TY - JOUR
T1 - The minimal, phase-transition model for the cell-number maintenance by the hyperplasia-extended homeorhesis
AU - Mamontov, E.
AU - Koptioug, A.
AU - Psiuk-Maksymowicz, K.
N1 - Funding Information:
The authors are grateful to the European Commission Marie Curie Research Training Network MRTN-CT-2004-503661 “Modelling, Mathematical Methods and Computer Simulation of Tumour Growth and Therapy” (http://calvino.polito.it/∼mcrtn/) for the full support of the third author. The authors express their deep gratitude to Professor Lars Walldén, Ex-Dean of the Department of Physics, Chalmers University of Technology Corp. (Gothenburg, Sweden), who substantially contributed to the research environment enabling the authors to develop the results of the present work. Helen Bridle, Department of Chemistry and Biosciences, Chalmers University of Technology Corp. (Gothenburg, Sweden), is warmly acknowledged for reading the manuscript and useful remarks which helped the authors to improve the text.
Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.
PY - 2006/6
Y1 - 2006/6
N2 - Oncogenic hyperplasia is the first and inevitable stage of formation of a (solid) tumor. This stage is also the core of many other proliferative diseases. The present work proposes the first minimal model that combines homeorhesis with oncogenic hyperplasia where the latter is regarded as a genotoxically activated homeorhetic dysfunction. This dysfunction is specified as the transitions of the fluid of cells from a fluid, homeorhetic state to a solid, hyperplastic-tumor state, and back. The key part of the model is a nonlinear reaction-diffusion equation (RDE) where the biochemical-reaction rate is generalized to the one in the well-known Schlögl physical theory of the non-equilibrium phase transitions. A rigorous analysis of the stability and qualitative aspects of the model, where possible, are presented in detail. This is related to the spatially homogeneous case, i.e. when the above RDE is reduced to a nonlinear ordinary differential equation. The mentioned genotoxic activation is treated as a prevention of the quiescent G0-stage of the cell cycle implemented with the threshold mechanism that employs the critical concentration of the cellular fluid and the nonquiescent-cell-duplication time. The continuous tumor morphogeny is described by a time-space-dependent cellular-fluid concentration. There are no sharp boundaries (i.e. no concentration jumps exist) between the domains of the homeorhesis- and tumor-cell populations. No presumption on the shape of a tumor is used. To estimate a tumor in specific quantities, the model provides the time-dependent tumor locus, volume, and boundary that also points out the tumor shape and size. The above features are indispensable in the quantitative development of antiproliferative drugs or therapies and strategies to prevent oncogenic hyperplasia in cancer and other proliferative diseases. The work proposes an analytical-numerical method for solving the aforementioned RDE. A few topics for future research are suggested.
AB - Oncogenic hyperplasia is the first and inevitable stage of formation of a (solid) tumor. This stage is also the core of many other proliferative diseases. The present work proposes the first minimal model that combines homeorhesis with oncogenic hyperplasia where the latter is regarded as a genotoxically activated homeorhetic dysfunction. This dysfunction is specified as the transitions of the fluid of cells from a fluid, homeorhetic state to a solid, hyperplastic-tumor state, and back. The key part of the model is a nonlinear reaction-diffusion equation (RDE) where the biochemical-reaction rate is generalized to the one in the well-known Schlögl physical theory of the non-equilibrium phase transitions. A rigorous analysis of the stability and qualitative aspects of the model, where possible, are presented in detail. This is related to the spatially homogeneous case, i.e. when the above RDE is reduced to a nonlinear ordinary differential equation. The mentioned genotoxic activation is treated as a prevention of the quiescent G0-stage of the cell cycle implemented with the threshold mechanism that employs the critical concentration of the cellular fluid and the nonquiescent-cell-duplication time. The continuous tumor morphogeny is described by a time-space-dependent cellular-fluid concentration. There are no sharp boundaries (i.e. no concentration jumps exist) between the domains of the homeorhesis- and tumor-cell populations. No presumption on the shape of a tumor is used. To estimate a tumor in specific quantities, the model provides the time-dependent tumor locus, volume, and boundary that also points out the tumor shape and size. The above features are indispensable in the quantitative development of antiproliferative drugs or therapies and strategies to prevent oncogenic hyperplasia in cancer and other proliferative diseases. The work proposes an analytical-numerical method for solving the aforementioned RDE. A few topics for future research are suggested.
KW - Cancer
KW - Cell
KW - Cell cycle
KW - Concentration
KW - Formation and disintegration of tumor
KW - Genotoxicity
KW - Gradual process
KW - Homeorhesis
KW - Morphogeny
KW - Oncogenic hyperplasia
KW - Reaction-diffusion equation
KW - Schlögl's nonstationary phase transition
UR - http://www.scopus.com/inward/record.url?scp=33745853085&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33745853085&partnerID=8YFLogxK
U2 - 10.1007/s10441-006-8263-3
DO - 10.1007/s10441-006-8263-3
M3 - Review article
C2 - 16988902
AN - SCOPUS:33745853085
VL - 54
SP - 61
EP - 101
JO - Acta Biotheoretica
JF - Acta Biotheoretica
SN - 0001-5342
IS - 2
ER -