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Muscle strength capacities in elite football players after anterior cruciate ligament reconstruction

Milutinovic Andreja, Copic Nemanja, Petrovic Adam, Dabovic Milinko, Janicijevic Danica

Acta of Bioengineering and Biomechanics

2021

Vol. 23, no. 2

107--114

Purpose: The aim of this study was to explore the strength capacities of the injured and non-injured leg following a unilateral anterior cruciate ligament reconstruction. Methods: Eight elite soccer players (age = 25.5 ± 3.9 years; height = 1.83 ± 0.04 m; body mass = 78.9 ± 4.5 kg) volunteered to participate in this study. Nine months after the anterior cruciate ligament reconstruction and just before initiating the full training process, the maximal peak torque of the quadriceps and hamstring muscles were measured at 60 and 180 degrees/second using isokinetic dynamometry. Obtained peak torques were used for calculating hamstring-to-quadriceps ratio, limb symmetry index, and to estimate maximal torque capacity using a two-velocity method (i.e., linear torque-velocity relationship modeled considering peak torque obtained at 60 and 180 degrees/second). Results: No differences were found between hamstring-to--quadriceps ratios of the injured and non-injured leg (p = 0.165), nor between limb symmetry index of the quadriceps and hamstring muscles (p = 0.985), regardless of the angular velocity applied during tests. The two-point method revealed significant differences between quadriceps and hamstring muscle groups both in the injured and non-injured leg (p < 0.001; maximal estimated torque was higher for quadriceps compared to hamstring muscles), while the differences between same muscle groups of the different legs were not significant. Conclusions: Collectively, these findings indicate that 9 months were enough for reaching a certain strength level of the injured leg that permits a safe return to play.

An efficient nonlinear analysis of 2D frames using a Newton-like technique

Mansouri I., Saffari H.

Archives of Civil and Mechanical Engineering

2012

Vol. 12, no. 4

485--492

The Newton–Raphson method, which is based on the Taylor series and uses the tangent stiffness matrix, has been widely used to solve nonlinear problems. In this paper, a Newton-like algorithm is used for analyses involving geometric nonlinearity. This iterative technique that requires two initial guesses is known as two-point iterative method. In this method, a real function is assumed to approximate the tangent stiffness matrix of the structure. This paper, proposes an efficient function for reducing the computing time and, number of iterations in the Newton–Raphson method coupled with the two-point methodology. The computational nonlinear analysis on planar frames shows that the proposed strategy can reduce the computing time up to around 40%. Compared with the classic Newton–Raphson algorithm, the presented method proposes a methodology which also can reduce the number of iterations.