Biomedical Engineering Reference
In-Depth Information
4.3 Coupling Agent Based Models with Constrained
Mixture Models
In this section we focus on coupling an ABM with a CMM, but the overall
procedure can be applied to the coupling of many types of models. Any model is
only as good as the data upon which it is built. Hence, we suggest that the first step
in a multistep process of coupling different models should be to substantiate the
goodness of the published data used to build both models. This can be done, in
part, by evaluating the credibility of each data set based on four categories: (1)
agreement with other published findings, (2) physiological conditions (e.g., in vitro
versus in vivo), (3) appropriateness to the computational model (this metric
assesses how well the data match the particular situation, that is, same cell type,
organ system, species, environmental condition, and so forth) and (4) data preci-
sion (e.g., data measured directly and quantified numerically are better than
extrapolated or theoretical); please see Ref. [
58
] for more details. After performing
this data assessment one can then use the highest scored findings to update or
create a data-driven computational model with more confidence.
The second step involves further model verification through stability and
parameter sensitivity analyses. After the governing equations, parameters, and
outputs have been defined for each model, one should confirm that the model is
stable over known situations. For example, constituents within the vascular wall
are synthesized and turned over at different rates; collagen may be secreted by the
cell in less than an hour and has a half-life of *30-70 days, whereas elastin is
primarily produced during the perinatal period and remains for the majority of
one's lifetime. Despite these changes, the average geometry of a healthy, mature
artery remains fairly constant over long periods. Therefore, it is expected that,
under homeostatic conditions, the ABM and CMM should predict no net change in
geometry, microstructure, mechanical properties, or biological response over such
periods. Moreover, one should confirm that the model can capture acute reactions
to transient perturbations. For example, a 10 % increase in pressure over a few
hours can lead to transient spikes in growth factor production and yet no net
changes in collagen or SMC content. In order to assess the sensitivity of each
model to parameters that influence production and removal rates, it is important to
conduct a one-dimensional, and if possible, a two-dimensional sensitivity analysis.
A one-dimensional analysis will reveal to what degree a single parameter can be
increased or decreased before outputs diverge from what is physiologically
expected. For example, in a recently reported ABM, the production of new SMCs
depended in part on a gain-type parameter multiplied by the concentration of
PDGF; if this parameter increased, then SMC content increased and so too wall
thickness, which could decrease the circumferential stress (Fig.
4
). Yet, PDGF
production is a function of circumferential stress, thus less PDGF should be
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