Biology subjects

Bogacz, R.

Publications and source records attributed to Bogacz, R..

At least 37 records · Page 2Linked to original sources

bioRxiv2022

Neural underpinnings of action adaptation in the subthalamic nucleus.

Adapting our actions to changing goals and environments is central to intelligent behavior. There is substantial evidence that the basal ganglia play a crucial role in reinforcing actions that have led to favorable outcomes. However, little is known about the neural mechanisms underlying action adaptation following unfavorable outcomes when change is warranted. Here, we recorded electrophysiological activity and applied bursts of electrical stimulation to the subthalamic nucleus (STN), a core area of the basal ganglia, in patients with Parkinsons disease using deep brain stimulation electrodes. During a task where patients continuously had to adapt their force depending on changing action-value associations, decreases in STN beta (13-30 Hz) activity in two critical time windows were associated with poorer outcomes and stronger action adaptation. STN stimulation reduced beta activity and led to stronger action adaptation if applied within the time windows when STN activity reflected action evaluation and adaptation. These results suggest that dynamic modulation of STN activity facilitates adaptive behavior.

neuroscience↗

bioRxiv2022

Inferring Neural Activity Before Plasticity: A Foundation for Learning Beyond Backpropagation

For both humans and machines, the essence of learning is to pinpoint which components in its information processing pipeline are responsible for an error in its output -- a challenge that is known as credit assignment. How the brain solves credit assignment is a key question in neuroscience, and also of significant importance for artificial intelligence. It has long been assumed that credit assignment is best solved by backpropagation, which is also the foundation of modern machine learning. However, it has been questioned whether it is possible for the brain to implement backpropagation and learning in the brain may actually be more efficient and effective than backpropagation. Here, we set out a fundamentally different principle on credit assignment, called prospective configuration. In prospective configuration, the network first infers the pattern of neural activity that should result from learning, and then the synaptic weights are modified to consolidate the change in neural activity. We demonstrate that this distinct mechanism, in contrast to backpropagation, (1) underlies learning in a well-established family of models of cortical circuits, (2) enables learning that is more efficient and effective in many contexts faced by biological organisms, and (3) reproduces surprising patterns of neural activity and behaviour observed in diverse human and animal learning experiments. Our findings establish a new foundation for learning beyond backpropagation, for both understanding biological learning and building artificial intelligence.

neuroscience↗

bioRxiv2022

Reward Bases: Instantaneous reward revaluation with temporal difference learning

AO_SCPLOWBSTRACTC_SCPLOWAn influential theory posits that dopaminergic neurons in the mid-brain implement a model-free reinforcement learning algorithm based on temporal difference (TD) learning. A fundamental assumption of this model is that the reward function being optimized is fixed. However, for biological creatures the reward function can fluctuate substantially over time depending on the internal physiological state of the animal. For instance, food is rewarding when you are hungry, but not when you are satiated. While a variety of experiments have demonstrated that animals can instantly adapt their behaviour when their internal physiological state changes, under current thinking this requires model-based planning since the standard model of TD learning requires retraining from scratch if the reward function changes. Here, we propose a novel and simple extension to TD learning that allows for the zero-shot (instantaneous) generalization to changing reward functions. Mathematically, we show that if we assume the reward function is a linear combination of reward basis vectors, and if we learn a value function for each reward basis using TD learning, then we can recover the true value function by a linear combination of these value function bases. This representational scheme allows instant and perfect generalization to any reward function in the span of the reward basis vectors as well as possesses a straightforward implementation in neural circuitry by parallelizing the standard circuitry required for TD learning. We demonstrate that our algorithm can also reproduce behavioural data on reward revaluation tasks, predict dopamine responses in the nucleus accumbens, as well as learn equally fast as successor representations while requiring much less memory.

neuroscience↗

bioRxiv2022

Sub-harmonic Entrainment of Cortical Gamma Oscillations to Deep Brain Stimulation in Parkinson's Disease: Predictions and Validation of a Patient-Specific Non-Linear Model

ObjectivesThe exact mechanisms of deep brain stimulation (DBS) are still an active area of investigation, in spite of its clinical successes. This is due in part to the lack of understanding of the effects of stimulation on neuronal rhythms. Entrainment of brain oscillations has been hypothesised as a potential mechanism of neuromodulation. A better understanding of entrainment might further inform existing methods of continuous DBS, and help refine algorithms for adaptive methods. The purpose of this study is to develop and test a theoretical framework to predict entrainment of cortical rhythms to DBS across a wide range of stimulation parameters. Materials and MethodsWe fit a model of interacting neural populations to selected features characterising PD patients off-stimulation finely-tuned gamma rhythm recorded through electrocorticography. Using the fitted models, we predict basal ganglia DBS parameters that would result in 1:2 entrainment, a special case of sub-harmonic entrainment observed in patients and predicted by theory. ResultsWe show that the neural circuit models fitted to patient data exhibit 1:2 entrainment when stimulation is provided across a range of stimulation parameters. Furthermore, we verify key features of the region of 1:2 entrainment in the stimulation frequency/amplitude space with follow-up recordings from the same patients, such as the loss of 1:2 entrainment above certain stimulation amplitudes. ConclusionOur results reveal that continuous, constant frequency DBS in patients may lead to nonlinear patterns of neuronal entrainment across stimulation parameters, and that these responses can be predicted by modelling. Should entrainment prove to be an important mechanism of therapeutic stimulation, our modelling framework may reduce the parameter space that clinicians must consider when programming devices for optimal benefit.

neuroscience↗

bioRxiv2022

Uncertainty-guided learning with scaled prediction errors in the basal ganglia

To accurately predict rewards associated with states or actions, the variability of observations has to be taken into account. In particular, when the observations are noisy, the individual rewards should have less influence on tracking of average reward, and the estimate of the mean reward should be updated to a smaller extent after each observation. However, it is not known how the magnitude of the observation noise might be tracked and used to control prediction updates in the brain reward system. Here, we introduce a new model that uses simple, tractable learning rules that track the mean and standard deviation of reward, and leverages prediction errors scaled by uncertainty as the central feedback signal. We provide a normative analysis, comparing the performance of the new model with that of conventional models in a value tracking task. We find that the new model has an advantage over conventional models when tested across various levels of observation noise. Further, we propose a possible biological implementation of the model in the basal ganglia circuit. The scaled prediction error feedback signal is consistent with experimental findings concerning dopamine prediction error scaling relative to reward magnitude, and the update rules are found to be consistent with many features of striatal plasticity. Our results span across the levels of implementation, algorithm, and computation, and might have important implications for understanding the dopaminergic prediction error signal and its relation to adaptive and effective learning. Author SummaryThe basal ganglia system is a collection of subcortical nuclei in the mammalian brain. This system and its dopaminergic inputs are associated with learning from rewards. Here, dopamine is thought to signal errors in reward prediction. The structure and function of the basal ganglia system are not fully understood yet--for example, the basal ganglia are split into two antagonistic pathways, but the reason for this split and the role of the two pathways are unknown. Further, it has been found that under some circumstances, rewards of different sizes lead to dopamine responses of similar size, which cannot be explained with the reward prediction error theory. Here, we propose a new model of learning in the basal ganglia--the scaled prediction error model. According to our model, both reward average and reward uncertainty are tracked and represented in the two basal ganglia pathways. The learned reward uncertainty is then used to scale dopaminergic reward prediction errors, which effectively renders learning adaptive to reward noise. We show that such learning is more robust than learning from unscaled prediction errors and that it explains several physiological features of the basal ganglia system.

neuroscience↗

bioRxiv2021

Hunger improves reinforcement-driven but not planned action

Human decisions can be reflexive or planned, being governed respectively by model-free and model-based learning systems. These two systems might differ in their responsiveness to our needs. Hunger drives us to specifically seek food rewards, but here we ask whether it might have more general effects on these two decision systems. On one hand, the model-based system is often considered flexible and context-sensitive, and might therefore be modulated by metabolic needs. On the other hand, the model-free systems primitive reinforcement mechanisms may have closer ties to biological drives. Here, we tested participants on a well-established two-stage sequential decision-making task that dissociates the contribution of model-based and model-free control. Hunger enhanced overall performance by increasing model-free control, without affecting model-based control. These results demonstrate a generalised effect of hunger on decision-making that enhances reliance on primitive reinforcement learning, which in some situations translates into adaptive benefits. Significance statementThe prevalence of obesity and eating disorder is steadily increasing. To counteract problems related to eating, people need to make rational decisions. However, appetite may switch us to a different decision mode, making it harder to achieve long-term goals. Here we show that planned and reinforcement-driven actions are differentially sensitive to hunger. Hunger specifically affected reinforcement-driven actions, and did not affect the planning of actions. Our data shows that people behave differently when they are hungry. We also provide a computational model of how the behavioural changes might arise.

neuroscience↗

bioRxiv2021

Gambling on an empty stomach: Hunger modulates preferences for learned but not described risks

We assess risks differently when they are explicitly described, compared to when we learn directly from experience, suggesting dissociable decision-making systems. Our needs, such as hunger, could globally affect our risk preferences, but do they affect described and learned risks equally? On one hand, explicit decision-making is often considered flexible and contextsensitive, and might therefore be modulated by metabolic needs. On the other hand, implicit preferences learned through reinforcement might be more strongly coupled to biological drives. To answer this, we asked participants to choose between two options with different risks, where the probabilities of monetary outcomes were either described or learned. In agreement with previous studies, rewarding contexts induced risk-aversion when risks were explicitly described, but risk-seeking when they were learned through experience. Crucially, hunger attenuated these contextual biases, but only for learned risks. The results suggest that our metabolic state determines risk-taking biases when we lack explicit descriptions.

neuroscience↗

bioRxiv2020

Optimal Closed-loop Deep Brain Stimulation with Multi-Contact Electrodes

Deep brain stimulation (DBS) is a well-established treatment option for a variety of neurological disorders, including Parkinsons disease (PD) and essential tremor (ET). It is widely believed that the efficacy, efficiency and side-effects of the treatment can be improved by stimulating closed-loop, according to the symptoms of a patient. Multi-contact electrodes powered by independent current sources are a recent development in DBS technology which allow for greater precision when targeting one or more pathological regions but, in order to realise the potential of such systems, algorithms must be developed to deal with their increased complexity. This motivates the need to understand how applying DBS to multiple regions (or neural populations) can affect the efficacy and efficiency of the treatment. On the basis of a theoretical model, our paper aims to address the question of how to best apply DBS to multiple neural populations to maximally desynchronise brain activity. Using a coupled oscillator model, we derive analytical expressions which predict how the symptom severity should change as a result of applying stimulation. On the basis of these expressions we derive an algorithm describing when the stimulation should be delivered to individual contacts. Remarkably, these expressions also allow us to determine the conditions for when stimulation using information from individual contacts is likely to be advantageous. Using numerical simulation, we demonstrate that our methods have the potential to be both more effective and efficient than existing methods found in the literature.

neuroscience↗

bioRxiv2020

Neural signatures of pathological hyperdirect pathway activity in Parkinson's disease

Parkinsons disease (PD) is characterised by the emergence of pathological patterns of oscillatory synchronisation across the cortico-basal-ganglia circuit. The relationship between anatomical connectivity and oscillatory synchronisation within this system remains poorly understood. We address this by integrating evidence from invasive electrophysiology, magnetoencephalography, tractography and computational modelling in patients. Coupling between supplementary motor area (SMA) and subthalamic nucleus (STN) within the high beta frequency (21-30 Hz) range correlated with fibre tract densities between these two structures. Additionally within the STN, non-linear waveform features suggestive of cortical synchronisation correlated with cortico-STN fibre densities. Finally, computational modelling revealed that exaggerated hyperdirect cortical inputs to the STN in the upper beta frequency range can provoke the generation of widespread pathological synchrony at lower beta (13-20 Hz) frequencies. These observations reveal a spectral signature of the hyperdirect pathway at high beta frequencies and provide evidence for its pathophysiological role in oscillatory network dysfunction in PD. One sentence summarySignatures of the hyperdirect pathway and its likely role in pathological network disruption in Parkinsons disease are identified.

neuroscience↗

bioRxiv2020

Conflict detection in a sequential decision task is associated with increased cortico-subthalamic coherence and prolonged subthalamic oscillatory response in the beta band.

Making accurate decisions often involves the integration of current and past evidence. Here we examine the neural correlates of conflict and evidence integration during sequential decision making. Patients implanted with deep-brain stimulation (DBS) electrodes and age-matched healthy controls performed an expanded judgement task, in which they were free to choose how many cues to sample. Behaviourally, we found that while patients sampled numerically more cues, they were less able to integrate evidence and showed suboptimal performance. Using recordings of Magnetoencephalography (MEG) and local field potentials (LFP, in patients) in the subthalamic nucleus (STN), we found that beta oscillations signalled conflict between cues within a sequence. Following cues that differed from previous cues, beta power in the STN and cortex first decreased and then increased. Importantly, the conflict signal in the STN outlasted the cortical one, carrying over to the next cue in the sequence. Furthermore, after a conflict, there was an increase in coherence between the dorsal premotor cortex and subthalamic nucleus in the beta band. These results extend our understanding of cortico-subcortical dynamics of conflict processing, and do so in a context where evidence must be accumulated in discrete steps, much like in real life. Thus, the present work leads to a more nuanced picture of conflict monitoring systems in the brain and potential changes due to disease.

neuroscience↗

bioRxiv2020

A normative account of confirmatory biases during reinforcement learning

Reinforcement learning involves updating estimates of the value of states and actions on the basis of experience. Previous work has shown that in humans, reinforcement learning exhibits a confirmatory bias: when updating the value of a chosen option, estimates are revised more radically following positive than negative reward prediction errors, but the converse is observed when updating the unchosen option value estimate. Here, we simulate performance on a multi-arm bandit task to examine the consequences of a confirmatory bias for reward harvesting. We report a paradoxical finding: that confirmatory biases allow the agent to maximise reward relative to an unbiased updating rule. This principle holds over a wide range of experimental settings and is most influential when decisions are corrupted by noise. We show that this occurs because on average, confirmatory biases lead to overestimating the value of more valuable bandits, and underestimating the value of less valuable bandits, rendering decisions overall more robust in the face of noise. Our results show how apparently suboptimal learning policies can in fact be reward-maximising if decisions are made with finite computational precision.

animal behavior and cognition↗

bioRxiv2020

Reward prediction errors induce risk-seeking

Reward prediction errors (RPEs) and risk preferences have two things in common: both can shape decision making behavior, and both are commonly associated with dopamine. RPEs drive value learning and are thought to be represented in the phasic release of striatal dopamine. Risk preferences bias choices towards or away from uncertainty; they can be manipulated with drugs that target the dopaminergic system. The common neural substrate suggests that RPEs and risk preferences might be linked on the level of behavior as well, but this has never been tested. Here, we aim to close this gap. First, we apply a recent theory of learning in the basal ganglia to predict how exactly RPEs might influence risk preferences. We then test our behavioral predictions using a novel bandit task in which value and risk vary independently across options. Critically, conditions are included where options vary in risk but are matched for value. We find that subjects become more risk seeking if choices are preceded by positive RPEs, and more risk averse if choices are preceded by negative RPEs. These findings cannot be explained by other known effects, such as nonlinear utility curves or dynamic learning rates. Finally, we show that RPE-induced risk-seeking is indexed by pupil dilation: participants with stronger pupillary correlates of RPE also show more pronounced behavioral effects. Authors summaryMany of our decisions are based on expectations. Sometimes, however, surprises happen: outcomes are not as expected. Such discrepancies between expectations and actual outcomes are called prediction errors. Our brain recognises and uses such prediction errors to modify our expectations and make them more realistic--a process known as reinforcement learning. In particular, neurons that release the neurotransmitter dopamine show activity patterns that strongly resemble prediction errors. Interestingly, the same neurotransmitter is also known to regulate risk preferences: dopamine levels control our willingness to take risks. We theorised that, since learning signals cause dopamine release, they might change risk preferences as well. In this study, we test this hypothesis. We find that participants are more likely to make a risky choice just after they experienced an outcome that was better than expected, which is precisely what out theory predicts. This suggests that dopamine signalling can be ambiguous--a learning signal can be mistaken for an impulse to take a risk.

neuroscience↗

bioRxiv2020

Average beta burst duration profiles provide a signature of dynamical changes between the ON and OFF medication states in Parkinson's disease

Parkinsons disease motor symptoms are associated with an increase in subthalamic nucleus beta band oscillatory power. However, these oscillations are phasic, and there is a growing body of evidence suggesting that beta burst duration may be of critical importance to motor symptoms. This makes insights into the dynamics of beta bursting generation valuable, in particular to refine closed-loop deep brain stimulation in Parkinsons disease. In this study, we ask the question "Can average burst duration reveal how dynamics change between the ON and OFF medication states?". Our analysis of local field potentials from the subthalamic nucleus demonstrates using linear surrogates that the system generating beta oscillations is more likely to act in a non-linear regime OFF medication and that the change in a non-linearity measure is correlated with motor impairment. In addition, we pinpoint the simplest dynamical changes that could be responsible for changes in the temporal patterning of beta oscillations between medication states by fitting to data biologically inspired models, and simpler beta envelope models. Finally, we show that the non-linearity can be directly extracted from average burst duration profiles under the assumption of constant noise in envelope models. This reveals that average burst duration profiles provide a window into burst dynamics, which may underlie the success of burst duration as a biomarker. In summary, we demonstrate a relationship between average burst duration profiles, dynamics of the system generating beta oscillations, and motor impairment, which puts us in a better position to understand the pathology and improve therapies such as deep brain stimulation. Author summaryIn Parkinsons disease, motor impairment is associated with abnormal oscillatory activity of neurons in deep motor regions of the brain. These oscillations come in the shape of bursts, and the duration of these bursts has recently been shown to be of importance to motor symptoms. To better understand the disease and refine therapies, we relate the duration of these bursts to properties of the system generating them in the pathological state and in a proxy of the healthy state. The data suggest that the system generating bursts involves more complexity in the pathological state, and we show that a measure of this complexity is associated with motor impairment. We propose biologically inspired models and simpler models that can generate the burst patterns observed in the pathological and healthy state. The models confirm what was observed in data, and tell us how burst generation mechanisms could differ in the disease. Finally, we identify a mathematical link allowing us to infer properties of the burst generating system from burst duration measurements in patient recordings. This sheds some light on the significance of burst duration as a marker of pathology.

neuroscience↗

bioRxiv2020

Bayesian confidence for drift diffusion observers in dynamic stimuli tasks

We introduce a new approach to modelling decision confidence, with the aim of enabling computationally cheap predictions while taking into account, and thereby exploiting, trial-by-trial variability in dynamic stimuli. Using the framework of the drift diffusion model of decision making, along with time-dependent thresholds and the idea of a Bayesian confidence readout, we derive expressions for the probability distribution over confidence reports. In line with current models of confidence, the derivations allow for the accumulation of "pipeline" evidence that has been received but not processed by the time of response, the effect of drift rate variability, and metacognitive noise. The expressions are valid for stimuli that change over the course of a trial with normally-distributed fluctuations in the evidence they provide. A number of approximations are made to arrive at the final expressions, and we test all approximations via simulation. The derived expressions contain only a small number of standard functions, and require evaluating only once per trial, making trial-by-trial modelling of confidence data in dynamic stimuli tasks more feasible. We conclude by using the expressions to gain insight into the confidence of optimal observers, and empirically observed patterns.

animal behavior and cognition↗

bioRxiv2019

Dopamine role in learning and action inference

This paper describes a framework for modelling dopamine function in the mammalian brain. In this framework, dopaminergic neurons projecting to different parts of the striatum encode errors in predictions made by the corresponding systems within the basal ganglia. These prediction errors are equal to differences between rewards and expectations in the goal-directed system, and to differences between the chosen and habitual actions in the habit system. The prediction errors enable learning about rewards resulting from actions and habit formation. During action planning, the expectation of reward in the goal-directed system arises from formulating a plan to obtain that reward. Thus dopaminergic neurons in this system provide feedback on whether the current motor plan is sufficient to obtain the available reward, and they facilitate action planning until a suitable plan is found. Presented models account for dopaminergic responses during movements, effects of dopamine depletion on behaviour, and make several experimental predictions.

bioinformatics↗

bioRxiv2019

Modeling the effects of motivation on choice and learning in the basal ganglia

Decision making relies on adequately evaluating the consequences of actions on the basis of past experience and the current physiological state. A key role in this process is played by the basal ganglia, where neural activity and plasticity are modulated by dopaminergic input from the midbrain. Internal physiological factors, such as hunger, scale signals encoded by dopaminergic neurons and thus they alter the motivation for taking actions and learning. However, to our knowledge, no formal mathematical formulation exists for how a physiological state affects learning and action selection in the basal ganglia. We developed a framework for modelling the effect of motivation on choice and learning. The framework defines the motivation to obtain a particular resource as the difference between the desired and the current level of this resource, and proposes how the utility of reinforcements depends on the motivation. To account for dopaminergic activity previously recorded at different physiological states, the paper argues that the prediction error encoded in the dopaminergic activity needs to be redefined as the difference between utility and expected utility, which depends on both the objective reinforcement and the motivation. We also demonstrate a possible mechanism by which the evaluation and learning of utility of actions can be implemented in the basal ganglia network. The presented theory brings together models of learning in the basal ganglia with the incentive salience theory in a single simple framework, and it provides a mechanistic insight into how decision processes and learning in the basal ganglia are modulated by the motivation. Moreover, this theory is also consistent with data on neural underpinnings of overeating and obesity, and makes further experimental predictions.\n\nAuthor summaryBehaviour is made of decisions that are based on the evaluation of costs and benefits of potential actions in a given situation. Actions are usually generated in response to reinforcement cues which are potent triggers of desires that can range from normal appetites to compulsive addictions. However, learned cues are not constant in their motivating power. Food cues are more potent when you are hungry than when you have just finished a meal. These changes in cue-triggered desire produced by a change in biological state present a challenge to many current computational models of motivation and learning. Here, we demonstrate concrete examples of how motivation can instantly modulate reinforcement values and actions; we propose an overarching framework of learning and action selection based on maintaining the physiological balance to better capture the dynamic interaction between learning and physiology that controls the incentive salience mechanism of motivation for reinforcements. These models provide a unified account of state-dependent learning of the incentive value of actions and selecting actions according to the learned positive and negative consequences of those actions and with respect to the physiological state. We propose a biological implementation of how these processes are controlled by an area in the brain called the basal ganglia, which is associated with error-driven learning.

neuroscience↗

bioRxiv2019

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

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. Investigators have been looking at stimulating less, chiefly to reduce side effects. One strategy, phase-locked deep brain stimulation, consists of stimulating according to the phase of the tremor, once per period. In this study, we aim to reproduce the phase dependent effects of stimulation seen in patient data with a biologically inspired Wilson-Cowan model. To this end, we first analyse patient data, and conclude that half of the datasets have response curves that are better described by sinusoidal curves than by straight lines, while an effect of phase cannot be consistently identified in the remaining half. Using the Hilbert phase we derive analytical expressions for phase and amplitude responses to phase-dependent stimulation and study their relationship in the linearisation of a stable focus model, a simplification of the Wilson-Cowan model in the stable focus regime. Analytical results provide a good approximation for response curves observed in patients with consistent significance. Additionally, we fitted the full non-linear Wilson-Cowan model to these patients, and we show that the model can fit in each case to the dynamics of patient tremor as well as the phase response curve, and the best fits are found to be stable foci for each patients (tied best fit in one instance). 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. This can be partially explained by the relationship between the response curves in the model being compatible with what is found in the data. We also note that the non-linear Wilson-Cowan model is able to describe response to stimulation more precisely than the linearisation.

neuroscience↗

bioRxiv2018

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 Parkinsons 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. We predict that, provided certain conditions are satisfied, 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 strategies found in the literature, namely phase-locked and adaptive DBS.\n\nAuthor summaryDeep brain stimulation (DBS) involves delivering electrical impulses to target sites within the brain and is a proven therapy for a variety of neurological disorders. Closed loop DBS is a promising new approach where stimulation is applied according to the state of a patient. Crucial to the success of this approach is being able to predict how a patient should respond to stimulation. Our work focusses on DBS as applied to patients with essential tremor (ET). On the basis of a theoretical model, which describes neurons as oscillators that respond to stimulation and have a certain tendency to synchronize, we provide predictions for how a patient should respond when stimulation is applied at a particular phase and amplitude of the ongoing tremor oscillations. Previous experimental studies of closed loop DBS provided stimulation either on the basis of ongoing phase or amplitude of pathological oscillations. Our study suggests how both of these measurements can be used to control stimulation. As part of this work, we also look for evidence for our theories in experimental data and find our predictions to be satisfied in one patient. The insights obtained from this work should lead to a better understanding of how to optimise closed loop DBS strategies.

neuroscience↗