A Sagittal Plane Model of the Knee and Cruciate Ligaments With Application of a Sensitivity Analysis

Abstract

In this investigation the complex multi-bundle structure of the cruciate ligaments and their interaction with the tibiofemoral joint was modeled analytically by representing the different regions of the cruciates with ligament elements. A sensitivity analysis was then performed to describe the effect that variations of the model input parameters had on the model variables (outputs). The effect that the cruciate ligament bundles had in controlling joint kinematics was dependent on knee flexion angle, and the load applied to the tibiofemoral joint. For passive range of knee motion with the thigh in the horizontal plane (a common rehabilitation activity), all cruciate ligament bundles were strained with the joint positioned between 0 and 10 deg of knee flexion, between 10 and 50 deg only the anterior bundle of the posterior cruciate ligament A-PCL was strained, and from 50 to 90 deg both the anteromedial portion of the anterior cruciate ligament A-ACL and the A-PCL were strained. This finding indicates that a strain distribution about a transverse cross section of the cruciates exists, and demonstrates the importance of differentiating between the strained and unstrained (unloaded) states of these ligaments. The strain value of a cruciate ligament bundle was an indication of how the bundle controls joint kinematics, while the unstrained values describe how much the ligament bundle must deform before it becomes strained and a restraint to tibiofemoral joint motion. In response to anterior and posterior directed loads, applied parallel to the tibial plateau, the respective, ACL and PCL load values were larger in magnitude. The sensitivity of the model outputs to the input parameters was highly dependent on knee flexion angle. The geometrical input parameters of the model (including the ligament insertion site locations and articular surface geometry) had the most pronounced effect on the model output quantities, while the stiffness and initial strain conditions of the ligament bundles had less of an effect on the model outputs. When loaded, the strain values of the ligament bundles were sensitive to the ligament insertion site position. The greatest sensitivity of the model outputs was the femoral insertion of the ACL; supporting clinical impressions and previous experimental findings. Changes in the anterior-posterior dimension of the femoral articular surface did not produce a substantial effect on the model outputs, while changes in the proximal-distal dimension created a large effect; similar results were found for the tibial surface dimensions. These findings indicate that rigid body contact between the articular surfaces may not be a realistic assumption particularly with application to the prediction of tibiofemoral compressive loading and the force/strain values of the cruciate ligament elements. This also has important implications for the design and clinical application of total knee replacements (that function as rigid bodies), particularly those that spare the PCL.

The Geometry of the Tibial Plateau and Its Influence on the Biomechanics of the Tibiofemoral Joint

“…T he articular surfaces of the tibiofemoral joint in combination with the primary ligaments play an important role in controlling the biomechanical behavior of the joint 1,2 . In particular, the contact mechanics between the femoral and tibial articular surfaces are complex, are threedimensional, and consist of many unique features.…”

Experimental Evaluation of 3-Dimensional Kinematic Behavior of the Cruciate Ligaments

“…A large number of the studies that we analyzed presented a standard movement similar to ours, ie, constant and decreasing, 13,22,23 although sometimes with small variations, such as in the study of Horwitz 15 who reported a small initial increase (0°-30°) followed by the relaxing of the fibers up to the 90° flexion. As a counterpoint, other researchers, such as Penner et al, 12 have presented results totally contrary to those presented in our study and indicate an average increase of 8.1 mm in the total length of the posterior fiber bundle of the ACL, which has been supported by researchers such as Crowninshield et al 7 who also described a constant elongation of these fibers during flexion.…”

“…Crowninshield et al 7 and Makris et al 25 found that the most anterior portion of the cruciate ligament does not undergo much length change, while Kurosawa et al 30 found a slight slackening of the fibers at the end of flexion (60° to 90°). Fox et al 28 found the highest resistance at 60°, while Beynnon et al 22 and Li et al 23 found a tensioning of the ligament in its totality. Inderster et al, 24 when studying this fiber bundle, found a length variation of 6.3 mm in total length (0° to 90° of flexion), divided into 2.7 mm from 0° to 30°, 2.1 mm from 30° to 60°, and 1.5 mm from 60° to 90°.…”

“…Researchers who agree with the standards indicated by our results for these fiber bundles are Crowninshield et al 7 and Shelburne & Pandy, 27 although the latter reported a slight slackening of the fibers in the 30°-to-60° angular moment, and Fox et al 28 and Li et al 23 found a maximum tension of the bundle at 90°. On the other hand Kurosawa et al 29,30 described a slackening of the fibers in the most posterior positions, while Beynnon et al 22 reported a slackening of the fibers as a unit during knee flexion, and Amis et al 31 reported that the posterolateral and posteromedial structures tighten as the knee extends. Harner et al 32,33 indicated that this bundle plays an important role in joint stabilization after PCL reconstruction.…”

Mechanoactive Scaffold Induces Tendon Remodeling and Expression of Fibrocartilage Markers

“…Allografts are also used for ACL reconstruction [22,28], with the tibialis and Achilles tendons being the most common [22,24,49,50,57,62]. The long-term performance of ACL grafts depends on several factors, including the structural and material properties of the graft, the initial graft tension [6,7,15,16,21], the intraarticular position of the graft [37,42], and graft fixation [33,53]. Increased emphasis has been placed on graft fixation since postsurgical rehabilitation regimens require the immediate ability to regain the full range of motion, reestablish neuromuscular function, and bear weight [10,54].…”