Experimental and mathematical methods for representing relative surface elongation of the ACL

The common approach to assess the stabilizing role of the ACL in the knee has been to measure the elongation of a few marked fibers in the ligament. A comparison of the relative elongation (RE) of these marked fibers between different specimens and studies is delicate due to the difficulty of marking the same fibers. More consistent comparisons would be achieved if the RE of the whole ligament surface was presented. Hence, we developed a mathematical method leading to a continuous description of the relative elongation of the ligament's surface based on experimental measurements of the RE of five fibers. The ligament fibers of two knee specimens were marked by radiopaque markers and a Roentgen Stereophotogrammetric Analysis system was used to reconstruct the three-dimensional positions of these artificial landmarks. The mathematical procedure used isoparametric cubic splines to interpolate the contours of the insertion sites. The results showed that the general pattern of the RE for both specimens was similar, characterized by an undulation near full flexion. In fact, close to full flexion all the RE of the fibers increased. Such a representation describes the changes in the RE for a given fiber during knee flexion and at the same time characterizes the RE distribution at a given flexion angle.