Biomedical Engineering Reference
In-Depth Information
large periods or large enough numbers of diffusing charges are
involved, as in repairs of wounds (periods of perhaps several days)
or cellular division cycles (nine months for human reproduction
periods), stochastic diffusion processes involving ions and proteins
occur despite opinions to the contrary. We examine the case of
protein diffusion later in Chapter 5, where large numbers of cells,
eachwithmanymembraneproteinsandlongdiffusionperiods,need
consideration to achieve alignment of cells with latticed (liquid-
crystal) membranes to produce magnification of ambient biogenic
fields.
4.7 A Translational RandomWalk Model for Ion Diffusion
The single-ion model to be presented in this section uses a simple
hard-sphere model
a
for the electric charge and the collisions of
the ion. A simple magnetic dipole moment is added to study the
internal rotation of the ion. Both models use Monte Carlo methods
to choose the collision periods, the velocities associated with the
thermal and electrical energies and the velocity offsets associated
with the magnetic rotational energies. There are other models of
ionic diffusion (Allan and Tildesley, 1987; Birdsall, 1991), more
detailed than the random walk model that is presented below.
Randomwalkmodelsalsosufferthelimitationsmentionedabovein
regard viscous models. However, the present model is appropriate
as it is contemporary with bioeffect models and reveals magnetic
effects that havenot to date been reported in the literature.
Figure4.11aillustratesaBrownianmotionrandomwalkprocess
forseveralcollisions,whileFig.4.11bshowsthevelocitymagnitude.
In this case there are no external E or B fields. The model
assumes that only an impulsive collision force occurs that acts
instantaneously at some point in time to affect a change in
particle velocity, unlike, for example, more realistic Leonard-Jones
potentials that vary with distance. In the absence of applied fields,
noforcesareassumedtoexistbetweencollisionsandhencewehave
a
Compared with the computational sophistication used in current plasma and liquid
models, some might call a hard-sphere model primitive, yet it can be a useful
computational and theoretical tool of study.
