Biomedical Engineering Reference
In-Depth Information
Figure 3
. Pressure and flow in a typical simulation (equal viscosities). Velocity arrows are
localized at the tail of each arrow. Note that pressure gradients are extremely localized.
Reprinted with permission from Lubkin and Li (2002) (37).
ity equal to the epithelial viscosity; the other was embedded in a material (gel
or liquid medium) of negligible viscosity; a third was embedded in a material
more viscous than the epithelium.
2. To test the roles of clefting force and surface tension, initially 3-lobed
"rudiments," embedded in mesenchyme or ECM of the same viscosity as the
epithelium, were clefted with three identical inward-directed forces, for differ-
ent values of B and G.
3.5. Results
If no external force is applied to our branched rudiment, the preexisting
clefts disappear. The time scale of this relaxation depends strongly on the sur-
face tension and the viscosity ratio (35). High surface tension leads to faster cleft
loss, and high viscosity ratio leads to slower cleft loss.
In all simulations, the pressure distribution was extremely uniform, except
for a strong dipole near each point force (Figure 3).
In all our clefting experiments, our applied point forces were able to deform
the 3-lobed rudiment into a 6-lobed rudiment, if the force was applied for long
