The minimal, phase-transition model for the cell-number maintenance by the hyperplasia-extended homeorhesis

• 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.

Ämnesord

MEDICIN OCH HÄLSOVETENSKAP  -- Medicinsk bioteknologi -- Biomedicinsk laboratorievetenskap/teknologi (hsv//swe)

MEDICAL AND HEALTH SCIENCES  -- Medical Biotechnology -- Biomedical Laboratory Science/Technology (hsv//eng)

MEDICIN OCH HÄLSOVETENSKAP  -- Medicinska och farmaceutiska grundvetenskaper -- Immunologi inom det medicinska området (hsv//swe)

MEDICAL AND HEALTH SCIENCES  -- Basic Medicine -- Immunology in the medical area (hsv//eng)

MEDICIN OCH HÄLSOVETENSKAP  -- Medicinska och farmaceutiska grundvetenskaper -- Cell- och molekylärbiologi (hsv//swe)

MEDICAL AND HEALTH SCIENCES  -- Basic Medicine -- Cell and Molecular Biology (hsv//eng)

MEDICIN OCH HÄLSOVETENSKAP  -- Medicinska och farmaceutiska grundvetenskaper -- Fysiologi (hsv//swe)

MEDICAL AND HEALTH SCIENCES  -- Basic Medicine -- Physiology (hsv//eng)

NATURVETENSKAP  -- Biologi -- Bioinformatik och systembiologi (hsv//swe)

NATURAL SCIENCES  -- Biological Sciences -- Bioinformatics and Systems Biology (hsv//eng)

NATURVETENSKAP  -- Biologi -- Mikrobiologi (hsv//swe)

NATURAL SCIENCES  -- Biological Sciences -- Microbiology (hsv//eng)

NATURVETENSKAP  -- Biologi -- Biokemi och molekylärbiologi (hsv//swe)

NATURAL SCIENCES  -- Biological Sciences -- Biochemistry and Molecular Biology (hsv//eng)

NATURVETENSKAP  -- Fysik -- Annan fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences -- Other Physics Topics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering (hsv//eng)

Nyckelord

cell

cancer

oncogenic hyperplasia

homeorhesis

formation and disintegration of tumor

gradual process

concentration

genotoxicity

cell cycle

morphogeny

reaction-diffusion equation

Schlögl's nonstationary phase transition

Cancer

Electrical engineering, electronics and photonics

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