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A Cellular Potts model simulating cell migration on and in matrix environments
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), 11111115. 
[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), 1094610951. 
[3] 
J. E. Dick, Stem cell concepts renew cancer research, Blood, 112 (2008), 47934807. 
[4] 
A. Friedman, Cancer models and their mathematical analysis, Tutorials in mathematical biosciences. III, 223246, Lecture Notes in Math., 1872, Springer, Berlin, 2006. 
[5] 
A. Friedman and Y. Tao, Analysis of a model of a virus that replicates selectively in tumor cells, J. Math. Biol., 47 (2003), 391423. 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), e26233. 
[8] 
K. Qu and P. Ortoleva, Understanding stem cell differentiation through selforganization theory, Journal of Theoretical Biology, 250 (2008), 606620. 
[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), 257281. 
[11] 
J. I. Tello, Mathematical analysis of a model of Morphogenesis, Discrete and Continuous Dynamical Systems  Serie A., 25 (2009), 343361. 
[12] 
J. I. Tello, On the existence of solutions of a mathematical model of morphogens, in "Modern Mathematical Tools and Techniques in Capturing Complexity Series: Understanding Complex Systems" (Eds. L. Pardo, N. Balakrishnan and M. A. Gil), Springer 2011. 
show all references
References:
[1] 
M. F. Clarke and M. Fuller, Stem cells and cancer: Two faces of eve, Cell, 124 (2006), 11111115. 
[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), 1094610951. 
[3] 
J. E. Dick, Stem cell concepts renew cancer research, Blood, 112 (2008), 47934807. 
[4] 
A. Friedman, Cancer models and their mathematical analysis, Tutorials in mathematical biosciences. III, 223246, Lecture Notes in Math., 1872, Springer, Berlin, 2006. 
[5] 
A. Friedman and Y. Tao, Analysis of a model of a virus that replicates selectively in tumor cells, J. Math. Biol., 47 (2003), 391423. 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), e26233. 
[8] 
K. Qu and P. Ortoleva, Understanding stem cell differentiation through selforganization theory, Journal of Theoretical Biology, 250 (2008), 606620. 
[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), 257281. 
[11] 
J. I. Tello, Mathematical analysis of a model of Morphogenesis, Discrete and Continuous Dynamical Systems  Serie A., 25 (2009), 343361. 
[12] 
J. I. Tello, On the existence of solutions of a mathematical model of morphogens, in "Modern Mathematical Tools and Techniques in Capturing Complexity Series: Understanding Complex Systems" (Eds. L. Pardo, N. Balakrishnan and M. A. Gil), Springer 2011. 
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