Both individual-based models and PDE models have been developed to describe the active movement of cell populations in various contexts. Individual-based models can faithfully replicate the detailed mechanisms of cell signaling and movement but are computationally intensive. PDE models are amenable for fast computation and mathematical analysis but are often based on phenomenological descriptions of macroscopic cell fluxes. Multiscale methods must be developed to elucidate the connections between individual-based models and PDE models in order to combine the strengths of these approaches. This chapter summarizes recent progress in connecting individual-based models and PDE models for chemotaxis of bacterial populations, which is a classic example for multiscale modeling in biology. The application scope and limitations of the Keller-Segel chemotaxis equation are also discussed.
|Original language||English (US)|
|Title of host publication||Modeling and Simulation in Science, Engineering and Technology|
|Number of pages||25|
|State||Published - 2018|
|Name||Modeling and Simulation in Science, Engineering and Technology|
Bibliographical noteFunding Information:
Acknowledgements I would like to thank Professor Hans Othmer and Professor Radek Erban for past collaboration and discussion on the described research. I also thank my student Clinton Durney for proofreading this chapter. This work was supported by the National Science Foundation under grant No. DMS-1312966 and NSF CAREER Award 1553637.
© 2018, Springer Nature Switzerland AG.
Copyright 2018 Elsevier B.V., All rights reserved.