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

Duchet, Benoit; Weerasinghe, Gihan; Cagnan, Hayriye; Brown, Peter; Bick, Christian; Bogacz, Rafał

doi:10.1101/535880

Cited by 5 publications

(3 citation statements)

References 43 publications

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“…Such higher-dimensional systems are of particular interest when resets are considered in large coupled systems. Even when the coupling is through the mean-field dynamics, such systems can exhibit rich collective dynamics that are reflected in their PTCs [6,33]. We believe that our approach will be useful in this context, in particular, when the perturbation is a time-dependent stimulus.…”

Section: Discussionmentioning

confidence: 98%

A continuation approach to computing phase resetting curves

Langfield¹,

Krauskopf²,

Osinga³

2020

Preprint

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Phase resetting is a common experimental approach to investigating the behaviour of oscillating neurons. Assuming repeated spiking or bursting, a phase reset amounts to a brief perturbation that causes a shift in the phase of this periodic motion. The observed effects not only depend on the strength of the perturbation, but also on the phase at which it is applied. The relationship between the change in phase after the perturbation and the unperturbed old phase, the so-called phase resetting curve, provides information about the type of neuronal behaviour, although not all effects of the nature of the perturbation are well understood. In this chapter, we present a numerical method based on the continuation of a multi-segment boundary value problem that computes phase resetting curves in ODE models. Our method is able to deal effectively with phase sensitivity of a system, meaning that it is able to handle extreme variations in the phase resetting curve, including resets that are seemingly discontinuous. We illustrate the algorithm with two examples of planar systems, where we also demonstrate how qualitative changes of a phase resetting curve can be characterised and understood. A seven-dimensional example emphasises that our method is not restricted to planar systems, and illustrates how we can also deal with non-instantaneous, time-varying perturbations.

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Section: Discussionmentioning

confidence: 98%

A continuation approach to computing phase resetting curves

Langfield¹,

Krauskopf²,

Osinga³

2020

Preprint

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“…(Tass & Majtanik, 2006;Popovych & Tass, 2012;Ebert, Hauptmann, & Tass, 2014;Popovych et al, 2015;Manos, Zeitler, & Tass, 2018), or on analytical insights under the simplifying assumption that spiking is only triggered by stimulation pulses (Kromer & Tass, 2020). Other analytical approaches based on mean-field models are focused on short-term changes due to stimulation and do not consider plastic changes (Duchet et al, 2020;Weerasinghe et al, 2019Weerasinghe et al, , 2021. Our framework offers an alternative, where exact evolution equations for the average coupling within and between neural populations could inform the development of new therapies 0s) from N (5, σ 2 κ ).…”

Section: Discussionmentioning

confidence: 99%

Mean-field approximations with adaptive coupling for networks with spike-timing-dependent plasticity

Duchet

Bick

Byrne

2022

Preprint

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Understanding the effect of spike-timing-dependent plasticity (STDP) is key to elucidate how neural networks change over long timescales and to design interventions aimed at modulating such networks in neurological disorders. However, progress is restricted by the significant computational cost associated with simulating neural network models with STDP, and by the lack of low-dimensional description that could provide analytical insights. To approximate STDP in phase oscillator networks, simpler phase-difference-dependent plasticity (PDDP) rules have been developed, which prescribe synaptic changes based on phase differences of neuron pairs rather than differences in spike timing. Here we construct mean-field approximations for phase oscillator networks with STDP to describe the dynamics of large networks of adaptive oscillators. We first show that single-harmonic PDDP rules can approximate a simple form of symmetric STDP, while multi-harmonic rules are required to accurately approximate causal STDP. We then derive exact expressions for the evolution of the average PDDP coupling weight in terms of network synchrony. For adaptive networks of Kuramoto oscillators that form clusters, we formulate a low-dimensional description based on mean field dynamics and average coupling weight. Finally, we show that such a two-cluster mean-field model can be fitted to provide a low-dimensional approximation of a full adaptive network with symmetric STDP. Our framework represents a step towards a low-dimensional description of adaptive networks with STDP, and could for example inform the development of new therapies aimed at maximizing the long-lasting effects of brain stimulation.

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“…The general fitting procedure is similar to what was used in [70]. At each optimisation step, the optimiser returns the cost…”

mentioning

confidence: 99%

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

Duchet

Ghezzi

Weerasinghe

et al. 2020

Preprint

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1Parkinson's disease motor symptoms are associated with an increase in subthalamic 2 nucleus beta band oscillatory power. But these oscillations are phasic, and there is a 3 growing body of evidence suggesting that beta burst duration may be of critical 4 importance to motor symptoms, making insights into the dynamics of beta bursting 5 generation valuable. In this study, we ask the question "Can average burst duration 6 reveal how dynamics change between the ON and OFF medication states?". Our 7 analysis of local field potentials from the subthalamic nucleus demonstrates using linear 8 surrogates that the system generating beta oscillations acts in a more non-linear regime 9 OFF medication and that the change in the degree of non-linearity is correlated with 10 motor impairment. Further, we pinpoint specific dynamical changes responsible for 11 changes in the temporal patterning of beta oscillations between medication states by 12 fitting to data biologically inspired models, and simpler beta envelope models. Finally, 13 we show that the non-linearity can be directly extracted from average burst duration 14 profiles under the assumption of constant noise in envelope models. This reveals that 15 average burst duration profiles provide a window into burst dynamics, which may 16 underlie the success of burst duration as a biomarker. In summary, we demonstrate a 17 relationship between average burst duration profiles, dynamics of the system generating 18 beta oscillations, and motor impairment, which puts us in a better position to 19 understand the pathology and improve therapies such as deep brain stimulation. 20 April 27, 2020 1/39 65 OFF medication states to changes in dynamical properties of the system generating 66 beta oscillations? 67In previous studies, STN beta bursts have been mostly studied based on one 68 arbitrary threshold of the beta envelope as events above the threshold, potentially with 69April 27, 2020 2/39 a minimum duration condition (examples of various thresholds shown in Fig 1A). 70Average burst duration and amplitude profiles describing the average burst duration 71 and amplitude for a range of thresholds (see Fig 1A and Fig 1B for an illustration of 72 average burst duration profiles) have been introduced [13,14]. However, they played a 73 minor role and have not been considered systematically on an individual patient basis. 74 Here, we leave behind the arbitrary choice of a threshold by relying on profiles across 75 thresholds to provide an unbiased characterisation of beta oscillation temporal 76 patterning. It has been established that STN beta burst duration is a better metric 77 than burst amplitude to distinguish between the healthy and pathological states in an 78 animal model of PD [19]. We begin our study by investigating in STN recordings of PD 79 patients whether average burst duration profiles are better at distinguishing between the 80 ON and OFF medication states than average burst amplitude profiles. We only observe 81 changes in temporal patterning of beta oscillations in...

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

Cited by 5 publications

References 43 publications

A continuation approach to computing phase resetting curves

A continuation approach to computing phase resetting curves

Mean-field approximations with adaptive coupling for networks with spike-timing-dependent plasticity

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

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