The Biomechanical Relevance of the Mathematical Models of Torque-Angle and Torque-Velocity Relationships


  • Nevena Pencheva* Department of Kinesitherapy, South-West University, Blagoevgrad
  • Gergana Koroleova
  • Iliya kanelov
  • Peter Milanov



Mathematical models of torque-velocity and torque-angle relationships on different muscle groups and joints allow at least two things: (1) to generate and analyzeВ  characteristic curves based on experimental data and to assess their dynamics duringВ  neurogenic or myogenic dysfunctions, or to use them as a criterion for the changes in the level of training; and (2) to generate the predictive torque equations for various joints. Based on our previous studies [1-4] and on the classical force-velocity relationship of Hill [5], in this report we discussВ  the biomechanical relevanceВ  ofВ  mathematical models of torque-velocity and torque-angleВ  relationshipsВ  with polynomials, cubic splines and exponential functions. The cases concern different muscle groups and joints, as well as a comparative analysis of data between trained and untrained subjects, demonstrating the possibilities of mathemamical modellingВ  to differentiateВ  theВ  changes in the force profile of skeletal musclesВ В  as a response to long-term adaptation to training.

[1] Kanelov, I., Pencheva, N., Stefanov, S., Milanov, P., Dimitriev, M. (2014) Concentric torque-velocity realtionships of the elbow flexors and extensors in healthy females.  Book of Abstracts, 19th Annual Congress of the European College of Sport Science 2nd - 5th July 2014, Amsterdam – The Netherlands.

[2] Kanelov I., Koroleova G., Milanov P. Pencheva N. (2016) Impact of the joint angular positions on the peak torque of elbow flexors and extensors in healthy males. Research in Kinesiology, (in press).
[3] Koroleova, G., Mavrevski, R., Kanelov, I., Pencheva, N., Milanov, P. (2015) Assessment of elbow torque-velocity curve fitting with different optimization criteria.В  Book of Abstracts, 20th Annual Congress of the European College of Sport Science, 24th - 27th June 2015, Malmo,В  Sweden.

[4] Pencheva, N., Kokova, M., Dencheva, S. (2012) Torque-angle relationships of the elbow flexors and extensors in healthy females.В  Book of Abstracts, 18th Annual Congress of the European College of Sport Science, 26th - 29th June 2013, Barcelona, Spain.

[5] Hill A. V. (1938) The heat of shortening and the dynamic constraints of muscle, Proceedings of the Royal Society B: Biological Sciences, 126 (843), p. 136-195.






Conference Contributions