Original Research A New Mathematical Approach to Explore the Post- exercise Recovery Process and Its Applicability in a Cold Water Immersion Protocol J´ essica K. Micheletti, 1 Franciele M. Vanderlei, 2 Aryane F. Machado, 1 Aline C. de Almeida, 3 F´ abio Y. Nakamura, 4 Jayme Netto Junior, 2 and Carlos Marcelo Pastre 2 1 Postgraduate Program in Physiotherapy, Sa ˜o Paulo State University (UNESP), School of Technology and Sciences, Presidente Prudente, Sa ˜o Paulo, Brazil; 2 Department of Physiotherapy, Sa ˜o Paulo State University (UNESP), School of Technology and Sciences, Presidente Prudente, Sa ˜o Paulo, Brazil; 3 Postgraduate Program in Physiotherapy, Federal University of Sa ˜o Carlos, Sa ˜o Paulo, Brazil; and 4 Department of Physical Education, Federal University of Paraiba–UFPB, Joa ˜o Pessoa/PB, and The College of Healthcare Sciences, James Cook University, Townsville, Australia Abstract Micheletti, JK, Vanderlei, FM, Machado, AF, de Almeida, AC, Nakamura, FY, Netto Junior, J, and Pastre, CM. A new mathematical approach to explore the post-exercise recovery process and its applicability in a cold water immersion protocol. J Strength Cond Res 33(5): 1266–1275, 2019—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 6 1˚ 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 5 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 5 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. Key Words: cryotherapy, recovery of physiological function, sports, autonomic nervous system and lactate Introduction Post-exercise recovery strategies aim to return various systems of the body to their baseline state and are used in practice on a large- scale (47). Studies using distinct recovery strategies have evalu- ated several variables to gain information about this process (12,19,32); however, although recovery is a multifactorial pro- cess, these variables are discussed separately. A new consensus statement of recovery and performance in sports proposes the development of a holistic model to derive practical rules for re- covery evaluation using an integrated approach. Thus, the option of covering all aspects influenced by the recovery process in a unique response is appealing. Specifically in this research, re- covery was observed considering one of the most commonly in- vestigated strategies in the scientific field, cold water immersion (CWI), which consists of immersing parts of the body in water at a temperature equal to or lower than 15° C (16,66). For an integrated approach, it is necessary to identify the most commonly investigated variables in studies that use this technique and its effects regarding the proposed protocols. Ihsan et al. (31), in a review, investigated the physiological mechanisms of CWI asso- ciated with post-exercise recovery and noted that the main variables studied are related to the autonomic nervous system, cardiovascular system, removal of metabolic waste from muscles, glycogen resyn- thesis, performance tests, and muscle damage markers induced by delayed-onset muscle soreness (DOMS) and creatine kinase. Among these variables, there is evidence that the use of CWI reduces DOMS (9,15,24) and promotes better recovery after exercise in cardiac autonomic modulation (2,12,20). Machado et al. (36), in a recent meta-analysis, found that CWI is more effective than passive re- covery for reducing muscle soreness, with better results when applied between 11 and 15° C for 11–15 minutes, whereas Almeida et al. (2), suggest the use of the technique for 15 minutes at 14° C when the objective is restoration of cardiac autonomic modulation, analyzed through heart rate variability (HRV) (61). Regarding other recovery markers, there is no consensus on the effectiveness of CWI, with discrepant responses for the same Address correspondence to J ´ essica K. Micheletti, jessicamicheletti@hotmail.com. Supplemental digital content is available for this article. Direct URL citations appear in the printed text and are provided in the HTML and PDF versions of this article on the journal’s Web site (http://journals.lww.com/nsca-jscr). Journal of Strength and Conditioning Research 33(5)/1266–1275 ª 2019 National Strength and Conditioning Association 1266 Copyright © 2019 National Strength and Conditioning Association. Unauthorized reproduction of this article is prohibited.