`a`
Mathematical Biosciences and Engineering (MBE)
 

Models, measurement and inference in epithelial tissue dynamics
Pages: 1321 - 1340, Issue 6, December 2015

doi:10.3934/mbe.2015.12.1321      Abstract        References        Full text (515.2K)           Related Articles

Oliver J. Maclaren - Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Radcli e Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, United Kingdom (email)
Helen M. Byrne - Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD, United Kingdom (email)
Alexander G. Fletcher - Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Radcli e Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, United Kingdom (email)
Philip K. Maini - Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Radcli e Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, United Kingdom (email)

1 D. Ambrosi, G. A. Ateshian, E. M. Arruda, S. C. Cowin, J. Dumais, A. Goriely, G. A. Holzapfel, J. D. Humphrey, R. Kemkemer, E. Kuhl, J. E. Olberding, L. A. Taber and K. Garikipati, Perspectives on biological growth and remodeling, J. Mech. Phys. Solids, 59 (2011), 863-883.       
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), 940-947.
3 J. O. Berger, Bayesian analysis: A look at today and thoughts of tomorrow, J. Am. Statist. Assoc., 95 (2000), 1269-1276.       
4 G. B. Blanchard and R. J. Adams, Measuring the multi-scale integration of mechanical forces during morphogenesis, Curr. Opin. Genet. Dev., 21 (2011), 653-663.
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), 458-464.
6 M. Block, E. Schöll and D. Drasdo, Classifying the expansion kinetics and critical surface dynamics of growing cell populations, Phys. Rev. Lett., 99 (2007), 248101.
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), 20120263.
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), 531-541.
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), e1001045.
10 A. J. Carulli, L. C. Samuelson and S. Schnell, Unraveling intestinal stem cell behavior with models of crypt dynamics, Integr. Biol., 6 (2014), 243-257.
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), 3145-3154.
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), p107.
13 M. Dashti and A. M. Stuart, The Bayesian approach to inverse problems, arXiv:1302.6989v3
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), 1409-1462.       
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), 20140631.
16 A. Deutsch and S. Dormann, Cellular Automaton Modeling of Biological Pattern Formation: Characterization, Applications, and Analysis, Springer, 2005.
17 I. N. Figueiredo and C. Leal, Physiologic parameter estimation using inverse problems, SIAM J. Appl. Math., 73 (2013), 1164-1182.       
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, Editor: TS Deisboeck, 6 (2010), 111-134.
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), 118-133.       
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), 299-326.
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), 39-74.       
22 M. H. Friedman, Principles and Models of Biological Transport, Springer, New York, 2008.
23 K. Garikipati, The kinematics of biological growth, Appl. Mech. Rev., 62 (2009), 030801.
24 R. A. Gatenby, K. Smallbone, P. K. Maini, F. Rose, J. Averill, R. B. Nagle, L. Worrall and R. J. Gillies, Cellular adaptations to hypoxia and acidosis during somatic evolution of breast cancer, Brit. J. Cancer, BJC, 97 (2007), 646-653.
25 A. Gelman, J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari and D. B. Rubin, Bayesian Data Analysis, CRC press, 2013.
26 A. Gelman and C. R. Shalizi, Philosophy and the practice of Bayesian statistics, Br. J. Math. Stat. Psychol., 66 (2013), 8-38.       
27 J. A. Glazier and F. Graner, Simulation of the differential adhesion driven rearrangement of biological cells, Phys. Rev. E, 47 (1993), p2128.
28 J. A. Glazier, A. Balter and N. J. Popławski, Magnetization to morphogenesis: A brief history of the Glazier-Graner-Hogeweg model, In Single-Cell-Based Models in Biology and Medicine, pages 79-106. Springer, 2007.
29 F. Graner and J. A. Glazier, Simulation of biological cell sorting using a two-dimensional extended Potts model, Phys. Rev. Lett., 69 (1992), p2013.
30 F. Graner, B. Dollet, C. Raufaste and P. Marmottant, Discrete rearranging disordered patterns. Part I: Robust statistical tools in two or three dimensions, Eur. Phys. J. E Soft Matter, 25 (2008), 349-369.
31 M.E. Gurtin Configurational Forces as Basic Concepts of Continuum Physics, volume 137. Springer, 2000.       
32 M. E. Gurtin, E. Fried and L. Anand, The Mechanics and Thermodynamics of Continua, Cambridge University Press, 2010.       
33 A. Hawkins-Daarud, S. Prudhomme, K. G. van der Zee and J. T. Oden, Bayesian calibration, validation, and uncertainty quantification of diffuse interface models of tumor growth, J. Math. Biol., 67 (2013), 1457-1485.       
34 G. T. Houlsby and A. M. Puzrin, Principles of Hyperplasticity, Springer, 2007.
35 M. Iglesias and M. A. Stuart, Inverse problems and uncerrainty quantification, In SIAM News, volume July/August, 2014.
36 E. T. Jaynes, ET Jaynes: Papers on Probability, Statistics, and Statistical Physics, volume 50. Springer, 1989.
37 E. T. Jaynes, Probability Theory: the Logic of Science, Cambridge University Press, 2003.       
38 M. D. Johnston, C. M. Edwards, W. F. Bodmer, P. K. Maini and S. J. Chapman, Examples of mathematical modeling: Tales from the crypt, Cell Cycle, 6 (2007), 2106-2112.
39 M. D. Johnston, C. M. Edwards, W. F. Bodmer, P. K. Maini and S. J. Chapman, Mathematical modeling of cell population dynamics in the colonic crypt and in colorectal cancer, Proc. Natl. Acad. Sci. USA, 104 (2007), 4008-4013.
40 G. W. Jones and S. J. Chapman, Modeling growth in biological materials, SIAM Rev., 54 (2012), 52-118.       
41 S. K. Kershaw, H. M. Byrne, D. J. Gavaghan and J. M. Osborne, Colorectal cancer through simulation and experiment, IET Syst. Biol., 7 (2013), p57.
42 A. D. Lander, K. K. Gokoffski, F. Y. M. Wan, Q. Nie and A. L. Calof, Cell lineages and the logic of proliferative control, PLoS Biol., 7 (2009), e1000015.
43 Y. Lee, S. Kouvroukoglou, L. McIntire and K. Zygourakis, A cellular automaton model for the proliferation of migrating contact-inhibited cells, Biophys. J., 69 (1995), 1284-1298.
44 W.-C. Lo, C.-S. Chou, K. K. Gokoffski, F. Y.-M. Wan, A. D. Lander, A. L. Calof and Q. Nie, Feedback regulation in multistage cell lineages, Math. Biosci. Eng.: MBE, 6 (2009), 59-82.       
45 M. Loeffler, R. Stein, H.-E. Wichmann, C. S. Potten, P. Kaur and S. Chwalinski, Intestinal cell proliferation. I. a comprehensive model of steady-state proliferation in the crypt, Cell Prolif., 19 (1986), 627-645.
46 P. M. Lushnikov, N. Chen and M. Alber, Macroscopic dynamics of biological cells interacting via chemotaxis and direct contact, Phys Rev. E, 78 (2008), 061904.
47 A. M. Marchiando, W. V. Graham and J. R. Turner, Epithelial barriers in homeostasis and disease, Annu. Rev. Pathol. - Mech., 5 (2010), 119-144.
48 D. C. Markham, R. E. Baker and P. K. Maini, Modelling collective cell behaviour, Disc. Cont. Dyn. Syst., 34 (2014), 5123-5133.       
49 P. Marmottant, C. Raufaste and F. Graner, Discrete rearranging disordered patterns, part II: 2D plasticity, elasticity and flow of a foam, Eur. Phys. J.E, 25 (2008), 371-384.
50 G. A. Maugin, The Thermomechanics of Nonlinear Irreversible Behaviors, World Scientific, 1999.
51 F. A. Meineke, C. S. Potten and M. Loeffler, Cell migration and organization in the intestinal crypt using a lattice-free model, Cell Prolif., 34 (2001), 253-266.
52 A. Menzel and E. Kuhl, Frontiers in growth and remodeling, Mech. Res. Commun., 42 (2012), 1-14.
53 A. M. Middleton, C. Fleck and R. Grima, A continuum approximation to an off-lattice individual-cell based model of cell migration and adhesion, J. Theor. Biol., 359 (2014), 220-232.       
54 G. R. Mirams, A. G. Fletcher, P. K. Maini and H. M. Byrne, A theoretical investigation of the effect of proliferation and adhesion on monoclonal conversion in the colonic crypt, J. Theor. Biol., 312 (2012), 143-156.       
55 G. R. Mirams, C. J. Arthurs, M. O. Bernabeu, R. Bordas, J. Cooper, A. Corrias, Y. Davit, S.-J. Dunn, A. G. Fletcher, D. G. Harvey, M. E. Marsh, J. M. Osborne, P. Pathmanathan, J. M. Pitt-Francis, J. Southern, N. Zemzemi and D. J. Gavaghan, Chaste: an open source C++ library for computational physiology and biology, PLoS Comput. Biol., 9 (2013), e1002970, 8pp.       
56 K. Mosegaard and A. Tarantola, Probabilistic approach to inverse problems, Int. Geophys. Series, 81 (2002), 237-265.
57 P. J. Murray, C. M. Edwards, M. J. Tindall and P. K. Maini, From a discrete to a continuum model of cell dynamics in one dimension, Phys. Rev. E, 80 (2009), 031912.
58 P. J. Murray, C. M. Edwards, M. J. Tindall and P. K. Maini, Classifying general nonlinear force laws in cell-based models via the continuum limit, Phys. Rev. E, 85 (2012), 021921.
59 P. J. Murray, A. Walter, A. G. Fletcher, C. M. Edwards, M. J. Tindall and P. K. Maini, Comparing a discrete and continuum model of the intestinal crypt, Phys. Biol., 8 (2011), 026011.
60 T. Newman and R. Grima, Many-body theory of chemotactic cell-cell interactions, Phys. Rev. E, 70 (2004), 051916.
61 T. J. Newman, Modeling multicellular systems using subcellular elements, Math. Biosci. Eng.: MBE, 2 (2005), 613-624.       
62 J. T. Oden, A. Hawkins and S. Prudhomme, General diffuse-interface theories and an approach to predictive tumor growth modeling, Math. Mod. Meth. Appl. S., 20 (2010), 477-517.       
63 J. T. Oden, E. E. Prudencio and A. Hawkins-Daarud, Selection and assessment of phenomenological models of tumor growth, Math. Mod. Meth. Appl. S., 23 (2013), 1309-1338.       
64 J. M. Osborne, A. Walter, S. K. Kershaw, G. R. Mirams, A. G. Fletcher, P. Pathmanathan, D. Gavaghan, O. E. Jensen, P. K. Maini and H. M. Byrne, A hybrid approach to multi-scale modelling of cancer, Phil. Trans. R. Soc. A, 368 (2010), 5013-5028.       
65 N. B. Ouchi, J. A. Glazier, J.-P. Rieu, A. Upadhyaya and Y. Sawada, Improving the realism of the cellular Potts model in simulations of biological cells, Physica A, 329 (2003), 451-458.       
66 J. Ovadia and Q. Nie, Stem cell niche structure as an inherent cause of undulating epithelial morphologies, Biophys. J., 104 (2013), 237-246.
67 F. Radtke and H. Clevers, Self-renewal and cancer of the gut: Two sides of a coin, Science, 307 (2005), 1904-1909.
68 C. Raufaste, S. J. Cox, P. Marmottant and F. Graner, Discrete rearranging disordered patterns: Prediction of elastic and plastic behavior, and application to two-dimensional foams, Phys. Rev. E, 81 (2010), 031404.
69 L. Reuss, Epithelial Transport, Compr. Physiol., 2011.
70 S. A. Sandersius, M. Chuai, C. Weijer and T. J. Newman, A 'chemotactic dipole' mechanism for large-scale vortex motion during primitive streak formation in the chick embryo, Phys. Biol., 8 (2011), 045008.
71 S. A. Sandersius, C. Weijer and T. J. Newman, Emergent cell and tissue dynamics from subcellular modeling of active biomechanical processes, Phys. Biol., 8 (2011), 045007.
72 S. A. Sandersius and T. J. Newman, Modeling cell rheology with the subcellular element model, Phys. Biol., 5 (2008), 015002.
73 M. S. Steinberg, Mechanism of tissue reconstruction by dissociated cells. II. Time-course of events, Science, 137 (1962), 762-763.
74 M. S. Steinberg, On the mechanism of tissue reconstruction by dissociated cells. I. Population kinetics, differential adhesiveness, and the absence of directed migration, Proc. Natl. Acad. Sci. USA, 48 (1962), 1577-1582.
75 M. S. Steinberg, On the mechanism of tissue reconstruction by dissociated cells. III. Free energy relations and the reorganization of fused, heteronomic tissue fragments, Proc. Natl. Acad. Sci. USA, 48 (1962), 1769-1776.
76 M. S. Steinberg, Reconstruction of tissues by dissociated cells, Science, 141 (1963), 401-408.
77 A. M. Stuart, Inverse problems: A Bayesian perspective, Acta Numerica, 19 (2010), 451-559.       
78 A. Tarantola, Inverse Problem Theory and Methods for Model Parameter Estimation, SIAM, 2005.       
79 D. W. Thompson, On Growth and Form, 2nd ed., Cambridge University Press, Cambridge, 1942.       
80 S. Turner and J. A. Sherratt, Intercellular adhesion and cancer invasion: A discrete simulation using the extended potts model, J. Theor. Biol., 216 (2002), 85-100.       
81 I. M. M. van Leeuwen, G. R. Mirams, A. Walter, A. G. Fletcher, P. J. Murray, J. M. Osborne, S. Varma, S. J. Young, J. Cooper, B. Doyle, J. M. Pitt-Francis, P. Pathmanathan, L. Momtahan, J. P. Whiteley, S. J. Chapman, D. J. Gavaghan, O. E. Jense, J. R. King, P. K. Maini, S. L. Waters and H. M. Byrne, An integrative computational model for intestinal tissue renewal, Cell Prolif., 42 (2009), 617-636.
82 A. Voss-Böhme, Multi-scale modeling in morphogenesis: A critical analysis of the cellular potts model, PloS one, 7 (2012), e42852.
83 A. Walter, A Comparison of Continuum and Cell-based Models of Colorectal Cancer, PhD thesis, University of Nottingham, 2009.
84 N. A. Wright and M. Alison, The Biology of Epithelial Cell Populations, Volume 1. Clarendon Press Oxford, 1984.
85 L. Zhang, A. D. Lander and Q. Nie, A reaction-diffusion mechanism influences cell lineage progression as a basis for formation, regeneration, and stability of intestinal crypts, BMC Syst. Biol., 6 (2012), p93.
86 H. Ziegler, An Introduction to Thermomechanics, Elsevier, 1983.       

Go to top