Modelling suppressed muscle activation by means of an exponential sigmoid function: Validation and bounds

Abstract

The aim of this study was to establish how well a three-parameter sigmoid exponential function, DIFACT, follows experimentally obtained voluntary neural activation-angular velocity profiles and how robust it is to perturbed levels of maximal activation. Six male volunteers (age 26.3 ± 2.73 years) were tested before and after an 8-session, 3-week training protocol. Torque-angular velocity (T-ω) and experimental voluntary neural drive-angular velocity (%VA-ω) datasets, obtained via the interpolated twitch technique, were determined from pre-and post-training testing sessions. Non-linear regression fits of the product of DIFACT and a Hill type tetanic toque function and of the DIFACT function only were performed on the pre-and post-training T-ω and %VA-ω datasets for three different values of the DIFACT upper bound, α max , 100%, 95% & 90%. The determination coefficients, R 2 , and the RMS of the fits were compared using a two way mixed ANOVA and results showed that there was no significant difference (p < 0.05) due to changing α max values indicating the DIFACT remains robust to changes in maximal activation. Mean R 2 values of 0.95 and 0.96 for pre-and post-training sessions show that the maximal voluntary torque function successfully reproduces the T-ω raw dataset.

The hamstrings to quadriceps functional ratio expressed over the full angle-angular velocity range using a limited number of data points

“…The benchmark 17-parameter R T (ω, θ) function represented the H : Q fun increasing with angle and angular velocity as would be expected from both theory and experimental results. This function was based on a nine-parameter torque function that has been used multiple times to represent maximal voluntary joint torque as a function of angle and angular velocity with good results [39][40][41][42] and therefore it should be suitable to act (i) as a starting point for the derivation of a simpler ratio function, R E and (ii) as a benchmark against which the new function is tested.…”

“…Equation (2.1) is a nine-parameter function based on underlying muscle physiological properties that provides a three-dimensional description of the subject’s specific theoretical torque profile (figure 2 a , b ). This function has been used multiple times to represent the variation in maximal voluntary joint torque as a function of angular velocity and angle with good results [39–42]. Tconctetfalse(ωfalse) and Tecctetfalse(ωfalse) are two rectangular hyperbolas representing tetanic force output as a function of contraction velocity in concentric ( ω ≥ 0) and eccentric ( ω < 0) contractions, respectively [40].…”

Training induced changes in quadriceps activation during maximal eccentric contractions

“…The individual pre-and post-training T-ω data sets for each subject were statistically compared by performing a nonlinear regression fit of the 7-parameter MVT function defined in Forrester et al (2011), first separately and subsequently to the combined pre and post-training data sets (Figure 2). The fits for each profile were statistically compared using the extra-sum-ofsquares F-test (Motulsky & Christopoulos, 2004;Voukelatos & Pain, 2015). The same statistical process was repeated for the %VA-ω data set by fitting a 3 rd degree polynomial to establish the training effect on voluntary activation (Figure 3).…”