Biomedical Engineering Reference
In-Depth Information
64,65). The strongest evidence in favor of the mesenchymal theory is that a wide
variety of cell types, including fibroblasts, generate traction forces on ECM,
resulting in deformation and sometimes in pattern formation (22,23,47,57,
60,61). Also, collagenases inhibit clefting, while collagenase inhibitors enhance
clefting (44). Both theories are plausible, yet it would seem that if complete re-
moval of the mesenchyme does not prevent clefting, then the mesenchyme can-
not be causing the clefting. I believe that, as in most biological systems, the
reality here is more complicated and subtle than our preconceived notions. Can a
model help us understand the subtleties better?
We developed a mathematical model of the mechanical forces and deforma-
tions of the tissues involved in morphogenesis (37). We can use it to answer
some questions.
3.
MODEL
3.1. Hypothesis
It is clear that epithelia can generate morphogenetic forces in the absence of
a mechanical input from mesenchyme. These forces can generate clefts even if
the mesenchyme is not around the epithelium. But can the same forces generate
clefts if the epithelium is embedded in mesenchyme?
We hypothesize that the
branching morphogenesis observed in the mesenchyme-free experiments is not
mechanically equivalent to the branching morphogenesis observed in mechani-
cally intact rudiments or in vivo
. In this chapter we show numerical experiments
to illustrate the forces and deformations in the two experimental situations—
with and without mesenchyme.
To understand the relationship between forces and deformations in a
morphogenetic system, we must formulate a model of the mechanics of the tis-
sues and their interactions. But what is the constitutive law for an embryonic
tissue? If I pull on my skin and let go, it bounces back. A material like skin that
responds to short-term forces with reversible deformations is exhibiting short-
term elasticity. If I wear braces on my teeth for two years, then remove them, the
teeth do not bounce back. A material like the jawbone, which responds to long-
term forces with irreversible deformations, behaves in the long term as a viscous
fluid.
Most biomaterials are actually somewhere between an elastic solid and a
viscous fluid. A material with short-term elasticity and long-term viscosity is in
the Maxwell class of viscoelastic fluids. Embryonic tissues will bounce back
from a brief deformation, but the changes associated with development are per-
manent. If we are only interested in permanent deformations of branching rudi-
ments, we may ignore the short-term elastic component and focus on long-term
behavior. We therefore model the embryonic epithelium and mesenchyme as
