Biomedical Engineering Reference
In-Depth Information
As a further example, The EU funded FP6 project Complex Automata Simu-
lation Techniques (COAST) aims to develop computational methods to solve
multi-scale models where a number of single-scale models interact on different
length and timescales and pass information between themselves. The approach
involves coupling of single-scale cellular automata or agent based models. The
success of the approach has been demonstrated in the modelling of in-stent
restenosis within blood vessels.
Discrete, cell-based descriptions, such as cellular automata models, are well
suited to problems requiring the incorporation of cell signalling processes or
subcellular phenomena, including the cell cycle and signal transduction pathways:
see, for example, Van Leeuwen et al. ( 2009 ) and Alarcon et al. ( 2010 ). However,
it is not at present clear how to incorporate the influence of mechanical forces into
such a formulation; in this case, treating the cells as deformable objects is more
appropriate. For example, by following Drasdo and coworkers (Drasdo and Hohme
2005 ; Byrne and Drasdo 2009 ) and viewing the cells as homogeneous, isotropic,
elastic objects (or ellipsoids in 3D), it should be possible to compute the stresses
and strains experienced by individual cells and relate them to the subcellular
response that such mechanical stimuli elicit (Mullender et al. 2004 ).
• Hybrid models
In practice, as cells proliferate, the computational effort needed to track indi-
vidual cells quickly becomes prohibitive. In such situations, when cell numbers are
large, it may be more appropriate to resort once again to a continuum approach.
While there are now a number of alternative approaches for modelling at the cell-
and continuum scales, it is less clear how to transition between the two approaches
or how to relate parameters appearing in the continuum models to those that
appear in cell-level ones. A possible resolution to the latter problem is outlined in
Byrne and Drasdo ( 2009 ): simulations of an individual-based model of avascular
tumour growth, parameterised by measurable biophysical quantities, are compared
with simulations from a continuum mechanical model and, in this way, parameters
in the continuum model related to measurable quantities. The problem of deciding
when it is appropriate to switch from a continuum to a discrete description (or vice
versa) is considered in Kim et al. ( 2007 ). The authors propose a hybrid model for
the growth of an avascular tumour embedded within a deformable gel. A cell-
based approach is used in the outer annulus of the tumour, where nutrient levels
are high and the cells are proliferating, while continuum descriptions are used for
the gel surrounding the tumour and the central core of the tumour, where nutrient
levels are low and the cells undergo necrosis. Careful consideration is given to the
appropriate coupling of these representations at the boundary between the con-
tinuum and discrete domains.
• Computational challenges
The systems of governing equations arising from multiphase descriptions of bio-
logical tissues are complex: to solve these equations in the complex 2D and 3D
geometries typically encountered within bioreactor systems requires the development
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