# On the Effect of Friction on Tibiofemoral Joint Kinematics
## 8 Results and Discussion
### Dynamics and Tribology of the Joint  
The developed model is employed to compute linear and volumetric wear rates for one million cycles while using three available wear techniques that are listed in Table 2. The outcomes that are obtained for all seven friction models listed in Table 1 are reported in Table 5. The highest values of both linear and volumetric wear rates are reported employing Method \(i\) with a constant wear factor of 2.2 \(\times\) 10\({}^{-16}\) mm\({}^{3}\)N\({}^{-1}\)m [36]. Using the wear factor suggested by [PERSON] et al. [93], that is called Method \(ii\), gives less wear depth on the medial conodyle than that on the lateral one, which opposes the outcomes associated with the other two methodologies. The wear values resulted from Method \(iii\), associated with the concept presented by [PERSON] et al. [77] in which wear coefficient is considered instead of wear factor, stand between those from Method \(i\) and Method \(ii\). As can be seen from Table 5, the highest wear values are obtained using the friction models A\({}_{1}\) and C\({}_{1}\), while the lowest amounts are related to those acquired from A\({}_{3}\). Considerable variations in obtained wear rates are observed while using these three models. Hence, it can be concluded that care should be taken to estimate wear in terms of the wear model that one employs. The wear map and distribution obtained from the following four friction models, i.e., A\({}_{1}\), A\({}_{3}\), B\({}_{1}\), and C\({}_{1}\), considered in this article are illustrated in Figure 4. It can be observed that the maximum wear on the lateral conodyle is shifted from the tibial plateau to the lateral periphery of the joint when using model B\({}_{1}\). Moreover, the area undergoing high material losses on the medial conodyle splits into two sub-areas in Figure 4b while lower linear wear rates are observed when using the model B\({}_{1}\) compared to the others. The maximum medial conodyle wear rates are obtained once model A\({}_{1}\) is utilized as can be observed from the intense red color of the wear map. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Study**} & \multirow{2}{*}{**Study Type**} & \multirow{2}{*}{**Wear Depth mm/5 mc**} & \multicolumn{2}{c}{**Volumetric Wear**} & **Damage Depth** \\  & & & **mm\({}^{3}\)/mc** & **(mm/5 mc)** \\ \hline Present study & Numerical & 0.50 \({}^{1}\)/0.43 \({}^{2}\) & 8.8 \({}^{3}\)/6.8 \({}^{4}\) & 0.8 \\ [PERSON] et al. [36] & Numerical & 0.5 \({}^{1}\)/0.5 \({}^{2}\) & & 0.9 \\ [PERSON] et al. [75] & Exp./Numerical & 0.44 \({}^{1}\)/0.43 \({}^{2}\) & 7.8–8.5 & \\ [PERSON] et al. [77] & Numerical & 5.7–6.0 \({}^{*}\)/8.3–8.7 ** & \\ [PERSON] et al. [99] & Retrieval & 0.50 (0.10 mm/mc) & & \\ [PERSON] et al. [100] & Retrievals & 0.64 (0.13 mm/mc) & & \\ [PERSON] et al. [76] & Numerical & 0.37 \({}^{1}\)/0.35 \({}^{2}\) & 7.0 & 0.9 \\ [PERSON] et al. [101] & Experimental & & 8.6 \({}^{*}\)/15.9 ** & \\ [PERSON] et al. [102] & Retrievals & & 0.8 \\ \hline \hline \end{tabular} \({}^{1}\) medial conodyle; \({}^{2}\) lateral conodyle, \({}^{3}\) Method \(i\); \({}^{4}\) Method \(iii\); \({}^{*}\) Intermediate kinematic input; ** High kinematic inputs.  
\end{table} 
Table 4: Comparison of wear outcomes with those available in the literature. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & \multicolumn{2}{c}{**Method \(i\)1**} & \multicolumn{2}{c}{**Method \(ii\)2**} & \multicolumn{2}{c}{**Method \(iii\)3**} \\ \hline  & **W.D. ** & **V.W. ** & **W.D. ** & **V.W. ** & **W.D. ** & **V.W.