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Mathematical Biosciences and Engineering (MBE)
 

Mathematically modeling the biological properties of gliomas: A review
Pages: 879 - 905, Issue 4, August 2015

doi:10.3934/mbe.2015.12.879      Abstract        References        Full text (6066.4K)                  Related Articles

Nikolay L. Martirosyan - Division of Neurosurgery, University of Arizona, Tucson, AZ 85724, United States (email)
Erica M. Rutter - School of Mathematical & Statistical Sciences, Arizona State University, Tempe, AZ 85281, United States (email)
Wyatt L. Ramey - Creighton Medical School, Phoenix Campus, St. Joseph's Hospital and Medical Center, Phoenix, AZ 85013, United States (email)
Eric J. Kostelich - School of Mathematical & Statistical Sciences, Arizona State University, Tempe, AZ 85287, United States (email)
Yang Kuang - School of Mathematics and Statistical Sciences, Arizona State University, Tempe, AZ 85281, United States (email)
Mark C. Preul - Division of Neurological Surgery, Barrow Neurological Institute, St. Joseph's Hospital and Medical Center, Phoenix, AZ 85013, United States (email)

1 T. Alarcón, H. M. Byrne and P. K. Maini, A multiple scale model for tumor growth, Multiscale Modeling & Simulation, 3 (2005), 440-475.       
2 E. C. Alvord Jr, Simple model of recurrent gliomas, Journal of Neurosurgery, 75 (1991), 337-338.
3 M. Aubert, M. Badoual, S. Fereol, C. Christov and B. Grammaticos, A cellular automaton model for the migration of glioma cells, Physical Biology, 3 (2006), p93.
4 E. L. Bearer, J. S. Lowengrub, H. B. Frieboes, Y.-L. Chuang, F. Jin, S. M. Wise, M. Ferrari, D. B. Agus and V. Cristini, Multiparameter computational modeling of tumor invasion, Cancer Research, 69 (2009), 4493-4501.
5 P.-Y. Bondiau, O. Clatz, M. Sermesant, P.-Y. Marcy, H. Delingette, M. Frenay and N. Ayache, Biocomputing: Numerical simulation of glioblastoma growth using diffusion tensor imaging, Physics in Medicine and Biology, 53 (2008), p879.
6 R. Chignola, A. Schenetti, G. Andrighetto, E. Chiesa, R. Foroni, S. Sartoris, G. Tridente and D. Liberati, Forecasting the growth of multicell tumour spheroids: Implications for the dynamic growth of solid tumours, Cell Proliferation, 33 (2000), 219-229.
7 V. Cristini, X. Li, J. S. Lowengrub and S. M. Wise, Nonlinear simulations of solid tumor growth using a mixture model: Invasion and branching, Journal of Mathematical Biology, 58 (2009), 723-763.       
8 T. Deisboeck, M. Berens, A. Kansal, S. Torquato, A. Stemmer-Rachamimov and E. Chiocca, Pattern of self-organization in tumour systems: Complex growth dynamics in a novel brain tumour spheroid model, Cell Proliferation, 34 (2001), 115-134.
9 S. E. Eikenberry, T. Sankar, M. Preul, E. Kostelich, C. Thalhauser and Y. Kuang, Virtual glioblastoma: Growth, migration and treatment in a three-dimensional mathematical model, Cell Proliferation, 42 (2009), 511-528.
10 S. Ferreira Jr, M. Martins and M. Vilela, Reaction-diffusion model for the growth of avascular tumor, Physical Review E, 65 (2002), 021907, 8pp.       
11 J. Folkman and M. Hochberg, Self-regulation of growth in three dimensions, The Journal of Experimental Medicine, 138 (1973), 745-753.
12 J. Fort and R. V. Sole, Accelerated tumor invasion under non-isotropic cell dispersal in glioblastomas, New Journal of Physics, 15 (2013), 055001, 10pp.       
13 H. B. Frieboes, J. S. Lowengrub, S. Wise, X. Zheng, P. Macklin, E. L. Bearer and V. Cristini, Computer simulation of glioma growth and morphology, Neuroimage, 37 (2007), S59-S70.
14 H. B. Frieboes, X. Zheng, C.-H. Sun, B. Tromberg, R. Gatenby and V. Cristini, An integrated computational/experimental model of tumor invasion, Cancer Research, 66 (2006), 1597-1604.
15 S. Gao and X. Wei, Analysis of a mathematical model of glioma cells outside the tumor spheroid core, Applicable Analysis, 92 (2013), 1379-1392.       
16 R. A. Gatenby and E. T. Gawlinski, The glycolytic phenotype in carcinogenesis and tumor invasion insights through mathematical models, Cancer Research, 63 (2003), 3847-3854.
17 J. L. Gevertz and S. Torquato, Modeling the effects of vasculature evolution on early brain tumor growth, Journal of Theoretical Biology, 243 (2006), 517-531.       
18 J. Godlewski, M. O. Nowicki, A. Bronisz, G. Nuovo, J. Palatini, M. De Lay, J. Van Brocklyn, M. C. Ostrowski, E. A. Chiocca and S. E. Lawler, Microrna-451 regulates lkb1/ampk signaling and allows adaptation to metabolic stress in glioma cells, Molecular Cell, 37 (2010), 620-632.
19 A. Hagemann, K. Rohr, H. S. Stiehl, U. Spetzger and J. M. Gilsbach, Biomechanical modeling of the human head for physically based, nonrigid image registration, IEEE Transactions on Medical Imaging, 18 (1999), 875-884.
20 H. Hatzikirou, D. Basanta, M. Simon, K. Schaller and A. Deutsch, Go or grow': The key to the emergence of invasion in tumour progression?, Mathematical Medicine and Biology, 29 (2012), 49-65.       
21 H. Hatzikirou, A. Deutsch, C. Schaller, M. Simon and K. Swanson, Mathematical modelling of glioblastoma tumour development: A review, {Mathematical Models and Methods in Applied Sciences}, 15 (2005), 1779-1794.       
22 C. Hogea, G. Biros, F. Abraham and C. Davatzikos, A robust framework for soft tissue simulations with application to modeling brain tumor mass effect in 3D MR images, Physics in Medicine and Biology, 52 (2007), p6893.
23 C. Hogea, C. Davatzikos and G. Biros, An image-driven parameter estimation problem for a reaction-diffusion glioma growth model with mass effects, Journal of Mathematical Biology, 56 (2008), 793-825.       
24 J. Holash, S. Wiegand and G. Yancopoulos, New model of tumor angiogenesis: Dynamic balance between vessel regression and growth mediated by angiopoietins and VEGF, Oncogene, 18 (1999), 5356-5362.
25 J. Holash, P. Maisonpierre, D. Compton, P. Boland, C. Alexander, D. Zagzag, G. Yancopoulos and S. Wiegand, Vessel cooption, regression, and growth in tumors mediated by angiopoietins and VEGF, Science, 284 (1999), 1994-1998.
26 S. Jbabdi, E. Mandonnet, H. Duffau, L. Capelle, K. R. Swanson, M. Pélégrini-Issac, R. Guillevin and H. Benali, Simulation of anisotropic growth of low-grade gliomas using diffusion tensor imaging, Magnetic Resonance in Medicine, 54 (2005), 616-624.
27 B. Kanberoglu, N. Z. Moore, D. Frakes, L. J. Karam, J. P. Debbins and M. C. Preul, Neuronavigation using three-dimensional proton magnetic resonance spectroscopy data, Stereotactic and functional neurosurgery, 92 (2014), 306-314.
28 A. Kansal, S. Torquato, G. Harsh IV, E. Chiocca and T. Deisboeck, Simulated brain tumor growth dynamics using a three-dimensional cellular automaton, Journal of Theoretical Biology, 203 (2000), 367-382.
29 Y. Kim, Regulation of cell proliferation and migration in glioblastoma: New therapeutic approach, Frontiers in Oncology, 3 (2013), p53.
30 Y. Kim, S. Lawler, M. O. Nowicki, E. A. Chiocca and A. Friedman, A mathematical model for pattern formation of glioma cells outside the tumor spheroid core, Journal of Theoretical Biology, 260 (2009), 359-371.       
31 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.       
32 Y. Kim, S. Roh, S. Lawler and A. Friedman, mir451 and ampk mutual antagonism in glioma cell migration and proliferation: A mathematical model, PloS {ONE}, 6 (2011), e28293.
33 N. F. Kirkby, S. J. Jefferies, R. Jena and N. G. Burnet, A mathematical model of the treatment and survival of patients with high-grade brain tumours, Journal of Theoretical Biology, 245 (2007), 112-124.       
34 E. Konukoglu, O. Clatz, P.-Y. Bondiau, M. Sermesant, H. Delingette and N. Ayache, Towards an identification of tumor growth parameters from time series of images, in Medical Image Computing and Computer-Assisted Intervention-MICCAI 2007, Springer, 4791 (2007), 549-556.
35 E. Konukoglu, O. Clatz, B. H. Menze, B. Stieltjes, M.-A. Weber, E. Mandonnet, H. Delingette and N. Ayache, Image guided personalization of reaction-diffusion type tumor growth models using modified anisotropic eikonal equations, IEEE Transactions on Medical Imaging, 29 (2010), 77-95.
36 E. J. Kostelich, Y. Kuang, J. M. McDaniel, N. Z. Moore, N. L. Martirosyan and M. C. Preul, Accurate state estimation from uncertain data and models: An application of data assimilation to mathematical models of human brain tumors, Biology Direct, 6 (2011), p64.
37 S. K. Kyriacou, C. Davatzikos, S. J. Zinreich and R. N. Bryan, Nonlinear elastic registration of brain images with tumor pathology using a biomechanical model [mri], IEEE Transactions on Medical Imaging, 18 (1999), 580-592.
38 A. Martínez-González, G. F. Calvo, L. A. P. Romasanta and V. M. Pérez-García, Hypoxic cell waves around necrotic cores in glioblastoma: A biomathematical model and its therapeutic implications, Bulletin of Mathematical Biology, 74 (2012), 2875-2896.       
39 J. McDaniel, E. Kostelich, Y. Kuang, J. Nagy, M. C. Preul, N. Z. Moore and N. L. Matirosyan, Data assimilation in brain tumor models, in Mathematical Models and Methods in Biomedicine, eds Ledzewicz U., Schattler H., Friedman A., Kashdan E., Springer, Berlin, (2013), 233-262.       
40 A. Mohamed and C. Davatzikos, Finite element modeling of brain tumor mass-effect from 3d medical images, in Medical Image Computing and Computer-Assisted Intervention-MICCAI 2005, Springer, 3749 (2005), 400-408.
41 J. Murray, Glioblastoma brain tumours: Estimating the time from brain tumour initiation and resolution of a patient survival anomaly after similar treatment protocols, Journal of Biological Dynamics, 6 (2012), 118-127.       
42 M. Papadogiorgaki, P. Koliou, X. Kotsiakis and M. E. Zervakis, Mathematical modelling of spatio-temporal glioma evolution, Theoretical Biology and Medical Modelling, 10 (2013), p47.
43 A. A. Patel, E. T. Gawlinski, S. K. Lemieux and R. A. Gatenby, A cellular automaton model of early tumor growth and invasion: The effects of native tissue vascularity and increased anaerobic tumor metabolism, Journal of Theoretical Biology, 213 (2001), 315-331.       
44 G. Powathil, M. Kohandel, S. Sivaloganathan, A. Oza and M. Milosevic, Mathematical modeling of brain tumors: Effects of radiotherapy and chemotherapy, Physics in Medicine and Biology, 52 (2007), p3291.
45 M. C. Preul, R. Leblanc, Z. Caramanos, R. Kasrai, S. Narayanan and D. L. Arnold, Magnetic resonance spectroscopy guided brain tumor resection: differentiation between recurrent glioma and radiation change in two diagnostically difficult cases., The Canadian journal of neurological sciences. Le journal canadien des sciences neurologiques, 25 (1998), 13-22.
46 R. Rockne, E. Alvord Jr, J. Rockhill and K. Swanson, A mathematical model for brain tumor response to radiation therapy, Journal of Mathematical Biology, 58 (2009), 561-578.       
47 L. M. Sander and T. S. Deisboeck, Growth patterns of microscopic brain tumors, Physical Review E, 66 (2002), 051901.
48 T. Sankar, Y. E. Kuznetsov, R. W. Ryan, Z. Caramanos, S. B. Antel, D. L. Arnold and M. C. Preul, The metabolic epicenter of supratentorial gliomas: A 1 h-mrsi study, The Canadian Journal of Neurological Sciences, 36 (2009), 696-706.
49 T. Sankar, N. Z. Moore, J. Johnson, L. S. Ashby, A. C. Scheck, W. R. Shapiro, K. A. Smith, R. F. Spetzler and M. C. Preul, Magnetic resonance imaging volumetric assessment of the extent of contrast enhancement and resection in oligodendroglial tumors: Clinical article, Journal of neurosurgery, 116 (2012), 1172-1181.
50 H. Schättler, U. Ledzewicz, Y. Kim, A. de los Reyes and E. Jung, On the control of cell migration and proliferation in glioblastoma in 52nd IEEE Conference on Decision and Control, Florence, Italy, (2013), 1810-1815.
51 G. S. Stamatakos, V. P. Antipas and N. K. Uzunoglu, A spatiotemporal, patient individualized simulation model of solid tumor response to chemotherapy in vivo: the paradigm of glioblastoma multiforme treated by temozolomide, IEEE Transactions on Biomedical Engineering, 53 (2006), 1467-1477.
52 G. Stamatakos, V. Antipas, N. Uzunoglu and R. Dale, A four-dimensional computer simulation model of the in vivo response to radiotherapy of glioblastoma multiforme: studies on the effect of clonogenic cell density, The British Journal of Radiology, 79 (2004), 389-400.
53 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, Biophysical Journal, 92 (2007), 356-365.
54 A. M. Stein, M. O. Nowicki, T. Demuth, M. E. Berens, S. E. Lawler, E. A. Chiocca and L. M. Sander, Estimating the cell density and invasive radius of three-dimensional glioblastoma tumor spheroids grown in vitro, Applied Optics, 46 (2007), 5110-5118.
55 R. Stupp, W. P. Mason, M. J. Van Den Bent, M. Weller, B. Fisher, M. J. Taphoorn, K. Belanger, A. A. Brandes, C. Marosi and U. Bogdahn et al., Radiotherapy plus concomitant and adjuvant temozolomide for glioblastoma, New England Journal of Medicine, 352 (2005), 987-996.
56 R. Sullivan and C. H. Graham, Hypoxia-driven selection of the metastatic phenotype, Cancer and Metastasis Reviews, 26 (2007), 319-331.
57 K. Swanson, E. Alvord and J. Murray, A quantitative model for differential motility of gliomas in grey and white matter, Cell Proliferation, 33 (2000), 317-330.
58 K. Swanson, H. Harpold, D. Peacock, R. Rockne, C. Pennington, L. Kilbride, R. Grant, J. Wardlaw and E. Alvord Jr, Velocity of radial expansion of contrast-enhancing gliomas and the effectiveness of radiotherapy in individual patients: A proof of principle, Clinical Oncology, 20 (2008), 301-308.
59 K. R. Swanson, R. C. Rockne, J. Claridge, M. A. Chaplain, E. C. Alvord and A. R. Anderson, Quantifying the role of angiogenesis in malignant progression of gliomas: in silico modeling integrates imaging and histology, Cancer Research, 71 (2011), 7366-7375.
60 M. D. Szeto, G. Chakraborty, J. Hadley, R. Rockne, M. Muzi, E. C. Alvord, K. A. Krohn, A. M. Spence and K. R. Swanson, Quantitative metrics of net proliferation and invasion link biological aggressiveness assessed by mri with hypoxia assessed by fmiso-pet in newly diagnosed glioblastomas, Cancer Research, 69 (2009), 4502-4509.
61 J. P. Tian, A. Friedman, J. Wang and E. A. Chiocca, Modeling the effects of resection, radiation and chemotherapy in glioblastoma, Journal of Neuro-oncology, 91 (2009), 287-293.
62 P. Tracqui, G. Cruywagen, D. Woodward, G. Bartoo, J. Murray and E. Alvord, A mathematical model of glioma growth: The effect of chemotherapy on spatio-temporal growth, Cell Proliferation, 28 (1995), 17-31.
63 S. Turner and J. A. Sherratt, Intercellular adhesion and cancer invasion: A discrete simulation using the extended potts model, Journal of Theoretical Biology, 216 (2002), 85-100.       
64 A. Valster, N. L. Tran, M. Nakada, M. E. Berens, A. Y. Chan and M. Symons, Cell migration and invasion assays, Methods, 37 (2005), 208-215.
65 C. H. Wang, J. K. Rockhill, M. Mrugala, D. L. Peacock, A. Lai, K. Jusenius, J. M. Wardlaw, T. Cloughesy, A. M. Spence and R. Rockne et al., Prognostic significance of growth kinetics in newly diagnosed glioblastomas revealed by combining serial imaging with a novel biomathematical model, Cancer Research, 69 (2009), 9133-9140.
66 S. M. Wise, J. S. Lowengrub, H. B. Frieboes and V. Cristini, Three-dimensional multispecies nonlinear tumor growth-i: Model and numerical method, Journal of Theoretical Biology, 253 (2008), 524-543.       
67 D. Yang, J. P. Tian and J. Wang, A solvable hyperbolic free boundary problem modelling tumour regrowth, Applicable Analysis, 92 (2013), 1541-1558.       
68 E. I. Zacharaki, C. S. Hogea, G. Biros and C. Davatzikos, A comparative study of biomechanical simulators in deformable registration of brain tumor images, IEEE Transactions on Biomedical Engineering, 55 (2008), 1233-1236.
69 X. Zheng, S. Wise and V. Cristini, Nonlinear simulation of tumor necrosis, neo-vascularization and tissue invasion via an adaptive finite-element/level-set method, Bulletin of Mathematical Biology, 67 (2005), 211-259.       

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