Determining individual phase response curves from aggregate population data

Wilson, Dan; Moehlis, Jeff

doi:10.1103/physreve.92.022902

Cited by 10 publications

(5 citation statements)

References 41 publications

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“…Note that in some studies, the PRC refers instead to the response of individual neurons (e.g. [36, 37, 38]). This is in contrast with this study, where we consider changes on the population level.…”

Section: Resultsmentioning

confidence: 99%

How to design optimal brain stimulation to modulate phase-amplitude coupling?

Duchet,

Bogacz

2024

Preprint

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Objective. Phase-amplitude coupling (PAC), the coupling of the amplitude of a faster brain rhythm to the phase of a slower brain rhythm, plays a significant role in brain activity and has been implicated in various neurological disorders. For example, in Parkinson's disease, PAC between the beta (13-30 Hz) and gamma (50-200 Hz) rhythms in the motor cortex is exaggerated, while in Alzheimer's disease, PAC between the theta (4-8 Hz) and gamma rhythms is diminished. Modulating PAC (i.e. reducing or enhancing PAC) using brain stimulation could therefore open new therapeutic avenues. However, while it has been previously reported that phase-locked stimulation can increase PAC, it is unclear what the optimal stimulation strategy to modulate PAC might be. Here, we provide a theoretical framework to narrow down the experimental optimisation of stimulation aimed at modulating PAC, which would otherwise rely on trial and error. Approach. We make analytical predictions using a Stuart-Landau model, and confirm these predictions in a more realistic model of coupled neural populations. Main results. Our framework specifies the critical Fourier coefficients of the stimulation waveform which should be tuned to optimally modulate PAC. Depending on the characteristics of the amplitude response curve of the fast population, these components may include the slow frequency, the fast frequency, combinations of these, as well as their harmonics. We also show that the optimal balance of energy between these Fourier components depends on the relative strength of the endogenous slow and fast rhythms, and that the alignment of fast components with the fast rhythm should change throughout the slow cycle. Furthermore, we identify the conditions requiring to phase-lock stimulation to the fast and/or slow rhythms. Significance. Together, our theoretical framework lays the foundation for guiding the development of innovative and more effective brain stimulation aimed at modulating PAC for therapeutic benefit.

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Section: Resultsmentioning

confidence: 99%

How to design optimal brain stimulation to modulate phase-amplitude coupling?

Duchet,

Bogacz

2024

Preprint

View full text Add to dashboard Cite

show abstract

“…Note that in some studies, the PRC refers instead to the response of individual neurons (e.g. [ 36 – 38 ]). This is in contrast with this study, where we consider changes on the population level.…”

Section: Resultsmentioning

confidence: 99%

How to design optimal brain stimulation to modulate phase-amplitude coupling?

Duchet,

Bogacz

2024

J. Neural Eng.

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Objective. Phase-amplitude coupling (PAC), the coupling of the amplitude of a faster brain rhythm to the phase of a slower brain rhythm, plays a significant role in brain activity and has been implicated in various neurological disorders. For example, in Parkinson’s disease, PAC between the beta (13–30 Hz) and gamma (30–100 Hz) rhythms in the motor cortex is exaggerated, while in Alzheimer’s disease, PAC between the theta (4–8 Hz) and gamma rhythms is diminished. Modulating PAC (i.e. reducing or enhancing PAC) using brain stimulation could therefore open new therapeutic avenues. However, while it has been previously reported that phase-locked stimulation can increase PAC, it is unclear what the optimal stimulation strategy to modulate PAC might be. Here, we provide a theoretical framework to narrow down the experimental optimisation of stimulation aimed at modulating PAC, which would otherwise rely on trial and error. Approach. We make analytical predictions using a Stuart–Landau model, and confirm these predictions in a more realistic model of coupled neural populations. Main results. Our framework specifies the critical Fourier coefficients of the stimulation waveform which should be tuned to optimally modulate PAC. Depending on the characteristics of the amplitude response curve of the fast population, these components may include the slow frequency, the fast frequency, combinations of these, as well as their harmonics. We also show that the optimal balance of energy between these Fourier components depends on the relative strength of the endogenous slow and fast rhythms, and that the alignment of fast components with the fast rhythm should change throughout the slow cycle. Furthermore, we identify the conditions requiring to phase-lock stimulation to the fast and/or slow rhythms. Significance. Together, our theoretical framework lays the foundation for guiding the development of innovative and more effective brain stimulation aimed at modulating PAC for therapeutic benefit.

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“…It is worth noting that controlling either synchronization or desynchronization of the severely underactuated HH population through a single control and a single aggregated noisy measurement is a highly non-trivial task even when the system model is available [40][41][42][43]. To the best of our knowledge, no other data-driven control work has addressed this issue.…”

Section: Online Dynamic Adaption To System Variationmentioning

confidence: 99%

Data-Driven Control of Neuronal Networks with Population-Level Measurement

Singhal

Zeng

et al. 2023

Preprint

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Controlling complex networks of nonlinear neurons is an important problem pertinent to various applications in engineering and natural sciences. While in recent years the control of neural populations with comprehensive biophysical models or simplified models, e.g., phase models, has seen notable advances, learning appropriate controls directly from data without any model assumptions remains a challenging and less developed area of research. In this paper, we address this problem by leveraging the network’s local dynamics to iteratively learn an appropriate control without constructing a global model of the system. The proposed technique can effectively regulate synchrony in a neuronal network using only one input and one noisy population-level output measurement. We provide a theoretical analysis of our approach and illustrate its robustness to system variations and its generalizability to accommodate various physical constraints, such as charge-balanced inputs.

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Determining individual phase response curves from aggregate population data

Cited by 10 publications

References 41 publications

How to design optimal brain stimulation to modulate phase-amplitude coupling?

How to design optimal brain stimulation to modulate phase-amplitude coupling?

How to design optimal brain stimulation to modulate phase-amplitude coupling?

Data-Driven Control of Neuronal Networks with Population-Level Measurement

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