**4.1.1 Critical Speed (CV2par)**

PC was used initially to determine exercise intensity that could be theoretically maintained for a long period of time without exhaustion (Monod & Scherrer 1965). CP (or CV in running or swimming) proved to be valid for aerobic capacity prediction (Dekerle et al. 2005a) and sensitive to physiological changes from aerobic training programs (Jenkins & Quigley, 1991). CP or CV determined by two-parameter model (CP2par or CV2par) represents the lower boundary t of the severe intensity domain (Poole et al. 1990; Hill & Ferguson 1999). Poole et al. (1990) found that when subjects performed exercise intensity on CP2par, VO2 stabilized around 75%VO2max. In addition, studies have investigated the hyperbolic relationship between power and time to achieve VO2max. The results also suggest that this relationship is the lower boundary of the severe intensity domain, or CP2par (or CV2par) (Hill & Smith 1999; Hill & Ferguson 1999). Thus, CV2par can determine the exercise intensity equivalent to the lower boundary of the severe intensity domain.

#### **4.1.2 Anaerobic distance capacity (ADC2par)**

The physiological meaning of ADC2par is still subject of many studies (Moritani et al. 1981; Green et al. 1994; Miura et al. 2000; Heubert et al. 2005). Evidence trying to suggest the ADC2par anaerobic nature was observed in cyclists (Green et al. 1994). Also in cyclists, Heubert et al. (2005) found a decrease of 60 to 70% in ADC2par values as a result of a 7 s maximal effort performed before a protocol of four exercises at constant intensity (95, 100, 110 and 115%VO2max) and to determine the ADC2par and CP2par. CP2par values did not change. Moritani et al. (1981) also found no differences in ADC2par values in response to ischemia, hypoxia and hyperoxia. In relation to prior depletion of glycogen, Miura et al. (2000) found a decrease in ADC2par values (in cycle ergometer). Jenkins & Quigley (1993) found an increase in ADC2par values in response to high-intensity training in untrained individuals, but the CP2par values did not change. ADC2par values also showed increases in response to creatine supplementation (Miura et al. 1999) and demonstrated good correlation with predominantly anaerobic exercises (Vandewalle et al. 1989; Jenkins & Quigley 1991; Hill 1993; Dekerle et al. 2005b).

Bioenergetics Applied to Swimming: An Ecological Method to Monitor and Prescribe Training 167

and 1500 m from swimmers (adapted from Zacca et al. 2010). It is easy to see that the data fits more appropriately in three and four-parameter models. Thus, CV2par was higher than

Fig. 2. Swimming speed and tlim of 50, 100, 200, 300, 400, 800 and 1500 m from sprint swimmers and tted curves through two, three and four-parameter models (adapted from

that three and four-parameter models seem more suitable to predict ADC.

ADC2par was originally defined as the maximum distance (m) that could be covered anaerobically (Ettema 1966). However, Costill (1994) conceptualized ADC2par as the total work that can be performed by a set of limited power of the human body (phosphagen, anaerobic glycolysis and oxygen reserves) suggesting that the anaerobic energy system is predominant but not exclusive (Gastin 2001). Zacca et al. (2010) compared ADC2par, ADC3par and ADC4par values. The results showed that ADC2par (13.77 ± 2.34 m) was lower than ADC3par and ADC4par (30.89 ± 1.70 and 27.64 ± 0.03 m respectively). Moreover, ADC3par and ADC4par values were similar. These results are consistent with others that also observed an overestimation of the parameter ADC in two-parameter model (Billat et al. 2000). Dekerle et al. (2002) evaluated ten well-trained swimmers, when the objective was to verify the possibility of determining ADC2par. They concluded that ADC2par is not perfectly linear and is very sensitive to variations in performance. Thus, according to the authors, it is impossible to estimate the anaerobic capacity by two-parameter models. Toussaint et al. (1998) also suggest that the anaerobic capacity in swimming obtained by two-parameter model does not provide an accurate estimate of the real anaerobic capacity. It seems clear

CV3par and CV4par, as previously described.

Zacca et al. 2010).

**4.3.2 Anaerobic distance capacity (ADC4par)**

## **4.2 Three-parameter model**

#### **4.2.1 Critical Velocity (VC3par)**

The oxygen supply spends a period of time to reach a steady state or maximum. This has led some researchers (Vandewalle et al. 1989; Morton 1996) questioned the "immediate" availability of CV in two-parameter models (CV2par). As a result of this lapse of time, probably CV2par was being overestimated. In addition, studies found that CV2par could be sustained only by 14.3 to 39.4 min by swimmers (Dekerle et al. 2010). These results suggest that the concept of CV2par as a speed that could be sustained infinitely would not be appropriate.

There is little information on CV and the type of mathematical model used to obtain it in sports. Morton (1996) suggests that CV2par values may be overestimated. Gaesser et al. (1996) also found that three-parameter model generated CP values (CP3par) significantly lower, and the subjects were able to resist in a continuous work for a long period. Thus, CV3par seems not to be at the lower boundary of the severe intensity domain, requiring further investigation. Probably CV3par is below the lower boundary of the severe intensity domain.

#### **4.2.2 Anaerobic distance capacity (ADC3par)**

Vandewalle et al. (1989) question the assumption that at exhaustion all ADC2par is used, as theoretically is suggested by two-parameter models. Thus, ADC2par may be underestimated (Vandewalle et al. 1989; Morton 1996).

#### **4.2.3 Maximum instantaneous velocity (Vmax3par)**

As a result of the lapse of time ("immediate" availability of CV2par), Morton (1996) proposed a three-parameter model (Equation 3) which the "maximum instantaneous speed" (Vmax3par) was included (third parameter). With the addition of the parameter Vmax3par, the threeparameter model is more accurate in estimating the CV (and therefore ADC) surpassing the initial concept of the relationship velocity-*tlim*, that when *tlim* approaches zero, velocity is infinite (Morton 1996). Vmax3par allows a time asymptote below the x-axis, where time = zero, and provides a Vmax3par value in the intercept-x (MORTON 1996).

#### **4.3 Three-parameter model**

#### **4.3.1 Critical velocity (CV4par)**

Both models (two and three-parameter models) have an important limitation: do not predict the "aerobic inertia" (τ) (Wilkie 1980; Vandewalle et al. 1989), related to cardio respiratory adjustments so that the VO2 reach steady state or maximum. Thus, a four-parameter model (CV4par, ADC4par, Vmax4par and τ) proposed by Zacca et al. (2010) could provide more information on bioenergetics in cyclic sports. The four-parameter model proposed by Zacca et al. (2010) was based on the three-parameter model, and CV4par was corrected by an exponential factor, first proposed by Wilkie (1980). This exponential factor is theoretically defined as the time constant that describes the increased aerobic involvement, the "aerobic inertia" (τ). Zacca et al. (2010) suggest that CV is sensitive to additional parameters in young swimmers (93% of the variation was explained by the mathematical model used). The effect of the models showed that CV2par was higher than CV3par and CV4par. CV3par and CV4par were similar (and therefore the physiological meanings of both models are also similar). Thus, future studies are necessary to understand the physiological meaning of CV3par and CV4par in young swimmers and probably in other sports. Figure 2 shows the plot of the data using two, three and four-parameter models with speed and *tlim* data of 50, 100, 200, 300, 400, 800 and 1500 m from swimmers (adapted from Zacca et al. 2010). It is easy to see that the data fits more appropriately in three and four-parameter models. Thus, CV2par was higher than CV3par and CV4par, as previously described.

Fig. 2. Swimming speed and tlim of 50, 100, 200, 300, 400, 800 and 1500 m from sprint swimmers and tted curves through two, three and four-parameter models (adapted from Zacca et al. 2010).

#### **4.3.2 Anaerobic distance capacity (ADC4par)**

166 Bioenergetics

The oxygen supply spends a period of time to reach a steady state or maximum. This has led some researchers (Vandewalle et al. 1989; Morton 1996) questioned the "immediate" availability of CV in two-parameter models (CV2par). As a result of this lapse of time, probably CV2par was being overestimated. In addition, studies found that CV2par could be sustained only by 14.3 to 39.4 min by swimmers (Dekerle et al. 2010). These results suggest that the concept of

There is little information on CV and the type of mathematical model used to obtain it in sports. Morton (1996) suggests that CV2par values may be overestimated. Gaesser et al. (1996) also found that three-parameter model generated CP values (CP3par) significantly lower, and the subjects were able to resist in a continuous work for a long period. Thus, CV3par seems not to be at the lower boundary of the severe intensity domain, requiring further investigation. Probably CV3par is below the lower boundary of the severe intensity domain.

Vandewalle et al. (1989) question the assumption that at exhaustion all ADC2par is used, as theoretically is suggested by two-parameter models. Thus, ADC2par may be underestimated

As a result of the lapse of time ("immediate" availability of CV2par), Morton (1996) proposed a three-parameter model (Equation 3) which the "maximum instantaneous speed" (Vmax3par) was included (third parameter). With the addition of the parameter Vmax3par, the threeparameter model is more accurate in estimating the CV (and therefore ADC) surpassing the initial concept of the relationship velocity-*tlim*, that when *tlim* approaches zero, velocity is infinite (Morton 1996). Vmax3par allows a time asymptote below the x-axis, where time = zero,

Both models (two and three-parameter models) have an important limitation: do not predict the "aerobic inertia" (τ) (Wilkie 1980; Vandewalle et al. 1989), related to cardio respiratory adjustments so that the VO2 reach steady state or maximum. Thus, a four-parameter model (CV4par, ADC4par, Vmax4par and τ) proposed by Zacca et al. (2010) could provide more information on bioenergetics in cyclic sports. The four-parameter model proposed by Zacca et al. (2010) was based on the three-parameter model, and CV4par was corrected by an exponential factor, first proposed by Wilkie (1980). This exponential factor is theoretically defined as the time constant that describes the increased aerobic involvement, the "aerobic inertia" (τ). Zacca et al. (2010) suggest that CV is sensitive to additional parameters in young swimmers (93% of the variation was explained by the mathematical model used). The effect of the models showed that CV2par was higher than CV3par and CV4par. CV3par and CV4par were similar (and therefore the physiological meanings of both models are also similar). Thus, future studies are necessary to understand the physiological meaning of CV3par and CV4par in young swimmers and probably in other sports. Figure 2 shows the plot of the data using two, three and four-parameter models with speed and *tlim* data of 50, 100, 200, 300, 400, 800

CV2par as a speed that could be sustained infinitely would not be appropriate.

**4.2 Three-parameter model 4.2.1 Critical Velocity (VC3par)**

**4.2.2 Anaerobic distance capacity (ADC3par)**

**4.2.3 Maximum instantaneous velocity (Vmax3par)** 

and provides a Vmax3par value in the intercept-x (MORTON 1996).

(Vandewalle et al. 1989; Morton 1996).

**4.3 Three-parameter model 4.3.1 Critical velocity (CV4par)** 

ADC2par was originally defined as the maximum distance (m) that could be covered anaerobically (Ettema 1966). However, Costill (1994) conceptualized ADC2par as the total work that can be performed by a set of limited power of the human body (phosphagen, anaerobic glycolysis and oxygen reserves) suggesting that the anaerobic energy system is predominant but not exclusive (Gastin 2001). Zacca et al. (2010) compared ADC2par, ADC3par and ADC4par values. The results showed that ADC2par (13.77 ± 2.34 m) was lower than ADC3par and ADC4par (30.89 ± 1.70 and 27.64 ± 0.03 m respectively). Moreover, ADC3par and ADC4par values were similar. These results are consistent with others that also observed an overestimation of the parameter ADC in two-parameter model (Billat et al. 2000). Dekerle et al. (2002) evaluated ten well-trained swimmers, when the objective was to verify the possibility of determining ADC2par. They concluded that ADC2par is not perfectly linear and is very sensitive to variations in performance. Thus, according to the authors, it is impossible to estimate the anaerobic capacity by two-parameter models. Toussaint et al. (1998) also suggest that the anaerobic capacity in swimming obtained by two-parameter model does not provide an accurate estimate of the real anaerobic capacity. It seems clear that three and four-parameter models seem more suitable to predict ADC.

Bioenergetics Applied to Swimming: An Ecological Method to Monitor and Prescribe Training 169

recovery curve of VO2 (the back extrapolation method proposed by Di Prampero et al. 1976) was first tested on swimmers by Lavoie et al. back in 1983. Lavoie et al. (1983) found a high correlation between VO2max and *tlim* of T400. The possibility to prescribe training intensities using a single test has renewed expectations of swimming coaches and researchers. The attainment of VO2max values trough the back extrapolation involves obtaining VO2 after swimming and applying a simple regression curve between the time and the values of consumption in order to predict the value of VO2 in time zero (Lavoie & Montpetit 1986). It is believed that the high correlation between VO2max and *tlim* T400 m found by Lavoie et al. (1983) is probably the first indication of the T400 as a non-invasive alternative. Since then, T400 is a reference to verify the MAS and prescribe swimming training intensities (Montpetit et al. 1981; Lavoie et al. 1983; Rodrigues 2000; Pelayo et al. 2007). However, despite many studies reporting the use of T400 by swimming coaches (Wakayoshi et al. 1993b; Dekerle et al. 2005a; Alberty et al. 2006; Dekerle et al. 2006; Pelayo et al. 2007), we did not find a reliable protocol for prescribe more than one swimming training zone through the T400, i.e., a

protocol not only able to predict aerobic power, but also another training zone.

OBJECTIVE DISTANCE EQUATION

800 m (t800IVO2) = t400IVO2· 2 + 3 s 200 m (t200IVO2) = t400IVO2 /2 – 3 s 100 m (t100IVO2) = t200IVO2 /2 – 2 s 50 m (t50IVO2) = t100IVO2 /2 - 1,5 s

800 m (t800I LA) = t400ILA· 2 + 3 s 200 m (t200I LA) = t400ILA /2 – 3 s 100 m (t100I LA) = t200ILA /2 – 2 s 50 m (t50I LA) = t100ILA /2 - 1,5 s

800 m (t800ILAe) = t400ILAe· 2 + 3 s 200 m (t200ILAe) = t400ILAe /2 – 3 s 100 m (t100ILAe) = t200ILAe /2 – 2 s 50 m (t50ILAe) = t100ILAe /2 - 1,5 s Table 2. Equations used to calculate the SS for "aerobic threshold", "anaerobic threshold" and "VO2max". K is a constant: K = 0.94 if *tlim* is between 3 min 50 s to 4 min 40 s, K = 0.95 if *tlim* is between 4 min 41 s to 5 min 40 s, K = 0.96 the tlim is between 5 min 41 s to 6 min 40 s, K = 0.97 if *tlim* is above 6 min 41 s, t = time prescribed for a given distance; IVO2 = intensity prescribed to increase VO2max, ILA = intensity for anaerobic threshold and ILAe = intensity

In this protocol, the coach just needs that your athletes swim 400 m in front *crawl* under maximum intensity (in training situation, but preferably in competitive situation).

SS for "aerobic threshold", "anaerobic threshold" and "VO2max".

VO2max (IVO2)

ANAEROBIC THRESHOLD (ILA)

AEROBIC THRESHOLD (ILAe)

prescribed for aerobic threshold.

By questioning some brazilian coaches, we find that some of them use a protocol (of unknown origin) based on the T400 to monitor and to prescribe three different SS for swimmers and triathletes. Table 2 presents a summary of the equations used to calculate the

400 m (t400IVO2) = 400 / (400 / *tlim* 400 m)· k

400 m (t400ILA) = 400 / ((400 / *tlim* 400 m)· k)· 0,95

400 m (t400ILAe) = 400 / (((400 / *tlim* 400 m)· k)· 0,95)· 0,93

#### **4.3.3 Maximum instantaneous velocity**

There are gaps in the literature regarding the prediction of Vmax by mathematical models. Billat et al. (2000) found that Vmax3par was not different from the maximum speed obtained in 20 m at maximal effort. However, Bosquet et al. (2006) suggest that Vmax3par is smaller than the real Vmax (obtained by the average speed of the last 10 m of a maximal 40 m effort). Zacca et al. (2010) found that Vmax was higher in sprint than endurance swimmers (2.53 ± 0.15 m·s-1 and 2.07 ± 0.19 m·s-1 respectively) independent of the mathematical model used (three or four parameters). In addition, Vmax4par was greater than Vmax3par (2.42 ± 0.29 m·s-1 and 2.18 ± 0.34m·s-1 respectively), suggesting future studies to compare Vmax and real Vmax.

#### **4.3.4 Aerobic inertia**

The two-parameter model given by the relation "SS-*tlim*" (or *"Dlim*-*tlim*") and three-parameter model given by the relation "SS-*tlim*" have an important limitation: they do not take into account the "aerobic inertia" (τ) (Wilkie 1980; Vandewalle et al. 1989). The "τ" is a temporary delay in VO2 response because of dissociation between O2 absorbed in the lungs and the mainly used by skeletal muscle, lasting approximately 15 to 20 s. "τ" is associated to vasodilatation, i.e, the time it takes for the body to increase heart rate and redirect blood flow. Studies regarding oxygen kinetics during exercise with children and adolescents is limited to few articles and until recently was based on data collected with adults (FAWKNER & ARMSTRONG 2003). Invernizzi et al. (2008) suggest that the time to reach steady state in VO2 after the beginning of the exercise depends on the characteristics of the subject: endurance swimmers reach this balance sooner than sprint swimmers, and children reach earlier than adults. Thus, "τ" could be a good tool for evaluating cardiovascular and pulmonary performance in athletes (Kilding et al. 2006; Duffield et al. 2007).
