Biomedical Engineering Reference
In-Depth Information
where
is the
concentration of a chemoattractant. The first term is similar to a diffusion term in mass
transfer and is a measure of the dispersion of the cell population. The chemokinesis term
is a measure of the changes in cell speed with concentration and is normally negligible.
If
s
is the random motility coefficient,
w
is the chemotactic coefficient, and
a
0 and chemokinesis is negligible, then the motion of the cells is represented by a
random walk and is formally analogous to the process of molecular diffusion. The biased
movement of the cells directly attributable to concentration gradients is given by the
chemotaxis term, which is akin to convective mass transfer.
Individual cells.
w ΒΌ
As described, motile cells appear to undergo a random walk process
that mathematically can be described in a fashion similar to the diffusion process. Unlike
the diffusion process, the motion of each moving entity can be directly determined
(Figure 6.16). Thus, the motility characteristics of migrating cells can be measured on an
individual cell basis.
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FIGURE 6.16
Experimental paths of individual neutrophil leukocytes undergoing random motility in uniform
environments.
From [9].
