-
Previous Article
Calcium waves with mechano-chemical couplings
- MBE Home
- This Issue
-
Next Article
Mathematical modeling of citrus groves infected by huanglongbing
Hybrid discrete-continuous model of invasive bladder cancer
1. | School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Ramat Aviv, 69978, Israel |
2. | Department of Computer Science and Mathematics, Ariel University Center of Samaria, Ariel, 40700, Israel |
References:
[1] |
A. E. Anderson, A hybrid mathematical model of solid tumour invasion: The importance of cell adhesion,, Mathematical Medicine and Biology, 22 (2005), 163.
doi: 10.1093/imammb/dqi005. |
[2] |
F. Andreu, V. Caselles and J. Mazan, Diffusion equations with finite speed of propagation,, in, (2008), 17.
doi: 10.1007/978-3-7643-7794-6_2. |
[3] |
Atlas of Genetics and Cytogenetics in Oncology and Haematology, http://AtlasGeneticsOncology.org., Image available for use under CCA license., (). Google Scholar |
[4] |
A. H. Baker, D. R. Edwards and G. Murphy, Metalloproteinase inhibitors: Biological actions and therapeutic opportunities,, J. of Cell Science, 115 (2002), 3719.
doi: 10.1242/jcs.00063. |
[5] |
C. E. Brinckerhoff and L. M.Matrisian, Matrix metalloproteinases: A tail of frog that became a prince,, Nature Reviews, 3 (2002), 207. Google Scholar |
[6] |
H. M Byrne, M. A. J. Chaplain, G. J. Pettet and D. L. S. McElwain, A mathematical model of trophoblast invasion,, J. of Theor. Medicine, 1 (1999), 275.
doi: 10.1080/10273669908833026. |
[7] |
C. Chang and Z. Werb, The many faces of metalloproteases: cell growth, invasion, angiogenesis and metastasis,, Trends in Cell Biology, 11 (2001), 37. Google Scholar |
[8] |
M. A. J. Chaplain and G. Lolas, Mathematical modeling of cancer invasion of tissue: Dynamic heterogeneity,, Networks and Heterogeneous Media, 1 (2006), 399.
doi: 10.3934/nhm.2006.1.399. |
[9] |
L. M. Coussens, B. Fingleton and L. M. Matrisian, Matrix metalloproteinase inhibitors and cancer: Trials and tribulations,, Science, 295 (2002), 2387.
doi: 10.1126/science.1067100. |
[10] |
G. B. Ermentrout and L. Edelstein-Keshet, Cellular automata approaches to biological modelling,, J. Theor. Biol., 160 (1993), 97.
doi: 10.1006/jtbi.1993.1007. |
[11] |
R. A. Gatenby and E. T. Gawlinski, A reaction-diffusion model of cancer invasion,, Cancer Research, 56 (1996), 5745. Google Scholar |
[12] |
B. George, R. H. Datar and R. J. Cote, Molecular biology of bladder cancer: cell cycle alterations,, in, (2006), 107. Google Scholar |
[13] |
G. Giannelli, J. Falk-Marzillier, O. Schiraldi, W. G. Stetler-Stevenson and V. Quaranta, Induction of cell migration by matrix metalloprotease-2 cleavage of lamitiin-5,, Science, 277 (1997), 225. Google Scholar |
[14] |
F. Graner and J. A. Glazier, Simulation of biological cell sorting using a two-dimensional extended Potts model,, Phys. Rev. Lett., 69 (1992), 2013.
doi: 10.1103/PhysRevLett.69.2013. |
[15] |
G. P. Hemstreet III and E. M, Messing, Early detection for bladder cancer,, in, (2006), 257. Google Scholar |
[16] |
A. Jemal, F. Bray, M. M. Center, J. Ferlay, E. Ward and D. Forman, Global cancer statistics,, CA: A Cancer J. for Clinicians, 61 (2011), 69.
doi: 10.3322/caac.20107. |
[17] |
T. Kakizoe, Development and progression of urothelial carcinoma,, Cancer Science, 97 (1982), 821.
doi: 10.1111/j.1349-7006.2006.00264.x. |
[18] |
E. Kashdan and S. Bunimovich-Mendrazitsky, "Multi-Scale Model of Bladder Cancer Development,", Discrete and Continuous Dynamical Systems, (2011), 803.
|
[19] |
M. Kirsch-Voldersa, M. Aardemab and A. Elhajoujic, Concepts of threshold in mutagenesis and carcinogenesis,, Mutation Res., 464 (2000), 3.
doi: 10.1016/S1383-5718(99)00161-8. |
[20] |
C. J. Malemud, Matrix metalloproteinases (MMPs) in health and disease: an overview,, Frontiers in Bioscience, 11 (2006), 1696.
doi: 10.2741/1915. |
[21] |
B. P. Marchant, J. Norbury and J. A. Sherratt, Travelling wave solutions to a haptotaxis-dominated model of malignant invasion,, Nonlinearity, 14 (2001), 1653.
doi: 10.1088/0951-7715/14/6/313. |
[22] |
C. J. Marshall, L. M. Franks and A. W. Carbonell, Markers of neoplastic transformation in epithelial cell lines derived from human carcinomas,, J. Natl. Cancer Inst., 58 (1977), 1743. Google Scholar |
[23] |
L. L. Munn, C. Kunert and J. A. Tyrrell, Modeling tumor blood vessel dynamics,, in, (2012), 113.
doi: 10.1007/978-1-4614-4178-6_5. |
[24] |
G. Murphy and J. Gavrilovic, The mathematical modelling of Proteolysis and cell migration: Creating a path?,, Curr. Opin. Cell Biol., 11 (1999), 614. Google Scholar |
[25] |
K. Nabeshima, W. S. Lane and C. Biswas, Partial sequencing and characterisation of the tumour cell- derived collagenase stimulatory factor,, Arch. Biochem. Biophys., 285 (1991), 90. Google Scholar |
[26] |
U. 0. Nseyo and D. L. Lamm, Immunotherapy of bladder cancer,, Seminars in Surgical Oncology, 13 (1997), 342. Google Scholar |
[27] |
J. E. Nutt, G. C. Durkan, J. vK. Mellon and J. Lunce, Matrix metalloproteinases (MMPs) in bladder cancer: The induction of MMP9 by epidermal growth factor and its detection in urine,, BJU International, 91 (2003), 99.
doi: 10.1046/j.1464-410X.2003.04020.x. |
[28] |
A. J. Perumpanani, J. A. Sherratt, J. Norbury and H. M. Byrne, A two parameter family of travelling waves with a singular barrier arising from the modelling of extracellular matrix mediated cellular invasion,, Physica D, 126 (1999), 145.
doi: 10.1016/S0167-2789(98)00272-3. |
[29] |
V. Quaranta, K. A. Rejniak, P. Gerlee and A. R. A. Anderson, Invasion emerges from cancer cell adaptation to competitive microenvironments: Quantitative predictions from multiscale mathematical models,, Seminars in Cancer Biology, 18 (2008), 338.
doi: 10.1016/j.semcancer.2008.03.018. |
[30] |
I. Ramis-Conde, M. A. J. Chaplain and A. R. A. Anderson, Mathematical modelling of cancer cell invasion of tissue,, Mathematical and Computer Modelling, 47 (2008), 533.
doi: 10.1016/j.mcm.2007.02.034. |
[31] |
C. J. Sherr, Cancer cell cycles,, Science, 274 (1996), 1672.
doi: 10.1126/science.274.5293.1672. |
[32] |
W. G. Stetler- Stevenson, S. Aznavoorian and L. A. Liotta, Tumor cell interactions with the extracellular matrix during invasion and metastasis,, Ann. Rev. Cell Biol., 9 (1993), 541. Google Scholar |
[33] |
J. Testa, Loss of metastatic phenotype by a human epidermoid carcinoma cell line hep-3 is accompanied by increased expression of tissue inhibitor of matrix metalloproteinase-2,, Cancer Res., 52 (1992), 5597. Google Scholar |
[34] |
Transitional epithelium of the urinary bladder, http://en.wikipedia.org/wiki/Urothelium., Image available for use under CCA license., (). Google Scholar |
[35] |
S. Turner and J. A. Sheratt, Intercellular adhesion and cancer invasion: A discrete simulation using the extended potts model,, J. Theor. Biol., 216 (2002), 85.
doi: 10.1006/jtbi.2001.2522. |
[36] |
K. Vasala, P. Paakko and T. Turpeenniemi-Hujanen, Matrix metalloproteinase-9 ( MMP-9) immunoreactive protein in urinary bladder cancer: A marker of favorable prognosis,, Anticancer Research, 28 (2008), 1757. Google Scholar |
[37] |
J. L. Vasquez, "Porous Medium Equation. Mathematical Theory,", Oxford University Press, (2007).
|
[38] |
S. M. Wnek, M. K. Medeirosa, K. E. Eblinb and A. J. Gandolfi, Persistence of DNA damage following exposure of human bladder cells to chronic monomethylarsonous acid,, Tox. and Appl. Pharm., 241 (2009), 202.
doi: 10.1016/j.taap.2009.08.016. |
show all references
References:
[1] |
A. E. Anderson, A hybrid mathematical model of solid tumour invasion: The importance of cell adhesion,, Mathematical Medicine and Biology, 22 (2005), 163.
doi: 10.1093/imammb/dqi005. |
[2] |
F. Andreu, V. Caselles and J. Mazan, Diffusion equations with finite speed of propagation,, in, (2008), 17.
doi: 10.1007/978-3-7643-7794-6_2. |
[3] |
Atlas of Genetics and Cytogenetics in Oncology and Haematology, http://AtlasGeneticsOncology.org., Image available for use under CCA license., (). Google Scholar |
[4] |
A. H. Baker, D. R. Edwards and G. Murphy, Metalloproteinase inhibitors: Biological actions and therapeutic opportunities,, J. of Cell Science, 115 (2002), 3719.
doi: 10.1242/jcs.00063. |
[5] |
C. E. Brinckerhoff and L. M.Matrisian, Matrix metalloproteinases: A tail of frog that became a prince,, Nature Reviews, 3 (2002), 207. Google Scholar |
[6] |
H. M Byrne, M. A. J. Chaplain, G. J. Pettet and D. L. S. McElwain, A mathematical model of trophoblast invasion,, J. of Theor. Medicine, 1 (1999), 275.
doi: 10.1080/10273669908833026. |
[7] |
C. Chang and Z. Werb, The many faces of metalloproteases: cell growth, invasion, angiogenesis and metastasis,, Trends in Cell Biology, 11 (2001), 37. Google Scholar |
[8] |
M. A. J. Chaplain and G. Lolas, Mathematical modeling of cancer invasion of tissue: Dynamic heterogeneity,, Networks and Heterogeneous Media, 1 (2006), 399.
doi: 10.3934/nhm.2006.1.399. |
[9] |
L. M. Coussens, B. Fingleton and L. M. Matrisian, Matrix metalloproteinase inhibitors and cancer: Trials and tribulations,, Science, 295 (2002), 2387.
doi: 10.1126/science.1067100. |
[10] |
G. B. Ermentrout and L. Edelstein-Keshet, Cellular automata approaches to biological modelling,, J. Theor. Biol., 160 (1993), 97.
doi: 10.1006/jtbi.1993.1007. |
[11] |
R. A. Gatenby and E. T. Gawlinski, A reaction-diffusion model of cancer invasion,, Cancer Research, 56 (1996), 5745. Google Scholar |
[12] |
B. George, R. H. Datar and R. J. Cote, Molecular biology of bladder cancer: cell cycle alterations,, in, (2006), 107. Google Scholar |
[13] |
G. Giannelli, J. Falk-Marzillier, O. Schiraldi, W. G. Stetler-Stevenson and V. Quaranta, Induction of cell migration by matrix metalloprotease-2 cleavage of lamitiin-5,, Science, 277 (1997), 225. Google Scholar |
[14] |
F. Graner and J. A. Glazier, Simulation of biological cell sorting using a two-dimensional extended Potts model,, Phys. Rev. Lett., 69 (1992), 2013.
doi: 10.1103/PhysRevLett.69.2013. |
[15] |
G. P. Hemstreet III and E. M, Messing, Early detection for bladder cancer,, in, (2006), 257. Google Scholar |
[16] |
A. Jemal, F. Bray, M. M. Center, J. Ferlay, E. Ward and D. Forman, Global cancer statistics,, CA: A Cancer J. for Clinicians, 61 (2011), 69.
doi: 10.3322/caac.20107. |
[17] |
T. Kakizoe, Development and progression of urothelial carcinoma,, Cancer Science, 97 (1982), 821.
doi: 10.1111/j.1349-7006.2006.00264.x. |
[18] |
E. Kashdan and S. Bunimovich-Mendrazitsky, "Multi-Scale Model of Bladder Cancer Development,", Discrete and Continuous Dynamical Systems, (2011), 803.
|
[19] |
M. Kirsch-Voldersa, M. Aardemab and A. Elhajoujic, Concepts of threshold in mutagenesis and carcinogenesis,, Mutation Res., 464 (2000), 3.
doi: 10.1016/S1383-5718(99)00161-8. |
[20] |
C. J. Malemud, Matrix metalloproteinases (MMPs) in health and disease: an overview,, Frontiers in Bioscience, 11 (2006), 1696.
doi: 10.2741/1915. |
[21] |
B. P. Marchant, J. Norbury and J. A. Sherratt, Travelling wave solutions to a haptotaxis-dominated model of malignant invasion,, Nonlinearity, 14 (2001), 1653.
doi: 10.1088/0951-7715/14/6/313. |
[22] |
C. J. Marshall, L. M. Franks and A. W. Carbonell, Markers of neoplastic transformation in epithelial cell lines derived from human carcinomas,, J. Natl. Cancer Inst., 58 (1977), 1743. Google Scholar |
[23] |
L. L. Munn, C. Kunert and J. A. Tyrrell, Modeling tumor blood vessel dynamics,, in, (2012), 113.
doi: 10.1007/978-1-4614-4178-6_5. |
[24] |
G. Murphy and J. Gavrilovic, The mathematical modelling of Proteolysis and cell migration: Creating a path?,, Curr. Opin. Cell Biol., 11 (1999), 614. Google Scholar |
[25] |
K. Nabeshima, W. S. Lane and C. Biswas, Partial sequencing and characterisation of the tumour cell- derived collagenase stimulatory factor,, Arch. Biochem. Biophys., 285 (1991), 90. Google Scholar |
[26] |
U. 0. Nseyo and D. L. Lamm, Immunotherapy of bladder cancer,, Seminars in Surgical Oncology, 13 (1997), 342. Google Scholar |
[27] |
J. E. Nutt, G. C. Durkan, J. vK. Mellon and J. Lunce, Matrix metalloproteinases (MMPs) in bladder cancer: The induction of MMP9 by epidermal growth factor and its detection in urine,, BJU International, 91 (2003), 99.
doi: 10.1046/j.1464-410X.2003.04020.x. |
[28] |
A. J. Perumpanani, J. A. Sherratt, J. Norbury and H. M. Byrne, A two parameter family of travelling waves with a singular barrier arising from the modelling of extracellular matrix mediated cellular invasion,, Physica D, 126 (1999), 145.
doi: 10.1016/S0167-2789(98)00272-3. |
[29] |
V. Quaranta, K. A. Rejniak, P. Gerlee and A. R. A. Anderson, Invasion emerges from cancer cell adaptation to competitive microenvironments: Quantitative predictions from multiscale mathematical models,, Seminars in Cancer Biology, 18 (2008), 338.
doi: 10.1016/j.semcancer.2008.03.018. |
[30] |
I. Ramis-Conde, M. A. J. Chaplain and A. R. A. Anderson, Mathematical modelling of cancer cell invasion of tissue,, Mathematical and Computer Modelling, 47 (2008), 533.
doi: 10.1016/j.mcm.2007.02.034. |
[31] |
C. J. Sherr, Cancer cell cycles,, Science, 274 (1996), 1672.
doi: 10.1126/science.274.5293.1672. |
[32] |
W. G. Stetler- Stevenson, S. Aznavoorian and L. A. Liotta, Tumor cell interactions with the extracellular matrix during invasion and metastasis,, Ann. Rev. Cell Biol., 9 (1993), 541. Google Scholar |
[33] |
J. Testa, Loss of metastatic phenotype by a human epidermoid carcinoma cell line hep-3 is accompanied by increased expression of tissue inhibitor of matrix metalloproteinase-2,, Cancer Res., 52 (1992), 5597. Google Scholar |
[34] |
Transitional epithelium of the urinary bladder, http://en.wikipedia.org/wiki/Urothelium., Image available for use under CCA license., (). Google Scholar |
[35] |
S. Turner and J. A. Sheratt, Intercellular adhesion and cancer invasion: A discrete simulation using the extended potts model,, J. Theor. Biol., 216 (2002), 85.
doi: 10.1006/jtbi.2001.2522. |
[36] |
K. Vasala, P. Paakko and T. Turpeenniemi-Hujanen, Matrix metalloproteinase-9 ( MMP-9) immunoreactive protein in urinary bladder cancer: A marker of favorable prognosis,, Anticancer Research, 28 (2008), 1757. Google Scholar |
[37] |
J. L. Vasquez, "Porous Medium Equation. Mathematical Theory,", Oxford University Press, (2007).
|
[38] |
S. M. Wnek, M. K. Medeirosa, K. E. Eblinb and A. J. Gandolfi, Persistence of DNA damage following exposure of human bladder cells to chronic monomethylarsonous acid,, Tox. and Appl. Pharm., 241 (2009), 202.
doi: 10.1016/j.taap.2009.08.016. |
[1] |
Masaharu Taniguchi. Axisymmetric traveling fronts in balanced bistable reaction-diffusion equations. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3981-3995. doi: 10.3934/dcds.2020126 |
[2] |
Hideki Murakawa. Fast reaction limit of reaction-diffusion systems. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1047-1062. doi: 10.3934/dcdss.2020405 |
[3] |
Lin Shi, Xuemin Wang, Dingshi Li. Limiting behavior of non-autonomous stochastic reaction-diffusion equations with colored noise on unbounded thin domains. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5367-5386. doi: 10.3934/cpaa.2020242 |
[4] |
Nabahats Dib-Baghdadli, Rabah Labbas, Tewfik Mahdjoub, Ahmed Medeghri. On some reaction-diffusion equations generated by non-domiciliated triatominae, vectors of Chagas disease. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2021004 |
[5] |
Chungang Shi, Wei Wang, Dafeng Chen. Weak time discretization for slow-fast stochastic reaction-diffusion equations. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021019 |
[6] |
Kaixuan Zhu, Ji Li, Yongqin Xie, Mingji Zhang. Dynamics of non-autonomous fractional reaction-diffusion equations on $ \mathbb{R}^{N} $ driven by multiplicative noise. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020376 |
[7] |
Weiwei Liu, Jinliang Wang, Yuming Chen. Threshold dynamics of a delayed nonlocal reaction-diffusion cholera model. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020316 |
[8] |
Abdelghafour Atlas, Mostafa Bendahmane, Fahd Karami, Driss Meskine, Omar Oubbih. A nonlinear fractional reaction-diffusion system applied to image denoising and decomposition. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020321 |
[9] |
Maho Endo, Yuki Kaneko, Yoshio Yamada. Free boundary problem for a reaction-diffusion equation with positive bistable nonlinearity. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3375-3394. doi: 10.3934/dcds.2020033 |
[10] |
Shin-Ichiro Ei, Shyuh-Yaur Tzeng. Spike solutions for a mass conservation reaction-diffusion system. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3357-3374. doi: 10.3934/dcds.2020049 |
[11] |
Chihiro Aida, Chao-Nien Chen, Kousuke Kuto, Hirokazu Ninomiya. Bifurcation from infinity with applications to reaction-diffusion systems. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3031-3055. doi: 10.3934/dcds.2020053 |
[12] |
Leilei Wei, Yinnian He. A fully discrete local discontinuous Galerkin method with the generalized numerical flux to solve the tempered fractional reaction-diffusion equation. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020319 |
[13] |
H. M. Srivastava, H. I. Abdel-Gawad, Khaled Mohammed Saad. Oscillatory states and patterns formation in a two-cell cubic autocatalytic reaction-diffusion model subjected to the Dirichlet conditions. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020433 |
[14] |
Shin-Ichiro Ei, Hiroshi Ishii. The motion of weakly interacting localized patterns for reaction-diffusion systems with nonlocal effect. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 173-190. doi: 10.3934/dcdsb.2020329 |
[15] |
El Haj Laamri, Michel Pierre. Stationary reaction-diffusion systems in $ L^1 $ revisited. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 455-464. doi: 10.3934/dcdss.2020355 |
[16] |
Klemens Fellner, Jeff Morgan, Bao Quoc Tang. Uniform-in-time bounds for quadratic reaction-diffusion systems with mass dissipation in higher dimensions. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 635-651. doi: 10.3934/dcdss.2020334 |
[17] |
Gheorghe Craciun, Jiaxin Jin, Casian Pantea, Adrian Tudorascu. Convergence to the complex balanced equilibrium for some chemical reaction-diffusion systems with boundary equilibria. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1305-1335. doi: 10.3934/dcdsb.2020164 |
[18] |
Guillaume Cantin, M. A. Aziz-Alaoui. Dimension estimate of attractors for complex networks of reaction-diffusion systems applied to an ecological model. Communications on Pure & Applied Analysis, 2021, 20 (2) : 623-650. doi: 10.3934/cpaa.2020283 |
[19] |
Alexandra Köthe, Anna Marciniak-Czochra, Izumi Takagi. Hysteresis-driven pattern formation in reaction-diffusion-ODE systems. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3595-3627. doi: 10.3934/dcds.2020170 |
[20] |
Yongjie Wang, Nan Gao. Some properties for almost cellular algebras. Electronic Research Archive, 2021, 29 (1) : 1681-1689. doi: 10.3934/era.2020086 |
2018 Impact Factor: 1.313
Tools
Metrics
Other articles
by authors
[Back to Top]