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Computational and Mathematical Modeling of Human Knee Joints

Abstract

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Anterior cruciate ligament (ACL) reconstructive surgeries, employing a total of 48 models, were conducted by virtually removing the ACL and then modeling the surgical preparation, tunnel architecture, graft pre-tensioning and fixation angle of a bone-patellar-tendon-bone autograft. Multifactorial sensitivity analyses were performed to assess the relative influence of these surgical factors on the intraoperative joint laxity, graft-tunnel contact mechanics and graft forces. The sensitivity results indicated that the combined variation in tunnel architecture and graft pre-tension at the time of fixation accounts for most of the estimated variance of the three outcomes. Joint laxity was largely influenced by tunnel placement with a modest contribution of the pre-tensioning force. However, variations in pre-tensioning force yielded a significant effect on both the in tunnel and intra-articular graft forces. Tunnel directions played the dominant role in the expressions of the contact shear between the graft and tunnel aperture in the fully extended and reconstructed joint. Given the proposed significance of the shear mediated graft abrasion at the graft-tunnel aperture, these sensitivity results are consistent with the general observation in the Multicenter ACL Revision Study (MARS), femoral tunnel architecture is most correlated with incidences of graft failures. Tunnel direction and graft pre-tension had similar effect on the estimated variance of the contact pressure in the fully extended joint. Data derived from the 48 ACL reconstructed models indicated that the anatomic surgical design may not be the only design that recovers the healthy joint laxity. In the context of the design of prospective studies, our findings highlight the need to include the graft tension and not fixation angle at the time of fixation as a variable in the evaluation of the surgery.

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