Modelling of Torque-angle Relationships with Polynomials and Cubic Splines in Elbow Joint


  • Gergana Koroleova* South-West University "Neofit Rilski"
  • Iliya Kanelov
  • Peter Milanov
  • Nevena Pencheva



The aims of this study are: (1) to assess modeling of elbow torque-angle re-lationships in trained and untrained men using polynomial functions fromsecond to fth order with optimization criteria; and (2) to compere themodeling with cubic splines.Ten untrained men and fteen arm wrestlers were tesed by isokinetic dy-namometer with isometric protocol. The peak, net torque ofВ exors andextensors of the elbow joint was registrated in Nm and normalized in per-cent in the 10 angular positions at range of 10 to 125 degrees. The datawere modeled: with a polynomial function of the second to fth order bythe method of least squares by ussing Akaike's information criteria (AIC)and Bayesian information criteria (BIC); with a cubic spline.It was found that: (1) the dierierences between trained and untrained donot concerns the results of modeling, but the peak torque values and thebehavior of extensors in the area ofВ extion; (2) the assessment accordingto the criteria AIC and BIC in modeling of torque-angle relationships withpolynomial functions does not give a denite answer in both muscle groupsand both samples; the approximating curve excludes the maximum torque;and (3) in modeling the torque-angle relationship with cubic polynomialsplines the interpolating curves encompass all points, including the maxi-mal torque but the curves are not smooth and some additional requirementsprobably must be pointed out.Acknowledgement.This work is supported by the University project (Or-dinance 9) of South-West University, Code SRP фЂЂЂ A16/15.

Author Biographies

Gergana Koroleova*, South-West University "Neofit Rilski"

Iliya Kanelov

Peter Milanov

Nevena Pencheva






Conference Contributions