A generalised age and phasestructured 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 agelike 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, NonU.S. Gov't Date: 20070315 
Journal Detail:

Title: Bulletin of mathematical biology Volume: 69 ISSN: 00928240 ISO Abbreviation: Bull. Math. Biol. Publication Date: 2007 Jul 
Date Detail:

Created Date: 20070619 Completed Date: 20071018 Revised Date:  
Medline Journal Info:

Nlm Unique ID: 0401404 Medline TA: Bull Math Biol Country: United States 
Other Details:

Languages: eng Pagination: 167390 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:

33069624/Paclitaxel; 7689034/Camptothecin 
From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine
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