메뉴 건너뛰기




Volumn 53, Issue 3-4, 2007, Pages 647-663

From microscopic to macroscopic description of multicellular systems and biological growing tissues

Author keywords

Asymptotic limits; Kinetic theory; Multicellular systems; Nonlinear problems

Indexed keywords

ASYMPTOTIC STABILITY; BIOACTIVITY; BOLTZMANN EQUATION; GROWTH KINETICS; MATHEMATICAL MODELS; TISSUE;

EID: 34248193921     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2006.02.028     Document Type: Article
Times cited : (28)

References (41)
  • 2
    • 0036013702 scopus 로고    scopus 로고
    • A constrained mixture model and remodeling of soft tissues
    • Humphrey J.D., and Rajagopal K.R. A constrained mixture model and remodeling of soft tissues. Math. Models Methods Appl. Sci. 12 (2002) 407-430
    • (2002) Math. Models Methods Appl. Sci. , vol.12 , pp. 407-430
    • Humphrey, J.D.1    Rajagopal, K.R.2
  • 3
    • 0002976258 scopus 로고
    • Asymptotic analysis of nonlinear kinetic equations: The hydrodynamic limit
    • Bellomo N. (Ed), World Scientific, London, Singapore
    • Lachowicz M. Asymptotic analysis of nonlinear kinetic equations: The hydrodynamic limit. In: Bellomo N. (Ed). Lecture Notes on the Mathematical Theory of the Boltzmann Equation (1995), World Scientific, London, Singapore 64-148
    • (1995) Lecture Notes on the Mathematical Theory of the Boltzmann Equation , pp. 64-148
    • Lachowicz, M.1
  • 4
    • 0037288629 scopus 로고    scopus 로고
    • A diffusive limit for nonlinear discrete velocity models
    • Bellouquid A. A diffusive limit for nonlinear discrete velocity models. Math. Models Methods Appl. Sci. 13 (2003) 35-58
    • (2003) Math. Models Methods Appl. Sci. , vol.13 , pp. 35-58
    • Bellouquid, A.1
  • 5
    • 7244231027 scopus 로고    scopus 로고
    • The compressible Euler and acoustic limit for kinetic models
    • Bellouquid A. The compressible Euler and acoustic limit for kinetic models. Math. Models Methods Appl. Sci. 14 (2004) 853-882
    • (2004) Math. Models Methods Appl. Sci. , vol.14 , pp. 853-882
    • Bellouquid, A.1
  • 6
    • 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
  • 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. Models Methods Appl. Sci. 16 (2006) 1001-1029
    • (2006) Math. Models Methods Appl. Sci. , vol.16 , pp. 1001-1029
    • Bellomo, N.1    Forni, G.2
  • 8
    • 27644478289 scopus 로고    scopus 로고
    • Mathematical methods and tools of kinetic theory towards modelling of complex biological systems
    • Bellouquid A., and Delitala M. Mathematical methods and tools of kinetic theory towards modelling of complex biological systems. Math. Models Methods Appl. Sci. 15 (2005) 1639-1666
    • (2005) Math. Models Methods Appl. Sci. , vol.15 , pp. 1639-1666
    • Bellouquid, A.1    Delitala, M.2
  • 9
    • 0003784337 scopus 로고    scopus 로고
    • Alt W., Deutsch A., and Dunn G. (Eds), Birkhäuser, Boston
    • In: Alt W., Deutsch A., and Dunn G. (Eds). Dynamics of Cell and Tissue Motion (1997), Birkhäuser, Boston
    • (1997) Dynamics of Cell and Tissue Motion
  • 10
    • 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. Dynam. Syst. B 4 (2004) 59-80
    • (2004) Discrete Contin. Dynam. Syst. B , vol.4 , pp. 59-80
    • Bellomo, N.1    Bellouquid, A.2
  • 12
    • 0034917420 scopus 로고    scopus 로고
    • The diffusion limit of transport equations derived from velocity jump processes
    • Hillen T., and Othmer H. The diffusion limit of transport equations derived from velocity jump processes. SIAM J. Appl. Math. 61 (2000) 751-775
    • (2000) SIAM J. Appl. Math. , vol.61 , pp. 751-775
    • Hillen, T.1    Othmer, H.2
  • 13
    • 27644503155 scopus 로고    scopus 로고
    • Micro and meso scales of description corresponding to a model of tissue invasion by solid tumours
    • Lachowicz M. Micro and meso scales of description corresponding to a model of tissue invasion by solid tumours. Math. Models Methods Appl. Sci. 15 (2005) 1667-1683
    • (2005) Math. Models Methods Appl. Sci. , vol.15 , pp. 1667-1683
    • Lachowicz, M.1
  • 14
    • 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
  • 15
    • 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 (2006) 281-293
    • (2006) Internat. J. Nonlinear Mech. , vol.41 , pp. 281-293
    • Bellomo, N.1    Bellouquid, A.2
  • 16
    • 1842765539 scopus 로고    scopus 로고
    • Kinetic (cellular) approach to models of cell progression and competition with the immune system
    • Bellouquid A., and Delitala M. Kinetic (cellular) approach to 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
  • 18
    • 0034648765 scopus 로고    scopus 로고
    • Angiogenesis in cancer and other diseases
    • Carmeliet P., and Jain R.K. Angiogenesis in cancer and other diseases. Nature 407 (2000) 249-257
    • (2000) Nature , vol.407 , pp. 249-257
    • Carmeliet, P.1    Jain, R.K.2
  • 19
    • 0034845581 scopus 로고    scopus 로고
    • A mathematical model of capillary formation and development in tumor angiogenesis penetration into stroma
    • Levine H.A., Pamuk S., Sleeman B., and Nilsen-Hamilton M. A mathematical model of capillary formation and development in tumor angiogenesis penetration into stroma. Bull. Math. Biol. 63 (2001) 801-863
    • (2001) Bull. Math. Biol. , vol.63 , pp. 801-863
    • Levine, H.A.1    Pamuk, S.2    Sleeman, B.3    Nilsen-Hamilton, M.4
  • 20
    • 20444384411 scopus 로고    scopus 로고
    • Bone formation: Biological aspects and modeling problems
    • Herrero M.A., and López J.M. Bone formation: Biological aspects and modeling problems. J. Theor. Med. 6 (2005) 41-55
    • (2005) J. Theor. Med. , vol.6 , pp. 41-55
    • Herrero, M.A.1    López, J.M.2
  • 21
    • 20444381883 scopus 로고    scopus 로고
    • Reaction-diffusion systems: A mathematical biology approach
    • Preziosi L. (Ed), Chapman and Hall, London
    • Herrero M.A. Reaction-diffusion systems: A mathematical biology approach. In: Preziosi L. (Ed). Cancer Modelling and Simulation (2003), Chapman and Hall, London 367-420
    • (2003) Cancer Modelling and Simulation , pp. 367-420
    • Herrero, M.A.1
  • 22
    • 0014748565 scopus 로고
    • Initiation of slime mold aggregation viewed as an instability
    • Keller E.F., and Segel L.A. Initiation of slime mold aggregation viewed as an instability. J. Theor. Biol. (1970) 399-415
    • (1970) J. Theor. Biol. , pp. 399-415
    • Keller, E.F.1    Segel, L.A.2
  • 23
    • 0034191918 scopus 로고    scopus 로고
    • Just the right size: cell counting
    • Brown J.M., and Firtel R. Just the right size: cell counting. Dictyostelium TIG 16 (2000) 191-193
    • (2000) Dictyostelium TIG , vol.16 , pp. 191-193
    • Brown, J.M.1    Firtel, R.2
  • 25
    • 0015757937 scopus 로고
    • Chemotaxis, signal relaying and aggregation morphology
    • Nanjundiah V. Chemotaxis, signal relaying and aggregation morphology. J. Theor. Biol. 42 (1973) 63-105
    • (1973) J. Theor. Biol. , vol.42 , pp. 63-105
    • Nanjundiah, V.1
  • 26
    • 0039712703 scopus 로고    scopus 로고
    • Singularity patterns in a chemotaxis model
    • Herrero M.A., and Velázquez J.J.L. Singularity patterns in a chemotaxis model. Math. Ann. 306 (1996) 583-623
    • (1996) Math. Ann. , vol.306 , pp. 583-623
    • Herrero, M.A.1    Velázquez, J.J.L.2
  • 27
    • 0030334089 scopus 로고    scopus 로고
    • Chemotactic collapse for the Keller-Segel model
    • Herrero M.A., and Velázquez J.J.L. Chemotactic collapse for the Keller-Segel model. J. Math. Biol. 35 (1996) 177-196
    • (1996) J. Math. Biol. , vol.35 , pp. 177-196
    • Herrero, M.A.1    Velázquez, J.J.L.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 (2000) 183-212
    • (2000) SIAM J. Appl. Math. , vol.61 , pp. 183-212
    • Stevens, A.1
  • 29
    • 0023746235 scopus 로고
    • Models of dispersal in biological systems
    • Othmer H.G., Dunbar S.R., and Alt W. Models of dispersal in biological systems. J. Math. Biol. 26 (1988) 263-298
    • (1988) J. Math. Biol. , vol.26 , pp. 263-298
    • Othmer, H.G.1    Dunbar, S.R.2    Alt, W.3
  • 31
    • 19944408985 scopus 로고    scopus 로고
    • From individual to collective behaviour in bacterial chemotaxis
    • Erban R., and Othmer H.G. From individual to collective behaviour in bacterial chemotaxis. SIAM J. Appl. Math. 65 (2004) 361-391
    • (2004) SIAM J. Appl. Math. , vol.65 , pp. 361-391
    • Erban, R.1    Othmer, H.G.2
  • 32
    • 21844472976 scopus 로고    scopus 로고
    • From signal transduction to spatial pattern formation in E. Coli: A paradigm for multi-scale modeling in biology
    • Erban R., and Othmer H.G. From signal transduction to spatial pattern formation in E. Coli: A paradigm for multi-scale modeling in biology. SIAM J. Multiscale Modeling 3 (2005) 362-394
    • (2005) SIAM J. Multiscale Modeling , vol.3 , pp. 362-394
    • Erban, R.1    Othmer, H.G.2
  • 33
    • 0030739875 scopus 로고    scopus 로고
    • A model of excitation and adaptation in bacterial chemotaxis
    • Spiro P., Parkinson J.S., and Othmer H.G. A model of excitation and adaptation in bacterial chemotaxis. Proc. Natl. Acad. Sci. USA 94 (1997) 7263-7268
    • (1997) Proc. Natl. Acad. Sci. USA , vol.94 , pp. 7263-7268
    • Spiro, P.1    Parkinson, J.S.2    Othmer, H.G.3
  • 34
    • 0001138912 scopus 로고
    • Drei Vorträge über Diffusion, Brownische Bewegung und Koagulation von Kolloiden
    • Von Smoluchowski M. Drei Vorträge über Diffusion, Brownische Bewegung und Koagulation von Kolloiden. Physik Z. 17 (1916) 557-585
    • (1916) Physik Z. , vol.17 , pp. 557-585
    • Von Smoluchowski, M.1
  • 35
    • 0002121327 scopus 로고
    • Stochastic problems in physics and astronomy
    • Chandrasekhar S. Stochastic problems in physics and astronomy. Rev. Modern Phys. 15 (1943) 1-91
    • (1943) Rev. Modern Phys. , vol.15 , pp. 1-91
    • Chandrasekhar, S.1
  • 37
    • 7244232531 scopus 로고    scopus 로고
    • From discrete kinetic theory and stochastic game theory to modelling complex systems in applied sciences
    • Bertotti M.G., and Delitala M. From discrete kinetic theory and stochastic game theory to modelling complex systems in applied sciences. Math. Models Methods Appl. Sci. 14 (2004) 1061-1084
    • (2004) Math. Models Methods Appl. Sci. , vol.14 , pp. 1061-1084
    • Bertotti, M.G.1    Delitala, M.2
  • 38
    • 27644463491 scopus 로고    scopus 로고
    • Mathematical modelling of cancer cell invasion of tissue: The role of the urokinase plasminogen activation system
    • Chaplain M.A.J., and Lolas G. Mathematical modelling of cancer cell invasion of tissue: The role of the urokinase plasminogen activation system. Math. Models Methods Appl. Sci. 15 (2005) 1685-1734
    • (2005) Math. Models Methods Appl. Sci. , vol.15 , pp. 1685-1734
    • Chaplain, M.A.J.1    Lolas, G.2
  • 39
    • 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. Models Methods Appl. Sci. 15 (2005) 95-107
    • (2005) Math. Models Methods Appl. Sci. , vol.15 , pp. 95-107
    • Friedman, A.1    Lolas, G.2
  • 40
    • 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 (2005) 1735-1778
    • (2005) Math. Models Methods Appl. Sci. , vol.15 , pp. 1735-1778
    • Bertuzzi, A.1    Fasano, A.2    Gandolfi, A.3
  • 41
    • 34248209702 scopus 로고    scopus 로고
    • Mollica F., Preziosi L., and Rajagopal K.R. (Eds), Birkäuser, Boston
    • In: Mollica F., Preziosi L., and Rajagopal K.R. (Eds). Modelling Biological Tissues (2007), Birkäuser, Boston
    • (2007) Modelling Biological Tissues


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.