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Open AccessArticle

Modeling the Angle-Specific Isokinetic Hamstring to Quadriceps Ratio Using Multilevel Generalized Additive Models

1
School of Physical Education, University of Campinas, Campinas, São Paulo 13083-851, Brazil
2
Department of Physical Education, School of Sports, Federal University of Santa Catarina, Florianópolis, Santa Catarina 88040-900, Brazil
3
Department of Informatics and Statistics, School of Technology, Federal University of Santa Catarina, Florianópolis, Santa Catarina 88040-900, Brazil
*
Author to whom correspondence should be addressed.
Medicina 2019, 55(8), 411; https://doi.org/10.3390/medicina55080411
Received: 10 June 2019 / Revised: 11 July 2019 / Accepted: 23 July 2019 / Published: 26 July 2019
Background and Objectives: This study considered the use of a generalized additive multilevel model to describe the joint-angle-specific functional hamstring to quadriceps ratio (H:Q ratio) in the knee, using all of the available truly isokinetic data within the range. Materials and Methods: Thirty healthy male basketball players aged 15.0 (1.4) years (average stature = 180.0 cm, SD = 11.1 cm; average body mass = 71.2, SD = 14.9 kg) years were considered. All players considered had no history of lower extremity musculoskeletal injury at the time of testing or during the 6 months before testing, and had been engaged in formal basketball training and competition for 5.9 (2.4) years. Moments of force of the reciprocal concentric and eccentric muscular actions for the knee extensors and flexors assessed by isokinetic dynamometry at 60°∙s−1 were used. Results: Maximum moments of force were attained at different angle positions for knee extension. For knee flexion, it was apparent that there was an ability to maintain high levels of moment of force between 30° and 60° in the concentric muscular action, corresponding to the concentric action of the hamstrings. However, for the eccentric knee flexion, corresponding to the quadriceps action, there was a marked peak of moment of force at about 55°. The functional H:Q ratio for the knee extension was non-linear, remaining higher than 1.0 (i.e., point of equality) from the beginning of the extension until approximately 40° of the knee extension, leveling off below the point of equality thereafter. On average, the functional H:Q ratio for the knee flexion did not attain 1.0 across the range of motion. The functional H:Q ratio for the knee in the present sample peaked at 20° and 80°, declining between these angle positions to below 0.50 at about 0.54. Conclusions: Estimating the form of the non-linear relationship on-the-fly using a generalized additive multilevel model provides joint-angle-specific curves and joint-angle-specific functional H:Q ratio patterns, allowing the identification and monitoring of strength development, with potential implications for injury and performance. View Full-Text
Keywords: isokinetic; muscle function; strength; adolescent; Bayesian methods isokinetic; muscle function; strength; adolescent; Bayesian methods
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Sousa, L.A.; Soares, A.L.A.; Lima, A.B.; Paes, R.R.; Nakamura, L.R.; Carvalho, H.M. Modeling the Angle-Specific Isokinetic Hamstring to Quadriceps Ratio Using Multilevel Generalized Additive Models. Medicina 2019, 55, 411.

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