
Previous Article
Modeling prostate cancer response to continuous versus intermittent androgen ablation therapy
 DCDSB Home
 This Issue

Next Article
A mathematical model for the immunotherapeutic control of the Th1/Th2 imbalance in melanoma
A hybrid model for cell proliferation and migration in glioblastoma
1.  Department of Mathematics, Konkuk University, Seoul, South Korea 
2.  Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, United States 
References:
[1] 
B. D. Aguda, Y. Kim, M. G. Hunter, A. Friedman and C. B. Marsh, Microrna regulation of a cancer network: Consequences of the feedback loops involving mir1792, e2f, and myc,, PNAS, 105 (2008), 19678. 
[2] 
S. Alexander and P. Friedl, Cancer invasion and resistance: Interconnected processes of disease progression and therapy failure,, Trends. Mol. Med., 18 (2012), 13. 
[3] 
D. Angeli, J. E Ferrell Jr. and E. D. Sontag, Detection of multistability, bifurcations, and hysteresis in a large class of biological positivefeedback systems,, Proc. Natl. Acad. Sci. USA, 101 (2004), 1822. 
[4] 
R. P. Araujo and D. L. S. McElwain, A history of the study of solid tumour growth: The contribution of mathematical modelling,, Bull. Math. Biol., 66 (2004), 1039. doi: 10.1016/j.bulm.2003.11.002. 
[5] 
H. J. Aronen, F. S. Pardo, D. N. Kennedy, J. W. Belliveau, S. D. Packard, D. W. Hsu, F. H. Hochberg, A. J. Fischman and B. R. Rosen, High microvascular blood volume is associated with high glucose uptake and tumor angiogenesis in human gliomas,, Clin. Cancer Res., 6 (2000), 2189. 
[6] 
K. Asano, C. D. Duntsch, Q. Zhou, J. D. Weimar, D. Bordelon, J. H. Robertson and T. Pourmotabbed, Correlation of ncadherin expression in high grade gliomas with tissue invasion,, J. Neurooncol., 70 (2004), 3. 
[7] 
A. F. Baas, J. Kuipers, N. N. Wel, E. Batlle, H. K. Koerten, P. J. Peters and H. C. Clevers, Complete polarization of single intestinal epithelial cells upon activation of lkb1 by strad,, Cell, 116 (2004), 457. 
[8] 
E. Bandres, N. Bitarte, F. Arias, J. Agorreta, P. Fortes, X. Agirre, R. Zarate, J. A. DiazGonzalez, N. Ramirez and J. J. Sola, microrna451 regulates macrophage migration inhibitory factor production and proliferation of gastrointestinal cancer cells,, Clin. Cancer Res, 15 (2009), 2281. 
[9] 
D. P. Bartel, Micrornas: target recognition and regulatory functions,, Cell, 136 (2009), 215. 
[10] 
J. Boudeau, A. F. Baas, M. Deak, N. A. Morrice, A. Kieloch, M. Schutkowski, A. R. Prescott, H. C. Clevers and D. R. Alessi, Mo25alpha/beta interact with stradalpha/beta enhancing their ability to bind, activate and localize lkb1 in the cytoplasm,, EMBO J., 22 (2003), 5102. 
[11] 
H. Byrne and L. Preziosi, Modeling solid tumor growth using the theory of mixtures,, Math. Med. Biol., 20 (2004), 341. 
[12] 
H. M. Byrne, Dissecting cancer through mathematics: From the cell to the animal model,, Nature Reviews, 10 (2010), 221. 
[13] 
R. Cairns, I. Papandreou and N. Denko, Overcoming physiologic barriers to cancer treatment by molecularly targeting the tumor microenvironment,, Mol. Cancer Res., 4 (2006), 61. 
[14] 
A. Chauviere, L. Preziosi and H. Byrne, A model of cell migration within the extracellular matrix based on a phenotypic switching mechanism,, Math. Med. Biol., 27 (2010), 255. doi: 10.1093/imammb/dqp021. 
[15] 
J. D. Cheng and L. M. Weiner, Tumors and their microenvironments: tilling the soil. Commentary re: A. M. Scott et al., A Phase I doseescalation study of sibrotuzumab in patients with advanced or metastatic fibroblast activation proteinpositive cancer,, Clin. Cancer Res. 9 (2003), 9 (2003), 1590. 
[16] 
G. Cheng, J. Tse, R. K. Jain and L. L. Minn, Microenvironmental mechanical stress controls tumor spheroid size and morphology by supressing proliferation and inducing aopotosis in cancer cells,, PLoS One, (2009). 
[17] 
S. K. Chintala, J. C. Tonn and J. S. Rao, Matrix metalloproteinases and their biological function in human gliomas,, Int. J. Dev. Neurosci., 17 (1999), 495. 
[18] 
D. G. Chiro, R. L. DeLaPaz, R. A. Brooks, L. Sokoloff, P. L. Kornblith, B. H. Smith, N. J. Patronas, C. V. Kufta, R. M. Kessler, G. S. Johnston, R. G. Manning and A. P. Wolf, Glucose utilization of cerebral gliomas measured by [18f] fluorodeoxyglucose and positron emission tomography,, Neurology, 32 (1982), 1323. 
[19] 
A. Cho, Life's patterns: No need to spell it out?, Science, 303 (2004), 782. 
[20] 
G. Choe, J. K. Park, L. JoubenSteele, T. J. Kremen, L. M. Liau, H. V. Vinters, T. F. Cloughesy and P. S. Mischel, Active matrix metalloproteinase 9 expression is associated with primary glioblastoma subtype,, Clin. Cancer Res., 8(9) (2002), 2894. 
[21] 
M. Crawford, E. Brawner, K. Batte, L. Yu, M. G. Hunter, G. A. Otterson, G. Nuovo, C. B. Marsh and S. P. NanaSinkam, Microrna126 inhibits invasion in nonsmall cell lung carcinoma cell lines,, Biochem. Biophys. Res. Commun., 373 (2008), 607. 
[22] 
B. E. Crute, K. Seefeld, J. Gamble, B. E. Kemp and L. A. Witters, Functional domains of the alpha1 catalytic subunit of the ampactivated protein kinase,, J. Biol. Chem., 273 (1998), 35347. 
[23] 
J. C. Dallon and H. G. Othmer, A discrete cell model with adaptive signalling for aggregation of dictyostelium discoideum,, Phil. Trans. Roy. Soc. Lond, B352 (1997), 391. 
[24] 
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. 
[25] 
F. G. Davis and B. J. McCarthy, Current epidemiological trends and surveillance issues in brain tumors,, Expert Rev. Anticancer Ther., 1 (2001), 395. 
[26] 
S. J. Day and P. A. Lawrence, Measuring dimensions: The regulation of size and shape,, Development, 127 (2000), 2977. 
[27] 
T. S. Deisboeck, M. E. Berens, A. R. Kansal, S. Torquato, A. O. StemmerRachamimov and E. A. Chiocca, Pattern of selforganization in tumour systems: Complex growth dynamics in a novel brain tumour spheroid model,, Cell Prolif., 34 (2001), 115. 
[28] 
T. S. Deisboeck and I. D. Couzin, Collective behavior in cancer cell populations,, Bioessays, 31 (2009), 190. 
[29] 
T. Demuth and M. E. Berens, Molecular mechanisms of glioma cell migration and invasion,, J. Neurooncol., 70 (2004), 217. 
[30] 
J. B. Easton and P. J. Houghton, mtor and cancer therapy,, Oncogene, 25 (2006), 6436. 
[31] 
A. EsquelaKerscher and F. J. Slack, Oncomirs  micrornas with a role in cancer,, Nat. Rev. Cancer, 6 (2006), 259. 
[32] 
J. E. Ferrell Jr, Selfperpetuating states in signal transduction: Positive feedback, doublenegative feedback and bistability,, Curr. Opin. Cell Biol., 14 (2002), 140. 
[33] 
P. Friedl and S. Alexander, Cancer invasion and the microenvironment: Plasticity and reciprocity,, Cell, 147 (2011), 992. 
[34] 
G. Gabriely, T. Wurdinger, S. Kesari, C. C. Esau, J. Burchard, P. S. Linsley and A. M. Krichevsky, Microrna 21 promotes glioma invasion by targeting matrix metalloproteinase regulators,, Mol. Cell Biol., 28 (2008), 5369. 
[35] 
H. Gal, G. Pandi, A. A. Kanner, Z. Ram, G. LithwickYanai, N. Amariglio, G. Rechavi and D. Givol, Mir451 and imatinib mesylate inhibit tumor growth of glioblastoma stem cells biochem.,, Biophys. Res. Commun., 376 (2008), 86. 
[36] 
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. 
[37] 
M. P. Gantier, C. E. McCoy, I. Rusinova, D. Saulep, D. Wang, D. Xu, A. T. Irving, M. A. Behlke, P. J. Hertzog, F. Mackay and B. R. Williams, Analysis of microrna turnover in mammalian cells following dicer1 ablation,, Nucleic Acids. Res., 39 (2011), 5692. 
[38] 
R. A. Gatenby and R. J. Gillies, Why do cancers have high aerobic glycolysis?, Nat. Rev. Cancer, 4 (2004), 891. 
[39] 
J. Godlewski, M. O. Nowicki, A. Bronisz, S. Williams, A. Otsuki, G. Nuovo, A. Raychaudhury, H. B. Newton, E. A. Chiocca and S. Lawler, Targeting of the bmi1 oncogene/stem cell renewal factor by microrna128 inhibits glioma proliferation and selfrenewal,, Cancer Res., 68 (2008), 9125. 
[40] 
J. Godlewski, A. Bronisz, M. O. Nowicki, E. A. Chiocca and S. Lawler, microRNA451: A conditional switch controlling glioma cell proliferation and migration,, Cell Cycle, 9 (2010), 2742. 
[41] 
J. Godlewski, M. O. Nowicki, A. Bronisz, G. Nuovo J. Palatini, M. D. Lay, J. V. Brocklyn, M. C. Ostrowski, E. A. Chiocca and S. E. Lawler, MircroRNA451 regulates lkb1/ampk signaling and allows adaptation to metabolic stress in glioma cells,, Molecular Cell, 37 (2010), 620. 
[42] 
S. Goldman, M. Levivier, B. Pirotte, J. M. Brucher, D. Wikler, P. Damhaut, E. Stanus, J. Brotchi and J. Hildebrand, Regional glucose metabolism and histopathology of gliomas. A study based on positron emission tomographyguided stereotactic biopsy,, Cancer, 78 (1996), 1098. 
[43] 
M. Gotte and G. W. Yip, Heparanase, hyaluronan, and CD44 in cancers: A breast carcinoma perspective,, Cancer Research, 66 (2006), 10233. 
[44] 
R. G. Hahn and T. Nystom, Plasma Volume Expansion Resulting from Intravenous Glucose Tolerance Test,, Comput. Math. Methods Med., (2011). doi: doi:10.1155/2011/965075. 
[45] 
D. G. Hardie, Ampactivated/snf1 protein kinases: Conserved guardians of cellular energy,, Nat. Rev. Mol. Cell Biol., 8 (2007), 774. 
[46] 
D. G. Hardie, I. P. Salt, S. A. Hawley and S. P. Davies, Ampactivated protein kinase: An ultrasensitive system for monitoring cellular energy charge,, Biochem. J., 338 (1999), 717. 
[47] 
H. L. Harpold, J.r. EC and K. R. Swanson, The evolution of mathematical modeling of glioma proliferation and invasion,, J. Neuropathol. Exp. Neurol., 66 (2007), 1. 
[48] 
H. Hatzikirou, D. Basanta, M. Simon, K. Schaller and A. Deutsch, 'Go or grow': The key to the emergence of invasion in tumour progression?, Math. Med. Biol., 27 (2010), 255. doi: 10.1093/imammb/dqq011. 
[49] 
S. A. Hawley, J. Boudeau, J. L. Reid, K. J. Mustard, L. Udd, T. P. Makela, D. R. Alessi and D. G. Hardie, Complexes between the lkb1 tumor suppressor, strad alpha/beta and mo25 alpha/beta are upstream kinases in the ampactivated protein kinase cascade,, J. Biol., 2 (2003). 
[50] 
S. A. Hawley, M. A. Selbert, E. G. Goldstein, A. M. Edelman, D. Carling and D. G. Hardie, 5'amp activates the ampactivated protein kinase cascade, and ca2+/calmodulin activates the calmodulindependent protein kinase i cascade, via three independent mechanisms,, J. Biol. Chem., 270 (1995), 27186. 
[51] 
M. G. Heiden, L. C. Cantley and C. B. Thompson, Understanding the warburg effect: The metabolic requirements of cell proliferation,, Science, 324 (2009), 1029. 
[52] 
B. Hegedus, A. Czirok, I. Fazekas, T. Babel, E. Madarasz and T. Vicsek, Locomotion and proliferation of glioblastoma cells in vitro: Statistical evaluation of videomicroscopic observations,, J. Neurosurg., 92 (2000), 428. 
[53] 
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(8) (1997), 778. 
[54] 
A. F. Hezel and N. Bardeesy, Lkb1; linking cell structure and tumor suppression,, Oncogene, 27 (2008), 6908. 
[55] 
O. Ilina, G. Bakker, A. Vasaturo, R. M. Hofmann and P. Friedl, Twophoton lasergenerated microtracks in 3d collagen lattices: principles of mmpdependent and independent collective cancer cell invasion,, Phys. Biol., 8 (2011). 
[56] 
K. Inoki, Y. Li, T. Xu and K. L. Guan, Rheb gtpase is a direct target of tsc2 gap activity and regulates mtor signaling,, Genes. Dev., 17 (2003), 1829. 
[57] 
K. Inoki, Y. Li, T. Zhu, J. Wu and K. L. Guan, Tsc2 is phosphorylated and inhibited by akt and suppresses mtor signalling,, Nat. Cell Biol., 4 (2002), 648. 
[58] 
J. Jaalinoja, R. Herva, M. Korpela, M. Hoyhtya and T. TurpeenniemiHujanen, Matrix metalloproteinase 2 (mmp2) immunoreactive protein is associated with poor grade and survival in brain neoplasms,, J. Neurooncol., 46 (2000), 81. 
[59] 
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 cns1 tumour model,, ASN NEURO, 3 (2011). 
[60] 
R. K. Jain, Transport of molecules in the tumor interstitium: a review,, Cancer Res., 47 (1987), 3039. 
[61] 
R. G. Jones and C. B. Thompson, Tumor suppressors and cell metabolism: A recipe for cancer growth,, Genes Dev., 23 (2009), 537. 
[62] 
L. J. Kaufma, C. P. Brangwynn, K. E. Kasz, E. Filippidi, V. D. Gordon, T. S. Deisboeck and D. A. Weitz, lioma expansion in Collagen I matrices: Analyzing Collagen concentrationdependent growth and motility patterns,, Biophys. J., 89 (2005), 635. 
[63] 
E. Khain and L. M. Sander, Dynamics and pattern formation in invasive tumor growth,, Phys. Rev. Lett., 96 (2006). 
[64] 
R. Khanin and V. Vinciotti, Computational modeling of posttranscriptional gene regulation by micrornas,, J. Comput. Biol., 15 (2008), 305. doi: 10.1089/cmb.2007.0184. 
[65] 
J. W. Kim and C. V. Dang, Cancer's molecular sweet tooth and the warburg effect,, Cancer Res., 66 (2006), 8927. 
[66] 
H. D. Kim, T. W. Guo, A. P. Wu, A. Wells, F. B. Gertler and D. A. Lauffenburger, Epidermal growth factor induced enhancement of glioblastoma cell migration in 3D arises from an intrinsic increase in speed but an extrinsic matrix and proteolysisdependent increase in persistence,, Mol. Biol. Cell, 19 (2008), 4249. 
[67] 
Y. Kim and A. Friedman, Interaction of tumor with its microenvironment: A mathematical model,, Bull. Math. Biol., 72 (2010), 1029. doi: 10.1007/s115380099481z. 
[68] 
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. 
[69] 
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. Scis., 17 (2007), 1773. doi: 10.1142/S0218202507002479. 
[70] 
Y. Kim, S. Roh, S. Lawler and A. Friedman, miR451 and AMPK mutual antagonism in glioma cells migration and proliferation,, PLoS One, 6 (2011). 
[71] 
Y. Kim, M. Stolarska and H. G. Othmer, The role of the microenvironment in tumor growth and invasion,, Prog. Biophys. Mol. Biol., 106 (2011), 353. 
[72] 
Y. Kim, J. Wallace, F. Li, M. Ostrowski and A. Friedman, Transformed epithelial cells and fibroblasts/myofibroblasts interaction in breast tumor: A mathematical model and experiments,, J. Math. Biol., 61 (2010), 401. doi: 10.1007/s0028500903072. 
[73] 
W. P. Kloosterman and R. H. Plasterk, The diverse functions of micrornas in animal development and disease,, Dev. Cell, 11 (2006), 441. 
[74] 
C. Koike, T. D. McKee, A. Pluen, S. Ramanujan, K. Burton, L. L. Munn, Y. Boucher and R. K. Jain, Solid stress facilitates spheroid formation: potential involvement of hyaluronan,, British Journal of Cancer, 86 (2002), 947. 
[75] 
K. Lamszus, N. O. Schmidt, L. Jin, J. Laterra, D. Zagzag, D. Way, M. Witte, M. Weinand, I. D. Goldberg, M. Westphal and E. M. Rosen, Scatter factor promotes motility of human glioma and neuromicrovascular endothelial cells,, Int. J. Cancer, 75 (1998), 19. 
[76] 
S. Lawler and E. A. Chiocca, Emerging functions of micrornas in glioblastoma,, J. Neurooncol., 92 (2009), 297. 
[77] 
J. H. Lee, H. Koh, M. Kim, Y. Kim, S. Y. Lee, R. E. Karess, S. H. Lee, M. Shong, J. M. Kim, J. Kim and J. Chung, Energydependent regulation of cell structure by ampactivated protein kinase,, Nature, 447 (2007), 1017. 
[78] 
C. K. Li, The glucose distribution in 9l rat brain multicell tumor spheroids and its effect on cell necrosis,, Cancer, 50 (1982), 2066. 
[79] 
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: 10.1088/09517715/23/1/001. 
[80] 
A. D. Luca, Niccolo Arena, L. M. Sena and E. Medico, Met overexpression confers hgfdependent invasive phenotype to human thyroid carcinoma cells in vitro,, Journal of Cellular Physiology, 180 (1999), 365. 
[81] 
M. LundJohansen, R. Bjerkvig, P. A. Humphrey, S. H. Bigner, D. D. Bigner and O. D. Laerum, Effect of epidermal growth factor on glioma cell growth, migration, and invasion in vitro,, Cancer Res., 50 (1990), 6039. 
[82] 
L. Ma, J. TeruyaFeldstein and R. A. Weinberg, Tumour invasion and metastasis initiated by microrna10b in breast cancer,, Nature, 449 (2007), 682. 
[83] 
E. Mandonnet, J. Y. Delattre, M. L. Tanguy, K. R. Swanson, A. F. Carpentier, H. Duffau, P. Cornu, R. Effenterre, J.r. EC and L. Capelle, Continuous growth of mean tumor diameter in a subset of grade ii gliomas,, Ann. Neurol., 53 (2003), 524. 
[84] 
S. Marino, I. B. Hogue, C. J. Ray and D. E. Kirschner, A methodology for performing global uncertainty and sensitivity analysis in systems biology,, J. Theor. Biol., 254 (2008), 178. 
[85] 
N. I. Markevich, J. B. Hoek and B. N. Kholodenko, Signaling switches and bistability arising from multisite phosphorylation in protein kinase cascades,, J. Cell Biol., 164 (2004), 353. 
[86] 
M. O. Nowicki, N. Dmitrieva, A. M. Stein, J. L. Cutter, J. Godlewski, Y. Saeki, M. Nita, M. E. Berens, L. M. Sander and H. B. Newton, Lithium inhibits invasion of glioma cells; possible involvement of glycogen synthase kinase3,, Neurooncol, 10 (2008), 690. 
[87] 
I. Papandreou, R. A. Cairns, L. Fontana, A. L. Lim and N. C. Denko, Hif1 mediates adaptation to hypoxia by actively downregulating mitochondrial oxygen consumption,, Cell Metab., 3 (2006), 187. 
[88] 
J. B. Park, H. J. Kwak and S. H. Lee, Role of hyaluronan in glioma invasion,, Cell Adhesion and Migration, 2 (2008), 202. 
[89] 
M. J. Paszek and V. M. Weaver, The tension mounts: Mechanics meets morphogenesis and malignancy,, J. Mammary Gland Biol. Neoplasia, 9 (2004), 325. 
[90] 
M. J. Paszek, N. Zahir, K. R. Johnson, J. N. Lakins, G. I. Rozenberg, A. Gefen, C. A. ReinhartKing, S. S. Margulies, M. Dembo, D. Boettiger, D. A. Hammer and V. M. Weaver, Tensional homeostasis and the malignant phenotype,, Cancer cell, 8 (2005), 241. 
[91] 
C. Perego, C. Vanoni, S. Massari, A. Raimondi, S. Pola, M.G. Cattaneo, M. Francolini, L. M. Vicentini and G. Pietrini, Invasive behaviour of glioblastoma cell lines is associated with altered organisation of the cadherincatenin adhesion system,, J. Cell Sci., 115 (2002), 3331. 
[92] 
K. Pham, A. Chauviere, H. Hatzikirou, X. Li, H. M. Byrne, V. Cristini and J. Lowengrub, Densitydependent quiescence in glioma invasion: Instability in a simple reactiondiffusion model for the migration/proliferation dichotomy,, Journal of Biological dynamics, (2011). doi: 10.1080/17513758.2011.590610. 
[93] 
M. Platten, W. Wick and M. Weller, Malignant glioma biology: role for tgfbeta in growth, motility, angiogenesis, and immune escape,, Microsc. Res. Tech., 52 (2001), 401. 
[94] 
C. J. Potter, L. G. Pedraza and T. Xu, Akt regulates growth by directly phosphorylating tsc2,, Nat. Cell Biol., 4 (2002), 658. 
[95] 
L. Preziosi and A. Tosin, Multiphase and multiscale trends in cancer modelling,, Math. Model. Natl. Phenom., 4 (2009), 1. doi: 10.1051/mmnp/20094301. 
[96] 
L. Preziosi and G. Vitale, A multiphase model of tumor and tissue growth including cell adhesion and plastic reorganization,, Math. Model. Method. Appl. Sci., 21 (2011), 1901. doi: 10.1142/S0218202511005593. 
[97] 
C. Ragan and M. Zuker amd M. A. Ragan, Quantitative prediction of miRNAmRNA interaction based on equilibrium concentrations,, PLoS Comput. Biol., 7 (2011). doi: 10.1371/journal.pcbi.1001090. 
[98] 
K. A. Rejniak and C. J. McCawley, Current trends in mathematical modeling of tumor microenvironment interaction: A survey of tools and applications,, Experimental Biology and Medicine (Maywood), 235 (2010), 411. 
[99] 
K. A. Rejniak and A. R. A. Anderson, Hybrid models of tumor growth,, WIRES Syst. Biol. Med., 3 (2011), 115. 
[100] 
K. A. Rejniak and C. J. McCawley, Current trends in mathematical modeling of tumor microenvironment interaction: A survey of tools and applications,, Exp. Biol. Med. (Maywood), 235 (2010), 411. 
[101] 
A. Ridley, M. Schwartz, K. Burridge, R. Firtel, M. Ginsberg, G. B. Parsons and A. Horwitz, Cell migration: Integrating signals from front to back,, Science, 302 (2003), 1704. 
[102] 
Z. Rong, U. Cheema and P. Vadgama, Needle enzyme electrode based glucose diffusive transport measurement in a collagen gel and validation of a simulation model,, Analyst, 131 (2006), 816. 
[103] 
J. M. Rozental, R. L. Levine and R. J. Nickles, Changes in glucose uptake by malignant gliomas: Preliminary study of prognostic significance,, J. Neurooncol., 10 (1991), 75. 
[104] 
O. Sampetrean, I. Saga, M. Nakanishi, E. Sugihara, R. Fukaya, N. Onishi, S. Osuka, M. Akahata, K. Kai, H. Sugimoto, A. Hirao and H. Saya, Invasion precedes tumor mass formation in a malignant brain tumor model of genetically modified neural stem cells,, Neoplasia, 13 (2011), 784. 
[105] 
L. M. Sander and T. S. Deisboeck, Growth patterns of microscopic brain tumors,, Phys. Rev. E, 66 (2002). 
[106] 
M. Scianna, R. M. Merks, L. Preziosi and E. Medico, Individual cellbased models of cell scatter of aro and mlp29 cells in response to hepatocyte growth factor,, J. Theor. Biol., 260 (2009), 151. 
[107] 
S. Sen, M. Dong and S. Kumar, Isoformspecific contributions of aActinin to Glioma cell mechanobiology,, PLoS One, 4 (2009). 
[108] 
R. J. Shaw, N. Bardeesy, B. D. Manning, L. Lopez, M. Kosmatka, R. A. DePinho and L. C. Cantley, The lkb1 tumor suppressor negatively regulates mtor signaling,, Cancer Cell, 6 (2004), 91. 
[109] 
B. I. Shraiman, Mechanicall feedback as a possible regulator of tissue growth,, PNAS, 102 (2005), 3318. 
[110] 
S. C. Stein, A. Woods, N. A. Jones, M. D. Davison and D. Carling, The regulation of ampactivated protein kinase by phosphorylation,, Biochem. J., 345 (2000), 437. 
[111] 
A. M. Stein, T. Demuth, D. Mobley, M. Berens and L. M. Sander, A mathematical model of glioblastoma tumor spheroid invasion in a threedimensional in vitro experiment,, Biophys. J., 92 (2007), 356. 
[112] 
A. Stein, D. Vader, D. Weitz and L. Sander, The micromechanics of threedimensional collagenI gels,, Complexity, 16 (2011), 22. 
[113] 
M. C. Stella and P. M. Comoglio, HGF: A multifunctional growth factor controlling cell scattering,, Int. J. Biochem. Cell Biol., 31(12) (1999), 1357. 
[114] 
M. Stolarska, Y. Kim and H. G. Othmer, Multiscale models of cell and tissue dynamics,, Phil. Trans. Roy. Soc. A, 367 (2009), 3525. doi: 10.1098/rsta.2009.0095. 
[115] 
S. S. Stylli, A. H. Kaye, L. MacGregor, M. Howes and P. Rajendra, Photodynamic therapy of high grade glioma  long term survival,, J. Clin. Neurosci., 12 (2005), 389. 
[116] 
K. R. Swanson, E. C. Alvord and J. D. Murray, Virtual resection of gliomas: Effect of extent of resection on recurrence,, Math. Comp. Modelling, 37 (2003), 1177. 
[117] 
K. R. Swanson, J.r. EC and J. D. Murray, A quantitative model for differential motility of gliomas in grey and white matter,, Cell Prolif., 33 (2000), 317. 
[118] 
L. Tamagnone and P. M. Comoglio, Control of invasive growth by hepatocyte growth factor (hgf) and related scatter factors,, Cytokine Growth Factor Rev., 8(2) (1997), 129. 
[119] 
L. Trusolino and P. M. Comoglio, Scatterfactor and semaphorin receptors: Cell signalling for invasive growth,, Nat. Rev. Cancer, 2 (2002), 289. 
[120] 
J. C. ValleCasuso, A. GonzalezSanchez, J. M. Medina and A. Tabernero, Hif1 and csrc mediate increased glucose uptake induced by endothelin1 and connexin43 in astrocytes,, PLoS One, 7 (2012). 
[121] 
O. Warburg, On the origin of cancer cells,, Science, 123 (1956), 309. 
[122] 
O. Wartlick, P. Mumcu, A. Kicheva, T. Bittig, C. Seum, F. Julicher and M. GonzalezGaitan, Dynamics of DPP signaling and proliferation control,, Science, 331 (2011), 1154. 
[123] 
O. Wartlick, P. Mumcu, F. Julicher and M. GonzalezGaitan, Understanding morphogenetic growth control  lessons from flies,, Nat. Rev. Mol. Cell Biol., 12 (2011), 594. 
[124] 
J. J. Watters, J. M. Schartner and B. Badie, Microglia function in brain tumors,, J. Neurosci. Res., 81 (2005), 447. 
[125] 
T. Williams and J. E. Brenman, Lkb1 and ampk in cell polarity and division,, Trends. Cell Biol., 18 (2008), 193. 
[126] 
M. Wiranowska and M. V. Rojiani, "Extracellular Matrix Microenvironment in Glioma Progression,", Glioma  Exploring Its Biology and Practical Relevance, (2011). 
[127] 
K. Wolf, Y. Wu, Y. Liu, J. Geiger, E. Tam, C. Overall, M. Stack and P. Friedl, Multistep pericellular proteolysis controls the transition from individual to collective cancer cell invasion,, Nat. Cell Biol., 9(8) (2007), 893. 
[128] 
K. Wolf, S. Alexander, V. Schacht, L. Coussens, U.H. von Andrian, J. van Rheenen, E. Deryugina and P. Friedl, Collagenbased cell migration models in vitro and in vivo,, Semin. Cell Dev. Biol., 20(8) (2009), 931. 
[129] 
A. Woods, S. R. Johnstone, K. Dickerson, F. C. Leiper, L. G. Fryer, D. Neumann, U. Schlattner, T. Wallimann, M. Carlson and D. Carling, Lkb1 is the upstream kinase in the ampactivated protein kinase cascade,, Curr. Biol., 13 (2003), 2004. 
[130] 
W. Xiong and J. E. Ferrell Jr, A positivefeedbackbased bistable 'memory module' that governs a cell fate decision,, Nature, 426 (2003), 460. 
[131] 
R. H. Xu, H. Pelicano, Y. Zhou, J. S. Carew, L. Feng, K. N. Bhalla, M. J. Keating and P. Huang, Inhibition of glycolysis in cancer cells: A novel strategy to overcome drug resistance associated with mitochondrial respiratory defect and hypoxia,, Cancer Res., 65 (2005), 613. 
[132] 
G. Yao, T. J. Lee, S. Mori, J. R. Nevins and L. You, A bistable rbe2f switch underlies the restriction point,, Nat. Cell Biol., 10 (2008), 476. 
[133] 
N. Young and J. R. Brocklyn, Roles of sphingosine1phosphate (s1p) receptors in malignant behavior of glioma cells. Differential effects of s1p2 on cell migration and invasiveness,, Exp. Cell Res., 313 (2007), 1615. 
[134] 
K. Yuan, R. K. Singh, G. Rezonzew and G. P. Siegal, Cell motility in cancer invasion and metastasis, in "Cancer Metastasis  Biology and Treatment,", Springer, (2006), 25. 
[135] 
Y. Zhou, P. H. Larsen, C. Hao and V. W. Yong, Cxcr4 is a major chemokine receptor on glioma cells and mediates their survival,, J. Biol. Chem., 277 (2002), 49481. 
show all references
References:
[1] 
B. D. Aguda, Y. Kim, M. G. Hunter, A. Friedman and C. B. Marsh, Microrna regulation of a cancer network: Consequences of the feedback loops involving mir1792, e2f, and myc,, PNAS, 105 (2008), 19678. 
[2] 
S. Alexander and P. Friedl, Cancer invasion and resistance: Interconnected processes of disease progression and therapy failure,, Trends. Mol. Med., 18 (2012), 13. 
[3] 
D. Angeli, J. E Ferrell Jr. and E. D. Sontag, Detection of multistability, bifurcations, and hysteresis in a large class of biological positivefeedback systems,, Proc. Natl. Acad. Sci. USA, 101 (2004), 1822. 
[4] 
R. P. Araujo and D. L. S. McElwain, A history of the study of solid tumour growth: The contribution of mathematical modelling,, Bull. Math. Biol., 66 (2004), 1039. doi: 10.1016/j.bulm.2003.11.002. 
[5] 
H. J. Aronen, F. S. Pardo, D. N. Kennedy, J. W. Belliveau, S. D. Packard, D. W. Hsu, F. H. Hochberg, A. J. Fischman and B. R. Rosen, High microvascular blood volume is associated with high glucose uptake and tumor angiogenesis in human gliomas,, Clin. Cancer Res., 6 (2000), 2189. 
[6] 
K. Asano, C. D. Duntsch, Q. Zhou, J. D. Weimar, D. Bordelon, J. H. Robertson and T. Pourmotabbed, Correlation of ncadherin expression in high grade gliomas with tissue invasion,, J. Neurooncol., 70 (2004), 3. 
[7] 
A. F. Baas, J. Kuipers, N. N. Wel, E. Batlle, H. K. Koerten, P. J. Peters and H. C. Clevers, Complete polarization of single intestinal epithelial cells upon activation of lkb1 by strad,, Cell, 116 (2004), 457. 
[8] 
E. Bandres, N. Bitarte, F. Arias, J. Agorreta, P. Fortes, X. Agirre, R. Zarate, J. A. DiazGonzalez, N. Ramirez and J. J. Sola, microrna451 regulates macrophage migration inhibitory factor production and proliferation of gastrointestinal cancer cells,, Clin. Cancer Res, 15 (2009), 2281. 
[9] 
D. P. Bartel, Micrornas: target recognition and regulatory functions,, Cell, 136 (2009), 215. 
[10] 
J. Boudeau, A. F. Baas, M. Deak, N. A. Morrice, A. Kieloch, M. Schutkowski, A. R. Prescott, H. C. Clevers and D. R. Alessi, Mo25alpha/beta interact with stradalpha/beta enhancing their ability to bind, activate and localize lkb1 in the cytoplasm,, EMBO J., 22 (2003), 5102. 
[11] 
H. Byrne and L. Preziosi, Modeling solid tumor growth using the theory of mixtures,, Math. Med. Biol., 20 (2004), 341. 
[12] 
H. M. Byrne, Dissecting cancer through mathematics: From the cell to the animal model,, Nature Reviews, 10 (2010), 221. 
[13] 
R. Cairns, I. Papandreou and N. Denko, Overcoming physiologic barriers to cancer treatment by molecularly targeting the tumor microenvironment,, Mol. Cancer Res., 4 (2006), 61. 
[14] 
A. Chauviere, L. Preziosi and H. Byrne, A model of cell migration within the extracellular matrix based on a phenotypic switching mechanism,, Math. Med. Biol., 27 (2010), 255. doi: 10.1093/imammb/dqp021. 
[15] 
J. D. Cheng and L. M. Weiner, Tumors and their microenvironments: tilling the soil. Commentary re: A. M. Scott et al., A Phase I doseescalation study of sibrotuzumab in patients with advanced or metastatic fibroblast activation proteinpositive cancer,, Clin. Cancer Res. 9 (2003), 9 (2003), 1590. 
[16] 
G. Cheng, J. Tse, R. K. Jain and L. L. Minn, Microenvironmental mechanical stress controls tumor spheroid size and morphology by supressing proliferation and inducing aopotosis in cancer cells,, PLoS One, (2009). 
[17] 
S. K. Chintala, J. C. Tonn and J. S. Rao, Matrix metalloproteinases and their biological function in human gliomas,, Int. J. Dev. Neurosci., 17 (1999), 495. 
[18] 
D. G. Chiro, R. L. DeLaPaz, R. A. Brooks, L. Sokoloff, P. L. Kornblith, B. H. Smith, N. J. Patronas, C. V. Kufta, R. M. Kessler, G. S. Johnston, R. G. Manning and A. P. Wolf, Glucose utilization of cerebral gliomas measured by [18f] fluorodeoxyglucose and positron emission tomography,, Neurology, 32 (1982), 1323. 
[19] 
A. Cho, Life's patterns: No need to spell it out?, Science, 303 (2004), 782. 
[20] 
G. Choe, J. K. Park, L. JoubenSteele, T. J. Kremen, L. M. Liau, H. V. Vinters, T. F. Cloughesy and P. S. Mischel, Active matrix metalloproteinase 9 expression is associated with primary glioblastoma subtype,, Clin. Cancer Res., 8(9) (2002), 2894. 
[21] 
M. Crawford, E. Brawner, K. Batte, L. Yu, M. G. Hunter, G. A. Otterson, G. Nuovo, C. B. Marsh and S. P. NanaSinkam, Microrna126 inhibits invasion in nonsmall cell lung carcinoma cell lines,, Biochem. Biophys. Res. Commun., 373 (2008), 607. 
[22] 
B. E. Crute, K. Seefeld, J. Gamble, B. E. Kemp and L. A. Witters, Functional domains of the alpha1 catalytic subunit of the ampactivated protein kinase,, J. Biol. Chem., 273 (1998), 35347. 
[23] 
J. C. Dallon and H. G. Othmer, A discrete cell model with adaptive signalling for aggregation of dictyostelium discoideum,, Phil. Trans. Roy. Soc. Lond, B352 (1997), 391. 
[24] 
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. 
[25] 
F. G. Davis and B. J. McCarthy, Current epidemiological trends and surveillance issues in brain tumors,, Expert Rev. Anticancer Ther., 1 (2001), 395. 
[26] 
S. J. Day and P. A. Lawrence, Measuring dimensions: The regulation of size and shape,, Development, 127 (2000), 2977. 
[27] 
T. S. Deisboeck, M. E. Berens, A. R. Kansal, S. Torquato, A. O. StemmerRachamimov and E. A. Chiocca, Pattern of selforganization in tumour systems: Complex growth dynamics in a novel brain tumour spheroid model,, Cell Prolif., 34 (2001), 115. 
[28] 
T. S. Deisboeck and I. D. Couzin, Collective behavior in cancer cell populations,, Bioessays, 31 (2009), 190. 
[29] 
T. Demuth and M. E. Berens, Molecular mechanisms of glioma cell migration and invasion,, J. Neurooncol., 70 (2004), 217. 
[30] 
J. B. Easton and P. J. Houghton, mtor and cancer therapy,, Oncogene, 25 (2006), 6436. 
[31] 
A. EsquelaKerscher and F. J. Slack, Oncomirs  micrornas with a role in cancer,, Nat. Rev. Cancer, 6 (2006), 259. 
[32] 
J. E. Ferrell Jr, Selfperpetuating states in signal transduction: Positive feedback, doublenegative feedback and bistability,, Curr. Opin. Cell Biol., 14 (2002), 140. 
[33] 
P. Friedl and S. Alexander, Cancer invasion and the microenvironment: Plasticity and reciprocity,, Cell, 147 (2011), 992. 
[34] 
G. Gabriely, T. Wurdinger, S. Kesari, C. C. Esau, J. Burchard, P. S. Linsley and A. M. Krichevsky, Microrna 21 promotes glioma invasion by targeting matrix metalloproteinase regulators,, Mol. Cell Biol., 28 (2008), 5369. 
[35] 
H. Gal, G. Pandi, A. A. Kanner, Z. Ram, G. LithwickYanai, N. Amariglio, G. Rechavi and D. Givol, Mir451 and imatinib mesylate inhibit tumor growth of glioblastoma stem cells biochem.,, Biophys. Res. Commun., 376 (2008), 86. 
[36] 
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. 
[37] 
M. P. Gantier, C. E. McCoy, I. Rusinova, D. Saulep, D. Wang, D. Xu, A. T. Irving, M. A. Behlke, P. J. Hertzog, F. Mackay and B. R. Williams, Analysis of microrna turnover in mammalian cells following dicer1 ablation,, Nucleic Acids. Res., 39 (2011), 5692. 
[38] 
R. A. Gatenby and R. J. Gillies, Why do cancers have high aerobic glycolysis?, Nat. Rev. Cancer, 4 (2004), 891. 
[39] 
J. Godlewski, M. O. Nowicki, A. Bronisz, S. Williams, A. Otsuki, G. Nuovo, A. Raychaudhury, H. B. Newton, E. A. Chiocca and S. Lawler, Targeting of the bmi1 oncogene/stem cell renewal factor by microrna128 inhibits glioma proliferation and selfrenewal,, Cancer Res., 68 (2008), 9125. 
[40] 
J. Godlewski, A. Bronisz, M. O. Nowicki, E. A. Chiocca and S. Lawler, microRNA451: A conditional switch controlling glioma cell proliferation and migration,, Cell Cycle, 9 (2010), 2742. 
[41] 
J. Godlewski, M. O. Nowicki, A. Bronisz, G. Nuovo J. Palatini, M. D. Lay, J. V. Brocklyn, M. C. Ostrowski, E. A. Chiocca and S. E. Lawler, MircroRNA451 regulates lkb1/ampk signaling and allows adaptation to metabolic stress in glioma cells,, Molecular Cell, 37 (2010), 620. 
[42] 
S. Goldman, M. Levivier, B. Pirotte, J. M. Brucher, D. Wikler, P. Damhaut, E. Stanus, J. Brotchi and J. Hildebrand, Regional glucose metabolism and histopathology of gliomas. A study based on positron emission tomographyguided stereotactic biopsy,, Cancer, 78 (1996), 1098. 
[43] 
M. Gotte and G. W. Yip, Heparanase, hyaluronan, and CD44 in cancers: A breast carcinoma perspective,, Cancer Research, 66 (2006), 10233. 
[44] 
R. G. Hahn and T. Nystom, Plasma Volume Expansion Resulting from Intravenous Glucose Tolerance Test,, Comput. Math. Methods Med., (2011). doi: doi:10.1155/2011/965075. 
[45] 
D. G. Hardie, Ampactivated/snf1 protein kinases: Conserved guardians of cellular energy,, Nat. Rev. Mol. Cell Biol., 8 (2007), 774. 
[46] 
D. G. Hardie, I. P. Salt, S. A. Hawley and S. P. Davies, Ampactivated protein kinase: An ultrasensitive system for monitoring cellular energy charge,, Biochem. J., 338 (1999), 717. 
[47] 
H. L. Harpold, J.r. EC and K. R. Swanson, The evolution of mathematical modeling of glioma proliferation and invasion,, J. Neuropathol. Exp. Neurol., 66 (2007), 1. 
[48] 
H. Hatzikirou, D. Basanta, M. Simon, K. Schaller and A. Deutsch, 'Go or grow': The key to the emergence of invasion in tumour progression?, Math. Med. Biol., 27 (2010), 255. doi: 10.1093/imammb/dqq011. 
[49] 
S. A. Hawley, J. Boudeau, J. L. Reid, K. J. Mustard, L. Udd, T. P. Makela, D. R. Alessi and D. G. Hardie, Complexes between the lkb1 tumor suppressor, strad alpha/beta and mo25 alpha/beta are upstream kinases in the ampactivated protein kinase cascade,, J. Biol., 2 (2003). 
[50] 
S. A. Hawley, M. A. Selbert, E. G. Goldstein, A. M. Edelman, D. Carling and D. G. Hardie, 5'amp activates the ampactivated protein kinase cascade, and ca2+/calmodulin activates the calmodulindependent protein kinase i cascade, via three independent mechanisms,, J. Biol. Chem., 270 (1995), 27186. 
[51] 
M. G. Heiden, L. C. Cantley and C. B. Thompson, Understanding the warburg effect: The metabolic requirements of cell proliferation,, Science, 324 (2009), 1029. 
[52] 
B. Hegedus, A. Czirok, I. Fazekas, T. Babel, E. Madarasz and T. Vicsek, Locomotion and proliferation of glioblastoma cells in vitro: Statistical evaluation of videomicroscopic observations,, J. Neurosurg., 92 (2000), 428. 
[53] 
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(8) (1997), 778. 
[54] 
A. F. Hezel and N. Bardeesy, Lkb1; linking cell structure and tumor suppression,, Oncogene, 27 (2008), 6908. 
[55] 
O. Ilina, G. Bakker, A. Vasaturo, R. M. Hofmann and P. Friedl, Twophoton lasergenerated microtracks in 3d collagen lattices: principles of mmpdependent and independent collective cancer cell invasion,, Phys. Biol., 8 (2011). 
[56] 
K. Inoki, Y. Li, T. Xu and K. L. Guan, Rheb gtpase is a direct target of tsc2 gap activity and regulates mtor signaling,, Genes. Dev., 17 (2003), 1829. 
[57] 
K. Inoki, Y. Li, T. Zhu, J. Wu and K. L. Guan, Tsc2 is phosphorylated and inhibited by akt and suppresses mtor signalling,, Nat. Cell Biol., 4 (2002), 648. 
[58] 
J. Jaalinoja, R. Herva, M. Korpela, M. Hoyhtya and T. TurpeenniemiHujanen, Matrix metalloproteinase 2 (mmp2) immunoreactive protein is associated with poor grade and survival in brain neoplasms,, J. Neurooncol., 46 (2000), 81. 
[59] 
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 cns1 tumour model,, ASN NEURO, 3 (2011). 
[60] 
R. K. Jain, Transport of molecules in the tumor interstitium: a review,, Cancer Res., 47 (1987), 3039. 
[61] 
R. G. Jones and C. B. Thompson, Tumor suppressors and cell metabolism: A recipe for cancer growth,, Genes Dev., 23 (2009), 537. 
[62] 
L. J. Kaufma, C. P. Brangwynn, K. E. Kasz, E. Filippidi, V. D. Gordon, T. S. Deisboeck and D. A. Weitz, lioma expansion in Collagen I matrices: Analyzing Collagen concentrationdependent growth and motility patterns,, Biophys. J., 89 (2005), 635. 
[63] 
E. Khain and L. M. Sander, Dynamics and pattern formation in invasive tumor growth,, Phys. Rev. Lett., 96 (2006). 
[64] 
R. Khanin and V. Vinciotti, Computational modeling of posttranscriptional gene regulation by micrornas,, J. Comput. Biol., 15 (2008), 305. doi: 10.1089/cmb.2007.0184. 
[65] 
J. W. Kim and C. V. Dang, Cancer's molecular sweet tooth and the warburg effect,, Cancer Res., 66 (2006), 8927. 
[66] 
H. D. Kim, T. W. Guo, A. P. Wu, A. Wells, F. B. Gertler and D. A. Lauffenburger, Epidermal growth factor induced enhancement of glioblastoma cell migration in 3D arises from an intrinsic increase in speed but an extrinsic matrix and proteolysisdependent increase in persistence,, Mol. Biol. Cell, 19 (2008), 4249. 
[67] 
Y. Kim and A. Friedman, Interaction of tumor with its microenvironment: A mathematical model,, Bull. Math. Biol., 72 (2010), 1029. doi: 10.1007/s115380099481z. 
[68] 
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. 
[69] 
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. Scis., 17 (2007), 1773. doi: 10.1142/S0218202507002479. 
[70] 
Y. Kim, S. Roh, S. Lawler and A. Friedman, miR451 and AMPK mutual antagonism in glioma cells migration and proliferation,, PLoS One, 6 (2011). 
[71] 
Y. Kim, M. Stolarska and H. G. Othmer, The role of the microenvironment in tumor growth and invasion,, Prog. Biophys. Mol. Biol., 106 (2011), 353. 
[72] 
Y. Kim, J. Wallace, F. Li, M. Ostrowski and A. Friedman, Transformed epithelial cells and fibroblasts/myofibroblasts interaction in breast tumor: A mathematical model and experiments,, J. Math. Biol., 61 (2010), 401. doi: 10.1007/s0028500903072. 
[73] 
W. P. Kloosterman and R. H. Plasterk, The diverse functions of micrornas in animal development and disease,, Dev. Cell, 11 (2006), 441. 
[74] 
C. Koike, T. D. McKee, A. Pluen, S. Ramanujan, K. Burton, L. L. Munn, Y. Boucher and R. K. Jain, Solid stress facilitates spheroid formation: potential involvement of hyaluronan,, British Journal of Cancer, 86 (2002), 947. 
[75] 
K. Lamszus, N. O. Schmidt, L. Jin, J. Laterra, D. Zagzag, D. Way, M. Witte, M. Weinand, I. D. Goldberg, M. Westphal and E. M. Rosen, Scatter factor promotes motility of human glioma and neuromicrovascular endothelial cells,, Int. J. Cancer, 75 (1998), 19. 
[76] 
S. Lawler and E. A. Chiocca, Emerging functions of micrornas in glioblastoma,, J. Neurooncol., 92 (2009), 297. 
[77] 
J. H. Lee, H. Koh, M. Kim, Y. Kim, S. Y. Lee, R. E. Karess, S. H. Lee, M. Shong, J. M. Kim, J. Kim and J. Chung, Energydependent regulation of cell structure by ampactivated protein kinase,, Nature, 447 (2007), 1017. 
[78] 
C. K. Li, The glucose distribution in 9l rat brain multicell tumor spheroids and its effect on cell necrosis,, Cancer, 50 (1982), 2066. 
[79] 
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: 10.1088/09517715/23/1/001. 
[80] 
A. D. Luca, Niccolo Arena, L. M. Sena and E. Medico, Met overexpression confers hgfdependent invasive phenotype to human thyroid carcinoma cells in vitro,, Journal of Cellular Physiology, 180 (1999), 365. 
[81] 
M. LundJohansen, R. Bjerkvig, P. A. Humphrey, S. H. Bigner, D. D. Bigner and O. D. Laerum, Effect of epidermal growth factor on glioma cell growth, migration, and invasion in vitro,, Cancer Res., 50 (1990), 6039. 
[82] 
L. Ma, J. TeruyaFeldstein and R. A. Weinberg, Tumour invasion and metastasis initiated by microrna10b in breast cancer,, Nature, 449 (2007), 682. 
[83] 
E. Mandonnet, J. Y. Delattre, M. L. Tanguy, K. R. Swanson, A. F. Carpentier, H. Duffau, P. Cornu, R. Effenterre, J.r. EC and L. Capelle, Continuous growth of mean tumor diameter in a subset of grade ii gliomas,, Ann. Neurol., 53 (2003), 524. 
[84] 
S. Marino, I. B. Hogue, C. J. Ray and D. E. Kirschner, A methodology for performing global uncertainty and sensitivity analysis in systems biology,, J. Theor. Biol., 254 (2008), 178. 
[85] 
N. I. Markevich, J. B. Hoek and B. N. Kholodenko, Signaling switches and bistability arising from multisite phosphorylation in protein kinase cascades,, J. Cell Biol., 164 (2004), 353. 
[86] 
M. O. Nowicki, N. Dmitrieva, A. M. Stein, J. L. Cutter, J. Godlewski, Y. Saeki, M. Nita, M. E. Berens, L. M. Sander and H. B. Newton, Lithium inhibits invasion of glioma cells; possible involvement of glycogen synthase kinase3,, Neurooncol, 10 (2008), 690. 
[87] 
I. Papandreou, R. A. Cairns, L. Fontana, A. L. Lim and N. C. Denko, Hif1 mediates adaptation to hypoxia by actively downregulating mitochondrial oxygen consumption,, Cell Metab., 3 (2006), 187. 
[88] 
J. B. Park, H. J. Kwak and S. H. Lee, Role of hyaluronan in glioma invasion,, Cell Adhesion and Migration, 2 (2008), 202. 
[89] 
M. J. Paszek and V. M. Weaver, The tension mounts: Mechanics meets morphogenesis and malignancy,, J. Mammary Gland Biol. Neoplasia, 9 (2004), 325. 
[90] 
M. J. Paszek, N. Zahir, K. R. Johnson, J. N. Lakins, G. I. Rozenberg, A. Gefen, C. A. ReinhartKing, S. S. Margulies, M. Dembo, D. Boettiger, D. A. Hammer and V. M. Weaver, Tensional homeostasis and the malignant phenotype,, Cancer cell, 8 (2005), 241. 
[91] 
C. Perego, C. Vanoni, S. Massari, A. Raimondi, S. Pola, M.G. Cattaneo, M. Francolini, L. M. Vicentini and G. Pietrini, Invasive behaviour of glioblastoma cell lines is associated with altered organisation of the cadherincatenin adhesion system,, J. Cell Sci., 115 (2002), 3331. 
[92] 
K. Pham, A. Chauviere, H. Hatzikirou, X. Li, H. M. Byrne, V. Cristini and J. Lowengrub, Densitydependent quiescence in glioma invasion: Instability in a simple reactiondiffusion model for the migration/proliferation dichotomy,, Journal of Biological dynamics, (2011). doi: 10.1080/17513758.2011.590610. 
[93] 
M. Platten, W. Wick and M. Weller, Malignant glioma biology: role for tgfbeta in growth, motility, angiogenesis, and immune escape,, Microsc. Res. Tech., 52 (2001), 401. 
[94] 
C. J. Potter, L. G. Pedraza and T. Xu, Akt regulates growth by directly phosphorylating tsc2,, Nat. Cell Biol., 4 (2002), 658. 
[95] 
L. Preziosi and A. Tosin, Multiphase and multiscale trends in cancer modelling,, Math. Model. Natl. Phenom., 4 (2009), 1. doi: 10.1051/mmnp/20094301. 
[96] 
L. Preziosi and G. Vitale, A multiphase model of tumor and tissue growth including cell adhesion and plastic reorganization,, Math. Model. Method. Appl. Sci., 21 (2011), 1901. doi: 10.1142/S0218202511005593. 
[97] 
C. Ragan and M. Zuker amd M. A. Ragan, Quantitative prediction of miRNAmRNA interaction based on equilibrium concentrations,, PLoS Comput. Biol., 7 (2011). doi: 10.1371/journal.pcbi.1001090. 
[98] 
K. A. Rejniak and C. J. McCawley, Current trends in mathematical modeling of tumor microenvironment interaction: A survey of tools and applications,, Experimental Biology and Medicine (Maywood), 235 (2010), 411. 
[99] 
K. A. Rejniak and A. R. A. Anderson, Hybrid models of tumor growth,, WIRES Syst. Biol. Med., 3 (2011), 115. 
[100] 
K. A. Rejniak and C. J. McCawley, Current trends in mathematical modeling of tumor microenvironment interaction: A survey of tools and applications,, Exp. Biol. Med. (Maywood), 235 (2010), 411. 
[101] 
A. Ridley, M. Schwartz, K. Burridge, R. Firtel, M. Ginsberg, G. B. Parsons and A. Horwitz, Cell migration: Integrating signals from front to back,, Science, 302 (2003), 1704. 
[102] 
Z. Rong, U. Cheema and P. Vadgama, Needle enzyme electrode based glucose diffusive transport measurement in a collagen gel and validation of a simulation model,, Analyst, 131 (2006), 816. 
[103] 
J. M. Rozental, R. L. Levine and R. J. Nickles, Changes in glucose uptake by malignant gliomas: Preliminary study of prognostic significance,, J. Neurooncol., 10 (1991), 75. 
[104] 
O. Sampetrean, I. Saga, M. Nakanishi, E. Sugihara, R. Fukaya, N. Onishi, S. Osuka, M. Akahata, K. Kai, H. Sugimoto, A. Hirao and H. Saya, Invasion precedes tumor mass formation in a malignant brain tumor model of genetically modified neural stem cells,, Neoplasia, 13 (2011), 784. 
[105] 
L. M. Sander and T. S. Deisboeck, Growth patterns of microscopic brain tumors,, Phys. Rev. E, 66 (2002). 
[106] 
M. Scianna, R. M. Merks, L. Preziosi and E. Medico, Individual cellbased models of cell scatter of aro and mlp29 cells in response to hepatocyte growth factor,, J. Theor. Biol., 260 (2009), 151. 
[107] 
S. Sen, M. Dong and S. Kumar, Isoformspecific contributions of aActinin to Glioma cell mechanobiology,, PLoS One, 4 (2009). 
[108] 
R. J. Shaw, N. Bardeesy, B. D. Manning, L. Lopez, M. Kosmatka, R. A. DePinho and L. C. Cantley, The lkb1 tumor suppressor negatively regulates mtor signaling,, Cancer Cell, 6 (2004), 91. 
[109] 
B. I. Shraiman, Mechanicall feedback as a possible regulator of tissue growth,, PNAS, 102 (2005), 3318. 
[110] 
S. C. Stein, A. Woods, N. A. Jones, M. D. Davison and D. Carling, The regulation of ampactivated protein kinase by phosphorylation,, Biochem. J., 345 (2000), 437. 
[111] 
A. M. Stein, T. Demuth, D. Mobley, M. Berens and L. M. Sander, A mathematical model of glioblastoma tumor spheroid invasion in a threedimensional in vitro experiment,, Biophys. J., 92 (2007), 356. 
[112] 
A. Stein, D. Vader, D. Weitz and L. Sander, The micromechanics of threedimensional collagenI gels,, Complexity, 16 (2011), 22. 
[113] 
M. C. Stella and P. M. Comoglio, HGF: A multifunctional growth factor controlling cell scattering,, Int. J. Biochem. Cell Biol., 31(12) (1999), 1357. 
[114] 
M. Stolarska, Y. Kim and H. G. Othmer, Multiscale models of cell and tissue dynamics,, Phil. Trans. Roy. Soc. A, 367 (2009), 3525. doi: 10.1098/rsta.2009.0095. 
[115] 
S. S. Stylli, A. H. Kaye, L. MacGregor, M. Howes and P. Rajendra, Photodynamic therapy of high grade glioma  long term survival,, J. Clin. Neurosci., 12 (2005), 389. 
[116] 
K. R. Swanson, E. C. Alvord and J. D. Murray, Virtual resection of gliomas: Effect of extent of resection on recurrence,, Math. Comp. Modelling, 37 (2003), 1177. 
[117] 
K. R. Swanson, J.r. EC and J. D. Murray, A quantitative model for differential motility of gliomas in grey and white matter,, Cell Prolif., 33 (2000), 317. 
[118] 
L. Tamagnone and P. M. Comoglio, Control of invasive growth by hepatocyte growth factor (hgf) and related scatter factors,, Cytokine Growth Factor Rev., 8(2) (1997), 129. 
[119] 
L. Trusolino and P. M. Comoglio, Scatterfactor and semaphorin receptors: Cell signalling for invasive growth,, Nat. Rev. Cancer, 2 (2002), 289. 
[120] 
J. C. ValleCasuso, A. GonzalezSanchez, J. M. Medina and A. Tabernero, Hif1 and csrc mediate increased glucose uptake induced by endothelin1 and connexin43 in astrocytes,, PLoS One, 7 (2012). 
[121] 
O. Warburg, On the origin of cancer cells,, Science, 123 (1956), 309. 
[122] 
O. Wartlick, P. Mumcu, A. Kicheva, T. Bittig, C. Seum, F. Julicher and M. GonzalezGaitan, Dynamics of DPP signaling and proliferation control,, Science, 331 (2011), 1154. 
[123] 
O. Wartlick, P. Mumcu, F. Julicher and M. GonzalezGaitan, Understanding morphogenetic growth control  lessons from flies,, Nat. Rev. Mol. Cell Biol., 12 (2011), 594. 
[124] 
J. J. Watters, J. M. Schartner and B. Badie, Microglia function in brain tumors,, J. Neurosci. Res., 81 (2005), 447. 
[125] 
T. Williams and J. E. Brenman, Lkb1 and ampk in cell polarity and division,, Trends. Cell Biol., 18 (2008), 193. 
[126] 
M. Wiranowska and M. V. Rojiani, "Extracellular Matrix Microenvironment in Glioma Progression,", Glioma  Exploring Its Biology and Practical Relevance, (2011). 
[127] 
K. Wolf, Y. Wu, Y. Liu, J. Geiger, E. Tam, C. Overall, M. Stack and P. Friedl, Multistep pericellular proteolysis controls the transition from individual to collective cancer cell invasion,, Nat. Cell Biol., 9(8) (2007), 893. 
[128] 
K. Wolf, S. Alexander, V. Schacht, L. Coussens, U.H. von Andrian, J. van Rheenen, E. Deryugina and P. Friedl, Collagenbased cell migration models in vitro and in vivo,, Semin. Cell Dev. Biol., 20(8) (2009), 931. 
[129] 
A. Woods, S. R. Johnstone, K. Dickerson, F. C. Leiper, L. G. Fryer, D. Neumann, U. Schlattner, T. Wallimann, M. Carlson and D. Carling, Lkb1 is the upstream kinase in the ampactivated protein kinase cascade,, Curr. Biol., 13 (2003), 2004. 
[130] 
W. Xiong and J. E. Ferrell Jr, A positivefeedbackbased bistable 'memory module' that governs a cell fate decision,, Nature, 426 (2003), 460. 
[131] 
R. H. Xu, H. Pelicano, Y. Zhou, J. S. Carew, L. Feng, K. N. Bhalla, M. J. Keating and P. Huang, Inhibition of glycolysis in cancer cells: A novel strategy to overcome drug resistance associated with mitochondrial respiratory defect and hypoxia,, Cancer Res., 65 (2005), 613. 
[132] 
G. Yao, T. J. Lee, S. Mori, J. R. Nevins and L. You, A bistable rbe2f switch underlies the restriction point,, Nat. Cell Biol., 10 (2008), 476. 
[133] 
N. Young and J. R. Brocklyn, Roles of sphingosine1phosphate (s1p) receptors in malignant behavior of glioma cells. Differential effects of s1p2 on cell migration and invasiveness,, Exp. Cell Res., 313 (2007), 1615. 
[134] 
K. Yuan, R. K. Singh, G. Rezonzew and G. P. Siegal, Cell motility in cancer invasion and metastasis, in "Cancer Metastasis  Biology and Treatment,", Springer, (2006), 25. 
[135] 
Y. Zhou, P. H. Larsen, C. Hao and V. W. Yong, Cxcr4 is a major chemokine receptor on glioma cells and mediates their survival,, J. Biol. Chem., 277 (2002), 49481. 
[1] 
Eugene Kashdan, Svetlana BunimovichMendrazitsky. Hybrid discretecontinuous model of invasive bladder cancer. Mathematical Biosciences & Engineering, 2013, 10 (3) : 729742. doi: 10.3934/mbe.2013.10.729 
[2] 
Hongbin Guo, Michael Yi Li. Global dynamics of a staged progression model for infectious diseases. Mathematical Biosciences & Engineering, 2006, 3 (3) : 513525. doi: 10.3934/mbe.2006.3.513 
[3] 
Sebastián Ferrer, Francisco Crespo. Parametric quartic Hamiltonian model. A unified treatment of classic integrable systems. Journal of Geometric Mechanics, 2014, 6 (4) : 479502. doi: 10.3934/jgm.2014.6.479 
[4] 
Ghendrih Philippe, Hauray Maxime, Anne Nouri. Derivation of a gyrokinetic model. Existence and uniqueness of specific stationary solution. Kinetic & Related Models, 2009, 2 (4) : 707725. doi: 10.3934/krm.2009.2.707 
[5] 
Margherita Carletti, Matteo Montani, Valentina Meschini, Marzia Bianchi, Lucia Radici. Stochastic modelling of PTEN regulation in brain tumors: A model for glioblastoma multiforme. Mathematical Biosciences & Engineering, 2015, 12 (5) : 965981. doi: 10.3934/mbe.2015.12.965 
[6] 
Danilo T. PérezRivera, Verónica L. TorresTorres, Abraham E. TorresColón, Mayteé CruzAponte. Development of a computational model of glucose toxicity in the progression of diabetes mellitus. Mathematical Biosciences & Engineering, 2016, 13 (5) : 10431058. doi: 10.3934/mbe.2016029 
[7] 
Faker Ben Belgacem. Uniqueness for an illposed reactiondispersion model. Application to organic pollution in streamwaters. Inverse Problems & Imaging, 2012, 6 (2) : 163181. doi: 10.3934/ipi.2012.6.163 
[8] 
Christoph Sadée, Eugene Kashdan. A model of thermotherapy treatment for bladder cancer. Mathematical Biosciences & Engineering, 2016, 13 (6) : 11691183. doi: 10.3934/mbe.2016037 
[9] 
Zijuan Wen, Meng Fan, Asim M. Asiri, Ebraheem O. Alzahrani, Mohamed M. ElDessoky, Yang Kuang. Global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with application to a glioblastoma growth model. Mathematical Biosciences & Engineering, 2017, 14 (2) : 407420. doi: 10.3934/mbe.2017025 
[10] 
Tracy L. Stepien, Erica M. Rutter, Yang Kuang. A datamotivated densitydependent diffusion model of in vitro glioblastoma growth. Mathematical Biosciences & Engineering, 2015, 12 (6) : 11571172. doi: 10.3934/mbe.2015.12.1157 
[11] 
Tiberiu Harko, Man Kwong Mak. Travelling wave solutions of the reactiondiffusion mathematical model of glioblastoma growth: An Abel equation based approach. Mathematical Biosciences & Engineering, 2015, 12 (1) : 4169. doi: 10.3934/mbe.2015.12.41 
[12] 
Urszula Ledzewicz, Heinz Schättler. Controlling a model for bone marrow dynamics in cancer chemotherapy. Mathematical Biosciences & Engineering, 2004, 1 (1) : 95110. doi: 10.3934/mbe.2004.1.95 
[13] 
Eugene Kashdan, Svetlana BunimovichMendrazitsky. Multiscale model of bladder cancer development. Conference Publications, 2011, 2011 (Special) : 803812. doi: 10.3934/proc.2011.2011.803 
[14] 
Avner Friedman, Harsh Vardhan Jain. A partial differential equation model of metastasized prostatic cancer. Mathematical Biosciences & Engineering, 2013, 10 (3) : 591608. doi: 10.3934/mbe.2013.10.591 
[15] 
Esther Chigidi, Edward M. Lungu. HIV model incorporating differential progression for treatmentnaive and treatmentexperienced infectives. Mathematical Biosciences & Engineering, 2009, 6 (3) : 427450. doi: 10.3934/mbe.2009.6.427 
[16] 
Wei Feng, Shuhua Hu, Xin Lu. Optimal controls for a 3compartment model for cancer chemotherapy with quadratic objective. Conference Publications, 2003, 2003 (Special) : 544553. doi: 10.3934/proc.2003.2003.544 
[17] 
HsiuChuan Wei. Mathematical and numerical analysis of a mathematical model of mixed immunotherapy and chemotherapy of cancer. Discrete & Continuous Dynamical Systems  B, 2016, 21 (4) : 12791295. doi: 10.3934/dcdsb.2016.21.1279 
[18] 
J. Ignacio Tello. On a mathematical model of tumor growth based on cancer stem cells. Mathematical Biosciences & Engineering, 2013, 10 (1) : 263278. doi: 10.3934/mbe.2013.10.263 
[19] 
Marcello Delitala, Tommaso Lorenzi. Recognition and learning in a mathematical model for immune response against cancer. Discrete & Continuous Dynamical Systems  B, 2013, 18 (4) : 891914. doi: 10.3934/dcdsb.2013.18.891 
[20] 
Ben Sheller, Domenico D'Alessandro. Analysis of a cancer dormancy model and control of immunotherapy. Mathematical Biosciences & Engineering, 2015, 12 (5) : 10371053. doi: 10.3934/mbe.2015.12.1037 
2017 Impact Factor: 0.972
Tools
Metrics
Other articles
by authors
[Back to Top]