Introduction. One of the main functions of bone is to provide support to soft tissue and protect the organs of the body. This structural function of bone is enhanced by the characteristics of bone tissue. In fact, bone is a natural biological material that can adapt its structure depending on diverse factors including the mechanical environment. The structural arrangement of bone tissue can be observed at different scales. At a first level (macroscale) a non-homogeneous distribution of apparent density leads to different type of bone, the compact bone and spongy bone; at a second level the trabecular architecture of bone characterizes the mechanical properties such as bone anisotropy, and at the lowest levels we can distinguish different stages of mineralization and arrangements of the collagen fibres, among others. A mathematical description of the behaviour of bone at these different scales is essential not only to understand the bone adaptation but also to evaluate the bone quality helping on the diagnosis of bone disease such as osteoporosis and to build models that are able to support the design of new bone implants and scaffolds for bone tissue engineering. Methods. In this work the multiscale model proposed by the authors [1 ,2] is explored to study its capabilities as a design tool for bone substitutes as well as to analyse the bone behaviour in case of disease. The bone adaptation is modelled as a two-scale material distribution problem where not only the apparent density is determined but also the trabecular structure of bone is characterized. The solution is obtained assuming that bone adapts itself to maximize stiffness and to satisfy biological driven constrains such as the cost of bone formation, the relation between volume fraction and bone surface area density and the permeability necessary for mass transport (nutrients, blood suply, etc). The model is compared with some clinical data obtained by DXA enabling to understand the influence of the parameter in the model that controls the bone formation. Furthermore, the multiscale model is applied to design bone substitutes presenting a microstructure with properties equivalent to the actual bone. Results.The bone density distribution on the macoscale is equivalent to the one obtained by models which work with a single design scale only. The microstructure for each bone site has properties that are equivalent to bone anisotropic properties and it respects the bone surface area and permeability constraints when that information is included in the model (figure 1). The distribution of bone density is comparable with the data obtained by DXA and the microstructure evolution predicted by the model as bone becomes osteoporotic shows that there are preferential directions that tend to maintain its structural strength.
|Title of host publication||MATHMOD|
|Publication status||Published - 1 Jan 2012|
|Event||7th Vienna Conference on Mathematical Modelling - |
Duration: 1 Jan 2012 → …
|Conference||7th Vienna Conference on Mathematical Modelling|
|Period||1/01/12 → …|