A New Mathematical Approach to Explore the Post-exercise Recovery Process and Its Applicability in a Cold Water Immersion Protocol

The objective of this study was to propose a mathematical model to analyze the post-training recovery of perceptive, functional, metabolic, and autonomic parameters from the use of cold water immersion (CWI) through isolated and combined analysis. Following simulated training, 64 male soccer players were randomized into an experimental group (EG: CWI, 13 +/- 1[degrees] C; 15 minutes) and a control group (CG: passive recovery; 15 minutes). Perceptive (soreness and perception of recovery), autonomic (heart rate variability [HRV]), metabolic (lactate concentration), and functional parameters (squat jump, T agility test, sprint test, 40-second test, and maximal voluntary isometric contraction) were analyzed before and at specific moments after training (without exceeding 2 hours after training). The variables were analyzed using the raw data, dichotomization of each variable (isolated analysis), and through a mathematical model using the combination of all parameters analyzed (combined analysis). The combined analysis did not demonstrate better efficacy of the EG compared with the CG (69.17 and 63.4%, p = 0.09). In the isolated analysis, a chance of the technique being better was observed in the metabolic parameter at 1 and 2 hours after training (odds ratio, 95% confidence interval = 3.75 [1.01-13.88] and 11.11 [1.25-98.49]), respectively, and in the autonomic parameter at 40-45 minutes after training (4.4 [1.09-17.67]). For the raw data, all parameters analyzed presented recovery by 2 hours after training for both groups. Based on the proposed mathematical model, it is concluded that CWI is not better than the control condition. However, considering the analysis of variables in isolation, the technique presents a better chance of recovery for blood lactate concentration and HRV.