reverse engineering – recent advances and applications - OpenLibra

250 Reverse Engineering – Recent Advances and Applications
8 Will-be-set-by-IN-TECH
The total current, Eqn. 11, crucially depends on how the effective surface area responds to the
current physiological conditions. Integrating directly from the concentrations, as in Eqn. 9,
requires a solution to the difficult boundary-valued diffusion-reaction problem defined above
(Eqns. 4 to 6). In the next section, we review an entirely geometrical method, termed the
Rope-Walk Algorithm, permitting us to side-step the difficult integration required by equation
9, and, through Eqn. 11, allows for a solution of Eqns. 4 to 6 to be found without directly
solving the full diffusion-reaction problem.
3.5 Rope-Walk algorithm: solving the diffusion equation without solving the diffusion
equation
We consider a self-similar surface with fractal dimension D f , surface area S, and composed
of cubic elementary units of side length, l, which serves as a molecular “receptor” in
the diffusion-reaction problem. Molecules encounter this surface after diffusing from the
source with area Ss, which is much smaller than the receptor’s total surface area Ss