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...

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Bibliographic Details
Published in:PloS one 2016-06, Vol.11 (6), p.e0157689-e0157689
Main Authors: López, Álvaro G, Seoane, Jesús M, Sanjuán, Miguel A F
Format: Article
Language:English
Subjects:
Apoptosis
Biology and Life Sciences
Cancer therapies
Cell Count
Cellular automata
Computer Simulation
Cytotoxicity
Cytotoxicity, Immunologic
Decay
Enzyme kinetics
Humans
Hypotheses
Immune system
Kinetics
Lymphocytes
Mathematical analysis
Mathematical functions
Mathematical models
Medicine and Health Sciences
Models, Statistical
Neoplasms - immunology
Neoplasms - pathology
Parameter estimation
Physical Sciences
Research and Analysis Methods
Solid tumors
T-Lymphocytes, Cytotoxic - cytology
T-Lymphocytes, Cytotoxic - enzymology
T-Lymphocytes, Cytotoxic - immunology
Tumors
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Summary: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.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0157689