Mean-field modeling of the basal ganglia-thalamocortical system. I Firing rates in healthy and parkinsonian states

Valence-dependent dopaminergic modulation during reversal learning in Parkinson's disease: A neurocomputational approach

Reinforcement learning, crucial for behavior in dynamic environments, is driven by rewards and punishments, modulated by dopamine (DA) changes. This study explores the dopaminergic system's influence on learning, particularly in Parkinson's disease (PD), where medication leads to impaired adaptability. Highlighting the role of tonic DA in signaling the valence of actions, this research investigates how DA affects response vigor and decision-making in PD. DA not only influences reward and punishment learning but also indicates the cognitive effort level and risk propensity in actions, which are essential for understanding and managing PD symptoms. In this work, we adapt our existing neurocomputational model of basal ganglia (BG) to simulate two reversal learning tasks proposed by Cools et al. We first optimized a Hebb rule for both probabilistic and deterministic reversal learning, conducted a sensitivity analysis (SA) on parameters related to DA effect, and compared performances between three groups: PD-ON, PD-OFF, and control subjects. In our deterministic task simulation, we explored switch error rates after unexpected task switches and found a U-shaped relationship between tonic DA levels and switch error frequency. Through SA, we classify these three groups. Then, assuming that the valence of the stimulus affects the tonic levels of DA, we were able to reproduce the results by Cools et al. As for the probabilistic task simulation, our results are in line with clinical data, showing similar trends with PD-ON, characterized by higher tonic DA levels that are correlated with increased difficulty in both acquisition and reversal tasks. Our study proposes a new hypothesis: valence, signaled by tonic DA levels, influences learning in PD, confirming the uncorrelation between phasic and tonic DA changes. This hypothesis challenges existing paradigms and opens new avenues for understanding cognitive processes in PD, particularly in reversal learning tasks.

CBGTPy: An extensible cortico-basal ganglia-thalamic framework for modeling biological decision making

Here we introduce CBGTPy, a virtual environment for designing and testing goal-directed agents with internal dynamics that are modeled on the cortico-basal-ganglia-thalamic (CBGT) pathways in the mammalian brain. CBGTPy enables researchers to investigate the internal dynamics of the CBGT system during a variety of tasks, allowing for the formation of testable predictions about animal behavior and neural activity. The framework has been designed around the principle of flexibility, such that many experimental parameters in a decision making paradigm can be easily defined and modified. Here we demonstrate the capabilities of CBGTPy across a range of single and multi-choice tasks, highlighting the ease of set up and the biologically realistic behavior that it produces. We show that CBGTPy is extensible enough to apply to a range of experimental protocols and to allow for the implementation of model extensions with minimal developmental effort.

Practical Bayesian Inference in Neuroscience: Or How I Learned to Stop Worrying and Embrace the Distribution

Typical statistical practices in the biological sciences have been increasingly called into question due to difficulties in the replication of an increasing number of studies, many of which are confounded by the relative difficulty of null significance hypothesis testing designs and interpretation of p-values. Bayesian inference, representing a fundamentally different approach to hypothesis testing, is receiving renewed interest as a potential alternative or complement to traditional null significance hypothesis testing due to its ease of interpretation and explicit declarations of prior assumptions. Bayesian models are more mathematically complex than equivalent frequentist approaches, which have historically limited applications to simplified analysis cases. However, the advent of probability distribution sampling tools with exponential increases in computational power now allows for quick and robust inference under any distribution of data. Here we present a practical tutorial on the use of Bayesian inference in the context of neuroscientific studies in both rat electrophysiological and computational modeling data. We first start with an intuitive discussion of Bayes' rule and inference followed by the formulation of Bayesian-based regression and ANOVA models using data from a variety of neuroscientific studies. We show how Bayesian inference leads to easily interpretable analysis of data while providing an open-source toolbox to facilitate the use of Bayesian tools.

Computational models advance deep brain stimulation for Parkinson's disease

Deep brain stimulation(DBS) has become an effective intervention for advanced Parkinson's disease(PD), but the exact mechanism of DBS is still unclear. In this review, we discuss the history of DBS, the anatomy and internal architecture of the basal ganglia (BG), the abnormal pathological changes of the BG in PD, and how computational models can help understand and advance DBS. We also describe two types of models: mathematical theoretical models and clinical predictive models. Mathematical theoretical models simulate neurons or neural networks of BG to shed light on the mechanistic principle underlying DBS, while clinical predictive models focus more on patients' outcomes, helping to adapt treatment plans for each patient and advance novel electrode designs. Finally, we provide insights and an outlook on future technologies.

Mathematical derivation and mechanism analysis of beta oscillations in a cortex-pallidum model

In this paper, we develop a new cortex-pallidum model to study the origin mechanism of Parkinson's oscillations in the cortex. In contrast to many previous models, the globus pallidus internal (GPi) and externa (GPe) both exert direct inhibitory feedback to the cortex. Using Hopf bifurcation analysis, two new critical conditions for oscillations, which can include the self-feedback projection of GPe, are obtained. In this paper, we find that the average discharge rate (ADR) is an important marker of oscillations, which can divide Hopf bifurcations into two types that can uniformly be used to explain the oscillation mechanism. Interestingly, the ADR of the cortex first increases and then decreases with increasing coupling weights that are projected to the GPe. Regarding the Hopf bifurcation critical conditions, the quantitative relationship between the inhibitory projection and excitatory projection to the GPe is monotonically increasing; in contrast, the relationship between different coupling weights in the cortex is monotonically decreasing. In general, the oscillation amplitude is the lowest near the bifurcation points and reaches the maximum value with the evolution of oscillations. The GPe is an effective target for deep brain stimulation to alleviate oscillations in the cortex.

Speech, voice, and language outcomes following deep brain stimulation: A systematic review

BACKGROUND

Deep brain stimulation (DBS) reliably ameliorates cardinal motor symptoms in Parkinson's disease (PD) and essential tremor (ET). However, the effects of DBS on speech, voice and language have been inconsistent and have not been examined comprehensively in a single study.

OBJECTIVE

We conducted a systematic analysis of literature by reviewing studies that examined the effects of DBS on speech, voice and language in PD and ET.

METHODS

A total of 675 publications were retrieved from PubMed, Embase, CINHAL, Web of Science, Cochrane Library and Scopus databases. Based on our selection criteria, 90 papers were included in our analysis. The selected publications were categorized into four subcategories: Fluency, Word production, Articulation and phonology and Voice quality.

RESULTS

The results suggested a long-term decline in verbal fluency, with more studies reporting deficits in phonemic fluency than semantic fluency following DBS. Additionally, high frequency stimulation, left-sided and bilateral DBS were associated with worse verbal fluency outcomes. Naming improved in the short-term following DBS-ON compared to DBS-OFF, with no long-term differences between the two conditions. Bilateral and low-frequency DBS demonstrated a relative improvement for phonation and articulation. Nonetheless, long-term DBS exacerbated phonation and articulation deficits. The effect of DBS on voice was highly variable, with both improvements and deterioration in different measures of voice.

CONCLUSION

This was the first study that aimed to combine the outcome of speech, voice, and language following DBS in a single systematic review. The findings revealed a heterogeneous pattern of results for speech, voice, and language across DBS studies, and provided directions for future studies.

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.

Biophysical Principles and Computational Modeling of Deep Brain Stimulation

BACKGROUND

Deep brain stimulation (DBS) has revolutionized the treatment of neurological disorders, yet the mechanisms of DBS are still under investigation. Computational models are important in silico tools for elucidating these underlying principles and potentially for personalizing DBS therapy to individual patients. The basic principles underlying neurostimulation computational models, however, are not well known in the clinical neuromodulation community.

OBJECTIVE

In this study, we present a tutorial on the derivation of computational models of DBS and outline the biophysical contributions of electrodes, stimulation parameters, and tissue substrates to the effects of DBS.

RESULTS

Given that many aspects of DBS are difficult to characterize experimentally, computational models have played an important role in understanding how material, size, shape, and contact segmentation influence device biocompatibility, energy efficiency, the spatial spread of the electric field, and the specificity of neural activation. Neural activation is dictated by stimulation parameters including frequency, current vs voltage control, amplitude, pulse width, polarity configurations, and waveform. These parameters also affect the potential for tissue damage, energy efficiency, the spatial spread of the electric field, and the specificity of neural activation. Activation of the neural substrate also is influenced by the encapsulation layer surrounding the electrode, the conductivity of the surrounding tissue, and the size and orientation of white matter fibers. These properties modulate the effects of the electric field and determine the ultimate therapeutic response.

CONCLUSION

This article describes biophysical principles that are useful for understanding the mechanisms of neurostimulation.

Estimation of the transmission delays in the basal ganglia of the macaque monkey and subsequent predictions about oscillatory activity under dopamine depletion

The timescales of the dynamics of a system depend on the combination of the timescales of its components and of its transmission delays between components. Here, we combine experimental stimulation data from 10 studies in macaque monkeys that reveal the timing of excitatory and inhibitory events in the basal ganglia circuit, to estimate its set of transmission delays. In doing so, we reveal possible inconsistencies in the existing data, calling for replications, and we propose two possible sets of transmission delays. We then integrate these delays in a model of the primate basal ganglia that does not rely on direct and indirect pathways' segregation and show that extrastriatal dopaminergic depletion in the external part of the globus pallidus and in the subthalamic nucleus is sufficient to generate β-band oscillations (in the high part, 20-35 Hz, of the band). More specifically, we show that D2 and D5 dopamine receptors in these nuclei play opposing roles in the emergence of these oscillations, thereby explaining how completely deactivating D5 receptors in the subthalamic nucleus can, paradoxically, cancel oscillations.

Modeling Instantaneous Firing Rate of Deep Brain Stimulation Target Neuronal Ensembles in the Basal Ganglia and Thalamus

OBJECTIVE

Deep brain stimulation (DBS) is an effective treatment for movement disorders, including Parkinson disease and essential tremor. However, the underlying mechanisms of DBS remain elusive. Despite the capability of existing models in interpreting experimental data qualitatively, there are very few unified computational models that quantitatively capture the dynamics of the neuronal activity of varying stimulated nuclei-including subthalamic nucleus (STN), substantia nigra pars reticulata (SNr), and ventral intermediate nucleus (Vim)-across different DBS frequencies.

MATERIALS AND METHODS

Both synthetic and experimental data were used in the model fitting; the synthetic data were generated by an established spiking neuron model that was reported in our previous work, and the experimental data were provided using single-unit microelectrode recordings (MERs) during DBS (microelectrode stimulation). Based on these data, we developed a novel mathematical model to represent the firing rate of neurons receiving DBS, including neurons in STN, SNr, and Vim-across different DBS frequencies. In our model, the DBS pulses were filtered through a synapse model and a nonlinear transfer function to formulate the firing rate variability. For each DBS-targeted nucleus, we fitted a single set of optimal model parameters consistent across varying DBS frequencies.

RESULTS

Our model accurately reproduced the firing rates observed and calculated from both synthetic and experimental data. The optimal model parameters were consistent across different DBS frequencies.

CONCLUSIONS

The result of our model fitting was in agreement with experimental single-unit MER data during DBS. Reproducing neuronal firing rates of different nuclei of the basal ganglia and thalamus during DBS can be helpful to further understand the mechanisms of DBS and to potentially optimize stimulation parameters based on their actual effects on neuronal activity.

A dynamic computational model of the parallel circuit on the basal ganglia-cortex associated with Parkinson's disease dementia

The cognitive impairment will gradually appear over time in Parkinson's patients, which is closely related to the basal ganglia-cortex network. This network contains two parallel circuits mediated by putamen and caudate nucleus, respectively. Based on the biophysical mean-field model, we construct a dynamic computational model of the parallel circuit in the basal ganglia-cortex network associated with Parkinson's disease dementia. The simulated results show that the decrease of power ratio in the prefrontal cortex is mainly caused by dopamine depletion in the caudate nucleus and is less related to that in the putamen, which indicates Parkinson's disease dementia may be caused by a lesion of the caudate nucleus rather than putamen. Furthermore, the underlying dynamic mechanism behind the decrease of power ratio is investigated by bifurcation analysis, which demonstrates that the decrease of power ratio is due to the change of brain discharge pattern from the limit cycle mode to the point attractor mode. More importantly, the spatiotemporal course of dopamine depletion in Parkinson's disease patients is well simulated, which states that with the loss of dopaminergic neurons projecting to the striatum, motor dysfunction of Parkinson's disease is first observed, whereas cognitive impairment occurs after a period of onset of motor dysfunction. These results are helpful to understand the pathogenesis of cognitive impairment and provide insights into the treatment of Parkinson's disease dementia.

Criticality supports cross-frequency cortical-thalamic information transfer during conscious states

Consciousness is thought to be regulated by bidirectional information transfer between the cortex and thalamus, but the nature of this bidirectional communication - and its possible disruption in unconsciousness - remains poorly understood. Here, we present two main findings elucidating mechanisms of corticothalamic information transfer during conscious states. First, we identify a highly preserved spectral channel of cortical-thalamic communication that is present during conscious states, but which is diminished during the loss of consciousness and enhanced during psychedelic states. Specifically, we show that in humans, mice, and rats, information sent from either the cortex or thalamus via δ/θ/α waves (∼1-13 Hz) is consistently encoded by the other brain region by high γ waves (52-104 Hz); moreover, unconsciousness induced by propofol anesthesia or generalized spike-and-wave seizures diminishes this cross-frequency communication, whereas the psychedelic 5-methoxy-N,N-dimethyltryptamine (5-MeO-DMT) enhances this low-to-high frequency interregional communication. Second, we leverage numerical simulations and neural electrophysiology recordings from the thalamus and cortex of human patients, rats, and mice to show that these changes in cross-frequency cortical-thalamic information transfer may be mediated by excursions of low-frequency thalamocortical electrodynamics toward/away from edge-of-chaos criticality, or the phase transition from stability to chaos. Overall, our findings link thalamic-cortical communication to consciousness, and further offer a novel, mathematically well-defined framework to explain the disruption to thalamic-cortical information transfer during unconscious states.

Surgical Advances in Parkinson's Disease

While symptomatic pharmacological therapy remains the main therapeutic strategy for Parkinson's disease (PD), over the last two decades, surgical approaches have become more commonly used to control levodopa-induced motor complications and dopamine-resistant and non-motor symptoms of PD. In this paper, we discuss old and new surgical treatments for PD and the many technological innovations in this field. We have initially reviewed the relevant surgical anatomy as well as the pathological signaling considered to be the underlying cause of specific symptoms of PD. Subsequently, early attempts at surgical symptom control will be briefly reviewed. As the most well-known surgical intervention for PD is deep brain stimulation, this subject is discussed at length. As deciding on whether a patient stands to benefit from DBS can be quite difficult, the different proposed paradigms for precisely this are covered. Following this, the evidence regarding different targets, especially the subthalamic nucleus and internal globus pallidus, is reviewed as well as the evidence for newer proposed targets for specific symptoms. Due to the rapidly expanding nature of knowledge and technological capabilities, some of these new and potential future capabilities are given consideration in terms of their current and future use. Following this, we have reviewed newer treatment modalities, especially magnetic resonance-guided focused ultrasound and other potential surgical therapies, such as spinal cord stimulation for gait symptoms and others. As mentioned, the field of surgical alleviation of symptoms of PD is undergoing a rapid expansion, and this review provides a general overview of the current status and future directions in the field.

Suppression of absence seizures by using different stimulations in a reduced corticothalamic-basal ganglion-pedunculopontine nucleus model

Coupled neural network models are playing an increasingly important part in the modulation of absence seizures today. However, it is currently unclear how basal ganglia, corticothalamic network and pedunculopontine nucleus can coordinate with each other to develop a whole coupling circuit, theoretically. In addition, it is still difficult to select effective parameters of electrical stimulation on the regulation of absence seizures in clinical trials. Therefore, to develop a coupled model and reduce computation cost, a new model constructed by a simplified basal ganglion, two corticothalamic circuits and a pedunculopontine nucleus was proposed. Further, to seek better inhibition therapy, three electrical stimulations, high frequency stimulation (HFS), 1:0 coordinate reset stimulation (CRS) and 3:2 CRS, were applied to the thalamic reticular nucleus (RE) in the first corticothalamic circuit in the coupled model. The simulation results revealed that increasing the frequency and pulse width of an electrical stimulation within a certain range can also suppress seizures. Under the same parameters of electrical stimulation, the inhibitory effect of HFS on seizures was better than that of 1:0 CRS and 3:2 CRS. The research established a reduced corticothalamic-basal ganglion-pedunculopontine nucleus model, which lays a theoretical foundation for future optimal parameters selection of electrical stimulation. We hope that the findings will provide new insights into the role of theoretical models in absence seizures.

A computational network dynamical modeling for abnormal oscillation and deep brain stimulation control of obsessive-compulsive disorder

Obsessive-compulsive disorder (OCD) is associated with multi-nodal abnormalities in brain networks, characterized by recurrent intrusive thoughts (obsessions) and repetitive behaviours or mental acts (compulsions), which might manifest as pathological low-frequency oscillations in the frontal EEG and low-frequency bursting firing patterns in the subthalamus nucleus (STN). Abnormalities in the cortical-striatal-thalamic-cortical (CSTC) loop, including dysregulation of serotonin, dopamine, and glutamate systems, are considered to contribute to certain types of OCD. Here, we extend a biophysical computational model to investigate the effect of orbitofronto-subcortical loop abnormalities on network oscillations. Particularly, the OCD lesion process is simulated by the loss of connectivity from striatal parvalbumin interneurons (PV) to medium spiny neurons (MSNs), excessive activation to the hyperdirect pathway, and high dopamine concentrations. By calculating low-frequency oscillation power in the STN, STN burst index, and average firing rates levels of the cortex and thalamus, we demonstrate that the model can explain the pathology of glutamatergic and dopamine system dysregulation, the effects of pathway imbalance, and neuropsychiatric treatment in OCD. In addition, results indicate the abnormal brain rhythms caused by the dysregulation of orbitofronto-subcortical loop may serve as a biomarker of OCD. Our studies can help to understand the cause of OCD, thereby facilitating the diagnosis of OCD and the development of new therapeutics.

Method for quantifying arousal and consciousness in healthy states and severe brain injury via EEG-based measures of corticothalamic physiology

BACKGROUND

Characterization of normal arousal states has been achieved by fitting predictions of corticothalamic neural field theory (NFT) to electroencephalographic (EEG) spectra to yield relevant physiological parameters.

NEW METHOD

A prior fitting method is extended to distinguish conscious and unconscious states in healthy and brain injured subjects by identifying additional parameters and clusters in parameter space.

RESULTS

Fits of NFT predictions to EEG spectra are used to estimate neurophysiological parameters in healthy and brain injured subjects. Spectra are used from healthy subjects in wake and sleep and from patients with unresponsive wakefulness syndrome, in a minimally conscious state (MCS), and emerged from MCS. Subjects cluster into three groups in parameter space: conscious healthy (wake and REM), sleep, and brain injured. These are distinguished by the difference X-Y between corticocortical (X) and corticothalamic (Y) feedbacks, and by mean neural response rates α and β to incoming spikes. X-Y tracks consciousness in healthy individuals, with smaller values in wake/REM than sleep, but cannot distinguish between brain injuries. Parameters α and β differentiate deep sleep from wake/REM and brain injury.

COMPARISON WITH EXISTING METHODS

Other methods typically rely on laborious clinical assessment, manual EEG scoring, or evaluation of measures like Φ from integrated information theory, for which no efficient method exists. In contrast, the present method can be automated on a personal computer.

CONCLUSION

The method provides a means to quantify consciousness and arousal in healthy and brain injured subjects, but does not distinguish subtypes of brain injury.

A multi-layer mean-field model of the cerebellum embedding microstructure and population-specific dynamics

Mean-field (MF) models are computational formalism used to summarize in a few statistical parameters the salient biophysical properties of an inter-wired neuronal network. Their formalism normally incorporates different types of neurons and synapses along with their topological organization. MFs are crucial to efficiently implement the computational modules of large-scale models of brain function, maintaining the specificity of local cortical microcircuits. While MFs have been generated for the isocortex, they are still missing for other parts of the brain. Here we have designed and simulated a multi-layer MF of the cerebellar microcircuit (including Granule Cells, Golgi Cells, Molecular Layer Interneurons, and Purkinje Cells) and validated it against experimental data and the corresponding spiking neural network (SNN) microcircuit model. The cerebellar MF was built using a system of equations, where properties of neuronal populations and topological parameters are embedded in inter-dependent transfer functions. The model time constant was optimised using local field potentials recorded experimentally from acute mouse cerebellar slices as a template. The MF reproduced the average dynamics of different neuronal populations in response to various input patterns and predicted the modulation of the Purkinje Cells firing depending on cortical plasticity, which drives learning in associative tasks, and the level of feedforward inhibition. The cerebellar MF provides a computationally efficient tool for future investigations of the causal relationship between microscopic neuronal properties and ensemble brain activity in virtual brain models addressing both physiological and pathological conditions.

A neurorobotics approach to behaviour selection based on human activity recognition

Behaviour selection has been an active research topic for robotics, in particular in the field of human-robot interaction. For a robot to interact autonomously and effectively with humans, the coupling between techniques for human activity recognition and robot behaviour selection is of paramount importance. However, most approaches to date consist of deterministic associations between the recognised activities and the robot behaviours, neglecting the uncertainty inherent to sequential predictions in real-time applications. In this paper, we address this gap by presenting an initial neurorobotics model that embeds, in a simulated robot, computational models of parts of the mammalian brain that resembles neurophysiological aspects of the basal ganglia-thalamus-cortex (BG-T-C) circuit, coupled with human activity recognition techniques. A robotics simulation environment was developed for assessing the model, where a mobile robot accomplished tasks by using behaviour selection in accordance with the activity being performed by the inhabitant of an intelligent home. Initial results revealed that the initial neurorobotics model is advantageous, especially considering the coupling between the most accurate activity recognition approaches and the computational models of more complex animals.

Dopamine depletion leads to pathological synchronization of distinct basal ganglia loops in the beta band

Motor symptoms of Parkinson's Disease (PD) are associated with dopamine deficits and pathological oscillation of basal ganglia (BG) neurons in the β range ([12-30] Hz). However, how dopamine depletion affects the oscillation dynamics of BG nuclei is still unclear. With a spiking neurons model, we here capture the features of BG nuclei interactions leading to oscillations in dopamine-depleted condition. We highlight that both the loop between subthalamic nucleus (STN) and Globus Pallidus pars externa (GPe) and the loop between striatal fast spiking and medium spiny neurons and GPe display resonances in the β range, and synchronize to a common β frequency through interaction. Crucially, the synchronization depends on dopamine depletion: the two loops are largely independent for high levels of dopamine, but progressively synchronize as dopamine is depleted due to the increased strength of the striatal loop. The model is validated against recent experimental reports on the role of cortical inputs, STN and GPe activity in the generation of β oscillations. Our results highlight the role of the interplay between the GPe-STN and the GPe-striatum loop in generating sustained β oscillations in PD subjects, and explain how this interplay depends on the level of dopamine. This paves the way to the design of therapies specifically addressing the onset of pathological β oscillations.

Combined effect of stimulation and electromagnetic induction on absence seizure inhibition in coupled thalamocortical circuits

Deep brain stimulation (DBS) and electromagnetic induction are new techniques that are increasingly used in modern epilepsy treatments; however, the mechanism of action remains unclear. In this study, we constructed a bidirectional-coupled cortico-thalamic model, based on which we proposed three regulation schemes: isolated regulation of DBS, isolated regulation of electromagnetic induction and combined regulation of the previous two. In particular, we introduced DBS with a lower amplitude and considered the influence of electromagnetic induction caused by the transmembrane current on the membrane potential. The most striking finding of this study is that the three therapeutic schemes could effectively control abnormal discharge, and combined regulation could reduce the occurrence of epileptic seizures more effectively. The present study bridges the gap between the bidirectional coupling model and combined control. In this way, the damage induced by electrical stimulation of the patient's brain tissue could be reduced, and the abnormal physiological discharge pattern of the cerebral cortex was simultaneously regulated by different techniques. This work opens new avenues for improving brain dysfunction in patients with epilepsy, expands ideas for promoting the development of neuroscience and is meaningful for improving the health of modern society and developing the field of science.

The mechanism of Parkinson oscillation in the cortex: Possible evidence in a feedback model projecting from the globus pallidus to the cortex

The origin, location and cause of Parkinson's oscillation are not clear at present. In this paper, we establish a new cortex-basal ganglia model to study the origin mechanism of Parkinson beta oscillation. Unlike many previous models, this model includes two direct inhibitory projections from the globus pallidus external (GPe) segment to the cortex. We first obtain the critical calculation formula of Parkinson's oscillation by using the method of Quasilinear analysis. Different from previous studies, the formula obtained in this paper can include the self-feedback connection of GPe. Then, we use the bifurcation analysis method to systematically explain the influence of some key parameters on the oscillation. We find that the bifurcation principle of different cortical nuclei is different. In general, the increase of the discharge capacity of the nuclei will cause oscillation. In some special cases, the sharp reduction of the discharge rate of the nuclei will also cause oscillation. The direction of bifurcation simulation is consistent with the critical condition curve. Finally, we discuss the characteristics of oscillation amplitude. At the beginning of the oscillation, the amplitude is relatively small; with the evolution of oscillation, the amplitude will gradually strengthen. This is consistent with the experimental phenomenon. In most cases, the amplitude of cortical inhibitory nuclei (CIN) is greater than that of cortical excitatory nuclei (CEX), and the two direct inhibitory projections feedback from GPe can significantly reduce the amplitude gap between them. We calculate the main frequency of the oscillation generated in this model, which basically falls between 13 and 30 Hz, belonging to the typical beta frequency band oscillation. Some new results obtained in this paper can help to better understand the origin mechanism of Parkinson's disease and have guiding significance for the development of experiments.

The adjustment mechanism of the spike and wave discharges in thalamic neurons: a simulation analysis

Different from many previous theoretical studies, this paper explores the regulatory mechanism of the spike and wave discharges (SWDs) in the reticular thalamic nucleus (TRN) by a dynamic computational model. We observe that the SWDs appears in the TRN by changing the coupling weights and delays in the thalamocortical circuit. The abundant poly-spikes wave discharges is also induced when the delay increases to large enough. These discharges can be inhibited by tuning the inhibitory output from the basal ganglia to the thalamus. The mechanisms of these waves can be explained in this model together with simulation results, which are different from the mechanisms in the cortex. The TRN is an important target in treating epilepsy, and the results may be a theoretical evidence for experimental study in the future.

Regulating absence seizures by tri-phase delay stimulation applied to globus pallidus internal

In this paper, a reduced globus pallidus internal (GPI)-corticothalamic (GCT) model is developed, and a tri-phase delay stimulation (TPDS) with sequentially applying three pulses on the GPI representing the inputs from the striatal D ₁ neurons, subthalamic nucleus (STN), and globus pallidus external (GPE), respectively, is proposed. The GPI is evidenced to control absence seizures characterized by 2 Hz-4 Hz spike and wave discharge (SWD). Hence, based on the basal ganglia-thalamocortical (BGCT) model, we firstly explore the triple effects of D _l-GPI, GPE-GPI, and STN-GPI pathways on seizure patterns. Then, using the GCT model, we apply the TPDS on the GPI to potentially investigate the alternative and improved approach if these pathways to the GPI are blocked. The results show that the striatum D ₁, GPE, and STN can indeed jointly and significantly affect seizure patterns. In particular, the TPDS can effectively reproduce the seizure pattern if the D ₁-GPI, GPE-GPI, and STN-GPI pathways are cut off. In addition, the seizure abatement can be obtained by well tuning the TPDS stimulation parameters. This implies that the TPDS can play the surrogate role similar to the modulation of basal ganglia, which hopefully can be helpful for the development of the brain-computer interface in the clinical application of epilepsy.

Fully Closed Loop Test Environment for Adaptive Implantable Neural Stimulators Using Computational Models

Implantable brain stimulation devices continue to be developed to treat and monitor brain conditions. As the complexity of these devices grows to include adaptive neuromodulation therapy, validating the operation and verifying the correctness of these systems becomes more complicated. The new complexities lie in the functioning of the device being dependent on the interaction with the patient and environmental factors such as noise and artifacts. Here, we present a hardware-in-the-loop (HIL) testing framework that employs computational models of pathological neural dynamics to test adaptive deep brain stimulation (DBS) devices prior to animal or human testing. A brain stimulation and recording electrode array is placed in the saline tank and connected to an adaptive neuromodulation system that measures and processes the synthetic signals and delivers stimulation back into the saline tank. A data acquisition system is used to detect the stimulation and provide feedback to the computational model in order to simulate the effects of stimulation on the neural dynamics. In this study, we used real-time computational models to emulate the dynamics of epileptic seizures observed in the anterior nucleus of the thalamus (ANT) in epilepsy patients and beta band (11-35 Hz) oscillations observed in the subthalamic nucleus (STN) of Parkinson's disease (PD) patients. These models simulated neuronal responses to electrical stimulation pulses and the saline tank tested hardware interactions between the detection algorithms and stimulation interference. We tested and validated the operation of adaptive DBS algorithms for seizure and beta band power suppression embedded in an implantable DBS system (Medtronic Summit RC+S). This study highlights the utility of the proposed hardware-in-the-loop framework to systematically test the adaptive DBS systems in the presence of system aggressors such as environmental noise and stimulation-induced electrical artifacts. This testing procedure can help ensure correctness and robustness of adaptive DBS devices prior to animal and human testing.

Phasic Dopamine Changes and Hebbian Mechanisms during Probabilistic Reversal Learning in Striatal Circuits: A Computational Study

Cognitive flexibility is essential to modify our behavior in a non-stationary environment and is often explored by reversal learning tasks. The basal ganglia (BG) dopaminergic system, under a top-down control of the pre-frontal cortex, is known to be involved in flexible action selection through reinforcement learning. However, how adaptive dopamine changes regulate this process and learning mechanisms for training the striatal synapses remain open questions. The current study uses a neurocomputational model of the BG, based on dopamine-dependent direct (Go) and indirect (NoGo) pathways, to investigate reinforcement learning in a probabilistic environment through a task that associates different stimuli to different actions. Here, we investigated: the efficacy of several versions of the Hebb rule, based on covariance between pre- and post-synaptic neurons, as well as the required control in phasic dopamine changes crucial to achieving a proper reversal learning. Furthermore, an original mechanism for modulating the phasic dopamine changes is proposed, assuming that the expected reward probability is coded by the activity of the winner Go neuron before a reward/punishment takes place. Simulations show that this original formulation for an automatic phasic dopamine control allows the achievement of a good flexible reversal even in difficult conditions. The current outcomes may contribute to understanding the mechanisms for active control of dopamine changes during flexible behavior. In perspective, it may be applied in neuropsychiatric or neurological disorders, such as Parkinson’s or schizophrenia, in which reinforcement learning is impaired.

The inhibition mechanism of epilepsy disease in a computational model

BACKGROUND:

The mechanism of prevention and treatment of epilepsy is a hot issue in theoretical research.

OBJECTIVE:

In this paper, we studied the control mechanism of the generalized spike-and-wave discharges (GSWD) by different types of external electrical stimulation acting on the subthalamic nucleus (STN) in a computational model.

METHODS:

Firstly, we analyzed the pathological mechanism of seizures, which were induced by different parameters in the thalamocortical (TC) circuit. Then, a voltage V was exerted in the STN. At last, we used the sine wave and square wave current stimulation in the STN.

RESULTS:

We found that seizures can be inhibited by tuning stimulus intensity into suitable range, and the direction of adjustment depended on the size of the parameter. We observed that the seizure can also be inhibited by tuning different parameters in current.

CONCLUSIONS:

Different inhibition mechanisms can be explained in this model, which may provide theoretical evidences for selecting the optimal treatment scheme in the clinical.

A data-informed mean-field approach to mapping of cortical parameter landscapes

Constraining the many biological parameters that govern cortical dynamics is computationally and conceptually difficult because of the curse of dimensionality. This paper addresses these challenges by proposing (1) a novel data-informed mean-field (MF) approach to efficiently map the parameter space of network models; and (2) an organizing principle for studying parameter space that enables the extraction biologically meaningful relations from this high-dimensional data. We illustrate these ideas using a large-scale network model of the Macaque primary visual cortex. Of the 10-20 model parameters, we identify 7 that are especially poorly constrained, and use the MF algorithm in (1) to discover the firing rate contours in this 7D parameter cube. Defining a "biologically plausible" region to consist of parameters that exhibit spontaneous Excitatory and Inhibitory firing rates compatible with experimental values, we find that this region is a slightly thickened codimension-1 submanifold. An implication of this finding is that while plausible regimes depend sensitively on parameters, they are also robust and flexible provided one compensates appropriately when parameters are varied. Our organizing principle for conceptualizing parameter dependence is to focus on certain 2D parameter planes that govern lateral inhibition: Intersecting these planes with the biologically plausible region leads to very simple geometric structures which, when suitably scaled, have a universal character independent of where the intersections are taken. In addition to elucidating the geometry of the plausible region, this invariance suggests useful approximate scaling relations. Our study offers, for the first time, a complete characterization of the set of all biologically plausible parameters for a detailed cortical model, which has been out of reach due to the high dimensionality of parameter space.

Multiscale dynamic mean field (MDMF) model relates resting-state brain dynamics with local cortical excitatory-inhibitory neurotransmitter homeostasis

Previous computational models have related spontaneous resting-state brain activity with local excitatory–inhibitory balance in neuronal populations. However, how underlying neurotransmitter kinetics associated with E–I balance govern resting-state spontaneous brain dynamics remains unknown. Understanding the mechanisms by virtue of which fluctuations in neurotransmitter concentrations, a hallmark of a variety of clinical conditions, relate to functional brain activity is of critical importance. We propose a multiscale dynamic mean field (MDMF) model—a system of coupled differential equations for capturing the synaptic gating dynamics in excitatory and inhibitory neural populations as a function of neurotransmitter kinetics. Individual brain regions are modeled as population of MDMF and are connected by realistic connection topologies estimated from diffusion tensor imaging data. First, MDMF successfully predicts resting-state functional connectivity. Second, our results show that optimal range of glutamate and GABA neurotransmitter concentrations subserve as the dynamic working point of the brain, that is, the state of heightened metastability observed in empirical blood-oxygen-level-dependent signals. Third, for predictive validity the network measures of segregation (modularity and clustering coefficient) and integration (global efficiency and characteristic path length) from existing healthy and pathological brain network studies could be captured by simulated functional connectivity from an MDMF model.

How changes in neurotransmitter kinetics impact the organization of large-scale neurocognitive networks is an open question in neuroscience. Here, we propose a multiscale dynamic mean field (MDMF) model that incorporates biophysically realistic kinetic parameters of receptor binding in a dynamic mean field model and captures brain dynamics from the “whole brain.” MDMF could reliably reproduce the resting-state brain functional connectivity patterns. Further employing graph theoretic methods, MDMF could qualitatively explain the idiosyncrasies of network integration and segregation measures reported by previous clinical studies.

Neuro4PD: An Initial Neurorobotics Model of Parkinson's Disease

In this work, we present the first steps toward the creation of a new neurorobotics model of Parkinson's Disease (PD) that embeds, for the first time in a real robot, a well-established computational model of PD. PD mostly affects the modulation of movement in humans. The number of people suffering from this neurodegenerative disease is set to double in the next 15 years and there is still no cure. With the new model we were capable to further explore the dynamics of the disease using a humanoid robot. Results show that the embedded model under both conditions, healthy and parkinsonian, was capable of performing a simple behavioural task with different levels of motor disturbance. We believe that this neurorobotics model is a stepping stone to the development of more sophisticated models that could eventually test and inform new PD therapies and help to reduce and replace animals in research.

Computational neuronal correlation with enhanced synchronized activity in the basal ganglia and the slowing of thalamic theta and alpha rhythms in Parkinson's disease

The aim of this work is computationally to correlate the synchronized neuronal activity of basal ganglia and slowing in theta and alpha rhythms in electroencephalogram (EEG) signal in thalamic region in case of dopamine depletion and decrease of synaptic connections. The used network topology is a scale-free network with constant node degree. The dopamine-modulated type Izikhevich neuron model is used for modeling the striatal region, consisting of fast-spiking interneurons, D1 and D2 type dopamine expressing medium spiny neurons. On the other hand, the ordinary Izikhevich neuron model is used in the modeling of extrastriatal basal ganglia (BG) regions where globus pallidus (GP) subregion neurons have also dopamine-dependent parameters. The thalamic region of the network is mass modeled including inhibitory input from basal ganglia. Depending on the decrease of synaptic connections and dopamine level, the synchronization among basal ganglia neuron populations is investigated. The effect of synaptic delay on synchronization is also considered. It is observed that the decrease of dopamine neurotransmitter and decrease in the number of synaptic connections cause an increased synchronous activity in BG. Also, slowing in theta and alpha bands in thalamus EEG signals is observed. This shows the causal relation between synchronization and power shifting to lower frequency components in the case of neurodegenerative diseases such as Parkinson's disease (PD).

Thalamocortical Spectral Transmission Relies on Balanced Input Strengths

The thalamus is a key element of sensory transmission in the brain, as it gates and selects sensory streams through a modulation of its internal activity. A preponderant role in these functions is played by its internal activity in the alpha range ([8–14] Hz), but the mechanism underlying this process is not completely understood. In particular, how do thalamocortical connections convey stimulus driven information selectively over the back-ground of thalamic internally generated activity? Here we investigate this issue with a spiking network model of feedforward connectivity between thalamus and primary sensory cortex reproducing the local field potential of both areas. We found that in a feedforward network, thalamic oscillations in the alpha range do not entrain cortical activity for two reasons: (i) alpha range oscillations are weaker in neurons projecting to the cortex, (ii) the gamma resonance dynamics of cortical networks hampers oscillations over the 10–20 Hz range thus weakening alpha range oscillations. This latter mechanism depends on the balance of the strength of thalamocortical connections toward excitatory and inhibitory neurons in the cortex. Our results highlight the relevance of corticothalamic feedback to sustain alpha range oscillations and pave the way toward an integrated understanding of the sensory streams traveling between the periphery and the cortex.

Non-invasive suppression of essential tremor via phase-locked disruption of its temporal coherence

Aberrant neural oscillations hallmark numerous brain disorders. Here, we first report a method to track the phase of neural oscillations in real-time via endpoint-corrected Hilbert transform (ecHT) that mitigates the characteristic Gibbs distortion. We then used ecHT to show that the aberrant neural oscillation that hallmarks essential tremor (ET) syndrome, the most common adult movement disorder, can be transiently suppressed via transcranial electrical stimulation of the cerebellum phase-locked to the tremor. The tremor suppression is sustained shortly after the end of the stimulation and can be phenomenologically predicted. Finally, we use feature-based statistical-learning and neurophysiological-modelling to show that the suppression of ET is mechanistically attributed to a disruption of the temporal coherence of the aberrant oscillations in the olivocerebellar loop, thus establishing its causal role. The suppression of aberrant neural oscillation via phase-locked driven disruption of temporal coherence may in the future represent a powerful neuromodulatory strategy to treat brain disorders.

The therapeutic mechanism of epilepsy seizures in different target areas: Research on a theoretical model

BACKGROUND

The selection of optimal target areas in the surgical treatment of epilepsy is always a difficult problem in medicine.

OBJECTIVE

We employed a theoretical calculation model to explore the control mechanism of seizures by an external voltage stimulus acting in different nerve nuclei.

METHODS

Theoretical analysis and numerical simulation were combined.

RESULTS

The globus pallidus, excitatory pyramidal neurons, striatal D1 neurons, thalamic reticular nucleus and specific relay nuclei were selected, we analyzed that the electrical stimulation has different effects in these target areas.

CONCLUSIONS

The data selected were reasonable in study, the results may give a theoretical support for similar studies in clinical.

Insights on the role of external globus pallidus in controlling absence seizures

Absence epilepsy, characterized by transient loss of awareness and bilaterally synchronous 2-4 Hz spike and wave discharges (SWDs) on electroencephalography (EEG) during absence seizures, is generally believed to arise from abnormal interactions between the cerebral cortex (Ctx) and thalamus. Recent animal electrophysiological studies suggested that changing the neural activation level of the external globus pallidus (GPe) neurons can remarkably modify firing rates of the thalamic reticular nucleus (TRN) neurons through the GABAergic GPe-TRN pathway. However, the existing experimental evidence does not provide a clear answer as to whether the GPe-TRN pathway contributes to regulating absence seizures. Here, using a biophysically based mean-field model of the GPe-corticothalamic (GCT) network, we found that both directly decreasing the strength of the GPe-TRN pathway and inactivating GPe neurons can effectively suppress absence seizures. Also, the pallido-cortical pathway and the recurrent connection of GPe neurons facilitate the regulation of absence seizures through the GPe-TRN pathway. Specifically, in the controllable situation, enhancing the coupling strength of either of the two pathways can successfully terminate absence seizures. Moreover, the competition between the GPe-TRN and pallido-cortical pathways may lead to the GPe bidirectionally controlling absence seizures, and this bidirectional control manner can be significantly modulated by the Ctx-TRN pathway. Importantly, when the strength of the Ctx-TRN pathway is relatively strong, the bidirectional control of absence seizures by changing GPe neural activities can be observed at both weak and strong strengths of the pallido-cortical pathway.These findings suggest that the GPe-TRN pathway may have crucial functional roles in regulating absence seizures, which may provide a testable hypothesis for further experimental studies and new perspectives on the treatment of absence epilepsy.

The theoretical mechanism of Parkinson's oscillation frequency bands: a computational model study

Excessive synchronous oscillation activities appear in the brain is a key pathological feature of Parkinson's disease, the mechanism of which is still unclear. Although some previous studies indicated that β oscillation (13-30 Hz) may directly originate in the network composed of the subthalamic nucleus (STN) and external globus pallidus (GPe) neurons, specific onset mechanisms of which are unclear, especially theoretical evidences in numerical simulation are still little. In this paper, we employ a STN-GPe mean-field model to explore the onset mechanism of Parkinson's oscillation. In addition to β oscillation, we find that some other common oscillation frequency bands can appear in this network, such as the α oscillation band (8-12 Hz), the θ oscillation band (4-7 Hz) and δ oscillation band (1-3 Hz). In addition to the coupling weight between the STN and GPe, the delay is also a critical factor to affect oscillatory activities, which can not be neglected compared to other parameters. Through simulation and analysis, we propose two possible theories may induce the system to transfer from the stable state to the oscillatory state in this model: (1). The oscillation activity can be induced when the firing activation level of the population increases to large enough; (2). In some special cases, the population may stay in the high firing rate stable state and the mean discharge rate of which is too large to induce oscillations, then oscillation activities may be induced as the MD decreases to moderate value. In most situations, the change trends of the MD and oscillation dominant frequency are contrary, which may be an important physiological phenomenon shown in this model. The delays and firing rates were obtained by simulating, which may be verified in the experiment in the future.

A Basal Ganglia Computational Model to Explain the Paradoxical Sensorial Improvement in the Presence of Huntington's Disease

The basal ganglia (BG) represent a critical center of the nervous system for sensorial discrimination. Although it is known that Huntington's disease (HD) affects this brain area, it still remains unclear how HD patients achieve paradoxical improvement in sensorial discrimination tasks. This paper presents a computational model of the BG including the main nuclei and the typical firing properties of their neurons. The BG model has been embedded within an auditory signal detection task. We have emulated the effect that the altered levels of dopamine and the degree of HD affectation have in information processing at different layers of the BG, and how these aspects shape transient and steady states differently throughout the selection task. By extracting the independent components of the BG activity at different populations, it is evidenced that early and medium stages of HD affectation may enhance transient activity in the striatum and the substantia nigra pars reticulata. These results represent a possible explanation for the paradoxical improvement that HD patients present in discrimination task performance. Thus, this paper provides a novel understanding on how the fast dynamics of the BG network at different layers interact and enable transient states to emerge throughout the successive neuron populations.

A non-linear deterministic model of action selection in the basal ganglia to simulate motor fluctuations in Parkinson's disease

Motor fluctuations and dyskinesias are severe complications of Parkinson's disease (PD), especially evident at its advanced stage, under long-term levodopa therapy. Despite their strong clinical prevalence, the neural origin of these motor symptoms is still a subject of intense debate. In this work, a non-linear deterministic neurocomputational model of the basal ganglia (BG), inspired by biology, is used to provide more insights into possible neural mechanisms at the basis of motor complications in PD. In particular, the model is used to simulate the finger tapping task. The model describes the main neural pathways involved in the BG to select actions [the direct or Go, the indirect or NoGo, and the hyperdirect pathways via the action of the sub-thalamic nucleus (STN)]. A sensitivity analysis is performed on some crucial model parameters (the dopamine level, the strength of the STN mechanism, and the strength of competition among different actions in the motor cortex) at different levels of synapses, reflecting major or minor motor training. Depending on model parameters, results show that the model can reproduce a variety of clinically relevant motor patterns, including normokinesia, bradykinesia, several attempts before movement, freezing, repetition, and also irregular fluctuations. Motor symptoms are, especially, evident at low or high dopamine levels, with excessive strength of the STN and with weak competition among alternative actions. Moreover, these symptoms worsen if the synapses are subject to insufficient learning. The model may help improve the comprehension of motor complications in PD and, ultimately, may contribute to the treatment design.

A biologically constrained spiking neural network model of the primate basal ganglia with overlapping pathways exhibits action selection

Action selection has been hypothesized to be a key function of the basal ganglia, yet the nuclei involved, their interactions and the importance of the direct/indirect pathway segregation in such process remain debated. Here, we design a spiking computational model of the monkey basal ganglia derived from a previously published population model, initially parameterized to reproduce electrophysiological activity at rest and to embody as much quantitative anatomical data as possible. As a particular feature, both models exhibit the strong overlap between the direct and indirect pathways that has been documented in non-human primates. Here, we first show how the translation from a population to an individual neuron model was achieved, with the addition of a minimal number of parameters. We then show that our model performs action selection, even though it was built without any assumption on the activity carried out during behaviour. We investigate the mechanisms of this selection through circuit disruptions and found an instrumental role of the off-centre/on-surround structure of the MSN-STN-GPi circuit, as well as of the MSN-MSN and FSI-MSN projections. This validates their potency in enabling selection. We finally study the pervasive centromedian and parafascicular thalamic inputs that reach all basal ganglia nuclei and whose influence is therefore difficult to anticipate. Our model predicts that these inputs modulate the responsiveness of action selection, making them a candidate for the regulation of the speed-accuracy trade-off during decision-making.

A review of computational modeling and deep brain stimulation: applications to Parkinson's disease

Biophysical computational models are complementary to experiments and theories, providing powerful tools for the study of neurological diseases. The focus of this review is the dynamic modeling and control strategies of Parkinson's disease (PD). In previous studies, the development of parkinsonian network dynamics modeling has made great progress. Modeling mainly focuses on the cortex-thalamus-basal ganglia (CTBG) circuit and its sub-circuits, which helps to explore the dynamic behavior of the parkinsonian network, such as synchronization. Deep brain stimulation (DBS) is an effective strategy for the treatment of PD. At present, many studies are based on the side effects of the DBS. However, the translation from modeling results to clinical disease mitigation therapy still faces huge challenges. Here, we introduce the progress of DBS improvement. Its specific purpose is to develop novel DBS treatment methods, optimize the treatment effect of DBS for each patient, and focus on the study in closed-loop DBS. Our goal is to review the inspiration and insights gained by combining the system theory with these computational models to analyze neurodynamics and optimize DBS treatment.

Model-based optimized phase-deviation deep brain stimulation for Parkinson 's disease

High-frequency deep brain stimulation (HF-DBS) of the subthalamic nucleus (STN), globus pallidus interna (GPi) and globus pallidus externa (GPe) are often considered as effective methods for the treatment of Parkinson's disease (PD). However, the stimulation of a single nucleus by HF-DBS can cause specific physical damage, produce side effects and usually consume more electrical energy. Therefore, we use a biophysically-based model of basal ganglia-thalamic circuits to explore more effective stimulation patterns to reduce adverse effects and save energy. In this paper, we computationally investigate the combined DBS of two nuclei with the phase deviation between two stimulation waveforms (CDBS). Three different stimulation combination strategies are proposed, i.e., STN and GPe CDBS (SED), STN and GPi CDBS (SID), as well as GPi and GPe CDBS (GGD). Resultantly, it is found that anti-phase CDBS is more effective in improving parkinsonian dynamical properties, including desynchronization of neurons and the recovery of the thalamus relay ability. Detailed simulation investigation shows that anti-phase SED and GGD are superior to SID. Besides, the energy consumption can be largely reduced by SED and GGD (72.5% and 65.5%), compared to HF-DBS. These results provide new insights into the optimal stimulation parameter and target choice of PD, which may be helpful for the clinical practice.

Regulation and control roles of the basal ganglia in the development of absence epileptiform activities

Absence epileptiform activities are traditionally considered to be primarily induced by abnormal interactions between the cortical and thalamic neurons, which form the thalamocortical circuit in the brain. The basal ganglia, as an organizational unit in the brain, has close input and output relationships with the thalamocortical circuit. Although several studies report that the basal ganglia may participate in controlling and regulating absence epileptiform activities, to date, there have been no studies regarding whether the basal ganglia directly cause absence epileptiform activities. In this paper, we built a basal ganglia-corticothalamic network model to determine the role of basal ganglia in this disease. We determined that absence epileptiform activities might be directly induced by abnormal coupling strengths on certain pivotal pathways in the basal ganglia. These epileptiform activities can be well controlled by the coupling strengths of three major pathways that project from the thalamocortical network to the basal ganglia. The results implied that the substantia nigra pars compacta (SNc) can be considered to be the effective treatment target area for inhibiting epileptiform activities, which supports the observations of previous studies. Particularly, as a major contribution of this paper, we determined that the final presentation position of the epileptic slow spike waves is not limited to the cerebral cortex; these waves may additionally appear in the thalamus, striatal medium spiny neurons, striatal fast spiking interneuron, the SNc, subthalamic nucleus, substantia nigra pars reticulata and globus pallidus pars externa. In addition, consistent with several previous studies, the delay in the network was observed to be a critical factor for inducing transitions between different types of absence epileptiform activities. Our new model not only explains the onset and control mechanism but also provides a unified framework to study similar problems in neuron systems.

The onset mechanism of Parkinson's beta oscillations: A theoretical analysis

In this paper, we build a basal ganglia-cortex-thalamus model to study the oscillatory mechanisms and boundary conditions of the beta frequency band (13-30 Hz) that appears in the subthalamic nucleus. First, a theoretical oscillatory boundary formula is obtained in a simplified model by using the Laplace transform and linearization process of the system at fixed points. Second, we simulate the oscillatory boundary conditions through numerical calculations, which fit with our theoretical results very well, at least in the changing trend. We find that several critical coupling strengths in the model exert great effects on the oscillations, the mechanisms of which differ but can be explained in detail by our model and the oscillatory boundary formula. Specifically, we note that the relatively small or large sizes of the coupling strength from the fast-spiking interneurons to the medium spiny neurons and from the cortex to the fast-spiking interneurons both have obvious maintenance roles on the states. Similar phenomena have been reported in other neurological diseases, such as absence epilepsy. However, some of those interesting mutual regulation mechanisms in the model have rarely been considered in previous studies. In addition to the coupling weight in the pathway, in this work, we show that the delay is a key parameter that affects oscillations. On the one hand, the system needs a minimum delay to generate oscillations; on the other hand, in the appropriate range, a longer delay leads to a higher activation level of the subthalamic nucleus. In this paper, we study the oscillation activities that appear on the subthalamic nucleus. Moreover, all populations in the model show the dynamic behaviour of a synchronous resonance. Therefore, we infer that the mechanisms obtained can be expanded to explore the state of other populations, and that the model provides a unified framework for studying similar problems in the future. Moreover, the oscillatory boundary curves obtained are all critical conditions between the stable state and beta frequency oscillation. The method is also suitable for depicting other common frequency bands during brain oscillations, such as the alpha band (8-12 Hz), theta band (4-7 Hz) and delta band (1-3 Hz). Thus, the results of this work are expected to help us better understand the onset mechanism of parkinson's oscillations and can inspire related experimental research in this field.

The beta oscillation conditions in a simplified basal ganglia network

Parkinson's disease is a type of motor dysfunction disease that is induced mainly by abnormal interactions between the subthalamic nucleus (STN) and globus pallidus (GP) neurons. Periodic oscillatory activities with frequencies of 13-30 Hz are the main physiological characteristics of Parkinson's disease. In this paper, we built a class of STN-GP networks to explore beta oscillation conditions. A theoretical formula was obtained for generating oscillations without internal GP connections. Based on this formula, we studied the effects of cortex inputs, striatum inputs, coupling weights and delays on oscillation conditions, and the theoretical results are in good agreement with the numerical results. The onset mechanism can be explained by the model, and the internal GP connection has little effect on oscillations. Finally, we compared oscillation conditions with those in previous studies and found that the delays and coupling weights required for generating oscillations may decrease as the number of nuclei increases. We hope that the results obtained will inspire future theoretical and experimental studies.

Suppression of Parkinsonian Beta Oscillations by Deep Brain Stimulation: Determination of Effective Protocols

A neural field model of the corticothalamic-basal ganglia system is developed that describes enhanced beta activity within subthalamic and pallidal circuits in Parkinson's disease (PD) via system resonances. A model of deep brain stimulation (DBS) of typical clinical targets, the subthalamic nucleus (STN) and globus pallidus internus (GPi), is added and studied for several distinct stimulation protocols that are used for treatment of the motor symptoms of PD and that reduce pathological beta band activity (13-30 Hz) in the corticothalamic-basal ganglia network. The resulting impact of DBS on enhanced beta activity in the STN and GPi, as well as cortico-subthalamic and cortico-pallidal coherence, are studied. Both STN-DBS and GPi-DBS are found to be effective for suppressing peak STN and GPi power in the beta band, with GPi-DBS being slightly more effective in both the STN and the GPi for all stimulus protocols tested. The largest decrease in cortico-STN coherence is observed during STN-DBS, whereas GPi-DBS is most effective for reducing cortico-GPi coherence. A reduction of the pathologically large STN connection strengths that define the parkinsonian state results in enhanced 6 Hz activity and could thus represent a compensatory mechanism that has the side effect of driving parkinsonian tremor-like oscillations. This model provides a method for systematically testing effective DBS protocols that agrees with experimental and clinical findings. Furthermore, the model suggests GPi-DBS and STN-DBS have distinct impacts on elevated synchronization between the basal ganglia and motor cortex in PD.

Bayesian adaptive dual control of deep brain stimulation in a computational model of Parkinson's disease

In this paper, we present a novel Bayesian adaptive dual controller (ADC) for autonomously programming deep brain stimulation devices. We evaluated the Bayesian ADC's performance in the context of reducing beta power in a computational model of Parkinson's disease, in which it was tasked with finding the set of stimulation parameters which optimally reduced beta power as fast as possible. Here, the Bayesian ADC has dual goals: (a) to minimize beta power by exploiting the best parameters found so far, and (b) to explore the space to find better parameters, thus allowing for better control in the future. The Bayesian ADC is composed of two parts: an inner parameterized feedback stimulator and an outer parameter adjustment loop. The inner loop operates on a short time scale, delivering stimulus based upon the phase and power of the beta oscillation. The outer loop operates on a long time scale, observing the effects of the stimulation parameters and using Bayesian optimization to intelligently select new parameters to minimize the beta power. We show that the Bayesian ADC can efficiently optimize stimulation parameters, and is superior to other optimization algorithms. The Bayesian ADC provides a robust and general framework for tuning stimulation parameters, can be adapted to use any feedback signal, and is applicable across diseases and stimulator designs.

Roles for globus pallidus externa revealed in a computational model of action selection in the basal ganglia

The basal ganglia are considered vital to action selection - a hypothesis supported by several biologically plausible computational models. Of the several subnuclei of the basal ganglia, the globus pallidus externa (GPe) has been thought of largely as a relay nucleus, and its intrinsic connectivity has not been incorporated in significant detail, in any model thus far. Here, we incorporate newly revealed subgroups of neurons within the GPe into an existing computational model of the basal ganglia, and investigate their role in action selection. Three main results ensued. First, using previously used metrics for selection, the new extended connectivity improved the action selection performance of the model. Second, low frequency theta oscillations were observed in the subpopulation of the GPe (the TA or 'arkypallidal' neurons) which project exclusively to the striatum. These oscillations were suppressed by increased dopamine activity - revealing a possible link with symptoms of Parkinson's disease. Third, a new phenomenon was observed in which the usual monotonic relationship between input to the basal ganglia and its output within an action 'channel' was, under some circumstances, reversed. Thus, at high levels of input, further increase of this input to the channel could cause an increase of the corresponding output rather than the more usually observed decrease. Moreover, this phenomenon was associated with the prevention of multiple channel selection, thereby assisting in optimal action selection. Examination of the mechanistic origin of our results showed the so-called 'prototypical' GPe neurons to be the principal subpopulation influencing action selection. They control the striatum via the arkypallidal neurons and are also able to regulate the output nuclei directly. Taken together, our results highlight the role of the GPe as a major control hub of the basal ganglia, and provide a mechanistic account for its control function.

Physiology-based ERPs in normal and abnormal states

Evoked response potentials (ERPs) and other transients are modeled as impulse responses using physiology-based neural field theory (NFT) of the corticothalamic system of neural activity in the human brain that incorporates synaptic and dendritic dynamics, firing response, axonal propagation, and corticocortical and corticothalamic pathways. The properties of model-predicted ERPs are explored throughout the stability zone of the corticothalamic system, and predicted time series and wavelet spectra are also analyzed. This provides a unified treatment of predicted ERPs for both normal and abnormal states within the brain's stability zone, including likely parameters to represent abnormal states of reduced arousal.

Model and Analysis for the Onset of Parkinsonian Firing Patterns in a Simplified Basal Ganglia

Parkinson's disease (PD) is a degenerative neurological disease that disrupts the movement cycle in the basal ganglia. As the disease progresses, dopamine depletion leads to changes to how the basal ganglia functions as well as the appearance of abnormal beta oscillations. There is much debate on just exactly how these connection strengths change and just how the oscillations emerge. One leading hypothesis claims that the oscillations develop in the globus pallidus external, subthalamic nucleus, and globus pallidus internal loop. We introduce a mathematical model that calculates the average firing rates of this loop while still accounting for the larger closed loop of the entire basal ganglia system. This model is constructed such that physiologically realistic results can be obtained while not sacrificing the use of analytic methods. Because of this, it is possible to determine how the change in the connection strengths can drive the necessary changes in firing rates seen in recordings and account for the generation of trademark beta oscillations of PD without relying on highly specific time delays, stochastic approaches, or numerical approximations. Additionally, we find that the entire cortico-basal ganglia-thalamo-cortical loop is essential for abnormal oscillations to originate.

The oscillatory boundary conditions of different frequency bands in Parkinson's disease

Parkinson's disease (PD) is a neurodegenerative disease that is common in the elderly population. The most important pathological change in PD is the degeneration and death of dopaminergic neurons in the substantia nigra of the midbrain, which results in a decrease in the dopamine (DA) content of the striatum. The exact cause of this pathological change is still unknown. Numerous studies have shown that the evolution of PD is associated with abnormal oscillatory activities in the basal ganglia, with different oscillation frequency ranges, such as the typical beta band (13-30 Hz), the alpha band (8-12 Hz), the theta band (4-7 Hz) and the delta band (1-3 Hz). Although some studies have implied that abnormal interactions between the subthalamic nucleus (STN) and globus pallidus (GP) neurons may be a key factor required to induce these oscillations, the relative mechanism is still unclear. The effects of other nerve nuclei in the basal ganglia, such as the striatum, on these oscillations are still unknown. The thalamus and cortex both have close input and output relationships with the basal ganglia, and many previous studies have indicated that they may also exert effects on Parkinson's disease oscillation, but the mechanisms involved are unclear. In this paper, we built a corticothalamic-basal ganglia (CTBG) mean firing-rate model to explore the onset mechanisms of these different oscillation phenomena. We found that, in addition to the STN-GP network, Parkinson's disease oscillations may also be induced by changing the coupling strength and delays in other pathways. Different frequency bands appear in the oscillating region, and various boundary conditions are depicted in parameter diagrams. The onset mechanism is well explained both by the model and by the numerical simulation results. Therefore, this model provides a unifying framework for studying the mechanism of Parkinson's disease oscillations, and we hope that the results obtained in this work can inspire future experimental studies.