Recent work on anatomical face modeling focuses mainly on facial muscles and their activation. This paper considers a different aspect of anatomical face modeling: kinematic modeling of the jaw, i.e., the temporomandibular joint (TMJ). Previous work often relies on simple models of jaw kinematics, even though the actual physiological behavior of the TMJ is quite complex, allowing not only for mouth opening, but also for some amount of sideways (lateral) and front-to-back (protrusion) motions. Fortuitously, the TMJ is the only joint whose kinematics can be accurately measured with optical methods, because the bones of the lower and upper jaw are rigidly connected to the lower and upper teeth. We construct a person-specific jaw kinematic model by asking an actor to exercise the entire range of motion of the jaw while keeping the lips open so that the teeth are at least partially visible. This performance is recorded with three calibrated cameras. We obtain highly accurate 3D models of the teeth with a standard dental scanner and use these models to reconstruct the rigid body trajectories of the teeth from the videos (markerless tracking). The relative rigid transformations samples between the lower and upper teeth are mapped to the Lie algebra of rigid body motions in order to linearize the rotational motion. Our main contribution is to fit these samples with a three-dimensional nonlinear model parameterizing the entire range of motion of the TMJ. We show that standard principal component analysis (PCA) fails to capture the nonlinear trajectories of the moving mandible. However, we found these nonlinearities can be captured with a special modification of autoencoder neural networks known as nonlinear PCA. By mapping back to the Lie group of rigid transformations, we obtain a parametrization of the jaw kinematics which provides an intuitive interface allowing the animators to explore realistic jaw motions in a user-friendly way.
The mechanical function of the jaw has been studied in biomechanics, often using full six degrees of freedom for the rigid body motion of the jaw relative to the skull @cite_34 , even though reduced models were also considered, e.g., @cite_17 who proposed a planar constraint along which the condyles can slide, resulting in four degrees of freedom. A simulation platform can be used to create computational models using variables for modeling gravity, external forces, and jaw muscle activity @cite_8 . These models were shown to be capable of predicting jaw movements for mundane, but complex actions like chewing @cite_9 or post-reconstruction surgery @cite_8 .
@cite_8 @cite_9 @cite_34 @cite_17
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Statement of problem Composite mandibular resection resulting in mandibular discontinuity can alter jaw motion, occlusal forces, and mastication, whether or not the jaw is reconstructed. The biomechanical events associated with these changes are difficult to assess clinically and, therefore, are not well documented or researched. Purpose The purpose of this study was to model movements of a mandible with a discontinuity defect, and to compare them to movements of a mandible with its continuity restored by alloplastic reconstruction. Material and methods Computational models were created with a novel simulation platform. The variables designed into the models included gravity, external forces, and jaw muscle activity. Each jaw was observed at rest, when opened by external force or by muscle drive, and during the generation of unilateral occlusal force on the nonoperated side. Scarring was simulated with springlike forces. Outputs included individual muscle forces and torques, as well as mandibular incisor and condylar motions. Results Both models displayed plausible resting postures, and jaw opening with deviation toward the defect side when scarring was simulated. Opening caused by downward force on the incisors differed from that due to muscle activation. Jaw rotations during unilateral molar contact on the unaffected side were muscle specific and influenced by mandibular discontinuity. Conclusions Plausible jaw movements after hemimandibulectomy and or alloplastic reconstruction could be predicted by dynamic modeling. The effect of soft tissue forces on jaw posture and movements varied with the condylar support available. In both models, different opening trajectories were produced by external force on the jaw and by jaw muscle activation. Mandibular rotation during unilateral molar contact depended on which muscles were activated, and the availability of bilateral condylar support. Abstract Our understanding of human jaw biomechanics has been enhanced by computational modelling, but comparatively few studies have addressed the dynamics of chewing. Consequently, ambiguities remain regarding predicted jaw-gapes and forces on the mandibular condyles. Here, we used a new platform to simulate unilateral chewing. The model, based on a previous study, included curvilinear articular guidance, a mobile hyoid apparatus, and a compressible food bolus. Muscles were represented by Hill-type actuators with drive profiles tuned to produce target jaw and hyoid movements. The cycle duration was 732 ms. At maximum gape, the lower incisor-point was 20.1 mm down, 5.8 mm posterior, and 2.3 mm lateral to its initial, tooth-contact position. Its maximum laterodeviation to the working-side during closing was 6.1 mm, at which time the bolus was struck. The hyoid's movement, completed by the end of jaw-opening, was 3.4 mm upward and 1.6 mm forward. The mandibular condyles moved asymmetrically. Their compressive loads were low during opening, slightly higher on the working-side at bolus-collapse, and highest bilaterally when the teeth contacted. The model's movements and the directions of its condylar forces were consistent with experimental observations, resolving seeming discordances in previous simulations. Its inclusion of hyoid dynamics is a step towards modelling mastication. In this review, the movement characteristics of the human masticatory system are discussed from a biomechanical perspective. The discussion is based upon the three fundamental laws of mechanics applied to the various anatomical structures that are part of the masticatory system. An analysis of the forces and torques applied to the mandible by muscles, joints, articular capsules, and teeth is used to assess the determinants of jaw movement. The principle of relating the interplay of forces to the center of gravity of the lower jaw, in contrast to a hinge axis near its joints, is introduced. It is evident that the muscles are the dominant determinants of jaw movement. The contributions of the individual muscles to jaw movements can be derived from the orientation of their lines of action with respect to the center of gravity of the lower jaw. They cause the jaw to accelerate with six degrees of freedom. The ratio between linear and angular accelerations is subtly dependent on the mass and moments of inertia... Abstract Mandibular distraction osteogenesis will lead to a change in muscle coordination and load transfer to the temporomandibular joints (TMJ). The objective of this work is to present and validate a rigid-body musculo-skelet al model of the mandible based on inverse dynamics for calculation of the muscle activations, muscle forces and TMJ reaction forces for different types of clenching tasks and dynamic tasks. This approach is validated on a symmetric mandible model and an application will be presented where the TMJ reaction forces during unilateral clenching are estimated for a virtual distraction patient with a shortened left ramus. The mandible model consists of 2 rigid segments and has 4 degrees-of-freedom. The model was equipped with 24 hill-type musculotendon actuators. During the validation experiment one subject was asked to do several tasks while measuring EMG activity, bite force and kinematics. The bite force and kinematics were used as input for the simulations of the same tasks after which the estimated muscle activities were compared with the measured muscle activities. This resulted in an average correlation coefficient of 0.580 and an average of the Mean Absolute Error of 0.109. The virtual distraction model showed a large difference in the TMJ reaction forces between left and right compared with the symmetric model for the same loading case. The present work is a step in the direction of building patient-specific mandible models, which can assess the mechanical effects on the TMJ before mandibular distraction osteogenesis surgery.