From microscopic to macroscopic description of multicellular systems and biological growing tissues
| dc.contributor.author | Bellomo, Nicola | |
| dc.contributor.author | Bellouquid, Abdelghani | |
| dc.contributor.author | Herrero, Miguel A. | |
| dc.date.accessioned | 2023-06-20T09:38:31Z | |
| dc.date.available | 2023-06-20T09:38:31Z | |
| dc.date.issued | 2007-02 | |
| dc.description.abstract | This paper presents an asymptotic theory for a large class of Boltzmann-type equations suitable to model the evolution of multicellular systems in biology. The mathematical approach described herein shows how various types of diffusion phenomena, linear and nonlinear, can be obtained in suitable asymptotic limits. Time scaling related to cell movement and biological activity are shown to play a crucial role in determining the macroscopic equations corresponding to each case. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | EU Network Modelling, Mathematical Methods and Computer Simulation of Tumor Growth and Therapy | |
| dc.description.sponsorship | Italian Council of University and Scientific Research | |
| dc.description.sponsorship | Universidad Complutense Acción Especial | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/16308 | |
| dc.identifier.doi | 10.1016/j.camwa.2006.02.028 | |
| dc.identifier.issn | 0898-1221 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0898122107001198 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/50095 | |
| dc.issue.number | 3-4 | |
| dc.journal.title | Computers & Mathematics with Applications | |
| dc.language.iso | eng | |
| dc.page.final | 663 | |
| dc.page.initial | 647 | |
| dc.publisher | Pergamon-Elsevier Science Ltd | |
| dc.relation.projectID | MRTN-CT-2004-503661 | |
| dc.relation.projectID | AE5/06-14364 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 519.87 | |
| dc.subject.cdu | 51-76 | |
| dc.subject.keyword | Kinetic theory | |
| dc.subject.keyword | multicellular systems | |
| dc.subject.keyword | asymptotic limits | |
| dc.subject.keyword | nonlinear problems | |
| dc.subject.keyword | bacterial chemotaxis | |
| dc.subject.keyword | asymptotic analysis | |
| dc.subject.keyword | mathematical-model | |
| dc.subject.keyword | diffusion limit | |
| dc.subject.keyword | kinetic-models | |
| dc.subject.keyword | equations | |
| dc.subject.keyword | aggregation | |
| dc.subject.keyword | dictyostelium | |
| dc.subject.keyword | angiogenesis | |
| dc.subject.keyword | invasion | |
| dc.subject.ucm | Biomatemáticas | |
| dc.subject.ucm | Investigación operativa (Matemáticas) | |
| dc.subject.unesco | 2404 Biomatemáticas | |
| dc.subject.unesco | 1207 Investigación Operativa | |
| dc.title | From microscopic to macroscopic description of multicellular systems and biological growing tissues | |
| dc.type | journal article | |
| dc.volume.number | 53 | |
| dcterms.references | H.L. Hartwell, J.J. Hopfield, S. Leibner, A.W. Murray, From molecular to modular cell biology, Nature 402 (1999) c47–c52. J.D. Humphrey, K.R. Rajagopal, A constrained mixture model and remodeling of soft tissues, Math. Models Methods Appl. Sci. 12 (2002) 407–430. M. Lachowicz, Asymptotic analysis of nonlinear kinetic equations: The hydrodynamic limit, in: N. Bellomo (Ed.), Lecture Notes on the Mathematical Theory of the Boltzmann Equation, World Scientific, London, Singapore, 1995, pp. 64–148. A. Bellouquid, A diffusive limit for nonlinear discrete velocity models, Math. Models Methods Appl. Sci. 13 (2003) 35–58. A. Bellouquid, The compressible Euler and acoustic limit for kinetic models, Math. Models Methods Appl. Sci. 14 (2004) 853–882. N. Bellomo, E. De Angelis, L. Preziosi, Multiscale modeling and mathematical problems related to tumor evolution and medical therapy, J. Theor. Med. 5 (2003) 111–136. N. Bellomo, G. Forni, Looking for new paradigms towards a biological mathematical theory of complex multicellular systems, Math. Models Methods Appl. Sci. 16 (2006) 1001–1029. A. Bellouquid, M. Delitala, Mathematical methods and tools of kinetic theory towards modelling of complex biological systems, Math. Models Methods Appl. Sci. 15 (2005) 1639–1666. W. Alt, A. Deutsch, G. Dunn (Eds.), Dynamics of Cell and Tissue Motion, Birkhäuser, Boston, 1997. N. Bellomo, A. Bellouquid, From a class of kinetic models to macroscopic equations for multicellular systems in biology, Discrete Contin. Dynam. Syst. B 4 (2004) 59–80. C. Hadeler, T. Hillen, F. Lutscher, The Langevin or Kramers approach to biological modelling, Math. Models Methods Appl. Sci. 14 (2004) 1561–1583. T. Hillen, H. Othmer, The diffusion limit of transport equations derived from velocity jump processes, SIAM J. Appl. Math. 61 (2000) 751–775. M. Lachowicz, 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. H.G. Othmer, T. Hillen, The diffusion limit of transport equations II: Chemotaxis equations, SIAM J. Appl. Math. 62 (2002) 1222–1250. N. Bellomo, A. Bellouquid, 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. A. Bellouquid, M. Delitala, Kinetic (cellular) approach to models of cell progression and competition with the immune system, Z. Angew. Math. Phys. 55 (2004) 295–317. G.D. Yancopoulos, S. Davis, N.W. Gale, J.S. Rudge, S.J. Wiegand, J. Holash, Vascular-specific growth factor and blood vessel formation, Nature (2000) 242–248. P. Carmeliet, R.K. Jain, Angiogenesis in cancer and other diseases, Nature 407 (2000) 249–257. H.A. Levine, S. Pamuk, B Sleeman, M. Nilsen-Hamilton, A mathematical model of capillary formation and development in tumor angiogenesis penetration into stroma, Bull. Math. Biol. 63 (2001) 801–863. M.A. Herrero, J.M. López, Bone formation: Biological aspects and modeling problems, J. Theor. Med. 6 (2005) 41–55. M.A. Herrero, Reaction-diffusion systems: A mathematical biology approach, in: L. Preziosi (Ed.), Cancer Modelling and Simulation, Chapman and Hall, London, 2003, pp. 367–420. E.F. Keller, L.A. Segel, Initiation of slime mold aggregation viewed as an instability, J. Theor. Biol. (1970) 399–415. J.M. Brown, R. Firtel, Just the right size: cell counting, Dictyostelium TIG 16 (2000) 191–193. R. Gomer, T. Gao, Y. Tang, D. Kecht, M.A. Titus, Cell motility mediates tissue size regulation in Dictyostelium, J. Muscle Res. Cell Motil. 23 (2002) 809–815. V. Nanjundiah, Chemotaxis, signal relaying and aggregation morphology, J. Theor. Biol. 42 (1973) 63–105. M.A. Herrero, J.J.L. Velázquez, Singularity patterns in a chemotaxis model, Math. Ann. 306 (1996) 583–623. M.A. Herrero, J.J.L. Velázquez, Chemotactic collapse for the Keller-Segel model, J. Math. Biol. 35 (1996) 177–196. A. Stevens, The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particles systems, SIAM J. Appl. Math. 61 (2000) 183–212. H.G. Othmer, S.R. Dunbar, W. Alt, Models of dispersal in biological systems, J. Math. Biol. 26 (1988) 263–298. F. Chalub, Y. Dolak-Struss, P. Markowich, D. Oeltz, C. Schmeiser, A. Soref, Model hierarchies for cell aggregation by chemotaxis, Math. Models Methods Appl. Sci. 16 (2006) 1174–1198. R. Erban, H.G. Othmer, From individual to collective behaviour in bacterial chemotaxis, SIAM J. Appl. Math. 65 (2004) 361–391. R. Erban, H.G. Othmer, 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. P. Spiro, J.S. Parkinson, H.G. Othmer, A model of excitation and adaptation in bacterial chemotaxis, Proc. Natl. Acad. Sci. USA 94 (1997) 7263–7268. M. Von Smoluchowski, Drei Vorträge über Diffusion, Brownische Bewegung und Koagulation von Kolloiden, Physik Z. 17 (1916) 557–585. S. Chandrasekhar, Stochastic problems in physics and astronomy, Rev. Modern Phys. 15 (1943) 1–91. N. Bellomo, M. Lo Schiavo, Lecture Notes on the Generalized Boltzmann Equation, World Scientific, London, Singapore, 2000. M.G. Bertotti, M. Delitala, From discrete kinetic theory and stochastic game theory to modelling complex systems in applied sciences, Math. Models Methods Appl. Sci. 14 (2004) 1061–1084. M.A.J. Chaplain, G. Lolas, 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. A. Friedman, G. Lolas, Analysis of a mathematical model of tumor lymphangiogenesis, Math. Models Methods Appl. Sci. 15 (2005) 95–107. A. Bertuzzi, A. Fasano, A. Gandolfi, A mathematical model for tumor cords incorporating the flow of interstitial fluids, Math. Models Methods Appl. Sci. 15 (2005) 1735–1778. F. Mollica, L. Preziosi, K.R. Rajagopal (Eds.), Modelling Biological Tissues, Birkäuser, Boston, 2007. | |
| dspace.entity.type | Publication |
Download
Original bundle
1 - 1 of 1