Enhancing cardiovascular monitoring: a non-linear model for characterizing RR interval fluctuations in exercise and recovery

Figures

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  Fig. 1. Example data of RRi recordings of 6 subjects over a 20-minute rest-exercise-recovery protocol in a sample of elderly individuals. The subject-level data shows the inter-individual variability of RRi time-dependent fluctuations in response to exercised-induced cardiovascular stress, with similar behavior and recovery trajectories over time.

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  Fig. 2. The RRi time-dependent fluctuations in response to exercise are expressed as a linear combination of model constituents based on the baseline RRi \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document} and two logistic functions, denoted \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${f}_{1}\left(t\right)$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${f}_{2}\left(t\right),$$\end{document} respectively. The vertical dashed lines represent the time at which the exercise and recovery onset given by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}…

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  Fig. 3. (A) Mean and SD from each subject’s RRi recordings were used for the standardization process. (B) 2D kernel density of standardized RRi dynamics over time from a sample of individuals subjected to the rest-exercise-rest protocol. Darker colors indicate greater probability density. The contrary can be said about lighter colors.

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  Fig. 4. (A) Simulated standardized RRi time-dependent fluctuations based on prior parameter distributions, illustrating predicted RRi responses to exercise. Shaded areas represent 95%, 80%, and 60% quantile CI, offering insight into expected physiological variability across parameters. (B) Prior distributions and 95% CI were used to generate predictions based on physiological constraints and graphical visualization of standardized RRi data.

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  Fig. 5. (A) Posterior probability distributions of the expectation for each population-parameter estimate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(E[\theta])$$\end{document} with quantile-based 95% CI. (B) Transformed rate parameters into a percentage scale using the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1-\text{e}\text{x}\text{p}\left(\theta\right)$$\end{document} transformation.

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  Fig. 6. Individual-level performance metrics. (A) Bootstrapped MAPE and RMSE are statistical metrics of relative and absolute model deviance from observed RRi. (B) Individual-level estimates of model performance and the relationship between them. (C) Partial autocorrelation function (ACF) of model residuals with corresponding quantile-based CI. (D) Example data with model estimates of RRi fluctuations and corresponding quantile-based CI initially displayed.