Finite-difference and pseudo-spectral methods for the numerical simulations of in vitro human tumor cell population kinetics

Pages: 561 - 572, Volume 6, Issue 3, July 2009

doi:10.3934/mbe.2009.6.561       Abstract        Full Text (374.6K)       Related Articles

Z. Jackiewicz - Department of Mathematics and Statistics, Arizona State University, Tempe, Arizona 85287, United States (email)
B. Zubik-Kowal - Department of Mathematics, Boise State University, 1910 University Drive, Boise, Idaho 83725, United States (email)
B. Basse - Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, New Zealand (email)

Abstract: Pseudo-spectral approximations are constructed for the model equations describing the population kinetics of human tumor cells in vitro and their responses to radiotherapy or chemotherapy. These approximations are more efficient than finite-difference approximations. The spectral accuracy of the pseudo-spectral method allows us to resolve the model with a much smaller number of spatial grid-points than required for the finite-difference method to achieve comparable accuracy. This is demonstrated by numerical experiments which show a good agreement between predicted and experimental data.

Keywords:  Population kinetics of human cancer cells in vitro, human tumor cells, cell cycle dynamics, mathematical model, pseudo-spectral methods, finite-difference methods.
Mathematics Subject Classification:  Primary: 45K05, 34K28; Secondary: 62P10.

Received: January 2008;      Accepted: February 2009;      Published: June 2009.