Stochastic models for tumor growth in (1+1) dimension

Authors

Abstract

Strong experimental evidences and scaling analysis have shown that tumors growth belongs to the molecular beam
epitaxy (MBE) universality class. This type of growth is described by three characteristics: 1) linear growth rate 2)
the constraint of cell proliferation to the tumor border 3) surface diffusion of cells at the growing edge. All of these
features have been experimentally seen. Stochastic partial differential equations with correct geometrical
symmetries are reproduced some of the fundamental mechanisms of the tumor growth as a statistical approach. In
the present article we presented a more general model in (1+1) dimension by adding 1 r term to the deterministic
term  .By solving this equation, we understand that with this approximation tumor reach faster to radially
symmetric solution and its growth will become more favorable.

Keywords

References

[1]  A.L. Barabasi H.E. and Stanley, “Fractal Concepts in Surface Growth”, Cambridge Univ. Press, Cambridge (1995).
[2]  A. Bru, S. Albertos, J.L. Subiza, J.L. Garcia-Asenlo, and I. Bru, Biophys. J. 88 (2003) 2948.
[3]  A. Bru and D. Casero, Journal of theoretical Biology 243 (2006) 171-180
[4]   A. Bru, S. Albertos, J.L. Garcia-Asenlo, and I. Bru, Phys. Rev. Lett. 92 (2003) 238101.
[5] C. Esudero, Phys. Rev. E 73 (2006) R020902.
[6] C. Esudero, Phys. Rev. E 74 (2006) 021901.
[7]  A. Bru, S. Albertos, J.L. Subiza, J.L. Garcia-Asenlo, and I. Bru, Biophys. J. 88 (2005) 3737-3738.
[8]  A. Bru, J.M. Pastor, I. Fernaud, I. Bru, S. Melle, and C. Berenguer, Phys. Rev. Lett. 81 (1998) 4008.
[9]  A. Bru, S. Albertos, F. Garcia-Hoz, and I. Bru, Clin. J. Res. 8 (2005) 9.
[10]  M. Marsili, A. Maritan, F. Toigo, and J.R. Banavar, Rev. Mod. Phys. 68 (1996) 963.
Iranian Journal of Applied Physics
Volume 2, Issue 2 - Serial Number 2
December 2012
Pages 43-51

Files

History

  • Receive Date: 24 September 2012
  • Revise Date: 03 November 2012
  • Accept Date: 28 January 2013

Share

How to cite

Statistics