A New Mathematical Approach to Explore the Post-exercise Recovery Process and Its Applicability in a Cold Water Immersion Protocol : The Journal of Strength & Conditioning Research

Secondary Logo

Journal Logo

Original Research

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

Micheletti, Jéssica K.1; Vanderlei, Franciele M.2; Machado, Aryane F.1; de Almeida, Aline C.3; Nakamura, Fábio Y.4; Netto Junior, Jayme2; Pastre, Carlos Marcelo2

Author Information
Journal of Strength and Conditioning Research 33(5):p 1266-1275, May 2019. | DOI: 10.1519/JSC.0000000000003041


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 ± 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 = 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.


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 evaluated several variables to gain information about this process (12,19,32); however, although recovery is a multifactorial process, 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 recovery 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, recovery was observed considering one of the most commonly investigated 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 associated 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 resynthesis, 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 recovery 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 variable. Studies have observed the influence of CWI on muscle strength with both positive (7,51) and negative results (23,54). Other variables present different responses between studies that observed the effectiveness of blood lactate concentration response (12,64) or not (4,58) and better perception of recovery (26,64) or not (35). However, these variables should also be part of an integrated approach.

The use of different methods of application of the technique, such as temperature used, application time, water level, type of stress (33,47), or a placebo effect (19), could explain these discrepancies. Thus, the use of a single mechanism of stress, with the same method of technique application, would be the best strategy to explore and control several variables already investigated in other studies, interpreting their results under a single scenario. To the best of our knowledge, there are no studies that address a set of perceptive, functional, metabolic, and autonomic variables in the same trial.

In addition, considering recovery as a complex concept and difficult to extrapolate, regardless of the strategy used, its assessment in specific scenarios should be relative to the demands of each sport (33), and thus, it is important to investigate specific sports training, as performed with Australian footballers (24,25), rugby players (58), and jiu-jitsu fighters (49), which seems consistent when the outcomes are not experimental, but clinical. However, current study designs involve a specific type of stress followed by the intervention to observe the behavior of outcomes (19,24,35), where comparison of groups by means of raw data is used. Although this is appropriate, more individual observation, taking into account the high intra- and inter-individual variability of the recovery process, may present new information for interpretation of the results (33).

Thus, a complex approach could be adopted by constructing a mathematical model that standardizes a set of variables with different characteristics for consideration in the same study. This can be performed using specific cut-point classifications for each variable and dichotomizing the results case-by-case. Arthurs et al. (6) mention that mathematical models are a means of controlling components, arbitrary systems, and variables to study their complexity. A similar design has recently been adopted in the area of health. Skillgate et al. (56) investigated risk factors that may influence low back pain. Because this is a multifactorial disorder, a single category variable seemed to be interesting to infer risk factors.

The justification for conducting this research takes into account an approach that integrates several elements that make up the recovery process and the possibility of observing its application in a practical scenario of the sports field. The choice of CWI was made because it is a widely used strategy in the field and has also been tested in research (47). Finally, an analysis routine that addresses individual responses and adds different outcomes may provoke discussion about the concept of post-exercise recovery in the field of sports science.

The objective of this study was to propose a mathematical model to analyze post-training recovery using the CWI technique on perceptive, functional, metabolic, and autonomic parameters by means of isolated and combined analysis.


Experimental Approach to the Problem

Post-exercise recovery is a multidimensional process that affects performance. Studies (9,12,15,19,24,35) have analyzed several variables to provide the best recovery for the athlete to perform subsequent exercises. However, there are, to date, no multifactorial observations of this process, encompassing several variables in a single score, which could help coaches, physiotherapists, and clinical and sports researchers in their training or rehabilitation programs. Thus, this study intended to create a mathematical model based on the sums of the varied responses to the exercise, to shed new light on discussions of the theme. Furthermore, the mathematical model is based on a case-by-case classification, which provides the possibility of comparing the occurrence of recovery between groups, with or without an intervention, in all isolated parameters. In this sense, a training simulation was performed and the responses of 2 groups, the control group (CG, passive recovery) and experimental group (EG, CWI), were observed.


The sample consisted of a local soccer team, chosen for convenience. A total of 64 male participants from the youth category, aged 13–17 years, participated in the study. Based on a Student's t-test for independent samples (comparing mean values between control and CWI), this sample size is appropriate for a significance level of 5% (Z = 1.96) and statistical power of 80% (2-tailed test). The parameters used in this sample size equation are those presented by Bastos et al. (12) (SD of 6.54 for CWI and 6.11 for control, mean difference between the groups of 8.3-ms SD of all normal RR intervals (SDNN). Finally, based on the aforementioned parameters, the minimum sample size was 11 participants per group (overall sample, n = 22).

To be included, participants were required to be members of the local male soccer team in the under-15 or under-17 category. The following were the exclusion criteria: smokers, drinkers, the chronic use of drugs that influence the autonomic activity of the heart, or nonsteroidal anti-inflammatory drugs, and presenting metabolic or known endocrine disorders.

All procedures were previously approved by the Ethics Committee on Human Research at São Paulo State University (UNESP), School of Technology and Sciences, President Prudente (number: 037745/2014; CAAE: 31076814.0.0000.5402) and registered in the Brazilian Registry of Clinical Trials (ReBEC; protocol: RBR-5jjzhy). Participants and their legal guardians were informed about the procedures and objectives of the study, including the risk and benefits, and then both gave written informed consent to participate.


Randomization Process and Composition of Groups

Randomization by stratified sample of the under-15 and under-17 categories and player position was used to prevent the formation of distinct groups regarding age and practical experience. The randomization sequence was developed using Microsoft Office Excel 2007 software, and the random list generated by the computer was used to allocate the participants into 2 groups after training: CG (n = 32), in which participants remained seated in a chair resting and supervised by a therapist for 15 minutes, and the EG (n = 32), which was submitted to CWI (15 minutes at 13 ± 1° C). The participants of the EG group underwent the recuperative intervention in a plastic pool immersed in 2,400 L of water to the level of the anterior superior iliac spine; the water temperature was measured every 5 minutes using a thermometer with an accuracy of 0.1° C. This technique and the water level used were chosen because they presented the best responses when compared with other techniques such as whole body cryotherapy (1,68) and partial-body cryotherapy with vaporized liquid nitrogen (30).

The water temperature for this study was selected based on a priori data from a systematic review of Bleakley et al. (15), in which it was noted that the most common temperatures used in studies (approximately 75% of the trials) varied between 10 and 15° C. Corroborating, the meta-analysis of Machado et al. (36) observed the best dose response for DOMS from the application of the technique at a temperature between 11 and 15° C and a period of 11–15 minutes. The above intervals were tested, and 13 ± 1° C for 15 minutes was chosen. Figure 1 represents the flowchart of the study.

Figure 1.:
Flowchart. CG = control group; EG = experimental group.

Study Design

The longitudinal study procedure was conducted at the Center for Studies and Treatment in Physiotherapy and Rehabilitation and at the soccer team training camp. All procedures were performed between 8 am and 6 pm, and all protocols were performed according to the climatic conditions of the day, so the temperature and relative humidity values were measured on collection days (average temperature: 25.7 ± 0.56° C, range: 19–31° C and variation in humidity between 39 and 95%). Owing to the climatic variations, the participants were randomized according to the period of the day (morning and afternoon). This randomization remained for the 2 stages of the study. In addition, the same number of participants from the EG and CG performed the procedures in the morning and in the afternoon.

The athletes attended a baseline training period and were subjected to 2 testing stages. In the first stage, conducted over 2 days, baseline functional tests and collection of anthropometric data (body mass, height, and age) were performed. After an interval of 1 week, the second stage was performed, conducted on a single day composed of a simulation training session and the postfunctional tests. To perform this stage, first, baseline values were measured for soreness and blood lactate, and heart rate was captured beat to beat using a heart rate monitor with the participants at rest for 10 minutes. Next, the players performed 50 minutes of training followed by 15 minutes of recovery, during which blood lactate concentration samples were collected. Information regarding perception of soreness, perception of recovery, and blood lactate were collected immediately after training, after the intervention (15 minutes after training), and 1 and 2 hours after training. The maximum voluntary isometric contraction (MVIC) values were collected 1 hour after completion of the training and the other functional tests were performed 2 hours later. Heart rate was captured at specific moments after training, described later. The time intervals for performing the postfunctional tests were based on the studies of de Oliveira Ottone et al. (45) and Almeida et al. (2), which indicated that 1 hour after exercise, the HRV indices are recovered, considering baseline, for participants who have performed CWI and passive recovery.

Participants maintained their training routines, which since it was the beginning of the preseason were still low intensity, without any danger of interference in the tests performed. Furthermore, the participants were instructed to maintain their daily diet routine during the study. This information was reinforced on the data collection days. Figure 2 represents the study design.

Figure 2.:
Study design. MVIC = maximal voluntary isometric contraction; HRV = heart rate variability.


The training conducted was proposed by the team's physical trainer, involving the main skills routinely trained. Other studies have adopted similar options to study the specific stress of each modality (24,25), which can help coaches, athletes, and team staff to understand the efficacy of the technique and the best methods to apply. The training consisted of 4 stages: warm-up, stretching, squats, and sprints. The warm-up lasted 5 minutes and included skipping and kick-backs. Next, the athletes performed stretching of the quadriceps, adductors, and hamstrings, twice, for 20 seconds each, followed immediately by squat exercises, performed twice with a rest interval of 1 minute between executions, in which the participant moved around a square of 10 m on each side performing forward and lateral steps with flexion of the lower limbs and the upper limbs in horizontal flexion. After a 5-minute rest interval, the participant performed a series of sprints lasting approximately 30 minutes, where 10 sprints of 300 me were performed, with an intensity of 80–85% of the maximum capacity of the athlete according to their perceived exertion, controlled by performance time. After each sprint, an interval of one and a half minutes was allowed and after 5 sprints, a 5-minute interval.

The high intensity chosen to perform the sprints training and squat session have previously been used and proven to alter the autonomic, metabolic, and structural systems (17,38,62).

Parameters Assessed

For the perceptive parameters, participants were asked about the presence of soreness in the dominant leg after performing an isometric submaximal contraction with the knee flexed at 90° (11), through the visual analogue scale (VAS 0–10) of soreness (54), and about perception of recovery through the Likert perception scale (20). The evaluated moments for perceptive parameters were as follows: basal (T1), 0 minutes after training (T2), 15 minutes after training (T3), 1 hour after training (T4), and 2 hours after training (T5).

To evaluate the metabolic parameter blood lactate concentration [LAC], 25 μl of capillary blood was collected from the earlobe before training, in the 1st, 3rd, 5th, 7th, 9th, 11th, 13th, and 15th minute of the intervention, and 1 and 2 hours after the end of the training, using heparinized capillaries and disposable plastic Eppendorf tubes (polyethylene 1.5 ml) containing 50 μl of sodium fluoride (NaF—1%) for further lactacidemic analysis conducted in a lactimeter (YSI, Yellow Springs—1,500) (12). The collection site (earlobe) was chosen because it is easy, fast, and inexpensive (59), as well as being appropriate for sports medicine research where rapid lactate measurement could be clinically useful for monitoring lactate clearance among athletes. In addition, studies have not observed significant differences when using other collection sites, such as the finger capillary (43).

For the functional parameter, 5 tests were evaluated at baseline and after a training simulation session. In the MVIC, the participant was positioned with the dominant leg on an isokinetic dynamometer, Biodex System 4 Pro (Biodex Medical Systems, Shirley, NY, USA). As suggested by Baroni et al. (11), before the evaluation, the participant performed a warm-up of 10 maximal repetitions of isokinetic concentric contractions of flexion-extension of the knee at 180 °·s−1 throughout the range of motion. The muscle function was assessed as the highest torque value obtained from 3 repetitions of 5 seconds MVIC at 60° knee flexion (with 0° corresponding to the maximum extension). A 2-minute interval between repetitions was given to minimize possible effects of fatigue.

To evaluate the 30-m sprint test (8) and T agility test (48), 2 pairs of photocells were used (Smart Speed, Fusion Equipment, AUS) (8). For both tests, each participant performed 2 trials with an interval of 2 minutes between attempts. For the 30-m sprint test, after the first attempt, the participant returned to the starting line, performing active recovery (30 m), and waited for the end of the rest interval before beginning the second attempt (8). For the T agility test, the participant performed a path in a T format, running forward, sideways, and back touching the cones arranged along the route (48).

The squat jump (37) was composed of 3 attempts with a 30-second interval between each attempt. The participant remained with their feet in contact with the jump platform (Smart Jump; Fusion Sport, Coopers Plains, Australia), legs flexed at 90°, hands on hips, torso erect, and without previous movements and then performed a jump landing with straight legs. In the case of an invalid test, an interval of 30 seconds was given before an additional attempt, not exceeding a total of 5 trials.

For the 40-second test, we used the boundary of the soccer field, demarcated every 15 m. The participant was required to cover the greatest distance possible in 40 seconds (39).

For all functional tests, the best value obtained in all attempts was considered for the analysis, except for the 40-second test.

For the autonomic parameter, HRV analysis was performed from data captured by a heart rate monitor (RS800cx model; Polar Electro Oy, Kempele, Finland) (10). The SDNN index was chosen to compose the model because it represents global variability of systems. The HRV indices were obtained using HRV Kubios software—release 2.1 (60,65).

The time series of RR intervals was subjected to digital filtering using Polar Pro Trainer 5 software (version 5.35.160) complemented by manual filtering with Microsoft Excel software to eliminate premature ectopic beats and artifacts. Only series with more than 95% sinus beats were included (27). The following points of time were analyzed: M1 (final 5 minutes of rest before beginning training), M2 (0–5 minutes after training), M3 (5–10 minutes after training), M4 (10–15 minutes after training), M5 (15–20 minutes after training), M6 (40–45 minutes after training), M7 (70–75 minutes after training), M8 (100–105 minutes after training), and M9 (115–120 minutes after training); a minimum of 256 consecutive RR intervals was obtained for each moment (12).

Dichotomization Process

For the combined analysis of the parameters from the construction of the mathematical model, the results of the variables of each participant were dichotomized as recovered or not recovered (1 or 0, respectively). This characterization occurred differently for each variable, as demonstrated in Table 1.

Table 1:
Summary of dichotomization.*

After these procedures, the proposed mathematical model that contained each parameter (perceptive, metabolic, functional, and autonomic) presented with a mass of 1. The sum of dichotomized outcomes of all tests within a category was divided by the number of tests or moments in each parameter (functional = 5, perceptive = 6, biochemical = 2, and autonomic = 5). The combined category values were divided by the number of parameters. Finally, the result obtained was multiplied by 100, representing the percentage recovery of each of the participants, according to the mathematical model below:F1: functional test 1; F2: functional test 2; F3: functional test 3; F4: functional test 4; F5: functional test 5; SPS: subjective perception of soreness; RP: recovery perception; T3: 15 minutes after training; T4: 1 hour after training; T5: 2 hours after training; [LAC]: blood lactate concentration; SDNN: SD of all normal RR intervals index; M5 (15–20 minutes after training), M6 (40–45 minutes after training), M7 (70–75 minutes after training), M8 (100–105 minutes after training), and M9 (115–120 minutes after training).

Statistical Analyses

Descriptive statistics were composed of median values, quartile values (first and third), and minimum and maximum values. Categorical variables were expressed as rates. Quartile values were chosen for the following reasons: the data analyzed are quantitative (frequency of cases of recovered and not recovered subjects), the combined analysis was conducted with the same number of subjects in both groups, and this analysis allows for representation with a greater number of statistical positions of the sample and a simple representation by means of tables (3).

The association between “being recovered” (dependent variable) and the independent variable (CG and EG) was assessed using the chi-square test (Yates' correction was adopted) (41), whereas the magnitude of these associations was identified through the use of the Binary Logistic Regression (expressed as odds ratio [OR] and 95% confidence intervals [95% CIs]) as already used in an associated study (21). Numerical variables with nonparametric distribution were compared according to the CG and EG using the Mann-Whitney test.

Univariate linear regression analyses were used to assess correlations between the variable total recovery (dependent variable) and each parameter of the variables perceptive, functional, metabolic, and autonomic (as independent variables). The values of correlation were interpreted as small or no relationship (from 0.00 to 0.25), fair relationship (from 0.25 to 0.50), moderate to good relationship (from 0.50 to 0.75), and good to excellent relationship (above 0.75). The coefficient of explanation is expressed as values of r squared (r2) (50).

Receiver operating characteristic (ROC) curves with the default parameters sensitivity (true-positive rate), specificity (true-negative), area under the curve, lower limit, upper limit, and Youden's index were performed, to determine the best cutoff. Considering the area under the curve, an area of 1 represents a perfect test and an area of 0.5 represents a worthless test. The statistical package SPSS (version 22; SPSS Inc, Chicago, IL, USA) was used in all analyses, and the significance level (p-value) was set at ≤0.05.

Raw data analysis was performed. See supplementary material of Statistical analysis (https://links.lww.com/JSCR/A123) and results (https://links.lww.com/JSCR/A124)


Regarding the age and anthropometric data, no statistically significant differences were observed between the groups, characterizing a homogeneous sample. Age: CG: 15.19 year old ± 1.05; EG: 15.21 ± 1.06, p = 0.9387; mass: CG: 66.46 ± 7.82 kg; EG: 62.64 ± 8.46 kg, p = 0.111; and height: CG: 176 ± 6 cm; EG: 174 ± 9 cm, p = 0.358.

Considering the univariate analyses, all parameters were significantly (p < 0.05) correlated with the total recovery variable. The correlation values observed were as follows: functional parameter: r = 0.65 and r2 = 0.420; perceptive parameter: r = 0.58 and r2 = 0.34; metabolic parameter: r = 0.56 and r2 = 0.31; and autonomic parameter: r = 0.63 and r2 = 0.39.

The general framework of dichotomization with all the parameters provides the percentage of total recovery of both groups, and no statistically significant differences were observed (p = 0.0931). For each parameter, there was a statistically significant difference between groups only for the autonomic parameter, with p = 0.0343 (Table 2). Considering the results of the isolated variables, significant ORs were observed only for the [LAC] at 1 and 2 hours post-training moments with an OR = 3.75 (95% CI = 1.01–13.88) and OR = 11.11 (95% CI = 1.25–98.49), respectively, and for the SDNN index only at M6 (OR = 4.4 [95% CI = 1.09–17.67]) (Table 3).

Table 2:
Descriptive measures.*†
Table 3:
Distribution of the absolute frequency of perceptive, metabolic, functional, and autonomic variables.*

Regarding the determination of cutoff points, values referring to ROC curves presented good sensitivity for all the variables included in the model and good specificity for the variables sprints of 30 m, the T agility test, MVIC, perception of recovery, [LAC], and SDNN at M5 (Table 4).

Table 4:
Values of ROC curve.*


The use of the mathematical model built for the accomplishment of this study allowed for estimation of a percentage of total recovery for each observed group, for each parameter evaluated, and for each individual participant. The total recovery values of each participant, though not presented, integrate the equations that make up the study variables. In practice, knowledge of the total individual recovery percentage of the athlete can represent an interesting clinical repercussion, serving as a parameter for decision-making related to training and competitions.

The approach used for the formulation of the study design should be considered for discussion. The strategy to aggregate outcomes in a single result is an intuitive process in health sciences, based on a priori experiences (46,52,56). In addition, considering the recovery after exercise process as multifactorial (33,47), because of the various systems disturbed during physical exercises (31), the combination of physiological and psychological measures in a categorical variable may result in a more complex investigation (33). Thus, the construction of a mathematical model with the variables most commonly used in current studies (9,24,35,54) could establish a guiding principle for future discussions.

The mathematical model is based on a model of balance of outcomes (positive and negative) of exercise modalities (46) and adapted to the reality of the recovery process, with the objective of only gains. To this end, it was necessary to determine different actions. We opted to aggregate variables into groups of similar responses (perceptive, metabolic, functional, and autonomic), to represent all responses. This process of aggregation has already been performed in previous studies in the health area (29,56). The selection of variables that composed the model was based on the outcomes most commonly observed in studies of the same nature (9,24,35,54), including, in addition to performance and physiological markers, the perception of the athlete, which has been proven to be a critical determinant in the recovery process (33). However, it is known that other variables could also be comprised in the concept of recovery, such as the variable sleep, which has been addressed previously (53). In addition, similar weights were determined for each parameter, since, until the present time, the classification variables which have the best representation in the recovery process have not been established. However, univariate linear regression was used to verify the correlation between each parameter (independent variables) and the total recovery variable (dependent variable). All independent variables were significantly related to the total recovery, denoting the importance of each one in the recovery conception, as already suggested in a current consensus (33). Thus, although we suggest that future studies identify the burden of each of these parameters, the usage of similar weights for all parameters in this seems not to be harmful to the model.

With regard to the model used, although there are limitations in the form (categorization), it is believed to be a promising tool. The dichotomization process has been recommended when the underlying continuous variable is truly categorical (22), as is the case with the recovery process. The mathematical model to date is more sensitive than specific, being able to identify the actual recovered cases accurately for all variables. Furthermore, the model demonstrates good specificity for some variables such as sprints of 30 m, the T agility test, MVIC, perception of recovery, [LAC], and SDNN in specific times. This reflects the cut-points chosen. To the best of our knowledge, in the current literature, only 1 cutoff point for the VAS scale was found (18), where the value of 3.8 was suggested as mild pain. In this sense, the other variables were categorized by means of values of the sample itself (individual) such as coefficient of variation and Z score. The use of statistical approaches that can account for measurement error in the follow-up of athletes during the recovery process has previously been suggested, such as the Z score (33). However, more studies are needed to improve this tool and make it more accurate.

This study is an initial framework for a broader view of the concept of post-exercise recovery using the technique of CWI, and in this sense, it is interesting to present the results dichotomized for each variable from the proposed model in a separate discussion. This option opens greater discussions about the concept itself and the proposed model, and is one of the focuses of this study. In addition, it allows for visualization of the practical applicability when following a recovery process.

Analysis of the investigated parameters (perceptive, metabolic, functional, and autonomic) in the total recovery process through the model adopted in this trial showed median values of 62 and 69% recovery in the control and intervention groups, respectively, with no statistically significant differences between the groups. However, when analyzing each variable separately, there was an improvement in autonomic recovery and blood lactate removal in favor of the intervention group, as observed in previous studies (12,20).

Therefore, by redirecting the focus of discussion to the findings of each variable separately, positive responses were observed in the outcomes [LAC] in blood and HRV. Bastos et al. (12) indicated that CWI may be related to bringing forward the peak [LAC] because these results were observed using the technique for 6 minutes at 11 ± 2° C compared with passive recovery. The authors attribute this anticipation of the increase in plasma volume to the displacement of fluid from the interstitial space due to the increased hydrostatic pressure and thermal stress, which in turn enhances the diffusion gradient and, consequently, the removal of metabolites. Vanderlei et al. (64) analyzed and compared the effects of post-exercise CWI at different temperatures and application times and verified an anticipation of peak lactate for immersion for 5 minutes at 14° C. In this study, despite it not being possible to verify the anticipation of peak [LAC], a higher probability of the CWI technique to promote improved recovery can be observed.

Furthermore, when considering the [LAC], it is believed that this study protocol was able to achieve high intensity and accumulate a high level of lactate in the blood. This can be verified by the peak lactate observed in this study, which exceeds the concentration of 2.5 mmol/L, the fixed concentration that represents the maximum physiological capacity of children-adolescents in the removal of lactate produced, thus representing a balance between production and clearance rates (5,67).

As for the autonomic nervous system response, this already seems to be clearer. According to the Task Force of 1996 (61), HRV analysis has proven to be a simple, noninvasive technique capable of assessing autonomic heart rate modulation by means of the instantaneous measurement of variations in the beat-to-beat RR intervals. In this sense, a wide range of previous studies examining the effects of CWI on HRV indices demonstrate a tendency to improvement in the indices (2,12,20). Authors ascribe this anticipation basically to 2 main effects, hydrostatic water pressure and a low water temperature. The increase in hydrostatic pressure stimulates central baroreceptors due to the increase in thoracic blood volume in the trunk, which may induce decreased sympathetic activity and greater parasympathetic modulation. With a temperature reduction, the peripheral thermoreceptors, subcutaneous tissue, and blood vessels are stimulated causing peripheral vasoconstriction and local blood loss, which is redirected to protect the vital organs. Thus, both factors stimulate the parasympathetic autonomic nervous system, resulting in the recovery of HRV indices (2,12,20).

de Oliveira Ottone et al. (45) investigated the effects of different temperatures (15, 28, and 38° C) and a control group on post-exercise parasympathetic reactivation. To analyze the parasympathetic reactivation, the experimental design involved a rest of 30 minutes, an exercise session followed by 1 of the 4 recovery methods in a randomized fashion. Thereafter, the subjects recovered at room temperature for 30 minutes, followed by another 195-minute period, totalizing 240 minutes after the exercise session. HRV indices were measured during the final 5 minutes of each period. The authors observed better reactivation at a temperature of 15° C compared with the CG. The authors also reported that the differences between the strategies did not remain for longer than 4 hours, indicating a short-term effect of the technique. This was also observed in this study, although in a shorter period (115–120 minutes after training) for the evaluated SDNN index, and in the study by Almeida et al. (2) where 60 minutes after exercise was sufficient to restore the values of the indices to pre-exercise conditions.

Despite the range of favorable CWI studies on the recovery of HRV, the impact of these findings on other body systems remains uncertain. It is known that the autonomic nervous system is principally responsible for the necessary adjustments to various systems, ensuring that the body remains in homeostasis after stress conditions (12). However, these effects on perceptive and functional outcomes were not evidenced in this study. Thus, further investigations into the possible correlations between the autonomic and functional/perceptive systems are suggested.

This study has both limitations and strengths. A potential limitation of the study is the absence of tools analyzing the maturational state of the subjects. The age range of the participants could include participants with different maturational status (prepubescent, peripubescent, and postpubescent), which might affect outcome measures of both the technique and training, such as [LAC] (63), clinical responses such as pain sensitivity (13), and performance (42). However, this limitation may have been mitigated by the fact that the groups presented homogeneity and the type of randomization used. In addition, there is a scarcity of studies that observe the effects of cold applications on physiological implications in the peripubertal population. Thus, as a meta-analysis was conducted in 2015 for this general population (44), we suggest that future studies focus on this maturational stage. Another limitation is the level of reliability and reproducibility of the subjective scale of perception of recovery (Likert's scale). Although this is a validated instrument (34), most studies with the application of CWI have used this instrument to investigate populations older than 20 years (14,28,57). On the other hand, the subjective perception scale of soreness is a validated instrument in populations of the same age (40,55). A strength of the study is that this is the first proposed model to assess post-exercise recovery in a large way, taking into account the responses of various systems and the individuality of each subject. Future studies should try to expand this new idea and strategy of considering the concept and involve other variables that could be affected by exercises and the technique. Finally, the sample was composed of male athletes, and in this sense, the extrapolation of the results to the female sex should be performed with caution.

In conclusion, combined analysis of the parameters by means of the proposed mathematical model presented similar recovery techniques without statistical differences, reflecting that specific variables do not represent the overall recovery.

Practical Applications

Studies have investigated the post-exercise recovery limit based on the concept of recovery of a system, or specific outcome. The model proposed with a combination of variables showed a similar response to the group that did not perform any intervention. In this sense, it is worth pointing out that the use of CWI does not promote any deleterious effects. Thus, coaches, clinicians, and researchers can use the technique according to the preference of the athlete or participant and to provide greater discussions in the exercise science and sports areas.


This study was financed in part by the Coordination of Improvement of Higher Level Personnel (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior) – Brasil (CAPES) – Finance Code 001 and by the São Paulo Research Foundation (FAPESP process number 2015/25220-9). The results of this study do not constitute endorsement of the product by the authors or the NSCA. The authors have no conflicts of interest to disclose.


1. Abaïdia AE, Lamblin J, Delecroix B, Leduc C, McCall A, Nédélec M, et al. Recovery from exercise-induced muscle damage: Cold-water immersion versus whole-body cryotherapy. Int J Sports Physiol Perform 12: 402–409, 2017.
2. Almeida AC, Machado AF, Albuquerque MC, Netto LM, Vanderlei FM, Vanderlei LCM, et al. The effects of cold water immersion with different dosages (duration and temperature variations) on heart rate variability post-exercise recovery: A randomized controlled trial. J Sci Med Sport 19: 676–681, 2016.
3. Altman DG, Bland JM. Quartiles, quintiles, centiles, and other quantiles. BMJ 309: 996, 1994.
4. Anderson D, Nunn J, Tyler CJ. Effect of cold (14° C) vs. Ice (5° C) water immersion on recovery from intermittent running exercise. J Strength Cond Res 32: 764–771, 2018.
5. Armstrong N, Welsman JR. Assessment and interpretation of aerobic fitness in children and adolescents. Exerc Sport Sci Rev 22: 435–476, 1994.
6. Arthurs CJ, Lau KD, Asrress KN, Redwood SR, Figueroa CA. A mathematical model of coronary blood flow control: Simulation of patient-specific three-dimensional hemodynamics during exercise. Am J Physiol Heart Circ Physiol 310: H1242–H1258, 2016.
7. Ascensão A, Leite M, Rebelo AN, Magalhäes S, Magalhäes J. Effects of cold water immersion on the recovery of physical performance and muscle damage following a one-off soccer match. J Sports Sci 29: 217–225, 2011.
8. Ávila AOV, Amadio AC, Guimarães ACS, David ACde, Mota CB, Borges DM, et al. Measurement methods in sports biomechanics: Description of protocols for application in sports centers of excellence(Rede CENESP-MET) (in Portuguese). Rev Bras Biomec 3: 57–67, 2002.
9. Bailey DM, Erith SJ, Griffin PJ, Dowson A, Brewer DS, Gant N, et al. Influence of cold-water immersion on indices of muscle damage following prolonged intermittent shuttle running. J Sports Sci 25: 1163–1170, 2007.
10. Barbosa MP, da Silva NT, de Azevedo FM, Pastre CM, Vanderlei LCM. Comparison of Polar® RS800G3TM heart rate monitor with Polar® S810iTM and electrocardiogram to obtain the series of RR intervals and analysis of heart rate variability at rest. Clin Physiol Funct Imaging 36: 112–117, 2016.
11. Baroni BM, Leal Junior ECP, De Marchi T, Lopes AL, Salvador M, Vaz MA. Low level laser therapy before eccentric exercise reduces muscle damage markers in humans. Eur J Appl Physiol 110: 789–796, 2010.
12. Bastos FN, Vanderlei LC, Nakamura FY, Bertollo M, Godoy MF, Hoshi RA, et al. Effects of cold water immersion and active recovery on post-exercise heart rate variability. Int J Sports Med 33: 873–879, 2012.
13. Birnie KA, Parker JA, Chambers CT. Relevance of water temperature, apparatus, and age to children's pain during the cold pressor Task. Pain Pract 16: 46–56, 2016.
14. Bishop PA, Jones E, Woods AK. Recovery from training: A brief review. J Strength Cond Res 22: 1015–1024, 2008.
15. Bleakley C, McDonough S, Gardner E, Baxter GD, Hopkins JT, Davison GW. Cold-water immersion (cryotherapy) for preventing and treating muscle soreness after exercise. Cochrane Database Syst Rev: CD008262, 2012.
16. Bleakley CM, Davison GW. What is the biochemical and physiological rationale for using cold-water immersion in sports recovery? A systematic review. Br J Sports Med 44: 179–187, 2010.
17. Bond B, Cockcroft EJ, Williams CA, Harris S, Gates PE, Jackman SR, et al. Two weeks of high-intensity interval training improves novel but not traditional cardiovascular disease risk factors in adolescents. Am J Physiol Heart Circ Physiol 309: H1039–H1047, 2015.
18. Boonstra AM, Schiphorst Preuper HR, Balk GA, Stewart RE. Cut-off points for mild, moderate, and severe pain on the visual analogue scale for pain in patients with chronic musculoskeletal pain. Pain 155: 2545–2550, 2014.
19. Broatch JR, Petersen A, Bishop DJ. Postexercise cold water immersion benefits are not greater than the placebo effect. Med Sci Sports Exerc 46: 2139–2147, 2014.
20. Buchheit M, Peiffer JJ, Abbiss CR, Laursen PB. Effect of cold water immersion on postexercise parasympathetic reactivation. Am J Physiol Heart Circ Physiol 296: H421–H427, 2009.
21. Capriolli TV, Visentainer JEL, Sell AM. Lack of association between Kidd blood group system and chronic kidney disease. Rev Bras Hematol E Hemoter 39: 301–305, 2017.
22. Carmona-Bayonas A, Jimenez-Fonseca P, Fernández-Somoano A, Álvarez-Manceñido F, Castañón E, Custodio A, et al. Top ten errors of statistical analysis in observational studies for cancer research. Clin Transl Oncol 20: 954–965, 2018.
23. Crystal NJ, Townson DH, Cook SB, LaRoche DP. Effect of cryotherapy on muscle recovery and inflammation following a bout of damaging exercise. Eur J Appl Physiol 113: 2577–2586, 2013.
24. Elias GP, Varley MC, Wyckelsma VL, McKenna MJ, Minahan CL, Aughey RJ. Effects of water immersion on posttraining recovery in Australian footballers. Int J Sports Physiol Perform 7: 357–366, 2012.
25. Elias GP, Wyckelsma VL, Varley MC, McKenna MJ, Aughey RJ. Effectiveness of water immersion on postmatch recovery in elite professional footballers. Int J Sports Physiol Perform 8: 243–253, 2013.
26. Fonseca LB, Brito CJ, Silva RJS, Silva-Grigoletto ME, da Silva WM, Franchini E. Use of cold-water immersion to reduce muscle damage and delayed-onset muscle soreness and preserve muscle power in jiu-jitsu athletes. J Athl Train 51: 540–549, 2016.
27. Godoy MF, Takakura IT, Correa PR. Relevance of the analysis of the non-linear dynamic behavior (Chaos Theory) as an element diagnosis of morbidity and mortality in patients undergoing surgery of myocardial revascularization [in Portuguese]. Arq Ciênc Saúde 12: 167–171, 2005.
28. Halson SL, Quod MJ, Martin DT, Gardner AS, Ebert TR, Laursen PB. Physiological responses to cold water immersion following cycling in the heat. Int J Sports Physiol Perform 3: 331–346, 2008.
29. Hao W, Marsh C, Friedman A. A mathematical model of idiopathic pulmonary fibrosis. PLoS One 10: e0135097, 2015.
30. Hohenauer E, Costello JT, Stoop R, Küng UM, Clarys P, Deliens T, et al. Cold-water or partial-body cryotherapy? Comparison of physiological responses and recovery following muscle damage. Scand J Med Sci Sports 28: 1252–1262, 2018.
31. Ihsan M, Watson G, Abbiss CR. What are the physiological mechanisms for post-exercise cold water immersion in the recovery from prolonged endurance and intermittent exercise? Sports Med Auckl NZ 46: 1095–1109, 2016.
32. Juliff LE, Halson SL, Bonetti DL, Versey NG, Driller MW, Peiffer JJ. Influence of contrast shower and water immersion on recovery in elite netballers. J Strength Cond Res 28: 2353–2358, 2014.
33. Kellmann M, Bertollo M, Bosquet L, Brink M, Coutts AJ, Duffield R, et al. Recovery and performance in sport: Consensus statement. Int J Sports Physiol Perform 13: 240–245, 2018.
34. Laurent CM, Green JM, Bishop PA, Sjökvist J, Schumacker RE, Richardson MT, Curtner-Smith M. A practical approach to monitoring recovery: Development of a perceived recovery status scale. J Strength Cond Res 25: 620–628, 2011.
35. Machado AF, Almeida AC, Micheletti JK, Vanderlei FM, Tribst MF, Netto Junior J, et al. Dosages of cold-water immersion post exercise on functional and clinical responses: A randomized controlled trial. Scand J Med Sci Sports 27: 1356–1363, 2017.
36. Machado AF, Ferreira PH, Micheletti JK, de Almeida AC, Lemes ÍR, Vanderlei FM, et al. Can water temperature and immersion time influence the effect of cold water immersion on muscle soreness? A systematic review and meta-analysis. Sports Med Auckl NZ 46: 503–514, 2016.
37. Markovic G, Dizdar D, Jukic I, Cardinale M. Reliability and factorial validity of squat and countermovement jump tests. J Strength Cond Res 18: 551–555, 2004.
38. Martorelli A, Bottaro M, Vieira A, Rocha-Júnior V, Cadore E, Prestes J, et al. Neuromuscular and blood lactate responses to squat power training with different rest intervals between sets. J Sports Sci Med 14: 269–275, 2015.
39. Matsudo V. Anaerobic capacity assessment: Running test of 40 seconds. RBCE 1: 8–16, 1979.
40. Maunuksela EL, Olkkola KT, Korpela R. Measurement of pain in children with self-reporting and behavioral assessment. Clin Pharmacol Ther 42: 137–141, 1987.
41. McHugh ML. The chi-square test of independence. Biochem Med (Zagreb) 23: 143–149, 2013.
42. Moran J, Parry DA, Lewis I, Collison J, Rumpf MC, Sandercock GRH. Maturation-related adaptations in running speed in response to sprint training in youth soccer players. J Sci Med Sport 21: 538–542, 2018.
43. Moran P, Prichard JG, Ansley L, Howatson G. The influence of blood lactate sample site on exercise prescription. J Strength Cond Res 26: 563–567, 2012.
44. Murray A, Cardinale M. Cold applications for recovery in adolescent athletes: A systematic review and meta analysis. Extrem Physiol Med 4: 17, 2015.
45. de Oliveira Ottone V, de Castro Magalhães F, de Paula F, Avelar NCP, Aguiar PF, de Matta Sampaio PF, et al. The effect of different water immersion temperatures on post-exercise parasympathetic reactivation. PLoS One 9: e113730, 2014.
46. Pastre CM. Construction and application of a model of balance of outcomes in concentric and eccentric resistive exercises. Thesis (Free Teaching): Faculty of Science and Technology-FCT / UNESP, President's Campus Prudente, 2013.
47. Pastre CM, Bastos FdoN, Netto Júnior J, Vanderlei LCM, Hoshi RA. Post-exercise recovery methods: A systematic review. Rev Bras Med Esporte 15: 138–144, 2009.
48. Pauole K, Madole K, Garhammer J, Lacourse M, Rozenek R. Reliability and validity of the T-test as a measure of agility, leg power, and leg speed in college-aged men and women. J Strength Cond Res 14, 443–450, 2000.
49. Pinho Júnior E, Brito C, Costa Santos W, Nardelli Valido C, Lacerda Mendes E, Franchini E. Influence of cryotherapy on muscle damage markers in jiu-jitsu fighters after competition: A cross-over study. Revista Andaluza de Medicina del Deporte 7: 7–12, 2014.
50. Portney L, Watkins M. 2nd, ed. Foundations of Clinical Research: Applications to Practice. Upper Saddle River, New Jersey: Prentice-Hall, 2000. pp. 579–580.
51. Pournot H, Bieuzen F, Duffield R, Lepretre PM, Cozzolino C, Hausswirth C. Short term effects of various water immersions on recovery from exhaustive intermittent exercise. Eur J Appl Physiol 111: 1287–1295, 2011.
52. Pronk NP, Lowry M, Kottke TE, Austin E, Gallagher J, Katz A. The association between optimal lifestyle adherence and short-term incidence of chronic conditions among employees. Popul Health Manag 13: 289–295, 2010.
53. Robey E, Dawson B, Halson S, Gregson W, King S, Goodman C, et al. Effect of evening postexercise cold water immersion on subsequent sleep. Med Sci Sports Exerc 45: 1394–1402, 2013.
54. Sellwood KL, Brukner P, Williams D, Nicol A, Hinman R. Ice-water immersion and delayed-onset muscle soreness: A randomised controlled trial. Br J Sports Med 41: 392–397, 2007.
55. Shields BJ, Palermo TM, Powers JD, Grewe SD, Smith GA. Predictors of a child's ability to use a visual analogue scale. Child Care Health Dev 29: 281–290, 2003.
56. Skillgate E, Pico-Espinosa OJ, Hallqvist J, Bohman T, Holm LW. Healthy lifestyle behavior and risk of long duration troublesome neck pain or low back pain among men and women: Results from the Stockholm Public Health Cohort. Clin Epidemiol 9: 491–500, 2017.
57. Stanley J, Buchheit M, Peake JM. The effect of post-exercise hydrotherapy on subsequent exercise performance and heart rate variability. Eur J Appl Physiol 112: 951–961, 2012.
58. Takeda M, Sato T, Hasegawa T, Shintaku H, Kato H, Yamaguchi Y, et al. The effects of cold water immersion after rugby training on muscle power and biochemical markers. J Sports Sci Med 13: 616–623, 2014.
59. Tang R, Yang H, Choi JR, Gong Y, You M, Wen T, et al. Capillary blood for point-of-care testing. Crit Rev Clin Lab Sci 54: 294–308, 2017.
60. Tarvainen MP, Niskanen JP, Lipponen JA, Ranta-Aho PO, Karjalainen PA. Kubios HRV—Heart rate variability analysis software. Comput Methods Programs Biomed 113: 210–220, 2014.
61. Task Force. Heart rate variability. Standards of measurement, physiological interpretation, and clinical use. Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology. Eur Heart J 17: 354–381, 1996.
62. Thum JS, Parsons G, Whittle T, Astorino TA. High-intensity interval training elicits higher enjoyment than moderate intensity continuous exercise. PLoS One 12: e0166299, 2017.
63. Tourinho Filho H, Tourinho LSPR. Crianças, adolescentes e atividade física: Aspectos maturacionais e funcionais. Rev Paul Educ Fís 12: 71–84, 1998.
64. Vanderlei FM, de Albuquerque MC, de Almeida AC, Machado AF, Netto J, Pastre CM. Post-exercise recovery of biological, clinical and metabolic variables after different temperatures and durations of cold water immersion: A randomized clinical trial. J Sports Med Phys Fitness 57: 1267–1275, 2017.
65. Vanderlei LCM, Pastre CM, Hoshi RA, Carvalho TDde, de Godoy MF. Basic notions of heart rate variability and its clinical applicability. Braz J Cardiovasc Surg 24: 205–217, 2009.
66. Wilcock IM, Cronin JB, Hing WA. Physiological response to water immersion: A method for sport recovery? Sports Med Auckl NZ 36: 747–765, 2006.
67. Williams JR, Armstrong N, Kirby B. The 4 mM blood lactate level as an index of exercise performance in 11–13 year old children. J Sports Sci 8: 139–147, 1990.
68. Wilson LJ, Cockburn E, Paice K, Sinclair S, Faki T, Hills FA, et al. Recovery following a marathon: A comparison of cold water immersion, whole body cryotherapy and a placebo control. Eur J Appl Physiol 118: 153–163, 2018.

cryotherapy; recovery of physiological function; sports; autonomic nervous system and lactate

Supplemental Digital Content

© 2019 National Strength and Conditioning Association