Biomedical Engineering Reference
In-Depth Information
very few investigations for irregular and disordered clusters, mostly because of the
difficulty in describing the geometry [24].
However, recently progress has been made to tackle the problem of diffusion in
the ECS of clusters of cells. In the following, we present a 2D numerical approach
based on a two-step calculation: first, the calculation of the cells boundaries, and
second a Monte-Carlo numerical scheme for the diffusion in the ECS morphology
defined in the preceding step.
5.4.2.2 Cell Boundaries
First, cell arrangement may be mimicked: cells rearrange inside the boundaries
of the cell cluster in a function of constraints like the surface tension of the mem-
branes and their volume (depending on the growth or the shrinking of cells). A
numerical software like the Surface Evolver [25] (see Chapter 3), is well adapted to
calculate the morphology of the cell cluster. In order to describe a cell cluster mor-
phology—a given set of points (vertices)—segments (edges) delimiting the initial
cells are introduced in the Evolver numerical program. Depending on line (surface)
tensions and cells volumes, the shape of the cells evolves until the convergence to
a minimum energy arrangement, mimicking real cell arrangement. It is assumed
here that cell membranes behave similarly to an interface with surface tension. The
initial edges are then refined and deformed depending on the specified constraints.
A calculated arrangement of cells mimicking a real cluster of cells has been plotted
in Figure 5.33.
In the Evolver approach, the computational nodes are located on the cells edges
and are referenced by their coordinates (
x,y
) and by the corresponding edge num-
ber. Besides, each cell is referenced by its oriented edges. In order to prepare step 2,
this information is memorized and stored.
5.4.2.3 Monte Carlo Numerical Scheme
Particles—or macromolecules—are initially placed in a central microregion, simu-
lating the injection point at the tip of the microneedle. Diffusion is then simulated
by following the particles execute random walks inside the ECS. In a two dimen-
sional system, the displacement (D
x
, D
y
) of any particle in the time step D
t
is given
by the relations
Figure 5.33
(a) Cell arrangement calculated with the Evolver numerical program; (b) cell cluster
morphology is enlightened by the calculated location of pharmaceutical molecules after they have
diffused in the ECS; (c) real cell cluster observed by fluorescence imaging.
