title: Multilevel Models for the Analysis of Angle-Specific Torque Curves with Application to Master Athletes.
abstract: 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.
authors.affiliation: School of Physical Education, University of Campinas, Campinas, Brazil; Faculty of Sport Sciences and Physical Education, University of Coimbra, Coimbra, Portugal.
authors.forename: Humberto M
authors.initials: HM
authors.lastname: Carvalho
keywords: isokinetic; multilevel regression modeling; muscle function; strength
references.citation: J Electromyogr Kinesiol. 1997 Jun;7(2):123-30
references.pmid: 20719697
references.citation: Arch Phys Med Rehabil. 1998 Aug;79(8):971-8
references.pmid: 9710172
references.citation: Arch Gen Psychiatry. 2004 Mar;61(3):310-7
references.pmid: 14993119
references.citation: Adv Physiol Educ. 2004 Dec;28(1-4):2-14
references.pmid: 14973047
references.citation: J Biomech. 2004 Jun;37(6):857-64
references.pmid: 15111073
references.citation: Med Sci Sports Exerc. 2001 May;33(5):783-90
references.pmid: 11323549
references.citation: Eur J Appl Physiol. 2004 Oct;93(1-2):237-44
references.pmid: 15293054
references.citation: Stat Med. 1994 Aug 30;13(16):1643-55
references.pmid: 7973240
references.citation: J Physiol. 2006 Feb 15;571(Pt 1):243-52
references.pmid: 16357013
references.citation: Med Sci Sports Exerc. 1991 Jan;23(1):108-14
references.pmid: 1997804
references.citation: In Vivo. 2009 Sep-Oct;23(5):859-65
references.pmid: 19779124
references.citation: J Biomech. 2004 Nov;37(11):1689-97
references.pmid: 15388311
references.citation: Exerc Sport Sci Rev. 1986;14:45-80
references.pmid: 3525192
references.citation: Medicina (Kaunas). 2011;47(8):446-52
references.pmid: 22123556
references.citation: J Muscle Res Cell Motil. 2012 Aug;33(3-4):167-75
references.pmid: 22825493
references.citation: Sports Med. 2007;37(9):807-26
references.pmid: 17722950
references.citation: J Orthop Sports Phys Ther. 1991;13(3):138-42
references.pmid: 18796847
references.citation: Pediatr Exerc Sci. 2011 Feb;23(1):1-2
references.pmid: 21598741
references.citation: J Sports Sci. 2004 Nov-Dec;22(11-12):1005-14
references.pmid: 15801494
references.citation: Sports Med. 1996 Jan;21(1):18-34
references.pmid: 8771283