Biomedical Engineering Reference
In-Depth Information
3.2.3 Rules
Agent-specific actions and interactions in an ABM are ultimately dictated by the
rule set. These rules can be theoretically or empirically based and can be deter-
ministic or stochastic. An example of a theoretically based rule is the use of Fick's
second law to describe the diffusion of a growth factor that affects other cells [ 44 ].
An example of an empirically based rule is a dose-response curve describing the
speed of cellular migration as a function of chemokine (e.g., IL-8) concentration.
Stochastic rules rely on probability distributions and are important when an agent
state does not explicitly dictate a behavior, but affects the likelihood of such a
behavior. Rules are most often derived or estimated from the literature; the
organization and presentation of these rules is facilitated by a table or flow chart
accompanying the ABM (cf. [ 7 ]). Rule sets can vary from fewer than ten rules [ 26 ]
to as many as 200 [ 7 ]. The composition, content, and accuracy of a rule set have a
profound impact on the output of an ABM. Slight modifications to a single rule can
dramatically alter the output of even the simplest ABM. Therefore, in designing,
constructing, and implementing ABM rule sets, caution is urged to ensure that the
rules are accurate, non-redundant, and necessary.
The validity of a rule set can be checked by contrasting model outputs against
experimental data [ 39 , 44 , 55 ], and by performing a sensitivity analysis, where
rules are systematically removed or adjusted incrementally to determine their
contribution to the overall ABM output [ 26 ]. Because the outputs of an ABM are
highly dependent on empirical rules, it is necessary to couple models with
experiments at all stages of model development and to validate an ABM's rule set
by performing iterative in silico and in vivo/in vitro experimentation. For a review
of the integration of experimental data with ABMs, see Ref. [ 57 ], and for a method
of assessing the quality of a model's rule set, see Ref. [ 58 ].
3.2.4 Inputs and Outputs
Most biological ABMs simplify tissue geometry by simulating cell behaviors in a
quasi-two-dimensional simulation space that reduces model complexity and
speeds up simulations. For example, one can use a one-cell thick axial slice of
vessel to model arterial adaptations to hypertension [ 58 ]. This simplification
enabled measurement of vascular wall thickness and cellularity and was sufficient
to enable calculation of the concentration and diffusion of extracellular proteins as
well as to facilitate direct comparisons with experimental data. An ABM simu-
lation space can have closed [ 39 ], open [ 7 ], or periodic boundary conditions [ 53 ],
and the positioning and state assignments for the agents at the start of a simulation
are specified by initial conditions that are frequently derived from microscopic
images obtained at a starting time [ 7 , 39 ]. Setting initial conditions in this way
enables direct comparisons with the experimental data at later time-points for
model validation. The initial agent states are assigned based on empirical obser-
vations (e.g., histology) that describe baseline conditions for agent states. The time
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