2015, 12(6): 1321-1340. doi: 10.3934/mbe.2015.12.1321

Models, measurement and inference in epithelial tissue dynamics

1. 

Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Radcli e Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, United Kingdom, United Kingdom, United Kingdom

2. 

Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD, United Kingdom

Received  October 2014 Revised  February 2015 Published  August 2015

The majority of solid tumours arise in epithelia and therefore much research effort has gone into investigating the growth, renewal and regulation of these tissues. Here we review different mathematical and computational approaches that have been used to model epithelia. We compare different models and describe future challenges that need to be overcome in order to fully exploit new data which present, for the first time, the real possibility for detailed model validation and comparison.
Citation: Oliver J. Maclaren, Helen M. Byrne, Alexander G. Fletcher, Philip K. Maini. Models, measurement and inference in epithelial tissue dynamics. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1321-1340. doi: 10.3934/mbe.2015.12.1321
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[2]

A.-M. Baker, B. Cereser, S. Melton, A. G. Fletcher, M. Rodriguez-Justo, P. J. Tadrous, A. Humphries, G. Elia, S. A. C. McDonald, N. A. Wright, B. D. Simons, M. Jansen and T. A. Graham, Quantification of crypt and stem cell evolution in the normal and neoplastic human colon,, Cell Rep., 8 (2014), 940. doi: 10.1016/j.celrep.2014.07.019. Google Scholar

[3]

J. O. Berger, Bayesian analysis: A look at today and thoughts of tomorrow,, J. Am. Statist. Assoc., 95 (2000), 1269. doi: 10.1080/01621459.2000.10474328. Google Scholar

[4]

G. B. Blanchard and R. J. Adams, Measuring the multi-scale integration of mechanical forces during morphogenesis,, Curr. Opin. Genet. Dev., 21 (2011), 653. doi: 10.1016/j.gde.2011.08.008. Google Scholar

[5]

G. B. Blanchard, A. J. Kabla, N. L. Schultz, L. C. Butler, B. Sanson, N. Gorfinkiel, L. Mahadevan and R. J. Adams, Tissue tectonics: Morphogenetic strain rates, cell shape change and intercalation,, Nat. Methods, 6 (2009), 458. doi: 10.1038/nmeth.1327. Google Scholar

[6]

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[7]

I. Bonnet, P. Marcq, F. Bosveld, L. Fetler, Y. Bellaïche and F. Graner, Mechanical state, material properties and continuous description of an epithelial tissue,, J. R. Soc. Interface, 9 (2012). doi: 10.1098/rsif.2012.0263. Google Scholar

[8]

N. F. Britton, N. A. Wright and J. D. Murray, A mathematical model for cell population kinetics in the intestine,, J. Theor. Biol., 98 (1982), 531. doi: 10.1016/0022-5193(82)90135-7. Google Scholar

[9]

P. Buske, J. Galle, N. Barker, G. Aust, H. Clevers and M. Loeffler, A comprehensive model of the spatio-temporal stem cell and tissue organisation in the intestinal crypt,, PLoS Comput. Biol., 7 (2011). doi: 10.1371/journal.pcbi.1001045. Google Scholar

[10]

A. J. Carulli, L. C. Samuelson and S. Schnell, Unraveling intestinal stem cell behavior with models of crypt dynamics,, Integr. Biol., 6 (2014), 243. doi: 10.1039/c3ib40163d. Google Scholar

[11]

C.-S. Chou, W.-C. Lo, K. K. Gokoffski, Y.-T. Zhang, F. Y. Wan, A. D. Lander, A. L. Calof and Q. Nie, Spatial dynamics of multistage cell lineages in tissue stratification,, Biophy. J., 99 (2010), 3145. doi: 10.1016/j.bpj.2010.09.034. Google Scholar

[12]

S. Christley, B. Lee, X. Dai and Q. Nie, Integrative multicellular biological modeling: A case study of 3d epidermal development using GPU algorithms,, BMC Sys. Biol., 4 (2010). doi: 10.1186/1752-0509-4-107. Google Scholar

[13]

M. Dashti and A. M. Stuart, The Bayesian approach to inverse problems,, , (). Google Scholar

[14]

G. De Matteis, A. Graudenzi and M. Antoniotti, A review of spatial computational models for multi-cellular systems, with regard to intestinal crypts and colorectal cancer development,, J. Math. Biol., 66 (2013), 1409. doi: 10.1007/s00285-012-0539-4. Google Scholar

[15]

A. Gord, W. R. Holmes, X. Dai and Q. Nie, Computational modelling of epidermal stratification highlights the importance of asymmetric cell division for predictable and robust layer formation,, J. R. Soc. Interface, 11 (2014). doi: 10.1098/rsif.2014.0631. Google Scholar

[16]

A. Deutsch and S. Dormann, Cellular Automaton Modeling of Biological Pattern Formation: Characterization, Applications, and Analysis,, Springer, (2005). Google Scholar

[17]

I. N. Figueiredo and C. Leal, Physiologic parameter estimation using inverse problems,, SIAM J. Appl. Math., 73 (2013), 1164. doi: 10.1137/120866403. Google Scholar

[18]

A. G. Fletcher, G. R. Mirams, P. J. Murray, A. Walter, J.-W. Kang, K.-H. Cho, P. K. Maini and H. M. Byrne, Multiscale modeling of colonic crypts and early colorectal cancer,, In Multiscale Cancer Modeling, 6 (2010), 111. doi: 10.1201/b10407-7. Google Scholar

[19]

A. G. Fletcher, C. J. W. Breward and S. J. Chapman, Mathematical modeling of monoclonal conversion in the colonic crypt,, J. Theor. Biol., 300 (2012), 118. doi: 10.1016/j.jtbi.2012.01.021. Google Scholar

[20]

A. G. Fletcher, J. M. Osborne, P. K. Maini and D. J. Gavaghan, Implementing vertex dynamics models of cell populations in biology within a consistent computational framework,, Prog. Biophys. Mol. Bio., 113 (2013), 299. doi: 10.1016/j.pbiomolbio.2013.09.003. Google Scholar

[21]

J. A. Fozard, H. M. Byrne, O. E. Jensen and J. R. King, Continuum approximations of individual-based models for epithelial monolayers,, Math. Med. Biol., 27 (2010), 39. doi: 10.1093/imammb/dqp015. Google Scholar

[22]

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