Biomedical Engineering Reference
In-Depth Information
Figure 1
. Sketch of the general sequence of events in a single branching event. As cleft deep-
ens, mesenchyme in and near it becomes denser in cells and ECM materials. New branches
grow, flatten, and also branch. Reprinted with permission from Lubkin and Li (2002) (37).
having fractal scaling (5). There are many interesting models that have been
written of the formation of an entire branched tree (27,38). When modeling the
formation of an entire branched structure, the major concern is elucidating the
mechanism while correctly reproducing the fractal scaling (compare with Part II,
chapter 3, by Savage and West, this volume).
For this chapter, let us focus on the single step of clefting and growth of one
lobule, under the assumption that repetition with eventual halting leads to a
branched structure. Our major concern is elucidating the mechanism while cor-
rectly reproducing the length and time scales and geometry observed in the real
system. The fractal scaling does not matter at the scale of a single clefting.
However, the focus can be made even tighter than that. To create a whole
branched tree, growth is of course essential for the volume contribution alone.
But while branching requires cell growth, clefting does not (42,54). Therefore in
the model presented in this chapter, in the interests of simplicity and robustness,
we omit growth and focus solely on clefting.
Individual glandular rudiments grow and branch normally in vitro, making
mechanical, chemical, and radiative manipulation relatively easy. It has been
known for decades that glandular epithelia separated from their mesenchymes
form normal organs when recombined with mesenchyme of the same organ type
and age, but branch abnormally or not at all when recombined with mesenchyme
from other organs (1,16,17,31-33,55). Whether the directive role of the mesen-
chyme is mechanical, chemical, or both has been the subject of a great deal of
investigation. Most dramatically, lung and salivary epithelia have been cultured
without any mesenchyme at all, embedded in gels with appropriate growth fac-
tors, and the epithelia form branched tubules without mechanical or chemical
support from mesenchyme (46,48).
