral Lobule R | 7 | 0.029 | ±0.005 | 403 | 63 |
Inferior Frontal Gyrus, opercular part L | 7 | 0.028 | ±0.006 | 405 | 31 |
Supramarginal Gyrus L | 7 | 0.028 | ±0.006 | 398 | 75 |
Gyrus Rectus L | 7 | 0.027 | ±0.004 | 394 | 63 |
Rolandic operculum L | 7 | 0.027 | ±0.005 | 398 | 110 |
Inferior Frontal Gyrus, triangular part L | 7 | 0.027 | ±0.004 | 396 | 101 |
Superior Frontal Gyrus, orbital part R | 7 | 0.026 | ±0.004 | 405 | 37 |
Inferior Parietal L | 7 | 0.026 | ±0.004 | 402 | 42 |
Inferior Temporal Gyrus R | 7 | 0.015 | ±0.003 | 394 | 109 |
Inferior Occipital Gyrus R | 6 | 0.031 | ±0.004 | 409 | 23 |
Olfactory cortex R | 6 | 0.025 | ±0.004 | 396 | 134 |
Parahippocampal Gyrus L | 6 | 0.025 | ±0.006 | 404 | 47 |
Temporal Pole: middle temporal gyrus L | 6 | 0.025 | ±0.004 | 402 | 45 |
Inferior Parietal R | 6 | 0.025 | ±0.005 | 394 | 112 |
Median Cingulate and paracingulate gyri L | 6 | 0.024 | ±0.004 | 405 | 43 |
Parahippocampal Gyrus R | 6 | 0.023 | ±0.005 | 399 | 60 |
Rolandic operculum R | 6 | 0.023 | ±0.003 | 410 | 35 |
Posterior cingulate Gyrus L | 6 | 0.021 | ±0.003 | 404 | 43 |
Inferior Frontal Gyrus triangular part R | 6 | 0.02 | ±0.005 | 404 | 45 |
Inferior Frontal Gyrus, orbital part R | 5 | 0.024 | ±0.006 | 404 | 31 |
Insula R | 5 | 0.021 | ±0.004 | 404 | 17 |
Temporal Pole: superior temporal gyrus L | 5 | 0.018 | ±0.003 | 405 | 29 |
Middle Frontal Gyrus, orbital part L | 5 | 0.017 | ±0.004 | 390 | 163 |
Posterior Cingulate Gyrus R | 5 | 0.013 | ±0.002 | 397 | 225 |
Middle Frontal Gyrus, orbital part R | 4 | 0.022 | ±0.004 | 406 | 19 |
Gyrus Rectus R | 4 | 0.014 | ±0.002 | 405 | 29 |
Olfactory cortex L | 4 | 0.013 | ±0.003 | 400 | 37 |
Temporal Pole: superior temporal gyrus R | 3 | 0.017 | ±0.003 | 403 | 17 |
Heschl Gyrus L | 2 | 0.012 | ±0.002 | 405 | 9 |
Heschl Gyrus R | 1 | 0.012 | ±0.002 | 403 | 6 |
List of human cortical regions included in the model, ranked in order of descending structural degree. Regions printed in bold were classified as hub regions.
Functional degree is based on broadband (0.5–45 Hz) functional connectivity.
S (coupling strength) was set at 1.5; different values of S produced different absolute values but no changes in functional degree rank. T (time delay) was kept constant at 0.002 s for all experiments (see
Since, according to our hypothesis, ADD lowers connectivity based on activity level, it was expected to disrupt both structural and functional networks. First we investigated the effect of ADD on the structural network, and whether it had different effects on hubs versus non-hub regions. In ADD, every time-unit represents a small amount of damage to the system, so as to simulate gradual, cumulative degeneration. However, the amount of real, absolute time that is required for these successive steps is not known. Time as presented in these figures should therefore not be interpreted as days or years, but as arbitrary units of undetermined length.
A: All cortical regions binned according to initial structural degree from low to high values, and their average normalized node strengths at different stages of activity dependent degeneration (ADD). T = time. Error bars indicate standard error of the mean. B: All cortical regions binned according to initial structural degree from low to high values, and their average normalized node strengths at different stages of random degeneration (RD). T = time. Error bars indicate standard error of the mean.
Next, we studied the effect of ADD on network dynamics. When visually inspecting the model-generated data it was apparent that there were notable changes in oscillation amplitude over time. The power spectrum of hub regions initially showed much higher alpha power than in non-hub areas, and a surprising slightly lower alpha peak frequency (see
A: Average total power of hub and non-hub regions plotted over time, for both the ADD and RD procedure. Error bars indicate standard error of the mean. B: Correlation between structural degree and total power for all regions at different time points during ADD.
We subsequently performed a similar analysis for spike density changes over time due to ADD and RD (see
A: Average level of spike density during ADD is plotted for hubs and non-hubs. Error bars indicate standard deviations. B: Average level of spike density during RD is plotted for hubs and non-hubs. Error bars indicate standard deviations.
Since we expected ADD to affect functional network topology as well, we examined changes over time in the synchronization likelihood, as well as basic graph measures like average clustering coefficient, characteristic path length, and modularity. Since data generated by the NMM is most reliable in the alpha band, and AD-related functional network changes have most consistently been found in the lower alpha band, we report just the results of this representative band in
Mean levels of synchronization likelihood, modularity, clustering coefficient and path length during ADD are plotted for hubs and non-hubs. Error bars indicate standard deviations.
In this study we used a computational model with 78 dynamic neural masses coupled according to realistic human cortical topology to investigate the relation between connectivity and neuronal activity. We find that cortical hub regions have the highest level of intrinsic activity, and that the minimal assumption of higher local neuronal activity leading to more severe neurodegeneration can predict a range of AD hallmarks observed in patient data such as oscillatory slowing, a subsequent increase and breakdown of functional connectivity, and a loss of functional network integrity. These results suggest an ‘activity dependent degeneration’ (ADD) hypothesis of AD, and below we will discuss our findings and possible consequences in greater detail.
Our first aim was to find out whether the level of activity in a region is related to its degree of structural connectivity. An expected positive correlation was indeed found in repeated experiments across all degrees of connectivity (see
Still, although high neuronal activity in hub regions was a solid finding that might have been expected intuitively, it should ultimately be verified in experimental data. As can be judged from
Based on the findings in our first experiment, we expected that ADD would probably preferentially target hub regions, since they possessed the highest level of activity. Analyses of both structural and functional connectivity changes due to ADD seem to be in agreement with this expectation (see
Surprisingly, the steady loss of power is accompanied by an initial rise of spike density on average (see
The proposed relation between connectivity and activity is summarized for three different stages of ADD. Structural hubs have a higher baseline intrinsic activity, making them most susceptible to ADD. The second phase might represent the ‘Mild Cognitive Impairment’ (MCI) stage; structural connectivity declines steadily, but functional connectivity, power and spike density initially increase, leading to a pathologic spiral of increasing activity and metabolic burden in progressively weaker neurons. In the third “AD” phase, the damaged neurons and decreasing structural connectivity can no longer support the high demands, and the network collapses.
Several authors have argued for a prominent role of neuronal disinhibition in AD pathophysiology: for example, Gleichmann et al. propose a process they call ‘homeostatic disinhibition’, which is based on a different underlying mechanism but might explain the higher prevalence of epilepsy that is seen in AD, reduced gamma band activity, and, interestingly, the increase in neuronal activity as measured by fMRI
An early but transient rise was also found in functional connectivity results (see
Finally, the ADD induced changes in functional network topology, such as the weakening of small-world structure and modularity (see
The results of this study suggest that hub regions are vulnerable due to their intrinsically high activity level. The assumption of activity dependent degeneration leads to hub vulnerability along with many neurophysiologic features of AD (i.e. as found in quantitative EEG and MEG literature). A recently conducted large fMRI study demonstrated that highly connected cortical regions like the precuneus are even stronger hubs in females than in males: could this perhaps explain the higher levels of early amyloid deposition ánd the higher prevalence of AD in women
In addition to the presumed role of disinhibition mentioned in the previous paragraph, a prominent role of excessive neuronal activity in AD pathogenesis has been suggested before: several studies have demonstrated a direct link between neuronal activity and the development of amyloid plaques in transgenic mice
Excessive neuronal activity might be a common pathway through which many of the known risk factors enlarge the chance to develop Alzheimer pathology. Hub regions are most likely to display activity-dependent pathology, since they have the highest intrinsic neuronal activity (which is further amplified in the initial phase of ADD).
This line of reasoning implies that changes in brain activity and connectivity are already involved in the very early stages of AD pathology. In this regard, it is interesting to note that an increasing number of studies show that changes in activity and functional connectivity can be detected before cognitive complaints arise or pathological levels of amyloid are detected with PET and CSF analysis
Although activity dependent degeneration is quite different from amyloid-induced damage, they need not be mutually exclusive: chronic, excessive activity might lead to amyloid deposition, which in turn causes aberrant activity and neuronal damage: a pathological cycle with different stages (see also
Several recent studies use similar computational modeling approaches to examine AD related neurophysiological phenomena: Bhattacharya et al. focus on thalamo-cortico-thalamic circuitry and its relation with alpha band power in AD
Various methodological choices might have affected our results, and should be taken into account when interpreting them. First, although the DTI-derived connectivity matrix that served as the basis of our model is in our opinion a solid overall large-scale representation of human cortical connectivity, it was based on data of healthy young adults
The main motivation to use an NMM network of this size was the observation that topographical maps and atlases of the human cerebral cortex of this order of magnitude are quite common in macroscopic structural and functional connectivity studies (for an overview, please refer to
Varying the structural coupling strength S in our neural mass model can lead to different results, and therefore we have reported its influence on our outcomes. Similarly, the arbitrary ‘loss’-rate parameter of the ADD function will affect the speed of the degeneration process. However, since we were mainly concerned with a topological ‘hub versus non-hub’ comparison, the absolute rate of degeneration was of minor importance for this study. Moreover, loss-rates were equally applied to
Observations from this study that could be explored further include ADD-induced changes in structural network topology, the relation between spike density and anatomical region, and the lower alpha peak frequency in hub regions (see
In this study we used a neural mass model with DTI-based human topology to demonstrate that brain hub regions possess the highest levels of neuronal activity. Moreover, ‘Activity dependent degeneration’ (ADD), a damage model motivated by this observation, generates many AD-related neurophysiologic features such as oscillatory slowing, disruption of functional network topology and hub vulnerability. Early-stage, transient rises of firing rate and functional connectivity in ADD matches observations in pre-clinical AD patients, suggesting that this chain of events is not compensatory, but pathological. Overall, the results of this study favor a central role of neuronal activity and connectivity in the development of Alzheimer's disease.
In this study we simulated neurophysiologic activity of 78 Neural Mass Models embedded in a realistic structural cortical network topology to evaluate hypotheses about the relation between (structural and functional) connectivity and neuronal activity. The output of this model provides information about the neuronal activity level in the form of average voltage and spike density per region, and generates EEG-like data that can be subjected to further spectral, functional connectivity and graph theoretical analysis. Hypotheses about brain pathophysiology can be tested by artificially damaging structural or dynamical properties of the brain model. The outline of the analysis procedure employed in this study is depicted in
Multi-step procedure from the simulation of realistic human neurophysiological activity to analyzing and correlating connectivity and activity results.
We used a model of interconnected neural masses, where each neural mass represents a large population of connected excitatory and inhibitory neurons generating an EEG or MEG like signal. The model was recently employed in two other graph theoretical studies
A diffusion tensor imaging (DTI) based study by Gong et al. published in 2009 that focused on large-scale structural connectivity of the human cortex resulted in a connectivity matrix of 78 cortical regions
For the present study the model was extended to be able to deal with activity dependent evolution of connection strength between multiple coupled NMMs. Activity dependent degeneration (ADD) was realized by lowering the ‘synaptic’ coupling strength as a function of the spike density of the main excitatory neurons. For each neural mass the spike density of the main excitatory population is stored in a memory buffer that contains the firing rates of the last 20 steps in the model. Step size depends on the sample frequency. At each new iteration, the highest spike density value of the last 20 sample steps is determined and designated as maxAct. From maxAct a loss is determined according to the following relation:
Since spectral analysis is a common neurophysiological procedure that provides clinically relevant information in neurodegenerative dementia, we included this in our experiments. Fast Fourier transformation of the EEG-like oscillatory output signal was used to calculate for all separate regions the total power (absolute broadband power, 0–70 Hz) as well as the absolute power in the commonly used frequency bands delta (0.5–4 Hz), theta (4–8 Hz), lower alpha (8–10 Hz), higher alpha (10–13 Hz), beta (13–30 Hz) and gamma (30–45 Hz).
To quantify large-scale synchronization as a measure of interaction between different cortical areas, we used the Synchronization likelihood (SL), which is sensitive to both linear and non-linear coupling
Graph theoretical properties of the structural DTI network that were relevant for our hub study such as node degree, betweenness centrality, and local path length were published in the original article by Gong et al
Measure | Description | |
Degree | k | Number of connections of a node. Average for all nodes in a network produces the average degree K. |
Node strength (or weighted degree) | kw | Sum of all connection weights of a node. |
Clustering coefficient | Cp | Number of directly connected neighbors of a node divided by the maximally possible number of interconnected neighbors. The mean of this value for all nodes gives the average clustering coefficient; a measure of local integration. |
Path length | Lp | Shortest number of steps from one node to another. Average over all possible shortest paths is the characteristic path length of a network; a measure of global integration. |
Gamma | γ | Normalized average clustering coefficient, obtained by dividing Cp by the average Cp of a set randomized networks of the same size and density. |
Lambda | λ | Normalized characteristic path length, obtained by dividing Lp by the characteristic Lp of a set randomized networks of the same size and density. |
Modularity | Q | Expresses the strength of the modular character of a network. |
Glossary of graph theoretical measures used in this study. For exact definitions, please refer to
For the baseline, pre-ADD analysis in experiment 1 and 2, the data-generating procedure using the model was repeated twenty times to obtain a representative amount of data. On each run the subsequent spectral, functional connectivity and graph theoretical analysis was performed, and then all results of these twenty runs were averaged prior to further statistical analysis. Regional results were visualized using 6 bins ascending in structural degree, each containing 13 regions. All 13 regions in the bin with the highest mean degree were classified as hubs. Standard deviations of bins are displayed as error bars. For bivariate correlations Pearson's test was used.
Correlation between functional degree and total power in all frequency bands.
(TIF)
Relation between structural and functional connectivity. Left panel: matrix of the structural connections between all 78 cortical regions, adapted from Gong et al.
(TIFF)
Relation between structural and functional degree in all frequency bands. Error bars depict standard deviations within each bin after 20 simulated runs.
(TIF)
Specifications of the neural mass model. A: Schematic presentation of single neural mass model. The upper rectangle represents a mass of excitatory neurons, the lower rectangle a mass of inhibitory neurons. The state of each mass is modeled by an average membrane potential [Ve(t) and Vi(t)] and a pulse density [E(t) and I(t)]. Membrane potentials are converted to pulse densities by sigmoid functions S1[x] and S2[x]. Pulse densities are converted to membrane potentials by impulse responses he(t) and hi(t). C1 and C2 are coupling strengths between the two populations. P(t) and Ej(t) are pulse densities coming from thalamic sources or other cortical areas respectively. B: Coupling of two neural mass models. Two masses are coupled via excitatory connections. These are characterized by a fixed delay T and a strength g. C: Essential functions of the model. The upper left panel shows the excitatory [he(t)] and inhibitory [hi(t)] impulse responses of
(TIF)
Power spectrum of hubs. Power spectrum of a hub region (precuneus) in black, and a non-hub region in blue. Note the difference in power, but also the lower alpha peak of the hub region.
(TIFF)
Alpha peak frequency in hubs. The alpha peak frequency of all cortical regions plotted against their structural degree. A negative correlation can be observed (r = −0.53). Hubs (the 13 regions with highest structural degree) have a significantly lower alpha peak (p<0.001) compared to non-hubs.
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Overview of model parameters. The final model consisted of 78 of the NMMs as described above, which were coupled together based on the structural DTI network results from Gong et al.
(TIF)
Supporting information. 1. Relation between functional degree and total power. 2. Relation between structural and functional degree. 3. Network dynamics: the neural mass model. 4. Relation between structural degree and alpha power peak frequency.
(DOC)
The authors would like to thank Gaolang Gong and Alan C. Evans for their valuable comments, and for making available their DTI-based structural connectivity data.