Mathematical Biosciences and Engineering (MBE)

A multiscale model for heterogeneous tumor spheroid in vitro
Pages: 361 - 392, Issue 2, April 2018

doi:10.3934/mbe.2018016      Abstract        References        Full text (3563.9K)           Related Articles

Zhan Chen - Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA, 30460, United States (email)
Yuting Zou - Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA, 30460, United States (email)

1 S. Aland, H. Hatzikirou, J. Lowengrub and A. Voigt, A mechanistic collective cell model for epithelial colony growth and contact inhibition, Biophysical Journal, 109 (2015), 1347-1357.
2 R. K. Banerjee, W. W. van Osdol, P. M. Bungay, C. Sung and R. L. Dedrick, Finite element model of antibody penetration in a prevascular tumor nodule embedded in normal tissue, Journal of Controlled Release, 74 (2001), 193-202.
3 S. Breslin and L. O'Driscoll, Three-dimensional cell culture: The missing link in drug discovery, Drug Discovery Today, 18 (2013), 240-249.
4 G. W. Brodland, Computational modeling of cell sorting, tissue engulfment, and related phenomena: A review, Applied Mechanics Reviews, 57 (2004), 47-76.
5 G. W. Brodland, D. Viens and J. H. Veldhuis, A new cell-based fe model for the mechanics of embryonic epithelia, Computer Methods in Biomechanics and Biomedical Engineering, 10 (2007), 121-128.
6 J. C. Butcher, Numerical Methods for Ordinary Differential Equations, John Wiley & Sons, 2016.       
7 L. L. Campbell and K. Polyak et al., Breast tumor heterogeneity: Cancer stem cells or clonal evolution?, Cell Cycle, 6 (2007), 2332-2338.
8 J. Casciari, S. Sotirchos and R. Sutherland, Mathematical modelling of microenvironment and growth in emt6/ro multicellular tumour spheroids, Cell Proliferation, 25 (1992), 1-22.
9 J. Casciari, S. Sotirchos and R. Sutherland, Variations in tumor cell growth rates and metabolism with oxygen concentration, glucose concentration, and extracellular ph, Journal of Cellular Physiology, 151 (1992), 386-394.
10 P. Cirri and P. Chiarugi, Cancer-associated-fibroblasts and tumour cells: A diabolic liaison driving cancer progression, Cancer and Metastasis Reviews, 31 (2012), 195-208.
11 J. C. Dallon and H. G. Othmer, How cellular movement determines the collective force generated by the Dictyostelium discoideum slug, J. Theor. Biol., 231 (2004), 203-222.       
12 T. S. Deisboeck, Z. Wang, P. Macklin and V. Cristini, Multiscale cancer modeling, Ann. Rev. Biomed. Eng., 13 (2011), 127-155.
13 M. J. Dorie, R. F. Kallman and M. A. Coyne, Effect of cytochalasin b, nocodazole and irradiation on migration and internalization of cells and microspheres in tumor cell spheroids, Experimental Cell Research, 166 (1986), 370-378.
14 M. J. Dorie, R. F. Kallman, D. F. Rapacchietta, D. Van Antwerp and Y. R. Huang, Migration and internalization of cells and polystyrene microspheres in tumor cell spheroids, Experimental Cell Research, 141 (1982), 201-209.
15 D. Drasdo and S. Höhme, A single-cell-based model of tumor growth in vitro: Monolayers and spheroids, Physical Biology, 2 (2005), 133-147.
16 D. Duguay, R. A. Foty and M. S. Steinberg, Cadherin-mediated cell adhesion and tissue segregation: Qualitative and quantitative determinants, Developmental Biology, 253 (2003), 309-323.
17 K. Erbertseder, J. Reichold, B. Flemisch, P. Jenny and R. Helmig, A coupled discrete/continuum model for describing cancer-therapeutic transport in the lung, PloS One, 7 (2012), e31966.
18 E. Evans, Detailed mechanics of membrane-membrane adhesion and separation. ii. discrete kinetically trapped molecular cross-bridges, Biophysical Journal, 48 (1985), 185-192.
19 E. A. Evans, Detailed mechanics of membrane-membrane adhesion and separation. i. continuum of molecular cross-bridges, Biophysical Journal, 48 (1985), 175-183.
20 E. M. Felipe De Sousa, L. Vermeulen, E. Fessler and J. P. Medema, Cancer heterogeneity-a multifaceted view, EMBO Reports, 14 (2013), 686-695.
21 T. Fiaschi and P. Chiarugi, Oxidative stress, tumor microenvironment, and metabolic reprogramming: A diabolic liaison, International Journal of Cell Biology, 2012 (2012), Article ID 762825, 8pp.
22 R. A. Foty and M. S. Steinberg, Cadherin-mediated cell-cell adhesion and tissue segregation in relation to malignancy, International Journal of Developmental Biology, 48 (2004), 397-409.
23 R. A. Foty and M. S. Steinberg, The differential adhesion hypothesis: A direct evaluation, Developmental Biology, 278 (2005), 255-263.
24 R. A. Foty and M. S. Steinberg, Differential adhesion in model systems, Wiley Interdisciplinary Reviews: Developmental Biology 2 (2013), 631-645.
25 J. Freyer and R. Sutherland, A reduction in the in situ rates of oxygen and glucose consumption of cells in emt6/ro spheroids during growth, Journal of Cellular Physiology, 124 (1985), 516-524.
26 J. Galle, G. Aust, G. Schaller, T. Beyer and D. Drasdo, Individual cell-based models of the spatial-temporal organization of multicellular systems-achievements and limitations, Cytometry Part A, 69 (2006), 704-710.
27 D. Garrod and M. Steinberg, Tissue-specific sorting-out in two dimensions in relation to contact inhibition of cell movement, Nature, 244 (1973), 568-569.
28 P. Gerlee and A. R. Anderson, An evolutionary hybrid cellular automaton model of solid tumour growth, Journal of Theoretical Biology, 246 (2007), 583-603.       
29 M. Gerlinger, A. J. Rowan, S. Horswell, J. Larkin, D. Endesfelder, E. Gronroos, P. Martinez, N. Matthews, A. Stewart, P. Tarpey et al., Intratumor heterogeneity and branched evolution revealed by multiregion sequencing, New England Journal of Medicine, 366 (2012), 883-892.
30 R. H. Grantab and I. F. Tannock, Penetration of anticancer drugs through tumour tissue as a function of cellular packing density and interstitial fluid pressure and its modification by bortezomib, BMC Cancer, 12 (2012), 214.
31 J. B. Green, Sophistications of cell sorting, Nature Cell Biology, 10 (2008), 375-377.
32 E. Hairer, S. Nǿrsett and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems, Second edition. Springer Series in Computational Mathematics, 8. Springer-Verlag, Berlin, 1993.       
33 J. W. Haycock, 3d cell culture: A review of current approaches and techniques, 3D Cell Culture,695 (2010), 1-15.
34 G. Helmlinger, P. A. Netti, H. C. Lichtenbeld, R. J. Melder and R. K. Jain, Solid stress inhibits the growth of multicellular tumor spheroids, Nature Biotechnology, 15 (1997), 778-783.
35 F. Hirschhaeuser, H. Menne, C. Dittfeld, J. West, W. Mueller-Klieser and L. A. Kunz-Schughart, Multicellular tumor spheroids: An underestimated tool is catching up again, Journal of Biotechnology, 148 (2010), 3-15.
36 M. S. Hutson, G. W. Brodland, J. Yang and D. Viens, Cell sorting in three dimensions: Topology, fluctuations, and fluidlike instabilities, Physical Review Letters, 101 (2008), 148105.
37 J. N. Jennings, A New Computational Model for Multi-cellular Biological Systems, PhD thesis, University of Cambridge, 2014.
38 Y. Jiang, H. Levine and J. Glazier, Possible cooperation of differential adhesion and chemotaxis in mound formation of dictyostelium, Biophysical Journal, 75 (1998), 2615-2625.
39 Y. Jiang, J. Pjesivac-Grbovic, C. Cantrell and J. P. Freyer, A multiscale model for avascular tumor growth, Biophysical journal, 89 (2005), 3884-3894.
40 K. Kendall, Adhesion: Molecules and mechanics, Science, 263 (1994), 1720-1725.
41 Z. I. Khamis, Z. J. Sahab and Q. X. A. Sang, Active roles of tumor stroma in breast cancer metastasis, International Journal of Breast Cancer, 2012 (2012), Article ID 574025, 10pp.
42 Y. Kim, M. Stolarska and H. Othmer, The role of the microenvironment in tumor growth and invasion, Progress in Biophysics and Molecular Biology, 106 (2011), 353-379.
43 Y. Kim and H. G. Othmer, A hybrid model of tumor-stromal interactions in breast cancer, Bull. Math. Biol., 75 (2013), 1304-1350.       
44 Y. KIM and S. ROH, A hybrid model for cell proliferation and migration in glioblastoma, Discrete & Continuous Dynamical Systems-Series B, 18 (2013), 969-1015.       
45 Y. Kim, M. A. Stolarska and H. G. Othmer, A hybrid model for tumor spheroid growth in vitro i: Theoretical development and early results, Mathematical Models and Methods in Applied Sciences, 17 (2007), 1773-1798.       
46 L. C. Kimlin, G. Casagrande and V. M. Virador, In vitro three-dimensional (3d) models in cancer research: An update, Molecular Carcinogenesis, 52 (2013), 167-182.
47 T. Lecuit and P.-F. Lenne, Cell surface mechanics and the control of cell shape, tissue patterns and morphogenesis, Nature Reviews Molecular Cell Biology, 8 (2007), 633-644.
48 X.-F. Li, S. Carlin, M. Urano, J. Russell, C. C. Ling and J. A. O'Donoghue, Visualization of hypoxia in microscopic tumors by immunofluorescent microscopy, Cancer Research, 67 (2007), 7646-7653.
49 D. Loessner, J. P. Little, G. J. Pettet and D. W. Hutmacher, A multiscale road map of cancer spheroids-incorporating experimental and mathematical modelling to understand cancer progression, J Cell Sci, 126 (2013), 2761-2771.
50 P. Macklin, S. McDougall, A. R. Anderson, M. A. Chaplain, V. Cristini and J. Lowengrub, Multiscale modelling and nonlinear simulation of vascular tumour growth, Journal of Mathematical Biology, 58 (2009), 765-798.       
51 J.-L. Maître, H. Berthoumieux, S. F. G. Krens, G. Salbreux, F. Jülicher, E. Paluch and C.-P. Heisenberg, Adhesion functions in cell sorting by mechanically coupling the cortices of adhering cells, Science, 338 (2012), 253-256.
52 M. Martins, S. Ferreira and M. Vilela, Multiscale models for the growth of avascular tumors, Physics of Life Reviews, 4 (2007), 128-156.
53 A. Marusyk, V. Almendro and K. Polyak, Intra-tumour heterogeneity: A looking glass for cancer?, Nature Reviews Cancer,12 (2012), 323-334.
54 D. McElwain and G. Pettet, Cell migration in multicell spheroids: Swimming against the tide, Bulletin of Mathematical Biology, 55 (1993), 655-674.
55 E. Méhes, E. Mones, V. Németh and T. Vicsek, Collective motion of cells mediates segregation and pattern formation in co-cultures, PloS One, 7.
56 L. M. F. Merlo, J. W. Pepper, B. J. Reid and C. C. Maley, Cancer as an evolutionary and ecological process, Nature Reviews Cancer, 6 (2006), 924-935.
57 D. Miller, Sugar uptake as a function of cell volume in human erythrocytes, The Journal of Physiology, 170 (1964), 219-225.
58 W. F. Mueller-Klieser and R. M. Sutherland, Oxygen consumption and oxygen diffusion properties of multicellular spheroids from two different cell lines, in Oxygen Transport to Tissue-VI, Springer, 180 (1984), 311-321.
59 S. M. Mumenthaler, J. Foo, N. C. Choi, N. Heise, K. Leder, D. B. Agus, W. Pao, F. Michor and P. Mallick, The impact of microenvironmental heterogeneity on the evolution of drug resistance in cancer cells, Cancer Informatics, 14 (2015), 19-31.
60 S. Mumenthaler, J. Foo, K. Leder, N. Choi, D. Agus, W. Pao, P. Mallick and F. Michor, Evolutionary modeling of combination treatment strategies to overcome resistance to tyrosine kinase inhibitors in non-small cell lung cancer, Molecular Pharmaceutics, 8 (2011), 2069-2079.
61 T. J. Newman, Modeling multi-cellular systems using sub-cellular elements, Math. Biosci. Eng., 2 (2005), 613-624, arXiv preprint q-bio/0504028.       
62 H. Ninomiya, R. David, E. W. Damm, F. Fagotto, C. M. Niessen and R. Winklbauer, Cadherin-dependent differential cell adhesion in xenopus causes cell sorting in vitro but not in the embryo, Journal of Cell Science, 125 (2012), 1877-1883.
63 E. Palsson, A three-dimensional model of cell movement in multicellular systems, Future Generation Computer Systems, 17 (2001), 835-852.
64 E. Palsson, A 3-d model used to explore how cell adhesion and stiffness affect cell sorting and movement in multicellular systems, Journal of Theoretical Biology, 254 (2008), 1-13.       
65 E. Palsson and H. G. Othmer, A model for individual and collective cell movement in dictyostelium discoideum, Proceedings of the National Academy of Sciences, 97 (2000), 10448-10453.
66 G. Pettet, C. Please, M. Tindall and D. McElwain, The migration of cells in multicell tumor spheroids, Bulletin of Mathematical Biology, 63 (2001), 231-257.
67 K. Polyak, Heterogeneity in breast cancer, The Journal of Clinical Investigation, 121 (2011), 3786.
68 N. J. Popławski, U. Agero, J. S. Gens, M. Swat, J. A. Glazier and A. R. Anderson, Front instabilities and invasiveness of simulated avascular tumors, Bulletin of Mathematical Biology, 71 (2009), 1189-1227.       
69 A. Quarteroni, R. Sacco and F. Saleri, Matematica Numerica, Springer Science & Business Media, 1998.       
70 A. A. Qutub, F. M. Gabhann, E. D. Karagiannis, P. Vempati and A. S. Popel, Multiscale models of angiogenesis, Engineering in Medicine and Biology Magazine, IEEE, 28 (2009), 14-31.
71 K. A. Rejniak and R. H. Dillon, A single cell-based model of the ductal tumour microarchitecture, Computational and Mathematical Methods in Medicine, 8 (2007), 51-69.       
72 T. Roose, P. A. Netti, L. L. Munn, Y. Boucher and R. K. Jain, Solid stress generated by spheroid growth estimated using a linear poroelastisity model, Microvascular Research, 66 (2003), 204-212.
73 G. Schaller and M. Meyer-Hermann, Multicellular tumor spheroid in an off-lattice voronoi-delaunay cell model, Physical Review E, 71 (2005), 051910, 16pp.       
74 G. Schaller and M. Meyer-Hermann, Continuum versus discrete model: a comparison for multicellular tumour spheroids, Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 364 (2006), 1443-1464.       
75 E.-M. Schötz, R. D. Burdine, F. Jülicher, M. S. Steinberg, C.-P. Heisenberg and R. A. Foty, Quantitative differences in tissue surface tension influence zebrafish germ layer positioning, HFSP journal, 2 (2008), 42-56.
76 R. Shipley and S. Chapman, Multiscale modelling of fluid and drug transport in vascular tumours, Bulletin of Mathematical Biology, 72 (2010), 1464-1491.       
77 A. Shirinifard, J. S. Gens, B. L. Zaitlen, N. J. Popławski, M. Swat and J. A. Glazier, 3d multi-cell simulation of tumor growth and angiogenesis, PloS One, 4 (2009), e7190.
78 K. Smalley, M. Lioni and M. Herlyn, Life ins't flat: Taking cancer biology to the next dimension, In Vitro Cellular & Developmental Biology-Animal, 42 (2006), 242-247.
79 A. Starzec, D. Briane, M. Kraemer, J.-C. Kouyoumdjian, J.-L. Moretti, R. Beaupain and O. Oudar, Spatial organization of three-dimensional cocultures of adriamycin-sensitive and-resistant human breast cancer mcf-7 cells, Biology of the Cell, 95 (2003), 257-264.
80 M. S. Steinberg, Reconstruction of tissues by dissociated cells, Science, 141 (1963), 401-408.
81 M. S. Steinberg, Adhesion in development: An historical overview, Developmental Biology, 180 (1996), 377-388.
82 M. Steinberg and D. Garrod, Observations on the sorting-out of embryonic cells in monolayer culture, Journal of Cell Science, 18 (1975), 385-403.
83 M. A. Stolarska, Y. Kim and H. G. Othmer, Multi-scale models of cell and tissue dynamics, Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 367 (2009), 3525-3553.       
84 K. Sung, C. Dong, G. Schmid-Schönbein, S. Chien and R. Skalak, Leukocyte relaxation properties, Biophysical Journal, 54 (1988), 331-336.
85 M. H. Swat, S. D. Hester, R. W. Heiland, B. L. Zaitlen, J. A. Glazier and A. Shirinifard, Compucell3d manual and tutorial version 3.5. 0.
86 G. Taraboletti, D. D. Roberts and L. A. Liotta, Thrombospondin-induced tumor cell migration: Haptotaxis and chemotaxis are mediated by different molecular domains, The Journal of Cell Biology, 105 (1987), 2409-2415.
87 K. Thompson and H. Byrne, Modelling the internalization of labelled cells in tumour spheroids, Bulletin of Mathematical Biology, 61 (1999), 601-623.
88 P. L. Townes and J. Holtfreter, Directed movements and selective adhesion of embryonic amphibian cells, Journal of Experimental Zoology, 128 (1955), 53-120.
89 G. Wayne Brodland and H. H. Chen, The mechanics of cell sorting and envelopment, Journal of Biomechanics, 33 (2000), 845-851.
90 D. G. Wilkinson, How attraction turns to repulsion, Nature Cell Biology, 5 (2003), 851-853.
91 M. Zanoni, F. Piccinini, C. Arienti, A. Zamagni, S. Santi, R. Polico, A. Bevilacqua and A. Tesei, 3d tumor spheroid models for in vitro therapeutic screening: A systematic approach to enhance the biological relevance of data obtained, Scientific Reports, 6 (2016), 19103.
92 Y. Zhang, G. Thomas, M. Swat, A. Shirinifard and J. Glazier, Computer simulations of cell sorting due to differential adhesion, PloS One, 6 (2011), e24999.
93 M. Zimmermann, C. Box and S. A. Eccles, Two-dimensional vs. three-dimensional in vitro tumor migration and invasion assays, in Target Identification and Validation in Drug Discovery, Springer, 2013, 227-252.

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