Over the past 20 years, numerous studies in humans have demonstrated the usefulness of Heart Rate Variability (HRV) as a tool for investigating the activity of Autonomic Nervous System (ANS). Longitudinal and transversal studies have also shown a strong relationship between ANS activity, training load and performance. Monitoring of the training load has led to the study of various physiological parameters including the HRV. The goal of all this work was the study of the abilities of ANS parameters to predict the level of performance in swimming, as well as, modeling the effects of training load on the parameters of ANS. Study I models the effects of training on parasympathetic activity through the Banister model, originally designed to represent the effects of training on performance. A significant logarithmic relationship was demonstrated between parasympathetic activity and performance. Study II demonstrates the relevance of HRV and mathematical modeling to drive and optimize the training load. This study, using model parameters calculated from linear and non-linear mathematical formulation for 10 swimmers, analyzes the ability of computer simulation to predict performance and parasympathetic activity in response to the training load. The results demonstrate the practical application of mathematical modeling and computer simulations in predicting the performance and optimization of the training load to maximize both performance gains and parasympathetic activity All this work demonstrates, through mathematical modeling, the relevance of HF spectral power of HRV as a non-invasive tool, easy to use in routine, to optimize the training load and predict the performance in swimming. Beyond the demonstration of a significant relationship between parasympathetic activity and performance, it was an evolution in phase of these two parameters that was highlighted
