Biomedical Engineering Reference
In-Depth Information
sion with components at the molecular level (incorporated via diusion and
taxis processes), the cellular level (incorporated via a cell age variable), and
the tissue level (incorporated via spatial variables). They provided biologi-
cal justications for the model components, present computational results
from the models, and discussed the scientic-computing methodology used
to solve the model equations. Their models and methodology form the ba-
sis for developing and treating increasingly complex, mechanistic models of
tumor invasion that will be more predictive and less phenomenological.
10. Conclusions and outlook
The new mathematical models should link all the approaches at dierent
scales in order to gain better insight into dynamics of tumor growth or
should be a multiscale models. These models will not only replicate ex-
perimental observation but also, more importantly, predict behaviors that
have not yet been observed.
Acknowledgments
This work was supported by the Department of Mathematical Sciences at
Middle Tennessee State University. I would like to thank Dr. Don Hong for
introducing me to mathematical modeling in cancer. I also would like to
thank the anonymous referee for very constructive comments.
References
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