메뉴 건너뛰기




Volumn 81, Issue , 2008, Pages 485-502

Complex Multicellular Systems and Immune Competition: New Paradigms Looking for a Mathematical Theory

Author keywords

[No Author keywords available]

Indexed keywords

ANIMAL; BIOLOGICAL MODEL; EXPERIMENTAL NEOPLASM; GENETICS; MATHEMATICS; MUTATION; PATHOLOGY; REVIEW; SYSTEMS BIOLOGY;

EID: 36048964200     PISSN: 00702153     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0070-2153(07)81017-9     Document Type: Review
Times cited : (62)

References (53)
  • 1
    • 3042594418 scopus 로고    scopus 로고
    • A mathematical model of the effects of hypoxia on the cell-cycle of normal cancer cells
    • Alarcón T., Byrne H.M., and Maini P.K. A mathematical model of the effects of hypoxia on the cell-cycle of normal cancer cells. J. Theor. Biol. 229 (2004) 395-411
    • (2004) J. Theor. Biol. , vol.229 , pp. 395-411
    • Alarcón, T.1    Byrne, H.M.2    Maini, P.K.3
  • 2
    • 25144494216 scopus 로고    scopus 로고
    • A hybrid mathematical model of solid tumor invasion: The importance of cell adhesion
    • Anderson A.R.A. A hybrid mathematical model of solid tumor invasion: The importance of cell adhesion. Math. Med. Biol. 22 (2005) 163-186
    • (2005) Math. Med. Biol. , vol.22 , pp. 163-186
    • Anderson, A.R.A.1
  • 3
    • 33751217466 scopus 로고    scopus 로고
    • Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment
    • Anderson A.R.A., Weaver A.M., Cummings P.T., and Quaranta V. Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment. Cell 127 (2006) 905-915
    • (2006) Cell , vol.127 , pp. 905-915
    • Anderson, A.R.A.1    Weaver, A.M.2    Cummings, P.T.3    Quaranta, V.4
  • 4
    • 33644846509 scopus 로고    scopus 로고
    • Epigenetic gene silencing in cancer-a mechanism for early oncogenic pathway addition
    • Baylin S.B., and Ohm J.E. Epigenetic gene silencing in cancer-a mechanism for early oncogenic pathway addition. Nat. Rev. Cancer 6 (2006) 107-116
    • (2006) Nat. Rev. Cancer , vol.6 , pp. 107-116
    • Baylin, S.B.1    Ohm, J.E.2
  • 5
    • 0028120597 scopus 로고
    • Dynamics of tumor interaction with the host immune system
    • Bellomo N., and Forni G. Dynamics of tumor interaction with the host immune system. Math. Comput. Model. 20 (1994) 107-122
    • (1994) Math. Comput. Model. , vol.20 , pp. 107-122
    • Bellomo, N.1    Forni, G.2
  • 6
    • 30344453406 scopus 로고    scopus 로고
    • On the onset of nonlinearity for diffusion models of binary mixtures of biological materials by asymptotic analysis
    • Bellomo N., and Bellouquid A. On the onset of nonlinearity for diffusion models of binary mixtures of biological materials by asymptotic analysis. Int. J. Nonlinear Mech. 41 (2006) 281-293
    • (2006) Int. J. Nonlinear Mech. , vol.41 , pp. 281-293
    • Bellomo, N.1    Bellouquid, A.2
  • 7
    • 33746069282 scopus 로고    scopus 로고
    • Looking for new paradigms towards a biological-mathematical theory of complex multicellular systems
    • Bellomo N., and Forni G. Looking for new paradigms towards a biological-mathematical theory of complex multicellular systems. Math. Mod. Meth. Appl. Sci. 16 (2006) 1001-1029
    • (2006) Math. Mod. Meth. Appl. Sci. , vol.16 , pp. 1001-1029
    • Bellomo, N.1    Forni, G.2
  • 9
    • 2542462118 scopus 로고    scopus 로고
    • Multiscale modeling and mathematical problems related to tumor evolution and medical therapy
    • Bellomo N., De Angelis E., and Preziosi L. Multiscale modeling and mathematical problems related to tumor evolution and medical therapy. J. Theor. Med. 5 (2003) 111-136
    • (2003) J. Theor. Med. , vol.5 , pp. 111-136
    • Bellomo, N.1    De Angelis, E.2    Preziosi, L.3
  • 10
    • 18744372738 scopus 로고    scopus 로고
    • A free boundary problem with unilateral constraints describing the evolution of a tumor cord under the influence of cell killing agents
    • Bertuzzi A., Fasano A., and Gandolfi A. A free boundary problem with unilateral constraints describing the evolution of a tumor cord under the influence of cell killing agents. SIAM J. Math. Anal. 36 (2004) 882-915
    • (2004) SIAM J. Math. Anal. , vol.36 , pp. 882-915
    • Bertuzzi, A.1    Fasano, A.2    Gandolfi, A.3
  • 11
    • 27644540984 scopus 로고    scopus 로고
    • A mathematical model for tumor cords incorporating the flow of interstitial fluids
    • Bertuzzi A., Fasano A., and Gandolfi A. A mathematical model for tumor cords incorporating the flow of interstitial fluids. Math. Mod. Meth. Appl. Sci. 15 (2005) 1735-1777
    • (2005) Math. Mod. Meth. Appl. Sci. , vol.15 , pp. 1735-1777
    • Bertuzzi, A.1    Fasano, A.2    Gandolfi, A.3
  • 12
    • 1842765539 scopus 로고    scopus 로고
    • Kinetic (cellular) models of cell progression and competition with the immune system
    • Bellouquid A., and Delitala M. Kinetic (cellular) models of cell progression and competition with the immune system. Z. Angew. Math. Phys. 55 (2004) 295-317
    • (2004) Z. Angew. Math. Phys. , vol.55 , pp. 295-317
    • Bellouquid, A.1    Delitala, M.2
  • 13
    • 27644478289 scopus 로고    scopus 로고
    • Mathematical methods and tools of kinetic theory towards modeling complex biological systems
    • Bellouquid A., and Delitala M. Mathematical methods and tools of kinetic theory towards modeling complex biological systems. Math. Mod. Meth. Appl. Sci. 15 (2005) 1639-1666
    • (2005) Math. Mod. Meth. Appl. Sci. , vol.15 , pp. 1639-1666
    • Bellouquid, A.1    Delitala, M.2
  • 15
    • 14844297325 scopus 로고    scopus 로고
    • The role of tumor stroma in the interaction between tumor and immune system
    • Blankenstein T. The role of tumor stroma in the interaction between tumor and immune system. Curr. Opin. Immunol. 17 (2005) 180-186
    • (2005) Curr. Opin. Immunol. , vol.17 , pp. 180-186
    • Blankenstein, T.1
  • 16
    • 33750102084 scopus 로고    scopus 로고
    • On the discrete kinetic theory for active particles: Modelling the immune competition
    • Brazzoli I., and Chauviere A. On the discrete kinetic theory for active particles: Modelling the immune competition. Comput. Math. Meth. Med. 7 (2006) 142-1158
    • (2006) Comput. Math. Meth. Med. , vol.7 , pp. 142-1158
    • Brazzoli, I.1    Chauviere, A.2
  • 17
    • 33750056098 scopus 로고    scopus 로고
    • From the physical laws of tumor growth to modeling cancer process
    • Bru A., and Herrero M.A. From the physical laws of tumor growth to modeling cancer process. Math. Mod. Meth. Appl. Sci. 16 (2006) 1199-1218
    • (2006) Math. Mod. Meth. Appl. Sci. , vol.16 , pp. 1199-1218
    • Bru, A.1    Herrero, M.A.2
  • 19
    • 33750078422 scopus 로고    scopus 로고
    • Modelling the response of vascular tumors to chemotherapy: A multiscale approach
    • Byrne H.M., Alarcon T.A., Murphy J., and Maini P.K. Modelling the response of vascular tumors to chemotherapy: A multiscale approach. Math. Mod. Meth. Appl. Sci. 16 (2006) 1219-1241
    • (2006) Math. Mod. Meth. Appl. Sci. , vol.16 , pp. 1219-1241
    • Byrne, H.M.1    Alarcon, T.A.2    Murphy, J.3    Maini, P.K.4
  • 21
    • 27644463491 scopus 로고    scopus 로고
    • Spatiotemporal heterogeneity arising in a mathematical model of cancer invasion of tissue
    • Chaplain M.A.J., and Lolas G. Spatiotemporal heterogeneity arising in a mathematical model of cancer invasion of tissue. Math. Mod. Meth. Appl. Sci. 15 (2005) 1685-1734
    • (2005) Math. Mod. Meth. Appl. Sci. , vol.15 , pp. 1685-1734
    • Chaplain, M.A.J.1    Lolas, G.2
  • 22
    • 84979081677 scopus 로고    scopus 로고
    • Hyperbolic free boundary problem modeling tumor growth
    • Cui S., and Friedman A. Hyperbolic free boundary problem modeling tumor growth. Interfaces Free Bound. 5 (2003) 159-181
    • (2003) Interfaces Free Bound. , vol.5 , pp. 159-181
    • Cui, S.1    Friedman, A.2
  • 23
    • 0037296957 scopus 로고    scopus 로고
    • Qualitative analysis of a mean field model of tumor-immune system competition
    • De Angelis E., and Jabin P.E. Qualitative analysis of a mean field model of tumor-immune system competition. Math. Mod. Meth. Appl. Sci. 13 (2003) 187-206
    • (2003) Math. Mod. Meth. Appl. Sci. , vol.13 , pp. 187-206
    • De Angelis, E.1    Jabin, P.E.2
  • 24
    • 27744605399 scopus 로고    scopus 로고
    • Qualitative analysis of a mean field model of tumor-immune system competition
    • De Angelis E., and Jabin P.E. Qualitative analysis of a mean field model of tumor-immune system competition. Math. Meth. Appl. Sci. 28 (2005) 2061-2083
    • (2005) Math. Meth. Appl. Sci. , vol.28 , pp. 2061-2083
    • De Angelis, E.1    Jabin, P.E.2
  • 25
    • 36048959083 scopus 로고    scopus 로고
    • Delitala, M., and Forni, G. (2007). From the mathematical kinetic theory of active particles to modeling genetic mutations and immune competition. Internal Report. Dept. Mathematics, Politecnico, Torino
  • 26
    • 31744436379 scopus 로고    scopus 로고
    • Mixed immunotherapy and chemotherapy of tumors: Modeling, applications, and biological interpretations
    • De Pillis L.G., Gu W., and Radunskaya A.E. Mixed immunotherapy and chemotherapy of tumors: Modeling, applications, and biological interpretations. J. Theor. Biol. 238 (2006) 841-862
    • (2006) J. Theor. Biol. , vol.238 , pp. 841-862
    • De Pillis, L.G.1    Gu, W.2    Radunskaya, A.E.3
  • 27
    • 8744228120 scopus 로고    scopus 로고
    • Analysis of a new model for tumor-immune system competition including long time scale effects
    • Derbel L. Analysis of a new model for tumor-immune system competition including long time scale effects. Math. Mod. Meth. Appl. Sci. 14 (2004) 1657-1681
    • (2004) Math. Mod. Meth. Appl. Sci. , vol.14 , pp. 1657-1681
    • Derbel, L.1
  • 28
    • 33747088162 scopus 로고    scopus 로고
    • Tumor-immune system interaction: Modeling the tumor-stimulated proliferation of effectors and immunotherapy
    • d'Onofrio A. Tumor-immune system interaction: Modeling the tumor-stimulated proliferation of effectors and immunotherapy. Math. Mod. Meth. Appl. Sci. 16 (2006) 1375-1401
    • (2006) Math. Mod. Meth. Appl. Sci. , vol.16 , pp. 1375-1401
    • d'Onofrio, A.1
  • 30
    • 21844440052 scopus 로고    scopus 로고
    • Tuning immune responses: Diversity and adaptation of the immunological synapse
    • Friedl P., de Boer A.T., and Gunzer M. Tuning immune responses: Diversity and adaptation of the immunological synapse. Nat. Rev. Immunol. 5 (2005) 532-545
    • (2005) Nat. Rev. Immunol. , vol.5 , pp. 532-545
    • Friedl, P.1    de Boer, A.T.2    Gunzer, M.3
  • 32
    • 0030417280 scopus 로고    scopus 로고
    • Tumor heterogeneity and progression: Conceptual foundation for modeling
    • Greller L., Tobin F., and Poste G. Tumor heterogeneity and progression: Conceptual foundation for modeling. Invas. Metast. 16 (1996) 177-208
    • (1996) Invas. Metast. , vol.16 , pp. 177-208
    • Greller, L.1    Tobin, F.2    Poste, G.3
  • 33
    • 12144264054 scopus 로고    scopus 로고
    • Analysis of a mathematical model of tumor lymphangiogenesis
    • Friedman A., and Lolas G. Analysis of a mathematical model of tumor lymphangiogenesis. Math. Mod. Meth. Appl. Sci. 15 (2005) 95-107
    • (2005) Math. Mod. Meth. Appl. Sci. , vol.15 , pp. 95-107
    • Friedman, A.1    Lolas, G.2
  • 34
    • 0034614637 scopus 로고    scopus 로고
    • The Hallmarks of cancer
    • Hanahan D., and Weinberg R.A. The Hallmarks of cancer. Cell 100 (2000) 57-70
    • (2000) Cell , vol.100 , pp. 57-70
    • Hanahan, D.1    Weinberg, R.A.2
  • 36
    • 8744237323 scopus 로고    scopus 로고
    • Mathematical modeling of the competition between acquired immunity and cancer
    • Kolev M. Mathematical modeling of the competition between acquired immunity and cancer. Appl. Math. Comput. Sci. 13 (2003) 289-297
    • (2003) Appl. Math. Comput. Sci. , vol.13 , pp. 289-297
    • Kolev, M.1
  • 37
    • 26844512863 scopus 로고    scopus 로고
    • A mathematical model of cellular immune response to leukemia
    • Kolev M. A mathematical model of cellular immune response to leukemia. Math. Comput. Model. 41 (2005) 1071-1082
    • (2005) Math. Comput. Model. , vol.41 , pp. 1071-1082
    • Kolev, M.1
  • 38
    • 26844505021 scopus 로고    scopus 로고
    • Mathematical model of tumor invasion along linear or tubular structures
    • Kolev M., Kozlowska E., and Lachowicz M. Mathematical model of tumor invasion along linear or tubular structures. Math. Comput. Model. 41 (2005) 1083-1096
    • (2005) Math. Comput. Model. , vol.41 , pp. 1083-1096
    • Kolev, M.1    Kozlowska, E.2    Lachowicz, M.3
  • 39
    • 33644931688 scopus 로고    scopus 로고
    • Stochastic modeling of drug resistance in cancer
    • Komarova N. Stochastic modeling of drug resistance in cancer. J. Theor. Biol. 239 (2006) 351-366
    • (2006) J. Theor. Biol. , vol.239 , pp. 351-366
    • Komarova, N.1
  • 40
    • 27644503155 scopus 로고    scopus 로고
    • Micro and meso scales of description corresponding to a model of tissue invasion by solid tumors
    • Lachowicz M. Micro and meso scales of description corresponding to a model of tissue invasion by solid tumors. Math. Mod. Meth. Appl. Sci. 15 (2005) 1667-1684
    • (2005) Math. Mod. Meth. Appl. Sci. , vol.15 , pp. 1667-1684
    • Lachowicz, M.1
  • 42
    • 0034845581 scopus 로고    scopus 로고
    • Mathematical modeling of capillary formation and development in tumor angiogenesis: Penetration into the stroma
    • Levine H., Pamuk S., Sleeman B., and Nilsen-Hamilton S. Mathematical modeling of capillary formation and development in tumor angiogenesis: Penetration into the stroma. Bull. Math. Biol. 63 (2001) 801-863
    • (2001) Bull. Math. Biol. , vol.63 , pp. 801-863
    • Levine, H.1    Pamuk, S.2    Sleeman, B.3    Nilsen-Hamilton, S.4
  • 43
    • 0842309879 scopus 로고    scopus 로고
    • Uses and abuses of mathematics in biology
    • May R.M. Uses and abuses of mathematics in biology. Science 303 (2004) 790-793
    • (2004) Science , vol.303 , pp. 790-793
    • May, R.M.1
  • 45
    • 0842288340 scopus 로고    scopus 로고
    • Evolutionary dynamics of biological games
    • Nowak M.A., and Sigmund K. Evolutionary dynamics of biological games. Science 303 (2004) 793-799
    • (2004) Science , vol.303 , pp. 793-799
    • Nowak, M.A.1    Sigmund, K.2
  • 46
    • 0036376720 scopus 로고    scopus 로고
    • Tumor progression: A brief historical perspective
    • Nowell P.C. Tumor progression: A brief historical perspective. Semin. Cancer Biol. 12 (2002) 261-266
    • (2002) Semin. Cancer Biol. , vol.12 , pp. 261-266
    • Nowell, P.C.1
  • 47
    • 0036553052 scopus 로고    scopus 로고
    • The diffusion limit of transport equations. II. Chemotaxis equations
    • Othmer H.G., and Hillen T. The diffusion limit of transport equations. II. Chemotaxis equations. SIAM J. Appl. Math. 62 (2002) 1222-1250
    • (2002) SIAM J. Appl. Math. , vol.62 , pp. 1222-1250
    • Othmer, H.G.1    Hillen, T.2
  • 48
    • 0031558747 scopus 로고    scopus 로고
    • Pattern formation and spatiotemporal irregularity in a model for macrophage-tumor interactions
    • Owen T., and Sherrat J. Pattern formation and spatiotemporal irregularity in a model for macrophage-tumor interactions. J. Teor. Biol. 189 (2000) 63-80
    • (2000) J. Teor. Biol. , vol.189 , pp. 63-80
    • Owen, T.1    Sherrat, J.2
  • 49
  • 50
    • 27844440786 scopus 로고    scopus 로고
    • Why is mathematical biology so hard?
    • Reed R. Why is mathematical biology so hard?. Not. Am. Math. Soc. 51 (2004) 338-342
    • (2004) Not. Am. Math. Soc. , vol.51 , pp. 338-342
    • Reed, R.1
  • 51
    • 0034455986 scopus 로고    scopus 로고
    • The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particles systems
    • Stevens A. The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particles systems. SIAM J. Appl. Math. 61 (2002) 183-212
    • (2002) SIAM J. Appl. Math. , vol.61 , pp. 183-212
    • Stevens, A.1
  • 52
    • 33846256703 scopus 로고    scopus 로고
    • A parabolic-hyperbolic free boundary problem modeling tumor treatment with virus
    • Tao Y., and Zhang H. A parabolic-hyperbolic free boundary problem modeling tumor treatment with virus. Math. Mod. Meth. Appl. Sci. 17 (2007) 63-80
    • (2007) Math. Mod. Meth. Appl. Sci. , vol.17 , pp. 63-80
    • Tao, Y.1    Zhang, H.2
  • 53
    • 2442670526 scopus 로고    scopus 로고
    • Nonlinear analysis of a model of vascular tumor growth and treatment
    • Tao Y., Yoshida N., and Guo Q. Nonlinear analysis of a model of vascular tumor growth and treatment. Nonlinearity 17 (2004) 867-895
    • (2004) Nonlinearity , vol.17 , pp. 867-895
    • Tao, Y.1    Yoshida, N.2    Guo, Q.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.