메뉴 건너뛰기




Volumn 45, Issue 5-6, 2007, Pages 564-578

Mathematical tools of the kinetic theory of active particles with some reasoning on the modelling progression and heterogeneity

Author keywords

Active particles; Biology; Kinetic theory; Living systems; Nonlinearity

Indexed keywords

BIOLOGY; COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; CONTROL NONLINEARITIES; KINETIC THEORY; MATHEMATICAL MODELS;

EID: 33751401909     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2006.07.005     Document Type: Article
Times cited : (23)

References (70)
  • 2
    • 0026932946 scopus 로고
    • On the distribution of dominance in a population of interacting anonymous organisms
    • Jager E., and Segel L. On the distribution of dominance in a population of interacting anonymous organisms. SIAM J. Appl. Math. 52 5 (1992) 1442-1468
    • (1992) SIAM J. Appl. Math. , vol.52 , Issue.5 , pp. 1442-1468
    • Jager, E.1    Segel, L.2
  • 3
    • 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. Modelling 20 1 (1994) 107-122
    • (1994) Math. Comput. Modelling , vol.20 , Issue.1 , pp. 107-122
    • Bellomo, N.1    Forni, G.2
  • 4
    • 2542432804 scopus 로고    scopus 로고
    • Mathematical Topics on the modelling of Multicellular Systems in the competition between Tumor and Immune cells
    • Bellomo N., Bellouquid A., and Delitala M. Mathematical Topics on the modelling of Multicellular Systems in the competition between Tumor and Immune cells. Math. Models Methods Appl. Sci. 14 11 (2004) 1683-1733
    • (2004) Math. Models Methods Appl. Sci. , vol.14 , Issue.11 , pp. 1683-1733
    • Bellomo, N.1    Bellouquid, A.2    Delitala, M.3
  • 6
    • 32044444445 scopus 로고    scopus 로고
    • Kinetic modelling and electoral competition
    • Lo Schiavo M. Kinetic modelling and electoral competition. Math. Comput. Modeling 42 13 (2005) 1463-1486
    • (2005) Math. Comput. Modeling , vol.42 , Issue.13 , pp. 1463-1486
    • Lo Schiavo, M.1
  • 7
    • 33748085721 scopus 로고    scopus 로고
    • A dynamical model for electoral competition
    • Lo Schiavo M. A dynamical model for electoral competition. Math. Comput. Modeling 43 11-12 (2006) 1288-1309
    • (2006) Math. Comput. Modeling , vol.43 , Issue.11-12 , pp. 1288-1309
    • Lo Schiavo, M.1
  • 8
    • 23244450458 scopus 로고    scopus 로고
    • A second step towards mathematical models in psychology: a stochastic description of human feelings
    • Carbonaro B., and Giordano C. A second step towards mathematical models in psychology: a stochastic description of human feelings. Math. Comput. Modelling 41 4-5 (2005) 587-614
    • (2005) Math. Comput. Modelling , vol.41 , Issue.4-5 , pp. 587-614
    • Carbonaro, B.1    Giordano, C.2
  • 9
    • 33645664533 scopus 로고    scopus 로고
    • On the modelling of complex sociopsychological systems with some reasoning about Kate, Jules, and Jim
    • Article ID 86816
    • Bellomo N., and Carbonaro B. On the modelling of complex sociopsychological systems with some reasoning about Kate, Jules, and Jim. Differ. Equ. Nonlinear Mech. (2006) 1-26 Article ID 86816
    • (2006) Differ. Equ. Nonlinear Mech. , pp. 1-26
    • Bellomo, N.1    Carbonaro, B.2
  • 11
    • 0348142119 scopus 로고    scopus 로고
    • Nonlinear models of traffic flow. New frameworks of mathematical kinetic theory
    • Delitala M. Nonlinear models of traffic flow. New frameworks of mathematical kinetic theory. CR Mécanique 331 12 (2003) 817-822
    • (2003) CR Mécanique , vol.331 , Issue.12 , pp. 817-822
    • Delitala, M.1
  • 12
    • 6044260170 scopus 로고    scopus 로고
    • Modelling living fluids with the subdivision in terms of probability distributions
    • Willander M., Mamontov E., and Chiragwandi Z. Modelling living fluids with the subdivision in terms of probability distributions. Math. Models Methods Appl. Sci. 14 10 (2004) 1495-1520
    • (2004) Math. Models Methods Appl. Sci. , vol.14 , Issue.10 , pp. 1495-1520
    • Willander, M.1    Mamontov, E.2    Chiragwandi, Z.3
  • 14
    • 2142694481 scopus 로고    scopus 로고
    • Mathematical tools for kinetic equations
    • Perthame B. Mathematical tools for kinetic equations. Bull. Amer. Math. Soc. 41 2 (2004) 205-244
    • (2004) Bull. Amer. Math. Soc. , vol.41 , Issue.2 , pp. 205-244
    • Perthame, B.1
  • 15
    • 0004001984 scopus 로고
    • Springer, Berlin
    • Gatignol R. Théorie Cinétique d'un Gaz à Répartition Discréte des Vitèsses. Springer Lecture Notes in Physics vol. 36 (1975), Springer, Berlin
    • (1975) Springer Lecture Notes in Physics , vol.36
    • Gatignol, R.1
  • 17
    • 2542462118 scopus 로고    scopus 로고
    • Mathematical topics on the modelling of complex multicellular systems and tumor immune system competition
    • Bellomo N., De Angelis E., and Preziosi L. Mathematical topics on the modelling of complex multicellular systems and tumor immune system competition. 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
  • 19
    • 0036000662 scopus 로고    scopus 로고
    • Generalized kinetic (Boltzmann) models: Mathematical structures and applications
    • Arlotti L., Bellomo N., and De Angelis E. Generalized kinetic (Boltzmann) models: Mathematical structures and applications. Math. Models Methods Appl. Sci. 12 4 (2002) 567-591
    • (2002) Math. Models Methods Appl. Sci. , vol.12 , Issue.4 , pp. 567-591
    • Arlotti, L.1    Bellomo, N.2    De Angelis, E.3
  • 20
    • 2342452566 scopus 로고    scopus 로고
    • From the mathematical kinetic theory to modelling complex systems in applied sciences
    • Bellomo N. From the mathematical kinetic theory to modelling complex systems in applied sciences. Internat. J. Modern Phys. B 18 4-5 (2004) 487-500
    • (2004) Internat. J. Modern Phys. B , vol.18 , Issue.4-5 , pp. 487-500
    • Bellomo, N.1
  • 21
    • 33646148037 scopus 로고    scopus 로고
    • Modelling complex systems in applied sciences: Methods and tools of the mathematical kinetic theory for active particles
    • De Angelis E., and Delitala M. Modelling complex systems in applied sciences: Methods and tools of the mathematical kinetic theory for active particles. Math. Comput. Modelling 43 11-12 (2006) 1310-1328
    • (2006) Math. Comput. Modelling , vol.43 , Issue.11-12 , pp. 1310-1328
    • De Angelis, E.1    Delitala, M.2
  • 22
    • 27644478289 scopus 로고    scopus 로고
    • Mathematical models and tools of kinetic theory towards modelling complex biological systems
    • Bellouquid A., and Delitala M. Mathematical models and tools of kinetic theory towards modelling complex biological systems. Math. Models Methods Appl. Sci. 15 11 (2005) 1639-1666
    • (2005) Math. Models Methods Appl. Sci. , vol.15 , Issue.11 , pp. 1639-1666
    • Bellouquid, A.1    Delitala, M.2
  • 26
    • 0842288340 scopus 로고    scopus 로고
    • Evolutionary dynamics of biological games
    • Novak M.A., and Sigmund K. Evolutionary dynamics of biological games. Science 303 (2004) 793-799
    • (2004) Science , vol.303 , pp. 793-799
    • Novak, M.A.1    Sigmund, K.2
  • 27
    • 0033595250 scopus 로고    scopus 로고
    • On the origin of species by sympathic speciation
    • Dieckmann U., and Doebeli M. On the origin of species by sympathic speciation. Nature 400 (2004) 354-367
    • (2004) Nature , vol.400 , pp. 354-367
    • Dieckmann, U.1    Doebeli, M.2
  • 28
    • 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 1 (2000) 183-212
    • (2000) SIAM J. Appl. Math. , vol.61 , Issue.1 , pp. 183-212
    • Stevens, A.1
  • 29
    • 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 4 (2002) 1222-1250
    • (2002) SIAM J. Appl. Math. , vol.62 , Issue.4 , pp. 1222-1250
    • Othmer, H.G.1    Hillen, T.2
  • 31
    • 1042302643 scopus 로고    scopus 로고
    • From a class of kinetic models to macroscopic equations for multicellular systems in biology
    • Bellomo N., and Bellouquid A. From a class of kinetic models to macroscopic equations for multicellular systems in biology. Discrete Contin. Dyn. Syst. B 4 1 (2004) 59-80
    • (2004) Discrete Contin. Dyn. Syst. B , vol.4 , Issue.1 , pp. 59-80
    • Bellomo, N.1    Bellouquid, A.2
  • 32
    • 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. Internat. J. Nonlinear Mech. 41 2 (2006) 281-293
    • (2006) Internat. J. Nonlinear Mech. , vol.41 , Issue.2 , pp. 281-293
    • Bellomo, N.1    Bellouquid, A.2
  • 33
    • 33751431816 scopus 로고    scopus 로고
    • N. Bellomo, A. Bellouquid, M.A. Herrero, From microscopic to macroscopic description of multicellular systems and biological growing tissues, Comput. Math. Appl. (2006) (in press)
  • 34
    • 8744228120 scopus 로고    scopus 로고
    • Analysis of a new model for tumor-immune system including long time scale effects
    • Derbel L. Analysis of a new model for tumor-immune system including long time scale effects. Math. Models Methods Appl. Sci. 14 11 (2004) 1657-1681
    • (2004) Math. Models Methods Appl. Sci. , vol.14 , Issue.11 , pp. 1657-1681
    • Derbel, L.1
  • 36
    • 35348813494 scopus 로고    scopus 로고
    • Recent advances in the theory and applications of mass transport
    • Villani C. Recent advances in the theory and applications of mass transport. Contemp. Math. Amer. Math. Soc. 353 (2004) 95-109
    • (2004) Contemp. Math. Amer. Math. Soc. , vol.353 , pp. 95-109
    • Villani, C.1
  • 37
    • 33750101066 scopus 로고    scopus 로고
    • À chaque cancer son scénario aléatoire
    • Gillet È. À chaque cancer son scénario aléatoire. La Récherche 390 (2005) 73
    • (2005) La Récherche , vol.390 , pp. 73
    • Gillet, È.1
  • 38
    • 2942526841 scopus 로고    scopus 로고
    • A new biology for a new century
    • Woese C.R. A new biology for a new century. Microbiol. Mol. Biol. Rev. 68 2 (2004) 173-186
    • (2004) Microbiol. Mol. Biol. Rev. , vol.68 , Issue.2 , pp. 173-186
    • Woese, C.R.1
  • 39
    • 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 2 (2005) 180-186
    • (2005) Curr. Opin. Immunol. , vol.17 , Issue.2 , pp. 180-186
    • Blankenstein, T.1
  • 40
    • 21844440052 scopus 로고    scopus 로고
    • Tuning immune responses: Diversity and adaptation of the immunological synapse
    • Friendl P., de Boer A.T., and Gunzer M. Tuning immune responses: Diversity and adaptation of the immunological synapse. Nat. Rev. Immunol. 5 7 (2005) 532-545
    • (2005) Nat. Rev. Immunol. , vol.5 , Issue.7 , pp. 532-545
    • Friendl, P.1    de Boer, A.T.2    Gunzer, M.3
  • 42
    • 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 2 (2004) 295-317
    • (2004) Z. Angew. Math. Phys. , vol.55 , Issue.2 , pp. 295-317
    • Bellouquid, A.1    Delitala, M.2
  • 43
    • 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. Modelling 41 10 (2005) 1071-1082
    • (2005) Math. Comput. Modelling , vol.41 , Issue.10 , pp. 1071-1082
    • Kolev, M.1
  • 44
    • 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. Modelling 41 10 (2005) 1083-1096
    • (2005) Math. Comput. Modelling , vol.41 , Issue.10 , pp. 1083-1096
    • Kolev, M.1    Kozlowska, E.2    Lachowicz, M.3
  • 45
    • 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. Models Methods Appl. Sci. 13 2 (2003) 187-206
    • (2003) Math. Models Methods Appl. Sci. , vol.13 , Issue.2 , pp. 187-206
    • De Angelis, E.1    Jabin, P.E.2
  • 46
    • 27744605399 scopus 로고    scopus 로고
    • Mathematical models of therapeutical actions related to tumor and immune system competition
    • De Angelis E., and Jabin P.E. Mathematical models of therapeutical actions related to tumor and immune system competition. Math. Methods Appl. Sci. 28 17 (2005) 2061-2083
    • (2005) Math. Methods Appl. Sci. , vol.28 , Issue.17 , pp. 2061-2083
    • De Angelis, E.1    Jabin, P.E.2
  • 47
    • 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. Models Methods Appl. Sci. 15 11 (2005) 1667-1683
    • (2005) Math. Models Methods Appl. Sci. , vol.15 , Issue.11 , pp. 1667-1683
    • Lachowicz, M.1
  • 49
    • 33747088162 scopus 로고    scopus 로고
    • Tumor-immune system interaction and immunotherapy: Modelling the tumor-stimulated proliferation of effectors
    • d'Onofrio A. Tumor-immune system interaction and immunotherapy: Modelling the tumor-stimulated proliferation of effectors. Math. Models Methods Appl. Sci. 16 8 (2006) 1375-1402
    • (2006) Math. Models Methods Appl. Sci. , vol.16 , Issue.8 , pp. 1375-1402
    • d'Onofrio, A.1
  • 50
    • 0025687227 scopus 로고
    • A nonlinear structured population model of tumour growth with quiescence
    • Gyllenberg M., and Webb G. A nonlinear structured population model of tumour growth with quiescence. J. Math. Biol. 28 6 (1990) 671-684
    • (1990) J. Math. Biol. , vol.28 , Issue.6 , pp. 671-684
    • Gyllenberg, M.1    Webb, G.2
  • 51
    • 33750058285 scopus 로고    scopus 로고
    • Existence of solution of the cell division eigenproblem
    • Michel P. Existence of solution of the cell division eigenproblem. Math. Models Methods Appl. Sci. 16 7b (2006) 1125-1154
    • (2006) Math. Models Methods Appl. Sci. , vol.16 , Issue.7 b , pp. 1125-1154
    • Michel, P.1
  • 52
    • 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. and Metast. 16 (1996) 177-208
    • (1996) Invas. and Metast. , vol.16 , pp. 177-208
    • Greller, L.1    Tobin, F.2    Poste, G.3
  • 53
    • 27644463491 scopus 로고    scopus 로고
    • Spatio-temporal heterogeneity arising in a mathematical model of cancer invasion of tissue
    • Chaplain M.A.J., and Lolas G. Spatio-temporal heterogeneity arising in a mathematical model of cancer invasion of tissue. Math. Models Methods Appl. Sci. 15 11 (2005) 1685-1734
    • (2005) Math. Models Methods Appl. Sci. , vol.15 , Issue.11 , pp. 1685-1734
    • Chaplain, M.A.J.1    Lolas, G.2
  • 54
    • 33750078422 scopus 로고    scopus 로고
    • Modelling the response of vascular tumours to chemotherapy: A multiscale approach
    • Byrne H.M., Owen M.R., Alarcon T., Murphy J., and Maini P.K. Modelling the response of vascular tumours to chemotherapy: A multiscale approach. Math. Models Methods Appl. Sci. 16 7b (2006) 1219-1242
    • (2006) Math. Models Methods Appl. Sci. , vol.16 , Issue.7 b , pp. 1219-1242
    • Byrne, H.M.1    Owen, M.R.2    Alarcon, T.3    Murphy, J.4    Maini, P.K.5
  • 56
    • 33750056098 scopus 로고    scopus 로고
    • On the physical law of tumor growth
    • Bru A., and Herrero M.A. On the physical law of tumor growth. Math. Models Methods Appl. Sci. 16 7b (2006) 1199-1218
    • (2006) Math. Models Methods Appl. Sci. , vol.16 , Issue.7 b , pp. 1199-1218
    • Bru, A.1    Herrero, M.A.2
  • 57
    • 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. Models Methods Appl. Sci. 16 7 (2006) 1001-1030
    • (2006) Math. Models Methods Appl. Sci. , vol.16 , Issue.7 , pp. 1001-1030
    • Bellomo, N.1    Forni, G.2
  • 59
    • 27844440786 scopus 로고    scopus 로고
    • Why is mathematical biology so hard?
    • Reed R. Why is mathematical biology so hard?. Notices Amer. Math. Soc. 51 3 (2004) 338-342
    • (2004) Notices Amer. Math. Soc. , vol.51 , Issue.3 , pp. 338-342
    • Reed, R.1
  • 60
    • 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
  • 61
    • 4043181214 scopus 로고    scopus 로고
    • Cancer genes and the pathways they control
    • Vogelstein B., and Kinzler K.W. Cancer genes and the pathways they control. Nat. Med. 10 8 (2004) 789-799
    • (2004) Nat. Med. , vol.10 , Issue.8 , pp. 789-799
    • Vogelstein, B.1    Kinzler, K.W.2
  • 62
    • 7244232531 scopus 로고    scopus 로고
    • From discrete kinetic and stochastic game theory to modeling complex systems in applied sciences
    • Bertotti M.L., and Delitala M. From discrete kinetic and stochastic game theory to modeling complex systems in applied sciences. Math. Models Methods Appl. Sci. 14 8 (2004) 1061-1084
    • (2004) Math. Models Methods Appl. Sci. , vol.14 , Issue.8 , pp. 1061-1084
    • Bertotti, M.L.1    Delitala, M.2
  • 63
    • 33645034895 scopus 로고    scopus 로고
    • On the discrete kinetic theory for active particles. Mathematical tools
    • Chauviere A., and Brazzoli I. On the discrete kinetic theory for active particles. Mathematical tools. Math. Comput. Modelling 43 (2006) 933-944
    • (2006) Math. Comput. Modelling , vol.43 , pp. 933-944
    • Chauviere, A.1    Brazzoli, I.2
  • 64
    • 33744916996 scopus 로고    scopus 로고
    • On the mathematical kinetic theory of active particles with discrete states - The derivation of macroscopic equations
    • Bellomo N., and Bellouquid A. On the mathematical kinetic theory of active particles with discrete states - The derivation of macroscopic equations. Math. Comput. Modelling 44 (2006) 397-404
    • (2006) Math. Comput. Modelling , vol.44 , pp. 397-404
    • Bellomo, N.1    Bellouquid, A.2
  • 65
    • 16644400591 scopus 로고    scopus 로고
    • Mathematical modeling of tumor-induced angiogenesis
    • Mantzaris N.W., Webb S., and Othmer H. Mathematical modeling of tumor-induced angiogenesis. J. Math. Biol. 47 (2004) 111-187
    • (2004) J. Math. Biol. , vol.47 , pp. 111-187
    • Mantzaris, N.W.1    Webb, S.2    Othmer, H.3
  • 66
    • 3843079723 scopus 로고    scopus 로고
    • A history of the study of solid tumor growth: The contribution of mathematical Modelling
    • Araujo R.P., and McElwain D.S.L. A history of the study of solid tumor growth: The contribution of mathematical Modelling. Bull. Math. Biol. 66 (2004) 1039-1091
    • (2004) Bull. Math. Biol. , vol.66 , pp. 1039-1091
    • Araujo, R.P.1    McElwain, D.S.L.2
  • 68
    • 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. Models Methods Appl. Sci. 15 11 (2005) 1735-1778
    • (2005) Math. Models Methods Appl. Sci. , vol.15 , Issue.11 , pp. 1735-1778
    • Bertuzzi, A.1    Fasano, A.2    Gandolfi, A.3
  • 70
    • 84900088439 scopus 로고    scopus 로고
    • Stochastic geometry and related statistical problems in biomedicine
    • Quarteroni A., Formaggia L., and Veneziani A. (Eds), Springer, New York
    • Capasso V., and Micheletti A. Stochastic geometry and related statistical problems in biomedicine. In: Quarteroni A., Formaggia L., and Veneziani A. (Eds). Complex Systems in Biomedicine (2006), Springer, New York 35-70
    • (2006) Complex Systems in Biomedicine , pp. 35-70
    • Capasso, V.1    Micheletti, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.