Biomedical Engineering Reference
In-Depth Information
Figure 5.28
Schematic view of the linear motion
M
1
M
2
during the random walk.
5.4.2 Diffusion in Confined Volumes: Drug Diffusion in the Human Body
5.4.2.1 Introduction
One of the most useful applications of the Monte-Carlo method is the diffusion
inside a confined domain. It is striking to see how diffusion occurs in very small
volumes. In chemistry, there is the example of a solid alloy composed of aluminum
with lead inclusions. At a temperature where the lead is molten and the aluminum
still solid, one can follow the random walk of the lead molecules inside the alumi-
num matrix (Figure 5.29).
In biology, there are many examples of diffusion in very confined media: pro-
teins diffuse in cells [13], and macromolecules diffuse in cells' interstitial spaces.
Due to its importance, diffusion processes in confined media is the object of many
studies, and there is abundant literature on this topic. We present here an important
example in biology—that of diffusion in extracellular spaces of cell clusters.
Figure 5.29
Example of very confined diffusion. Lead molecules diffusing inside an aluminum
matrix [12].
