Biomedical Engineering Reference
In-Depth Information
where only one parameter is altered (e.g. [ 66 ] to give but one example). This
provides information on the main effects of this parameter but it does not provide
any information on the combined effects or the interactions between different
parameters. Design of experiment techniques have been successfully applied to
mathematical models to overcome the limitations of the OAT technique [ 27 , 67 ].
In the above discussion on the optimal way to determine parameter values for
quantitative models, a completely different point of view is taken by a number of
researchers. Gutenkunst and co-workers argue against the focus on optimizing
experimental design to best constrain model parameters with collective fits as dis-
cussed above, particularly in cases when the understanding of a system is tentative and
incomplete. An important consideration underlying their point of view is the question
of how we should deal with uncertainties in the data [ 68 ], in the fitting of parameters,
and in resulting predictions. Brown et al. rigorously explored one source of uncertainty
in their model of growth-factor signalling in PC12 cells; their analysis considered not
just the set of parameters that best fit the data but a statistical sampling of all parameter
sets that fit the data [ 69 , 70 ]. Like in many other systems [ 71 ], the space of parameter
sets that could fit the data was vast. Perhaps surprisingly, some predictions were still
very well constrained even in the face of this enormous parameter uncertainty. Brown
et al. found a striking 'sloppy' pattern in the sensitivity of their model to parameter
changes; when plotted on a logarithmic scale, the sensitivity eigenvalues were roughly
evenly spaced over many decades. This sloppy nature was then further investigated by
Gutenkunst and others [ 72 - 74 ]. Even though sloppiness is not unique to biological
systems, it is particularly relevant to biology [ 75 ] because the collective behaviour of
most biological systems is much easier to measure in vivo than the values of individual
parameters. Using sloppy parameter analysis, concrete predictions can be extracted
from models long before their parameters are even roughly known [ 70 ], and when a
system is not already well-understood, it can be more profitable to design experiments
to directly improve predictions of interesting system behaviour [ 76 ]ratherthanto
improve estimates of parameters.
5 Conclusion
In conclusion, this chapter has provided an overview of how computational modelling
could contribute to advancing the tissue engineering field. Regardless of whether the
models focus on the product, the process or the in vivo results, the aim is always to try to
understand the biological process and to design strategies in silico to enhance the
desired in vitro or in vivo behaviour. Finally, if models are to be applied in a quanti-
tative way, experiments need be designed as to feed the models in the most intelligent
way. Also here computational tools and models can play an important role.
Acknowledgments The author gratefully acknowledges funding from the Special Research
Fund of the University of Liège (FRS.D-10/20), the Belgian National Fund for Scientific
Research (FNRS) grant FRFC 2.4564.12 and the European Research Council under the European
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