A Consistent Definition of Phase Resetting Using Hilbert Transform

Oprisan, Sorinel A.

doi:10.1155/2017/5865101

Cited by 10 publications

(16 citation statements)

References 70 publications

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“…Brief perturbations applied to intrinsic oscillatory activities lead only to transient changes of the rhythm, which eventually dissipate after a few cycles. Since our focus is on identifying similarities among steady state LFPs, any transient changes in the phases of LFP oscillations should be removed (Oprisan, 2017 ). As previously described (Oprisan, 2017 ; Oprisan and Austin, 2017 ), the phase resetting was estimated by the amount of required circular shift on each LFP trace (Figure 1A ) in order to maximize the coefficient of correlation between any trial and an arbitrary selected “reference” trial (Figure 1B ).…”

Section: Discussionmentioning

confidence: 99%

“…Ongoing oscillatory activity could be reset by sensory inputs, such as visual (Kambe et al, 2015 ; Woelders et al, 2017 ) or auditory (Mercier et al, 2013 ) stimuli, or by extrinsic stimuli, such as deep brain stimulation (Tass, 2003 ), or temperature (Rensing and Ruoff, 2002 ). We measured the phase resetting induced by brief light stimuli using both the autocorrelation (Oprisan, 2013 ; Oprisan et al, 2015 ) and the Hilbert's transform (Oprisan, 2017 ) methods. The phase resetting correction allowed an accurate estimate of the delay (lag) time and embedding dimension of LFP data (Oprisan and Canavier, 2002 ; Oprisan et al, 2003 , 2015 ).…”

Section: Introductionmentioning

confidence: 99%

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Cocaine-Induced Changes in Low-Dimensional Attractors of Local Field Potentials in Optogenetic Mice

Oprisan

Imperatore

Helms

et al. 2018

Front. Comput. Neurosci.

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Optogenetically evoked local field potential (LFP) recorded from the medial prefrontal cortex (mPFC) of mice during basal conditions and following a systemic cocaine administration were analyzed. Blue light stimuli were delivered to mPFC through a fiber optic every 2 s and each trial was repeated 100 times. As in the previous study, we used a surrogate data method to check that nonlinearity was present in the experimental LFPs and only used the last 1.5 s of steady activity to measure the LFPs phase resetting induced by the brief 10 ms light stimulus. We found that the steady dynamics of the mPFC in response to light stimuli could be reconstructed in a three-dimensional phase space with topologically similar “8”-shaped attractors across different animals. Therefore, cocaine did not change the complexity of the recorded nonlinear data compared to the control case. The phase space of the reconstructed attractor is determined by the LFP time series and its temporally shifted versions by a multiple of some lag time. We also compared the change in the attractor shape between cocaine-injected and control using (1) dendrogram clustering and (2) Frechet distance. We found about 20% overlap between control and cocaine trials when classified using dendrogram method, which suggest that it may be possible to describe mathematically both data sets with the same model and slightly different model parameters. We also found that the lag times are about three times shorter for cocaine trials compared to control. As a result, although the phase space trajectories for control and cocaine may look similar, their dynamics is significantly different.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Cocaine-Induced Changes in Low-Dimensional Attractors of Local Field Potentials in Optogenetic Mice

Oprisan

Imperatore

Helms

et al. 2018

Front. Comput. Neurosci.

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Section: Discussionmentioning

confidence: 99%

“…41in Appendix D and Eqs. (37) and (39) in Appendix C). A Taylor expansion around δX 1 = 0 yields, to lowest order in δX 1 (for weak stimulation), hPRC (1)…”

Section: Phase Responsementioning

confidence: 99%

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

et al. 2020

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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.

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“…This is not a concern from the perspective of describing patient data, as this is the observable choice we are making for both the data and the model. Commonly used with data, the Hilbert transform has also been proposed as a robust method to measure steady state PRCs in single neuron models [33]. Moreover, stimulation is assumed to be small in our analytical expressions (section 4), but not in the full model, contrary to standard asymptotic phase reduction strategies.…”

Section: Discussionmentioning

confidence: 99%

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

Duchet

Weerasinghe

Cagnan

et al. 2019

Preprint

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AbstractEssential 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.

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A Consistent Definition of Phase Resetting Using Hilbert Transform

Cited by 10 publications

References 70 publications

Cocaine-Induced Changes in Low-Dimensional Attractors of Local Field Potentials in Optogenetic Mice

Cocaine-Induced Changes in Low-Dimensional Attractors of Local Field Potentials in Optogenetic Mice

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

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

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