Origins and suppression of oscillations in a computational model of Parkinson's disease

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.

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.

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

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

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.

Intensity-Varied Closed-Loop Noise Stimulation for Oscillation Suppression in the Parkinsonian State

This work explores the effectiveness of the intensity-varied closed-loop noise stimulation on the oscillation suppression in the Parkinsonian state. Deep brain stimulation (DBS) is the standard therapy for Parkinson's disease (PD), but its effects need to be improved. The noise stimulation has compelling results in alleviating the PD state. However, in the open-loop control scheme, the noise stimulation parameters cannot be self-adjusted to adapt to the amplitude of the synchronized neuronal activities in real time. Thus, based on the delayed-feedback control algorithm, an intensity-varied closed-loop noise stimulation strategy is proposed. Based on a computational model of the basal ganglia (BG) that can present the intrinsic properties of the BG neurons and their interactions with the thalamic neurons, the proposed stimulation strategy is tested. Simulation results show that the noise stimulation suppresses the pathological beta (12-35 Hz) oscillations without any new rhythms in other bands compared with traditional high-frequency DBS. The intensity-varied closed-loop noise stimulation has a more profound role in removing the pathological beta oscillations and improving the thalamic reliability than open-loop noise stimulation, especially for different PD states. And the closed-loop noise stimulation enlarges the parameter space of the delayed-feedback control algorithm due to the randomness of noise signals. We also provide a theoretical analysis of the effective parameter domain of the delayed-feedback control algorithm by simplifying the BG model to an oscillator model. This exploration may guide a new approach to treating PD by optimizing the noise-induced improvement of the BG dysfunction.

Topographic connectivity and cellular profiling reveal detailed input pathways and functionally distinct cell types in the subthalamic nucleus

The subthalamic nucleus (STN) controls psychomotor activity and is an efficient therapeutic deep brain stimulation target in individuals with Parkinson's disease. Despite evidence indicating position-dependent therapeutic effects and distinct functions within the STN, the input circuit and cellular profile in the STN remain largely unclear. Using neuroanatomical techniques, we construct a comprehensive connectivity map of the indirect and hyperdirect pathways in the mouse STN. Our circuit- and cellular-level connectivities reveal a topographically graded organization with three types of indirect and hyperdirect pathways (external globus pallidus only, STN only, and collateral). We confirm consistent pathways into the human STN by 7 T MRI-based tractography. We identify two functional types of topographically distinct glutamatergic STN neurons (parvalbumin [PV+/-]) with synaptic connectivity from indirect and hyperdirect pathways. Glutamatergic PV+ STN neurons contribute to burst firing. These data suggest a complex interplay of information integration within the basal ganglia underlying coordinated movement control and therapeutic effects.

Closing the loop of DBS using the beta oscillations in cortex

Cortical information has great importance to reflect the deep brain stimulation (DBS) effects for Parkinson's disease patients. Using cortical activities to feedback is an available closed-loop idea for DBS. Previous studies have demonstrated the pathological beta (12-35 Hz) cortical oscillations can be suppressed by appropriate DBS settings. Thus, here we propose to close the loop of DBS based on the beta oscillations in cortex. By modify the cortico-basal ganglia-thalamic neural loop model, more biologically realistic underlying the Parkinsonian phenomenon is approached. Stimulation results show the proposed closed-loop DBS strategy using cortical beta oscillation as feedback information has more profound roles in alleviating the pathological neural abnormality than the traditional open-loop DBS. Additionally, we compare the stimulation effects with subthalamic nucleus feedback strategy. It is shown that using cortical beta information as the feedback signals can further enlarge the control parameter space based on proportional-integral control structure with a lower energy expenditure. This work may pave the way to optimizing the DBS effects in a closed-loop arrangement.

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.

Leveraging deep learning to control neural oscillators

Modulation of the firing times of neural oscillators has long been an important control objective, with applications including Parkinson's disease, Tourette's syndrome, epilepsy, and learning. One common goal for such modulation is desynchronization, wherein two or more oscillators are stimulated to transition from firing in phase with each other to firing out of phase. The optimization of such stimuli has been well studied, but this typically relies on either a reduction of the dimensionality of the system or complete knowledge of the parameters and state of the system. This limits the applicability of results to real problems in neural control. Here, we present a trained artificial neural network capable of accurately estimating the effects of square-wave stimuli on neurons using minimal output information from the neuron. We then apply the results of this network to solve several related control problems in desynchronization, including desynchronizing pairs of neurons and achieving clustered subpopulations of neurons in the presence of coupling and noise.

Interaction of Indirect and Hyperdirect Pathways on Synchrony and Tremor-Related Oscillation in the Basal Ganglia

Low-frequency oscillatory activity (3-9 Hz) and increased synchrony in the basal ganglia (BG) are recognized to be crucial for Parkinsonian tremor. However, the dynamical mechanism underlying the tremor-related oscillations still remains unknown. In this paper, the roles of the indirect and hyperdirect pathways on synchronization and tremor-related oscillations are considered based on a modified Hodgkin-Huxley model. Firstly, the effects of indirect and hyperdirect pathways are analysed individually, which show that increased striatal activity to the globus pallidus external (GPe) or strong cortical gamma input to the subthalamic nucleus (STN) is sufficient to promote synchrony and tremor-related oscillations in the BG network. Then, the mutual effects of both pathways are analysed by adjusting the related currents simultaneously. Our results suggest that synchrony and tremor-related oscillations would be strengthened if the current of these two paths are in relative imbalance. And the network tends to be less synchronized and less tremulous when the frequency of cortical input is in the theta band. These findings may provide novel treatments in the cortex and striatum to alleviate symptoms of tremor in Parkinson's disease.

Optimal open-loop desynchronization of neural oscillator populations

Deep brain stimulation (DBS) is an increasingly used medical treatment for various neurological disorders. While its mechanisms are not fully understood, experimental evidence suggests that through application of periodic electrical stimulation DBS may act to desynchronize pathologically synchronized populations of neurons resulting desirable changes to a larger brain circuit. However, the underlying mathematical mechanisms by which periodic stimulation can engender desynchronization in a coupled population of neurons is not well understood. In this work, a reduced phase-amplitude reduction framework is used to characterize the desynchronizing influence of periodic stimulation on a population of coupled oscillators. Subsequently, optimal control theory allows for the design of periodic, open-loop stimuli with the capacity to destabilize completely synchronized solutions while simultaneously stabilizing rotating block solutions. This framework exploits system nonlinearities in order to strategically modify unstable Floquet exponents. In the limit of weak neural coupling, it is shown that this method only requires information about the phase response curves of the individual neurons. The effects of noise and heterogeneity are also considered and numerical results are presented. This framework could ultimately be used to inform the design of more efficient deep brain stimulation waveforms for the treatment of neurological disease.

Model-Based Evaluation of Closed-Loop Deep Brain Stimulation Controller to Adapt to Dynamic Changes in Reference Signal

High-frequency deep brain stimulation (DBS) of the subthalamic nucleus (STN) is effective in suppressing the motor symptoms of Parkinson's disease (PD). Current clinically-deployed DBS technology operates in an open-loop fashion, i.e., fixed parameter high-frequency stimulation is delivered continuously, invariant to the needs or status of the patient. This poses two major challenges: (1) depletion of the stimulator battery due to the energy demands of continuous high-frequency stimulation, (2) high-frequency stimulation-induced side-effects. Closed-loop deep brain stimulation (CL DBS) may be effective in suppressing parkinsonian symptoms with stimulation parameters that require less energy and evoke fewer side effects than open loop DBS. However, the design of CL DBS comes with several challenges including the selection of an appropriate biomarker reflecting the symptoms of PD, setting a suitable reference signal, and implementing a controller to adapt to dynamic changes in the reference signal. Dynamic changes in beta oscillatory activity occur during the course of voluntary movement, and thus there may be a performance advantage to tracking such dynamic activity. We addressed these challenges by studying the performance of a closed-loop controller using a biophysically-based network model of the basal ganglia. The model-based evaluation consisted of two parts: (1) we implemented a Proportional-Integral (PI) controller to compute optimal DBS frequencies based on the magnitude of a dynamic reference signal, the oscillatory power in the beta band (13-35 Hz) recorded from model globus pallidus internus (GPi) neurons. (2) We coupled a linear auto-regressive model based mapping function with the Routh-Hurwitz stability analysis method to compute the parameters of the PI controller to track dynamic changes in the reference signal. The simulation results demonstrated successful tracking of both constant and dynamic beta oscillatory activity by the PI controller, and the PI controller followed dynamic changes in the reference signal, something that cannot be accomplished by constant open-loop DBS.

Different Dopaminergic Dysfunctions Underlying Parkinsonian Akinesia and Tremor

Although the occurrence of Parkinsonian akinesia and tremor is traditionally associated to dopaminergic degeneration, the multifaceted neural processes that cause these impairments are not fully understood. As a consequence, current dopamine medications cannot be tailored to the specific dysfunctions of patients with the result that generic drug therapies produce different effects on akinesia and tremor. This article proposes a computational model focusing on the role of dopamine impairments in the occurrence of akinesia and resting tremor. The model has three key features, to date never integrated in a single computational system: (a) an architecture constrained on the basis of the relevant known system-level anatomy of the basal ganglia-thalamo-cortical loops; (b) spiking neurons with physiologically-constrained parameters; (c) a detailed simulation of the effects of both phasic and tonic dopamine release. The model exhibits a neural dynamics compatible with that recorded in the brain of primates and humans. Moreover, it suggests that akinesia might involve both tonic and phasic dopamine dysregulations whereas resting tremor might be primarily caused by impairments involving tonic dopamine release and the responsiveness of dopamine receptors. These results could lead to develop new therapies based on a system-level view of the Parkinson's disease and targeting phasic and tonic dopamine in differential ways.

Isostable reduction of oscillators with piecewise smooth dynamics and complex Floquet multipliers

Phase-amplitude reduction is a widely applied technique in the study of limit cycle oscillators with the ability to represent a complicated and high-dimensional dynamical system in a more analytically tractable set of coordinates. Recent work has focused on the use of isostable coordinates, which characterize the transient decay of solutions toward a periodic orbit, and can ultimately be used to increase the accuracy of these reduced models. The breadth of systems to which this phase-amplitude reduction strategy can be applied, however, is still rather limited. In this work, the theory of phase-amplitude reduction using isostable coordinates is further developed to accommodate a broader set of dynamical systems. In the first part, limit cycles of piecewise smooth dynamical systems are considered and strategies are developed to compute the associated reduced equations. In the second part, the notion of isostable coordinates for complex-valued Floquet multipliers is introduced, resulting in one phaselike coordinate and one amplitudelike coordinate for each pair of complex conjugate Floquet multipliers. Examples are given with relevance to piecewise smooth representations of excitable cardiomyocytes and the relationship between the reduced coordinate system and the emergence of cardiac alternans is discussed. Also, phase-amplitude reduction is implemented for a chaotic, externally forced pendulum with complex Floquet multipliers and a resulting control strategy for the stabilization of its periodic solution is investigated.

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.

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.

Robust desynchronization of Parkinson's disease pathological oscillations by frequency modulation of delayed feedback deep brain stimulation

The hyperkinetic symptoms of Parkinson's Disease (PD) are associated with the ensembles of interacting oscillators that cause excess or abnormal synchronous behavior within the Basal Ganglia (BG) circuitry. Delayed feedback stimulation is a closed loop technique shown to suppress this synchronous oscillatory activity. Deep Brain Stimulation (DBS) via delayed feedback is known to destabilize the complex intermittent synchronous states. Computational models of the BG network are often introduced to investigate the effect of delayed feedback high frequency stimulation on partially synchronized dynamics. In this study, we develop a reduced order model of four interacting nuclei of the BG as well as considering the Thalamo-Cortical local effects on the oscillatory dynamics. This model is able to capture the emergence of 34 Hz beta band oscillations seen in the Local Field Potential (LFP) recordings of the PD state. Train of high frequency pulses in a delayed feedback stimulation has shown deficiencies such as strengthening the synchronization in case of highly fluctuating neuronal activities, increasing the energy consumed as well as the incapability of activating all neurons in a large-scale network. To overcome these drawbacks, we propose a new feedback control variable based on the filtered and linearly delayed LFP recordings. The proposed control variable is then used to modulate the frequency of the stimulation signal rather than its amplitude. In strongly coupled networks, oscillations reoccur as soon as the amplitude of the stimulus signal declines. Therefore, we show that maintaining a fixed amplitude and modulating the frequency might ameliorate the desynchronization process, increase the battery lifespan and activate substantial regions of the administered DBS electrode. The charge balanced stimulus pulse itself is embedded with a delay period between its charges to grant robust desynchronization with lower amplitudes needed. The efficiency of the proposed Frequency Adjustment Stimulation (FAS) protocol in a delayed feedback method might contribute to further investigation of DBS modulations aspired to address a wide range of abnormal oscillatory behavior observed in neurological disorders.

Systems approaches to optimizing deep brain stimulation therapies in Parkinson's disease

Over the last 30 years, deep brain stimulation (DBS) has been used to treat chronic neurological diseases like dystonia, obsessive-compulsive disorders, essential tremor, Parkinson's disease, and more recently, dementias, depression, cognitive disorders, and epilepsy. Despite its wide use, DBS presents numerous challenges for both clinicians and engineers. One challenge is the design of novel, more efficient DBS therapies, which are hampered by the lack of complete understanding about the cellular mechanisms of therapeutic DBS. Another challenge is the existence of redundancy in clinical outcomes, that is, different DBS programs can result in similar clinical benefits but very little information (e.g., predictive models, longitudinal data, metrics, etc.) is available to select one program over another. Finally, there is high variability in patients' responses to DBS, which forces clinicians to carefully adjust the stimulation settings to each patient via lengthy programming sessions. Researchers in neural engineering and systems biology have been tackling these challenges over the past few years with the specific goal of developing novel DBS therapies, design methodologies, and computational tools that optimize the therapeutic effects of DBS in each patient. Furthermore, efforts are being made to automatically adapt the DBS treatment to the fluctuations of disease symptoms. A review of the quantitative approaches currently available for the treatment of Parkinson's disease is presented here with an emphasis on the contributions that systems theoretical approaches have provided to understand the global dynamics of complex neuronal circuits in the brain under DBS. This article is categorized under: Translational, Genomic, and Systems Medicine > Therapeutic Methods Analytical and Computational Methods > Computational Methods Analytical and Computational Methods > Dynamical Methods Physiology > Mammalian Physiology in Health and Disease.

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.

Modeling and Analysis of Beta Oscillations in the Basal Ganglia

Enhanced beta (12-30 Hz) oscillatory activity in the basal ganglia (BG) is a prominent feature of the Parkinsonian state in animal models and in patients with Parkinson's disease. Increased beta oscillations are associated with severe dopaminergic striatal depletion. However, the mechanisms underlying these pathological beta oscillations remain elusive. Inspired by the experimental observation that only subsets of neurons within each nucleus in the BG exhibit oscillatory activities, a computational model of the BG-thalamus neuronal network is proposed, which is characterized by subdivided nuclei within the BG. Using different currents externally applied to the neurons within a given nucleus, neurons behave according to one of the two subgroups, named "-N" and "-P," where "-N" and "-P" denote the normal and the Parkinsonian states, respectively. The ratio of "-P" to "-N" neurons indicates the degree of the Parkinsonian state. Simulation results show that if "-P" neurons have a high degree of connectivity in the subthalamic nucleus (STN), they will have a significant downstream effect on the generation of beta oscillations in the globus pallidus. Interestingly, however, the generation of beta oscillations in the STN is independent of the selection of the "-P" neurons in the external segment of the globus pallidus (GPe), despite the reciprocal structure between STN and GPe. This computational model may pave the way to revealing the mechanism of such pathological behaviors in a realistic way that can replicate experimental observations. The simulation results suggest that the STN is more suitable than GPe as a deep brain stimulation target.

Pallidal Deep-Brain Stimulation Disrupts Pallidal Beta Oscillations and Coherence with Primary Motor Cortex in Parkinson's Disease

In Parkinson's disease (PD), subthalamic nucleus beta band oscillations are decreased by therapeutic deep-brain stimulation (DBS) and this has been proposed as important to the mechanism of therapy. The globus pallidus is a common alternative target for PD with similar motor benefits as subthalamic DBS, but effects of pallidal stimulation in PD are not well studied, and effects of pallidal DBS on cortical function in PD are unknown. Here, in 20 PD and 14 isolated dystonia human patients of both genders undergoing pallidal DBS lead implantation, we recorded local field potentials from the globus pallidus and in a subset of these, recorded simultaneous sensorimotor cortex ECoG potentials. PD patients had elevated resting pallidal low beta band (13-20 Hz) power compared with dystonia patients, whereas dystonia patients had elevated resting pallidal theta band (4-8 Hz) power compared with PD. We show that this results in disease-specific patterns of interaction between the pallidum and motor cortex: PD patients demonstrated relatively elevated phase coherence with the motor cortex in the beta band and this was reduced by therapeutic pallidal DBS. Dystonia patients had greater theta band phase coherence. Our results support the hypothesis that specific motor phenomenology observed in movement disorders are associated with elevated network oscillations in specific frequency bands, and that DBS in movement disorders acts in general by disrupting elevated synchronization between basal ganglia output and motor cortex.SIGNIFICANCE STATEMENT Perturbations in synchronized oscillatory activity in brain networks are increasingly recognized as important features in movement disorders. The globus pallidus is a commonly used target for deep-brain stimulation (DBS) in Parkinson's disease (PD), however, the effects of pallidal DBS on basal ganglia and cortical oscillations are unknown. Using invasive intraoperative recordings in patients with PD and isolated dystonia, we found disease-specific patterns of elevated oscillatory synchronization within the pallidum and in coherence between pallidum and motor cortex. Therapeutic pallidal DBS in PD suppresses these elevated synchronizations, reducing the influence of diseased basal ganglia on cortical physiology. We propose a general mechanism for DBS therapy in movement disorders: functional disconnection of basal ganglia output and motor cortex by coherence suppression.

Designing Patient-Specific Optimal Neurostimulation Patterns for Seizure Suppression

Neurostimulation is a promising therapy for abating epileptic seizures. However, it is extremely difficult to identify optimal stimulation patterns experimentally. In this study, human recordings are used to develop a functional 24 neuron network statistical model of hippocampal connectivity and dynamics. Spontaneous seizure-like activity is induced in silico in this reconstructed neuronal network. The network is then used as a testbed to design and validate a wide range of neurostimulation patterns. Commonly used periodic trains were not able to permanently abate seizures at any frequency. A simulated annealing global optimization algorithm was then used to identify an optimal stimulation pattern, which successfully abated 92% of seizures. Finally, in a fully responsive, or closed-loop, neurostimulation paradigm, the optimal stimulation successfully prevented the network from entering the seizure state. We propose that the framework presented here for algorithmically identifying patient-specific neurostimulation patterns can greatly increase the efficacy of neurostimulation devices for seizures.

A Population of Indirect Pathway Striatal Projection Neurons Is Selectively Entrained to Parkinsonian Beta Oscillations

Classical schemes of basal ganglia organization posit that parkinsonian movement difficulties presenting after striatal dopamine depletion stem from the disproportionate firing rates of spiny projection neurons (SPNs) therein. There remains, however, a pressing need to elucidate striatal SPN firing in the context of the synchronized network oscillations that are abnormally exaggerated in cortical-basal ganglia circuits in parkinsonism. To address this, we recorded unit activities in the dorsal striatum of dopamine-intact and dopamine-depleted rats during two brain states, respectively defined by cortical slow-wave activity (SWA) and activation. Dopamine depletion escalated striatal net output but had contrasting effects on "direct pathway" SPNs (dSPNs) and "indirect pathway" SPNs (iSPNs); their firing rates became imbalanced, and they disparately engaged in network oscillations. Disturbed striatal activity dynamics relating to the slow (∼1 Hz) oscillations prevalent during SWA partly generalized to the exaggerated beta-frequency (15-30 Hz) oscillations arising during cortical activation. In both cases, SPNs exhibited higher incidences of phase-locked firing to ongoing cortical oscillations, and SPN ensembles showed higher levels of rhythmic correlated firing, after dopamine depletion. Importantly, in dopamine-depleted striatum, a widespread population of iSPNs, which often displayed excessive firing rates and aberrant phase-locked firing to cortical beta oscillations, preferentially and excessively synchronized their firing at beta frequencies. Conversely, dSPNs were neither hyperactive nor synchronized to a large extent during cortical activation. These data collectively demonstrate a cell type-selective entrainment of SPN firing to parkinsonian beta oscillations. We conclude that a population of overactive, excessively synchronized iSPNs could orchestrate these pathological rhythms in basal ganglia circuits.SIGNIFICANCE STATEMENT Chronic depletion of dopamine from the striatum, a part of the basal ganglia, causes some symptoms of Parkinson's disease. Here, we elucidate how dopamine depletion alters striatal neuron firing in vivo, with an emphasis on defining whether and how spiny projection neurons (SPNs) engage in the synchronized beta-frequency (15-30 Hz) oscillations that become pathologically exaggerated throughout basal ganglia circuits in parkinsonism. We discovered that a select population of so-called "indirect pathway" SPNs not only fire at abnormally high rates, but are also particularly prone to being recruited to exaggerated beta oscillations. Our results provide an important link between two complementary theories that explain the presentation of disease symptoms on the basis of changes in firing rate or firing synchronization/rhythmicity.

Mechanisms for pattern specificity of deep-brain stimulation in Parkinson's disease

Deep brain stimulation (DBS) has become a widely used technique for treating advanced stages of neurological and psychiatric illness. In the case of motor disorders related to basal ganglia (BG) dysfunction, several mechanisms of action for the DBS therapy have been identified which might be involved simultaneously or in sequence. However, the identification of a common key mechanism underlying the clinical relevant DBS configurations has remained elusive due to the inherent complexity related to the interaction between the electrical stimulation and the neural tissue, and the intricate circuital structure of the BG-thalamocortical network. In this work, it is shown that the clinically relevant range for both, the frequency and intensity of the electrical stimulation pattern, is an emergent property of the BG anatomy at the system-level that can be addressed using mean-field descriptive models of the BG network. Moreover, it is shown that the activity resetting mechanism elicited by electrical stimulation provides a natural explanation to the ineffectiveness of irregular (i.e., aperiodic) stimulation patterns, which has been commonly observed in previously reported pathophysiology models of Parkinson’s disease. Using analytical and numerical techniques, these results have been reproduced in both cases: 1) a reduced mean-field model that can be thought as an elementary building block capable to capture the underlying fundamentals of the relevant loops constituting the BG-thalamocortical network, and 2) a detailed model constituted by the direct and hyperdirect loops including one-dimensional spatial structure of the BG nuclei. We found that the optimal ranges for the essential parameters of the stimulation patterns can be understood without taking into account biophysical details of the relevant structures.

A Consistent Definition of Phase Resetting Using Hilbert Transform

A phase resetting curve (PRC) measures the transient change in the phase of a neural oscillator subject to an external perturbation. The PRC encapsulates the dynamical response of a neural oscillator and, as a result, it is often used for predicting phase-locked modes in neural networks. While phase is a fundamental concept, it has multiple definitions that may lead to contradictory results. We used the Hilbert Transform (HT) to define the phase of the membrane potential oscillations and HT amplitude to estimate the PRC of a single neural oscillator. We found that HT's amplitude and its corresponding instantaneous frequency are very sensitive to membrane potential perturbations. We also found that the phase shift of HT amplitude between the pre- and poststimulus cycles gives an accurate estimate of the PRC. Moreover, HT phase does not suffer from the shortcomings of voltage threshold or isochrone methods and, as a result, gives accurate and reliable estimations of phase resetting.

The Use of Neurocomputational Models as Alternatives to Animal Models in the Development of Electrical Brain Stimulation Treatments

Recent publications call for more animal models to be used and more experiments to be performed, in order to better understand the mechanisms of neurodegenerative disorders, to improve human health, and to develop new brain stimulation treatments. In response to these calls, some limitations of the current animal models are examined by using Deep Brain Stimulation (DBS) in Parkinson's disease as an illustrative example. Without focusing on the arguments for or against animal experimentation, or on the history of DBS, the present paper argues that given recent technological and theoretical advances, the time has come to consider bioinspired computational modelling as a valid alternative to animal models, in order to design the next generation of human brain stimulation treatments. However, before computational neuroscience is fully integrated in the translational process and used as a substitute for animal models, several obstacles need to be overcome. These obstacles are examined in the context of institutional, financial, technological and behavioural lock-in. Recommendations include encouraging agreement to change long-term habitual practices, explaining what alternative models can achieve, considering economic stakes, simplifying administrative and regulatory constraints, and carefully examining possible conflicts of interest.

Using Biophysical Models to Understand the Effect of tDCS on Neurorehabilitation: Searching for Optimal Covariates to Enhance Poststroke Recovery

Stroke is a leading cause of worldwide disability, and up to 75% of survivors suffer from some degree of arm paresis. Recently, rehabilitation of stroke patients has focused on recovering motor skills by taking advantage of use-dependent neuroplasticity, where high-repetition of goal-oriented movement is at times combined with non-invasive brain stimulation, such as transcranial direct current stimulation (tDCS). Merging the two approaches is thought to provide outlasting clinical gains, by enhancing synaptic plasticity and motor relearning in the motor cortex primary area. However, this general approach has shown mixed results across the stroke population. In particular, stroke location has been found to correlate with the likelihood of success, which suggests that different patients might require different protocols. Understanding how motor rehabilitation and stimulation interact with ongoing neural dynamics is crucial to optimize rehabilitation strategies, but it requires theoretical and computational models to consider the multiple levels at which this complex phenomenon operate. In this work, we argue that biophysical models of cortical dynamics are uniquely suited to address this problem. Specifically, biophysical models can predict treatment efficacy by introducing explicit variables and dynamics for damaged connections, changes in neural excitability, neurotransmitters, neuromodulators, plasticity mechanisms, and repetitive movement, which together can represent brain state, effect of incoming stimulus, and movement-induced activity. In this work, we hypothesize that effects of tDCS depend on ongoing neural activity and that tDCS effects on plasticity may be also related to enhancing inhibitory processes. We propose a model design for each step of this complex system, and highlight strengths and limitations of the different modeling choices within our approach. Our theoretical framework proposes a change in paradigm, where biophysical models can contribute to the future design of novel protocols, in which combined tDCS and motor rehabilitation strategies are tailored to the ongoing dynamics that they interact with, by considering the known biophysical factors recruited by such protocols and their interaction.

Neural mass models describing possible origin of the excessive beta oscillations correlated with Parkinsonian state

In Parkinson's disease, the enhanced beta rhythm is closely associated with akinesia/bradykinesia and rigidity. An increase in beta oscillations (12-35 Hz) within the basal ganglia (BG) nuclei does not proliferate throughout the cortico-basal ganglia loop in uniform fashion; rather it can be subdivided into two distinct frequency bands, i.e. the lower beta (12-20 Hz) and upper beta (21-35 Hz). A computational model of the excitatory and inhibitory neural network that focuses on the population properties is proposed to explore the mechanism underlying the pathological beta oscillations. Simulation results show several findings. The upper beta frequency in the BG originates from a high frequency cortical beta, while the emergence of exaggerated lower beta frequency in the BG depends greatly on the enhanced excitation of a reciprocal network consisting of the globus pallidus externus (GPe) and the subthalamic nucleus (STN). There is also a transition mechanism between the upper and lower beta oscillatory activities, and we explore the impact of self-inhibition within the GPe on the relationship between the upper beta and lower beta oscillations. It is shown that increased self-inhibition within the GPe contributes to increased upper beta oscillations driven by the cortical rhythm, while decrease in the self-inhibition within the GPe facilitates an enhancement of the lower beta oscillations induced by the increased excitability of the BG. This work provides an analysis for understanding the mechanism underlying pathological synchronization in neurological diseases.

A neural mass model of basal ganglia nuclei simulates pathological beta rhythm in Parkinson's disease

An increase in beta oscillations within the basal ganglia nuclei has been shown to be associated with movement disorder, such as Parkinson's disease. The motor cortex and an excitatory-inhibitory neuronal network composed of the subthalamic nucleus (STN) and the external globus pallidus (GPe) are thought to play an important role in the generation of these oscillations. In this paper, we propose a neuron mass model of the basal ganglia on the population level that reproduces the Parkinsonian oscillations in a reciprocal excitatory-inhibitory network. Moreover, it is shown that the generation and frequency of these pathological beta oscillations are varied by the coupling strength and the intrinsic characteristics of the basal ganglia. Simulation results reveal that increase of the coupling strength induces the generation of the beta oscillation, as well as enhances the oscillation frequency. However, for the intrinsic properties of each nucleus in the excitatory-inhibitory network, the STN primarily influences the generation of the beta oscillation while the GPe mainly determines its frequency. Interestingly, describing function analysis applied on this model theoretically explains the mechanism of pathological beta oscillations.

Phasic Burst Stimulation: A Closed-Loop Approach to Tuning Deep Brain Stimulation Parameters for Parkinson's Disease

We propose a novel, closed-loop approach to tuning deep brain stimulation (DBS) for Parkinson's disease (PD). The approach, termed Phasic Burst Stimulation (PhaBS), applies a burst of stimulus pulses over a range of phases predicted to disrupt pathological oscillations seen in PD. Stimulation parameters are optimized based on phase response curves (PRCs), which would be measured from each patient. This approach is tested in a computational model of PD with an emergent population oscillation. We show that the stimulus phase can be optimized using the PRC, and that PhaBS is more effective at suppressing the pathological oscillation than a single phasic stimulus pulse. PhaBS provides a closed-loop approach to DBS that can be optimized for each patient.

Neurological Diseases from a Systems Medicine Point of View

The difficulty to understand, diagnose, and treat neurological disorders stems from the great complexity of the central nervous system on different levels of physiological granularity. The individual components, their interactions, and dynamics involved in brain development and function can be represented as molecular, cellular, or functional networks, where diseases are perturbations of networks. These networks can become a useful research tool in investigating neurological disorders if they are properly tailored to reflect corresponding mechanisms. Here, we review approaches to construct networks specific for neurological disorders describing disease-related pathology on different scales: the molecular, cellular, and brain level. We also briefly discuss cross-scale network analysis as a necessary integrator of these scales.

Computational Models Describing Possible Mechanisms for Generation of Excessive Beta Oscillations in Parkinson's Disease

In Parkinson's disease, an increase in beta oscillations within the basal ganglia nuclei has been shown to be associated with difficulty in movement initiation. An important role in the generation of these oscillations is thought to be played by the motor cortex and by a network composed of the subthalamic nucleus (STN) and the external segment of globus pallidus (GPe). Several alternative models have been proposed to describe the mechanisms for generation of the Parkinsonian beta oscillations. However, a recent experimental study of Tachibana and colleagues yielded results which are challenging for all published computational models of beta generation. That study investigated how the presence of beta oscillations in a primate model of Parkinson's disease is affected by blocking different connections of the STN-GPe circuit. Due to a large number of experimental conditions, the study provides strong constraints that any mechanistic model of beta generation should satisfy. In this paper we present two models consistent with the data of Tachibana et al. The first model assumes that Parkinsonian beta oscillation are generated in the cortex and the STN-GPe circuits resonates at this frequency. The second model additionally assumes that the feedback from STN-GPe circuit to cortex is important for maintaining the oscillations in the network. Predictions are made about experimental evidence that is required to differentiate between the two models, both of which are able to reproduce firing rates, oscillation frequency and effects of lesions carried out by Tachibana and colleagues. Furthermore, an analysis of the models reveals how the amplitude and frequency of the generated oscillations depend on parameters.

Modeling sequence and quasi-uniform assumption in computational neurostimulation

Computational neurostimulation aims to develop mathematical constructs that link the application of neuromodulation with changes in behavior and cognition. This process is critical but daunting for technical challenges and scientific unknowns. The overarching goal of this review is to address how this complex task can be made tractable. We describe a framework of sequential modeling steps to achieve this: (1) current flow models, (2) cell polarization models, (3) network and information processing models, and (4) models of the neuroscientific correlates of behavior. Each step is explained with a specific emphasis on the assumptions underpinning underlying sequential implementation. We explain the further implementation of the quasi-uniform assumption to overcome technical limitations and unknowns. We specifically focus on examples in electrical stimulation, such as transcranial direct current stimulation. Our approach and conclusions are broadly applied to immediate and ongoing efforts to deploy computational neurostimulation.

Hippocampal closed-loop modeling and implications for seizure stimulation design

OBJECTIVE

Traditional hippocampal modeling has focused on the series of feedforward synapses known as the trisynaptic pathway. However, feedback connections from CA1 back to the hippocampus through the entorhinal cortex (EC) actually make the hippocampus a closed-loop system. By constructing a functional closed-loop model of the hippocampus, one may learn how both physiological and epileptic oscillations emerge and design efficient neurostimulation patterns to abate such oscillations.

APPROACH

Point process input-output models where estimated from recorded rodent hippocampal data to describe the nonlinear dynamical transformation from CA3 → CA1, via the schaffer-collateral synapse, and CA1 → CA3 via the EC. Each Volterra-like subsystem was composed of linear dynamics (principal dynamic modes) followed by static nonlinearities. The two subsystems were then wired together to produce the full closed-loop model of the hippocampus.

MAIN RESULTS

Closed-loop connectivity was found to be necessary for the emergence of theta resonances as seen in recorded data, thus validating the model. The model was then used to identify frequency parameters for the design of neurostimulation patterns to abate seizures.

SIGNIFICANCE

Deep-brain stimulation (DBS) is a new and promising therapy for intractable seizures. Currently, there is no efficient way to determine optimal frequency parameters for DBS, or even whether periodic or broadband stimuli are optimal. Data-based computational models have the potential to be used as a testbed for designing optimal DBS patterns for individual patients. However, in order for these models to be successful they must incorporate the complex closed-loop structure of the seizure focus. This study serves as a proof-of-concept of using such models to design efficient personalized DBS patterns for epilepsy.

Analysis of Oscillatory Neural Activity in Series Network Models of Parkinson's Disease During Deep Brain Stimulation

Parkinson's disease is a progressive, neurodegenerative disorder, characterized by hallmark motor symptoms. It is associated with pathological, oscillatory neural activity in the basal ganglia. Deep brain stimulation (DBS) is often successfully used to treat medically refractive Parkinson's disease. However, the selection of stimulation parameters is based on qualitative assessment of the patient, which can result in a lengthy tuning period and a suboptimal choice of parameters. This study explores fourth-order, control theory-based models of oscillatory activity in the basal ganglia. Describing function analysis is applied to examine possible mechanisms for the generation of oscillations in interacting nuclei and to investigate the suppression of oscillations with high-frequency stimulation. The theoretical results for the suppression of the oscillatory activity obtained using both the fourth-order model, and a previously described second-order model, are optimized to fit clinically recorded local field potential data obtained from Parkinsonian patients with implanted DBS. Close agreement between the power of oscillations recorded for a range of stimulation amplitudes is observed ( R(2)=0.69-0.99 ). The results suggest that the behavior of the system and the suppression of pathological neural oscillations with DBS is well described by the macroscopic models presented. The results also demonstrate that in this instance, a second-order model is sufficient to model the clinical data, without the need for added complexity. Describing the system behavior with computationally efficient models could aid in the identification of optimal stimulation parameters for patients in a clinical environment.