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The dynamics of the masticatory system discloses the mutual relationship between the mandibular movement and the applied muscular forces subject to passive restraints and morphological features; and dynamic studies rely on the models established in two aspects, the kinematics and the kinetics, contained in the simulation [92].

2.2.1 Dynamic Model of the Masticatory System

Instead of the diversity in the descriptions of the jaw movement, the dynamic model firstly proposed by Koolstra and van Eijden [93] has been built with a similarly ubiquitous construction, which lays a theoretical basis for extensive simulations incorporating muscular forces. The model is composed of a mandible bone considered as a rigid-body; the muscular forces located anatomically, the reaction force from joints and passive components as the movement restraints in the model.

Figure 2-12 Ventro-lateral view of masticatory system [55]

The involved components play a crucial role in the course of model building, lying in not only their morphology, but also the anatomical definition in the model such as the location and orientation, the physiological length, and the PCSA size, which have be acquired by 3D reconstruction of sliced CT images or the direct measurement on a cadaver [92]. The mandible bone is generally simplified to a mass point standing on the center of gravity; its geometry is not so critical as the physical properties that seldom engaged in the simulations; apart from the reconstructed jaw, a polynomial has been created via an iteration to represent the geometry mathematically with the satisfaction of the assigned physical properties [94-96]. Muscles as the dominant actuation involved in the mastication are replaced by one string or a pinnate group in the model along the lines of action that depends on the fan-shaped area; though more than 20 muscle portions participate independently in the mandibular movement, only dominant ones are contained in the model, as shown in Figure 2-12 [96]. The muscular force whose magnitude is configured as the computational variable representing its contraction is estimated in two ways: by the general Hill-type muscular model that correlates the force with activation level plus the sarcomere length, or by distributing the assigned resultant force proportionally to the PCSA of each muscle portion [97, 98]. Muscles denoted in Figure 2-12 can be referred to the literature [55]. Passive components that include the damped structures such as the ligament, cartilaginous disc and the passive muscular forces were not incorporated in the dynamic model initially, but have been accrued in the subsequent studies to investigate the affection to the overall movement. The ligament was included to prevent the jaw from dislocation, behaving as a boundary limit, so was the passive

muscular force that was occasionally recruited but only shown some affection at the largest gape [57].

The mandible is initiated to move subject to the forces and the consequent torques along kinematic definitions in most studies that are given with the guidance against the condyle and morphological constraints. There is no distinct evidence to demonstrate the proportion of contribution from each pair of active muscle to a specific jaw movement, but preliminary study shows that the muscular force has been testified to be minimized or consistent with the minimization of joint loads during the jaw movement [99].

2.2.2 Chewing Force

Muscle force is the dominant motivator to actuate the jaw, while the gravity and TMJ ligaments only take limited part in the mandibular movement, e.g. in the opening phase; so the muscular force exerted in various jaw movements overcomes the resistance from the passive forces of the other group of muscles or the food corresponding to unloaded or loaded circumstance, and should also be restrained within a certain value to avoid too much force damaging the periodontal tissues. Studies that examined the passive resistance of the jaw focused only on the natural opening path and showed that a low resultant force of 5–10 N was sufficient to sustain a wide gape. Values of 15–25 N were necessary to reach maximal displacement [95, 100, 101].

The chewing force has been measured quantitatively amid several studies involving in-vivo trials; the teeth exert chewing force spatially on the food, and the magnitude displays a large variation over these researches, which can be ascribed to the difference of implementing scenarios, such as the position of the sensor and the type of food. Generally, chewing food like biscuits and carrots exerts force about 70-150N on a single tooth [102], while the total bite force at occlusion was given within 190-260N, although the maximal force has been measured up to the range of 500-700N on molars, which occurs in the process of the gosis or grinding teeth to sharpen the cusps [103]. Latest researches on the chewing food in terms of the different factors are not included in the section; but factors that escalate the bite force have been concluded to five criteria, and the magnitude of the force is differentiated spread to the every single tooth. The force on the incisor accounts for 40% and 47% of the force at the molars for biting and chewing respectively [104]. This also explains the distinctive mechanical advantage possessed by the incisors and molars.