Mathematical description of in-vivo muscle function

Mathematical relationships have long been used to describe many aspects of muscle function such as the relationship between muscle force and muscle length, muscle force and velocity of contraction or the degree of muscle activation during a contraction. During this work various mathematical expressions have been employed in order to gain an insight into different aspects of muscle activity. The first part of the work examined whether performing a strength protocol on a dynamometer can lead to an increase in eccentric strength output as well as in the neuromuscular activation of the quadriceps group of muscles that appears inhibited during slow concentric and fast eccentric contractions. Neuromuscular activation was modelled via a three-parameter sigmoid function that was also tested for robustness to perturbations in the maximum activation values. During the second part of the study the "functional" hamstrings to quadriceps ratio H:Qfun was expressed as a function of two variables i.e., angular velocity and joint angle. Initially nine-parameter torque-angular velocity-angle profiles were obtained for the knee extensors and flexors from a group of participants. A theoretical 17- parameter H:Qfun function was then derived for each dataset. Subsequently, a simpler, 6-parameter function was derived, RE = aexp(bωn + cθm)-dω1/2θ2 that best reproduced the original 17-parameter fit. Finally, a six-segment subject specific torque-driven model of the Snatch lift was developed in order to investigate the optimal mechanics of the lift. The model simulated the lift from its initiation until the end of the second pull when the feet of the athlete momentarily leave the platform. The six-segment model comprised of foot, shank, thigh, torso (head + trunk), arm and forearm segments with torque generators at the ankle, knee, hip and shoulder joints respectively. The torque profiles were obtained using an isokinetic dynamometer

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

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 torque 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, αmax, 100%, 95% & 90%. The determination coefficients, R2, 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 αmax values indicating the DIFACT remains robust to changes in maximal activation. Mean R2 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

Training induced changes in quadriceps activation during maximal eccentric contractions

Despite full voluntary effort, neuromuscular activation of the quadriceps group of muscles appears inhibited during eccentric contractions. A nerve stimulation protocol during dynamic contractions of the quadriceps was developed that employed triplets of supramaximal pulses to assess suppressed eccentric activation. Subsequently the effects of a short training intervention, performed on a dynamometer, on eccentric strength output and neural inhibition were examined. Torque-angular velocity (T-ω) and experimental voluntary neural drive-angular velocity (%VA-ω; %VA, obtained via the interpolated twitch technique) datasets, were obtained from pre- and post-training testing sessions. Non-linear regression fits of a seven parameter torque function and of a 3rd degree polynomial were performed on the pre- and post-training T-ω and %VA-ω datasets respectively. T-test showed a significant (p < 0.05) increase in the overall torque output post-training for the group, with three out of the six subjects demonstrating a significant (p < 0.05) increase in the torque output across the range of angular velocities as shown by the extra-sum-of-squares F-test. A significant increase (p < 0.05) in the %VA post-training was also observed as well as a reduction in the plateauing of the torque output during fast eccentric contractions

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

This article was accepted for publication in the Journal of Biomechanics [© Elsevier Ltd.] and the definitive version is available at: http://dx.doi.org/10.1016/j.jbiomech.2015.01.009The 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 torque 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, αmax, 100%, 95% & 90%. The determination coefficients, R2, 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 αmax values indicating the DIFACT remains robust to changes in maximal activation. Mean R2 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

Binding energy and geometry for the adsorption of NO on Cu

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

Supplementary files for article The hamstrings to quadriceps functional ratio expressed over the full angle-angular velocity range using a limited number of data pointsThe hamstring to quadriceps (H : Q) strength ratio is widely used to identify individuals at risk of sustaining hamstring strain injuries. However, its efficacy is not supported by the current evidence. Current methods for the calculation of the H : Q ratio provide only a one- or two-dimensional ratio, often ignoring fundamental muscle mechanical properties. Based on isokinetic torque measurements of the knee flexors and extensors (0-400° s-1) in 25 young, physically active males, we derived a model equation that creates a threedimensional H : Q functional ratio profile. The model robustness was tested against a different number of input torque data (8, 11, 14 and 17 pairs of points) and small perturbation of the knee joint angle data (5°). The model was consistent and behaved well under all conditions apart from the eight pairs of points (R2= 0.84-0.96; RMSE = 0.14-0.25; NRMSE = 0.12-0.27), and the H : Q functional ratio was successfully described even at angles and velocities that cannot be normally assessed with isokinetic dynamometry. Overall, our results suggest that the model can provide a fast and accurate three-dimensional description of the knee joint muscle strength balance using as few as 11 experimental data points and this could be an easy-to-employ screening tool.</p

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

The hamstring to quadriceps (H : Q) strength ratio is widely used to identify individuals at risk of sustaining hamstring strain injuries. However, its efficacy is not supported by the current evidence. Current methods for the calculation of the H : Q ratio provide only a one- or two-dimensional ratio, often ignoring fundamental muscle mechanical properties. Based on isokinetic torque measurements of the knee flexors and extensors (0-400° s-1) in 25 young, physically active males, we derived a model equation that creates a threedimensional H : Q functional ratio profile. The model robustness was tested against a different number of input torque data (8, 11, 14 and 17 pairs of points) and small perturbation of the knee joint angle data (5°). The model was consistent and behaved well under all conditions apart from the eight pairs of points (R2= 0.84-0.96; RMSE = 0.14-0.25; NRMSE = 0.12-0.27), and the H : Q functional ratio was successfully described even at angles and velocities that cannot be normally assessed with isokinetic dynamometry. Overall, our results suggest that the model can provide a fast and accurate three-dimensional description of the knee joint muscle strength balance using as few as 11 experimental data points and this could be an easy-to-employ screening tool.</p

Changes in inertial parameters of the lower limb during the impact phase of dynamic tasks

Mechanical analysis at the whole human body level typically assumes limbs are rigid bodies with fixed inertial parameters, however, as the human body consists mainly of deformable soft tissue, this is not the case. The aim of this study was to investigatechanges in the inertial parameters of the lower limb during landing and stamping tasks using high frequency three-dimensional motion analysis. Seven males performed active and passive drop landings from 30 and 45 cm and a stamp onto a force plate. A sixteen-camera 750 Hz Vicon system recorded markers for standardrigid body analysis using inverse kinematics in Visual 3D and 7×8 and 7×9 marker arrays on the shank and thigh. Frame by frame segment volumes from marker arrays were calculated as a collection of tetrahedra using the Delaunay triangulation method in 3D and further inertial parameters were calculated using the method of Tonon (2004). Distance between the centres of mass (COM) of the rigid and soft tissues changed during impact in a structured manner indicative of a damped oscillation. Group mean amplitudes for COM motion of the soft tissues relative to therigid body of up to 1.4 cm, and changes of up to 17% in moment of inertia of the soft tissue about the rigid body COM were found. This study has shown that meaningful changes in inertial parameters can be observed and quantified during even moderate impacts. Further examination of the effects these could have onmovement dynamics and energetics seems pertinent.</div