Advanced search
Publication Cover
Computer Methods in Biomechanics and Biomedical Engineering Volume 19, 2016 - Issue 8
Submit an article Journal homepage
424
Views
6
CrossRef citations to date
0
Altmetric
Articles

Simulation of 3D tumor cell growth using nonlinear finite element method

Shoubing DongSchool of Computer Science & Engineering, South China University of Technology, Guangzhou, ChinaCorrespondence[email protected]
View further author information
,
Yannan YanSchool of Computer Science & Engineering, South China University of Technology, Guangzhou, ChinaView further author information
,
Liqun TangSchool of Civil Engineering & Transportation, South China University of Technology, Guangzhou, ChinaView further author information
,
Junping MengSchool of Computer Science & Engineering, South China University of Technology, Guangzhou, ChinaView further author information
&
Yi JiangDepartment of Mathematics & Statistics, Georgia State University, Atlanta, GA, USAView further author information
Pages 807-818 | Received 12 May 2014, Accepted 19 Jun 2015, Published online: 27 Jul 2015

References

  • Ambrosi D, Mollica F. 2002. On the mechanics of a growing tumor. Int J Eng Sci. 40:1297–1316.
  • Bauer AL, Jackson TL, Jiang Y. 2009. Topography of extracellular matrix mediates vascular morphogenesis and migration speeds in angiogenesis. PLoS Comput Biol. 5:e1000445.
  • Berg OG, Paulsson J, Ehrenberg M. 2000. Fluctuations and quality of control in biological cells: zero-order ultrasensitivity reinvestigated. Biophys J. 79:1228–1236.
  • Cao Y, Linden P, Farnebo J, Cao R, Eriksson A, Kumar V, Qi JH, Claesson-Welsh L, Alitalo K. 1998. Vascular endothelial growth factor C induces angiogenesis in vivo. Proc Natl Acad Sci USA. 95:14389–14394.
  • Dong S, Long Z, Tang L, Jiang Y, Yan Y. 2014. Simulation of growth and division of 3D cells based on finite element method. Int J Appl Mechanics. 6:1450041-1–1450041-17.
  • Graner F, Glazier JA. 1992. Simulation of biological cell sorting using a two-dimensional extended Potts model. Phys Rev Lett. 69:2013–2016.
  • Hoppe H, DeRose T, Duchamp T, McDonald J, Stuetzle W. 1993. Mesh optimization. ACM Sig-graph; Anaheim (CA): ACM Press.
  • [hypre] A Library of High Performance Preconditioners. 2012. Center for Applied Scientific Computing Lawrence Livermore National Laboratory. Available from: http://acts.nersc.gov/hypre/
  • Jiang Y, Pjesivac-Grbovic J, Cantrell C, Freyer JP. 2005. A multiscale model for avascular tumor growth. Biophys J. 89:3884–3894.
  • Liu S, Liao W, Liu H. 2007. Triangle regularity measurement based on cosine sum of inner angles and mesh optimization. Mec Sci Technol. 26:420–423.
  • Merks RMH, Perryn ED, Shirinifard A, Glazier JA. 2008. Contact inhibited chemotaxis in de novo and sprouting blood-vessel growth. PLoSComput Biol. 4:e1000163.
  • Popławski NJ, Agero U, Gens JS, Swat M, Glazier JA, Anderson AR. 2009. Front instabilities and invasiveness of simulated avascular tumors. Bull Math Biol. 71:1189–1227.
  • Rubenstein BM, Kaufman LJ. 2008. The role of extracellular matrix in glioma invasion: a cellular Potts model approach. Biophys J. 95:5661–5680.
  • Shirinifard A, Gens JS, Zaitlen BL, Popławski NJ, Swat M, Glazier JA. 2009. 3D multi-cell simulation of tumor growth and angiogenesis. PLoS ONE. 4:e7190.
  • Smith AE, Coit DW. 1996. Penalty functions handbook of evolutionary computation, Section C 5.2. London: Oxford University Press and Institute of Physics Publishing.
  • Zhang B, Xing Y, Ruan X. 2004. Mesh simplification based on features preserving and triangles optimization. J Shanghai Jiaotong Univ. 38:1373–1377.
  • Zhang L, Athale CA, Deisboeck TS. 2007. Development of a three-dimensional multiscale agent-based tumor model: simulating gene–protein interaction profiles, cell phenotypes and multicellular patterns in brain cancer. J Theor Biol. 244:96–107.
  • Zimmer H. 2005. Voronoi and Delaunay techniques. Lecture notes computer sciences VIII; July 30; RWTH Aachen, Aachen, Germany.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.