ON THE ASYMPTOTIC THEORY FROM MICROSCOPIC TO MACROSCOPIC GROWING TISSUE MODELS: AN OVERVIEW WITH PERSPECTIVES

2012 ◽  
Vol 22 (01) ◽  
pp. 1130001 ◽  
Author(s):  
N. BELLOMO ◽  
A. BELLOUQUID ◽  
J. NIETO ◽  
J. SOLER
Keyword(s):  
Kinetic Theory ◽  
Asymptotic Analysis ◽  
Critical Analysis ◽  
Asymptotic Theory ◽  
Blow Up ◽  
Cellular Interactions ◽  
Biological Functions ◽  
Active Particles ◽  
Tissue Models ◽  
Macroscopic Equations

This paper proposes a review and critical analysis of the asymptotic limit methods focused on the derivation of macroscopic equations for a class of equations modeling complex multicellular systems by methods of the kinetic theory for active particles. Cellular interactions generate both modification of biological functions and proliferative/destructive events. The asymptotic analysis deals with suitable parabolic, hyperbolic, and mixed limits. The review includes the derivation of the classical Keller–Segel model and flux limited models that prevent non-physical blow up of solutions.

scholarly journals MULTISCALE BIOLOGICAL TISSUE MODELS AND FLUX-LIMITED CHEMOTAXIS FOR MULTICELLULAR GROWING SYSTEMS

2010 ◽  
Vol 20 (07) ◽  
pp. 1179-1207 ◽  
Author(s):  
NICOLA BELLOMO ◽  
ABDELGHANI BELLOUQUID ◽  
JUAN NIETO ◽  
JUAN SOLER
Keyword(s):  
Kinetic Theory ◽  
Asymptotic Analysis ◽  
Binary Mixtures ◽  
Biological Tissue ◽  
Cellular Interactions ◽  
Biological Functions ◽  
Active Particles ◽  
Tissue Models

This paper deals with the derivation of macroscopic tissue models from the underlying description delivered by a class of equations that models binary mixtures of multicellular systems by methods of the kinetic theory for active particles. Cellular interactions generate both modification of the biological functions and proliferative and destructive events. The asymptotic analysis deals with suitable parabolic and hyperbolic limits, and is specifically focused on the modeling of the chemotaxis phenomena.

scholarly journals MULTICELLULAR BIOLOGICAL GROWING SYSTEMS: HYPERBOLIC LIMITS TOWARDS MACROSCOPIC DESCRIPTION

2007 ◽  
Vol 17 (supp01) ◽  
pp. 1675-1692 ◽  
Author(s):  
N. BELLOMO ◽  
A. BELLOUQUID ◽  
J. NIETO ◽  
J. SOLER
Keyword(s):  
Immune System ◽  
Asymptotic Analysis ◽  
Hyperbolic Systems ◽  
Cellular Interactions ◽  
Biological Functions ◽  
Macroscopic Description ◽  
Linear And Nonlinear ◽  
Growth Of Tumor ◽  
Macroscopic Equations ◽  
Nonlinear Hyperbolic Systems

This paper deals with the analysis of the asymptotic limit towards the derivation of hyperbolic macroscopic equations for a class of equations modeling complex multicellular systems. Cellular interactions generate both modification of biological functions and proliferating destructive events related to growth of tumor cells in competition with the immune system. The asymptotic analysis refers to the hyperbolic limit to show how the macroscopic tissue behavior can be described by linear and nonlinear hyperbolic systems which seem the most natural in this context.

LOOKING FOR NEW PARADIGMS TOWARDS A BIOLOGICAL-MATHEMATICAL THEORY OF COMPLEX MULTICELLULAR SYSTEMS

2006 ◽  
Vol 16 (07) ◽  
pp. 1001-1029 ◽  
Author(s):  
NICOLA BELLOMO ◽  
GUIDO FORNI
Keyword(s):  
Kinetic Theory ◽  
Complex Systems ◽  
Critical Analysis ◽  
Mathematical Theory ◽  
Classical Mechanics ◽  
Biological Functions ◽  
Living Matter ◽  
Research Perspectives ◽  
Active Particles ◽  
Large Systems

This paper deals with the development of new paradigms based on the methods of the mathematical kinetic theory for active particles to model the dynamics of large systems of interacting cells. Interactions are ruled, not only by laws of classical mechanics, but also by a few biological functions which are able to modify the above laws. The paper technically shows, also by reasoning on specific examples, how the theory can be applied to model large complex systems in biology. The last part of the paper deals with a critical analysis and with the indication of research perspectives concerning the challenging target of developing a biological-mathematical theory for the living matter.

DLX6-AS1: a putative lncRNA candidate in multiple human cancers

2021 ◽  
Vol 23 ◽  
Author(s):  
Mohsen Sheykhhasan ◽  
Yaghoub Ahmadyousefi ◽  
Reihaneh Seyedebrahimi ◽  
Hamid Tanzadehpanah ◽  
Hamed Manoochehri ◽  
...  
Keyword(s):  
Cancer Progression ◽  
Critical Analysis ◽  
Molecular Mechanisms ◽  
Signalling Pathways ◽  
Biological Functions ◽  
Initial Development ◽  
Human Cancers ◽  
Expression Of Genes ◽  
Non Coding Rnas ◽  
Research Studies

Abstract Long non-coding RNAs (lncRNAs) have important roles in regulating the expression of genes and act as biomarkers in the initial development of different cancers. Increasing research studies have verified that dysregulation of lncRNAs occurs in various pathological processes including tumorigenesis and cancer progression. Among the different lncRNAs, DLX6-AS1 has been reported to act as an oncogene in the development and prognoses of different cancers, by affecting many different signalling pathways. This review summarises and analyses the recent research studies describing the biological functions of DLX6-AS1, its overall effect on signalling pathways and the molecular mechanisms underlying its action on the expression of genes in multiple human cancers. Our critical analysis suggests that different signalling pathways associated to this lncRNA may be used as a biomarker for diagnosis, or targets of treatment in cancers.

Active particles methods and challenges in behavioral systems

2020 ◽  
Vol 30 (04) ◽  
pp. 653-658 ◽  
Author(s):  
N. Bellomo ◽  
F. Brezzi ◽  
J. Soler
Keyword(s):  
Qualitative Analysis ◽  
Critical Analysis ◽  
Mathematical Approach ◽  
Special Issue ◽  
Behavioral Systems ◽  
Research Perspectives ◽  
Active Particles ◽  
Challenging Research ◽  
Large Systems

This paper first provides an introduction to the mathematical approach to the modeling, qualitative analysis, and simulation of large systems of living entities, specifically self-propelled particles. Subsequently, a presentation of the papers published in this special issue follows. Finally, a critical analysis of the overall contents of the issue is proposed, thus leading to define some challenging research perspectives.

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