Conrad Smith Biomedical Engineering Program, University of California, One Shields Avenue, Davis, CA 95616 M. L. Hull 1 Biomedical Engineering Program, and Department of Mechanical Engineering, University of California, One Shields Avenue, Davis, CA 95616 e-mail: mlhull@ucdavis.edu S. M. Howell Department of Mechanical Engineering, University of California, One Shields Avenue, Davis, CA 95616 Roentgen Stereophotogrammetric Analysis Methods for Determining Ten Causes of Lengthening of a Soft-Tissue Anterior Cruciate Ligament Graft Construct There are many causes of lengthening of an anterior cruciate ligament soft-tissue graft construct (i.e., graft + fixation devices + bone), which can lead to an increase in anterior laxity. These causes can be due to plastic deformation and/or an increase in elastic deformation. The purposes of this in vitro study were (1) to develop the methods to quantify eight causes (four elastic and four plastic) associated with the tibial and femoral fixations using Roentgen stereophotogrammetric analysis (RSA) and to demonstrate the usefulness of these methods, (2) to assess how well an empirical relationship between an increase in length of the graft construct and an increase in anterior laxity predicts two causes (one elastic and one plastic) associated with the graft midsubstance, and (3) to determine the increase in anterior tare laxity (i.e., laxity under the application of a 30 N anterior tare force) before the graft force reaches zero. Markers were injected into the tibia, femur, and graft in six cadaveric legs whose knees were reconstructed with single- loop tibialis grafts. To satisfy the first objective, legs were subjected to 1500 cycles at 1 4 Hz of 150 N anterior force transmitted at the knee. Based on marker 3D coordinates, equations were developed for determining eight causes associated with the fixations. After 1500 load cycles, plastic deformation between the graft and WasherLoc tibial fixation was the greatest cause with an average of 0.8  0.5 mm followed by plastic deformation between the graft and cross-pin-type femoral fixation with an average of 0.5  0.1 mm. The elastic deformations between the graft and tibial fixation and between the graft and femoral fixation decreased averages of 0.3  0.3 mm and 0.2  0.1 mm, respectively. The remaining four causes associated with the fixations were close to 0. To satisfy the remaining two objectives, after cyclic loading, the graft was lengthened incre- mentally while the 30 N anterior tare laxity, 150 N anterior laxity, and graft tension were measured. The one plastic cause and one elastic cause associated with the graft midsub- stance were predicted by the empirical relationships with random errors (i.e., precision) of 0.9 mm and 0.5 mm, respectively. The minimum increase in 30 N anterior tare laxity before the graft force reached zero was 5 mm. Hence, each of the eight causes of an increase in the 150 N anterior laxity associated with the fixations can be determined with RSA as long as the overall increase in the 30 N anterior tare laxity does not exceed 5 mm. However, predicting the two causes associated with the graft using empirical relationships is prone to large errors. DOI: 10.1115/1.2904897 Keywords: knee, anterior cruciate ligament graft, X-rays, laxity, lengthening, elongation Introduction Single-loop tibialis tendon allografts have increased in popular- ity owing to their many advantages over patellar tendon and double-loop hamstring tendon autografts for anterior cruciate liga- ment ACL reconstructions 1–5. Nevertheless, clinically impor- tant increases in anterior laxity occur postoperatively in 9–22% of patients following ACL reconstruction for single-looped tibialis allografts 1,3. Although the causes are unknown, increased an- terior laxity can be traced to lengthening of the graft construct i.e., graft-fixation-bone complex. To prevent clinically important increases in anterior laxity, it is of interest to determine the causes and corresponding amounts of lengthening of the graft construct because this information would be beneficial in devising measures to limit increases in anterior laxity. Lengthening of the graft construct can be due to many causes, ten of which include plastic i.e., nonrecoverable deformations and increases in elastic deformations Fig. 1. Plastic causes in- clude plastic deformation 1 between femoral fixation and bone, 2 between the graft and femoral fixation, 3 between the graft and tibial fixation, 4 between the tibial fixation and bone, and 5 of the graft substance between the fixations. Elastic causes include an increase in elastic deformations due to a decrease in elastic stiffness 6 between the femoral fixation and bone, 7 between the graft and femoral fixation, 8 between the graft and tibial fixation, 9 between the tibial fixation and bone, and 10 of the graft substance between the fixations. Hence, eight of these ten causes are associated with the fixations four plastic and four elas- tic and two are associated with the graft one plastic and one 1 Corresponding author. Contributed by the Bioengineering Division of ASME for publication in the JOUR- NAL OF BIOMECHANICAL ENGINEERING. Manuscript received January 16, 2007; final manuscript received September 19, 2007; published online May 16, 2008. Review conducted by Jeffrey A. Weiss. Journal of Biomechanical Engineering AUGUST 2008, Vol. 130 / 041002-1 Copyright © 2008 by ASME