ForPatient 1, the FE-model predictions showed a decrease in FCD content near the cartilage lesion, near the surface of the tibial cartilage in models driven by absolute maximum shear strain and deviatoric strain criteria (Fig 7.9a). Using the fluid velocity mechanism, FCD loss was predicted around the chondral lesion (Fig 7.9a).
Around the cartilage lesion, both the T2 and T1ρ relaxation times more than doubled between 1- and 3-year follow-up times. For Patient 2, the FE-model predicted minor FCD losses mainly in the medial and lateral tibial compartments when using absolute maximum shear and deviatoric strain driven degeneration mechanisms (Fig. 7.9b). T2 and T1ρ relaxation times were also only slightly increased in the same compartments. Using the fluid velocity mechanism in the FE model, minor FCD loss was predicted around the defect in the femoral cartilage (Fig. 7.9b).
Figure 7.9: Predicted FCD loss as a result of absolute maximum shear strains, deviatoric strain, fluid velocity and T2and T1ρ sagittal slices near cartilage defects for (a)Patient 1and (b)Patient 2.
Figure 7.10 shows the total volumes susceptible to OA identified by the FE models and the volumes of increased T2 and T1ρ relaxation times. For Patient 1, decreased FCD content near the cartilage lesion was predicted using absolute maximum shear strain (∼9%), deviatoric strain (∼6.5%) and fluid velocity (∼2%) mechanisms (Fig. 7.10a). This results was supported by increased T2 and T1ρ
relaxation times in ∼16% and ∼17% of the tibial cartilage volume, near the cartilage lesion. The FE models did not predict any decrease in FCD content in the medial tibial cartilage, in agreement with T2 and T1ρ follow-up information. In both the medial and lateral femoral cartilage the FE models did not predict any FCD loss, despite increasedT2andT1ρin∼3.5% and∼5% of the volumes.
For Patient 2, the analysis revealed decreased FCD content in the medial and lateral tibial cartilage using absolute maximum shear and deviatoric strain criteria (∼3.5% and∼0.5%, respectively). T2andT1ρ relaxation times indicated only minor degeneration on lateral tibial cartilage in∼2% of the volumes. On the other hand, high T2 and T1ρ relaxation time values were seen in ∼7% of the medial cartilage volume, while FCD loss was only predicted in∼2.5% of the volume. FCD loss was predicted in the lateral femoral cartilage compartment, around the cartilage lesion, using fluid velocity mechanisms in∼0.2% of the total cartilage volume (Fig. 7.10b).
T2andT1ρrelaxation time values were also increased in only∼0.75% of the cartilage volume and were mainly seen around the cartilage lesion. Despite increasedT2and T1ρin∼1% of the medial femoral cartilage, no FCD loss was predicted.
Figure 7.10: Degenerated volumes predicted by the FE model (absolute maximum shear strain, deviatoric strain and fluid velocity) and measured from MRI follow-up (T2and T1ρ) as a percentage of the entire cartilage volume. The volumes were calculated for the lateral and medial tibial and femoral cartilage forPatient 1(a) and Patient 2(b).
8 Discussion
8.1 MOTION IMPLEMENTATION METHODS FOR FE MODELS In most of the analyzed parameters, differences between the models were small.
Particularly, varus-valgus rotation, translations and cartilage responses in each model were highly similar (see Figs. 7.1-7.4, and the the original publication in Appendix). Even though the axial (distal-proximal) joint reaction force was at maximum 0.6 BW different between ModelAand ModelC, the average maximum principal stress, logarithmic strain and pore pressure of cartilage at the lateral tibial contact area were similar in all models, independent of the motion implementation.
In addition, differences in these parameters between the models were observed in the medial joint compartment only at around 10-30% of the stance, while during the last 70% of the stance the differences between the models were nearly negligible (see Fig. 7.3). The differences were mainly caused by the internal-external rotations and contact areas between the four models.
Furthermore, differences in the joint reaction forces between kinetic (with patella) and kinetic-kinematic (without patella) driven models could be minimized by adding an additional force component to estimate the effects of patella and quadriceps forces (ModelD).
We cannot conclude whether moment or rotation is better to drive the FE models, especially since both methods produced results that are within the range of values presented in the literature (Fig. 7.1 and original publication in Appendix). The moment scaling (i.e. assumed absorption of forces by muscles) may influence the results [207, 209]. On the other hand, measurement uncertainties from motion analysis, such as skin marker movement and cross-talk, may affect the accuracy of the rotation measurements [235–237]. For varus-valgus rotation, all models behaved almost identically. This was due to the fact that all models had the same ligament prestrain and stiffness, and ligaments have been suggested to have a significant role in varus-valgus rotation [86, 299, 300].
These results suggest that the simple kinetic-kinematic model (ModelC) would be sufficient when only studying the tibiofemoral joint. Adding the anterior-posterior component of the quadriceps force to the anterior-posterior component of the translational force in Model D, we obtained the same joint reaction forces as in Models Aand B. This approach may offer a simple and fast solution for modeling the effect of the patella on the tibiofemoral joint. A better solution, though more time-consuming, might be to estimate the patello-femoral joint force using for example musculoskeletal modeling [16, 140, 192, 294, 295], and implement it directly into the femoral reference point in ModelC.
Generation and simulation of the complex models required ∼10 times more time than the simpler models. Adding the patella, tendons and patello-femoral ligaments increased mainly the time needed for the FE models to converge. This is because the added contact interactions, constraints and boundary conditions forced us to refine meshes several times and to find optimal convergence parameters, introducing additional work. However, the general trend in time needed to
generate and simulate these kinds of models would remain the same. Therefore, Model C is best suited for rapid assessment of the OA susceptibility in the tibiofemoral knee joint. For rapid evaluation the patellofemoral knee joint, a modified version of ModelsAorB that include the contribution of the hamstring muscle is needed [16, 140, 192, 294, 295], especially since the patellofemoral joint forces and kinematics were within literature limits.
8.2 FE MODEL PREDICTIONS AND MRI RELAXATION TIMES