Biomedical Engineering Reference
In-Depth Information
or biophysical meaning. The languages encourage modularization and have import
mechanisms for creating complex models from modular components. Model repos-
itories have been established, together with freely available Open Source software
tools to create, visualize and execute the models. The CellML model repository
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,for
example (discussed below), now includes models for a wide variety of subcellular
processes.
Many models of biological processes at the subcellular level ignore the detailed
3D structure of the cell and model the cell excitability, mechanics, calcium (or other
second messenger) transients, motility, signalling, metabolism or gene regulation,
etc, in a 'lumped parameter' system of DAEs. These models generally either include
explicit discretisation of spatial variation, or make the approximating assumption
that the model will remain spatially homogeneous (the well-stirred reactor assump-
tion). Sometimes the models also include non-linear algebraic equations or need to
solve constrained optimisation problems as part of the solution strategy, but they do
not require the solution of PDEs. In some cases the models are 'systems physiology'
models at the whole body level, but again without the need for solving PDEs. The
markup language CellML (www.cellml.org) has been developed to provide an un-
ambiguous definition of these lumped parameter models. The language is designed
to support the definition and sharing of models of biological processes by including
information about: model structure (how the parts of a model are organizationally
related to one another); mathematics (equations describing the underlying biolog-
ical processes); and metadata (additional information about the model that allows
scientists to search for specific models or model components in a database or other
repository, and which indicates the biological meaning associated with a model and
its parts, allowing the model to be manipulated or interpreted correctly).
The development of a biophysically based mathematical model is, at present, a
creative endeavor, often requiring a great deal of insight into the physical processes
being modelled and personal judgment about the approximations needed. Once cre-
ated, however, a model should stand independent of its creator and be reproducible
and testable by others. The model and data files, that together can demonstrate repro-
ducibility of a model on an automated basis, are called the
reference description
of
the model. This includes protocols for running the model with appropriate param-
eter sets and comparing simulation results against suitably encoded experimental
data (possibly multiple times to generate typical phenotypic outputs). The issue of
robustness and reproducibility is particularly important when a model representing
some small component of physiological function is incorporated into a more com-
prehensive model - and especially one that is to be used in a clinical setting. To be
worthy of reuse in this fashion, each independently developed component should be
demonstrably 'correct' for the function it claims to represent, in the sense both of
biological validity
- it matches some aspect of biological reality - and
mathematical
validity
- for example, it has consistent units and does not violate physical principles
such as conservation of mass or charge.
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www.cellml.org/models
