Delaunay-Object-Dynamics: Cell Mechanics with a 3D Kinetic and Dynamic Weighted Delaunay-Triangulation

Current Topics in Developmental Biology

Volumn 81, Issue , 2008, Pages 373-399

  Meyer Hermann, Michael ^a  

^a FRANKFURT INSTITUTE FOR ADVANCED STUDIES   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ANIMAL; BIOLOGICAL MODEL; BIOMECHANICS; CELL FUNCTION; CELL MOTION; EXPERIMENTAL NEOPLASM; GROWTH, DEVELOPMENT AND AGING; LYMPHOID TISSUE; MORPHOGENESIS; PATHOLOGY; PATHOPHYSIOLOGY; REVIEW; SYSTEMS BIOLOGY;

ANIMALS; BIOMECHANICS; CELL MOVEMENT; CELL PHYSIOLOGY; LYMPHOID TISSUE; MODELS, BIOLOGICAL; MORPHOGENESIS; NEOPLASMS, EXPERIMENTAL; SYSTEMS BIOLOGY;

EID: 36048998460     PISSN: 00702153     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0070-2153(07)81013-1     Document Type: Review

References (62)

1. Aurenhammer F., and Imai H. Geometric relations among Voronoi diagrams. Geometriae Dedicata 27 (1988) 65-75
2. Bajenoff M., Egen J.G., Koo L.Y., Laugier J.P., Brau F., Glaichenhaus N., and Germain R.N. Stromal cell networks regulate lymphocyte entry, migration, and territoriality in lymph nodes. Immunity 25 (2006) 989-1001
3. Bettelheim E., Agam O., and Shnerb N.M. "Quantum phase transitions" in classical nonequilibrium processes. Physica E 9 (2001) 600-608
4. Beyer, T. (2007). Spatio-temporal dynamics of primary lymphoid follicles during organogenesis and lymphoneogenesis. Ph.D. thesis
5. Beyer T., and Meyer-Hermann M. The treatment of non-flippable configurations in three-dimensional regular triangulations. WSEAS Trans. Syst. 5 (2006) 1100-1107
6. Beyer, T., and Meyer-Hermann, M. (2007a). Modeling emergent tissue organization involving high-speed migrating cells in a flow equilibrium. Phys. Rev. E, http://arXiv.org/, q-bio.TO/0611057 (in press)
7. Beyer, T., and Meyer-Hermann, M. (2007b). Mechanisms of organogenesis of primary lymphoid follicles. http://arXiv.org/, q-bio.TO/0611058
8. Beyer T., Meyer-Hermann M., and Soff G. A possible role of chemotaxis in germinal center formation. Int. Immunol. 14 (2002) 1369-1381
9. Beyer T., Schaller G., Deutsch A., and Meyer-Hermann M. Parallel dynamic and kinetic regular triangulation in three dimensions. Comp. Phys. Commun. 172 (2005) 86-108
10. Boissonnat J.-D., and Teillaud M. On the randomized construction of the Delaunay tree. Theor. Comput. Sci. 112 (1993) 339-354
11. Bowyer A. Computing Dirichlet tessellations. Comput. J. 24 (1981) 162-166
12. Brilliantov N.N., and Poeschel T. Collision of adhesive viscoelastic particles. In: Hinrichsen H., and Wolf D.E. (Eds). The Physics of Granular Media (2004), Wiley-VCH, Berlin
13. Chu Y.S., Dufour S., Thiery J.P., Perez E., and Pincet F. Johnson-Kendall-Roberts theory applied to living cells. Phys. Rev. Lett. 94 (2005) 028102
14. Cignoni, P., Montani, C., Perego, R., and Scopigno, R. (1993). Parallel 3D Delaunay-triangulation. In "Eurographics 1993." (R. J. Hubbold and R. Juan), Vol. 12. Blackwell Publishers, Cambridge, MA, pp. C129-C142
15. Cupedo T., Jansen W., Kraal G., and Mebius R.E. Induction of secondary and tertiary lymphoid structures in the skin. Immunity 21 (2004) 655-667
16. Cyster J.G. Chemokines, sphingosine-1-phosphate, and cell migration in secondary lymphoid tissue. Annu. Rev. Immunol. 23 (2005) 127-159
17. Dallon J.C., and Othmer H.G. How cellular movement determines the collective force generated by the Dictyostelium discoideum slug. J. Theor. Biol. 231 (2004) 203-222
18. Deutsch A., and Dormann S. Cellular Automaton Modeling of Biological Pattern Formation (2004), Birkhäuser, Basel
19. Devillers, O., Pion, S., and Teillaud, M. (2001). Walking in a triangulation. In: Proceedings of the 17th Annual ACM Symposium on Computational Geometry, pp. 106-14
20. Dormann S., and Deutsch A. Modeling of self-organized avascular tumor growth with a hybrid cellular automaton. In Silico Biol. 2 (2002) 393-406
21. Drasdo D. On selected individual-based approaches to the dynamics in multicellular systems. In: Alt W., Chaplain M., Griebel M., and Lenz J. (Eds). Polymer and Cell Dynamics: Multiscale Modeling and Numerical Simulations (2003), Birkhäuser 169-204
22. Drasdo D., Kree R., and McCaskill J.S. Monte Carlo approach to tissue-cell populations. Phys. Rev. E 52 (1995) 6635-6657
23. Edelsbrunner H., and Shah N.R. Incremental topological flipping works for regular triangulations. Algorithmica 15 (1996) 223-241
24. Evans E., (1995). Physical actions in biological adhesion. In "Handbook of Biological Physics." (R. Lipowsky and E. Sackmann), Vol. I. Elsevier, Amsterdam, pp. 723-753
25. Ferrez, J.-A. (2001). Dynamic triangulations for efficient 3d simulations of granular materials. EPFL thesis
26. Folkman J., and Hochberg M. Self-regulation of growth in three dimensions. J. Exp. Med. 138 (1973) 745-753
27. Freyer J.P., and Sutherland R.M. Proliferative and clonogenic heterogeneity of cells from EMT6/Ro multicellular spheroids induced by the glucose and oxygen supply. Cancer Res. 46 (1986) 3504-3512
28. Fu Y.X., Molina H., Matsumoto M., Huang G., Min J., and Chaplin D.D. Lymphotoxin-alpha (LTalpha) supports development of splenic follicular structure that is required for IgG responses. J. Exp. Med. 185 (1997) 2111-2120
29. Galle J., Loeffler M., and Drasdo D. Modeling the effect of deregulated proliferation and apoptosis on the growth dynamics of epithelial cell populations in vitro. Biophys. J. 88 (2005) 62-75
30. Goodman J., and O'Rourke J. Handbook of Discrete and Computational Geometry (1997), CRC Press, Boca Raton, FL
31. Graner F., and Glazier J.A. Simulation of biological cell sorting using a two-dimensional extended Potts model. Phys. Rev. Lett. 69 (1992) 2013-2016
32. Gunzer M., Weishaupt C., Hillmer A., Basoglu Y., Friedl P., Dittmar K.E., Kolanus W., Varga G., and Grabbe S. A spectrum of biophysical interaction modes between T cells and different antigen-presenting cells during priming in 3-D collagen and in vivo. Blood 104 (2004) 2801-2809
33. Halleraker M., Press C.M., and Landsverk T. Development and cell phenotypes in primary follicles of foetal sheep lymph nodes. Cell. Tissue Res. 275 (1994) 51-62
34. Hertz H. Über die Berührung fester elastischer Körper. J. Reine Angew. Math. 92 (1882) 156-171
35. Howard J. Mechanics of Motor Proteins and the Cytoskeleton (2001), Sinauer Associates Inc
36. Jiang Y., Pjesivac-Grbovic J., Cantrell C., and Freyer J.P. A multiscale model for avascular tumor growth. Biophys. J. 89 (2005) 3884-3894
37. Johnson K.L., Kendall K., and Roberts A.D. Surface energy and the contact of elastic solids. Proc. R. Soc. London Ser. A 324 (1971) 301-313
38. Lewis W. Locomotion of lymphocytes. Bull. Johns Hopkins Hosp. 49 (1931) 29-36
39. Lindenmayer A., and Rozenberg G. Automata, Languages, Development (1976), North-Holland, Amsterdam
40. MacLennan I.C.M. Germinal Centers. Annu. Rev. Immunol. 12 (1994) 117-139
41. Maree A.F., and Hogeweg P. How amoeboids self-organize into a fruiting body: Multicellular coordination in Dictyostelium discoideum. Proc. Natl. Acad. Sci. USA 98 (2001) 3879-3883
42. Meinhardt H. Models of Biological Pattern Formation (1982), Academic Press
43. Merks R.M., Brodsky S.V., Goligorksy M.S., Newman S.A., and Glazier J.A. Cell elongation is key to in silico replication of in vitro vasculogenesis and subsequent remodeling. Dev. Biol. 289 (2006) 44-54
44. Meyer-Hermann M. A mathematical model for the germinal center morphology and affinity maturation. J. Theor. Biol. 216 (2002) 273-300
45. Meyer-Hermann M., and Maini P.K. Interpreting two-photon imaging data of lymphocyte motility. Phys. Rev. E 71 (2005) 061912-1-12
46. Moser B., Wolf M., Walz A., and Loetscher P. Chemokines: Multiple levels of leukocyte migration control. Trends Immunol. 25 (2004) 75-84
47. Muecke E. A robust implementation for three-dimensional Delaunay-triangulations. Int. J. Comput. Geom. Appl. 2 (1998) 255-276
48. Murray J.D. Mathematical Biology. 2 ed (1993), Springer-Verlag, New York
49. Newman T.J. Modeling multicellular systems using subcellular elements. Math. Biosci. Eng. 2 (2005) 611-622
50. Palsson E. A three-dimensional model of cell movement in multicellular systems. Future Gener. Comput. Syst. 17 (2001) 835-852
51. Ribba B., Colin T., and Schnell S. A multiscale mathematical model of cancer, and its use in analyzing irradiation therapies. Theor. Biol. Med. Mod. 3 (2006) 7
52. Rumfelt L.L., McKinney E.C., Taylor E., and Flajnik M.F. The development of primary and secondary lymphoid tissues in the nurse shark Ginglymostoma cirratum: B-cell zones precede dendritic cell immigration and T-cell zone formation during ontogeny of the spleen. Scand. J. Immunol. 56 (2002) 130-148
53. Schaller, G. (2005). On selected numerical approaches to cellular tissue. Ph.D. thesis
54. Schaller G., and Meyer-Hermann M. Kinetic and dynamic Delaunay tetrahedralizations in three dimensions. Comput. Phys. Commun. 162 (2004) 9-23
55. Schaller G., and Meyer-Hermann M. Multicellular tumor spheroid in an off-lattice Voronoi/Delaunay cell model. Phys. Rev. E 71 (2005) 051910-1-16
56. Schaller G., and Meyer-Hermann M. A modeling approach towards an epidermal homoeostasis control. J. Theor. Biol. 247 (2007) 554-573
57. Schnell S., Grima R., and Maini P.K. Multiscale modeling in biology. Am. Sci. 95 (2007) 134-142
58. Shnerb N.M., Louzon Y., Bettelheim E., and Solomon S. The importance of being discrete: Life always wins on the surface. Proc. Natl. Acad. Sci. USA 97 (2000) 10322-10324
59. Tumanov A.V., Grivennikov S.I., Shakhov A.N., Rybtsov S.A., Koroleva E.P., Takeda J., Nedospasov S.A., and Kuprash D.V. Dissecting the role of lymphotoxin in lymphoid organs by conditional targeting. Immunol. Rev. 195 (2003) 106-116
60. Watson D.F. Computing the n-dimensional Delaunay-tessellation with application to Voronoi polytopes. Comput. J. 24 (1981) 167-172
61. Wolf K., Muller R., Borgmann S., Brocker E.B., and Friedl P. Amoeboid shape change and contact guidance: T-lymphocyte crawling through fibrillar collagen is independent of matrix remodeling by MMPs and other proteases. Blood 102 (2003) 3262-3269
62. Wolfram S. Theory and Application of Cellular Automata (1986), World Publishing Co., Singapore