I want to calculate the maximum tendon stiffness. I know that it corresponds to the slope of the force-length curve in the linear region. However, the limits of linear region are a little subjective. So, which method do you suggest me to set objectively this linear region?
I read a method where the authors defined the linear region "...as the one in which the least-squares-fitted line had the correlation coefficient value of 0.98" (Link: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2907260/#R5) but in this method there is a lack of objectivity too. I was thinking in define some percentages as 25 - 75% of maximum force and calculate the stiffness there, but i didn't found researches that support this.
Thank you!
Pd: Sorry for my english, i'm trying to improve it!
There are two fundamental reasons why any method you choose is subjective. (1) Tendons are viscoelastic structures, so the nature of the force-length curve is a function of strain rate. The curves are likely to have more linear-appearing regions at higher strain rates, because higher strain rates will minimize the contribution of the viscous component of tendon stiffness.
(2) Tendons are structures not materials. Therefore any attempt to interpret stress/strain behavior of tendons as e.g. a "Young's Modulus" is based on the gross assumption that the tendon is homogeneous and isotropic in structure.
Best solution to measuring and understanding tendon force/length behavior:
Run strain-controlled cyclic dynamic tests at various strain rates and constant amplitude. At each rate, you will be able to determine the tissue's aggregate complex structural modulus (Es*) and determine the elastic (Es') and viscous (Es") contributions to it. With data at various rates, you will be able to determine how the these structural properties change with strain rate. If dynamic mechanical analysis is new to you, a basic introduction is at: https://en.wikipedia.org/wiki/Dynamic_mechanical_analysis
Peter Magnusson's group has always used high force levels when determining stiffness, which is a good way to go: "deformation–force and stress–strain curves with r2 ≥ 0.98 (the curves were fitted with fourth degree polynomial fit) were selected for stiffness and modulus calculations, and the final 10% of the curves were used for these calculations (Hansen et al., 2003; Kongsgaard et al., 2007; Couppe et al., 2008)."
@Taija Finni
I don't doubt that one can get reproducible tendon stiffness values using a reproducible protocol. But since tendons are viscoelastic structures, the stiffness values will depend on the strain rate used. If the only goal of the tests is to get an idea of tendon stiffness at some particular functionally significant strain rate, fine. However that is an extremely limited approach.
It is fundamentally more relevant to determine the change in stiffness as a function of strain rate in a functionally significant range of strain amplitude. Further, as i said previously above, strain rate controlled cyclic dynamic tests allow one to determine the extent to which the tendon is functioning elastically or viscously at various functionally significant strain rates. That is the only way I know to get a complete picture of tendon functional stiffness.
You can calculate instantaneous stiffness using the slope of the tangential line at a specific force, what I then tend to do is compute the instantaneous stiffness at regular intervals along the stress-strain curve. The average value is the mean stiffness for that tendon. A colleague and I wrote a paper comparing the effect of different methods of calculating K on the outcome and hence derived correction factors to help compare data from different papers (different labs stll adopt their own methods which renders data between labs incomparable).
Pearson SJ & Onambélé GL, 2011. Computation methods affect the reported values of in vivo human tendon stiffness. Journal of the Mechanical Behaviour of Biomedical Materials. 5(1):291-7.
I hope this helps
https://www.ncbi.nlm.nih.gov/pubmed/22100104
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