Biomedical Engineering Reference
In-Depth Information
collagen production currently requires extrapolation from a few data points or
parameterization of the ABM [
58
]. Conversely, if the appropriate intracellular
signaling pathways were well understood, experimentally inferred rules could be
improved
by coupling
the determination
of
collagen production
to
an
ISM
resulting in more physiological model output.
The scenario described above, however, would require each agent to run its
own ISM or to query a single ISM running separately at every timestep. As the
number of agents increases, this could become computationally expensive.
Therefore, it is advisable to carefully select which rules or outputs should receive
this treatment. A thorough sensitivity analysis of the ABM assists in this process
by determining which cellular outputs are most important to model predictions. In
contrast, another way to approach this coupling would be to pre-calculate outputs
of the ISM within physiological ranges of the input parameters and then store
results in a look-up table to be accessed by agents during the ABM simulation.
Other things to consider when determining how to couple cell-level with
intracellular models is that temporal and spatial scales may differ by orders of
magnitude. While the ideal time-step for an ABM may be on the order of minutes
to days (e.g., depending on whether one is simulating cell migration or prolifer-
ation), intracellular protein interactions may occur on the order of nanoseconds to
seconds. The majority of vascular models using some form of ABM-ISM inte-
gration to date have been in the field of angiogenesis. For example, Bauer et al. [
8
]
developed a model of tumor induced angiogenesis using a cellular Potts model. In
order to understand contributions of cadherins and ECM binding integrins to
VEGF signaling, and the associated decision of a cell to migrate, proliferate, or
apoptose, the authors went on to develop a Boolean network model incorporating
the crosstalk between these three intracellular signaling pathways [
9
]. This model
could potentially be used in conjunction with the CPM to dictate cellular behavior
during angiogenesis. Likewise, Scianna [
52
] developed a hybrid approach cou-
pling a CPM of vasculogenesis with an ISM using reaction-diffusion equations to
couple VEGF signaling, arachidonic acid, and NO with calcium entry into the cell.
These reactions occur with ten diffusion time steps per main time step.
The issue of very small time-scales for the ISM is much more easily addressed
than the converse: when the signaling pathway being modeled contains tran-
scription and translation, critical functions may occur over multiple ABM time-
steps. In this case, the ISM might need to be capable of integrating changes in
growth factor concentrations as a cell migrates, which may influence protein
outputs 30 or more ABM time-steps later. While this has been addressed in pre-
vious ABMs by assuming that changes in protein levels happen instantaneously, or
within one time-step [
7
], this may not always be possible when predicting sensitive
outputs that require sufficient physiological detail. To our knowledge, this problem
has not yet been satisfactorily solved and is something that needs to be seriously
considered in the design phase of any integrated model.
Search WWH ::
Custom Search