Leonid L. Rubchinsky

Neural dynamics in Parkinsonian brain: The boundary between synchronized and nonsynchronized dynamics

Synchronous oscillatory dynamics is frequently observed in the human brain. We analyze the fine temporal structure of phase-locking in a realistic network model and match it with the experimental data from Parkinsonian patients. We show that the experimentally observed intermittent synchrony can be generated just by moderately increased coupling strength in the basal ganglia circuits due to the lack of dopamine. Comparison of the experimental and modeling data suggest that brain activity in Parkinsons disease resides in the large boundary region between synchronized and nonsynchronized dynamics. Being on the edge of synchrony may allow for easy formation of transient neuronal assemblies.

Modeling facilitation and inhibition of competing motor programs in basal ganglia subthalamic nucleus–pallidal circuits

The motor symptoms of Parkinsons disease (PD) implicate the basal ganglia (BG) in some aspect of motor control, although the role the BG play in regulation of motor behavior is not completely understood. The modeling study presented here takes advantage of available cellular, systems, and clinical data on BG and PD to begin to build a biophysically based network model of pallidosubthalamic circuits of BG, to integrate this information and better understand the physiology of the normal BG and PD pathophysiology. The model reflects the experimentally supported hypothesis that the BG are involved in facilitation of the desired motor program and inhibition of competing motor programs that interfere with the desired movement. Our model network consists of subthalamic and pallidal (both external and internal segments) neural assemblies, with inputs from cortex and striatum. Functional subsets within each of the BG nuclei correspond to the desired motor program and the unwanted motor programs. A single compartment conductance-based model represents each subset. This network can discriminate between competing signals for motor program initiation, thus facilitating a single motor program. This ability depends on metabotropic γ-aminobutyric acid B projections from the external pallidum to subthalamic nucleus and rebound properties of subthalamic cells, as well as on the structure of projections between pallidum and subthalamus. The loss of this ability leads to hypokinesia, known PD motor deficits characterized by a slowness or inability to switch between motor programs.

On the Origin of Tremor in Parkinson’s Disease

The exact origin of tremor in Parkinson’s disease remains unknown. We explain why the existing data converge on the basal ganglia-thalamo-cortical loop as a tremor generator and consider a conductance-based model of subthalamo-pallidal circuits embedded into a simplified representation of the basal ganglia-thalamo-cortical circuit to investigate the dynamics of this loop. We show how variation of the strength of dopamine-modulated connections in the basal ganglia-thalamo-cortical loop (representing the decreasing dopamine level in Parkinson’s disease) leads to the occurrence of tremor-like burst firing. These tremor-like oscillations are suppressed when the connections are modulated back to represent a higher dopamine level (as it would be the case in dopaminergic therapy), as well as when the basal ganglia-thalamo-cortical loop is broken (as would be the case for ablative anti-parkinsonian surgeries). Thus, the proposed model provides an explanation for the basal ganglia-thalamo-cortical loop mechanism of tremor generation. The strengthening of the loop leads to tremor oscillations, while the weakening or disconnection of the loop suppresses them. The loop origin of parkinsonian tremor also suggests that new tremor-suppression therapies may have anatomical targets in different cortical and subcortical areas as long as they are within the basal ganglia-thalamo-cortical loop.

Detecting the temporal structure of intermittent phase locking

This study explores a method to characterize the temporal structure of intermittent phase locking in oscillatory systems. When an oscillatory system is in a weakly synchronized regime away from a synchronization threshold, it spends most of the time in parts of its phase space away from the synchronization state. Therefore characteristics of dynamics near this state (such as its stability properties and Lyapunov exponents or distributions of the durations of synchronized episodes) do not describe the systems dynamics for most of the time. We consider an approach to characterize the system dynamics in this case by exploring the relationship between the phases on each cycle of oscillations. If some overall level of phase locking is present, one can quantify when and for how long phase locking is lost, and how the system returns back to the phase-locked state. We consider several examples to illustrate this approach: coupled skewed tent maps, the stability of which can be evaluated analytically; coupled Rössler and Lorenz oscillators, undergoing through different intermittency types on the way to phase synchronization; and a more complex example of coupled neurons. We show that the obtained measures can describe the differences in the dynamics and temporal structure of synchronization and desynchronization events for the systems with a similar overall level of phase locking and similar stability of the synchronized state.

Failure of Delayed Feedback Deep Brain Stimulation for Intermittent Pathological Synchronization in Parkinson’s Disease

Suppression of excessively synchronous beta-band oscillatory activity in the brain is believed to suppress hypokinetic motor symptoms of Parkinson’s disease. Recently, a lot of interest has been devoted to desynchronizing delayed feedback deep brain stimulation (DBS). This type of synchrony control was shown to destabilize the synchronized state in networks of simple model oscillators as well as in networks of coupled model neurons. However, the dynamics of the neural activity in Parkinson’s disease exhibits complex intermittent synchronous patterns, far from the idealized synchronous dynamics used to study the delayed feedback stimulation. This study explores the action of delayed feedback stimulation on partially synchronized oscillatory dynamics, similar to what one observes experimentally in parkinsonian patients. We employ a computational model of the basal ganglia networks which reproduces experimentally observed fine temporal structure of the synchronous dynamics. When the parameters of our model are such that the synchrony is unphysiologically strong, the feedback exerts a desynchronizing action. However, when the network is tuned to reproduce the highly variable temporal patterns observed experimentally, the same kind of delayed feedback may actually increase the synchrony. As network parameters are changed from the range which produces complete synchrony to those favoring less synchronous dynamics, desynchronizing delayed feedback may gradually turn into synchronizing stimulation. This suggests that delayed feedback DBS in Parkinson’s disease may boost rather than suppress synchronization and is unlikely to be clinically successful. The study also indicates that delayed feedback stimulation may not necessarily exhibit a desynchronization effect when acting on a physiologically realistic partially synchronous dynamics, and provides an example of how to estimate the stimulation effect.

Short desynchronization episodes prevail in synchronous dynamics of human brain rhythms.

Neural synchronization is believed to be critical for many brain functions. It frequently exhibits temporal variability, but it is not known if this variability has a specific temporal patterning. This study explores these synchronization/desynchronization patterns. We employ recently developed techniques to analyze the fine temporal structure of phase-locking to study the temporal patterning of synchrony of the human brain rhythms. We study neural oscillations recorded by electroencephalograms in α and β frequency bands in healthy human subjects at rest and during the execution of a task. While the phase-locking strength depends on many factors, dynamics of synchrony has a very specific temporal pattern: synchronous states are interrupted by frequent, but short desynchronization episodes. The probability for a desynchronization episode to occur decreased with its duration. The transition matrix between synchronized and desynchronized states has eigenvalues close to 0 and 1 where eigenvalue 1 has multiplicity 1, and therefore if the stationary distribution between these states is perturbed, the system converges back to the stationary distribution very fast. The qualitative similarity of this patterning across different subjects, brain states and electrode locations suggests that this may be a general type of dynamics for the brain. Earlier studies indicate that not all oscillatory networks have this kind of patterning of synchronization/desynchronization dynamics. Thus, the observed prevalence of short (but potentially frequent) desynchronization events (length of one cycle of oscillations) may have important functional implications for the brain. Numerous short desynchronizations (as opposed to infrequent, but long desynchronizations) may allow for a quick and efficient formation and break-up of functionally significant neuronal assemblies.

Potential Mechanisms for Imperfect Synchronization in Parkinsonian Basal Ganglia

Neural activity in the brain of parkinsonian patients is characterized by the intermittently synchronized oscillatory dynamics. This imperfect synchronization, observed in the beta frequency band, is believed to be related to the hypokinetic motor symptoms of the disorder. Our study explores potential mechanisms behind this intermittent synchrony. We study the response of a bursting pallidal neuron to different patterns of synaptic input from subthalamic nucleus (STN) neuron. We show how external globus pallidus (GPe) neuron is sensitive to the phase of the input from the STN cell and can exhibit intermittent phase-locking with the input in the beta band. The temporal properties of this intermittent phase-locking show similarities to the intermittent synchronization observed in experiments. We also study the synchronization of GPe cells to synaptic input from the STN cell with dependence on the dopamine-modulated parameters. Earlier studies showed how the strengthening of dopamine-modulated coupling may lead to transitions from non-synchronized to partially synchronized dynamics, typical in Parkinsons disease. However, dopamine also affects the cellular properties of neurons. We show how the changes in firing patterns of STN neuron due to the lack of dopamine may lead to transition from a lower to a higher coherent state, roughly matching the synchrony levels observed in basal ganglia in normal and parkinsonian states. The intermittent nature of the neural beta band synchrony in Parkinsons disease is achieved in the model due to the interplay of the timing of STN input to pallidum and pallidal neuronal dynamics, resulting in sensitivity of pallidal output to the phase of the arriving STN input. Thus the mechanism considered here (the change in firing pattern of subthalamic neurons through the dopamine-induced change of membrane properties) may be one of the potential mechanisms responsible for the generation of the intermittent synchronization observed in Parkinsons disease.

Patterns in networks of oscillators formed via synchronization and oscillator death

Pattern formation via synchronization and oscillator death is considered in networks of diffusively coupled limit-cycle oscillators. Different examples of patterns and their dynamics are presented including nontrivial effects such as: (i) synchronized clusters induced by disorder and (ii) transitions from non-propagation to propagation of fronts via the intermittency.

Interaction of synchronized dynamics in cortex and basal ganglia in Parkinson's disease

Parkinsons disease pathophysiology is marked by increased oscillatory and synchronous activity in the beta frequency band in cortical and basal ganglia circuits. This study explores the functional connections between synchronized dynamics of cortical areas and synchronized dynamics of subcortical areas in Parkinsons disease. We simultaneously recorded neuronal units (spikes) and local field potentials (LFP) from subthalamic nucleus (STN) and electroencephalograms (EEGs) from the scalp in parkinsonian patients, and analysed the correlation between the time courses of the spike–LFP synchronization and inter‐electrode EEG synchronization. We found the (non‐invasively obtained) time course of the synchrony strength between EEG electrodes and the (invasively obtained) time course of the synchrony between spiking units and LFP in STN to be weakly, but significantly, correlated with each other. This correlation is largest for the bilateral motor EEG synchronization, followed by bilateral frontal EEG synchronization. Our observations suggest that there may be multiple functional modes by which the cortical and basal ganglia circuits interact with each other in Parkinsons disease: not only may synchronization be observed between some areas in cortex and the basal ganglia, but also synchronization within cortex and within basal ganglia may be related, suggesting potentially a more global functional interaction. More coherent dynamics in one brain region may modulate or activate the dynamics of another brain region in a more powerful way, causing correlations between changes in synchrony strength in the two regions.

Dynamical Reorganization of Synchronous Activity Patterns in Prefrontal Cortex–Hippocampus Networks During Behavioral Sensitization

Neural synchrony exhibits temporal variability and, therefore, the temporal patterns of synchronization and desynchronization may have functional relevance. This study employs novel time-series analysis to explore how neural signals become transiently phase locked and unlocked in the theta frequency band in prefrontal cortex and hippocampus of awake, behaving rats during repeated injections of the psychostimulant, d-Amphetamine (AMPH). Short (but frequent) desynchronized events dominate synchronized dynamics in each of the animals we examined. After the first AMPH injection, only increases in the relative prevalence of short desynchronization episodes (but not in average synchrony strength) were significant. Throughout sensitization, both strength and the fine temporal structure of synchrony (measured as the relative prevalence of short desynchronizations) were similarly altered with AMPH injections, with each measure decreasing in the preinjection epoch and increasing after injection. Sensitization also induced decoupling between locomotor activity and synchrony. The increase in numerous short desynchronizations (as opposed to infrequent, but long desynchronizations) in AMPH-treated animals may indicate that synchrony is easy to form yet easy to break. These data yield a novel insight into how synchrony is dynamically altered in cortical networks by AMPH and identify neurophysiological changes that may be important to understand the behavioral pathologies of addiction.