Biomedical Engineering Reference
In-Depth Information
5 Discussion
A bioregulated fracture healing model was adapted from literature [
7
,
8
] and im-
plemented in a finite element framework. A Time Discontinuous Galerkin scheme
was coupled with the Finite Calculus method [
14
] to obtain stable solutions for the
advection-diffusion-reaction problem at hand. Additionally, a mechanical stimulus
for stem cell differentiation has been added.
This model was able to predict the general healing pattern of a long bone fracture.
The evolution of the tissue distribution is in good agreement with descriptions of the
bone repair histology in literature. However, as seen in Fig.
5
the simulation predicts
a very expeditious healing. The interfragmental movement decreases very rapidly
from day 10 to 20, so that the bone has already then regained its functionality.
Stem cell differentiation to fibroblasts and osteoblasts has no significant influence
on the tissue development for a wide range of parameters. The population of these
cells is dominated by the logistic growth used to model cell proliferation. This has
to be taken into account when the mechanical stimulation of cell differentiation is
considered.
From a numerical point of view it has to be remarked, that the mathematical
model incorporates a vast number of parameters, which rely on data obtained in very
few studies. While this means the shown computations cannot safely predict the
development of an individual healing fracture, an analysis of sensitive parameters
helps to identify critical parameters of the biological entities taking part in the repair
process.
Future work might include extending the mechanical stimulation to additional
cell functions like proliferation, growth factor or matrix production and incorporat-
ing further measures of the local mechanical demand like the hydrostatic pressure.
A 3D implementation of the model would allow for a more complex bone and callus
geometry, i.e. an asymmetric callus and enable a greater variety of load cases like
bending.
Acknowledgments
This research was founded by the German Research Foundation (Deutsche
Forschungsgemeinschaft Na330/8-1).
References
1. Carter, D.R., Blenman, P.R., Beauprè, G.S.: Correlations between mechanical stress history
and tissue differentiation in initial fracture healing. J. Orthop. Res.
6
, 736-748 (1988)
2. Lacroix, D., Prendergast, P.J., Li, G., Marsh, D.: Biomechanical model to simulate tissue
differentiation and bone regeneration: application to fracture healing. Med. Biol. Eng. Comput.
40
, 14-21 (2002)
3. Garcìa-Aznar, J.M., Kuiper, J.H., Gòmez-Benito, M.J., Doblarè, M., Richardson, J.B.: Compu-
tational simulation of fracture healing: influence of interfragmentary movement on the callus
growth. J. Biomech.
40
, 1467-1476 (2007)
