Multiscale mathematical modelling in biology and medicine

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Volumn 76, Issue 3, 2011, Pages 371-388

  Chaplain, Mark A J ^a  

^a UNIVERSITY OF DUNDEE   (United Kingdom)

Author keywords

cancer; invasion; metastasis; multiscale mathematical modelling

Indexed keywords

BIOLOGICAL DATA; BIOLOGICAL PROCESS; BIOLOGY AND MEDICINE; CANCER; CANCER GROWTH; CAUSES OF DEATH; CLINICAL TREATMENTS; COMPUTATIONAL SIMULATION; CURRENT TRENDS; HUMAN BODIES; INVASION; LONG-TERM GOALS; MATHEMATICAL MODELLING; METASTASIS; MULTISCALES; PARAMETERIZED; QUANTITATIVE PREDICTIVE MODELS; SUB-CELLULAR; TEMPORAL SCALE; WORLD HEALTH ORGANIZATION;

BIOLOGICAL ORGANS; CURING; DISEASES; GENES; PATIENT TREATMENT; TISSUE;

MATHEMATICAL MODELS;

EID: 79957955371     PISSN: 02724960     EISSN: 14643634     Source Type: Journal    
DOI: 10.1093/imamat/hxr025     Document Type: Article

References (25)

1. ALBER, M. S., KISKOWSKI, M. A., GLAZIER J. A. & JIANG, Y. (2002) On cellular automaton approaches to modeling biological cells. Mathematical Systems Theory in Biology, Communication, and Finance (J. Rosenthal & D. S. Gilliam eds). New York: Springer, pp. 1-40.
2. ANDASARI, V., GERISCH, A., LOLAS, G., SOUTH, A. P. & CHAPLAIN, M. A. J. (2011) Mathematical modeling of cancer cell invasion of tissue: Biological insight from mathematical analysis and computational simulation. J. Math. Biol., doi: 10.1007/s00285-010-0369-1.
3. ANDERSON, A. R. A. (2005) A hybrid mathematical model of solid tumour invasion: The importance of cell adhesion. Math. Med. Biol., 22, 163-186. (Pubitemid 41511340)
4. ANDERSON, A. R. A., CHAPLAIN, M. A. J. & REJNIAK, K. A. (eds) (2007) Single-Cell-Based Models in Biology and Medicine. Basel: Birkhäuser.
5. ARAUJO, R. P. & MCELWAIN, D. L. (2004) A history of the study of solid tumour growth: The contribution of mathematical models. Bull. Math. Biol., 66, 1039-1091. (Pubitemid 39033599)
6. ARMSTRONG, N. J., PAINTER, K. J. & SHERRATT, J. A. (2006) A continuum approach to modelling cell-cell adhesion. J. Theor. Biol., 243, 98-113. (Pubitemid 44465967)
7. BLOCK, M., SCHOELL, E. & DRASDO, D. (2007) Classifying the growth kinetics and surface dynamics in growing cell populations. Phys. Rev. Lett., 99, 248101.
8. BYRNE, H. M. & CHAPLAIN, M. A. J. (1996) Modelling the role of cell-cell adhesion in the growth and development of carcinomas. Math. Comp. Modelling, 24, 1-17. (Pubitemid 27118822)
9. BYRNE, H. M. & CHAPLAIN, M. A. J. (1997) Free boundary value problems associated with the growth and development of multicellular spheroids. Euro. J. Appl. Math., 8, 639-658.
10. CHAPLAIN, M. A. J., GRAZIANO, L. & PREZIOSI, L. (2006) Mathematical modelling of the loss of tissue compression responsiveness and its role in solid tumour development. Math. Med. Biol., 23, 197-229. (Pubitemid 44592715)
11. CHAPLAIN, M. A. J., LACHOWICZ, M., SZYMAŃSKA, Z. & WRZOSEK, D. (2011) Mathematical modelling of cancer invasion: The importance of cell-cell adhesion and cell-matrix adhesion. Math. Mod. Meth. Appl. Sci., 21, 1-25.
12. DRASDO, D. (2003) On selected individual-based approaches to the dynamics of multicellular systems. Multiscale Modeling. (W. Alt, M. Griebel, & J. Lenz eds). Basel: Birkhäuser, 169-203.
13. DRASDO, D. (2005) Coarse graining in simulated cell populations. Adv. Complex Syst., 8, 319-363. (Pubitemid 41811002)
14. DRASDO, D. & HOEHME, S. (2005) A single-cell based model to tumor growth in-vitro: Monolayers and spheroids. Phys. Biol., 2, 133-147. (Pubitemid 41483079)
15. DRASDO, D., HOEHME, S. & BLOCK, M. (2007) On the role of physics in the growth and pattern formation of multi-cellular systems: What can we learn from individual-cell based models? J. Stat. Phys., 128, 287-345.
16. GALLE, J., LOEFFER, M. & DRASDO, D. (2005) Modelling the effect of deregulated proliferation and apoptosis on the growth dynamics of epithelial cell populations in vitro. Biophys. J., 88, 62-75. (Pubitemid 40070658)
17. GERISCH, A. & CHAPLAIN, M. A. J. (2008) Mathematical modelling of cancer cell invasion of tissue: Local and non-local models and the effect of adhesion. J. Theor. Biol., 250, 684-704.
18. HARDY, R. G., MELTZER, S. J. & JANKOWSKY, J. A. (2000) ABC of colorectal cancer: Molecular basis of risk factors. Clin. Rev., 321, 886-889.
19. MOREIRA, J. & DEUTSCH, A. (2002) Cellular automata models of tumour development-a critical review. Adv. Complex Syst., 5, 247-267.
20. NATKE, I. S. (2004) The adenomatous, polyposis coli protein: The achilles heel of the gut epithelium, Annu. Rev. Cell Dev. Biol., 20, 337-366.
21. RAMIS-CONDE, I., CHAPLAIN, M. A. J. & ANDERSON, A. R. A. (2008a) Mathematical modelling of cancer cell invasion of tissue. Math. Comp. Modelling, 47, 533-545. (Pubitemid 351199978)
22. RAMIS-CONDE I., CHAPLAIN, M. A. J., ANDERSON, A. R. A. & DRASDO, D. (2009) Multi-scale modelling of cancer cell intravasation: The role of cadherins in metastasis. Phys. Biol., 6, 016008.
23. RAMIS-CONDE, I., DRASDO, D., ANDERSON, A. R. A. & CHAPLAIN, M. A. J. (2008b) Modeling the influence of the E-cadherin-beta-catenin pathway in cancer cell invasion: A multiscale approach. Biophys. J., 95, 155-165.
24. SCHALLER, G. & MEYER-HERMANN, M. (2005) Multicellular tumor spheroid in an off-lattice Voronoi-Delaunay cell model. Phys. Rev. E, 71, 051910-1-051910-16.
25. STEVENS, A. (2000) The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many particles systems. SIAM J. Appl. Math., 61, 183-212. (Pubitemid 32286522)