메뉴 건너뛰기




Volumn 71, Issue 5, 2015, Pages 1049-1079

Differentiated cell behavior: a multiscale approach using measure theory

Author keywords

Cell populations; Discrete vs. continuous descriptions; Functional subsystems; Multiscale dynamics

Indexed keywords

ANIMAL; BIOLOGICAL MODEL; BIOPHYSICS; CELL AGGREGATION; CELL DIFFERENTIATION; CELLULAR, SUBCELLULAR AND MOLECULAR BIOLOGICAL PHENOMENA AND FUNCTIONS; CHEMOTAXIS; COMPUTER SIMULATION; HUMAN; MATHEMATICAL PHENOMENA;

EID: 84943456949     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-014-0846-z     Document Type: Article
Times cited : (31)

References (38)
  • 2
    • 0032170064 scopus 로고    scopus 로고
    • Continuous and discrete mathematical models of tumor-induced angiogenesis
    • Anderson ARA, Chaplain MAJ (1998) Continuous and discrete mathematical models of tumor-induced angiogenesis. Bull Math Biol 60(5):857–899
    • (1998) Bull Math Biol , vol.60 , Issue.5 , pp. 857-899
    • Anderson, A.R.A.1    Chaplain, M.A.J.2
  • 4
    • 33751217466 scopus 로고    scopus 로고
    • Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment
    • Anderson ARA, Weaver AM, Cummings PT, Quaranta V (2006) Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment. Cell 127(5):905–915
    • (2006) Cell , vol.127 , Issue.5 , pp. 905-915
    • Anderson, A.R.A.1    Weaver, A.M.2    Cummings, P.T.3    Quaranta, V.4
  • 5
    • 70449515071 scopus 로고    scopus 로고
    • Asymptotic behavior of a system of stochastic particles subject to nonlocal interactions
    • Capasso V, Morale D (2009) Asymptotic behavior of a system of stochastic particles subject to nonlocal interactions. Stoch Anal Appl 27(3):574–603
    • (2009) Stoch Anal Appl , vol.27 , Issue.3 , pp. 574-603
    • Capasso, V.1    Morale, D.2
  • 6
    • 63249119539 scopus 로고    scopus 로고
    • Stochastic modelling of tumour-induced angiogenesis
    • Capasso V, Morale D (2009) Stochastic modelling of tumour-induced angiogenesis. J Math Biol 58(1–2):219–233
    • (2009) J Math Biol , vol.58 , Issue.1-2 , pp. 219-233
    • Capasso, V.1    Morale, D.2
  • 8
    • 0034470377 scopus 로고    scopus 로고
    • Mathematical modeling of angiogenesis
    • Chaplain MAJ (2000) Mathematical modeling of angiogenesis. J Neurol Oncol 50(1–2):37–51
    • (2000) J Neurol Oncol , vol.50 , Issue.1-2 , pp. 37-51
    • Chaplain, M.A.J.1
  • 10
    • 84922947289 scopus 로고    scopus 로고
    • A measure-theoretic model for cell migration and aggregation
    • Colombi A, Scianna M, Preziosi L (2014) A measure-theoretic model for cell migration and aggregation. Math Model Nat Pheno 10(1):32–63
    • (2014) Math Model Nat Pheno , vol.10 , Issue.1 , pp. 32-63
    • Colombi, A.1    Scianna, M.2    Preziosi, L.3
  • 11
    • 79955908614 scopus 로고    scopus 로고
    • Multiscale modeling of granular flows with application to crowd dynamics
    • Cristiani E, Piccoli B, Tosin A (2011) Multiscale modeling of granular flows with application to crowd dynamics. Multiscale Model Simul 9(1):155–182
    • (2011) Multiscale Model Simul , vol.9 , Issue.1 , pp. 155-182
    • Cristiani, E.1    Piccoli, B.2    Tosin, A.3
  • 15
    • 84939883612 scopus 로고    scopus 로고
    • A hybrid mathematical model for self-organizing cell migration in the zebrafish lateral line. J Math Biol
    • Di Costanzo E, Natalini R, Preziosi L (2014) A hybrid mathematical model for self-organizing cell migration in the zebrafish lateral line. J Math Biol. doi:10.1007/s00285-014-0812-9
    • (2014) doi:10.1007/s00285-014-0812-9
    • Di Costanzo, E.1    Natalini, R.2    Preziosi, L.3
  • 16
    • 84885362764 scopus 로고    scopus 로고
    • Measure solutions for non-local interaction PDEs with two species
    • Di Francesco M, Fagioli S (2013) Measure solutions for non-local interaction PDEs with two species. Nonlinearity 26(10):2777
    • (2013) Nonlinearity , vol.26 , Issue.10 , pp. 2777
    • Di Francesco, M.1    Fagioli, S.2
  • 17
    • 29144486760 scopus 로고    scopus 로고
    • Coarse graining in simulated cell populations
    • Drasdo D (2005) Coarse graining in simulated cell populations. Adv Complex Syst 8(2–3):319–363
    • (2005) Adv Complex Syst , vol.8 , Issue.2-3 , pp. 319-363
    • Drasdo, D.1
  • 19
    • 84959485833 scopus 로고    scopus 로고
    • Modeling steps from a benign tumor to an invasive cancer: examples of intrinsically multi-scale problems
    • Chauviere A, Preziosi L, Verdier C, (eds), CRC/Academic Press, London
    • Drasdo D, Jagiella N, Ramis-Conde I, Vignon-Clementel I, Weens W (2009) Modeling steps from a benign tumor to an invasive cancer: examples of intrinsically multi-scale problems. In: Chauviere A, Preziosi L, Verdier C (eds) From single scale-based models to multiscale modeling. CRC/Academic Press, London, pp 379–416
    • (2009) From single scale-based models to multiscale modeling , pp. 379-416
    • Drasdo, D.1    Jagiella, N.2    Ramis-Conde, I.3    Vignon-Clementel, I.4    Weens, W.5
  • 20
    • 77952954625 scopus 로고    scopus 로고
    • Three-dimensional multispecies nonlinear tumor growth-II: tumor invasion and angiogenesis
    • Frieboes HB, Jin F, Chuang YL, Wise SM, Lowengrub JS, Cristini V (2010) Three-dimensional multispecies nonlinear tumor growth-II: tumor invasion and angiogenesis. J Theor Biol 264(4):1254–1278
    • (2010) J Theor Biol , vol.264 , Issue.4 , pp. 1254-1278
    • Frieboes, H.B.1    Jin, F.2    Chuang, Y.L.3    Wise, S.M.4    Lowengrub, J.S.5    Cristini, V.6
  • 21
    • 67649528138 scopus 로고    scopus 로고
    • Collective cell migration in morphogenesis, regeneration and cancer
    • Friedl P, Gilmour D (2009) Collective cell migration in morphogenesis, regeneration and cancer. Nat Rev Mol Cell Biol 10:445–457
    • (2009) Nat Rev Mol Cell Biol , vol.10 , pp. 445-457
    • Friedl, P.1    Gilmour, D.2
  • 22
    • 70350400725 scopus 로고    scopus 로고
    • Mechanisms of collective cell migration at a glance
    • Ilina O, Friedl P (2009) Mechanisms of collective cell migration at a glance. J Cell Sci 122:3203–3208
    • (2009) J Cell Sci , vol.122 , pp. 3203-3208
    • Ilina, O.1    Friedl, P.2
  • 23
    • 84881377835 scopus 로고    scopus 로고
    • A hybrid model of tumor-stromal interactions in breast cancer
    • Kim Y, Othmer HG (2013) A hybrid model of tumor-stromal interactions in breast cancer. Bull Math Biol 75(8):1304–1350
    • (2013) Bull Math Biol , vol.75 , Issue.8 , pp. 1304-1350
    • Kim, Y.1    Othmer, H.G.2
  • 24
    • 35348824187 scopus 로고    scopus 로고
    • A hybrid model for tumor spheroid growth in vitro I: theoretical development and early results
    • Kim Y, Stolarska MA, Othmer HG (2007) A hybrid model for tumor spheroid growth in vitro I: theoretical development and early results. Math Models Methods Appl Sci 17(suppl):1773–1798
    • (2007) Math Models Methods Appl Sci , vol.17 , pp. 1773-1798
    • Kim, Y.1    Stolarska, M.A.2    Othmer, H.G.3
  • 25
    • 13844298300 scopus 로고    scopus 로고
    • An interacting particle system modelling aggregation behavior: from individuals to populations
    • Morale D, Capasso V, Oelschläger K (2005) An interacting particle system modelling aggregation behavior: from individuals to populations. J Math Biol 50(1):49–66
    • (2005) J Math Biol , vol.50 , Issue.1 , pp. 49-66
    • Morale, D.1    Capasso, V.2    Oelschläger, K.3
  • 26
    • 84874873960 scopus 로고    scopus 로고
    • Transport equation with nonlocal velocity in Wasserstein spaces: convergence of numerical schemes
    • Piccoli B, Rossi F (2013) Transport equation with nonlocal velocity in Wasserstein spaces: convergence of numerical schemes. Acta Appl Math 124(1):73–105
    • (2013) Acta Appl Math , vol.124 , Issue.1 , pp. 73-105
    • Piccoli, B.1    Rossi, F.2
  • 27
    • 84891557737 scopus 로고    scopus 로고
    • Generalized Wasserstein distance and its application to transport equations with source
    • Piccoli B, Rossi F (2014) Generalized Wasserstein distance and its application to transport equations with source. Arch Ration Mech Anal 211(1):335–358
    • (2014) Arch Ration Mech Anal , vol.211 , Issue.1 , pp. 335-358
    • Piccoli, B.1    Rossi, F.2
  • 28
    • 68149136534 scopus 로고    scopus 로고
    • Pedestrian flows in bounded domains with obstacles
    • Piccoli B, Tosin A (2009) Pedestrian flows in bounded domains with obstacles. Contin Mech Thermodyn 21(2):85–107
    • (2009) Contin Mech Thermodyn , vol.21 , Issue.2 , pp. 85-107
    • Piccoli, B.1    Tosin, A.2
  • 29
    • 79951811654 scopus 로고    scopus 로고
    • Time-evolving measures and macroscopic modeling of pedestrian flow
    • Piccoli B, Tosin A (2011) Time-evolving measures and macroscopic modeling of pedestrian flow. Arch Ration Mech Anal 199(3):707–738
    • (2011) Arch Ration Mech Anal , vol.199 , Issue.3 , pp. 707-738
    • Piccoli, B.1    Tosin, A.2
  • 30
    • 46749151795 scopus 로고    scopus 로고
    • Modeling the influence of the E-cadherin-$$\beta $$β-catenin pathway in cancer cell invasion: a multiscale approach
    • Ramis-Conde I, Drasdo D, Chaplain MAJ, Anderson ARA (2008) Modeling the influence of the E-cadherin-$$\beta $$β-catenin pathway in cancer cell invasion: a multiscale approach. Biophys J 95(1):155–165
    • (2008) Biophys J , vol.95 , Issue.1 , pp. 155-165
    • Ramis-Conde, I.1    Drasdo, D.2    Chaplain, M.A.J.3    Anderson, A.R.A.4
  • 31
    • 84865676266 scopus 로고    scopus 로고
    • Multiscale developments of the cellular Potts model
    • Scianna M, Preziosi L (2012) Multiscale developments of the cellular Potts model. Multiscale Model Simul 10:342–382
    • (2012) Multiscale Model Simul , vol.10 , pp. 342-382
    • Scianna, M.1    Preziosi, L.2
  • 33
    • 84874745309 scopus 로고    scopus 로고
    • A cellular Potts model simulating cell migration on and in matrix environments
    • Scianna M, Preziosi L, Wolf K (2013) A cellular Potts model simulating cell migration on and in matrix environments. Math Biosci Eng 10(1):235–261
    • (2013) Math Biosci Eng , vol.10 , Issue.1 , pp. 235-261
    • Scianna, M.1    Preziosi, L.2    Wolf, K.3
  • 34
    • 0034455986 scopus 로고    scopus 로고
    • The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particle systems
    • Stevens A (2000) The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particle systems. SIAM J Appl Math 61(1):183–212
    • (2000) SIAM J Appl Math , vol.61 , Issue.1 , pp. 183-212
    • Stevens, A.1
  • 35
    • 69649101260 scopus 로고    scopus 로고
    • Multiscale models of cells and tissue dynamics
    • Stolarska MA, Kim YJ, Othmer H (2009) Multiscale models of cells and tissue dynamics. Phil Trans R Soc A 367(1902):3525–3553
    • (2009) Phil Trans R Soc A , vol.367 , Issue.1902 , pp. 3525-3553
    • Stolarska, M.A.1    Kim, Y.J.2    Othmer, H.3
  • 36
    • 69549121855 scopus 로고    scopus 로고
    • Hybrid mathematical model of glioma progression
    • Tanaka ML, Debinski W, Puri IK (2009) Hybrid mathematical model of glioma progression. Cell Prolif 42(5):637–646
    • (2009) Cell Prolif , vol.42 , Issue.5 , pp. 637-646
    • Tanaka, M.L.1    Debinski, W.2    Puri, I.K.3
  • 37
    • 80053101516 scopus 로고    scopus 로고
    • Existence and approximation of probability measure solutions to models of collective behaviors
    • Tosin A, Frasca P (2011) Existence and approximation of probability measure solutions to models of collective behaviors. Netw Heterog Media 6(3):561–596
    • (2011) Netw Heterog Media , vol.6 , Issue.3 , pp. 561-596
    • Tosin, A.1    Frasca, P.2
  • 38
    • 34547569807 scopus 로고    scopus 로고
    • Multi-step pericellular proteolysis controls the transition from individual to collective cancer cell invasion
    • Wolf K, Wu Y, Liu Y, Geiger J, Tam E (2007) Multi-step pericellular proteolysis controls the transition from individual to collective cancer cell invasion. Nat Cell Biol 9:893–904
    • (2007) Nat Cell Biol , vol.9 , pp. 893-904
    • Wolf, K.1    Wu, Y.2    Liu, Y.3    Geiger, J.4    Tam, E.5


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.