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Elucidating how adaptive and maladaptive changes to the structural connectivity of brain networks influences neural synchrony, and how this structure–function coupling impacts cognition is an important question in human neuroscience. This study assesses these links in the default mode and executive control networks during resting state, a visual-motor task, and through computational modeling in the developing brain and in acquired brain injuries. Pediatric brain tumor survivors were used as an injury model as they are known to exhibit cognitive deficits, structural connectivity compromise, and perturbations in neural communication. Focusing on information processing speed to assess cognitive performance, we demonstrate that during the presence and absence of specific task demands, structural connectivity of these critical brain networks directly influences neural communication and information processing speed, and white matter compromise has an indirect adverse impact on reaction time via perturbed neural synchrony. Further, when our experimentally acquired structural connectomes simulated neural activity, the resulting functional simulations aligned with our empirical results and accurately predicted cognitive group differences. Overall, our synergistic findings further our understanding of the neural underpinnings of cognition and when it is perturbed. Further establishing alterations in structural–functional coupling as biomarkers of cognitive impairments could facilitate early intervention and monitoring of these deficits.

Brain areas must be able to interact and share information in a time-varying, dynamic manner on a fast timescale. Such flexibility in information sharing has been linked to the synchronization of rhythm phases between areas. One definition of flexibility is the number of local maxima in the delayed mutual information curve between two connected areas. However, the precise relationship between phase synchronization and information sharing is not clear, nor is the flexibility in the face of the fixed structural connectivity and noise. Here, we consider two coupled oscillatory excitatory-inhibitory networks connected through zero-delay excitatory connections, each of which mimics a rhythmic brain area. We numerically compute phase-locking and delayed mutual information between the phases of excitatory local field potential (LFPs) of the two networks, which measures the shared information and its direction. The flexibility in information sharing is shown to depend on the dynamical origin of oscillations, and its properties in different regimes are found to persist in the presence of asymmetry in the connectivity as well as system heterogeneity. For coupled noise-induced rhythms (quasi-cycles), phase synchronization is robust even in the presence of asymmetry and heterogeneity. However, they do not show flexibility, in contrast to noise-perturbed rhythms (noisy limit cycles), which are shown here to exhibit two local information maxima, i.e., flexibility. For quasi-cycles, phase difference and information measures for the envelope-phase dynamics obtained from previous analytical work using the Stochastic Averaging Method (SAM) are found to be in good qualitative agreement with those obtained from the original dynamics. The relation between phase synchronization and communication patterns is not trivial, particularly in the noisy limit cycle regime. There, complex patterns of information sharing can be observed for a single value of the phase difference. The mechanisms reported here can be extended to I-I networks since their phase synchronizations are similar. Our results set the stage for investigating information sharing between several connected noisy rhythms in neural and other complex biological networks.

We derive a unified amplitude-phase decomposition for both noisy limit cycles and quasicycles; in the latter case, the oscillatory motion has no deterministic counterpart. We extend a previous amplitude-phase decomposition approach using the stochastic averaging method (SAM) for quasicycles by taking into account nonlinear terms up to order 3. We further take into account the case of coupled networks where each isolated network can be in a quasi- or noisy limit-cycle regime. The method is illustrated on two models which exhibit a deterministic supercritical Hopf bifurcation: the Stochastic Wilson-Cowan model of neural rhythms, and the Stochastic Stuart-Landau model in physics. At the level of a single oscillatory module, the amplitude process of each of these models decouples from the phase process to the lowest order, allowing a Fokker-Planck estimate of the amplitude probability density. The peak of this density captures well the transition between the two regimes. The model describes accurately the effect of Gaussian white noise as well as of correlated noise. Bursting epochs in the limit-cycle regime are in fact favored by noise with shorter correlation time or stronger intensity. Quasicycle and noisy limit-cycle dynamics are associated with, respectively, Rayleigh-type and Gaussian-like amplitude densities. This provides an additional tool to distinguish quasicycle from limit-cycle origins of bursty rhythms. The case of multiple oscillatory modules with excitatory all-to-all delayed coupling results in a system of stochastic coupled amplitude-phase equations that keeps all the biophysical parameters of the initial networks and again works across the Hopf bifurcation. The theory is illustrated for small heterogeneous networks of oscillatory modules. Numerical simulations of the amplitude-phase dynamics obtained through the SAM are in good agreement with those of the original oscillatory networks. In the deterministic and nearly identical oscillators limits, the stochastic Stuart-Landau model leads to the stochastic Kuramoto model of interacting phases. The approach can be tailored to networks with different frequency, topology, and stochastic inputs, thus providing a general and flexible framework to analyze noisy oscillations continuously across the underlying deterministic bifurcation.

We consider the phase locking of two delay-coupled quasi-cycles. A coupled envelope-phase system obtained via stochastic averaging enables a stability analysis. While for deterministic limit-cycle oscillators the coupling can produce in-phase, antiphase, and the intermediate “out-of-phase” locking (OPL) behavior via spontaneous symmetry breaking, such outcomes for the quasi-cycle case are shown to require instead both noise and coupling delay. The theory, which applies the stochastic averaging method to delayed dynamics, generates stochastic stability functions that predict the numerically observed OPL behavior as a function of all the system parameters. OPL for coupled quasi-cycles occurs for additive or multiplicative noise, and for coupled networks of excitatory and inhibitory neurons as well as networks of inhibitory neurons coupled to one another. Our theory also predicts that the bifurcation at which the in-phase state becomes unstable lies at smaller delays for stronger noise. The noise produces the realistic quasi-cycle rhythms and out-of-phase behavior, all the while causing random reversals of the phase leader. Asymmetry in the coupling between networks, as well as heterogeneity within each network, also allows for quasi-cycle OPL, although it produces asymmetric bifurcations that bias the leadership towards one of the networks. These results are relevant to communication between brain areas and other networks that rely on noise-induced rather than noise-perturbed rhythms.