Biomedical Engineering Reference
In-Depth Information
glioma cells in brain tumors may alter neuronal network communication and lead to
more glutamate release, exacerbating neuronal injury and favoring glioma prolifera-
tion as has been previously described (Takano
et al., 2001). In our model systems, a
3D matrix such as shown in
Figure 5
may be useful to elucidate the effect(s) of brain
tumor cells on normal brain cell function. Furthermore, in a predator-prey concept, we
suggest that excess glutamate release from glioma cells may “swamp” the normal bal-
ance of astrocyte glutamate uptake and removal following normal neuronal glutamate
release. This is exacerbated by the impaired uptake of glutamate by glioma cells (Ye
and Sontheimer, 1999) and by indications that glutamate may serve as an autocrine
factor for glioma cell growth (Lyons
et al., 2007). Thus, in the three dimensional envi-
ronment of the brain during tumor growth, the normal predator-prey balance between
astrocytes and neurons is altered by growing glioma cells which take up space and
alter the glutamate load on the system. A better understanding of these dynamics may
lead to better anti-cancer approaches.
While, much work is being done on cellular calcium modeling (see, for example,
(Falcke, 2004); (Guisoni and de Oliveira, 2005); (Means et al., 2006); and (Patterson
et al., 2007)), little effort is focused on single compartment calcium models of brain
cells in 0 (single cell), 1, 2, or 3 dimensions as we suggest in
Figure 1,
validated
against fluorescence data. The work in Means et al. (2006) has a similar flavor to that
presented here in that a 2D network, or lattice, is constructed to examine calcium
dynamics. However, it must be noted that this lattice, which is made up of two sub-
lattices, one consisting of calcium channels and the other of calcium ions, is used to
represent the calcium exchange of the endoplasmic reticulum membrane of a single
cell, not a cellular network.
Single compartment models are desirable in this work, because any interaction
between the mathematical models and the corresponding experimental systems should
be based on the same known quantities. It would not be reasonable to include vari-
ables in the models that either cannot be determined from separate equations or cannot
be provided as an input from the available experimental data. To check and validate
models, we are using microscopy and imaging techniques to capture dynamic calcium
events taking place within a cell as a whole, as opposed to calcium diffusion across a
cell or intracellular calcium waves, for example (Patterson et al., 2007).
The work in Ventura et al. (2006), which does focus on single compartmental mod-
eling of a single cell, is of particular relevance to that described here. To address the
inherent difficulty of numerous unknown parameters arising in traditional intracellular
calcium modeling, Ventura et al. (2006), present a data-driven approach where models
are simplified based on reasonable assumptions. The mathematical equations are s
implified but not abandoned in their entirety, which is desirable due to our other re-
search interests related to control and estimation techniques. Results indicate that the
model does reveal quantitative characteristics like amplitude and kinetics of a cal-
cium signal whenever calcium enters through “one or several distinguishable spa-
tially localized regions (channels or clusters of channels).” This requirement of the
calcium passing through particular channels is problematic from the perspective that
available fluorescence data does not provide this level of detail for contribution to
Search WWH ::
Custom Search