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Computational approaches and analysis for a spatio-structural-temporal invasive carcinoma model

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hodgkinson_etal_BMB2018_manuscript_accepted.pdf (38.11Mb)
Date
04/2018
Author
Hodgkinson, Arran
Chaplain, Mark Andrew Joseph
Domschke, Pia
Trucu, Dumitru
Keywords
Cancer invasion
Structured cell population dynamics
Computational modelling
QA Mathematics
QH301 Biology
RC0254 Neoplasms. Tumors. Oncology (including Cancer)
NDAS
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Abstract
Spatio-temporal models have long been used to describe biological systems of cancer, but it has not been until very recently that increased attention has been paid to structural dynamics of the interaction between cancer populations and the molecular mechanisms associated with local invasion. One system that is of particular interest is that of the urokinase plasminogen activator (uPA) wherein uPA binds uPA receptors on the cancer cell surface, allowing plasminogen to be cleaved into plasmin, which degrades the extracellular matrix and this way leads to enhanced cancer cell migration. In this paper, we develop a novel numerical approach and associated analysis for spatio-structuro-temporal modelling of the uPA system for up to two-spatial and two-structural dimensions. This is accompanied by analytical exploration of the numerical techniques used in simulating this system, with special consideration being given to the proof of stability within numerical regimes encapsulating a central differences approach to approximating numerical gradients. The stability analysis performed here reveals instabilities induced by the coupling of the structural binding and proliferative processes. The numerical results expound how the uPA system aids the tumour in invading the local stroma, whilst the inhibitor to this system may impede this behaviour and encourage a more sporadic pattern of invasion.
Citation
Hodgkinson , A , Chaplain , M A J , Domschke , P & Trucu , D 2018 , ' Computational approaches and analysis for a spatio-structural-temporal invasive carcinoma model ' , Bulletin of Mathematical Biology , vol. 80 , no. 4 , pp. 701-737 . https://doi.org/10.1007/s11538-018-0396-4
Publication
Bulletin of Mathematical Biology
Status
Peer reviewed
DOI
https://doi.org/10.1007/s11538-018-0396-4
ISSN
0092-8240
Type
Journal article
Rights
© 2018, Society for Mathematical Biology. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1007/s11538-018-0396-4
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/17200

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