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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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 |
work_keys_str_mv |
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