2015, 12(6): 1141-1156. doi: 10.3934/mbe.2015.12.1141

Hybrid models of cell and tissue dynamics in tumor growth

1. 

Department of Mathematics, Konkuk University, Seoul

2. 

School of Mathematics, University of Minnesota, Minneapolis, MN 55445, United States

Received  October 2014 Revised  March 2015 Published  August 2015

Hybrid models of tumor growth, in which some regions are described at the cell level and others at the continuum level, provide a flexible description that allows alterations of cell-level properties and detailed descriptions of the interaction with the tumor environment, yet retain the computational advantages of continuum models where appropriate. We review aspects of the general approach and discuss applications to breast cancer and glioblastoma.
Citation: Yangjin Kim, Hans G. Othmer. Hybrid models of cell and tissue dynamics in tumor growth. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1141-1156. doi: 10.3934/mbe.2015.12.1141
References:
[1]

M. C. Brahimi-Horn, J. Chiche and J. Pouysségur, Hypoxia signalling controls metabolic demand,, Current opinion in cell biology, 19 (2007), 223.   Google Scholar

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F. Calvo and E. Sahai, Cell communication networks in cancer invasion,, Curr Opin Cell Biol, 23 (2011), 621.   Google Scholar

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J. D. Cheng and L. M. Weiner, Tumors and their microenvironments: Tilling the soil Commentary re: A. M. Scott et al., A Phase I dose-escalation study of sibrotuzumab in patients with advanced or metastatic fibroblast activation protein-positive cancer,, Clin Cancer Res, 9 (2003), 1590.   Google Scholar

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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.  doi: 10.1016/j.jtbi.2004.06.015.  Google Scholar

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T. S. Deisboeck, Z. Wang, P. Macklin and V. Cristini, Multiscale cancer modeling,, Ann. Rev. Biomed. Eng., 13 (2011), 117.   Google Scholar

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P. Friedl and S. Alexander, Cancer invasion and the microenvironment: Plasticity and reciprocity,, Cell, 147 (2011), 992.   Google Scholar

[8]

P. Friedl and D. Gilmour, Collective cell migration in morphogenesis, regeneration and cancer,, Nature Reviews Molecular Cell Biology, 10 (2009), 445.   Google Scholar

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J. Galle, M. Loeffler and D. Drasdo, Modeling the effect of deregulated proliferation and apoptosis on the growth dynamics of epithelial cell populations in vitro,, Biophysical J., 88 (2005), 62.   Google Scholar

[10]

J. Godlewski, A. Bronisz, M. O. Nowicki, E. A. Chiocca and S. Lawler, microRNA-451: A conditional switch controlling glioma cell proliferation and migration,, Cell Cycle, 9 (2010), 2742.   Google Scholar

[11]

J. Godlewski, M. O. Nowicki, A. Bronisz, G. Palatini, J. Nuovo, M. D. Lay, J. V. Brocklyn, M. C. Ostrowski, E. A. Chiocca and S. E. Lawler, MircroRNA-451 regulates LKB1/AMPK signaling and allows adaptation to metabolic stress in glioma cells,, Molecular Cell, 37 (2010), 620.   Google Scholar

[12]

M. E. Gracheva and H. G. Othmer, A continuum model of motility in ameboid cells,, Bull. Math. Biol., 66 (2004), 167.  doi: 10.1016/j.bulm.2003.08.007.  Google Scholar

[13]

R. Grantab, S. Sivananthan and I. F. Tannock, The penetration of anticancer drugs through tumor tissue as a function of cellular adhesion and packing density of tumor cells,, Cancer Research, 66 (2006), 1033.   Google Scholar

[14]

P. G. Gritsenko, O. Ilina and P. Friedl, Interstitial guidance of cancer invasion,, The Journal of pathology, 226 (2012), 185.   Google Scholar

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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.   Google Scholar

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O. Ilina, G. J. Bakker, A. Vasaturo, R. M. Hofmann and P. Friedl, Two-photon laser-generated microtracks in 3D collagen lattices: Principles of MMP-dependent and -independent collective cancer cell invasion,, Phys Biol., 8 (2011).   Google Scholar

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J. Kalpathy-Cramer, E. R. Gerstner, K. E. Emblem, O. C. Andronesi and B. Rosen, Advanced magnetic resonance imaging of the physical processes in human glioblastoma,, Cancer Res, 74 (2014), 4622.   Google Scholar

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J. Kim and C. V. Dang, Cancer's molecular sweet tooth and the Warburg effect,, Cancer research, 66 (2006).   Google Scholar

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Y. Kim, Regulation of cell proliferation and migration in glioblastoma: New therapeutic approach,, Frontiers in Molecular and Cellular Oncology, 3 (2013).   Google Scholar

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Y. Kim and S. Roh, A hybrid model for cell proliferation and migration in glioblastoma,, Discrete and Continuous Dynamical Systems-B, 18 (2013), 969.  doi: 10.3934/dcdsb.2013.18.969.  Google Scholar

[22]

Y. Kim, M. Stolarska and H. G. Othmer, A hybrid model for tumor spheroid growth in vitro I: Theoretical development and early results,, Math. Models Methods in Appl Sci, 17 (2007), 1773.  doi: 10.1142/S0218202507002479.  Google Scholar

[23]

Y. Kim, S. Lawler, M. O. Nowicki, E. A. Chiocca and A. Friedman, A mathematical model of Brain tumor: Pattern formation of glioma cells outside the tumor spheroid core,, J. Theo. Biol., 260 (2009), 359.  doi: 10.1016/j.jtbi.2009.06.025.  Google Scholar

[24]

Y. Kim, S. Roh, S. Lawler and A. Friedman, miR451 and AMPK/MARK mutual antagonism in glioma cells migration and proliferation,, PLoS One, 6 (2011).   Google Scholar

[25]

Y. Kim, M. A. Stolarska and H. G. Othmer, The role of the microenvironment in tumor growth and invasion,, Progress in Biophysics and Molecular Biology, 106 (): 353.   Google Scholar

[26]

Y. Kim, H. G. Lee, N. Dmitrieva, J. Kim, B. Kaur and A. Friedman, Choindroitinase ABC I-mediated enhancement of oncolytic virus spread and anti-tumor efficacy: A mathematical model,, PLoS One, 9 (2014).   Google Scholar

[27]

Y. Kim and H. G. Othmer, A hybrid model of tumor-stromal interactions in breast cancer,, Bull. Math. Biol., 75 (2013), 1304.  doi: 10.1007/s11538-012-9787-0.  Google Scholar

[28]

J. S. Lowengrub, H. B. Frieboes, F. Jin, Y. L. Chuang, X. Li, P. Macklin, S. M. Wise and V. Cristini, Nonlinear modelling of cancer: Bridging the gap between cells and tumours,, Nonlinearity, 23 (2010).  doi: 10.1088/0951-7715/23/1/R01.  Google Scholar

[29]

P. Macklin, S. McDougall, A. R. A. Anderson, M. A. J. Chaplain, V. Cristini and J. Lowengrub, Multiscale modelling and nonlinear simulation of vascular tumour growth,, J. Math. Biol., 58 (2009), 765.  doi: 10.1007/s00285-008-0216-9.  Google Scholar

[30]

J. Massague, TGF-beta signal transduction,, Annual Review of Biochemistry, 67 (1998).   Google Scholar

[31]

J. Massagué, TGF [beta] in Cancer,, Cell, 134 (2008), 215.   Google Scholar

[32]

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.   Google Scholar

[33]

E. Palsson, A 3-D model used to explore how cell adhesion and stiffness affect cell sorting and movement in multicellular systems,, J Theor Biol, 254 (2008), 1.  doi: 10.1016/j.jtbi.2008.05.004.  Google Scholar

[34]

E. Palsson and H. G. Othmer, A model for individual and collective cell movement in dictyostelium discoideum,, Proceedings of the National Academy of Science, 97 (2000), 11448.   Google Scholar

[35]

D. J. Silver, F. A. Siebzehnrubl, M. J. Schildts, A. T. Yachnis, G. M. Smith, A. A. Smith, B. Scheffler, B. A. Reynolds, J. Silver and D. A. Steindler, Chondroitin sulfate proteoglycans potently inhibit invasion and serve as a central organizer of the brain tumor microenvironment,, The Journal of Neuroscience, 33 (2013), 15603.   Google Scholar

[36]

K. S. M. Smalley, M. Lioni and M. Herlyn, Life isn't flat: Taking cancer biology to the next dimension,, In Vitro Cell Dev Biol Anim, 42 (2006), 242.   Google Scholar

[37]

A. M. Stein, T. Demuth, D. Mobley, M. Berens and L. M. Sander, A mathematical model of glioblastoma tumor spheroid invasion in a three-dimensional in vitro experiment,, Biophys J, 92 (2007), 356.   Google Scholar

[38]

M. A. Stolarska, Y. Kim and H. G. Othmer, Multi-scale models of cell and tissue dynamics,, Philosophical Transactions of the Royal Society A, 367 (2009), 3525.  doi: 10.1098/rsta.2009.0095.  Google Scholar

[39]

T. D. Tlsty, Stromal cells can contribute oncogenic signals,, Semin Cancer Biol, 11 (2001), 97.   Google Scholar

[40]

R. Wani, N. S. Bharathi, J. Field, A. W. Tsang and C. M. Furdui, Oxidation of Akt2 kinase promotes cell migration and regulates G,, Cell cycle, 10 (2011), 3263.   Google Scholar

[41]

O. Warburg, On the origin of cancer cells,, Science, 123 (1956), 309.   Google Scholar

show all references

References:
[1]

M. C. Brahimi-Horn, J. Chiche and J. Pouysségur, Hypoxia signalling controls metabolic demand,, Current opinion in cell biology, 19 (2007), 223.   Google Scholar

[2]

F. Calvo and E. Sahai, Cell communication networks in cancer invasion,, Curr Opin Cell Biol, 23 (2011), 621.   Google Scholar

[3]

J. D. Cheng and L. M. Weiner, Tumors and their microenvironments: Tilling the soil Commentary re: A. M. Scott et al., A Phase I dose-escalation study of sibrotuzumab in patients with advanced or metastatic fibroblast activation protein-positive cancer,, Clin Cancer Res, 9 (2003), 1590.   Google Scholar

[4]

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.  doi: 10.1016/j.jtbi.2004.06.015.  Google Scholar

[5]

E. Dazert and M. N. Hall, mTOR signaling in disease,, Current opinion in cell biology, 23 (2011), 744.   Google Scholar

[6]

T. S. Deisboeck, Z. Wang, P. Macklin and V. Cristini, Multiscale cancer modeling,, Ann. Rev. Biomed. Eng., 13 (2011), 117.   Google Scholar

[7]

P. Friedl and S. Alexander, Cancer invasion and the microenvironment: Plasticity and reciprocity,, Cell, 147 (2011), 992.   Google Scholar

[8]

P. Friedl and D. Gilmour, Collective cell migration in morphogenesis, regeneration and cancer,, Nature Reviews Molecular Cell Biology, 10 (2009), 445.   Google Scholar

[9]

J. Galle, M. Loeffler and D. Drasdo, Modeling the effect of deregulated proliferation and apoptosis on the growth dynamics of epithelial cell populations in vitro,, Biophysical J., 88 (2005), 62.   Google Scholar

[10]

J. Godlewski, A. Bronisz, M. O. Nowicki, E. A. Chiocca and S. Lawler, microRNA-451: A conditional switch controlling glioma cell proliferation and migration,, Cell Cycle, 9 (2010), 2742.   Google Scholar

[11]

J. Godlewski, M. O. Nowicki, A. Bronisz, G. Palatini, J. Nuovo, M. D. Lay, J. V. Brocklyn, M. C. Ostrowski, E. A. Chiocca and S. E. Lawler, MircroRNA-451 regulates LKB1/AMPK signaling and allows adaptation to metabolic stress in glioma cells,, Molecular Cell, 37 (2010), 620.   Google Scholar

[12]

M. E. Gracheva and H. G. Othmer, A continuum model of motility in ameboid cells,, Bull. Math. Biol., 66 (2004), 167.  doi: 10.1016/j.bulm.2003.08.007.  Google Scholar

[13]

R. Grantab, S. Sivananthan and I. F. Tannock, The penetration of anticancer drugs through tumor tissue as a function of cellular adhesion and packing density of tumor cells,, Cancer Research, 66 (2006), 1033.   Google Scholar

[14]

P. G. Gritsenko, O. Ilina and P. Friedl, Interstitial guidance of cancer invasion,, The Journal of pathology, 226 (2012), 185.   Google Scholar

[15]

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.   Google Scholar

[16]

O. Ilina, G. J. Bakker, A. Vasaturo, R. M. Hofmann and P. Friedl, Two-photon laser-generated microtracks in 3D collagen lattices: Principles of MMP-dependent and -independent collective cancer cell invasion,, Phys Biol., 8 (2011).   Google Scholar

[17]

V. L. Jacobs, P. A. Valdes, W. F. Hickey and J. A. De Leo, Current review of in vivo GBM rodent models: emphasis on the CNS-1 tumour model,, ASN NEURO, 3 (2011).   Google Scholar

[18]

J. Kalpathy-Cramer, E. R. Gerstner, K. E. Emblem, O. C. Andronesi and B. Rosen, Advanced magnetic resonance imaging of the physical processes in human glioblastoma,, Cancer Res, 74 (2014), 4622.   Google Scholar

[19]

J. Kim and C. V. Dang, Cancer's molecular sweet tooth and the Warburg effect,, Cancer research, 66 (2006).   Google Scholar

[20]

Y. Kim, Regulation of cell proliferation and migration in glioblastoma: New therapeutic approach,, Frontiers in Molecular and Cellular Oncology, 3 (2013).   Google Scholar

[21]

Y. Kim and S. Roh, A hybrid model for cell proliferation and migration in glioblastoma,, Discrete and Continuous Dynamical Systems-B, 18 (2013), 969.  doi: 10.3934/dcdsb.2013.18.969.  Google Scholar

[22]

Y. Kim, M. Stolarska and H. G. Othmer, A hybrid model for tumor spheroid growth in vitro I: Theoretical development and early results,, Math. Models Methods in Appl Sci, 17 (2007), 1773.  doi: 10.1142/S0218202507002479.  Google Scholar

[23]

Y. Kim, S. Lawler, M. O. Nowicki, E. A. Chiocca and A. Friedman, A mathematical model of Brain tumor: Pattern formation of glioma cells outside the tumor spheroid core,, J. Theo. Biol., 260 (2009), 359.  doi: 10.1016/j.jtbi.2009.06.025.  Google Scholar

[24]

Y. Kim, S. Roh, S. Lawler and A. Friedman, miR451 and AMPK/MARK mutual antagonism in glioma cells migration and proliferation,, PLoS One, 6 (2011).   Google Scholar

[25]

Y. Kim, M. A. Stolarska and H. G. Othmer, The role of the microenvironment in tumor growth and invasion,, Progress in Biophysics and Molecular Biology, 106 (): 353.   Google Scholar

[26]

Y. Kim, H. G. Lee, N. Dmitrieva, J. Kim, B. Kaur and A. Friedman, Choindroitinase ABC I-mediated enhancement of oncolytic virus spread and anti-tumor efficacy: A mathematical model,, PLoS One, 9 (2014).   Google Scholar

[27]

Y. Kim and H. G. Othmer, A hybrid model of tumor-stromal interactions in breast cancer,, Bull. Math. Biol., 75 (2013), 1304.  doi: 10.1007/s11538-012-9787-0.  Google Scholar

[28]

J. S. Lowengrub, H. B. Frieboes, F. Jin, Y. L. Chuang, X. Li, P. Macklin, S. M. Wise and V. Cristini, Nonlinear modelling of cancer: Bridging the gap between cells and tumours,, Nonlinearity, 23 (2010).  doi: 10.1088/0951-7715/23/1/R01.  Google Scholar

[29]

P. Macklin, S. McDougall, A. R. A. Anderson, M. A. J. Chaplain, V. Cristini and J. Lowengrub, Multiscale modelling and nonlinear simulation of vascular tumour growth,, J. Math. Biol., 58 (2009), 765.  doi: 10.1007/s00285-008-0216-9.  Google Scholar

[30]

J. Massague, TGF-beta signal transduction,, Annual Review of Biochemistry, 67 (1998).   Google Scholar

[31]

J. Massagué, TGF [beta] in Cancer,, Cell, 134 (2008), 215.   Google Scholar

[32]

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.   Google Scholar

[33]

E. Palsson, A 3-D model used to explore how cell adhesion and stiffness affect cell sorting and movement in multicellular systems,, J Theor Biol, 254 (2008), 1.  doi: 10.1016/j.jtbi.2008.05.004.  Google Scholar

[34]

E. Palsson and H. G. Othmer, A model for individual and collective cell movement in dictyostelium discoideum,, Proceedings of the National Academy of Science, 97 (2000), 11448.   Google Scholar

[35]

D. J. Silver, F. A. Siebzehnrubl, M. J. Schildts, A. T. Yachnis, G. M. Smith, A. A. Smith, B. Scheffler, B. A. Reynolds, J. Silver and D. A. Steindler, Chondroitin sulfate proteoglycans potently inhibit invasion and serve as a central organizer of the brain tumor microenvironment,, The Journal of Neuroscience, 33 (2013), 15603.   Google Scholar

[36]

K. S. M. Smalley, M. Lioni and M. Herlyn, Life isn't flat: Taking cancer biology to the next dimension,, In Vitro Cell Dev Biol Anim, 42 (2006), 242.   Google Scholar

[37]

A. M. Stein, T. Demuth, D. Mobley, M. Berens and L. M. Sander, A mathematical model of glioblastoma tumor spheroid invasion in a three-dimensional in vitro experiment,, Biophys J, 92 (2007), 356.   Google Scholar

[38]

M. A. Stolarska, Y. Kim and H. G. Othmer, Multi-scale models of cell and tissue dynamics,, Philosophical Transactions of the Royal Society A, 367 (2009), 3525.  doi: 10.1098/rsta.2009.0095.  Google Scholar

[39]

T. D. Tlsty, Stromal cells can contribute oncogenic signals,, Semin Cancer Biol, 11 (2001), 97.   Google Scholar

[40]

R. Wani, N. S. Bharathi, J. Field, A. W. Tsang and C. M. Furdui, Oxidation of Akt2 kinase promotes cell migration and regulates G,, Cell cycle, 10 (2011), 3263.   Google Scholar

[41]

O. Warburg, On the origin of cancer cells,, Science, 123 (1956), 309.   Google Scholar

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