Biomedical Engineering Reference
In-Depth Information
made, the differentiation process is assumed to proceed at a fixed rate. This viewpoint leads
to a mathematical description in the form of first-order partial differential equations:
dX
dt
þ
d
dX
da
¼ð
m
ð
a
Þ
a
ð
a
ÞÞ
X
ð
6
:
3
Þ
where d is the rate of differentiation and
a
is a parameter that measures the differentiation
state of the cell.
m
and
a
are the growth and death rates, respectively, and vary between zero
and unity. Both
m
and
a
can be a function of
a
.
Cell Motion
THE BIOLOGICAL ROLES OF CELL MIGRATION
Cell migration plays an important role in all physiological functions of tissues and also some
pathological processes. Cellmigration is important during organogenesis and embryonic devel-
opment. It plays a role in the tissue repair response in both wound healing and angiogenesis.
The immune system relies on cell migration, and pathological situations like cancer metastasis
are characterized by cell motility. Cell migration represents an integrated molecular process.
Animal cells exhibit dynamic surface extensions when they migrate or change shape. Such
extensions, called lamellipodia and filopodia, are capable of dynamic formation and retraction.
Local actin polymerization at the plasma membrane is a key process in the generation of these
structures. These extensions are also regulated by a complex underlying process involvingmul-
tiprotein interactions. In neurites, filopodia are believed to play a role in the progression of cell
elongation by aiding the assembly of microtubules that are a significant component of these
cells. The filopodia in neurites extend from the lamellipodial region and act as radial sensors.
Filopodia on neurites have been found to be crucial to growth cone navigation. The filopodia
on neurite growth cones have also been found to carry receptors for certain cell adhesion mole-
cules. Mature leukocytes also can extend cytoplasmic extensions. Recently, structures termed
uropods have been found on T lymphocytes. These cytoplasmic projections form during lym-
phocyte-endothelial interaction. There is a redistribution of adhesion molecules, including
ICAM-1,-3, CD43, and CD44, to this structure. T cells have been found to use the uropods to
contact and communicate directly with other T cells. Uropod development was promoted by
physiologic factors such as chemokines. Cytoplasmic extensions, therefore, can perform a spec-
trum of functions in different cells that are related to migration and communication.
DESCRIBING CELL MOTION KINETICALLY
Whole populations.
The motion of whole, nonreplicating cell populations can be described by
dX
dx
¼
J
ð
6
:
4
Þ
where
J
is the flux vector of the system boundary (cells/distance/time in a two-dimensional
system),
is the flux dimension. The cellular fluxes are then
related to cellular concentration and chemokine concentrations using
J
X
is the cell number, and
x
¼
random motility
þ
chemokinesis
þ
chemotaxis
0
1
0
1
0
1
ð
6
:
5
Þ
s
da
s
dX
2
d
da
dx
w
Xda
dx
@
A
@
A
@
A
þ
¼
dx
