STN-GPe Network Research Articles

The network configuration in Parkinsonian state compensates network activity change caused by loss of dopamine.

Parkinson's disease is a movement disorder caused by dopamine depletion in the basal ganglia. Neural activity of the subthalamic nucleus (STN) and globus pallidus externus (GPe) in the basal ganglia are closely related to motor symptoms of Parkinson's disease. However, the pathogenesis of the disease and the transition from the normal state to the pathological state have yet to be elucidated. The functional organization of the GPe is gaining attention due to the recent finding that it consists of two distinct cell populations, namely prototypic GPe neurons and arkypallidal neurons. Identifying connectivity structures between these cell populations, as well as STN neurons, in relation to the dependence of the network activity on the dopaminergic effects is vital. In the present study, using a computational model of the STN-GPe network, we explored biologically plausible connectivity structures between these cell populations. We evaluated the experimentally reported neural activities of these cell types to elucidate the effects of dopaminergic modulation and changes caused by chronic dopamine depletion, such as strengthened connections in the neural activity of the STN-GPe network. Our results indicate that the arkypallidal neurons receive cortical inputs separately from the source for prototypic and STN neurons, suggesting that arkypallidal neurons might be responsible for an additional pathway with the cortex. Furthermore, changes caused by chronic dopamine depletion compensate for the loss of dopaminergic modulation. Changes caused by dopamine depletion itself likely induce the pathological activity observed in patients with Parkinson's disease. However, such changes counteract those of firing rates caused by loss of dopaminergic modulation. In addition, we observed that the STN-GPe tends to exhibit activity with pathological characteristics as side effects.

Adaptive closed-loop control strategy inhibiting pathological basal ganglia oscillations

The presence of pathological basal ganglia oscillations in the beta (12–35 Hz) frequency band is associated with Parkinson’s disease (PD). Suppressing the abnormal beta rhythm can effectively alleviate prominent PD movement disorders such as bradykinesia and rigidity. Brain stimulations, such as deep brain stimulation or transcranial stimulation, are effective therapeutic methods in managing the beta rhythm. However, electrostimulation using the current open-loop paradigm for stimulation is not optimal, especially when the controlled system experiences a substantial unknown disturbance. In this work we propose an adaptive radial basis function (ARBF) neural network strategy to achieve closed-loop brain stimulation based on real-time observed neural oscillation feedback. The underlying system is assumed to be an unknown nonlinear system, and the closed-loop strategy adaptively modulates the stimulation signal to cope with the abnormal neuronal discharge fluctuations, so as to eliminate the beta rhythm of the STN-GPe network. The proposed ARBF neural network closed-loop scheme is tested in a neural mass model composed of the subthalamic nucleus and external globus pallidus. It is shown that the performance of the ARBF controller is robust, including when internal synaptic connections within the basal ganglia network are enhanced to endogenously impact pathological conditions, and also when pathological oscillations are induced by exogenous cortical inputs. Simulation results demonstrate the effectiveness of the proposed closed-loop neuromodulation pattern based on an ARBF neural network. This work may help to develop DBS control systems with adaptive optimization and less network complexity.

FPGA-Based Real-Time Simulation Platform for Large-Scale STN-GPe Network.

The real-time simulation of large-scale subthalamic nucleus (STN)-external globus pallidus (GPe) network model is of great significance for the mechanism analysis and performance improvement of deep brain stimulation (DBS) for Parkinson's states. This paper implements the real-time simulation of a large-scale STN-GPe network containing 512 single-compartment Hodgkin-Huxley type neurons on the Altera Stratix IV field programmable gate array (FPGA) hardware platform. At the single neuron level, some resource optimization schemes such as multiplier substitution, fixed-point operation, nonlinear function approximation and function recombination are adopted, which consists the foundation of the large-scale network realization. At the network level, the simulation scale of network is expanded using module reuse method at the cost of simulation time. The correlation coefficient between the neuron firing waveform of the FPGA platform and the MATLAB software simulation waveform is 0.9756. Under the same physiological time, the simulation speed of FPGA platform is 75 times faster than the Intel Core i7-8700K 3.70 GHz CPU 32GB RAM computer simulation speed. In addition, the established platform is used to analyze the effects of temporal pattern DBS on network firing activities. The proposed large-scale STN-GPe network meets the need of real time simulation, which would be rather helpful in designing closed-loop DBS improvement strategies.

Self-Tuning Deep Brain Stimulation Controller for Suppression of Beta Oscillations: Analytical Derivation and Numerical Validation.

Closed-loop control strategies for deep brain stimulation (DBS) in Parkinson's disease offer the potential to provide more effective control of patient symptoms and fewer side effects than continuous stimulation, while reducing battery consumption. Most of the closed-loop methods proposed and tested to-date rely on controller parameters, such as controller gains, that remain constant over time. While the controller may operate effectively close to the operating point for which it is set, providing benefits when compared to conventional open-loop DBS, it may perform sub-optimally if the operating conditions evolve. Such changes may result from, for example, diurnal variation in symptoms, disease progression or changes in the properties of the electrode-tissue interface. In contrast, an adaptive or “self-tuning” control mechanism has the potential to accommodate slowly varying changes in system properties over a period of days, months, or years. Such an adaptive mechanism would automatically adjust the controller parameters to maintain the desired performance while limiting side effects, despite changes in the system operating point. In this paper, two neural modeling approaches are utilized to derive and test an adaptive control scheme for closed-loop DBS, whereby the gain of a feedback controller is continuously adjusted to sustain suppression of pathological beta-band oscillatory activity at a desired target level. First, the controller is derived based on a simplified firing-rate model of the reciprocally connected subthalamic nucleus (STN) and globus pallidus (GPe). Its efficacy is shown both when pathological oscillations are generated endogenously within the STN-GPe network and when they arise in response to exogenous cortical STN inputs. To account for more realistic biological features, the control scheme is then tested in a physiologically detailed model of the cortical basal ganglia network, comprised of individual conductance-based spiking neurons, and simulates the coupled DBS electric field and STN local field potential. Compared to proportional feedback methods without gain adaptation, the proposed adaptive controller was able to suppress beta-band oscillations with less power consumption, even as the properties of the controlled system evolve over time due to alterations in the target for beta suppression, beta fluctuations and variations in the electrode impedance.

Uncoupling the roles of firing rates and spike bursts in shaping the STN-GPe beta band oscillations.

The excess of 15-30 Hz (β-band) oscillations in the basal ganglia is one of the key signatures of Parkinson's disease (PD). The STN-GPe network is integral to generation and modulation of β band oscillations in basal ganglia. However, the role of changes in the firing rates and spike bursting of STN and GPe neurons in shaping these oscillations has remained unclear. In order to uncouple their effects, we studied the dynamics of STN-GPe network using numerical simulations. In particular, we used a neuron model, in which firing rates and spike bursting can be independently controlled. Using this model, we found that while STN firing rate is predictive of oscillations, GPe firing rate is not. The effect of spike bursting in STN and GPe neurons was state-dependent. That is, only when the network was operating in a state close to the border of oscillatory and non-oscillatory regimes, spike bursting had a qualitative effect on the β band oscillations. In these network states, an increase in GPe bursting enhanced the oscillations whereas an equivalent proportion of spike bursting in STN suppressed the oscillations. These results provide new insights into the mechanisms underlying the transient β bursts and how duration and power of β band oscillations may be controlled by an interplay of GPe and STN firing rates and spike bursts.

Beta-Band Resonance and Intrinsic Oscillations in a Biophysically Detailed Model of the Subthalamic Nucleus-Globus Pallidus Network.

Increased beta-band oscillatory activity in the basal ganglia network is associated with Parkinsonian motor symptoms and is suppressed with medication and deep brain stimulation (DBS). The origins of the beta-band oscillations, however, remains unclear with both intrinsic oscillations arising within the subthalamic nucleus (STN)—external globus pallidus (GPe) network and exogenous beta-activity, originating outside the network, proposed as potential sources of the pathological activity. The aim of this study was to explore the relative contribution of autonomous oscillations and exogenous oscillatory inputs in the generation of pathological oscillatory activity in a biophysically detailed model of the parkinsonian STN-GPe network. The network model accounts for the integration of synaptic currents and their interaction with intrinsic membrane currents in dendritic structures within the STN and GPe. The model was used to investigate the development of beta-band synchrony and bursting within the STN-GPe network by changing the balance of excitation and inhibition in both nuclei, and by adding exogenous oscillatory inputs with varying phase relationships through the hyperdirect cortico-subthalamic and indirect striato-pallidal pathways. The model showed an intrinsic susceptibility to beta-band oscillations that was manifest in weak autonomously generated oscillations within the STN-GPe network and in selective amplification of exogenous beta-band synaptic inputs near the network's endogenous oscillation frequency. The frequency at which this resonance peak occurred was determined by the net level of excitatory drive to the network. Intrinsic or endogenously generated oscillations were too weak to support a pacemaker role for the STN-GPe network, however, they were considerably amplified by sparse cortical beta inputs and were further amplified by striatal beta inputs that promoted anti-phase firing of the cortex and GPe, resulting in maximum transient inhibition of STN neurons. The model elucidates a mechanism of cortical patterning of the STN-GPe network through feedback inhibition whereby intrinsic susceptibility to beta-band oscillations can lead to phase locked spiking under parkinsonian conditions. These results point to resonance of endogenous oscillations with exogenous patterning of the STN-GPe network as a mechanism of pathological synchronization, and a role for the pallido-striatal feedback loop in amplifying beta oscillations.

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

Suppression of excessively synchronous beta frequency (12-35 Hz) oscillatory activity in the basal ganglia is believed to correlate with the alleviation of hypokinetic motor symptoms of the Parkinson's disease. Delayed feedback is an effective strategy to interrupt the synchronization and has been used in the design of closed-loop neuromodulation methods computationally. Although tremendous efforts in this are being made by optimizing delayed feedback algorithm and stimulation waveforms, there are still remaining problems in the selection of effective parameters in the delayed feedback control schemes. In most delayed feedback neuromodulation strategies, the stimulation signal is obtained from the local field potential (LFP) of the excitatory subthalamic nucleus (STN) neurons and then is administered back to STN itself only. The inhibitory external globus pallidus (GPe) nucleus in the excitatory-inhibitory STN-GPe reciprocal network has not been involved in the design of the delayed feedback control strategies. Thus, considering the role of GPe, this paper proposes three schemes involving GPe in the design of the delayed feedback strategies and compared their effectiveness to the traditional paradigm using STN only. Based on a neural mass model of STN-GPe network having capability of simulating the LFP directly, the proposed stimulation strategies are tested and compared. Our simulation results show that the four types of delayed feedback control schemes are all effective, even if with a simple linear delayed feedback algorithm. But the three new control strategies we propose here further improve the control performance by enlarging the oscillatory suppression space and reducing the energy expenditure, suggesting that they may be more effective in applications. This paper may guide a new approach to optimize the closed-loop deep brain stimulation treatment to alleviate the Parkinsonian state by retargeting the measurement and stimulation nucleus.

Delayed Feedback Frequency Adjustment for Deep Brain Stimulation of Subthalamic Nucleus Oscillations.

Neural oscillations within the Basal Ganglia (BG) circuitry are associated with Parkinson's Disease (PD) and are observable through the Local Field Potential (LFP) of the Subthalamic Nucleus (STN) or Globus Pallidus externa (GPe) neurons. LFP amplitude modulation in a delayed feedback protocol for Deep Brain Stimulation (DBS) is shown to destabilize the complex intermittent synchronous states. However, traditional High Frequency Stimulations (HFS) often intensify the synchronization of highly fluctuating neurons, are less efficient in activating all neurons in large scale networks and consume more battery of the DBS device. Here, we investigate the partially synchronous dynamics of a STN-GPe coupling network to examine the effect of frequency adjustment in the stimulation signal. The frequency of the stimulation signal is adjusted according to the nonlinear delayed feedback LFP of the STN population. Frequency adjustment protocol with a fixed stimulation amplitude is shown to increase the desynchronization efficiency and neuronal activation by 25% and 16.2%, respectively, while reducing the energy consumption by 31.5% compared to amplitude modulation methods for stimulation of large networks (1000 neurons).

Pulsatile desynchronizing delayed feedback for closed-loop deep brain stimulation.

High-frequency (HF) deep brain stimulation (DBS) is the gold standard for the treatment of medically refractory movement disorders like Parkinson’s disease, essential tremor, and dystonia, with a significant potential for application to other neurological diseases. The standard setup of HF DBS utilizes an open-loop stimulation protocol, where a permanent HF electrical pulse train is administered to the brain target areas irrespectively of the ongoing neuronal dynamics. Recent experimental and clinical studies demonstrate that a closed-loop, adaptive DBS might be superior to the open-loop setup. We here combine the notion of the adaptive high-frequency stimulation approach, that aims at delivering stimulation adapted to the extent of appropriately detected biomarkers, with specifically desynchronizing stimulation protocols. To this end, we extend the delayed feedback stimulation methods, which are intrinsically closed-loop techniques and specifically designed to desynchronize abnormal neuronal synchronization, to pulsatile electrical brain stimulation. We show that permanent pulsatile high-frequency stimulation subjected to an amplitude modulation by linear or nonlinear delayed feedback methods can effectively and robustly desynchronize a STN-GPe network of model neurons and suggest this approach for desynchronizing closed-loop DBS.

Incremental stability of delayed neural fields: a unifying framework for endogenous and exogenous sources of pathological oscillations

Neural fields are integro-differential equations that have been extensively used to model spatiotemporal evolution of neocortical areas (see [1] for a detailed review). Time-delayed neural fields have also been a matter of investigation since they take into account axonal delays [2]. On the other hand, time-delay finite dimensional systems have been used in models of Parkinson's disease: delays have been shown to play a possible role in the generation of pathological neural oscillations linked to motor symptoms of Parkinson disease in a firing-rate model of basal ganglia [3,4]. Nonetheless, these models fail at rendering the spatial distribution of the neural activity of the populations involved. Two possible mechanisms for the onset of pathological oscillations in basal ganglia have been investigated in the literature. The first one, the endogenous mechanism, hypothesizes that dopamine depletion tends to increase the synaptic gains between the excitatory neurons of the subthalamic nucleus (STN) and the inhibitory neurons of the external segment of globus pallidus (GPe), thus generating an instability that translates into sustained oscillations. The second one, the exogenous mechanism, explains these oscillations onset by a diffusion of spontaneous oscillations from external structures (such as Striatum) to the GPe-STN network [5]. The main goal of this work is to deepen this analysis by providing theoretical conditions under which a network of time-delayed neural field equations is incrementally stable. We believe that incremental stability constitutes an instrumental framework to investigate both the mechanisms evoked above. Indeed, by considering constant inputs to the basal ganglia, incremental stability ensures convergence to a unique equilibrium configuration, thus ruling out the possibility of endogenous mechanism for oscillations onset. On the other hand, incremental stability guarantees entrainability to periodic inputs (meaning convergence to a T-periodic solution in response to any T-periodic input), and can thus be useful to unravel the mechanism of pathological diffusion from external structures in the exogenous scenario. Relying on the Razumikhin-Lyapunov approach here we derive these sufficient conditions for incremental stability of delayed neural fields. This theoretical framework thus complements the Krasovskii-Lyapunov approach already used in the literature to address the stability of delayed neural fields equations [6]. Simulations confirm our theoretical expectations and demonstrate that interconnected neural fields can exhibit sustained oscillations, according to either the endogenous or the exogenous mechanism, depending on the strength of the synaptic weights between the excitatory (STN) and the inhibitory (GPe) populations. The derived theoretical results thus seem to constitute a fertile ground for further investigations based on experimental data, to discriminate between the endogenous and the exogenous hypotheses for Parkinsonian sustained oscillations in the STN-GPe network.

Closed-loop stimulation of a delayed neural fields model of parkinsonian STN-GPe network: a theoretical and computational study.

Several disorders are related to pathological brain oscillations. In the case of Parkinson's disease, sustained low-frequency oscillations (especially in the β-band, 13–30 Hz) correlate with motor symptoms. It is still under debate whether these oscillations are the cause of parkinsonian motor symptoms. The development of techniques enabling selective disruption of these β-oscillations could contribute to the understanding of the underlying mechanisms, and could be exploited for treatments. A particularly appealing technique is Deep Brain Stimulation (DBS). With clinical electrical DBS, electrical currents are delivered at high frequency to a region made of potentially heterogeneous neurons (the subthalamic nucleus (STN) in the case of Parkinson's disease). Even more appealing is DBS with optogenetics, which is until now a preclinical method using both gene transfer and deep brain light delivery and enabling neuromodulation at the scale of one given neural network. In this work, we rely on delayed neural fields models of STN and the external Globus Pallidus (GPe) to develop, theoretically validate and test in silico a closed-loop stimulation strategy to disrupt these sustained oscillations with optogenetics. First, we rely on tools from control theory to provide theoretical conditions under which sustained oscillations can be attenuated by a closed-loop stimulation proportional to the measured activity of STN. Second, based on this theoretical framework, we show numerically that the proposed closed-loop stimulation efficiently attenuates sustained oscillations, even in the case when the photosensitization effectively affects only 50% of STN neurons. We also show through simulations that oscillations disruption can be achieved when the same light source is used for the whole STN population. We finally test the robustness of the proposed strategy to possible acquisition and processing delays, as well as parameters uncertainty.

Controlling the Go / No-Go decision threshold in the striatum

A typical Go/No-Go decision is thought to be implemented via the activation of direct and indirect pathways in the basal ganglia. Indeed, optogenetic activation of the direct pathway increased ambulation, whereas that of the indirect pathway induced freezing [1]. Striatal neurons participating in these two pathways express D1 and D2 type dopamine receptors [2]. Furthermore, D1 and D2 expressing MSNs also differ in their passive properties [2] and recurrent connectivity [3]. To understand striatal function it is, therefore, important to identify factors that regulate the balance of activity in D1 and D2 MSNs. Here we used both, a reduced firing rate model and numerical simulations of the striatal networks to study the dynamic balance of spiking activity in D1 and D2 MSNs. Specifically, we show that: (i) Because D1 MSNs receive higher recurrent inhibition from FSIs [4] and D2 MSNs [3], they require a stronger cortical drive to overcome this inhibition. (ii) D1 and D2 firing rates change non-monotonically as a function of cortical input rates. For small cortical input rates, D1 MSNs have higher firing rates than D2 MSNs, due to the stronger synaptic input from cortex. For higher cortical input rates, D2 MSNs activity surpasses D1 MSN activity because cortical input rate is no longer sufficient to balance the strong inhibition coming from FSIs. The cortical rate at which D2 MSNs activity exceeds that of D1 MSNs is termed the decision threshold. (iii) The decision threshold depends on the strength of cortico-striatal synapses and the firing rate of FSIs. (iv) The STN could control the decision threshold via the massive pallidostriatal back-projections [5], via inhibition of the FSIs. (v) Finally, the difference between D1 and D2 firing rates is also modulated by the input correlations [6]. These observations help us to explain several experimental and behavioral findings involving the basal ganglia. The model suggest that under dopamine depletion conditions, even for weak cortical inputs, D2 MSNs activity is higher than D1 MSNs, which is consistent with the fact that Parkinson's disease (PD) patients have difficulty in initiating voluntary actions. We also observed that dopamine depletion reduced the parameter regime supporting D1 MSNs activation, by shifting the decision threshold towards lower cortical inputs. This suggests that under dopamine-depleted conditions, the striatum would require arbitration by the STN-GPe network, even for a low conflict task, providing a plausible explanation of increased reaction times in PD patients. Finally, increased activity in GPe under the influence of deep-brain stimulation (DBS) could also reduce the activity of FSIs on an average, thus shifting the decision threshold towards higher cortical input rates. Taken together, the model provides a mechanistic explanation of impulsive behavior in PD patients with DBS.

Influences of membrane properties on phase response curve and synchronization stability in a model globus pallidus neuron

The activity patterns of the globus pallidus (GPe) and subthalamic nucleus (STN) are closely associated with motor function and dysfunction in the basal ganglia. In the pathological state caused by dopamine depletion, the STN-GPe network exhibits rhythmic synchronous activity accompanied by rebound bursts in the STN. Therefore, the mechanism of activity transition is a key to understand basal ganglia functions. As synchronization in GPe neurons could induce pathological STN rebound bursts, it is important to study how synchrony is generated in the GPe. To clarify this issue, we applied the phase-reduction technique to a conductance-based GPe neuronal model in order to derive the phase response curve (PRC) and interaction function between coupled GPe neurons. Using the PRC and interaction function, we studied how the steady-state activity of the GPe network depends on intrinsic membrane properties, varying ionic conductances on the membrane. We noted that a change in persistent sodium current, fast delayed rectifier Kv3 potassium current, M-type potassium current and small conductance calcium-dependent potassium current influenced the PRC shape and the steady state. The effect of those currents on the PRC shape could be attributed to extension of the firing period and reduction of the phase response immediately after an action potential. In particular, the slow potassium current arising from the M-type potassium and the SK current was responsible for the reduction of the phase response. These results suggest that the membrane property modulation controls synchronization/asynchronization in the GPe and the pathological pattern of STN-GPe activity.