
Previous Article
A Cellular Potts model simulating cell migration on and in matrix environments
 MBE Home
 This Issue
 Next Article
On a mathematical model of tumor growth based on cancer stem cells
1.  Departamento de Matemática Aplicada, EUI Informática, Universidad Politécnica de Madrid, 28031 Madrid, Spain 
References:
[1] 
M. F. Clarke and M. Fuller, Stem cells and cancer: Two faces of eve,, Cell, 124 (2006), 1111. 
[2] 
A. T. Collins, P. A. Berry, C. Hyde, M. J. Stower and N. J. Maitland, Prospective identification of tumorigenic prostate cancer stem cells,, Cancer Res, 65 (2005), 10946. 
[3] 
J. E. Dick, Stem cell concepts renew cancer research,, Blood, 112 (2008), 4793. 
[4] 
A. Friedman, Cancer models and their mathematical analysis,, Tutorials in mathematical biosciences. III, (1872), 223. 
[5] 
A. Friedman and Y. Tao, Analysis of a model of a virus that replicates selectively in tumor cells,, J. Math. Biol., 47 (2003), 391. doi: 10.1007/s0028500301995. 
[6] 
C. Fornari, F. Cordero, D. Manini, R. A. Calogero and G. Balbo, Mathematical approach to predict the drug effects on cancer stem cell models,, Proceedings of the CS2Bio 2nd International Workshop on Interactions between Computer Science and Biology, (2011). 
[7] 
R. MolinaPeña and M. M. Álvarez, A simple mathematical model based on the cancer stem cell hypothesis suggests kinetic commonalities in solid tumor growth,, PLoS ONE, 7 (2012). 
[8] 
K. Qu and P. Ortoleva, Understanding stem cell differentiation through selforganization theory,, Journal of Theoretical Biology, 250 (2008), 606. 
[9] 
S. Bapat, "Cancer Steam Cells, Identification and Targets,", Willey Edt. New Jersey, (2009). 
[10] 
Z. Szymánska, C. Morales Rodrigo, M. Lachowicz and M. A. J. Chaplain, Mathematical modelling of cancer invasion of tissue: The role and effect of nonlocal interaction,, Mathematical Models and Methods in Applied Sciences, 19 (2009), 257. 
[11] 
J. I. Tello, Mathematical analysis of a model of Morphogenesis,, Discrete and Continuous Dynamical Systems  Serie A., 25 (2009), 343. 
[12] 
J. I. Tello, On the existence of solutions of a mathematical model of morphogens,, in, (2011). 
show all references
References:
[1] 
M. F. Clarke and M. Fuller, Stem cells and cancer: Two faces of eve,, Cell, 124 (2006), 1111. 
[2] 
A. T. Collins, P. A. Berry, C. Hyde, M. J. Stower and N. J. Maitland, Prospective identification of tumorigenic prostate cancer stem cells,, Cancer Res, 65 (2005), 10946. 
[3] 
J. E. Dick, Stem cell concepts renew cancer research,, Blood, 112 (2008), 4793. 
[4] 
A. Friedman, Cancer models and their mathematical analysis,, Tutorials in mathematical biosciences. III, (1872), 223. 
[5] 
A. Friedman and Y. Tao, Analysis of a model of a virus that replicates selectively in tumor cells,, J. Math. Biol., 47 (2003), 391. doi: 10.1007/s0028500301995. 
[6] 
C. Fornari, F. Cordero, D. Manini, R. A. Calogero and G. Balbo, Mathematical approach to predict the drug effects on cancer stem cell models,, Proceedings of the CS2Bio 2nd International Workshop on Interactions between Computer Science and Biology, (2011). 
[7] 
R. MolinaPeña and M. M. Álvarez, A simple mathematical model based on the cancer stem cell hypothesis suggests kinetic commonalities in solid tumor growth,, PLoS ONE, 7 (2012). 
[8] 
K. Qu and P. Ortoleva, Understanding stem cell differentiation through selforganization theory,, Journal of Theoretical Biology, 250 (2008), 606. 
[9] 
S. Bapat, "Cancer Steam Cells, Identification and Targets,", Willey Edt. New Jersey, (2009). 
[10] 
Z. Szymánska, C. Morales Rodrigo, M. Lachowicz and M. A. J. Chaplain, Mathematical modelling of cancer invasion of tissue: The role and effect of nonlocal interaction,, Mathematical Models and Methods in Applied Sciences, 19 (2009), 257. 
[11] 
J. I. Tello, Mathematical analysis of a model of Morphogenesis,, Discrete and Continuous Dynamical Systems  Serie A., 25 (2009), 343. 
[12] 
J. I. Tello, On the existence of solutions of a mathematical model of morphogens,, in, (2011). 
[1] 
Chengjun Guo, Chengxian Guo, Sameed Ahmed, Xinfeng Liu. Moment stability for nonlinear stochastic growth kinetics of breast cancer stem cells with timedelays. Discrete & Continuous Dynamical Systems  B, 2016, 21 (8) : 24732489. doi: 10.3934/dcdsb.2016056 
[2] 
Avner Friedman. Free boundary problems arising in biology. Discrete & Continuous Dynamical Systems  B, 2018, 23 (1) : 193202. doi: 10.3934/dcdsb.2018013 
[3] 
Avner Friedman. Free boundary problems for systems of Stokes equations. Discrete & Continuous Dynamical Systems  B, 2016, 21 (5) : 14551468. doi: 10.3934/dcdsb.2016006 
[4] 
Noriaki Yamazaki. Almost periodicity of solutions to free boundary problems. Conference Publications, 2001, 2001 (Special) : 386397. doi: 10.3934/proc.2001.2001.386 
[5] 
Serena Dipierro, Enrico Valdinoci. (Non)local and (non)linear free boundary problems. Discrete & Continuous Dynamical Systems  S, 2018, 11 (3) : 465476. doi: 10.3934/dcdss.2018025 
[6] 
Svetlana BunimovichMendrazitsky, Yakov Goltser. Use of quasinormal form to examine stability of tumorfree equilibrium in a mathematical model of bcg treatment of bladder cancer. Mathematical Biosciences & Engineering, 2011, 8 (2) : 529547. doi: 10.3934/mbe.2011.8.529 
[7] 
Evans K. Afenya, Calixto P. Calderón. Growth kinetics of cancer cells prior to detection and treatment: An alternative view. Discrete & Continuous Dynamical Systems  B, 2004, 4 (1) : 2528. doi: 10.3934/dcdsb.2004.4.25 
[8] 
Manuel Delgado, Ítalo Bruno Mendes Duarte, Antonio Suárez Fernández. Nonlocal elliptic system arising from the growth of cancer stem cells. Discrete & Continuous Dynamical Systems  B, 2018, 23 (4) : 17671795. doi: 10.3934/dcdsb.2018083 
[9] 
Daniela De Silva, Fausto Ferrari, Sandro Salsa. On two phase free boundary problems governed by elliptic equations with distributed sources. Discrete & Continuous Dynamical Systems  S, 2014, 7 (4) : 673693. doi: 10.3934/dcdss.2014.7.673 
[10] 
Huiqiang Jiang. Regularity of a vector valued two phase free boundary problems. Conference Publications, 2013, 2013 (special) : 365374. doi: 10.3934/proc.2013.2013.365 
[11] 
Jesús Ildefonso Díaz. On the free boundary for quenching type parabolic problems via local energy methods. Communications on Pure & Applied Analysis, 2014, 13 (5) : 17991814. doi: 10.3934/cpaa.2014.13.1799 
[12] 
Ugur G. Abdulla, Evan Cosgrove, Jonathan Goldfarb. On the Frechet differentiability in optimal control of coefficients in parabolic free boundary problems. Evolution Equations & Control Theory, 2017, 6 (3) : 319344. doi: 10.3934/eect.2017017 
[13] 
Mingxin Wang. Existence and uniqueness of solutions of free boundary problems in heterogeneous environments. Discrete & Continuous Dynamical Systems  B, 2017, 22 (11) : 17. doi: 10.3934/dcdsb.2018179 
[14] 
Alexander S. Bratus, Svetlana Yu. Kovalenko, Elena Fimmel. On viable therapy strategy for a mathematical spatial cancer model describing the dynamics of malignant and healthy cells. Mathematical Biosciences & Engineering, 2015, 12 (1) : 163183. doi: 10.3934/mbe.2015.12.163 
[15] 
Feimin Huang, Xiaoding Shi, Yi Wang. Stability of viscous shock wave for compressible NavierStokes equations with free boundary. Kinetic & Related Models, 2010, 3 (3) : 409425. doi: 10.3934/krm.2010.3.409 
[16] 
Nobuyuki Kato. Linearized stability and asymptotic properties for abstract boundary value functional evolution problems. Conference Publications, 1998, 1998 (Special) : 371387. doi: 10.3934/proc.1998.1998.371 
[17] 
Noriaki Yamazaki. Doubly nonlinear evolution equations associated with ellipticparabolic free boundary problems. Conference Publications, 2005, 2005 (Special) : 920929. doi: 10.3934/proc.2005.2005.920 
[18] 
Pierangelo Ciurlia. On a general class of free boundary problems for Europeanstyle installment options with continuous payment plan. Communications on Pure & Applied Analysis, 2011, 10 (4) : 12051224. doi: 10.3934/cpaa.2011.10.1205 
[19] 
Ugur G. Abdulla. On the optimal control of the free boundary problems for the second order parabolic equations. II. Convergence of the method of finite differences. Inverse Problems & Imaging, 2016, 10 (4) : 869898. doi: 10.3934/ipi.2016025 
[20] 
Joachim Escher, Christina Lienstromberg. A survey on second order free boundary value problems modelling MEMS with general permittivity profile. Discrete & Continuous Dynamical Systems  S, 2017, 10 (4) : 745771. doi: 10.3934/dcdss.2017038 
2016 Impact Factor: 1.035
Tools
Metrics
Other articles
by authors
[Back to Top]