Short communicationModelling suppressed muscle activation by means of an exponential sigmoid function: Validation and bounds
Introduction
In vivo measurements of the maximum voluntary force–velocity relationship show differences to the in vitro tetanic profile, with eccentric forces not increasing much above isometric and tending to decline with increasing lengthening velocity (Westing, 1988, Dudley et al., 1990, Weber and Kriellaars, 1997). This difference could be due to a neural, tension-limiting mechanism that reduces maximal neural drive at high levels of muscular tension (Westing et al., 1990; Westing et al., 1991, Pain and Forrester, 2009, Pain et al., 2013). Yeadon et al. (2006) represented the in vivo maximum voluntary torque–velocity relationship as a product of a theoretical four parameter Hill-type tetanic torque function, and a three parameter differential activation function (DIFACT). The latter representing the net reduction in neural drive to the muscle with low neural activation at high eccentric velocities to full activation at high concentric velocities. However, the DIFACT function was not explicitly based on measured neural changes and its validity was implicitly assumed through the ability of the combined seven parameter function to reproduce the in vivo torque-velocity profiles. Furthermore, due to its quadratic form, the DIFACT function had multiple equivalent solutions and is difficult to manipulate algebraically. Pain and Forrester (2009) used a sigmoid exponential function to represent the DIFACT function in order to simplify mathematical manipulation when finding solutions for the seven parameter MVC torque function (MVC). Again the function was only implicitly shown to be successful through scaling of voluntary EMG signals (Pain and Forrester, 2009).
Therefore, although now used repeatedly (Lewis et al., 2012, Forrester et al., 2011, Tillin et al., 2012, Pain et al., 2013) in the literature the DIFACT function has yet to be verified in an explicit way. The aims of this study were (i) to establish experimentally how well the DIFACT function follows the in vivo voluntary neural activation–angular velocity profiles in a group of subjects; and (ii) to test the robustness of the exponential DIFACT function to perturbed upper levels of maximal activation.
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Method
Measurements from six male volunteers (age 26.3±2.7 years, body mass 72.9±11.7 kg, height, 172.2±8.4 cm; mean±SD) tested before and after eight sessions (over three weeks) of high velocity strength training on an isovelocity dynamometer were used as the raw data to address the aims of this study. They all gave written, informed consent and the study was conducted in accordance with the approval given by Loughborough University Ethical Advisory Committee. In brief, testing followed similar methods
Results
Applying the extra-sum-of-squares F-Test on the seven parameter MVC function fit to the torque–angular velocity dataset, for αmax=100%, showed that 3 out of 6 subjects had a significant (p<0.05) higher torque output post-testing. The same outcome was obtained when the αmax values were set equal to 95% and 90%.
There was no significant difference between the R2 values of the three fits with different αmax values for both pre- and post-training datasets (p=0.95 & p=0.99 respectively) for any of
Discussion
The aim of this work was to determine how well the three-parameter exponential differential activation function DIFACT (Pain and Forrester, 2009) reproduces the in-vivo T–ω and %VA–ω profiles and whether changing the value of the maximum activation level, αmax, in DIFACT (Pain and Forrester, 2009) would affect its robustness. Results show that the MVC torque function reproduces the T–ω raw data set very well irrespective of the αmax value. The DIFACT function is also successful in reproducing
Conflict of interest statement
Neither author has any conflict of interests.
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