Biomechanics and Modeling in Mechanobiology

, Volume 12, Issue 2, pp 249–265

A mechanobiological model of orthodontic tooth movement

Original Paper

DOI: 10.1007/s10237-012-0396-5

Cite this article as:
Van Schepdael, A., Vander Sloten, J. & Geris, L. Biomech Model Mechanobiol (2013) 12: 249. doi:10.1007/s10237-012-0396-5


Orthodontic tooth movement is achieved by the process of repeated alveolar bone resorption on the pressure side and new bone formation on the tension side. In order to optimize orthodontic treatment, it is important to identify and study the biological processes involved. This article presents a mechanobiological model using partial differential equations to describe cell densities, growth factor concentrations, and matrix densities occurring during orthodontic tooth movement. We hypothesize that such a model can predict tooth movement based on the mechanobiological activity of cells in the PDL. The developed model consists of nine coupled non-linear partial differential equations, and two distinct signaling pathways were modeled: the RANKL–RANK–OPG pathway regulating the communication between osteoblasts and osteoclasts and the TGF-β pathway mediating the differentiation of mesenchymal stem cells into osteoblasts. The predicted concentrations and densities were qualitatively validated by comparing the results to experiments reported in the literature. In the current form, the model supports our hypothesis, as it is capable of conceptually simulating important features of the biological interactions in the alveolar bone—PDL complex during orthodontic tooth movement.


MechanobiologyMathematical modelTooth movementRANK–RANKL–OPG pathwayTGF-β pathway

Supplementary material

10237_2012_396_MOESM1_ESM.eps (193 kb)
ESM 1 (EPS 193 kb)
10237_2012_396_MOESM2_ESM.eps (213 kb)
ESM 2 (EPS 214 kb)

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Biomechanics SectionKU LeuvenHeverleeBelgium
  2. 2.Biomechanics Research UnitU. LiègeLiègeBelgium
  3. 3.Prometheus Division of Skeletal Tissue EngineeringKU LeuvenLeuvenBelgium