|
[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.doi: 10.1016/j.jmps.2010.12.011.
|
|
[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.doi: 10.1016/j.celrep.2014.07.019.
|
|
[3]
|
J. O. Berger, Bayesian analysis: A look at today and thoughts of tomorrow, J. Am. Statist. Assoc., 95 (2000), 1269-1276.doi: 10.1080/01621459.2000.10474328.
|
|
[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.doi: 10.1016/j.gde.2011.08.008.
|
|
[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.doi: 10.1038/nmeth.1327.
|
|
[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.doi: 10.1103/PhysRevLett.99.248101.
|
|
[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.doi: 10.1098/rsif.2012.0263.
|
|
[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.doi: 10.1016/0022-5193(82)90135-7.
|
|
[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.doi: 10.1371/journal.pcbi.1001045.
|
|
[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.doi: 10.1039/c3ib40163d.
|
|
[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.doi: 10.1016/j.bpj.2010.09.034.
|
|
[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.doi: 10.1186/1752-0509-4-107.
|
|
[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.doi: 10.1007/s00285-012-0539-4.
|
|
[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.doi: 10.1098/rsif.2014.0631.
|
|
[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.doi: 10.1137/120866403.
|
|
[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.doi: 10.1201/b10407-7.
|
|
[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.doi: 10.1016/j.jtbi.2012.01.021.
|
|
[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.doi: 10.1016/j.pbiomolbio.2013.09.003.
|
|
[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.doi: 10.1093/imammb/dqp015.
|
|
[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.doi: 10.1115/1.3090829.
|
|
[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.doi: 10.1038/sj.bjc.6603922.
|
|
[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.doi: 10.1111/j.2044-8317.2011.02037.x.
|
|
[27]
|
J. A. Glazier and F. Graner, Simulation of the differential adhesion driven rearrangement of biological cells, Phys. Rev. E, 47 (1993), p2128.doi: 10.1103/PhysRevE.47.2128.
|
|
[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.doi: 10.1007/978-3-7643-8123-3_4.
|
|
[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.doi: 10.1103/PhysRevLett.69.2013.
|
|
[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.doi: 10.1140/epje/i2007-10298-8.
|
|
[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.doi: 10.1017/CBO9780511762956.
|
|
[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.doi: 10.1007/s00285-012-0595-9.
|
|
[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.doi: 10.1017/CBO9780511790423.
|
|
[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.doi: 10.4161/cc.6.17.4649.
|
|
[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.doi: 10.1073/pnas.0611179104.
|
|
[40]
|
G. W. Jones and S. J. Chapman, Modeling growth in biological materials, SIAM Rev., 54 (2012), 52-118.doi: 10.1137/080731785.
|
|
[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.doi: 10.1049/iet-syb.2012.0019.
|
|
[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.doi: 10.1016/S0006-3495(95)79996-9.
|
|
[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.doi: 10.3934/mbe.2009.6.59.
|
|
[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.doi: 10.1111/j.1365-2184.1986.tb00763.x.
|
|
[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.doi: 10.1103/PhysRevE.78.061904.
|
|
[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.doi: 10.3934/dcds.2014.34.5123.
|
|
[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.doi: 10.1140/epje/i2007-10300-7.
|
|
[50]
|
G. A. Maugin, The Thermomechanics of Nonlinear Irreversible Behaviors, World Scientific, 1999.doi: 10.1142/3700.
|
|
[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.doi: 10.1046/j.0960-7722.2001.00216.x.
|
|
[52]
|
A. Menzel and E. Kuhl, Frontiers in growth and remodeling, Mech. Res. Commun., 42 (2012), 1-14.doi: 10.1016/j.mechrescom.2012.02.007.
|
|
[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.doi: 10.1016/j.jtbi.2014.06.011.
|
|
[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.doi: 10.1016/j.jtbi.2012.08.002.
|
|
[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.doi: 10.1371/journal.pcbi.1002970.
|
|
[56]
|
K. Mosegaard and A. Tarantola, Probabilistic approach to inverse problems, Int. Geophys. Series, 81 (2002), 237-265.doi: 10.1016/S0074-6142(02)80219-4.
|
|
[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.doi: 10.1103/PhysRevE.80.031912.
|
|
[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.doi: 10.1103/PhysRevE.85.021921.
|
|
[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.doi: 10.1088/1478-3975/8/2/026011.
|
|
[60]
|
T. Newman and R. Grima, Many-body theory of chemotactic cell-cell interactions, Phys. Rev. E, 70 (2004), 051916.doi: 10.1103/PhysRevE.70.051916.
|
|
[61]
|
T. J. Newman, Modeling multicellular systems using subcellular elements, Math. Biosci. Eng.: MBE, 2 (2005), 613-624.doi: 10.3934/mbe.2005.2.613.
|
|
[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.doi: 10.1142/S0218202510004313.
|
|
[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.doi: 10.1142/S0218202513500103.
|
|
[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.doi: 10.1098/rsta.2010.0173.
|
|
[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.doi: 10.1016/S0378-4371(03)00574-0.
|
|
[66]
|
J. Ovadia and Q. Nie, Stem cell niche structure as an inherent cause of undulating epithelial morphologies, Biophys. J., 104 (2013), 237-246.doi: 10.1016/j.bpj.2012.11.3807.
|
|
[67]
|
F. Radtke and H. Clevers, Self-renewal and cancer of the gut: Two sides of a coin, Science, 307 (2005), 1904-1909.doi: 10.1126/science.1104815.
|
|
[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.doi: 10.1103/PhysRevE.81.031404.
|
|
[69]
|
L. Reuss, Epithelial Transport, Compr. Physiol., 2011.doi: 10.1002/cphy.cp140108.
|
|
[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.doi: 10.1126/science.137.3532.762.
|
|
[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.doi: 10.1073/pnas.48.9.1577.
|
|
[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.doi: 10.1073/pnas.48.10.1769.
|
|
[76]
|
M. S. Steinberg, Reconstruction of tissues by dissociated cells, Science, 141 (1963), 401-408.doi: 10.1126/science.141.3579.401.
|
|
[77]
|
A. M. Stuart, Inverse problems: A Bayesian perspective, Acta Numerica, 19 (2010), 451-559.doi: 10.1017/S0962492910000061.
|
|
[78]
|
A. Tarantola, Inverse Problem Theory and Methods for Model Parameter Estimation, SIAM, 2005.doi: 10.1137/1.9780898717921.
|
|
[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.doi: 10.1006/jtbi.2001.2522.
|
|
[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.doi: 10.1111/j.1365-2184.2009.00627.x.
|
|
[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.doi: 10.1186/1752-0509-6-93.
|
|
[86]
|
H. Ziegler, An Introduction to Thermomechanics, Elsevier, 1983.
|
{{journal.titleEn}} 
DownLoad: