Delayed Feedback-Based Suppression of Pathological Oscillations in a Neural Mass Model

Multi-timescale neuromodulation strategy for closed-loop deep brain stimulation in Parkinson's disease

Objective.Beta triggered closed-loop deep brain stimulation (DBS) shows great potential for improving the efficacy while reducing side effect for Parkinson's disease. However, there remain great challenges due to the dynamics and stochasticity of neural activities. In this study, we aimed to tune the amplitude of beta oscillations with different time scales taking into account influence of inherent variations in the basal ganglia-thalamus-cortical circuit.Approach. A dynamic basal ganglia-thalamus-cortical mean-field model was established to emulate the medication rhythm. Then, a dynamic target model was designed to embody the multi-timescale dynamic of beta power with milliseconds, seconds and minutes. Moreover, we proposed a closed-loop DBS strategy based on a proportional-integral-differential (PID) controller with the dynamic control target. In addition, the bounds of stimulation amplitude increments and different parameters of the dynamic target were considered to meet the clinical constraints. The performance of the proposed closed-loop strategy, including beta power modulation accuracy, mean stimulation amplitude, and stimulation variation were calculated to determine the PID parameters and evaluate neuromodulation performance in the computational dynamic mean-field model.Main results. The Results show that the dynamic basal ganglia-thalamus-cortical mean-field model simulated the medication rhythm with the fasted and the slowest rate. The dynamic control target reflected the temporal variation in beta power from milliseconds to minutes. With the proposed closed-loop strategy, the beta power tracked the dynamic target with a smoother stimulation sequence compared with closed-loop DBS with the constant target. Furthermore, the beta power could be modulated to track the control target under different long-term targets, modulation strengths, and bounds of the stimulation increment.Significance. This work provides a new method of closed-loop DBS for multi-timescale beta power modulation with clinical constraints.

Suppression of beta oscillations by delayed feedback in a cortex-basal ganglia-thalamus-pedunculopontine nucleus neural loop model

Excessive neural synchronization of neural populations in the beta (β) frequency range (12-35 Hz) is intimately related to the symptoms of hypokinesia in Parkinson's disease (PD). Studies have shown that delayed feedback stimulation strategies can interrupt excessive neural synchronization and effectively alleviate symptoms associated with PD dyskinesia. Work on optimizing delayed feedback algorithms continues to progress, yet it remains challenging to further improve the inhibitory effect with reduced energy expenditure. Therefore, we first established a neural mass model of the cortex-basal ganglia-thalamus-pedunculopontine nucleus (CBGTh-PPN) closed-loop system, which can reflect the internal properties of cortical and basal ganglia neurons and their intrinsic connections with thalamic and pedunculopontine nucleus neurons. Second, the inhibitory effects of three delayed feedback schemes based on the external globus pallidum (GPe) on β oscillations were investigated separately and compared with those based on the subthalamic nucleus (STN) only. Our results show that all four delayed feedback schemes achieve effective suppression of pathological β oscillations when using the linear delayed feedback algorithm. The comparison revealed that the three GPe-based delayed feedback stimulation strategies were able to have a greater range of oscillation suppression with reduced energy consumption, thus improving control performance effectively, suggesting that they may be more effective for the relief of Parkinson's motor symptoms in practical applications.

Improved control effect of pathological oscillations by using delayed feedback stimulation in neural mass model with pedunculopontine nucleus

BACKGROUND

The role of delayed feedback stimulation in the discussion of Parkinson's disease (PD) has recently received increasing attention. Stimulation of pedunculopontine nucleus (PPN) is an emerging treatment for PD. However, the effect of PPN in regulating PD is ignored, and the delayed feedback stimulation algorithm is facing some problems in parameter selection.

METHODS

On the basis of a neural mass model, we established a new network for PPN. Four types of delayed feedback stimulation schemes were designed, such as stimulating subthalamic nucleus (STN) with the local field potentials (LFPs) of STN nucleus, globus pallidus (GPe) with the LFPs of Gpe nucleus, PPN with the LFPs of Gpe nucleus, and STN with the LFPs of PPN nucleus.

RESULTS

In this study, we found that all four kinds of delayed feedback schemes are effective, suggesting that the algorithm is simple and more effective in experiments. More specifically, the other three control schemes improved the control performance and reduced the stimulation energy expenditure compared with traditional stimulating STN itself only.

CONCLUSION

PPN stimulation can affect the new network and help to suppress pathological oscillations for each neuron. We hope that our results can gain an insight into the future clinical treatment.

Transition behavior of the seizure dynamics modulated by the astrocyte inositol triphosphate noise

Epilepsy is a neurological disorder with recurrent seizures, which convey complex dynamical characteristics including chaos and randomness. Until now, the underlying mechanism has not been fully elucidated, especially the bistable property beneath the epileptic random induction phenomena in certain conditions. Inspired by the recent finding that astrocyte GTPase-activating protein (G-protein)-coupled receptors could be involved in stochastic epileptic seizures, we proposed a neuron-astrocyte network model, incorporating the noise of the astrocytic second messenger, inositol triphosphate (IP3) that is modulated by G-protein-coupled receptor activation. Based on this model, we have statistically analyzed the transitions of epileptic seizures by performing repeatable simulation trials. Our simulation results show that the increase in the IP3 noise intensity induces depolarization-block epileptic seizures together with an increase in neuronal firing frequency, consistent with corresponding experiments. Meanwhile, the bistable states of the seizure dynamics were present under certain noise intensities, during which the neuronal firing pattern switches between regular sparse spiking and epileptic seizure states. This random presence of epileptic seizures is absent when the noise intensity continues to increase, accompanying with an increase in the epileptic depolarization block duration. The simulation results also shed light on the fact that calcium signals in astrocytes play significant roles in the pattern formations of the epileptic seizure. Our results provide a potential pathway for understanding the epileptic randomness in certain conditions.

Development of Mechanistic Neural Mass (mNM) Models that Link Physiology to Mean-Field Dynamics

Brain rhythms emerge from the mean-field activity of networks of neurons. There have been many efforts to build mathematical and computational embodiments in the form of discrete cell-group activities-termed neural masses-to understand in particular the origins of evoked potentials, intrinsic patterns of activities such as theta, regulation of sleep, Parkinson's disease related dynamics, and mimic seizure dynamics. As originally utilized, standard neural masses convert input through a sigmoidal function to a firing rate, and firing rate through a synaptic alpha function to other masses. Here we define a process to build mechanistic neural masses (mNMs) as mean-field models of microscopic membrane-type (Hodgkin Huxley type) models of different neuron types that duplicate the stability, firing rate, and associated bifurcations as function of relevant slow variables - such as extracellular potassium - and synaptic current; and whose output is both firing rate and impact on the slow variables - such as transmembrane potassium flux. Small networks composed of just excitatory and inhibitory mNMs demonstrate expected dynamical states including firing, runaway excitation and depolarization block, and these transitions change in biologically observed ways with changes in extracellular potassium and excitatory-inhibitory balance.

Eliminating synchronization of coupled neurons adaptively by using feedback coupling with heterogeneous delays

In this paper, we present an adaptive scheme involving heterogeneous delay interactions to suppress synchronization in a large population of oscillators. We analytically investigate the incoherent state stability regions for several specific kinds of distributions for delays. Interestingly, we find that, among the distributions that we discuss, the exponential distribution may offer great convenience to the performance of our adaptive scheme because this distribution renders an unbounded stability region. Moreover, we demonstrate our scheme in the realization of synchronization elimination in some representative, realistic neuronal networks, which makes it possible to deepen the understanding and even refine the existing techniques of deep brain stimulation in the treatment of some synchronization-induced mental disorders.