# On the Effect of Friction on Tibiofemoral Joint Kinematics
## 9 Conclusions and Future Research Directions  
This study developed a spatial dynamic methodology to investigate the effect of friction on nonlinear dynamics, vibration, wear, and creep of tibofemoral joints. A mesh density analysis was performed to end up with a fine mesh size that guarantees the accuracy of obtained outcomes. Comparing acquired results to those available in the literature also made it possible to evaluate the developed model. In conclusion, friction can considerably influence the motion and damage of TKAs. From the phase portrait diagrams, chaotic behaviors were observed in the tibofemoral movement. It was also inferred that friction-induced vibration takes place when the friction coefficient increases. Moreover, using an empirical friction model resulted in vibration occurrence. Making any changes in the magnitudes of parameters in the Stribeck friction model led to the alteration of wear rates on both condyles. Furthermore, it cannot be expected that increasing the friction coefficient can always cause wear to rise owing to the strong nonlinearities of the wear mechanism. The three wear models employed in this study to predict the wear of TKAs also produced outcomes with significant differences, which should be taken into account by designers and engineers in their designing process. Eventually, it was illustrated that friction models influenced both translational and rotational loci of tibofemoral motion, and consequently, the damage distribution. As future research directions, the proposed model can be extended to account for the dynamics of the patella-femoral joint in addition to the tibofemoral joint as well as to take fluid lubrication into account while handling fluid-structure interaction [105; 106; 107]. Moreover, the suggested approach can be utilized to optimize the design and material properties of TKAs to improve their lifetime and tribology performance, using optimization approaches such as genetic algorithm (GA) and particle swarm optimization (PSO) algorithms [108]. The friction models considered in this article are not able to capture dynamic characteristics of the friction phenomenon, e.g., pre-sliding and frictional lag. The dynamic-based friction approaches like Dahl and LuGre are to be employed accounting forthese characteristics, which can lead to much more precise outcomes than those obtained in our study. As was illustrated, increasing friction leads to friction-induced vibration that should be considered in more detail experimentally as well. In addition, the viscoelasticity of polyethylene tibial insert can be considered using more sophisticated models, namely the generalized Maxwell model, Wagner model, and Prony series [109]. The present study assumed that the geometry evolution of the polyethylene tibia owing to material loss and creep deformation does not affect the contact stresses and knee trajectory, whereby the wear magnitude varies linearly during the wear analysis. Surface evolution leads to a reduction in contact stresses over time, resulting in decreasing wear rates and creep deformation [36]. Therefore, it can be deduced that the present study overestimated linear wear rates and creep deformation, both of which are dependent on contact pressure. The presented methodology can be extended to include the surface variations of the plastic tibial insert due to the wear and creep phenomena. The improved model will address the effect of the geometry update on both contact stresses and contact point trajectory, and eventually, wear and creep. Furthermore, damage distribution was found to vary with changes in the friction coefficient of knee components. Therefore, a greater area of the polyethylene tibia can get damaged when friction increases. A future direction of this research is to consider how any alteration in the damage map can influence the performance and lifetime of TKAs. The knowledge gained through such a study can contribute to the design and material development of TKAs. Conceptualization, E.A. ; methodology, E.A. ; software, E.A. and M.S.A.