Key variables used to describe the limits of NMF 39 

Due to the discrepancy in the protocols and ergometers used by researchers as outlined in Table 2.1, the range of cadences captured during a F-V test and modelling procedure employed (i.e. order of polynomial) may have an impact on the variables commonly extracted from the T-C and P-C relationships to describe the limits of NMF. The equations describing the relationships between torque and cadence is used to predict maximal torque (T0) which corresponds to the intercept of the T-C relationship with the torque (y) axis; maximal cadence (C0) which corresponds to the intercept with the cadence (x) axis and the slope of the relationship (when the T-C relationship is assumed to be linear) (Dorel et al., 2010; Dorel et al., 2005; Martin et al., 1997; Yeo et al., 2015). Similar to studies investigating the F-V relationship in isolated muscle or single joint movements, F0/T0 indicates the theoretical maximal force/torque the limbs can produce at zero velocity, while V0/C0 represents the theoretical maximal velocity/cadence at

40

which the limbs can move (Dorel et al., 2005; Gardner et al., 2007; Martin et al., 1997; Samozino et al., 2012). In a general sense, F0/T0 is suggested to provide an estimate of strength of the lower limbs (Driss et al., 2002), while C0 provides an estimate of speed characteristics (Samozino et al., 2012). Extrapolated values of C0 and T0/F0 have been reported as high as 260 rpm and 236 N·m respectively in elite sprint cyclists (Dorel et al., 2005; Martin et al., 1997), but somewhat less in active volunteers with ~236 rpm and ~180 N·m respectively (Dorel et al., 2010). It is common practice in studies investigating the mechanical capabilities of single muscle fibers or single muscles to include both calculated and experimental measures of V0 via the slack test method (Claflin & Faulkner, 1985; Edman, 1979). However, in maximal cycling research C0 is typically calculated by extrapolation and not measured experimentally. It appears that the collection of an experimental measure of maximal cadence (Cmax) has only been reported once in the literature by McCartney and colleagues (1985) who documented values between 181-192 rpm for their cohort of non-cyclist females. Given that the removal of the chain from the cycle ergometer is quite easy and likely to result in pedalling against an external resistance that is close to zero, the lack of experimental cadence values reported in the literature is surprising.

As power is a product of force and velocity, estimated F0 and V0 have been used previously as a method of calculating maximal power (Pmax), using 0.5F0 and 0.5V0, or 0.25V0F0, based on the assumption that the T-C relationship is linear (Driss & Vandewalle, 2013; Seck et al., 1995), while 2Copt values have been used to predict C0 (Driss & Vandewalle, 2013), based upon the notion that the P-C relationship reflects a symmetrical parabola. However, given that the T-C and P-C relationships may not represent linear or symmetrical shapes, the implementation of these types of equations may misrepresent important information regarding the limits of the neuromuscular system.

More often in the literature P-C relationships are created alongside those for T-C (as outlined in Table 2.1), allowing the shape of the respective relationships to be visualised. Just as maximal power in isolated muscle or muscle fibers occurs at optimal shortening velocities (Figure 2.5) (Hill, 1938), it is well known that maximal mechanical power is achieved at optimal velocities/cadences (Copt) during maximal cycling (Arsac et al., 1996; Dorel et al., 2010; Dorel et al., 2005; Gardner et al., 2007; Martin et al., 1997; Samozino et al., 2007; Vandewalle et al., 1987; Yeo et al., 2015). Though, it has been shown with forward dynamics modelling (i.e. using joint torques to predict resultant motions) that Copt (i.e. the cadence at which maximal power is optimised) is not only determined by the relationship between power and velocity, but also by activation-deactivation dynamics (Bobbert et al., 2016; van Soest & Casius, 2000). The regressions fit to P-C relationships can be used to predict Pmax at the apex of the curve and the Copt to which it corresponds (Dorel et al., 2005; Driss et al., 2002; Gardner et al., 2007; Martin et al., 1997; McCartney et al., 1985; Samozino et al., 2012). Absolute Pmax values achieved in maximal

41

cycling have been reported around 1100 W in non-cyclists (Dorel et al., 2010) and up to 2500 W in highly trained elite cyclists (Dorel et al., 2005; Martin et al., 2006). When expressed in relation to body mass, power outputs of 12.4 W.kg-1 _{have been reported for active, non-cyclists (Davies} & Sandstrom, 1989), 17.1 W.kg-1 _{for power athletes (Vandewalle et al., 1987) and 19.3 W.kg}-1 for elite track cyclists. Values of Copt typically reported range between 110 and 140 rpm for both trained and un-trained cyclists (Dorel et al., 2005; Gardner et al., 2007; Martin et al., 2000b).

Although, T0, C0, Pmax, Copt provide important information regarding the limits of NMF with some of these parameters directly linked with performance (Hautier et al., 1996; Vandewalle et al., 1987) and strength of the knee extensor muscles (Driss et al., 2002) they characterize only a few points on the T-C and P-C curves. Recent studies have gone beyond interpretation of F0/T0 and V0/C0 values separately and have assessed the F-V mechanical profile during sprint running (Morin et al., 2002), squat jumping (Giroux et al., 2016; Samozino et al., 2014) and ballistic inclined push offs (Samozino et al., 2012) using the slope of the F-V relationship calculated from a linear regression (Giroux et al., 2016; Morin et al., 2002; Samozino et al., 2014; Samozino et al., 2012). Although these studies highlight the individualism of force and velocity producing capabilities, consideration must be given to their methods for F-V line fitting procedures. The slope appears to provide a nice method for assessment of NMF, but like the calculation of T0 and C0, if the relationship between force/torque and velocity is not actually linear then this approach may not be accurate.

This literature review section has outlined the current practices for the evaluation of NMF using stationary cycle ergometers. Although the F-V test has been commonly implemented to assess the limits of NMF of the lower limbs such as their torque and power producing capabilities, there exist several different methods for data collection and analysis. It appears that perhaps due to the complexity of the pedalling movement and different factors affecting the level of power that can be produced over a range of cadences (i.e. specifically either side of Pmax at low and high cadences) that previous methods may have overestimated the limits of NMF.

42

Table 2.1. Summary of studies that have used force-velocity test protocols on stationary cycle ergometers. Author(s)

(Date)

Test n Participants No. Sprints Sprint Length Rest Length # Data Points T-C/P-C Regressions Arsac et al. (1996) Isoinertial 15 Trained-Marathon, volleyball 6 8-s 5-min ~126- 200 2nd _order/ 3rd _order Buttelli et al. (1999)

Isoinertial 11 Well-trained males 1 6-s - - Linear

Capmal & Vandewalle (1997)

Isoinertial 6 3 active & 3 cyclist males 2 To maximal velocity 5-min ~13 Linear Capmal & Vandewalle (2010)

Isoinertial 4 Competitive cyclists 1 7-s - ~15 Linear/

2nd _order

Davies et al.(1984)

Isokinetic 5 Healthy males 8-10 10-s 5-min - Linear &

Hyperbolic Doré et al.

(2003)

Isoinertial 27 14 females &13 males

4 5 to 8-s 4-min ~30 2nd _order/

3rd _order

Dorel et al.

(2005) Isoinertial 12 Elite cyclists 3 5-s 5-min ~50 2Linear/ nd _order

Dorel et al.

(2010) Isoinertial 14 Active males 3 5-s 5-min - 2Linear/ nd _order

Driss et al.

(2002) Isoinertial 12 Male volley ball players 6-8 6-s 5-min 6 2Linear/ nd _order

Gardner et al.

(2007) Isoinertial 7 Elite cyclists 2 3 to 5-s 3-min ~12 2Linear/ nd _order

Hautier et al.

(1996) Isoinertial 10 Trained cyclists 3 5-s 5-min 15 2

nd _order/

3rd _order

Hintzy et al. (1999)

Isoinertial 22 Trained non-cyclists 4 6-s 5-min 55 Linear/

2nd _order

Linossier et al. (1996)

Isoinertial 10 8 men & 2 women, active

2-3 4 to 8-s 5-min 6 Linear/

2nd _order

Martin et al. (1997)

Isoinertial 13 Active males 1 3 to 4-s - 6.5 Linear/

2nd _order

Martin et al. (2000)

Isoinertial 48 13 cycle trained & 35 active men

1 3 to 4-s - 6.5 -/2nd _order

Martin & Spirduso (2001)

Isoinertial 16 Trained cyclists 1 3 to 4-s - 6.5 -/2nd _order

McCartney et

al. (1983b) Isokinetic 12 Healthy males 6 <10-s 2-min 6 Linear

McCartney et

al. (1985) Isokinetic 7 Healthy females 10 <10-s 2-min 10 Exponential/ 2nd _order

Nakamura et al. (1985)

Isoinertial 26 Active males 8 10-s >2-min - Linear

Pearson et al. (2006)

Isoinertial 14 7 young & 7 older men 15 1 to 5-s 30-s ~30 -/3rd _order Rouffet & Hautier (2008) Isoinertial 9 Recreationally trained males 2 - 5-min - - Samozino et

al. (2007) Isoinertial 11 Trained cyclists 4 8-s 5-min 12-31 2Linear/ nd _order

Sargeant et al.

(1981) Isokinetic 5 Untrained cyclists 8 20-s - 8 2Linear/ nd _order

Sargeant et

al.(1984) Isokinetic 55 31 adults & 24 children more 4 or 20-s - - 2Linear/ nd _order

Seck et al.

(1995) Isoinertial 7 Healthy males 4 7-s 5-min - 2Linear/ nd _order

Yeo et al.

(2015) Isoinertial 24 Competitive cyclists 3 5-s 6-min 15 2

nd _order/

3rd _order

43