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The minimal, phase-transition model for the cell-number maintenance by the hyperplasia-extended homeorhesis
Gothenburg University.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Information Technology and Media.
Gothenburg University.
2006 (English)In: Acta Biotheoretica, ISSN 0001-5342, E-ISSN 1572-8358, Vol. 54, no 2, p. 61-101Article in journal (Refereed) Published
Abstract [en]

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 Schlogl 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.

Place, publisher, year, edition, pages
2006. Vol. 54, no 2, p. 61-101
Keywords [en]
Cancer, Cell, Cell cycle, Concentration, Formation and disintegration of tumor, Genotoxicity, Gradual process, Homeorhesis, Morphogeny, Oncogenic hyperplasia, Reaction-diffusion equation, Schlögl's nonstationary phase transition
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:miun:diva-8681DOI: 10.1007/s10441-006-8263-3ISI: 000240726500001Scopus ID: 2-s2.0-33745853085OAI: oai:DiVA.org:miun-8681DiVA, id: diva2:174975
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VR-Mathematics

Available from: 2009-02-26 Created: 2009-02-26 Last updated: 2017-12-13Bibliographically approved

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Koptioug, Andrei

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