Biomedical Engineering Reference
In-Depth Information
S
¬
s
L
s
2
L
kL
-
=
D
-
®
,
[3]
-
2
--
s
t
s
x
K
+
L
M
where the first two terms constitute the standard diffusions equation and the
third term represents the point sinks: S is cell density,
x
is the distance from the
point sink, and
K
M
is the saturation constant and
k
the maximal uptake rate con-
stant of a single cell (23).
Figure 18
. Capillary length and diameter data from glomerulus regeneration (1).
The distribution of signaling molecules is more difficult; where nutrients
may be simply absorbed by the cell, growth factors and other regulatory mole-
cules have more complicated interactions with the cell. In such cases the mole-
cule-cell interaction can still be included in the diffusion equation, but a model
must be provided for the molecular binding (25). Many models are available for
describing molecular signaling interactions in terms of the number of binding
sites available on a cell and the rate at which those sites will interact with an
external molecule (48).
