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Global stability of an age-structured virus dynamics model with Beddington-DeAngelis infection function
Mathematically modeling the biological properties of gliomas: A review
1. | Division of Neurosurgery, University of Arizona, Tucson, AZ 85724, United States |
2. | School of Mathematical & Statistical Sciences, Arizona State University, Tempe, AZ 85281, United States |
3. | Creighton Medical School, Phoenix Campus, St. Joseph's Hospital and Medical Center, Phoenix, AZ 85013, United States |
4. | School of Mathematical & Statistical Sciences, Arizona State University, Tempe, AZ 85287, United States |
5. | School of Mathematics and Statistical Sciences, Arizona State University, Tempe, AZ 85281 |
6. | Division of Neurological Surgery, Barrow Neurological Institute, St. Joseph's Hospital and Medical Center, Phoenix, AZ 85013, United States |
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show all references
References:
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T. Alarcón, H. M. Byrne and P. K. Maini, A multiple scale model for tumor growth,, Multiscale Modeling & Simulation, 3 (2005), 440.
doi: 10.1137/040603760. |
[2] |
E. C. Alvord Jr, Simple model of recurrent gliomas,, Journal of Neurosurgery, 75 (1991), 337. Google Scholar |
[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).
doi: 10.1088/1478-3975/3/2/001. |
[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.
doi: 10.1158/0008-5472.CAN-08-3834. |
[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).
doi: 10.1088/0031-9155/53/4/004. |
[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.
doi: 10.1046/j.1365-2184.2000.00174.x. |
[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.
doi: 10.1007/s00285-008-0215-x. |
[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.
doi: 10.1046/j.1365-2184.2001.00202.x. |
[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.
doi: 10.1111/j.1365-2184.2009.00613.x. |
[10] |
S. Ferreira Jr, M. Martins and M. Vilela, Reaction-diffusion model for the growth of avascular tumor,, Physical Review E, 65 (2002).
doi: 10.1103/PhysRevE.65.021907. |
[11] |
J. Folkman and M. Hochberg, Self-regulation of growth in three dimensions,, The Journal of Experimental Medicine, 138 (1973), 745.
doi: 10.1084/jem.138.4.745. |
[12] |
J. Fort and R. V. Sole, Accelerated tumor invasion under non-isotropic cell dispersal in glioblastomas,, New Journal of Physics, 15 (2013).
doi: 10.1088/1367-2630/15/5/055001. |
[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).
doi: 10.1016/j.neuroimage.2007.03.008. |
[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.
doi: 10.1158/0008-5472.CAN-05-3166. |
[15] |
S. Gao and X. Wei, Analysis of a mathematical model of glioma cells outside the tumor spheroid core,, Applicable Analysis, 92 (2013), 1379.
doi: 10.1080/00036811.2012.678335. |
[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. Google Scholar |
[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.
doi: 10.1016/j.jtbi.2006.07.002. |
[18] |
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doi: 10.1016/j.molcel.2010.02.018. |
[19] |
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doi: 10.1109/42.811267. |
[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.
doi: 10.1093/imammb/dqq011. |
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doi: 10.1142/S0218202505000960. |
[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).
doi: 10.1088/0031-9155/52/23/008. |
[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.
doi: 10.1007/s00285-007-0139-x. |
[24] |
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doi: 10.1038/sj.onc.1203035. |
[25] |
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