Decay Dynamics of Tumors.
The fractional cell kill is a mathematical expression describing the rate at which a certain population of cells is reduced to a fraction of itself. We investigate the mathematical function that governs the rate at which a solid tumor is lysed by a cell population of cytotoxic lymphocytes. We do it in the context of enzyme kinetics, using geometrical and analytical arguments. We derive the equations governing the decay of a tumor in the limit in which it is plainly surrounded by immune cells. A cellular automaton is used to test such decay, confirming its validity. Finally, we introduce a modification in the fractional cell kill so that the expected dynamics is attained in the mentioned limit. We also discuss the potential of this new function for non-solid and solid tumors which are infiltrated with lymphocytes.
Nonlinear Dynamics, Chaos and Complex Systems Group. Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain.
Álvaro G
ÁG
López
Nonlinear Dynamics, Chaos and Complex Systems Group. Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain.
Jesús M
JM
Seoane
Nonlinear Dynamics, Chaos and Complex Systems Group. Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain.
Miguel A F
http://orcid.org/0000-0003-3515-0837
MA
Sanjuán
D017209:Apoptosis; D002452:Cell Count; D003198:Computer Simulation; D003602:Cytotoxicity, Immunologic; D006801:Humans; D007700:Kinetics; D015233:Models, Statistical; D009369:Neoplasms / Q000276:immunology* / Q000473:pathology; D013602:T-Lymphocytes, Cytotoxic / Q000166:cytology / Q000201:enzymology / Q000276:immunology