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Multiscale mathematical models for bone remodeling with applications in dentistry

Problem Description

Living bone is continuously adapting itself to external stimulus. The study of this process, called remodeling, has been considered the utmost importance from the point of view of medical studies due to its wide range of applications. e.g. in bone diseases such as osteoporosis, healing fractures, mechanics of sports and optimal installation of orthopedic implants.

The macroscopic behavior of porous materials like bone is strongly influenced by the microstructure related to the pore space. Therefore, multiscale modeling is necessary to couple the information of different scale levels. The purpose is to capture the macroscopic behavior of the system in a more efficient manner than solving the full microscopic model.

Multiscale and multiphysics modeling involves many challenges in the development of the numerical methods and in their analysis: understanding the significance of linkages between scales, computing information that depends on behaviors at different scales, dealing with a complex stability picture resulting from a fusion of the stability properties of different physical models and how all this affects the model output.

Research at LCM

The bone can be seen as a poroelastic material. The purpose of this work is, first, to establish poroelasticity as an effective and useful model to simulate the deformations of the bone. In the microscale, we consider models for single remodeling units, describing the dynamics of the involved bone cell populations. Multiscale modeling is then used to simulate the system behavior coupling the information of the two scale levels.

The general objectives of the project are:

  • Establish mathematical models to simulate the behavior and dynamics of bone remodeling taking into account the destruction and re-growth at the cellular level to explain the macroscopic behavior.
  • Propose efficient and robust numerical methods to solve the multiscale models and study their quantitative and qualitative properties.

Our final goal is to contribute to enhance the understanding of the mechanisms and multiple scales of the bone remodeling process.

In the work we intent to develop we will emphasize applications in dentistry, namely to predict the correct change in density in a bone, as a function of the external loading, in the case of dental implants.

Project Team

  • Sílvia Barbeiro, LCM/CMUC
  • João Carlos Sampaio Fernandes, FMDUP
  • João Rui Galvão Mendes, FMDUP
  • Gonçalo Pena, LCM/CMUC
  • Mário Vaz, FEUP


  • L’Oréal Medals of Honor For Women in Science, 2010