Sensitivity Analysis of Oscillator Models in the Space of Phase-Response Curves: Oscillators As Open Systems

Sacré, Pierre; Sepulchre, Rodolphe

doi:10.1109/mcs.2013.2295710

Cited by 32 publications

(7 citation statements)

References 59 publications

(95 reference statements)

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“…2.1.3 First-order circadian phase reduced model. Phase response function is widely used in the studies of circadian rhythms [30]. This function defines the effect of a light pulse on a circadian rhythm and reduces a high-order model into a one-dimensional phase-based model.…”

Section: Plos Onementioning

confidence: 99%

Optimization of light exposure and sleep schedule for circadian rhythm entrainment

2021

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The circadian rhythm, called Process C, regulates a wide range of biological processes in humans including sleep, metabolism, body temperature, and hormone secretion. Light is the dominant synchronizer of the circadian rhythm—it has been used to regulate the circadian phase to cope with jet-lag, shift work, and sleep disorder. The homeostatic oscillation of the sleep drive is called Process S. Process C and Process S together determine the sleep-wake cycle in what is known as the two-process model. This paper addresses the regulation of both Process C and Process S by scheduling light exposure and sleep based on numerical simulations of circadian rhythm and sleep mathematical models. This is a significant step beyond the existing literature that only considers the entrainment of Process C. Regulation of the two-process model poses several unique features and challenges: 1. Process S is non-smooth, i.e., the homeostatic dynamics are different in the sleep and wake regimes; 2. Light only indirectly affects Process S through Process C; 3. Light does not affect Process C during sleep. We consider two scenarios: optimizing light intensity as the control input with spontaneous (i.e., unscheduled) sleep/wake times and jointly optimizing the light intensity and the sleep/wake times, which allows limited delayed sleep and early waking as part of the decision variables. We solve the time-optimal entrainment problem for the two-process model for both scenarios using an extension of the gradient descent algorithm to non-smooth systems. To illustrate the efficacy of our time-optimal entrainment strategies, we consider two common use cases: transmeridian travelers and shift workers. For transmeridian travelers, joint optimization of the two-process model avoids the unrealistic long wake duration when only Process C is considered. The entrainment time also decreases when both the light input and the sleep schedule are optimized compared to when only the light input is optimized. For shift workers, we show that the entrainment time is significantly shortened by optimizing the night shift working light.

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Section: Plos Onementioning

confidence: 99%

Optimization of light exposure and sleep schedule for circadian rhythm entrainment

2021

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“…30 For type II, either an advance or a delay in the phase are possible depending upon the timing of the perturbation, while in the case of type I, the timing of the perturbation does not change the sign of the phase shift. The canonical examples of each type 13,15 are Q(θ ) ∝ 1 − cos θ for type I (e.g., the theta neuron) and Q(θ ) ∝ sin θ for type II (e.g., the Stuart-Landau oscillator). For non-infinitesimal PRCs, the previous classification falls short as the character of Q may change with the strength of the stimulus.…”

Section: Winfree Model With Non-infinitesimal Prcmentioning

confidence: 99%

“…For non-infinitesimal PRCs, the previous classification falls short as the character of Q may change with the strength of the stimulus. 13,15 The types of PRC we consider are conditioned by the applicability of the OA ansatz, as it enables a drastic dimensionality reduction. The OA ansatz imposes that no harmonics in θ beyond the first one are present in Q(θ , A).…”

Section: Winfree Model With Non-infinitesimal Prcmentioning

confidence: 99%

“…(1a)-which only holds in the limit of asymptotically small interactions. 11,[13][14][15][16] In this work, we generalized the Winfree model considering nonlinear interactions. Mathematical tractability imposes certain restrictions on the distribution of the natural frequencies and on the class of "non-infinitesimal" (also called "finite" or "non-linear") PRCs, but we believe it is remarkable that such analytic solutions exist.…”

Section: Introductionmentioning

confidence: 99%

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The Winfree model with non-infinitesimal phase-response curve: Ott–Antonsen theory

Pazó

Gallego

2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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A novel generalization of the Winfree model of globally coupled phase oscillators, representing phase reduction under finite coupling, is studied analytically. We consider interactions through a non-infinitesimal (or finite) phase-response curve (PRC), in contrast to the infinitesimal PRC of the original model. For a family of non-infinitesimal PRCs, the global dynamics is captured by one complex-valued ordinary differential equation resorting to the Ott-Antonsen ansatz. The phase diagrams are thereupon obtained for four illustrative cases of non-infinitesimal PRC. Bistability between collective synchronization and full desynchronization is observed in all cases.

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“…As such, the small-molecule pharmaceutical KL001 offers substantial potential for therapeutic action on the circadian phase. To quantify phase changes following perturbation, a phase response curve (PRC) is widely used [21]. These curves map the magnitude and direction of phase shifts resulting from an input.…”

Section: Introductionmentioning

confidence: 99%

Pharmacokinetic Model-Based Control across the Blood–Brain Barrier for Circadian Entrainment

Murdoch,

Aiello,

Doyle

2023

IJMS

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The ability to shift circadian phase in vivo has the potential to offer substantial health benefits. However, the blood–brain barrier prevents the absorption of the majority of large and many small molecules, posing a challenge to neurological pharmaceutical development. Motivated by the presence of the circadian molecule KL001, which is capable of causing phase shifts in a circadian oscillator, we investigated the pharmacokinetics of different neurological pharmaceuticals on the dynamics of circadian phase. Specifically, we developed and validated five different transport models that describe drug concentration profiles of a circadian pharmaceutical at the brain level under oral administration and designed a nonlinear model predictive control (MPC)-based framework for phase resetting. Performance of the novel control algorithm based on the identified pharmacokinetic models was demonstrated through simulations of real-world misalignment scenarios due to jet lag. The time to achieve a complete phase reset for 11-h phase delay ranged between 48 and 72 h, while a 5-h phase advance was compensated in 30 to 60 h. This approach provides mechanistic insight into the underlying structure of the circadian oscillatory system and thus leads to a better understanding of the feasibility of therapeutic manipulations of the system.

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Sensitivity Analysis of Oscillator Models in the Space of Phase-Response Curves: Oscillators As Open Systems

Cited by 32 publications

References 59 publications

Optimization of light exposure and sleep schedule for circadian rhythm entrainment

Optimization of light exposure and sleep schedule for circadian rhythm entrainment

The Winfree model with non-infinitesimal phase-response curve: Ott–Antonsen theory

Pharmacokinetic Model-Based Control across the Blood–Brain Barrier for Circadian Entrainment

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