Document Detail


A generalised age- and phase-structured model of human tumour cell populations both unperturbed and exposed to a range of cancer therapies.
MedLine Citation:
PMID:  17361361     Owner:  NLM     Status:  MEDLINE    
Abstract/OtherAbstract:
We develop a general mathematical model for a population of cells differentiated by their position within the cell division cycle. A system of partial differential equations governs the kinetics of cell densities in certain phases of the cell division cycle dependent on time t (hours) and an age-like variable tau (hours) describing the time since arrival in a particular phase of the cell division cycle. Transition rate functions control the transfer of cells between phases. We first obtain a theoretical solution on the infinite domain -infinity < t < infinity. We then assume that age distributions at time t=0 are known and write our solution in terms of these age distributions on t=0. In practice, of course, these age distributions are unknown. All is not lost, however, because a cell line before treatment usually lies in a state of asynchronous balanced growth where the proportion of cells in each phase of the cell cycle remain constant. We assume that an unperturbed cell line has four distinct phases and that the rate of transition between phases is constant within a short period of observation ('short' relative to the whole history of the tumour growth) and we show that under certain conditions, this is equivalent to exponential growth or decline. We can then gain expressions for the age distributions. So, in short, our approach is to assume that we have an unperturbed cell line on t </= 0, and then, at t=0 the cell line is exposed to cancer therapy. This corresponds to a change in the transition rate functions and perhaps incorporation of additional phases of the cell cycle. We discuss a number of these cancer therapies and applications of the model.
Authors:
Britta Basse; Paolo Ubezio
Publication Detail:
Type:  Journal Article; Research Support, Non-U.S. Gov't     Date:  2007-03-15
Journal Detail:
Title:  Bulletin of mathematical biology     Volume:  69     ISSN:  0092-8240     ISO Abbreviation:  Bull. Math. Biol.     Publication Date:  2007 Jul 
Date Detail:
Created Date:  2007-06-19     Completed Date:  2007-10-18     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  0401404     Medline TA:  Bull Math Biol     Country:  United States    
Other Details:
Languages:  eng     Pagination:  1673-90     Citation Subset:  IM    
Affiliation:
Auckland Cancer Society Research Centre, Faculty of Medical and Health Sciences, University of Auckland, Auckland, New Zealand. britta.basse@orcon.net.nz
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MeSH Terms
Descriptor/Qualifier:
Algorithms
Camptothecin / pharmacology,  therapeutic use
Cell Count
Cell Cycle / drug effects,  physiology*,  radiation effects
Cell Line, Tumor
Cell Proliferation / drug effects,  radiation effects
Cell Survival / drug effects,  radiation effects
Humans
Kinetics
Models, Biological*
Neoplasms / pathology,  physiopathology,  therapy*
Paclitaxel / pharmacology,  therapeutic use
Time Factors
Chemical
Reg. No./Substance:
33069-62-4/Paclitaxel; 7689-03-4/Camptothecin

From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine


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