Physical review. E, Statistical, nonlinear, and soft matter physics, 2001
We use a multifractal formalism to study the effect of stochastic resonance in a noisy bistable s... more We use a multifractal formalism to study the effect of stochastic resonance in a noisy bistable system driven by various input signals. To characterize the response of a stochastic bistable system we introduce a new measure based on the calculation of a singularity spectrum for a return time sequence. We use wavelet transform modulus maxima method for the singularity spectrum computations. It is shown that the degree of multifractality defined as a width of singularity spectrum can be successfully used as a measure of complexity both in the case of periodic and aperiodic (stochastic or chaotic) input signals. We show that in the case of periodic driving force, singularity spectrum can change its structure qualitatively becoming monofractal in the regime of stochastic synchronization. This fact allows us to consider the degree of multifractality as a new measure of stochastic synchronization also. Moreover, our calculations have shown that the effect of stochastic resonance can be ca...
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Papers by A. Silchenko
of the intracellular calcium concentration or can exhibit self-
sustained spontaneous activity. Both evoked and spontaneous astrocytic calcium oscillations are accompanied by exocytosis of glutamate caged in astrocytes leading to paroxysmal depolarization shifts (PDS) in neighboring neurons. Here, we present a simple mathematical model of the interaction between astrocytes and neurons that is able to numerically reproduce the experimental results concerning the initiation of the PDS. The timing of glutamate release from the astrocyte is studied by means of a combined modeling of a vesicle cycle and the dynamics of SNARE-proteins. The neuronal slow inward currents (SICs), induced by the astrocytic glutamate and leading to PDS, are modeled via the activation of presynaptic glutamate receptors. The dependence of the bi-directional communication between neurons and astrocytes on
the concentration of glutamate transporters is analyzed, as
well. Our numerical results are in line with experimental
findings showing that astrocyte can induce synchronous PDSs
in neighboring neurons, resulting in a transient synchronous
spiking activity.
activity. To reveal the directionality of coupling and time delays between interacting multi-scale signals,
we use a combination of a data-driven technique called empirical mode decomposition (EMD) and partial
directed coherence (PDC) together with the instantaneous causality test (ICT). EMD is used to separate multiple processes associated with different frequency bands, while PDC and ICT allow to explore directionality and characteristic time delays, respectively. We computationally validate our approach for the cases of both stochastic and chaotic oscillatory systems with different types of coupling. Moreover, we apply our approach to the analysis of the connectivity in different frequency bands between local field
potentials (LFPs) bilaterally recorded from the left and right of subthalamic nucleus (STN) in patients with Parkinson’s disease (PD). We reveal a bidirectional coupling between the left and right STN in the beta-band (10–30 Hz) for an akinetic PD patient and in the tremor band (3–5 Hz) for a tremor-dominant PD patient. We detect a short time delay, most probably reflecting the inter-hemispheric transmission time.
Additionally, in both patients we observe a long time delay of approximately a mean period of the beta-band activity in the akinetic PD patient or the tremor band activity in the tremor-dominant PD patient. These long delays may emerge in subcortico-thalamic loops or longer pathways, comprising reflex loops, respectively. We show that the replacement of EMD by conventional bandpass filtering complicates the
detection of directionality and leads to a spurious detection of time delays.
tion of neuronal activity in the basal ganglia in Parkin-
son’s disease (PD) has prompted the development of
novel neuromodulation paradigms. Coordinated reset
neuromodulation intends to specifically counteract
excessive synchronization and to induce cumulative
unlearning of pathological synaptic connectivity and
neuronal synchrony.
Methods: In this prospective case series, six PD
patients were evaluated before and after coordinated
reset neuromodulation according to a standardized
protocol that included both electrophysiological
recordings and clinical assessments.
Results: Coordinated reset neuromodulation of the
subthalamic nucleus (STN) applied to six PD patients
in an externalized setting during three stimulation days
induced a significant and cumulative reduction of beta
band activity that correlated with a significant improve-
ment of motor function.
Conclusions: These results highlight the potential
effects of coordinated reset neuromodulation of the
STN in PD patients and encourage further develop-
ment of this approach as an alternative to conventional
high-frequency deep brain stimulation in PD.
and motility of microglial cells via subsequent activation of P2Y2,12 as well as A3A/A2A adenosine receptors. The size and density of an insulating sheath around the electrode, formed by microglial cells, are important criteria for the optimization of the signal-to-noise ratio during microelectrode recordings or parameters of electrical current delivered to the brain tissue. Here, we study a purinergic
signaling pathway underlying the chemotactic motion of microglia towards implanted electrodes as well as the possible impact of an anti-inflammatory coating consisting of the interleukin-1 receptor antagonist. We present a model describing the formation of a stable aggregate around the electrode due to the joint chemo-attractive action of ATP and ADP and the mixed influence of extracellular adenosine. The bioactive coating is modeled as a source of chemo-repellent located near the electrode surface. The obtained analytical and numerical results allowed us to reveal the dependences of size and spatial location of the insulating sheath on the amount of released ATP and estimate the impact of
immune suppressive coating on the scarring process.
of the intracellular calcium concentration or can exhibit self-
sustained spontaneous activity. Both evoked and spontaneous astrocytic calcium oscillations are accompanied by exocytosis of glutamate caged in astrocytes leading to paroxysmal depolarization shifts (PDS) in neighboring neurons. Here, we present a simple mathematical model of the interaction between astrocytes and neurons that is able to numerically reproduce the experimental results concerning the initiation of the PDS. The timing of glutamate release from the astrocyte is studied by means of a combined modeling of a vesicle cycle and the dynamics of SNARE-proteins. The neuronal slow inward currents (SICs), induced by the astrocytic glutamate and leading to PDS, are modeled via the activation of presynaptic glutamate receptors. The dependence of the bi-directional communication between neurons and astrocytes on
the concentration of glutamate transporters is analyzed, as
well. Our numerical results are in line with experimental
findings showing that astrocyte can induce synchronous PDSs
in neighboring neurons, resulting in a transient synchronous
spiking activity.
activity. To reveal the directionality of coupling and time delays between interacting multi-scale signals,
we use a combination of a data-driven technique called empirical mode decomposition (EMD) and partial
directed coherence (PDC) together with the instantaneous causality test (ICT). EMD is used to separate multiple processes associated with different frequency bands, while PDC and ICT allow to explore directionality and characteristic time delays, respectively. We computationally validate our approach for the cases of both stochastic and chaotic oscillatory systems with different types of coupling. Moreover, we apply our approach to the analysis of the connectivity in different frequency bands between local field
potentials (LFPs) bilaterally recorded from the left and right of subthalamic nucleus (STN) in patients with Parkinson’s disease (PD). We reveal a bidirectional coupling between the left and right STN in the beta-band (10–30 Hz) for an akinetic PD patient and in the tremor band (3–5 Hz) for a tremor-dominant PD patient. We detect a short time delay, most probably reflecting the inter-hemispheric transmission time.
Additionally, in both patients we observe a long time delay of approximately a mean period of the beta-band activity in the akinetic PD patient or the tremor band activity in the tremor-dominant PD patient. These long delays may emerge in subcortico-thalamic loops or longer pathways, comprising reflex loops, respectively. We show that the replacement of EMD by conventional bandpass filtering complicates the
detection of directionality and leads to a spurious detection of time delays.
tion of neuronal activity in the basal ganglia in Parkin-
son’s disease (PD) has prompted the development of
novel neuromodulation paradigms. Coordinated reset
neuromodulation intends to specifically counteract
excessive synchronization and to induce cumulative
unlearning of pathological synaptic connectivity and
neuronal synchrony.
Methods: In this prospective case series, six PD
patients were evaluated before and after coordinated
reset neuromodulation according to a standardized
protocol that included both electrophysiological
recordings and clinical assessments.
Results: Coordinated reset neuromodulation of the
subthalamic nucleus (STN) applied to six PD patients
in an externalized setting during three stimulation days
induced a significant and cumulative reduction of beta
band activity that correlated with a significant improve-
ment of motor function.
Conclusions: These results highlight the potential
effects of coordinated reset neuromodulation of the
STN in PD patients and encourage further develop-
ment of this approach as an alternative to conventional
high-frequency deep brain stimulation in PD.
and motility of microglial cells via subsequent activation of P2Y2,12 as well as A3A/A2A adenosine receptors. The size and density of an insulating sheath around the electrode, formed by microglial cells, are important criteria for the optimization of the signal-to-noise ratio during microelectrode recordings or parameters of electrical current delivered to the brain tissue. Here, we study a purinergic
signaling pathway underlying the chemotactic motion of microglia towards implanted electrodes as well as the possible impact of an anti-inflammatory coating consisting of the interleukin-1 receptor antagonist. We present a model describing the formation of a stable aggregate around the electrode due to the joint chemo-attractive action of ATP and ADP and the mixed influence of extracellular adenosine. The bioactive coating is modeled as a source of chemo-repellent located near the electrode surface. The obtained analytical and numerical results allowed us to reveal the dependences of size and spatial location of the insulating sheath on the amount of released ATP and estimate the impact of
immune suppressive coating on the scarring process.