`a`
Mathematical Biosciences and Engineering (MBE)
 

A model for asymmetrical cell division
Pages: 491 - 501, Issue 3, June 2015

doi:10.3934/mbe.2015.12.491      Abstract        References        Full text (384.6K)           Related Articles

Ali Ashher Zaidi - Institute of Natural and Mathematical Sciences, Massey University, Auckland, New Zealand (email)
Bruce Van Brunt - Institute of Fundamental Sciences, Massey University, Palmerston North, New Zealand (email)
Graeme Charles Wake - Institute of Natural and Mathematical Sciences, Massey University, Auckland, New Zealand (email)

1 B. Basse, B. Baguley, E. Marshell, W. Joseph, B. Van-Brunt, G. C. Wake and D. Wall, Modelling cell death in human tumor cell lines exposed to the anticancer drug paclitaxel, J. Math. Biol., 49 (2004), 329-357.       
2 Basse, G. C. Wake, D. J. N. Wall and B. Van-Brunt, On a cell-growth model for plankton, Mathematical medicine and biology, 21 (2004), 49-61.
3 R. Begg, Cell-population Growth Modeling and Functional Differential Equations, Ph.D thesis, University of Canterbury, New Zealand, 2007.
4 R. Begg, D. J. N. Wall and G. C. Wake, On a functional equation model of transient cell growth, Mathematical medicine and biology, 22 (2005), 371-390.
5 M. J. Cáceres, J. A. Cañizo and S. Mischlerl, Rate of convergence to self similarity for the fragmentation equation in $L^1$ spaces, Communications in Applied and Industrial Mathematics, 1 (2010), 299-308.       
6 M. J. Cáceres, J. A. Cañizo and S. Mischlerl, Rate of convergence to an asymptotic profile for the self-similar fragmentation and growth-fragmentation equations, Journal de Mathémathiques Pures et Appliquée, 96 (2011), 334-362.       
7 F. P. Da Costa, M. Grinfeld and J. B. Mcleod, Unimodality of steady size distributions of growing cell populations, J.evol.equ., 1 (2001), 405-409.       
8 O. Diekmann, H. J. A. M. Heijmans and H. R. Thieme, On the stability of the cell size distribution, Jour. Math. Biol., 19 (1984), 227-248.       
9 A. J. Hall and G. C. Wake, A functional differential equation arising in modelling of cell growth, J. Aust. Math. Soc. Ser. B, 30 (1989), 424-435.       
10 A. J. Hall, G. C. Wake and P. W. Gandar, Steady size distributions for cells in one dimensional plant tissues, J. Math. Biol., 30 (1991), 101-123.
11 H. J. A. M. Heijmans, On the stable size distribution of populations reproducing by fission into two unequal parts, Mathematical Biosciences, 72 (1984), 19-50.       
12 P. Laurençot and B. Perthame, Exponential decay for the growth-fragmentation/cell-division equation, Commun. Math. Sci., 7 (2009), 503-510.       
13 T. R. Malthus, An Essay on the Principle of Population, St. Paul's London, 1798.
14 A. G. Mckendrick, Applications of mathematics to medical problems, Proc. Edinburgh Math. Soc., 44 (1926), 98-130.
15 J. A. J. Metz and O. Diekmann, The Dynamics of Physiologically Structured Populations, Lecture Notes in Biomathematics, 68. Springer-Verlag, Berlin, 1986.       
16 P. Michel, S. Mischler and B. Perthame, General entropy equations for structured population models and scattering, Comptes Rendus Mathematique, 338 (2004), 697-702.       
17 P. Michel, S. Mischler and B. Perthame, General relative entropy inequality: An illustration on growth models, J. Math. Pures Appl., 84 (2005), 1235-1260.       
18 R. A. Neumïler and J. A. Knoblich, Dividing cellular asymmetry: Asymmetric cell division and its implications for stem cells and cancer, Genes Dev., 23 (2009), 2675-2699.
19 B. Perthame and L. Ryzhik, Exponential decay for the fragmentation or cell-division equation, Journal of Differential Equations, 210 (2005), 155-177.       
20 T. Suebcharoen, B. Van-Brunt and G. C. Wake, Asymmetric cell division in a size-structured growth model, Differential and Integral Equations, 24 (2011), 787-799.       
21 B. Van-Brunt, G. C. Wake and H. K. Kim, A singular Sturm-Liouville problem involving an advanced functional differential equation, European Journal of Applied Mathematics, 12 (2001), 625-644.       
22 B. Van-Brunt and M. Vlieg-Hulstman, An eigenvalue problem involving a functional differential equation arising in a cell growth model, ANZIAM J., 51 (2010), 383-393.       

Go to top