Deciphering Fate Decision in Normal and Cancer Stem Cells: Mathematical Models and Their Experimental Verification - Mathematical Methods and Models in Biomedicine - page 218

therapeutic implications, for example with regard to the design of schedules for
radiotherapy [ 48 ], which are usually optimized assuming exponential tumor growth
during the intervals between irradiation [ 69 ].

7.3 A Robust Tool for Exploring and Manipulating Stem Cells

Behavior

The generality of the basic CA model makes it relevant for the research of
adult SCs of any kind. Refinement of the basic model by implementation of
various explicit limitations, describing specific tissue-dependent characteristics,
could enable researchers to model SC behavior in any tissue of interest, including
solid and non-solid tumors. The model can be adjusted to describe, for example, the
bone marrow with the migration of mature cells to the peripheral blood or colon
cancer with the specific spatial structure of the crypt.
The CA form of the model allows for consideration of the influence of
neighboring cells on fate decision in the dynamical process of tumor growth. This is
not possible in continuous CSC dynamical models, which describe the macroscopic
behavior of CSCs and rely on assumptions about tumor growth rate or spatial
homogeneity of environmental signals (cf. [ 23 , 30 ]). Agur et al. [ 4 ]werethefirstto
use a CA formulation to create a general model of SC behavior; other CA models,
in contrast, were built to model SC spatial behavior in the specific tissue structure
of the colon [ 59 , 64 , 91 ] or breast [ 8 ]. Enderling et al. [ 28 ]alsousedaCAmodel
to describe tumor growth dynamics, but they did not try to simulate homeostatic
properties in the tissue and had no constraints on the tissue's resilience, considering
no feedback of the SC population on SC differentiation.
The multi-scale model [ 5 ], which includes modeling of intracellular-level
dynamics in conjunction with the dynamics on the tissue level, is used for
distinguishing possible therapeutic targets for eliminating CSCs. Notwithstanding,
the model still captures the principal mechanism of SC fate decision regulation,
i.e., the QS mechanism. Analysis of the model could point out the most effective
therapeutic agents, those that attack the main control of CSCs' self-maintenance.
The intracellular part was modeled in view of the biological data for BCSCs;
however, a different approach could be adopted in order to gain insights for other
specific cancer types and therapies.
Currently, the intracellular SC model is being expanded to combine more of the
main relevant signaling pathways, including detailed molecular models for these
pathways. For example, a detailed model of the Wnt pathway has been built, and its
parameters were fitted and validated using experimental data [ 47 ]. Implementation
of this detailed molecular model in the multi-scale tissue model will have the
advantage of parameter availability. Thus, the resultant multi-scale model will be
able to make quantitative predictions of the effects of different therapeutic agents.
Such a model could be useful for the research of all cancer types, unlike the multi-
scale model of van Leeuwen et al. [ 91 ], which is specific for colorectal cancer SCs.