Biomedical Engineering Reference
In-Depth Information
pendent of local conditions and equal to six hours. In the refractory state, the
phagocytes shed a form of the PIC-soluble receptor. The mean time spent in the
refractory state is also unaffected by the environment, and equal to two hours.
The estimates for these lifetimes are necessarily rough, and indeed the identifi-
cation of these states as distinct physiological entities is to be taken as a simpli-
fication to be overcome as the model is refined.
The simulation volume is a 400-micrometer cube. Both cell types leave this
cube, and the simulation, when their stochastic path intersects the boundary of
this cube. To account for immigration of phagocytes as well as their emigration,
phagocytes are produced temporally as a Poisson process with a uniform spatial
distribution at the boundary of the cube.
To account for the increased extravasation of phagocytes induced by PIC,
the Poisson intensity of the emigration process is an increasing, saturating func-
tion of total PIC concentration within the cube.
The soluble factors are, as mentioned, a proinflammatory cytokine (PIC), a
soluble receptor for the PIC (sPICR), and a bacterial chemoattractant (BC). In
summary their properties are:
1.
PIC
is (1) secreted by activated phagocytes at a rate of 240 mole-
cules/min. (2) PIC induces activation of quiescent phagocytes. (3)
PIC is chemoattractive to phagocytes. (4) PIC strongly enhances
extravasation (immigration) of quiescent phagocytes.
2.
sPICR
is produced by refractory phagocytes and binds to PIC in
solution in a 1-1 stoichiometry, removing both from further activ-
ity. It has no other function.
3.
BC
is produced by the bacteria and is a chemoattractant to phago-
cytes; it has no other function.
3.
RESULTS
3.1. Chemotactic Superposition
For stationary constant sources, the steady-state solution for soluble factors
described by Eq. [6] is expressible in closed form:
£
²
¦
¦
TE
E
¦
¦
cr
()
=
exp
¤
r
,
»
¦
¦
4
Q
Dr
2
D
¦
¦
¥
¼
where
r
is the distance from the source. Figure 1 shows the net chemotactic sig-
nal from Eq. [5] for the case where the responding cell possesses two independ-
ent sets of chemotactic receptors. That is, the contours in this figure show the
