Increased Stability and Breakdown of Brain Effective Connectivity During Slow-Wave Sleep: Mechanistic Insights from Whole-Brain Computational Modelling

Abstract

Recent research has found that the human sleep cycle is characterised by changes in spatiotemporal patterns of brain activity. Yet, we are still missing a mechanistic explanation of the local neuronal dynamics underlying these changes. We used whole-brain computational modelling to study the differences in global brain functional connectivity and synchrony of fMRI activity in healthy humans during wakefulness and slow-wave sleep. We applied a whole-brain model based on the normal form of a supercritical Hopf bifurcation and studied the dynamical changes when adapting the bifurcation parameter for all brain nodes to best match wakefulness and slow-wave sleep. Furthermore, we analysed differences in effective connectivity between the two states. In addition to significant changes in functional connectivity, synchrony and metastability, this analysis revealed a significant shift of the global dynamic working point of brain dynamics, from the edge of the transition between damped to sustained oscillations during wakefulness, to a stable focus during slow-wave sleep. Moreover, we identified a significant global decrease in effective interactions during slow-wave sleep. These results suggest a mechanism for the empirical functional changes observed during slow-wave sleep, namely a global shift of the brain's dynamic working point leading to increased stability and decreased effective connectivity.

Figure 1

Data Analysis. In (a) the functional connectivity matrices averaged over participants are shown for the two different vigilance states. In (b) the difference of the mean of the upper triangle FC matrices (group average) between the awake and the sleep state are shown. The histogram (black) represents the distribution of the test-statistic under the null-hypothesis of no difference between vigilance states, whereas the green line shows the difference of the means of the empirical FC matrices. In the upper left corner the mean FCs and their standard deviations are shown. They are significantly different with a p-value of 0.0099. (c) demonstrates the difference between the mean synchrony in the awake state and the sleep state. The synchrony is calculated as the mean Kuramoto order parameter (see Methods). Again, the histogram represents the distribution of the test-statistic and the green line the difference between the synchrony in awake and sleep obtained from the empirical data. In the upper right corner the means and the standard deviations are shown, the mean synchrony is significantly higher in awake than in sleep with a p-value of 0.0099. In (d) the difference between the metastability in awake and in sleep is shown. The metastability is calculated as the standard deviation of the Kuramoto order parameter (see Methods). The histogram and the green line are to be read as in (b) and (c). In the upper right corner the metastability in awake and in sleep is represented, also in this modality a significant difference (p-value 0.0099) can be observed. In (e) the classification performance using a Gaussian classifier is shown for awake (violet) and sleep (yellow) test sets, respectively (see Methods). The vigilance state is predicted with high accuracy (83.33% and 94.44% for awake and sleep test sets, respectively) exceeding the 95th percentile of chance level.

Figure 2

Whole-brain model linking anatomical connections and FC. The anatomical connectivity data were obtained using DTI averaged over a group of healthy participants. Using the AAL 90 parcellation we obtained a structural connectivity (SC) matrix linking 90 cortical and subcortical nodes with each other anatomically. Based on this matrix, a Hopf whole-brain computational model is built which simulates the resting activity of the 90 coupled brain areas. The simulated functional connectivity matrix (FC_model) is then fitted to the empirical functional connectivity matrix (FC_emp) for different model parameter combinations using the Euclidean distance between the values of FC_model and FC_emp (see Methods). With this framework the model parameter space can be explored in order to find the optimal parameter combination for each brain state.

Figure 3

Whole-brain model parameter space exploration and fitting. (a) (i.,ii.) Euclidean distance between FC_model and FC_emp for different values of the global coupling strength G and the bifurcation parameter a in awake (i.) and sleep (ii.). Note that a is changed homogeneously over nodes. The optimal fit corresponds to a minimal Euclidean distance. In (b) the difference between the optimal Euclidean distance fit in awake and in sleep is shown as a function of G. The optimal fit is defined as the bifurcation parameter which corresponds to the minimum Euclidean distance for each value of G. The broken black lines represent the surrogate data constructed under the null-hypothesis of no difference between vigilance states, whereas the green line shows the difference between the optimal fit in awake and sleep. In the upper left corner the optimal fit for awake (violet) and sleep (yellow) is shown as a function of G. There is a significant difference between the two states from G = 1.6 onward with a corresponding p-value of 0.0396. In (c) the difference between the optimal Euclidean distance fit in awake and in sleep is displayed as a function of a. The broken black lines and the green line are to be read as in (b). In the upper right corner the optimal fit for awake (violet) and sleep (yellow) is shown as a function of a. There is a significant difference between the two states for −0.1 ≤ a ≤ 0 with a corresponding p-value of 0.0099. (d) represents the simulated global synchrony as a function of G and the bifurcation parameter a. The black line shows the optimal fit for the awake state, namely the closest value to the empirical global synchrony for each G, as a function of the global coupling strength. The gray line shows the same for the sleep state. In (e) the simulated metastability is displayed, also here as a function of G and the bifurcation parameter. The black and the gray line are to be read as in (d). Note the observable global shift to more negative bifurcation parameter values in (d) and (e).

Figure 4

Effective connectivity in awake and sleep. In (a) the final effective connectivity (EC) matrices are shown in awake (i.) and in sleep (ii.). The above row in (b) displays the empirical FC matrices in awake (i.) and in sleep (ii.), whereas in the row underneath the simulated FC matrices ((i.) awake, (ii.) sleep) after the EC optimisation procedure are shown. (c) demonstrates the fitting as a function of the iteration steps: in (i.) the Euclidean distances between FC_model and FC_emp for awake (violet) and sleep (yellow) are shown, and in (ii.) the Pearson correlation coefficients between the two matrices are represented (colour code as in (i.)). In order to assess the differences between the EC matrices in both modalities and to investigate whether the differences are of global or local nature, in (d) the node strength of the EC matrices are displayed (colour code as in (c)). With this, node-wise EC values are obtained. (e)(i.) shows the difference between the mean node strength in the awake and the sleep state. The histogram (black) represents the distribution of the test-statistic under the null-hypothesis of no difference between vigilance states, whereas the green line shows the difference of the mean node strengths of the actual EC matrices. In the upper left corner the mean node strengths and their standard deviations are shown. They are significantly different with a p-value of 0.0099. In (ii.) the number of nodes with node strength higher during wakefulness than during sleep are displayed. As before, the histogram represents the test-statistic and the green line the actual number of nodes. The number of nodes with higher node strength in awake than in sleep are significantly higher than obtained with the state-shuffling surrogate data (p-value: 0.0459). Note that the number of ROIs exhibiting higher EC in awake than in sleep is 84 out of 90 possible nodes, suggesting that the difference is of global nature.

Figure 5

Single node response to external stimulus for two different dynamic working regimes. In (a) the response – the absolute value of the simulated complex signal |Z| – of a single node is shown as a function of the input frequency for different input strengths F. ω ₀ is the intrinsic frequency, which was here set to 1. (b) displays the model response as a function of the input strength for different input frequencies. The red line shows hypothetical power law behaviour. Both (a) and (b) are simulated with the bifurcation parameter a very close to the bifurcation at a = 0. (c) and (d) show the same as (a) and (b), with the difference that the bifurcation parameter used for the simulations was set to a negative value in the noisy regime of the model. Note that for a close to the bifurcation the model response follows the power law $Z\propto F^{\frac{1}{3}}$ for an input frequency equal to ω ₀, whereas for a in the negative regime this is not the case: weak inputs are no more amplified. In this analysis no noise was added to the system.