From dawn till dusk: Time-adaptive bayesian optimization for neurostimulation.

Stimulation optimization has garnered considerable interest in recent years in order to efficiently parametrize neuromodulation-based therapies. To date, efforts focused on automatically identifying settings from parameter spaces that do not change over time. A limitation of these approaches, however, is that they lack consideration for time dependent factors that may influence therapy outcomes. Disease progression and biological rhythmicity are two sources of variation that may influence optimal stimulation settings over time. To account for this, we present a novel time-varying Bayesian optimization (TV-BayesOpt) for tracking the optimum parameter set for neuromodulation therapy. We evaluate the performance of TV-BayesOpt for tracking gradual and periodic slow variations over time. The algorithm was investigated within the context of a computational model of phase-locked deep brain stimulation for treating oscillopathies representative of common movement disorders such as Parkinson's disease and Essential Tremor. When the optimal stimulation settings changed due to gradual and periodic sources, TV-BayesOpt outperformed standard time-invariant techniques and was able to identify the appropriate stimulation setting. Through incorporation of both a gradual "forgetting" and periodic covariance functions, the algorithm maintained robust performance when a priori knowledge differed from observed variations. This algorithm presents a broad framework that can be leveraged for the treatment of a range of neurological and psychiatric conditions and can be used to track variations in optimal stimulation settings such as amplitude, pulse-width, frequency and phase for invasive and non-invasive neuromodulation strategies.

Attentional effects on local V1 microcircuits explain selective V1-V4 communication.

Selective attention implements preferential routing of attended stimuli, likely through increasing the influence of the respective synaptic inputs on higher-area neurons. As the inputs of competing stimuli converge onto postsynaptic neurons, presynaptic circuits might offer the best target for attentional top-down influences. If those influences enabled presynaptic circuits to selectively entrain postsynaptic neurons, this might explain selective routing. Indeed, when two visual stimuli induce two gamma rhythms in V1, only the gamma induced by the attended stimulus entrains gamma in V4. Here, we modelled induced responses with a Dynamic Causal Model for Cross-Spectral Densities and found that selective entrainment can be explained by attentional modulation of intrinsic V1 connections. Specifically, local inhibition was decreased in the granular input layer and increased in the supragranular output layer of the V1 circuit that processed the attended stimulus. Thus, presynaptic attentional influences and ensuing entrainment were sufficient to mediate selective routing.

When do bursts matter in the primary motor cortex? Investigating changes in the intermittencies of beta rhythms associated with movement states.

Brain activity exhibits significant temporal structure that is not well captured in the power spectrum. Recently, attention has shifted to characterising the properties of intermittencies in rhythmic neural activity (i.e. bursts), yet the mechanisms that regulate them are unknown. Here, we present evidence from electrocorticography recordings made over the motor cortex to show that the statistics of bursts, such as duration or amplitude, in the beta frequency (14-30 Hz) band, significantly aid the classification of motor states such as rest, movement preparation, execution, and imagery. These features reflect nonlinearities not detectable in the power spectrum, with states increasing in nonlinearity from movement execution to preparation to rest. Further, we show using a computational model of the cortical microcircuit, constrained to account for burst features, that modulations of laminar specific inhibitory interneurons are responsible for the temporal organisation of activity. Finally, we show that the temporal characteristics of spontaneous activity can be used to infer the balance of cortical integration between incoming sensory information and endogenous activity. Critically, we contribute to the understanding of how transient brain rhythms may underwrite cortical processing, which in turn, could inform novel approaches for brain state classification, and modulation with novel brain-computer interfaces.

MorpheusNet: Resource efficient sleep stage classifier for embedded on-line systems.

Sleep Stage Classification (SSC) is a labor-intensive task, requiring experts to examine hours of electrophysiological recordings for manual classification. This is a limiting factor when it comes to leveraging sleep stages for therapeutic purposes. With increasing affordability and expansion of wearable devices, automating SSC may enable deployment of sleep-based therapies at scale. Deep Learning has gained increasing attention as a potential method to automate this process. Previous research has shown accuracy comparable to manual expert scores. However, previous approaches require sizable amount of memory and computational resources. This constrains the ability to classify in real time and deploy models on the edge. To address this gap, we aim to provide a model capable of predicting sleep stages in real-time, without requiring access to external computational sources (e.g., mobile phone, cloud). The algorithm is power efficient to enable use on embedded battery powered systems. Our compact sleep stage classifier can be deployed on most off-the-shelf microcontrollers (MCU) with constrained hardware settings. This is due to the memory footprint of our approach requiring significantly fewer operations. The model was tested on three publicly available data bases and achieved performance comparable to the state of the art, whilst reducing model complexity by orders of magnitude (up to 280 times smaller compared to state of the art). We further optimized the model with quantization of parameters to 8 bits with only an average drop of 0.95% in accuracy. When implemented in firmware, the quantized model achieves a latency of 1.6 seconds on an Arm Cortex-M4 processor, allowing its use for on-line SSC-based therapies.

Stimulating at the right time to recover network states in a model of the cortico-basal ganglia-thalamic circuit.

Synchronization of neural oscillations is thought to facilitate communication in the brain. Neurodegenerative pathologies such as Parkinson's disease (PD) can result in synaptic reorganization of the motor circuit, leading to altered neuronal dynamics and impaired neural communication. Treatments for PD aim to restore network function via pharmacological means such as dopamine replacement, or by suppressing pathological oscillations with deep brain stimulation. We tested the hypothesis that brain stimulation can operate beyond a simple "reversible lesion" effect to augment network communication. Specifically, we examined the modulation of beta band (14-30 Hz) activity, a known biomarker of motor deficits and potential control signal for stimulation in Parkinson's. To do this we setup a neural mass model of population activity within the cortico-basal ganglia-thalamic (CBGT) circuit with parameters that were constrained to yield spectral features comparable to those in experimental Parkinsonism. We modulated the connectivity of two major pathways known to be disrupted in PD and constructed statistical summaries of the spectra and functional connectivity of the resulting spontaneous activity. These were then used to assess the network-wide outcomes of closed-loop stimulation delivered to motor cortex and phase locked to subthalamic beta activity. Our results demonstrate that the spatial pattern of beta synchrony is dependent upon the strength of inputs to the STN. Precisely timed stimulation has the capacity to recover network states, with stimulation phase inducing activity with distinct spectral and spatial properties. These results provide a theoretical basis for the design of the next-generation brain stimulators that aim to restore neural communication in disease.

Comparison between the modelled response of primary motor cortex neurons to pulse-width modulated and conventional TMS stimuli.

In this study, the neural response to pulse-width modulated (PWM) transcranial magnetic stimulation (TMS) is estimated using a computational neural model which simulates the response of cortical neurons to TMS. The recently introduced programmable TMS uses PWM to approximate conventional resonance-based TMS pulses by fast switching between voltage levels. The effect of such stimulation on the six cortical layers is modelled by estimating the activation threshold of the neurons. Modelling results are compared between the novel device and that of conventional TMS stimuli generated by Magstim stimulators. The neural responses to the PWM pulses and the conventional stimuli show a high correlation, which validates the use of pulse-width modulated pulses in TMS.Clinical Relevance- This computational modelling study demonstrates an equivalent effect of PWM and conventional TMS pulses on the nervous system which paves the way to more flexibility in exploring and choosing stimulation parameters for TMS treatment.

Identifying and modulating distinct tremor states through peripheral nerve stimulation in Parkinsonian rest tremor.

BACKGROUND: Resting tremor is one of the most common symptoms of Parkinson's disease. Despite its high prevalence, resting tremor may not be as effectively treated with dopaminergic medication as other symptoms, and surgical treatments such as deep brain stimulation, which are effective in reducing tremor, have limited availability. Therefore, there is a clinical need for non-invasive interventions in order to provide tremor relief to a larger number of people with Parkinson's disease. Here, we explore whether peripheral nerve stimulation can modulate resting tremor, and under what circumstances this might lead to tremor suppression. METHODS: We studied 10 people with Parkinson's disease and rest tremor, to whom we delivered brief electrical pulses non-invasively to the median nerve of the most tremulous hand. Stimulation was phase-locked to limb acceleration in the axis with the biggest tremor-related excursion. RESULTS: We demonstrated that rest tremor in the hand could change from one pattern of oscillation to another in space. Median nerve stimulation was able to significantly reduce (- 36%) and amplify (117%) tremor when delivered at a certain phase. When the peripheral manifestation of tremor spontaneously changed, stimulation timing-dependent change in tremor severity could also alter during phase-locked peripheral nerve stimulation. CONCLUSIONS: These results highlight that phase-locked peripheral nerve stimulation has the potential to reduce tremor. However, there can be multiple independent tremor oscillation patterns even within the same limb. Parameters of peripheral stimulation such as stimulation phase may need to be adjusted continuously in order to sustain systematic suppression of tremor amplitude.

Essential tremor amplitude modulation by median nerve stimulation.

Essential tremor is a common neurological disorder, characterised by involuntary shaking of a limb. Patients are usually treated using medications which have limited effects on tremor and may cause side-effects. Surgical therapies are effective in reducing essential tremor, however, the invasive nature of these therapies together with the high cost, greatly limit the number of patients benefiting from them. Non-invasive therapies have gained increasing traction to meet this clinical need. Here, we test a non-invasive and closed-loop electrical stimulation paradigm which tracks peripheral tremor and targets thalamic afferents to modulate the central oscillators underlying tremor. To this end, 9 patients had electrical stimulation delivered to the median nerve locked to different phases of tremor. Peripheral stimulation induced a subtle but significant modulation in five out of nine patients-this modulation consisted mainly of amplification rather than suppression of tremor amplitude. Modulatory effects of stimulation were more pronounced when patient's tremor was spontaneously weaker at stimulation onset, when significant modulation became more frequent amongst subjects. This data suggests that for selected individuals, a more sophisticated control policy entailing an online estimate of both tremor phase and amplitude, should be considered in further explorations of the treatment potential of tremor phase-locked peripheral stimulation.

Inference of brain networks with approximate Bayesian computation - assessing face validity with an example application in Parkinsonism.

This paper describes and validates a novel framework using the Approximate Bayesian Computation (ABC) algorithm for parameter estimation and model selection in models of mesoscale brain network activity. We provide a proof of principle, first pass validation of this framework using a set of neural mass models of the cortico-basal ganglia thalamic circuit inverted upon spectral features from experimental, in vivo recordings. This optimization scheme relaxes an assumption of fixed-form posteriors (i.e. the Laplace approximation) taken in previous approaches to inverse modelling of spectral features. This enables the exploration of model dynamics beyond that approximated from local linearity assumptions and so fit to explicit, numerical solutions of the underlying non-linear system of equations. In this first paper, we establish a face validation of the optimization procedures in terms of: (i) the ability to approximate posterior densities over parameters that are plausible given the known causes of the data; (ii) the ability of the model comparison procedures to yield posterior model probabilities that can identify the model structure known to generate the data; and (iii) the robustness of these procedures to local minima in the face of different starting conditions. Finally, as an illustrative application we show (iv) that model comparison can yield plausible conclusions given the known neurobiology of the cortico-basal ganglia-thalamic circuit in Parkinsonism. These results lay the groundwork for future studies utilizing highly nonlinear or brittle models that can explain time dependant dynamics, such as oscillatory bursts, in terms of the underlying neural circuits.

Entraining Stepping Movements of Parkinson's Patients to Alternating Subthalamic Nucleus Deep Brain Stimulation.

Patients with advanced Parkinson's can be treated by deep brain stimulation (DBS) of the subthalamic nucleus (STN). This affords a unique opportunity to record from this nucleus and stimulate it in a controlled manner. Previous work has shown that activity in the STN is modulated in a rhythmic pattern when Parkinson's patients perform stepping movements, raising the question whether the STN is involved in the dynamic control of stepping. To answer this question, we tested whether an alternating stimulation pattern resembling the stepping-related modulation of activity in the STN could entrain patients' stepping movements as evidence of the STN's involvement in stepping control. Group analyses of 10 Parkinson's patients (one female) showed that alternating stimulation significantly entrained stepping rhythms. We found a remarkably consistent alignment between the stepping and stimulation cycle when the stimulation speed was close to the stepping speed in the five patients that demonstrated significant individual entrainment to the stimulation cycle. Our study suggests that the STN is causally involved in dynamic control of step timing and motivates further exploration of this biomimetic stimulation pattern as a potential basis for the development of DBS strategies to ameliorate gait impairments.SIGNIFICANCE STATEMENT We tested whether the subthalamic nucleus (STN) in humans is causally involved in controlling stepping movements. To this end, we studied patients with Parkinson's disease who have undergone therapeutic deep brain stimulation (DBS), as in these individuals we can stimulate the STNs in a controlled manner. We developed an alternating pattern of stimulation that mimics the pattern of activity modulation recorded in this nucleus during stepping. The alternating DBS (altDBS) could entrain patients' stepping rhythm, suggesting a causal role of the STN in dynamic gait control. This type of stimulation may potentially form the basis for improved DBS strategies for gait.

Phase-dependence of response curves to deep brain stimulation and their relationship: from essential tremor patient data to a Wilson-Cowan model.

Essential tremor manifests predominantly as a tremor of the upper limbs. One therapy option is high-frequency deep brain stimulation, which continuously delivers electrical stimulation to the ventral intermediate nucleus of the thalamus at about 130 Hz. Constant stimulation can lead to side effects, it is therefore desirable to find ways to stimulate less while maintaining clinical efficacy. One strategy, phase-locked deep brain stimulation, consists of stimulating according to the phase of the tremor. To advance methods to optimise deep brain stimulation while providing insights into tremor circuits, we ask the question: can the effects of phase-locked stimulation be accounted for by a canonical Wilson-Cowan model? We first analyse patient data, and identify in half of the datasets significant dependence of the effects of stimulation on the phase at which stimulation is provided. The full nonlinear Wilson-Cowan model is fitted to datasets identified as statistically significant, and we show that in each case the model can fit to the dynamics of patient tremor as well as to the phase response curve. The vast majority of top fits are stable foci. The model provides satisfactory prediction of how patient tremor will react to phase-locked stimulation by predicting patient amplitude response curves although they were not explicitly fitted. We also approximate response curves of the significant datasets by providing analytical results for the linearisation of a stable focus model, a simplification of the Wilson-Cowan model in the stable focus regime. We report that the nonlinear Wilson-Cowan model is able to describe response to stimulation more precisely than the linearisation.

Comparing dynamic causal models of neurovascular coupling with fMRI and EEG/MEG.

This technical note presents a dynamic causal modelling (DCM) procedure for evaluating different models of neurovascular coupling in the human brain - using combined electromagnetic (M/EEG) and functional magnetic resonance imaging (fMRI) data. This procedure compares the evidence for biologically informed models of neurovascular coupling using Bayesian model comparison. First, fMRI data are used to localise regionally specific neuronal responses. The coordinates of these responses are then used as the location priors in a DCM of electrophysiological responses elicited by the same paradigm. The ensuing estimates of model parameters are then used to generate neuronal drive functions, which model pre- or post-synaptic activity for each experimental condition. These functions form the input to a model of neurovascular coupling, whose parameters are estimated from the fMRI data. Crucially, this enables one to evaluate different models of neurovascular coupling, using Bayesian model comparison - asking, for example, whether instantaneous or delayed, pre- or post-synaptic signals mediate haemodynamic responses. We provide an illustrative application of the procedure using a single-subject auditory fMRI and MEG dataset. The code and exemplar data accompanying this technical note are available through the statistical parametric mapping (SPM) software.

Emerging technologies for improved deep brain stimulation.

Deep brain stimulation (DBS) is an effective treatment for common movement disorders and has been used to modulate neural activity through delivery of electrical stimulation to key brain structures. The long-term efficacy of stimulation in treating disorders, such as Parkinson's disease and essential tremor, has encouraged its application to a wide range of neurological and psychiatric conditions. Nevertheless, adoption of DBS remains limited, even in Parkinson's disease. Recent failed clinical trials of DBS in major depression, and modest treatment outcomes in dementia and epilepsy, are spurring further development. These improvements focus on interaction with disease circuits through complementary, spatially and temporally specific approaches. Spatial specificity is promoted by the use of segmented electrodes and field steering, and temporal specificity involves the delivery of patterned stimulation, mostly controlled through disease-related feedback. Underpinning these developments are new insights into brain structure-function relationships and aberrant circuit dynamics, including new methods with which to assess and refine the clinical effects of stimulation.

Publisher Correction: Emerging technologies for improved deep brain stimulation.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Predicting the effects of deep brain stimulation using a reduced coupled oscillator model.

Deep brain stimulation (DBS) is known to be an effective treatment for a variety of neurological disorders, including Parkinson's disease and essential tremor (ET). At present, it involves administering a train of pulses with constant frequency via electrodes implanted into the brain. New 'closed-loop' approaches involve delivering stimulation according to the ongoing symptoms or brain activity and have the potential to provide improvements in terms of efficiency, efficacy and reduction of side effects. The success of closed-loop DBS depends on being able to devise a stimulation strategy that minimizes oscillations in neural activity associated with symptoms of motor disorders. A useful stepping stone towards this is to construct a mathematical model, which can describe how the brain oscillations should change when stimulation is applied at a particular state of the system. Our work focuses on the use of coupled oscillators to represent neurons in areas generating pathological oscillations. Using a reduced form of the Kuramoto model, we analyse how a patient should respond to stimulation when neural oscillations have a given phase and amplitude, provided a number of conditions are satisfied. For such patients, we predict that the best stimulation strategy should be phase specific but also that stimulation should have a greater effect if applied when the amplitude of brain oscillations is lower. We compare this surprising prediction with data obtained from ET patients. In light of our predictions, we also propose a new hybrid strategy which effectively combines two of the closed-loop strategies found in the literature, namely phase-locked and adaptive DBS.

Temporal evolution of beta bursts in the parkinsonian cortical and basal ganglia network.

Beta frequency oscillations (15 to 35 Hz) in cortical and basal ganglia circuits become abnormally synchronized in Parkinson's disease (PD). How excessive beta oscillations emerge in these circuits is unclear. We addressed this issue by defining the firing properties of basal ganglia neurons around the emergence of cortical beta bursts (ß bursts), transient (50 to 350 ms) increases in the beta amplitude of cortical signals. In PD patients, the phase locking of background spiking activity in the subthalamic nucleus (STN) to frontal electroencephalograms preceded the onset and followed the temporal profile of cortical ß bursts, with conditions of synchronization consistent within and across bursts. Neuronal ensemble recordings in multiple basal ganglia structures of parkinsonian rats revealed that these dynamics were recapitulated in STN, but also in external globus pallidus and striatum. The onset of consistent phase-locking conditions was preceded by abrupt phase slips between cortical and basal ganglia ensemble signals. Single-unit recordings demonstrated that ensemble-level properties of synchronization were not underlain by changes in firing rate but, rather, by the timing of action potentials in relation to cortical oscillation phase. Notably, the preferred angle of phase-locked action potential firing in each basal ganglia structure was shifted during burst initiation, then maintained stable phase relations during the burst. Subthalamic, pallidal, and striatal neurons engaged and disengaged with cortical ß bursts to different extents and timings. The temporal evolution of cortical and basal ganglia synchronization is cell type-selective, which could be key for the generation/ maintenance of excessive beta oscillations in parkinsonism.

Dynamic Causal Modelling of Active Vision.

In this paper, we draw from recent theoretical work on active perception, which suggests that the brain makes use of an internal (i.e., generative) model to make inferences about the causes of sensations. This view treats visual sensations as consequent on action (i.e., saccades) and implies that visual percepts must be actively constructed via a sequence of eye movements. Oculomotor control calls on a distributed set of brain sources that includes the dorsal and ventral frontoparietal (attention) networks. We argue that connections from the frontal eye fields to ventral parietal sources represent the mapping from "where", fixation location to information derived from "what" representations in the ventral visual stream. During scene construction, this mapping must be learned, putatively through changes in the effective connectivity of these synapses. Here, we test the hypothesis that the coupling between the dorsal frontal cortex and the right temporoparietal cortex is modulated during saccadic interrogation of a simple visual scene. Using dynamic causal modeling for magnetoencephalography with (male and female) human participants, we assess the evidence for changes in effective connectivity by comparing models that allow for this modulation with models that do not. We find strong evidence for modulation of connections between the two attention networks; namely, a disinhibition of the ventral network by its dorsal counterpart.SIGNIFICANCE STATEMENT This work draws from recent theoretical accounts of active vision and provides empirical evidence for changes in synaptic efficacy consistent with these computational models. In brief, we used magnetoencephalography in combination with eye-tracking to assess the neural correlates of a form of short-term memory during a dot cancellation task. Using dynamic causal modeling to quantify changes in effective connectivity, we found evidence that the coupling between the dorsal and ventral attention networks changed during the saccadic interrogation of a simple visual scene. Intuitively, this is consistent with the idea that these neuronal connections may encode beliefs about "what I would see if I looked there", and that this mapping is optimized as new data are obtained with each fixation.

A guide to group effective connectivity analysis, part 2: Second level analysis with PEB.

This paper provides a worked example of using Dynamic Causal Modelling (DCM) and Parametric Empirical Bayes (PEB) to characterise inter-subject variability in neural circuitry (effective connectivity). It steps through an analysis in detail and provides a tutorial style explanation of the underlying theory and assumptions (i.e, priors). The analysis procedure involves specifying a hierarchical model with two or more levels. At the first level, state space models (DCMs) are used to infer the effective connectivity that best explains a subject's neuroimaging timeseries (e.g. fMRI, MEG, EEG). Subject-specific connectivity parameters are then taken to the group level, where they are modelled using a General Linear Model (GLM) that partitions between-subject variability into designed effects and additive random effects. The ensuing (Bayesian) hierarchical model conveys both the estimated connection strengths and their uncertainty (i.e., posterior covariance) from the subject to the group level; enabling hypotheses to be tested about the commonalities and differences across subjects. This approach can also finesse parameter estimation at the subject level, by using the group-level parameters as empirical priors. The preliminary first level (subject specific) DCM for fMRI analysis is covered in a companion paper. Here, we detail group-level analysis procedures that are suitable for use with data from any neuroimaging modality. This paper is accompanied by an example dataset, together with step-by-step instructions demonstrating how to reproduce the analyses.