Rationale:
Epilepsy manifests in macroscopic neural recordings as both oscillatory and aperiodic activity. Consistent observations across recording modalities, experiments, and neural systems find aperiodic activity with 1/f-like scaling, eliciting many alternative theories to explain this universal phenomenon. Many studies have sought to characterize and interpret this 1/f-like scaling in efforts to reveal mechanisms that support brain function and dysfunction. In patients with epilepsy, changes in 1/f-like scaling have been reported as a spectral biomarker of epileptogenicity and the seizure onset zone, related to changes in the balance of excitatory and inhibitory network activity.
Methods:
To analyze the types of phenomena that support 1/f-like scaling, we implement a general nonlinear dynamical system driven by noise. We first analyze this model in its general form, without specifying the biophysical mechanisms that produce the dynamics. We apply standard mathematical techniques to identify an equilibrium in the general model and determine the spectrum near this equilibrium. In doing so, we provide an explicit expression relating the general model dynamics to the aperiodic exponent, (i.e., the value of the exponent in 1/f-like scaling). We then illustrate how features of the general system manifest in practice by simulating biophysical models of neural activity and seizure dynamics at different spatial scales and estimating how the aperiodic exponent depends on different types of physically-interpretable noise.
Results:
We show in the general model that dynamics near an equilibrium produce aperiodic exponents between -4 and -2, consistent with the range of values reported in vivo for human subjects. We analyze the general model to show how different types of noise produce this range of aperiodic exponents observed in vivo. To show that these general mathematical results hold in diverse physical systems, we implement models of neural activity across different spatial scales and supported by different biophysical mechanisms, and models of seizure dynamics. Simulation analysis of these biophysical models show that linking 1/f-like activity to biophysical mechanisms depends on the model choice.
Conclusions:
We conclude that the 1/f-scaling commonly observed in neural activity is a natural consequence of a noise driven dynamical system. We propose that mechanistic interpretations of the aperiodic exponent in epilepsy should first account for the aperiodic activity that can be explained by noise driven dynamics alone.
Funding:
The authors were supported in part by NSF #1451384, NIH R01NS110669, and R01NS119483.