Biomedical Engineering Reference
In-Depth Information
A limiting case is that of a gap width of the order of the mean free path of the
particle, in such a case, the particles are trapped inside the intercleft space. The rel-
evant theory is the “percolation theory” and there have been considerable efforts in
this domain for biological applications.
5.4.3.6 Conclusion
We have modeled the diffusion of biochemical species in a cluster of cells by a three
step algorithm:
1. Evolver generation of arrangement based cluster;
2. Monte Carlo random walk of the diffusing species;
3. particle tracking to constrain the diffusing species inside the ECS.
The results of the model show that the ratio between the apparent diffusion co-
efficient and the free diffusion coefficient in dense cell clusters with small extracel-
lular spacing is always the same, whatever the morphology of the cluster (ordered
or disordered). In a 2D cluster
D
D
1
1
2
eff
=
»
2
τ
where t is the tortuosity of the porous media. However the situation is much more
complex in the extracellular space of irregular and anisotropic clusters of cells,
especially if there exist intercleft spaces. Speed of diffusion can be considerably
reduced by particle entrapment in the intercleft spaces or if the desired diffusion
direction is not the same as the preferred direction of the anisotropic cluster.
5.5  Conclusion
Diffusion is very probably the main phenomenon concerning microparticles and
target macromolecules in biotechnological applications. Estimation of diffusion
time may be performed by solving the partial differential equation for the diffusion
of concentration, or by a discrete approach. The advantage of the first “continuum”
approach is the availability of numerical software—finite element method is recom-
mended because it adapts best to the shape of the boundaries—and the relative fast
computational time (at least in a two-dimensional case). A discrete approach—like
the Monte Carlo method—is perhaps more demonstrative because it mimics the
behavior of the particles and is well adapted to very complicated geometries. The
drawback of the method is the computational time.
For the technological applications, diffusion is at the same time advantageous
and not. For example, one takes advantage of the Brownian motion to make mol-
ecules recognize each other, which leads to the desired hybrization. However, diffu-
sion may disperse the target molecules or mix these molecules with other undesirable
molecules. The art of the design of biotechnological components resides in part in
the clever uses of molecular diffusion.
 
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