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Applications + Practical Conceptualization + Mathematics = fruitful InnovationAn Interaction with Biologists: Insights into Development and Disease

Applications + Practical Conceptualization + Mathematics = fruitful Innovation: An Interaction... [The enteric nervous system (ENS) in our gastrointestinal tract is responsible for normal gut function and peristaltic contraction. Embryonic development of the ENS involves the colonisation of the gut wall from one end to the other by a growing population of motile neural crest cells. The colonisation wave is strictly timetabled and predictable, but individual neural crest cell movement is unpredictable in speed and direction. Failure of these cells to invade the whole gut results in the relatively common, potentially fatal birth defect. Continuum modelsContinuum model of the population-level behaviour, based on the Fisher equation, are highly predictable. Discrete agent-based models, governed by agent probabilities, reproduce the population-level behaviour of the Fisher equation. However, individual agent contributions to the total population, measured by agent lineage, are highly variable. Both behaviours have been verified in a developmental invasion system. This work is the result of a rewarding long-standing and on-going collaboration between applied mathematicians and developmental biologists.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Applications + Practical Conceptualization + Mathematics = fruitful InnovationAn Interaction with Biologists: Insights into Development and Disease

Part of the Mathematics for Industry Book Series (volume 11)
Editors: Anderssen, Robert S.; Broadbridge, Philip; Fukumoto, Yasuhide; Kajiwara, Kenji; Takagi, Tsuyoshi; Verbitskiy, Evgeny; Wakayama, Masato
Landman, Kerry A.
Applications + Practical Conceptualization + Mathematics = fruitful Innovation — Sep 19, 2015
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Publisher
Springer Japan
Copyright
© Springer Japan 2016
ISBN
978-4-431-55341-0
Pages
51 –60
DOI
10.1007/978-4-431-55342-7_5
Publisher site
See Chapter on Publisher Site

Abstract

[The enteric nervous system (ENS) in our gastrointestinal tract is responsible for normal gut function and peristaltic contraction. Embryonic development of the ENS involves the colonisation of the gut wall from one end to the other by a growing population of motile neural crest cells. The colonisation wave is strictly timetabled and predictable, but individual neural crest cell movement is unpredictable in speed and direction. Failure of these cells to invade the whole gut results in the relatively common, potentially fatal birth defect. Continuum modelsContinuum model of the population-level behaviour, based on the Fisher equation, are highly predictable. Discrete agent-based models, governed by agent probabilities, reproduce the population-level behaviour of the Fisher equation. However, individual agent contributions to the total population, measured by agent lineage, are highly variable. Both behaviours have been verified in a developmental invasion system. This work is the result of a rewarding long-standing and on-going collaboration between applied mathematicians and developmental biologists.]

Published: Sep 19, 2015

Keywords: Mathematical biology; Cell invasion; Diffusion; Proliferation; Lineage

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