A clinically friendly viscoelastic finite element analysis model of the mandible with Herbst appliance

As a powerful numerical approximation tool, finite element analysis (FEA) has been widely used to predict stress and strain distributions in facial bones generated by orthodontic appliances. Previous FEA models were constructed on the basis of a linear elastic phase of the bone response (eg, elastic bone strains to loading). However, what is more useful for clinical understanding would be predicting long-term strains and displacements of bone-segments responding to loading, yet tissue responses are (1) not promptly observable and (2) hard to predict in nature.

Viscoelastic property of the mandibular bone was incorporated into FEA models to visualize long-term, time-dependent stress and strain patterns in the mandible after being exposed to orthopedic stress. A mandible under loading by a Herbst appliance was modeled, and outcomes of the constructed elastic and viscoelastic models were compared.

Patterns and magnitudes of the displacement throughout the mandible predicted by the viscoelastic model were exhibited in accordance with previous clinical outcomes of Herbst appliance therapy. The elastic models exhibited similar displacement patterns; however, the magnitude of the displacements in the models was invariably small (approximately 1 per 100) compared with those outputs of corresponding viscoelastic models. The corresponding maximum stress level in our viscoelastic mandible subjected to the Herbst appliance with the same loading was considerably low and relaxed in various regions when compared with the elastic model.

We suggest that a viscoelastic model of the mandible mimics our general prediction of orthopedic treatment outcomes better than those by elastic models.