Criticality and partial synchronization analysis in Wilson-Cowan and Jansen-Rit neural mass models.

Synchronization is a phenomenon observed in neuronal networks involved in diverse brain activities. Neural mass models such as Wilson-Cowan (WC) and Jansen-Rit (JR) manifest synchronized states. Despite extensive research on these models over the past several decades, their potential of manifesting second-order phase transitions (SOPT) and criticality has not been sufficiently acknowledged. In this study, two networks of coupled WC and JR nodes with small-world topologies were constructed and Kuramoto order parameter (KOP) was used to quantify the amount of synchronization. In addition, we investigated the presence of SOPT using the synchronization coefficient of variation. Both networks reached high synchrony by changing the coupling weight between their nodes. Moreover, they exhibited abrupt changes in the synchronization at certain values of the control parameter not necessarily related to a phase transition. While SOPT was observed only in JR model, neither WC nor JR model showed power-law behavior. Our study further investigated the global synchronization phenomenon that is known to exist in pathological brain states, such as seizure. JR model showed global synchronization, while WC model seemed to be more suitable in producing partially synchronized patterns.

Gait-related beta-gamma phase amplitude coupling in the subthalamic nucleus of parkinsonian patients.

Analysis of coupling between the phases and amplitudes of neural oscillations has gained increasing attention as an important mechanism for large-scale brain network dynamics. In Parkinson's disease (PD), preliminary evidence indicates abnormal beta-phase coupling to gamma-amplitude in different brain areas, including the subthalamic nucleus (STN). We analyzed bilateral STN local field potentials (LFPs) in eight subjects with PD chronically implanted with deep brain stimulation electrodes during upright quiet standing and unperturbed walking. Phase-amplitude coupling (PAC) was computed using the Kullback-Liebler method, based on the modulation index. Neurophysiological recordings were correlated with clinical and kinematic measurements and individual molecular brain imaging studies ([123I]FP-CIT and single-photon emission computed tomography). We showed a dopamine-related increase in subthalamic beta-gamma PAC from standing to walking. Patients with poor PAC modulation and low PAC during walking spent significantly more time in the stance and double support phase of the gait cycle. Our results provide new insights into the subthalamic contribution to human gait and suggest cross-frequency coupling as a gateway mechanism to convey patient-specific information of motor control for human locomotion.

Intelligibility of speech in Parkinson's disease relies on anatomically segregated subthalamic beta oscillations.

BACKGROUND: Speech impairment is commonly reported in Parkinson's disease and is not consistently improved by available therapies - including deep brain stimulation of the subthalamic nucleus (STN-DBS), which can worsen communication performance in some patients. Improving the outcome of STN-DBS on speech is difficult due to our incomplete understanding of the contribution of the STN to fluent speaking. OBJECTIVE: To assess the relationship between subthalamic neural activity and speech production and intelligibility. METHODS: We investigated bilateral STN local field potentials (LFPs) in nine parkinsonian patients chronically implanted with DBS during overt reading. LFP spectral features were correlated with clinical scores and measures of speech intelligibility. RESULTS: Overt reading was associated with increased beta-low ([1220) Hz) power in the left STN, whereas speech intelligibility correlated positively with beta-high ([2030) Hz) power in the right STN. CONCLUSION: We identified separate contributions from frequency and brain lateralization of the STN in the execution of an overt reading motor task and its intelligibility. This subcortical organization could be exploited for new adaptive stimulation strategies capable of identifying the occurrence of speaking behavior and facilitating its functional execution.

Effects of Contralateral Deep Brain Stimulation and Levodopa on Subthalamic Nucleus Oscillatory Activity and Phase-Amplitude Coupling.

BACKGROUND: The modulatory effects of medication and deep brain stimulation (DBS) on subthalamic nucleus (STN) neural activity in Parkinson's disease have been widely studied. However, effects on the contralateral side to the stimulated STN, in particular, changes in local field potential (LFP) oscillatory activity and phase-amplitude coupling (PAC), have not yet been reported. OBJECTIVE: The aim of this study was to examine changes in STN LFP activity across a range of frequency bands and STN PAC for different combinations of DBS and medication on/off on the side contralateral to the applied stimulation. MATERIALS AND METHODS: We examined STN LFPs that were recorded using externalized leads from eight parkinsonian patients during unilateral DBS from the side contralateral to the stimulation. LFP spectral power in alpha (5 to ∼13 Hz), low beta (13 to ∼20 Hz), high beta (20-30 Hz), and high gamma plus high-frequency oscillation (high gamma+HFO) (100-400 Hz) bands were estimated for different combinations of medication and unilateral stimulation (off/on). PAC between beta and high gamma+HFO in the STN LFPs was also investigated. The effect of the condition was examined using linear mixed models. RESULTS: PAC in the STN LFP was reduced by DBS when compared to the baseline condition (no medication and stimulation). Medication had no significant effect on PAC. Alpha power decreased with DBS, both alone and when combined with medication. Beta power decreased with DBS, medication, and DBS and medication combined. High gamma+HFO power increased during the application of contralateral DBS and was unaltered by medication. CONCLUSIONS: The results provide new insights into the effects of DBS and levodopa on STN LFP PAC and oscillatory activity on the side contralateral to stimulation. These may have important implications in understanding mechanisms underlying motor improvements with DBS, including changes on both contralateral and ipsilateral sides, while suggesting a possible role for contralateral sensing during unilateral DBS.

Cortical network effects of subthalamic deep brain stimulation in a thalamo-cortical microcircuit model.

Objective. High frequency deep brain stimulation (DBS) of the subthalamic nucleus (STN) suppresses excessive beta band (∼13-30 Hz) activity of the motor cortex in Parkinson's disease (PD). While the mechanisms of action of STN DBS are not well-understood, strong evidence supports a role for cortical network modulating effects elicited by antidromic activation of cortical axons via the hyperdirect pathway.Approach. A spiking model of the thalamo-cortical microcircuit was developed to examine modulation of cortical network activity by antidromic STN DBS, mediated by direct activation of deep pyramidal neurons (PNs) and subsequent indirect activation of other thalamo-cortical structures.Main results. Increasing synaptic coupling strength from cortical granular to superficial layers, from inhibitory neurons to deep PNs, and from thalamus reticular to relay cells, along with thalamocortical connection strength, accompanied by reduced coupling from cortical superficial to granular layers, from thalamus relay cells to reticular neurons, and corticothalamic connection strength, led to increased beta activity and neural synchrony, as observed in PD. High frequency DBS desynchronized correlated neural activity, resulting in clusters of both excited and inhibited deep cortical PNs. The emergence of additional frequency components in the local field potential (LFP), and increased power at subharmonics of the DBS frequency as observed in patients with dyskinesia during DBS, occurred under different stimulus amplitudes and frequencies. While high-frequency (>100 Hz) DBS suppressed the LFP beta power, low-frequency (<40 Hz) DBS increased beta power when more than 10% of PNs were activated, but reduced the total beta power at lower levels of neural activation.Significance. The results suggest a potential mechanism for experimentally observed alterations in cortical neural activity during DBS via the propagation of DBS stimuli throughout the cortical network, modulated by short-term synaptic plasticity, and the emergence of resonance due to interaction of DBS with existing M1 rhythms by engaging feedforward-feedback loops.

Theoretical principles of deep brain stimulation induced synaptic suppression.

BACKGROUND: Deep brain stimulation (DBS) is a successful clinical therapy for a wide range of neurological disorders; however, the physiological mechanisms of DBS remain unresolved. While many different hypotheses currently exist, our analyses suggest that high frequency (∼100 Hz) stimulation-induced synaptic suppression represents the most basic concept that can be directly reconciled with experimental recordings of spiking activity in neurons that are being driven by DBS inputs. OBJECTIVE: The goal of this project was to develop a simple model system to characterize the excitatory post-synaptic currents (EPSCs) and action potential signaling generated in a neuron that is strongly connected to pre-synaptic glutamatergic inputs that are being directly activated by DBS. METHODS: We used the Tsodyks-Markram (TM) phenomenological synapse model to represent depressing, facilitating, and pseudo-linear synapses driven by DBS over a wide range of stimulation frequencies. The EPSCs were then used as inputs to a leaky integrate-and-fire neuron model and we measured the DBS-triggered post-synaptic spiking activity. RESULTS: Synaptic suppression was a robust feature of high frequency stimulation, independent of the synapse type. As such, the TM equations were used to define alternative DBS pulsing strategies that maximized synaptic suppression with the minimum number of stimuli. CONCLUSIONS: Synaptic suppression provides a biophysical explanation to the intermittent, but still time-locked, post-synaptic firing characteristics commonly seen in DBS experimental recordings. Therefore, network models attempting to analyze or predict the effects of DBS on neural activity patterns should integrate synaptic suppression into their simulations.

A Thalamo-Cortex Microcircuit Model of Beta Oscillations in the Parkinsonian Motor Cortex.

Exaggerated beta oscillations (~13-30 Hz) observed in the cortical areas of the brain is one of the characteristics of disrupted information flow in the primary motor cortex in Parkinson's disease (PD). However, the mechanism underlying the generation of these enhanced beta rhythms remains unclear. The thalamo-cortex microcircuit (TCM) contains reciprocal synaptic connections that generate low frequency oscillations in the microcircuit in healthy conditions. Recent studies suggest that alterations in synaptic connections both within and between the cortex and thalamus play a critical role in the generation of pathological beta rhythms in PD. In this study, we examine this hypothesis in a spiking neuronal network model of the TCM. The model is compared and validated against neural firing patterns recorded in rodent models of PD from the literature.

Action potential initiation, propagation, and cortical invasion in the hyperdirect pathway during subthalamic deep brain stimulation.

BACKGROUND: High frequency (∼130 Hz) deep brain stimulation (DBS) of the subthalamic region is an established clinical therapy for the treatment of late stage Parkinson's disease (PD). Direct modulation of the hyperdirect pathway, defined as cortical layer V pyramidal neurons that send an axon collateral to the subthalamic nucleus (STN), has emerged as a possible component of the therapeutic mechanisms. However, numerous questions remain to be addressed on the basic biophysics of hyperdirect pathway stimulation. OBJECTIVE: Quantify action potential (AP) initiation, propagation, and cortical invasion in hyperdirect neurons during subthalamic stimulation. METHODS: We developed an anatomically and electrically detailed computational model of hyperdirect neuron stimulation with explicit representation of the stimulating electric field, axonal response, AP propagation, and synaptic transmission. RESULTS: We found robust AP propagation throughout the complex axonal arbor of the hyperdirect neuron. Even at therapeutic DBS frequencies, stimulation induced APs could reach all of the intracortical axon terminals with ∼100% fidelity. The functional result of this high frequency axonal driving of the thousands of synaptic connections made by each directly stimulated hyperdirect neuron is a profound synaptic suppression that would effectively disconnect the neuron from the cortical circuitry. CONCLUSIONS: The synaptic suppression hypothesis integrates the fundamental biophysics of electrical stimulation, axonal transmission, and synaptic physiology to explain a generic mechanism of DBS.

Mode-locking behavior of Izhikevich neurons under periodic external forcing.

Many neurons in the auditory system of the brain must encode periodic signals. These neurons under periodic stimulation display rich dynamical states including mode locking and chaotic responses. Periodic stimuli such as sinusoidal waves and amplitude modulated sounds can lead to various forms of n:m mode-locked states, in which a neuron fires n action potentials per m cycles of the stimulus. Here, we study mode-locking in the Izhikevich neurons, a reduced model of the Hodgkin-Huxley neurons. The Izhikevich model is much simpler in terms of the dimension of the coupled nonlinear differential equations compared with other existing models, but excellent for generating the complex spiking patterns observed in real neurons. We obtained the regions of existence of the various mode-locked states on the frequency-amplitude plane, called Arnold tongues, for the Izhikevich neurons. Arnold tongue analysis provides useful insight into the organization of mode-locking behavior of neurons under periodic forcing. We find these tongues for both class-1 and class-2 excitable neurons in both deterministic and noisy regimes.