Simple Linear Model of Tumor Growth in a Changing Environment

作者: Jose F. Nieves , Marcelo R. Ubriaco

DOI: 10.4236/AM.2015.67104

关键词: MathematicsConstant (mathematics)Simple (abstract algebra)Applied mathematicsLinear modelCoupling (computer programming)Mathematical optimizationState (functional analysis)Linear equationTumor growthGrowth rate

摘要: In an environment that is neither static nor in equilibrium, but dynamic and changing, the kinetics of reactions cause growth a tumor, which depend on state evolving environment, cannot be parametrized terms constant rates. We propose simple model for describing untreated tumor such environments, characterized by minimal number parameters generalizable to include effects various types therapies. simplest version we consider here, it consists linear equation with time-dependent rate, interpret as coupling system environment. A complete solution given integral rate. The essential features general are illustrated few examples, comparison made models have been proposed describe recent data.

参考文章(16)
Rick Durrett, Cancer modelling: a personal perspective Notices of the American Mathematical Society. ,vol. 60, pp. 304- 309 ,(2013) , 10.1090/NOTI953
David Dingli, Matthew D. Cascino, Krešimir Josić, Stephen J. Russell, Željko Bajzer, Mathematical modeling of cancer radiovirotherapy. Bellman Prize in Mathematical Biosciences. ,vol. 199, pp. 55- 78 ,(2006) , 10.1016/J.MBS.2005.11.001
Wei-Rong Zhong, Yuan-Zhi Shao, Zhen-Hui He, Spatiotemporal fluctuation-induced transition in a tumor model with immune surveillance. Physical Review E. ,vol. 74, pp. 011916- 011916 ,(2006) , 10.1103/PHYSREVE.74.011916
LARRY NORTON, RICHARD SIMON, HARMAR D. BRERETON, ARTHUR E. BOGDEN, Predicting the course of Gompertzian growth. Nature. ,vol. 264, pp. 542- 545 ,(1976) , 10.1038/264542A0
Pier Paolo Delsanto, Caterina Guiot, Piero Giorgio Degiorgis, Carlos A. Condat, Yuri Mansury, Thomas S. Deisboeck, Growth model for multicellular tumor spheroids Applied Physics Letters. ,vol. 85, pp. 4225- 4227 ,(2004) , 10.1063/1.1812842
Calixto P. Calderón, Tor A. Kwembe, Modeling tumor growth Mathematical Biosciences. ,vol. 103, pp. 97- 114 ,(1991) , 10.1016/0025-5564(91)90093-X
Wei-Rong Zhong, Yuan-Zhi Shao, Zhen-Hui He, Pure multiplicative stochastic resonance of a theoretical anti-tumor model with seasonal modulability. Physical Review E. ,vol. 73, pp. 060902- ,(2006) , 10.1103/PHYSREVE.73.060902
D Hart, E Shochat, Z Agur, The growth law of primary breast cancer as inferred from mammography screening trials data. British Journal of Cancer. ,vol. 78, pp. 382- 387 ,(1998) , 10.1038/BJC.1998.503