# A Critical Review of Human Jaw Biomechanical Modeling
## 4 Discussion
The study was conducted by applying rigid constraints corresponding to the TMJ and muscular forces as distributed loads over the attachments in proximity to the masseter (superficial and deep), temporal (frontal, middle and posterior), medial and lateral pterygoid and digastric muscles and the right first molar tooth. They found that the mandible biomechanics after resection is negatively influenced by muscular activity, especially for subjects in good clinical condition. [PERSON] et al. (2019) evaluated the kinematics of the mandible in order to fix obstructive sleep apnea. Starting with image analysis, achieved using a 3D Vicon system coupled with four cameras, the jaw movements were recorded. By imposing five degrees of freedom, divided into rigid assumptions for both condyles and the incisors (3) and the condyle movements in the glenoid fossa (2), an iterative process was conducted to calculate the position of any point on the human jaw. Finally, the realized 3D model provided more reliable results compared to a 2D model. [PERSON] et al. (2019) considered the muscular forces of the masseter (deep and superficial), temporalis (anterior, middle, posterior) and medial and inferior lateral pterygoid (2017) in three directions, localized in the patched areas on the outer surface of the cortical shell (2018) of the mandible. Moreover, the soft tissue layers in proximity to the articular condyle were applied using two blocks, permitting displacements and rotations and providing support to the apparatus at the same time. The simulations highlighted that, as expected, the presence of a tumor induces higher stress and strains, likely causing pathological fractures during daily activities, like eating. [PERSON] et al. (2022) proposed an interesting model in 2022, combining both inverse and forward dynamics: EMG activities and the maxillary plate landmarks acted as the input variables to obtain the activation function and the position of any point on the jaw. Furthermore, 24 muscles (temporalis, masseter, pterygoid and digastric) were considered in accordance with [PERSON]'s theory, whose insertion was achieved using a non-rigid iterative closest point algorithm (NICP). Two proportional, integral, and derivative (PID) controllers were applied in order to monitor the potential errors in the posterior temporalis and pterygoid muscles' length and that of the jaw-opening muscles. In conclusion, inverse-forward dynamics simulation was carried out (Equation (5)), taking into account also the effect of the fibrous capsule and the TMJ ligaments. The simulations showed unintentional movements of head-neck coupling, together with the activation profiles of the jaw-opening and lateral pterygoid muscles. Lastly, [PERSON] et al. (2022) proposed an in silico model developed in the ArtiSynth environment taking into consideration the bones as rigid bodies; the muscles (massetter, temporalis, pterygoid, phylohyoid, geniohyoid, digastric) as actuators, in accordance with [PERSON]'s theory, and the TMJ, composed of the articular disk and ligaments, as made up of elastic contact layers (2019). Moreover, the algorithm satisfied following next equation:  
\[\min_{a}\left(w_{v}\phi_{v}(a)+\frac{w_{a}}{2}a^{\prime}a+\frac{w_{d}}{2}|a_{ i-1}\,-\,a|^{2}\right)\ 0\leq a\leq 1 \tag{20}\]\(\Phi_{\rm v}\) is the quadratic optimization function between a movement goal and the motion activated by the muscles (motion tracking error). \(\rm W_{v}\), \(\rm w_{a}\), \(\rm w_{d}\) represent specific weights and \(a\) the vector of the muscle activations. The condyle displacement range on both the chewing and non-chewing sides, with the von Mises stress in the order of 0.5-2 MPa, was calculated for different bolus positions, sizes and stiffness values, noting that the latter had a significant influence on the mandibular joint only in terms of its size and stiffness. On the whole, the bond between medicine and engineering is more and more clear in the dental field [130,131].