A three-dimensional mathematical model of temporomandibular joint loading

Abstract 

Objective. A mathematical model of the temporomandibular joint was developed to study the magnitude and direction of the compressive loading experienced at the temporomandibular joint during clenching.

Design. The model was based on the principles of static equilibrium in three dimensions.

Background. Direct measurement of temporomandibular joint loading in humans is extremely difficult. Animal models have provided an alternative in the past. However, evidence suggests that primates are not the most accurate human analogues for temporomandibular joint studies. A mathematical model was used as an alternative to direct measurement.

Methods. The EMG activity of two masticatory muscles was combined with their cross-sectional areas to calculate the force exerted by each muscle. Experimentally determined forces were implemented into a quadratic programming model to solve for the compressive forces on the joint. Two objective functions were chosen and their ability to predict muscle and joint forces was evaluated.

Results. The maximum bite forces for normal men, normal women, and women with temporomandibular joint disorders were 300 N (SD 102 N), 210 N (SD 57.7 N), and 120 N (SD 77.1 N), respectively. The calculated joint force for normal males was 260 N (SD 84.1 N). Normal females and female temporomandibular joint disorder patients produced temporomandibular joint forces of 172 N (SD 37.5 N) and 152 N (SD 44.2 N), respectively.

Relevance

Over 10 million Americans suffer from disorders/diseases affecting the temporomandibular joints. It is important to know the magnitude of joint loading for treatment and prevention of temporomandibular joint disorders. This work is of interest to clinicians treating temporomandibular joint disorders and for designing artificial temporomandibular joints.

Keywords:  Biomechanics, Temporomandibular joint, TMJ loading, Optimization, Static 3D model