Biomedical Engineering Reference
In-Depth Information
1.2
1
0.8
0.6
0.4
0.2
0
0
5
10
15
20
25
30
Days
Fig. 5
Interfragmental Movement (IFM) during 30days of healing
and at the outer margin of the periosteal callus. The blood supply has also been re-
established. At the end of the simulation bony ingrowth into the fracture gap has taken
place and the soft tissues have been replaced in the main part of the callus. Figure
4
shows the evolution of the mean tissue densities in the endosteal, interfragmental
and periosteal callus. Formation of soft tissues in the fracture gap starts at around
day ten, while production of immature bone can be seen to start not until day 17. The
interfragmental movement determined at the end of the cortial bone in the fracture
gap is shown in Fig.
5
. It decreases rapidly after day ten and is reduced to nearly
0mm at the end of the simulation.
4.1 Parameter Study
Calculations of the model with a variation of several parameters of the advection-
diffusion-reaction equations were carried out to determine its sensitivity. Individual
parameters were varied between 50 and 400% of their original value. The focus here
will be the variation of the reaction terms controlling the differentiation of stem cells.
A change of the differentiation to fibroblasts or osteoblasts has remarkedly little
influence on the tissue development as shown in Figs.
6
and
7
. The lack of differ-
entiated cells is here balanced out by the logistic growth of the population, while
an abundance of differentiated cells is capped when the maximal capacity of the
population is reached.
A significant effect can be seen for the variation of the chondrocyte differentiation
of the stem cells in Fig.
8
. As can be expected an increase of the parameter leads to
an earlier and more pronounced cartilage production, which in turn reduces the
production of connective tissues and facilitates the ossification.
