Biological Systems: Multiscale Modeling Based on Mixture Theory - Multiscale Modeling in Biomechanics and Mechanobiology - page 277

peptide and protein folding modeling [ 60 - 62 ], mutation and immune competition
of cancer cells [ 63 ], organ level analysis [ 64 ], computational physiology [ 65 ], and
genetic regulatory networks [ 66 ]. The common goal of all these applications is to
create a predictive multiscale mathematical model to simulate a complex system.
The open question that spans each application of multiscale modeling is how to
validate and calibrate the model with experimental data. Although still a useful tool,
a mathematical model does not become a predictive tool until it has been validated
and calibrated with experimental data [ 56 ]. Another limitation and open question of
current multiscale methods is how to easily extend the analysis to three dimensions.
Most of the methods described in this chapter are useful only in one or two dimensions
[ 1 ]. Currently available multiscale methods have tremendous challenge in dealing
with nonlinear problems [ 67 ].
Moreover, a consistent difficulty in multiscale mathematical modeling is how to
bridge spatial and temporal scales in a systematic and seamless fashion. In many
biological phenomena, such as protein folding and cell proliferation, events at small
scales occur much quicker than events at larger scales. In some cases, multiscale
methods provide the tools to handle the different spatial scales, but not the temporal
scales [ 1 , 5 , 6 , 8 , 10 - 12 , 14 , 15 ].
The future direction of multiscale modeling calls for developing mathematical
methods to apply in three dimensions with the ability to simultaneously bridge spatial
and temporal scales. These additional capabilities will allow for development of more
biologically relevant and useful predictive models.

Acknowledgments The authors would like to express our sincere gratitude to J. Cliff Zhou for his
early involvement in this work, and Dr. M.N. Rylander and her group for providing information
regarding the 3D in vitro cell culture system. The funding from NSF/CREST program 0932339 is

highly appreciated and acknowledged.

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