Nada Santrač and Jasmina Pavkov,
Faculty of Medicine
University of Novi Sad, Serbia
nadasantrac@hotmail.com
Abstract
On the basis of recently published experimental results of Abramowitch et al. (2004), dealing
with viscoelastic properties of sham operated and healing MCL, we show that the fractional Zener
model of viscoelastic body seems to be very tractable tool for rheological description of different
states of biological tissues. In this paper medial collateral ligament of the knee will be described
by means of the method of Dankuc et al. 2010, who examined middle ear structures and ramp-and
hold stress relaxation experiments. Two different states of MCL were described by four different
constants representing modulus of elasticity, the order of fractional derivative and two relaxation
constants. Predictions of the model are in good agreement with the experimental results.
Keywords: medial collateral ligament biomechanics, ramp-and-hold stress relaxation
References
Abramowitch, S. D., Woo, S. L-Y., Clineff, T. D., & Debski, R. E. (2004). An evaluation of the
quasi-linear viscoelastic properties of the healing medial collateral ligament in a goat
model. Annals of Biomedical Engineering, 32(3), 329–334.
Atanackovic, T. M. (2002). A modified Zener model of viscoelastic body. Continuum Mechanics
and Thermodynamics, 14, 137–148.
Bagely, R. L. & Torvik, P. J. (1986). On the fractional calculus model of viscoelastic behavior.
Journal of Rheology, 30, 133–155.
Dankuc, D. V., Kovincic, N. I., & Spasic, D. T. (2010). A new model for middle ear structures with
fractional type dissipation pattern. In: Proceedings of FDA’10. The 4th IFAC Workshop on
Fractional Differentiation and its Applications, Badajoz, Spain, October 18–20th, 2010.
Article No FDA10_156. Laxenburg: by International Federation of Automatic Control.
Gorenflo, R., & Mainardi, F. (2000). Fractional calculus: Integral and differential equations of
fractional order. In A. Carpinteri & F. Mainardi (Eds), Fractals and Fractional Calculus in
Continuum Mechanics (pp. 223–276). Wien and New York: Springer-Verlag.
Grahovac, N. M., & Zigic, M. M. (2010). Modeling of the hamstring muscle group by use of
fractional derivatives. Computers and Mathematics with Applications, 59(5), 1695–1700.
Spasic, D. T., & Charalambakis, N. C. (2002). Forced vibrations with fractional type of dissipation.
In Proceedings of the International Conference on Nonsmooth/Nonconvex Mechanics
with Applications in Engeneering (pp. 323–330). Thessaloniki: Aristotle University of
Thessaloniki.
Woo, S. L-Y., Abramovitch, S. D., Kilger, R., & Liang, R. (2006). Biomechanics of knee ligaments:
injury, healing and repair. Journal of Biomechanics, 39, 1–20.