Estimation of the elastic stiffness coefficient c13 of fixed tendon and fixed myocardium

Recent studies from our laboratory have detailed the anisotropy of velocity of quasilongitudinal-mode ultrasonic waves through formalin fixed samples of normal human myocardium and bovine Achilles tendon. Results of these studies were used to determine the elastic stiffness coefficients c33, corresponding to the propagation of longitudinal-mode waves parallel to the fiber axis of the tissue, and c11, corresponding to the propagation of longitudinal-mode waves perpendicular to the fiber axis. For a tissue possessing a unidirectional arrangement of fibers with a random transverse distribution, three additional coefficients, c13, c44, and c12, are needed to describe its linear mechanical properties completely. Direct ultrasonic measurements of these coefficients in solids typically require the propagation of transverse-mode waves through the sample. Such measurements are difficult to perform in soft tissues because transverse-mode ultrasonic waves are very highly attenuated by the tissue. This study therefore employs a technique to estimate c13 based on measurements of the velocity of quasilongitudinal-mode ultrasonic waves for numerous angles of propagation relative to the fiber axis of the tissue. Analysis of data obtained from formalin fixed bovine Achilles tendon and human myocardium yield estimated values for c13 of 3.17 and 2.46 GPa, respectively.