Biomedical Engineering Reference
In-Depth Information
(72)). In the near term, modelers will have to be prepared to segment images
manually, possibly with the aid of interactive software, if for no other reason
than to validate results obtained with more automated methods.
2.2. Diffusion of Signal Molecules
The equations governing diffusion are well known (73, pp. 700-718). In
practice, distinction must be made between certain small molecules, such as
nitric oxide (NO), which can diffuse freely through cell membrane barriers (74),
and larger molecules, which cannot. To deal with the latter, one must in princi-
ple solve the diffusion equations in the highly irregular extracellular volume,
where diffusion is significantly hindered for all but the smallest molecules. This
can be handled by generalizing the numerical technique used by Gally et al.,
dividing the tissue into small volume elements and applying mass balance across
all the boundaries between the extracellular compartments. In the case of poly-
hedral meshing, these would be the irregular polygons delineating the compart-
ment boundaries. Fortunately, assuming the individual compartments are small
enough for an assumption of spatially constant concentration to apply, only the
area, not the detailed shape, of each boundary is required. This information can
be computed as part of the meshing process and stored in tables for use during
the simulation.
2.3. Contact Signaling
Computationally, contact signaling is a relatively minor problem once the
model geometry has been specified. A list of cell-cell contact areas can be main-
tained and the generation of signal molecules, their movement across each such
contact, and their effects on target cells updated at each iteration of the simula-
tion. The problem here is in defining what signals are important for the behavior
under study, where and under what conditions those signals are produced, what
concentrations are effective in modifying the behavior of target cells, and so on.
In general, all that can be said is that detailed rules for signaling are likely to be
among the hypothesis-driven model specifications that will need to be varied in
order to optimize the faithfulness with which the model mirrors the behavior of
real tissue.
2.4. Finite-Element Modeling
The techniques discussed so far address how to model electrical and chemi-
cal interactions of cells. This leaves mechanical interactions to be dealt with.
