**1. Introduction**

Systematic assessments of athletes' physiological conditions are central to monitor and prescribe swimming training according to the needs and goals. Thus, it is possible to understand the current physiological state and follow its development in order to assess the effects of training, to identify the swimmer's skills profile and to predict athletic performance (Vilas-Boas & Lamares 1997). Specifically regarding swimmers and their skills, aerobic capacity is a major determinant of these athletes performance, and it is defined as the ability to maintain a high percentage of maximal oxygen uptake (VO2max) for a long period of time (DI PRAMPERO et al., 2011). Furthermore, the endurance is influenced by VO2max, swimming economy (or energy cost, defined as the total energy expenditure required to move the body to a certain distance in a determined velocity) and anaerobic capacity (Dekerle & Pelayo 2011). In a group of swimmers with similar values of swimming economy and anaerobic capacity, those with greater aerobic potential (VO2max and aerobic capacity) will be faster at distances of 400 m and longer. Four hundred meters, when swimming in front *crawl*, is usually suggested as a trial in which VO2max is reached (Dekerle & Pelayo 2011). Thus, the longer events (800 m, 1500 m and open water marathon), which are covered primarily with energy from aerobic metabolism, are covered in a fraction of the VO2max. The intensity will be lower the longer is the distance, reaching 60-65% of VO2max on the 25 km open water marathon (Zamparo et al. 2005). In this sense, one of the objectives of the swimming training is to increase the aerobic capacity. Thus, a valid and reliable measure of the swimmer aerobic profile is essential to verify the benefits that the training program is or is not providing, and, also, to set training intensities according to the physiological profile of the athlete. Dekerle & Pelayo (2011) emphasize that the methodology used for this purpose cannot be considered valid unless it is reliable. Whenever possible, the degree of reliability should be assessed. The origin of the variability measurement (human error, equipment error, biological variation, or motivational factors when performing the test) needs to be taken into account**.** Thus, the aim of this chapter is to present a careful review of the bioenergetics contribution on the physiological assessment of the swimmer, especially related to aerobic profile.

Bioenergetics Applied to Swimming: An Ecological Method to Monitor and Prescribe Training 161

In Equation 1, the slope of the regression line corresponds to CV (obtained through a twoparameter model, CV2par), the y-intercept (second parameter) is mathematically defined as a finite stock of reserve power available pre-exercise (Ettema 1966; Wakayoshi et al. 1992),

The non-linear SS-time limit to exhaustion ("SS-*tlim*"), the linear relationship between distance limit and time limit (*dlim-tlim*) and the linear relationship between SS and the inverse of *tlim* (Equation 2) are two-parameter models commonly used to estimate the VC

2par

Equation 2 shows that the CV can be obtained by expressing SS as a function of *tlim* (Ettema 1966). In order to revise the statement that in the hyperbolic model SS is infinite when time approaches zero, Morton (1996) proposed a mathematical model including an additional parameter representing the maximum instantaneous velocity (Vmax obtained from a three-

Vmax3par allows a time asymptote (*tlim*) which is below the x-axis where *tlim* is zero, thus providing a Vmax in the y-intercept (Morton 1996). Equation 3 expresses SS as a function of

3par

V CV *par*

Where SS is the swimming speed, *tlim* is the time limit and ADC3par, Vmax3par and CV3par are the parameters. The fact that two-parameter model assumes that there is no upper limit for power output or SS (Morton et al. 1996; Dekerle et al. 2006) leads some authors choose three-

However, both (two and three parameters) models have an important limitation: they do not take into account the "aerobic inertia" (τ) (Wilkie 1980; Vandewalle et al. 1989), regarding to the cardio respiratory adjustments for the VO2 reaches the steady state or maximum value. Thus, a four-parameter model (CV4par, CDA4par, Vmax4par and τ) as proposed by Zacca

et al. (2010) could provide more information on bioenergetics in sports (Equation 4).

*SS*

Zacca et al. (2010) proposed to plot *tlim* and SS values using a four-parameter model (Equation 4). The CV was corrected on this model by an exponential factor, proposed by Wilkie (1980). This exponential factor represents the time constant of the increased aerobic

<sup>τ</sup> max4 4par

V CV 1 e *par*

ADC

*SS* 

tlim

parameter models (Gaesser et al. 1995; Bull et al. 2000; Hill et al. 2003).

A

*DC*

max3 3par

tlim *DC*

A

2par

3par 3par

4par <sup>τ</sup> 4par 4par

tlim

CV 1 e ADC

CV ADC

C

dlim tlim ADC *CV*2 2 *par* par (1)

*SS V* (2)

(3)

tlim

(4)

usually referred as "anaerobic distance capacity" (ADC2par).

(Billat et al. 1999; Housh et al. 2001; Whipp et al. 1982).

*tlim* (Zacca et al. 2010; adapted from Morton 1996).

tlim

parameter model, Vmax3par).

#### **2. Critical velocity (CV)**

The performance achieved in competitions is an important setting information from training sessions in swimmers (Sweetenham & Atkinson, 2003). However, constant evaluations are necessaries during the cycles and training sessions in order to verify the effectiveness of training and ensure the best performance in the competition (Sweetenham & Atkinson, 2003). Physiological and biomechanical swimmers conditions' knowledge is crucial to implement and/or to control the training processes that surround them (Pyne et al. 2001). These assessments can be applied in the field of competitive and / or recreational swimming. Tests used to evaluate and determine swimming speeds (SS) for the development of aerobic endurance training can be divided into invasive and noninvasive (Pyne et al. 2001), based on the relationship between oxygen consumption (VO2), blood lactate concentration ([La]), heart rate (HR) and SS (Vilas-Boas & Lamares 1997). Although the precision provided by some of these tests, which require invasive sampling, such as those using the [La], ethical conflicts may arise (Heck et al. 1985), especially when applied to children. Moreover, it is common a high number of athletes to be evaluated in a training session by only one coach, so that they may require a longer period for implementation. Another limiting factor is the high cost for each testing session (Heck et al. 1985).

Considering these difficulties, the tests that verify the SS in durations of 30 (T30) and 60 (T60) minutes (Olbrecht et al. 1985; Madsen 1982) or even over distances of 2000 m (T2000) (Touretski 1993) and 3000 m (T3000) (Madsen 1982), the perceived exertion (PE) (Lima et al. 2006), the critical velocity (CV) (Ettema 1966) and 400 m testing (T400) (Wakayoshi et al. 1993a; Dekerle et al. 2006; Alberty et al. 2006; Pelayo et al. 2007) have been widely disseminated in swimming. However, T30, T60, T2000 and T3000 can provide very subjective information to determine training intensities in young and/or low level of experience swimmers. These protocols require the maintenance e of a given SS for a long time require psychological and physiological capacity compatible with the demands of the test (Zacca & Castro 2008, 2009). Regarding the PE, the athlete needs good training base to swim extensive sets with minimal adjustments in intensity between each repetition (Zacca & Castro 2008, 2009). In this sense, determination of SS for swimming training through the CV (Dekerle et al. 2006; Greco et al. 2008; Leclair et al. 2008; Vandewalle et al. 2008) seems to correspond to these swimmers profiles. CV's use is also justified due to the low cost and facility to apply in various populations. Another advantage is that CV is able to be gotten even during competitions (Vilas-Boas & Lamares 1997).

Since Hill (1927), it is accepted that the relationship between power output and time to exhaustion is a hyperbole. The asymptote of this relationship of power (critical power or PC) is equivalent to the slope of the regression line related to the work and time to exhaustion (time limit or *tlim*) (Monod & Scherrer 1965). Since then, CP represents, at least theoretically, the largest power that could be sustained, whose energy would be derived preferably by the aerobic metabolism without fatigue, and is suggested as a good performance index in events of long duration (Vandewalle et al. 1997).

Ettema (1966) applied the CP concept in cyclists, swimmers, speed skaters and runners. Instead of power and work, the author used speed (S) and distance limit (*dlim*), respectively. The hyperbolic relationship between S and *tlim* (Hill 1927) and the linear relationship between *dlim* and *tlim* (Equation 1), usually called critical velocity (CV), have the same physiological meaning of CP (Pepper et al. 1992; Housh et al. 2001).

The performance achieved in competitions is an important setting information from training sessions in swimmers (Sweetenham & Atkinson, 2003). However, constant evaluations are necessaries during the cycles and training sessions in order to verify the effectiveness of training and ensure the best performance in the competition (Sweetenham & Atkinson, 2003). Physiological and biomechanical swimmers conditions' knowledge is crucial to implement and/or to control the training processes that surround them (Pyne et al. 2001). These assessments can be applied in the field of competitive and / or recreational swimming. Tests used to evaluate and determine swimming speeds (SS) for the development of aerobic endurance training can be divided into invasive and noninvasive (Pyne et al. 2001), based on the relationship between oxygen consumption (VO2), blood lactate concentration ([La]), heart rate (HR) and SS (Vilas-Boas & Lamares 1997). Although the precision provided by some of these tests, which require invasive sampling, such as those using the [La], ethical conflicts may arise (Heck et al. 1985), especially when applied to children. Moreover, it is common a high number of athletes to be evaluated in a training session by only one coach, so that they may require a longer period for implementation.

Another limiting factor is the high cost for each testing session (Heck et al. 1985).

Considering these difficulties, the tests that verify the SS in durations of 30 (T30) and 60 (T60) minutes (Olbrecht et al. 1985; Madsen 1982) or even over distances of 2000 m (T2000) (Touretski 1993) and 3000 m (T3000) (Madsen 1982), the perceived exertion (PE) (Lima et al. 2006), the critical velocity (CV) (Ettema 1966) and 400 m testing (T400) (Wakayoshi et al. 1993a; Dekerle et al. 2006; Alberty et al. 2006; Pelayo et al. 2007) have been widely disseminated in swimming. However, T30, T60, T2000 and T3000 can provide very subjective information to determine training intensities in young and/or low level of experience swimmers. These protocols require the maintenance e of a given SS for a long time require psychological and physiological capacity compatible with the demands of the test (Zacca & Castro 2008, 2009). Regarding the PE, the athlete needs good training base to swim extensive sets with minimal adjustments in intensity between each repetition (Zacca & Castro 2008, 2009). In this sense, determination of SS for swimming training through the CV (Dekerle et al. 2006; Greco et al. 2008; Leclair et al. 2008; Vandewalle et al. 2008) seems to correspond to these swimmers profiles. CV's use is also justified due to the low cost and facility to apply in various populations. Another advantage is that CV is able to be gotten even during

Since Hill (1927), it is accepted that the relationship between power output and time to exhaustion is a hyperbole. The asymptote of this relationship of power (critical power or PC) is equivalent to the slope of the regression line related to the work and time to exhaustion (time limit or *tlim*) (Monod & Scherrer 1965). Since then, CP represents, at least theoretically, the largest power that could be sustained, whose energy would be derived preferably by the aerobic metabolism without fatigue, and is suggested as a good performance index in events

Ettema (1966) applied the CP concept in cyclists, swimmers, speed skaters and runners. Instead of power and work, the author used speed (S) and distance limit (*dlim*), respectively. The hyperbolic relationship between S and *tlim* (Hill 1927) and the linear relationship between *dlim* and *tlim* (Equation 1), usually called critical velocity (CV), have the same

physiological meaning of CP (Pepper et al. 1992; Housh et al. 2001).

**2. Critical velocity (CV)** 

competitions (Vilas-Boas & Lamares 1997).

of long duration (Vandewalle et al. 1997).

In Equation 1, the slope of the regression line corresponds to CV (obtained through a twoparameter model, CV2par), the y-intercept (second parameter) is mathematically defined as a finite stock of reserve power available pre-exercise (Ettema 1966; Wakayoshi et al. 1992), usually referred as "anaerobic distance capacity" (ADC2par).

$$\text{dlim} = C V\_{2\text{par}} \cdot \text{tlim} + \text{ADC}\_{2\text{par}} \tag{1}$$

The non-linear SS-time limit to exhaustion ("SS-*tlim*"), the linear relationship between distance limit and time limit (*dlim-tlim*) and the linear relationship between SS and the inverse of *tlim* (Equation 2) are two-parameter models commonly used to estimate the VC (Billat et al. 1999; Housh et al. 2001; Whipp et al. 1982).

$$\text{LSS} = \frac{\text{ADC}\_{\text{2par}}}{\text{tlim}} + \text{CV}\_{\text{2par}} \tag{2}$$

Equation 2 shows that the CV can be obtained by expressing SS as a function of *tlim* (Ettema 1966). In order to revise the statement that in the hyperbolic model SS is infinite when time approaches zero, Morton (1996) proposed a mathematical model including an additional parameter representing the maximum instantaneous velocity (Vmax obtained from a threeparameter model, Vmax3par).

Vmax3par allows a time asymptote (*tlim*) which is below the x-axis where *tlim* is zero, thus providing a Vmax in the y-intercept (Morton 1996). Equation 3 expresses SS as a function of *tlim* (Zacca et al. 2010; adapted from Morton 1996).

$$\text{SS} = \frac{\text{ADC}\_{\text{3par}}}{\text{tlim} + \frac{\text{ADC}\_{\text{3par}}}{\text{V}\_{\text{max}\text{3par}} - \text{CV}\_{\text{3par}}}} + \text{CV}\_{\text{3par}} \tag{3}$$

Where SS is the swimming speed, *tlim* is the time limit and ADC3par, Vmax3par and CV3par are the parameters. The fact that two-parameter model assumes that there is no upper limit for power output or SS (Morton et al. 1996; Dekerle et al. 2006) leads some authors choose threeparameter models (Gaesser et al. 1995; Bull et al. 2000; Hill et al. 2003).

However, both (two and three parameters) models have an important limitation: they do not take into account the "aerobic inertia" (τ) (Wilkie 1980; Vandewalle et al. 1989), regarding to the cardio respiratory adjustments for the VO2 reaches the steady state or maximum value. Thus, a four-parameter model (CV4par, CDA4par, Vmax4par and τ) as proposed by Zacca et al. (2010) could provide more information on bioenergetics in sports (Equation 4).

$$\text{SS} = \frac{\text{ADC}\_{4\text{par}}}{\text{time} + \frac{\text{ADC}\_{4\text{par}}}{\text{VC}\_{4\text{par}} - \text{CV}\_{4\text{par}} \left(1 - \text{e}^{-\frac{\text{film}}{\text{r}}}\right)} + \text{CV}\_{4\text{par}} \left(1 - \text{e}^{-\frac{\text{film}}{\text{r}}}\right) \tag{4}$$

Zacca et al. (2010) proposed to plot *tlim* and SS values using a four-parameter model (Equation 4). The CV was corrected on this model by an exponential factor, proposed by Wilkie (1980). This exponential factor represents the time constant of the increased aerobic

Bioenergetics Applied to Swimming: An Ecological Method to Monitor and Prescribe Training 163

component of VO2). Although the metabolic stress is high, it is possible to maintain a state of physiological balance and to perform the exercise for a long period (Greco et al. 2008). However, Baron et al. (2008) found exercise performed at maximum intensity possible to maintain the stabilization of the [La], i.e., in the maximal lactate steady state (MLSS), depletion occurred while physiological reserve capacity still existed, but in association with an increase in PE assessments, as predicted by the central regulator model (Noakes & St Clair Gibson 2004; Noakes et al. 2005). The end of the exercise could then be induced by an integrative homeostatic control of peripheral physiological system to ensure specifically the

There is no stabilization in metabolic variables. Specifically, the rate of lactate production is greater than the rate of removal, with a consequent increase in the accumulation and the relationship between lactate and pyruvate and the concentration of protons ([H+]) (Greco et al. 2008). At the same time, VO2 increases towards to its maximum (VO2max) and the amplitude of the slow component is much higher than those that characterize the heavy intensity exercise (Xu & Rhodes 1999). This reduces exercise tolerance, with *tlim* related to the cellular level of disturbance (metabolites production and removal rates), caused by high

Dekerle & Pelayo (2011) propose a scale of five domains and their physiological effects. On this scale, lactate threshold (LT), MLSS and CV2par can be understood as boundaries that demarcate some intensity domains. Figure 1 shows the five intensity domains proposed by Dekerle & Pelayo (2011), in which the behavior of [La] and VO2 is illustrated in each

Fig. 1. Intensity domains (adapted from Dekerle & Pelayo 2011) and the response of each to

[La] and VO2 kinetics during exercise in different SS.

demand of muscle adenosine 3-phosphate (ATP) (Greco et al. 2008).

**3.4 Scale of five intensity domains proposed by Dekerle & Pelayo (2011)** 

maintenance of homeostasis.

**3.3 Severe intensity domain** 

domain.

involvement, called "aerobic inertia" (τ), understood as a temporary delay in the response of VO2, caused by dissociation of O2 absorbed in lungs and used especially by skeletal muscle. The use of CV in swimming training is suggested since 1966 (Ettema 1966). Studies by researchers about its use continue to be published (Dekerle & Pelayo 2011).
