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.