Multilevel Models for the Analysis of Angle-Specific Torque Curves with Application to Master Athletes

The aim of this paper was to outline a multilevel modeling approach to fit individual angle-specific torque curves describing concentric knee extension and flexion isokinetic muscular actions in Master athletes. The potential of the analytical approach to examine between individual differences across the angle-specific torque curves was illustrated including between-individuals variation due to gender differences at a higher level. Torques in concentric muscular actions of knee extension and knee extension at 60º·s(-1) were considered within a range of motion between 5º and 85º (only torques "truly" isokinetic). Multilevel time series models with autoregressive covariance structures with standard multilevel models were superior fits compared with standard multilevel models for repeated measures to fit angle-specific torque curves. Third and fourth order polynomial models were the best fits to describe angle-specific torque curves of isokinetic knee flexion and extension concentric actions, respectively. The fixed exponents allow interpretations for initial acceleration, the angle at peak torque and the decrement of torque after peak torque. Also, the multilevel models were flexible to illustrate the influence of gender differences on the shape of torque throughout the range of motion and in the shape of the curves. The presented multilevel regression models may afford a general framework to examine angle-specific moment curves by isokinetic dynamometry, and add to the understanding mechanisms of strength development, particularly the force-length relationship, both related to performance and injury prevention.