Biomedical Engineering Reference
In-Depth Information
Box 1. Temporal decomposition strategy for a three-tiered multiscale
model
Intracellular to multicellular time interfacing: Each time step of the ABM
will represent 1 h, and multi-cell level behaviors will occur on this time-
scale. For example, SMCs will proliferate over 8-24 h [ 44 ] or 8-24 time
steps in the ABM, while growth factor production will occur over 12-24 h
(or time steps) [ 44 ]. When the ABM calls the ISM (every 24 h for 120
simulated days), where biological events will be simulated on the order of
minutes, we will institute a time-delay, or essentially ''pause'' the ABM,
while the intracellular events are computed by the ISM.
Multicellular to tissue-level time interfacing: Each time step of the CMM
will represent 1 week, and tissue-level behaviors will occur on this time-
scale. For example, the strain state of the artery wall will change over the
course of 1-2 weeks (depending on vessel geometry and composition
alterations during this time window). Therefore, to account for these changes
on a time window that is biologically realistic, the ABM will call the CMM
every week (i.e., every CMM time step) in order to recompute and update
tissue-level changes that occurred during this window. Thus, in the ABM,
every 7 days (or 168 time steps in the ABM), the ABM module will be
''paused'' in order to run the CMM, whose output (computation of the
mechanical state of the media) will be imported back into the ABM.
Another hurdle to achieving a unified three-tiered multiscale model is defining
an appropriate level of resolution and abstraction for the relevant spatial scales
such that information at one level can be mapped to higher and/or lower levels of
biological scale. We have previously devised a method for coupling spatial scales
between an ABM and ISM [ 49 ]. In that ABM module, we simulated individual
biological cells using nine coupled agents that represented different cytoplasmic
and membrane compartments within each simulated cell. In this way, we could
simulate the differential behaviors of the leading versus trailing edge of a cell as it
migrated across a two-dimensional substrate. Intracellular signaling events were
simulated in the ISM and distributed equally to the nine agents comprising each
cell, but one could envision partitioning or compartmentalizing certain reactions
within spatially confined intracellular regions that would map directly to the dis-
cretized, multi-agent cells within the ABM. We have similarly devised a method
for comparing spatial scales between an ABM and CMM [ 29 ]. In this case, the
ABM consisted of layers of cells whereas the CMM consisted of a homogenized
structural wall. Data from the ABM could thus be averaged radially and applied to
the CMM at each time of interest.
We envision that a three-tiered, multiscale ISM-ABM-CMM will be united by
an umbrella program implemented in Java TM . This program will run the ISM,
ABM, and CMM modules in parallel, while transferring information between each
pair of modules. The CMM and ISM are implemented in Matlab , and the ABM is
implemented in Netlogo [ 63 ]. We have opted to use these modeling software
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