Nonparametric dynamical model of cardiorespiratory responses at the onset and offset of treadmill exercises

This paper applies a nonparametric modelling method with kernel-based regularization to estimate the carbon dioxide production during jogging exercises. The kernel selection and regularization strategies have been discussed; several commonly used kernels are compared regarding the goodness-of-fit, sensitivity, and stability. Based on that, the most appropriate kernel is then selected for the construction of the regularization term. Both the onset and offset of the jogging exercises are investigated. We compare the identified nonparametric models, which include both impulse response models and step response models for the two periods, as well as the relationship between oxygen consumption and carbon dioxide production. The result statistically indicates that the steady-state gain of the carbon dioxide production in the onset of exercise is bigger than that in the offset while the response time of both onset and offset are similar. Compared with oxygen consumption, the response speed of carbon dioxide production is slightly slower in both onset and offset period while its steady-state gains are similar for both periods. The effectiveness of the kernel-based method for the dynamic modelling of cardiorespiratory response to exercise is also well demonstrated. Graphical Abstract Comparison between VO₂ and VCO₂ during onset and offset of exercise.