# A Critical Review of Human Jaw Biomechanical Modeling
## 4 Discussion  
One of the first models of jaw mechanics was offered by the duo [PERSON] and [PERSON] [91] in 1990, concerning unilateral clenching on an acrylic shim and natural teeth. Their approach was founded, during an isometric regime, on the equilibrium theory of both translations and rotations among the muscular and reaction forces, explicated according to the condyle and tooth resistances. The first followed the analytical relationship indicated in (10), whereas the last two were the unknown variables. \[F_{M}=[X_{M}\cdot K]\cdot EMG_{M} \tag{10}\]  
in which \(X_{M}\) is the cross-sectional diameter of the muscle and \(K\) [N/m\({}^{2}\)] a constant [113]. Their product provides the weighting factor, whereas \(EMG_{M}\) represents the scaling factor, indicating the ratio of muscle contraction with respect to its maximum response. They noted that the two structures affected differently the load distribution, which was in the range of 100-400 N, and that when the occlusal load moved toward it, the balancing side suffered more than working side for natural teeth, with the opposite for the acrylic resin shim. [PERSON] and [PERSON] [92] analyzed the mandible biomechanics according to dynamic analysis with the aim of establishing the reaction forces at the condyle sites. To achieve this, the model, explicated in the sagittal and coronal planes, was based again on the mechanical equilibrium principle between the muscular and condylar forces on the working and balancing sides and the biting forces involved in the vertical and rotation movements. On the contrary, the former forces, involving the masmeter, medial and superior lateral pterygoid muscles and temporalis, were considered as a percentage of the biting forces. Analogously, the reaction forces, conveniently scaled on the coronal and sagittal planes using, respectively, asymmetry and activity indexes, were calculated as the percentage of the bite force determined using electromyography. The results showed that the balancing-side joint is not always loaded more than the corresponding working-side joint. [PERSON] and [PERSON] [93] studied the evolution of the muscular length, velocity and force during the opening and the closing of the mouth. This actuation is determined by the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Number** & **Authors** & **Title** & **Kind of Analysis** & **Aim** & **Year** \\ \hline \multirow{4}{*}{18} & \multirow{4}{*}{[PERSON] et al. [108]} & \multicolumn{3}{c}{Mandibular biomechanics after} & \multirow{4}{*}{Finite element} & \multirow{4}{*}{Investigation of mandibular biomechanics after marginal} \\  & & & & & \\  & & & & \\  & & & & & \\  & & & & & \\
19 & & & & & \\  & & & & & \\  & & & & & \\  & & & & & \\  & & & & & \\
20 & & & & & \\  & & & & & \\
21 & & & & & \\  & & & & & \\  & & & & & \\  & & & & & \\  & & & & & \\
22 & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._sarcomere's involvement, whose length (\(L_{s}(t)\)) was approximated by the authors using the following law:  
\[L_{s}(t)=\left[L_{m}(t)-(L_{mi}-L_{fi})\right]\cdot\left(\frac{L_{si}}{L_{fi}}\right) \tag{11}\]  
where \(L_{m}(t)\) is the muscle length at the instant of time \(t\), \(L_{mi}\) and \(L_{fi}\) the initial muscle and fiber lengths and \(L_{si}\) the initial sarcomere length. The force, therefore, can be obtained as a cubic expression as follows:  
\[F_{L}=0.4128L_{s}(t)^{3}-4.3957L_{s}(t)^{2}+14.8003L_{s}(t)-15.0515 \tag{12}\]  
in which \(F_{L}\) is the force-length factor representing the instantaneous isometric force as a fraction of the maximum force. On the other hand, the relationship with the sarcomere's shortening velocity (\(V_{s}(t)\)) is indicated in (13):  
\[F_{V}=\left\{ \begin{array}{ll}\frac{12.5-(V_{s}(t)/2.73)}{12.5+(V_{s}(t)/0.49 )}&V_{s}(t)\geq 0\\ 1.5-0.5\cdot\left\{\frac{12.5+V_{s}(t)/2.73}{12.5-2(V_{s}(t)/0.49)}\right\}&V _{s}(t)<0\end{array}