Biomedical Engineering Reference
In-Depth Information
The usage of new languages such as stochastic -calculus to describe and
simulate the migration of autoreactive lymphocytes in the target organ will help
us better understand the complex dynamics of lymphocyte recruitment during
autoimmune inflammation in live animal. Furthermore, our approach may represent
an important step toward future predictive studies on lymphocyte behavior in
inflamed brain venules. In fact, the biochemical stochastic -calculus simulation
of experimental data offers the possibility to model and predict data of biological
observations on a computer (
in silico
experiments). This new opportunity provided
by the computer science may allow the biologists and medical researchers to save
time by reducing the number of needed experiments in the case in which the
computer simulation can exclude inadequate hypothesis.
A
Dembo Adhesion Model
The kinetic reaction model proposed by Dembo et al. [
8
] simulates the rolling
lymphocyte as a viscous newtonian fluid enclosed in a pre-stressed elastic mem-
brane and the adhesion bonds formed between the rolling cell and its substrate are
simulated as elastic springs perpendicular to the substrate. The adhesion bond force
isassumedtobef
b
D
N
b
k.y
/,whereN
b
is the associated bond density, k is the
bond elastic constant, and y are the lengths of an unstretched bond and a stretched
bond, respectively.
The bond density N
b
, as function of time t , is computed using the following
equations
@N
b
@t
D
k
on
.N
l
N
b0
/.N
r
N
b
/
k
off
N
b
(4)
D
k
off
exp
.k
ts
/.y
/
2
2K
B
T
k
off
(5)
k
on
D
k
on
exp
.k
ts
/.y
/
2
(6)
2K
B
T
where k
on
and
k
off
are the forward and the reverse reaction rates respectively, N
l
and N
b
are the ligands and receptors densities respectively and k
on
and k
of f
are
the equilibrium forward and the reverse reaction rates respectively. The parameters
considered by this model are: N
l
D
N
r
D
400 m
2
, k
on
D
84 s
1
, k
off
D
1s
1
, k
D
5 dyne/cm,
ts
D
4.5 dyne/cm, K
B
T
D
3.8
10
7
ergs and
D
20 nm. With these
parameters values the solution N
b
.t / is given by the following
1
84t
C
400
N
b
.t /
D
(7)
and it is plotted in Fig.
7
a.
