Mathematical Biosciences and Engineering (MBE)

Hybrid models of cell and tissue dynamics in tumor growth
Pages: 1141 - 1156, Issue 6, December 2015

doi:10.3934/mbe.2015.12.1141      Abstract        References        Full text (3437.4K)                  Related Articles

Yangjin Kim - Department of Mathematics, Konkuk University, Seoul, South Korea (email)
Hans G. Othmer - School of Mathematics, University of Minnesota, Minneapolis, MN 55445, United States (email)

1 M. C. Brahimi-Horn, J. Chiche and J. Pouysségur, Hypoxia signalling controls metabolic demand, Current opinion in cell biology, 19 (2007), 223-229.
2 F. Calvo and E. Sahai, Cell communication networks in cancer invasion, Curr Opin Cell Biol, 23 (2011), 621-629.
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), 1590-1595.
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), 203-222.       
5 E. Dazert and M. N. Hall, mTOR signaling in disease, Current opinion in cell biology, 23 (2011), 744-755.
6 T. S. Deisboeck, Z. Wang, P. Macklin and V. Cristini, Multiscale cancer modeling, Ann. Rev. Biomed. Eng., 13 (2011), 117-155.
7 P. Friedl and S. Alexander, Cancer invasion and the microenvironment: Plasticity and reciprocity, Cell, 147 (2011), 992-1009.
8 P. Friedl and D. Gilmour, Collective cell migration in morphogenesis, regeneration and cancer, Nature Reviews Molecular Cell Biology, 10 (2009), 445-457.
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), 62-75.
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), 2742-2748.
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), 620-632.
12 M. E. Gracheva and H. G. Othmer, A continuum model of motility in ameboid cells, Bull. Math. Biol., 66 (2004), 167-193.       
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), 1033-1039.
14 P. G. Gritsenko, O. Ilina and P. Friedl, Interstitial guidance of cancer invasion, The Journal of pathology, 226 (2012), 185-199.
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), 778-783.
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), 015010.
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), e00063.
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), 4622-4637.
19 J. Kim and C. V. Dang, Cancer's molecular sweet tooth and the Warburg effect, Cancer research, 66 (2006), p8927.
20 Y. Kim, Regulation of cell proliferation and migration in glioblastoma: New therapeutic approach, Frontiers in Molecular and Cellular Oncology, 3 (2013), p53.
21 Y. Kim and S. Roh, A hybrid model for cell proliferation and migration in glioblastoma, Discrete and Continuous Dynamical Systems-B, 18 (2013), 969-1015.       
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), 1773-1798.       
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), 359-371.       
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), e28293.
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 (2011b), 353-379.
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), e102499.
27 Y. Kim and H. G. Othmer, A hybrid model of tumor-stromal interactions in breast cancer, Bull. Math. Biol., 75 (2013), 1304-1350.       
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), R1-R91.       
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), 765-798.       
30 J. Massague, TGF-beta signal transduction, Annual Review of Biochemistry, 67 ( 1998), p753.
31 J. Massagué, TGF [beta] in Cancer, Cell, 134 (2008), 215-230.
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), 924-935.
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), 1-13.       
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), 11448-11453.
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), 15603-15617.
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), 242-247.
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), 356-365.
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), 3525-3553.       
39 T. D. Tlsty, Stromal cells can contribute oncogenic signals, Semin Cancer Biol, 11 (2001), 97-104.
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), 3263-3268.
41 O. Warburg, On the origin of cancer cells, Science, 123 (1956), 309-314.

Go to top