Multiscale Modeling in Vascular Disease and Tissue Engineering - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 238

1 Introduction
Arterial growth, remodelling and vascular diseases are intrinsically multiscale and
depend on the interactions occurring at the tissue level, cell level and the intracellular
level. Consequently, multiscale computational modelling techniques can help to
elucidate the mechanisms underlying the onset and progression of vascular diseases
as well as vascular tissue regeneration. Mechanical perturbations at the tissue level
translate to cell level mechanical signals via cell-matrix interactions. How these
mechanical signals are further transduced through the cytoskeletal assembly, and
other signalling pathways such as calcium channels to the cell nucleus, resulting in
specific gene expressions which subsequently alter cellular behaviour, adds an
additional level of complexity to these multiscale systems. Cells alter their growth,
phenotype and their extracellular matrix in response to macro mechanical changes.
These cell level events can then in turn accumulate and emerge at the tissue level as
pathological conditions such as atherosclerosis and intimal hyperplasia.
Multiscale modelling is by its nature highly computationally expensive. With
recent advances in computational capabilities, a more mechanistic approach to
multiscale modelling, using discrete methodologies, has become possible which has
enabled a systems approach to understanding diseases. Agent based models (ABM)
or Cellular Automata (CA) models are notable examples whereby the behaviour of
each individual cell can be modelled explicitly. In recent years several agent based
approaches have been developed to provide a quantitative and mechanistic
understanding of pathologies such as inflammation and wound healing [ 1 , 2 ]
atherosclerosis [ 3 ], in-stent restenosis [ 4 - 8 ], and intimal hyperplasia in vascular
grafts [ 9 , 10 ]. In agent based modelling, a population of ''agents'' which are
autonomous individuals representing cells, are created and the rules of behaviour and
interactions between the agents are defined. In the context of cell biology, agent
behaviours such as migration, proliferation and differentiation can be defined for
each agent using mathematical formulations which describe the migration speed,
doubling time and extracellular matrix and chemokine synthesis as functions of
different stimuli such as stress/strain or species concentrations. Rules of interactions
between the cells such as contact inhibition and different paracrine signalling
pathways can also be defined.
One important advantage of using ABM to model cell populations is their ability
to better capture the discrete nature of events occurring at the cellular level
compared to continuous approaches such as differential equations. In contrast,
continuum methods such as the finite element method have been extensively used
as a robust and reliable tool for modelling tissue level events such as mechanical
interactions between the arterial wall and stents [ 11 - 15 ]. This has motivated
development of hybrid multiscale models that take advantage of continuum
methods such FEM at the tissue level and employ discrete methods such as CA or
ABM to capture cell level events. Recent studies by Boyle et al. [ 6 , 7 ] and
Zahedmanesh et al. [ 58 ] and Zahedmanesh and Lally [ 10 ] are good examples of