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5 - Mathematical modeling and simulation

Published online by Cambridge University Press:  05 September 2013

Tadashi Nakano ,
Andrew W. Eckford  and
Tokuko Haraguchi
Tadashi Nakano
Affiliation:
University of Osaka, Japan
Andrew W. Eckford
Affiliation:
York University, Toronto
Tokuko Haraguchi
Affiliation:
National Institute of Information and Communications Technology (NICT), Hyogo, Japan
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Summary

In this chapter, we are concerned with mathematical models for molecular communication systems, which allow engineers to perform mathematical analysis, design, and optimization on communication systems. Furthermore, the system model also provides a level of mathematical abstraction, which allows a communication system engineer to understand a molecular communication system along with the biochemical background provided elsewhere in this book. As a result, tools from the vast literature on communications systems may be adapted to molecular communication.

In this chapter, we review recent results in channel modeling for molecular communication. These, and related, models are used in Chapter 6 to calculate the channel capacity of molecular communication, but we present brief examples to introduce the communication problem. This chapter requires familiarity with basic probability and the Gaussian distribution; for a brief review, see Appendix.

Discrete diffusion and Brownian motion

Free molecules in a fluid propagate via Brownian motion, i.e., the random motion induced by collisions with the fluid's molecules. Although highly random, Brownian motion is always available, and has the advantage of zero energy cost to the user. Furthermore, Brownian motion is a very well studied phenomenon, with a rich mathematical literature. In this section, we exploit that literature to derive mathematical models for Brownian motion.

Type
Chapter
Information
Molecular Communication , pp. 71 - 96
Publisher: Cambridge University Press
Print publication year: 2013

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References

[1] I., Karatzas and S. E., Shreve, Brownian Motion and Stochastic Calculus, 2nd edition. New York: Springer, 1991.
[2] S., Goldstein, “Mechanical models of Brownian motion,” Lecture Notes in Physics, vol. 153, pp. 21–24, 1982.Google Scholar
[3] J., Berthier, Microfluidics for Biotechnology. Artech House, 2006.
[4] T., Nitta, A., Tanahashi, M., Hirano, and H., Hess, “Simulating molecular shuttle movements: Towards computer-aided design of nanoscale transport systems,” Labon a Chip,vol.6, pp. 881–885, 2006.Google Scholar
[5] A. W., Eckford, “Timing information rates for active transport molecular communication,” in Proc. 4th International Conference on Nano-Networks, Lucerne, Switzerland, 2009.
[6] N., Farsad, A. W., Eckford, S., Hiyama, and Y., Moritani, “Microchannel molecular communication with nanoscale carriers: Brownian motion versus active transport,” in IEEE International Conference on Nanotechnology, 2010.
[7] R. S, Chhikara and J. L., Folks, The Inverse Gaussian Distribution: Theory, Methodology, and Applications. Marcel Dekker, 1989.
[8] M., Pierobon and I. F., Akyildiz, “Diffusion-based noise analysis for molecular communication in nanonetworks,” IEEE Transactions on Signal Processing, vol. 59, no. 6, pp. 2532–2547, June 2011.Google Scholar
[9] L., Cui and A. W., Eckford, “The delay selector channel: Definition and capacity bounds,” in Proc. Canadian Workshop on Information Theory (CWIT), 2011.
[10] P. J., Thomas, D. J., Spencer, S. K., Hampton, P., Park, and J. P., Zurkus, “The diffusion mediated biochemical signal relay channel,” in 17th Annual Conference on Neural Information Processing Systems, 2003.

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