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P. K. Burgess, P. M. Kulesa, J. D. Murray and E. C. Alvord Jr., “The Interaction of Growth Rates and Diffusion Coefficients in a Three-Dimensional Mathematical Model of Gliomas,” Journal of Neuropathology & Experimental Neurology, Vol. 56, 1997, pp. 704-713.

has been cited by the following article:

• TITLE: FEM Based Study of Concentration of Proliferating Cell in Brain Tumor

  AUTHORS: Sushma Nema, V. P. Saxena

  KEYWORDS: Deterministic Model; Gliomas; White Matter; Gray Matter; Proliferation; Motile Cells

  JOURNAL NAME: Applied Mathematics, Vol.3 No.8, August 1, 2012

  ABSTRACT: In this chapter we have developed a deterministic model of growth of abnormal cell concentration in a human subject at different positions. The diffusion-reaction Equation has been applied to satisfy growth dynamics .The whole tumor region is divided into layers which, with the growth of tumor form necrotic, quiescent and region of proliferating of tumor cells. Finite element method for one dimension has been employed for solving the Equations. Here we have taken into account the cellular motility along with proliferative growth ,which is particularly required in case of some of the brain tumors, where motility of gliomas cells differ widely in gray and white matter.