Biomedical Engineering Reference
In-Depth Information
Figure 5
. Effect of viscosity ratio B on evolution of the clefting epithelium. Nondimensional
surface tension C = 0.01, nondimensional clefting force G = 2.5. Forces are in the same fixed
directions. Upper: viscosity ratio B = 1; lower: viscosity ratio B = 10. Epithelium embedded in
a material more viscous than itself takes longer to form the same depth cleft than if it were
embedded in a material of the same viscosity. Reprinted witih permission from Lubkin and Li
(2002) (37).
Viscosity ratio B had a significant effect not just on the time course of
branching but, surprisingly, also on the width of the clefts that formed. Larger B
(more viscous mesenchyme) led to narrower clefts (Figure 6).
4.
DISCUSSION AND CONCLUSIONS
Because of the way the model [6]-[8] is scaled, the dynamics depend
only on the three nondimensional ratios:
+
CH N
BNN
w
/
,
w
TL
and
/
,
0
w
f L
. Therefore, we can compare predicted deformations among differ-
ent tissue types simply by noticing which ratios are preserved. For example,
epithelial rudiments of different tissue viscosities but equal surface tensions and
equal sizes, grown in a mesenchyme-free medium, should take different times to
form the same size cleft from the same size force; the time should be propor-
tional to the tissue viscosity N
-
. If they take the same time, it must be that the
force or surface tension are also different. At an even simpler level, mesen-
chyme-free rudiments grown in gels identical in all respects except for the
amount of collagen (hence viscosity and/or stiffness) should form clefts at dif-
KH
0
