Time Window Determination for Inference of Time-Varying Dynamics: Application to Cardiorespiratory Interaction

Interacting dynamical systems abound in nature, with examples ranging from biology and population dynamics, through physics and chemistry, to communications and climate. Often their states, parameters and functions are time-varying, because such systems interact with other systems and the environmen...

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Main Authors: Dushko Lukarski, Margarita Ginovska, Hristina Spasevska, Tomislav Stankovski
Format: Article
Language:English
Published: Frontiers Media S.A. 2020-04-01
Series:Frontiers in Physiology
Subjects:
Online Access:https://www.frontiersin.org/article/10.3389/fphys.2020.00341/full
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spelling doaj-f9851199e98c48ea801e3cba4685e34c2020-11-25T03:02:46ZengFrontiers Media S.A.Frontiers in Physiology1664-042X2020-04-011110.3389/fphys.2020.00341519055Time Window Determination for Inference of Time-Varying Dynamics: Application to Cardiorespiratory InteractionDushko Lukarski0Dushko Lukarski1Margarita Ginovska2Hristina Spasevska3Tomislav Stankovski4Tomislav Stankovski5Faculty of Medicine, Ss. Cyril and Methodius University, Skopje, MacedoniaUniversity Clinic for Radiotherapy and Oncology, Skopje, MacedoniaFaculty of Electrical Engineering and Information Technologies, Ss. Cyril and Methodius University, Skopje, MacedoniaFaculty of Electrical Engineering and Information Technologies, Ss. Cyril and Methodius University, Skopje, MacedoniaFaculty of Medicine, Ss. Cyril and Methodius University, Skopje, MacedoniaDepartment of Physics, Lancaster University, Lancaster, United KingdomInteracting dynamical systems abound in nature, with examples ranging from biology and population dynamics, through physics and chemistry, to communications and climate. Often their states, parameters and functions are time-varying, because such systems interact with other systems and the environment, exchanging information and matter. A common problem when analysing time-series data from dynamical systems is how to determine the length of the time window for the analysis. When one needs to follow the time-variability of the dynamics, or the dynamical parameters and functions, the time window needs to be resolved first. We tackled this problem by introducing a method for adaptive determination of the time window for interacting oscillators, as modeled and scaled for the cardiorespiratory interaction. By investigating a system of coupled phase oscillators and utilizing the Dynamical Bayesian Inference method, we propose a procedure to determine the time window and the propagation parameter of the covariance matrix. The optimal values are determined so that the inferred parameters follow the dynamics of the actual ones and at the same time the error of the inference represented by the covariance matrix is minimal. The effectiveness of the methodology is presented on a system of coupled limit-cycle oscillators and on the cardiorespiratory interaction. Three cases of cardiorespiratory interaction were considered—measurement with spontaneous free breathing, one with periodic sine breathing and one with a-periodic time-varying breathing. The results showed that the cardiorespiratory coupling strength and similarity of form of coupling functions have greater values for slower breathing, and this variability follows continuously the change of the breathing frequency. The method can be applied effectively to other time-varying oscillatory interactions and carries important implications for analysis of general dynamical systems.https://www.frontiersin.org/article/10.3389/fphys.2020.00341/fulltime-series analysisdynamical systemsdynamical Bayesian inferencecoupled oscillatorscoupling functions
collection DOAJ
language English
format Article
sources DOAJ
author Dushko Lukarski
Dushko Lukarski
Margarita Ginovska
Hristina Spasevska
Tomislav Stankovski
Tomislav Stankovski
spellingShingle Dushko Lukarski
Dushko Lukarski
Margarita Ginovska
Hristina Spasevska
Tomislav Stankovski
Tomislav Stankovski
Time Window Determination for Inference of Time-Varying Dynamics: Application to Cardiorespiratory Interaction
Frontiers in Physiology
time-series analysis
dynamical systems
dynamical Bayesian inference
coupled oscillators
coupling functions
author_facet Dushko Lukarski
Dushko Lukarski
Margarita Ginovska
Hristina Spasevska
Tomislav Stankovski
Tomislav Stankovski
author_sort Dushko Lukarski
title Time Window Determination for Inference of Time-Varying Dynamics: Application to Cardiorespiratory Interaction
title_short Time Window Determination for Inference of Time-Varying Dynamics: Application to Cardiorespiratory Interaction
title_full Time Window Determination for Inference of Time-Varying Dynamics: Application to Cardiorespiratory Interaction
title_fullStr Time Window Determination for Inference of Time-Varying Dynamics: Application to Cardiorespiratory Interaction
title_full_unstemmed Time Window Determination for Inference of Time-Varying Dynamics: Application to Cardiorespiratory Interaction
title_sort time window determination for inference of time-varying dynamics: application to cardiorespiratory interaction
publisher Frontiers Media S.A.
series Frontiers in Physiology
issn 1664-042X
publishDate 2020-04-01
description Interacting dynamical systems abound in nature, with examples ranging from biology and population dynamics, through physics and chemistry, to communications and climate. Often their states, parameters and functions are time-varying, because such systems interact with other systems and the environment, exchanging information and matter. A common problem when analysing time-series data from dynamical systems is how to determine the length of the time window for the analysis. When one needs to follow the time-variability of the dynamics, or the dynamical parameters and functions, the time window needs to be resolved first. We tackled this problem by introducing a method for adaptive determination of the time window for interacting oscillators, as modeled and scaled for the cardiorespiratory interaction. By investigating a system of coupled phase oscillators and utilizing the Dynamical Bayesian Inference method, we propose a procedure to determine the time window and the propagation parameter of the covariance matrix. The optimal values are determined so that the inferred parameters follow the dynamics of the actual ones and at the same time the error of the inference represented by the covariance matrix is minimal. The effectiveness of the methodology is presented on a system of coupled limit-cycle oscillators and on the cardiorespiratory interaction. Three cases of cardiorespiratory interaction were considered—measurement with spontaneous free breathing, one with periodic sine breathing and one with a-periodic time-varying breathing. The results showed that the cardiorespiratory coupling strength and similarity of form of coupling functions have greater values for slower breathing, and this variability follows continuously the change of the breathing frequency. The method can be applied effectively to other time-varying oscillatory interactions and carries important implications for analysis of general dynamical systems.
topic time-series analysis
dynamical systems
dynamical Bayesian inference
coupled oscillators
coupling functions
url https://www.frontiersin.org/article/10.3389/fphys.2020.00341/full
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