# A Critical Review of Human Jaw Biomechanical Modeling
## 4 Discussion
[103] involved the following muscle contributions per side--the masseter (deep and superficial), temporalis (anterior, middle and posterior), medial pterygoid, lateral pterygoid (inferior and superior), digastric and mydibyoid (anterior and posterior) --according to [PERSON]'s theory [121]. Furthermore, the temporomandibular ligaments were considered spring elements [122]. The center of rotation was thus estimated using ArtiSynth software, determining that the motion was well described by pure rotation, although it was variable during the opening and closing tasks mainly around the condyle and the mandibular ramus. [PERSON] et al. [104], adopting the same muscles as [PERSON] et al. [101] and using [PERSON]'s theory for both active and passive forces [123], together with the viscoelastic behavior of the articular disk [124], calculated the stress-strain field of the TMJ, noting that the most loaded zone was the articular disk, which had the highest stress at the instant of the maximum mastication force. Lastly, the activation pattern of the lateral pterygoid muscle strongly influenced the biomechanical response of the mandible. [PERSON] and [PERSON] [105] validated a custom-made endoprosthesis made of Titanium Grade V realized to correct mandibular defects. By fixing the cordyles in all three directions and by involving the muscular forces of the masseter, temporalis and lateral and medial pterygoid and different biting loads in diverse tooth positions [125], they analyzed the stress-strain regime of the coupling of the mandible-prosthesis. The great similarity of the stress/strain field with respect to the intact mandible and strain values promoting bone health confirmed the reliability of the apparatus. [PERSON] et al. [106] investigated two kinds of meshing surfaces, parametric and triangular ones. A CT image was meshed according to these two techniques and successively imported into FEM tools. In this environment, after the definition of the bone's mechanical properties, the constraints and loads were applied. In this analysis, the cordyles were fixed in the three directions of translation, whereas the muscle forces, referring to the masseter, temporal (anterior and posterior), depressor and medial and lateral pterygoid, were represented as springs with no resistance [126]. Overall, the authors stated that the best choice was the triangular mesh due to the complexity of oral human apparatus. [PERSON] et al. [107] introduced a novel musculoskeletal model in the AnyBody tool, also contemplating the presence of kinematic joints, considering their degrees of freedom (DOFs). In further detail, Equation (1) was rewritten as:  
\[\left\{ \begin{array}{l}\Phi(q,t)=0\\ \Phi^{FDK}(q,t)-\alpha^{FDK}(q,t)=0\end{array} \right\} \tag{19}\]  
where \(\alpha^{FDK}\) represents the new DOFs whose dynamics can be neglected since their small range of movement. Equally, the authors proposed a division between hard constraints,which must be solved, and soft constraints, which should be solved as much as possible. This division arises from the greater number of experimentally measured DOFs with respect to the modeled ones. This idea thus determines the definition of an optimization problem for a specific scalar objective function (for example, the weighted least square). Successively, the inverse dynamics can be analyzed, for which the muscular, joint and residual forces \(F^{FDK}\) are calculated. The algorithm, based on a Newton-Raphson-based approach augmented with a golden section line, is stopped when the value of \(a^{FDK}\) makes these forces 0. In conclusion, the ligaments were also included as three non-linear line elements. The comparison with the experimental data confirmed good agreement concerning the kinematics but not for the joint forces, hence why this approach needs further future improvements. [PERSON] et al. (2018) evaluated the strain regime of a patient subjected to hemimandibulectomy 2.5 years after their first resection.