Fig 1.
Overview of the proposed workflow.
1. The workflow starts with segmentation of MRI data to obtain subject specific anatomical geometries. 2. We developed the “Surgery Modeling” tool that utilizes Blender scripting to model the ACLR parts (drilled bones and grafts). 3. We created the “FEBio Exporter” tool to assembly subject—specific FE models of the healthy, injured and ACLR knee and to solve them using the FEBio software. 4. We adjusted graft material properties based on experimental data. 5. We developed a suitable loading profile in an effort to simulate the standard physical clinical exam of PS. 6. We performed a series of FE simulations to compare the standalone ACLR versus the combined ACLR—LET surgery techniques in terms of kinematics restoration and ACLR graft stress development.
Fig 2.
In this figure we present form left to right the developed FE models used throughout this study. A: No—ACL (injured) knee FE model. B: Native—ACL FE model. C: Standalone SB ACLR FE model. D: Combined ACLR—LET FE model.
Fig 3.
Starting from left to right and from top to bottom, we observe the applied loads on the femoral reference frame to simulate the PS movement. A posterior force of 25 N is applied up to an initial flexion angle of 10° to induce the subluxation phase. As the knee flexes, an anterior force is applied to model the reduction phase. Additionally, we apply a femur varus torque of 7 Nm and an internal femur moment of 5 Nm. These forces are implemented using sigmoid functions and are applied as the knee flexes from the initial angle of 10°. The transition point of the sigmoids is set to 25° (green vertical line). Finally, we apply a compression force to engage contact between the tibial and femoral cartilages and assist the FEBio solver. The profile is a modified version of the profile in [11].
Fig 4.
Femur projections of LTC and MTC points.
In this figure, we illustrate the estimated LTC and MTC points and their projections on the femur mesh. These points are taken at 25% and 75% of the tibia width [40]. The LTC projection on the femur (LFP) is used to measure the PTT during the PS simulation.
Fig 5.
Assessment of standalone ACLR during PS.
In this figure, we illustrate the performance of standalone ACLR in restoringITR and ATT. At the bottom we present the magnitude of ETR and PTT ranges during the PS movement using bar plots. As the graft pretension increases, both variables reduce. In both cases, the ACLR knee model exhibits greater ETR and PTT values compared to the Native—ACL model. (at): ACLR graft tension.
Fig 6.
Assessment of LET graft pretension for the combined ACLR—LET during PS.
In this figure, we depict the results for the scenario where the LET graft pretension is altered and the ACL graft tension is kept constant. We observe that increasing LET graft pretension leads to decreased ETR and PTT. However, in all cases these values are lower than the performance of the Native—ACL model. (at): ACLR graft tension. (lt): LET graft tension.
Fig 7.
Grid analysis for ACLR and LET graft pretension.
In this figure, we present the sensitivity analysis results for all combinations (ACLR tension, LET tension) between ACLR and LET graft pretension values using contour lines. These lines delineate different values of MAE between each combination and the Native—ACL model. The performance of each model is presented by a blue dot. Yellow areas demonstrate the smallest errors whereas purple areas the largest. We also highlight the best combination in terms of minimum MAE with a red star for both variables. These are the pairs (80, 5) and (110, 10) for ETR and PTT, respectively. We observe that ETR is more sensitive to LET tension as illustrated by the almost vertical alignment of the contour plot lines. On the other hand, larger values for both ACLR and LET grafts are required to reduce MAE in PTT.
Table 1.
The ten best combinations of pretension for the ACLR and LET grafts in the combined ACLR-LET surgery.
The term “best” refers to the optimal restoration of native ETR. For each pair, we also provide the corresponding LTC PTT and von Mises stress values around the femoral tunnel.