Axial speed of sound is related to tendon's nonlinear elasticity

Axial speed of sound (SOS) measurements have been successfully applied to noninvasively evaluate tendon load, while preliminary studies showed that this technique also has a potential clinical interest in the follow up of tendon injuries. The ultrasound propagation theory predicts that the SOS is determined by the effective stiffness, mass density and Poisson's ratio of the propagating medium. Tendon stiffness characterizes the tissue's mechanical quality, but it is often measured in quasi-static condition and for entire tendon segments, so it might not be the same as the effective stiffness which determines the SOS. The objectives of the present study were to investigate the relationship between axial SOS and tendon's nonlinear elasticity, measured in standard laboratory conditions, and to evaluate if tendon's mass density and cross-sectional area (CSA) affect the SOS level. Axial SOS was measured during in vitro cycling of 9 equine superficial digital tendons. Each tendon's stiffness was characterized with a tangent modulus (the continuous derivative of the true stress/true strain curve) and an elastic modulus (the slope of this curve's linear region). Tendon's SOS was found to linearly vary with the square root of the tangent modulus during loading; tendon's SOS level was found correlated to the elastic modulus's square root and inversely correlated to the tendon's CSA, but it was not affected by tendon's mass density. These results confirm that tendon's tangent and elastic moduli, measured in laboratory conditions, are related to axial SOS and they represent one of its primary determinants.