Phase-dependent modulation as a novel approach for therapeutic brain stimulation

Control of coupled neural oscillations using near-periodic inputs

Deep brain stimulation (DBS) is a commonly used treatment for medication resistant Parkinson's disease and is an emerging treatment for other neurological disorders. More recently, phase-specific adaptive DBS (aDBS), whereby the application of stimulation is locked to a particular phase of tremor, has been proposed as a strategy to improve therapeutic efficacy and decrease side effects. In this work, in the context of these phase-specific aDBS strategies, we investigate the dynamical behavior of large populations of coupled neurons in response to near-periodic stimulation, namely, stimulation that is periodic except for a slowly changing amplitude and phase offset that can be used to coordinate the timing of applied input with a specified phase of model oscillations. Using an adaptive phase-amplitude reduction strategy, we illustrate that for a large population of oscillatory neurons, the temporal evolution of the associated phase distribution in response to near-periodic forcing can be captured using a reduced order model with four state variables. Subsequently, we devise and validate a closed-loop control strategy to disrupt synchronization caused by coupling. Additionally, we identify strategies for implementing the proposed control strategy in situations where underlying model equations are unavailable by estimating the necessary terms of the reduced order equations in real-time from observables.

Parkinson's disease uncovers an underlying sensitivity of subthalamic nucleus neurons to beta-frequency cortical input in vivo

Abnormally sustained beta-frequency synchronisation between the motor cortex and subthalamic nucleus (STN) is associated with motor symptoms in Parkinson's disease (PD). It is currently unclear whether STN neurons have a preference for beta-frequency input (12-35 Hz), rather than cortical input at other frequencies, and how such a preference would arise following dopamine depletion. To address this question, we combined analysis of cortical and STN recordings from awake human PD patients undergoing deep brain stimulation surgery with recordings of identified STN neurons in anaesthetised rats. In these patients, we demonstrate that a subset of putative STN neurons is strongly and selectively sensitive to magnitude fluctuations of cortical beta oscillations over time, linearly increasing their phase-locking strength with respect to the full range of instantaneous amplitude in the beta-frequency range. In rats, we probed the frequency response of STN neurons in the cortico-basal-ganglia-network more precisely, by recording spikes evoked by short bursts of cortical stimulation with variable frequency (4-40 Hz) and constant amplitude. In both healthy and dopamine-depleted rats, only beta-frequency stimulation led to a progressive reduction in the variability of spike timing through the stimulation train. This suggests, that the interval of beta-frequency input provides an optimal window for eliciting the next spike with high fidelity. We hypothesize, that abnormal activation of the indirect pathway, via dopamine depletion and/or cortical stimulation, could trigger an underlying sensitivity of the STN microcircuit to beta-frequency input.

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STN-neurons are selectively entrained to cortical beta oscillations in PD patients.

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Phase-locking of STN-neurons is linearly dependent on oscillation magnitude.

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Beta bursts in LFP/EEG are accompanied by transient synchronisation of STN spiking.

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STN neurons are selectively entrained to cortical beta stimulation in rats.

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Beta-selectivity of STN neurons is present in control and dopamine-depleted rats.

Perspective: Phase Amplitude Coupling-Based Phase-Dependent Neuromodulation in Parkinson's Disease

Deep brain stimulation (DBS) is an effective surgical therapy for Parkinson's disease (PD). However, limitations of the DBS systems have led to great interest in adaptive neuromodulation systems that can dynamically adjust stimulation parameters to meet concurrent therapeutic demand. Constant high-frequency motor cortex stimulation has not been remarkably efficacious, which has led to greater focus on modulation of subcortical targets. Understanding of the importance of timing in both cortical and subcortical stimulation has generated an interest in developing more refined, parsimonious stimulation techniques based on critical oscillatory activities of the brain. Concurrently, much effort has been put into identifying biomarkers of both parkinsonian and physiological patterns of neuronal activities to drive next generation of adaptive brain stimulation systems. One such biomarker is beta-gamma phase amplitude coupling (PAC) that is detected in the motor cortex. PAC is strongly correlated with parkinsonian specific motor signs and symptoms and respond to therapies in a dose-dependent manner. PAC may represent the overall state of the parkinsonian motor network and have less instantaneously dynamic fluctuation during movement. These findings raise the possibility of novel neuromodulation paradigms that are potentially less invasiveness than DBS. Successful application of PAC in neuromodulation may necessitate phase-dependent stimulation technique, which aims to deliver precisely timed stimulation pulses to a specific phase to predictably modulate to selectively modulate pathological network activities and behavior in real time. Overcoming current technical challenges can lead to deeper understanding of the parkinsonian pathophysiology and development of novel neuromodulatory therapies with potentially less side-effects and higher therapeutic efficacy.

Global phase-amplitude description of oscillatory dynamics via the parameterization method

In this paper, we use the parameterization method to provide a complete description of the dynamics of an n-dimensional oscillator beyond the classical phase reduction. The parameterization method allows us, via efficient algorithms, to obtain a parameterization of the attracting invariant manifold of the limit cycle in terms of the phase-amplitude variables. The method has several advantages. It provides analytically a Fourier-Taylor expansion of the parameterization up to any order, as well as a simplification of the dynamics that allows for a numerical globalization of the manifolds. Thus, one can obtain the local and global isochrons and isostables, including the slow attracting manifold, up to high accuracy, which offer a geometrical portrait of the oscillatory dynamics. Furthermore, it provides straightforwardly the infinitesimal phase and amplitude response functions, that is, the extended infinitesimal phase and amplitude response curves, which monitor the phase and amplitude shifts beyond the asymptotic state. Thus, the methodology presented yields an accurate description of the phase dynamics for perturbations not restricted to the limit cycle but to its attracting invariant manifold. Finally, we explore some strategies to reduce the dimension of the dynamics, including the reduction of the dynamics to the slow stable submanifold. We illustrate our methods by applying them to different three-dimensional single neuron and neural population models in neuroscience.

A data-driven phase and isostable reduced modeling framework for oscillatory dynamical systems

Phase-amplitude reduction is of growing interest as a strategy for the reduction and analysis of oscillatory dynamical systems. Augmentation of the widely studied phase reduction with amplitude coordinates can be used to characterize transient behavior in directions transverse to a limit cycle to give a richer description of the dynamical behavior. Various definitions for amplitude coordinates have been suggested, but none are particularly well suited for implementation in experimental systems where output recordings are readily available but the underlying equations are typically unknown. In this work, a reduction framework is developed for inferring a phase-amplitude reduced model using only the observed model output from an arbitrarily high-dimensional system. This framework employs a proper orthogonal reduction strategy to identify important features of the transient decay of solutions to the limit cycle. These features are explicitly related to previously developed phase and isostable coordinates and used to define so-called data-driven phase and isostable coordinates that are valid in the entire basin of attraction of a limit cycle. The utility of this reduction strategy is illustrated in examples related to neural physiology and is used to implement an optimal control strategy that would otherwise be computationally intractable. The proposed data-driven phase and isostable coordinate system and associated reduced modeling framework represent a useful tool for the study of nonlinear dynamical systems in situations where the underlying dynamical equations are unknown and in particularly high-dimensional or complicated numerical systems for which standard phase-amplitude reduction techniques are not computationally feasible.

Neural Circuit and Clinical Insights from Intraoperative Recordings During Deep Brain Stimulation Surgery

Observations using invasive neural recordings from patient populations undergoing neurosurgical interventions have led to critical breakthroughs in our understanding of human neural circuit function and malfunction. The opportunity to interact with patients during neurophysiological mapping allowed for early insights in functional localization to improve surgical outcomes, but has since expanded into exploring fundamental aspects of human cognition including reward processing, language, the storage and retrieval of memory, decision-making, as well as sensory and motor processing. The increasing use of chronic neuromodulation, via deep brain stimulation, for a spectrum of neurological and psychiatric conditions has in tandem led to increased opportunity for linking theories of cognitive processing and neural circuit function. Our purpose here is to motivate the neuroscience and neurosurgical community to capitalize on the opportunities that this next decade will bring. To this end, we will highlight recent studies that have successfully leveraged invasive recordings during deep brain stimulation surgery to advance our understanding of human cognition with an emphasis on reward processing, improving clinical outcomes, and informing advances in neuromodulatory interventions.

Levodopa Reduces the Phase lag Index of Parkinson's Disease Patients: A Magnetoencephalographic Study

Objectives. As a method of measuring the phase difference between 2 signals, the phase lag index (PLI) of the alpha and beta bands in patients with Parkinson's disease (PD) was investigated by using magnetoencephalography (MEG). Methods. Eighteen PD patients were measured by MEG in the state of overnight withdrawal of levodopa and after levodopa treatment; meanwhile, Unified Parkinson's Disease Rating Scale (UPDRS) III scale was evaluated. Results. Compared with healthy controls, alpha (8-13 Hz) PLI in the frontal and parietal areas elevated in PD patients, while the elevation was reversed by the levodopa treatment. The alterations of the UPDRS III total scale (r_s = 0.552, P = .013, n = 16) and the changes of akinesia scale (r_s = 0.622, P = .005, n = 16) were correlated to the change of beta (13-30 Hz) PLI in the left parietal area. The change of the UPDRS total scale was negatively correlated to duration of disease (r_s = 0.432, P = .047, n = 16). There was a negative correlation between the age of PD patients and the change of alpha PLI in the left frontal area (r_s = 0.519, P = .020, n = 16). Conclusions. PD patients showed a higher mu PLI in the sensorimotor area relative to the healthy controls. The improvement of motor symptoms of PD patients by levodopa was correlated to the inhibition of beta PLI in the sensorimotor area.

Phase-Dependent Suppression of Beta Oscillations in Parkinson's Disease Patients

Synchronized oscillations within and between brain areas facilitate normal processing, but are often amplified in disease. A prominent example is the abnormally sustained beta-frequency (∼20 Hz) oscillations recorded from the cortex and subthalamic nucleus of Parkinson's disease patients. Computational modeling suggests that the amplitude of such oscillations could be modulated by applying stimulation at a specific phase. Such a strategy would allow selective targeting of the oscillation, with relatively little effect on other activity parameters. Here, activity was recorded from 10 awake, parkinsonian patients (6 male, 4 female human subjects) undergoing functional neurosurgery. We demonstrate that stimulation arriving on a particular patient-specific phase of the beta oscillation over consecutive cycles could suppress the amplitude of this pathophysiological activity by up to 40%, while amplification effects were relatively weak. Suppressive effects were accompanied by a reduction in the rhythmic output of subthalamic nucleus (STN) neurons and synchronization with the mesial cortex. While stimulation could alter the spiking pattern of STN neurons, there was no net effect on firing rate, suggesting that reduced beta synchrony was a result of alterations to the relative timing of spiking activity, rather than an overall change in excitability. Together, these results identify a novel intrinsic property of cortico-basal ganglia synchrony that suggests the phase of ongoing neural oscillations could be a viable and effective control signal for the treatment of Parkinson's disease. This work has potential implications for other brain diseases with exaggerated neuronal synchronization and for probing the function of rhythmic activity in the healthy brain.SIGNIFICANCE STATEMENT In Parkinson's disease (PD), movement impairment is correlated with exaggerated beta frequency oscillations in the cerebral cortex and subthalamic nucleus (STN). Using a novel method of stimulation in PD patients undergoing neurosurgery, we demonstrate that STN beta oscillations can be suppressed when consecutive electrical pulses arrive at a specific phase of the oscillation. This effect is likely because of interrupting the timing of neuronal activity rather than excitability, as stimulation altered the firing pattern of STN spiking without changing overall rate. These findings show the potential of oscillation phase as an input for "closed-loop" stimulation, which could provide a valuable neuromodulation strategy for the treatment of brain disorders and for elucidating the role of neuronal oscillations in the healthy brain.

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.

An update on adaptive deep brain stimulation in Parkinson's disease

Advancing conventional open‐loop DBS as a therapy for PD is crucial for overcoming important issues such as the delicate balance between beneficial and adverse effects and limited battery longevity that are currently associated with treatment. Closed‐loop or adaptive DBS aims to overcome these limitations by real‐time adjustment of stimulation parameters based on continuous feedback input signals that are representative of the patient's clinical state. The focus of this update is to discuss the most recent developments regarding potential input signals and possible stimulation parameter modulation for adaptive DBS in PD. Potential input signals for adaptive DBS include basal ganglia local field potentials, cortical recordings (electrocorticography), wearable sensors, and eHealth and mHealth devices. Furthermore, adaptive DBS can be applied with different approaches of stimulation parameter modulation, the feasibility of which can be adapted depending on specific PD phenotypes. Implementation of technological developments like machine learning show potential in the design of such approaches; however, energy consumption deserves further attention. Furthermore, we discuss future considerations regarding the clinical implementation of adaptive DBS in PD. © 2018 The Authors. Movement Disorders published by Wiley Periodicals, Inc. on behalf of International Parkinson and Movement Disorder Society.

Greater accuracy and broadened applicability of phase reduction using isostable coordinates

The applicability of phase models is generally limited by the constraint that the dynamics of a perturbed oscillator must stay near its underlying periodic orbit. Consequently, external perturbations must be sufficiently weak so that these assumptions remain valid. Using the notion of isostables of periodic orbits to provide a simplified coordinate system from which to understand the dynamics transverse to a periodic orbit, we devise a strategy to correct for changing phase dynamics for locations away from the limit cycle. Consequently, these corrected phase dynamics allow for perturbations of larger magnitude without invalidating the underlying assumptions of the reduction. The proposed reduction strategy yields a closed set of equations and can be applied to periodic orbits embedded in arbitrarily high dimensional spaces. We illustrate the utility of this strategy in two models with biological relevance. In the first application, we find that an optimal control strategy for modifying the period of oscillation can be improved with the corrected phase reduction. In the second, the corrected phase reduced dynamics are used to understand adaptation and memory effects resulting from past perturbations.

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.

Adaptive deep brain stimulation in Parkinson's disease

Although Deep Brain Stimulation (DBS) is an established treatment for Parkinson's disease (PD), there are still limitations in terms of effectivity, side-effects and battery consumption. One of the reasons for this may be that not only pathological but also physiological neural activity can be suppressed whilst stimulating. For this reason, adaptive DBS (aDBS), where stimulation is applied according to the level of pathological activity, might be advantageous. Initial studies of aDBS demonstrate effectiveness in PD, but there are still many questions to be answered before aDBS can be applied clinically. Here we discuss the feedback signals and stimulation algorithms involved in adaptive stimulation in PD and sketch a potential road-map towards clinical application.

Dynamic network communication as a unifying neural basis for cognition, development, aging, and disease

Perception, cognition, and social interaction depend upon coordinated neural activity. This coordination operates within noisy, overlapping, and distributed neural networks operating at multiple timescales. These networks are built upon a structural scaffolding with intrinsic neuroplasticity that changes with development, aging, disease, and personal experience. In this article, we begin from the perspective that successful interregional communication relies upon the transient synchronization between distinct low-frequency (<80 Hz) oscillations, allowing for brief windows of communication via phase-coordinated local neuronal spiking. From this, we construct a theoretical framework for dynamic network communication, arguing that these networks reflect a balance between oscillatory coupling and local population spiking activity and that these two levels of activity interact. We theorize that when oscillatory coupling is too strong, spike timing within the local neuronal population becomes too synchronous; when oscillatory coupling is too weak, spike timing is too disorganized. Each results in specific disruptions to neural communication. These alterations in communication dynamics may underlie cognitive changes associated with healthy development and aging, in addition to neurological and psychiatric disorders. A number of neurological and psychiatric disorders-including Parkinson's disease, autism, depression, schizophrenia, and anxiety-are associated with abnormalities in oscillatory activity. Although aging, psychiatric and neurological disease, and experience differ in the biological changes to structural gray or white matter, neurotransmission, and gene expression, our framework suggests that any resultant cognitive and behavioral changes in normal or disordered states or their treatment are a product of how these physical processes affect dynamic network communication.