Golden rhythms as a theoretical framework for cross-frequency organization

While brain rhythms appear fundamental to brain function, why brain rhythms consistently organize into the small set of discrete frequency bands observed remains unknown. Here we propose that rhythms separated by factors of the golden ratio ($\phi=(1+ \sqrt{5})/2$) optimally support segregation and cross-frequency integration of information transmission in the brain. Organized by the golden ratio, pairs of transient rhythms support multiplexing by reducing interference between separate communication channels, and triplets of transient rhythms support integration of signals to establish a hierarchy of cross-frequency interactions. We illustrate this framework in simulation and apply this framework to propose four hypotheses.Comment: 8 figure

Gait-related frequency modulation of beta oscillatory activity in the subthalamic nucleus of parkinsonian patients

Background: Abnormal beta band activity in the subthalamic nucleus (STN) is known to be exaggerated in patients with Parkinson's disease, and the amplitude of such activity has been associated with akinetic rigid symptoms. New devices for deep brain stimulation (DBS) that operate by adapting the stimulation parameters generally rely on the detection of beta activity amplitude modulations in these patients. Movement-related frequency modulation of beta oscillatory activity has been poorly investigated, despite being an attractive variable for extracting information about basal ganglia activity. Objective: We studied the STN oscillatory activity associated with locomotion and proposed a new approach to extract movement related information from beta band activity. Methods: We recorded bilateral local field potential of the STN in eight parkinsonian patients implanted with DBS electrodes during upright quiet standing and unperturbed walking. Neurophysiological recordings were combined with kinematic measurements and individual molecular brain imaging studies. We then determined the information carried by the STN oscillatory activity about locomotion and we identified task-specific biomarkers. Results: We found a gait-related peak frequency modulation of the beta band of STN recordings of parkinsonian patients. This novel biomarker and the associated power modulations were highly informative to detect the walking state (with respect to standing) in each single patient. Conclusion: Frequency modulation in the human STN represents a fundamental aspect of information processing of locomotion. Our information-driven approach could significantly enrich the spectrum of Parkinson's neural markers, with input signals encoding ongoing tasks execution for an appropriate online tuning of DBS delivery

Phase description of oscillatory convection with a spatially translational mode

We formulate a theory for the phase description of oscillatory convection in a cylindrical Hele-Shaw cell that is laterally periodic. This system possesses spatial translational symmetry in the lateral direction owing to the cylindrical shape as well as temporal translational symmetry. Oscillatory convection in this system is described by a limit-torus solution that possesses two phase modes; one is a spatial phase and the other is a temporal phase. The spatial and temporal phases indicate the position and oscillation of the convection, respectively. The theory developed in this paper can be considered as a phase reduction method for limit-torus solutions in infinite-dimensional dynamical systems, namely, limit-torus solutions to partial differential equations representing oscillatory convection with a spatially translational mode. We derive the phase sensitivity functions for spatial and temporal phases; these functions quantify the phase responses of the oscillatory convection to weak perturbations applied at each spatial point. Using the phase sensitivity functions, we characterize the spatiotemporal phase responses of oscillatory convection to weak spatial stimuli and analyze the spatiotemporal phase synchronization between weakly coupled systems of oscillatory convection.Comment: 35 pages, 14 figures. Generalizes the phase description method developed in arXiv:1110.112

Short-Term EEG Spectral Pattern as a Single Event in EEG Phenomenology

Spectral decomposition, to this day, still remains the main analytical paradigm for the analysis of EEG oscillations. However, conventional spectral analysis assesses the mean characteristics of the EEG power spectra averaged out over extended periods of time and/or broad frequency bands, thus resulting in a “static” picture which cannot reflect adequately the underlying neurodynamic. A relatively new promising area in the study of EEG is based on reducing the signal to elementary short-term spectra of various types in accordance with the number of types of EEG stationary segments instead of using averaged power spectrum for the whole EEG. It is suggested that the various perceptual and cognitive operations associated with a mental or behavioural condition constitute a single distinguishable neurophysiological state with a distinct and reliable spectral pattern. In this case, one type of short-term spectral pattern may be considered as a single event in EEG phenomenology. To support this assumption the following issues are considered in detail: (a) the relations between local EEG short-term spectral pattern of particular type and the actual state of the neurons in underlying network and a volume conduction; (b) relationship between morphology of EEG short-term spectral pattern and the state of the underlying neurodynamical system i.e. neuronal assembly; (c) relation of different spectral pattern components to a distinct physiological mechanism; (d) relation of different spectral pattern components to different functional significance; (e) developmental changes of spectral pattern components; (f) heredity of the variance in the individual spectral pattern and its components; (g) intra-individual stability of the sets of EEG short-term spectral patterns and their percent ratio; (h) discrete dynamics of EEG short-term spectral patterns. Functional relevance (consistency) of EEG short-term spectral patterns in accordance with the changes of brain functional state, cognitive task and with different neuropsychopathologies is demonstrated

Towards a continuous dynamic model of the Hopfield theory on neuronal interaction and memory storage

The purpose of this work is to study the Hopfield model for neuronal interaction and memory storage, in particular the convergence to the stored patterns. Since the hypothesis of symmetric synapses is not true for the brain, we will study how we can extend it to the case of asymmetric synapses using a probabilistic approach. We then focus on the description of another feature of the memory process and brain: oscillations. Using the Kuramoto model we will be able to describe them completely, gaining the presence of synchronization between neurons. Our aim is therefore to understand how and why neurons can be seen as oscillators and to establish a strong link between this model and the Hopfield approach