MATHEMATICAL METHODS AND TOOLS OF KINETIC THEORY TOWARDS MODELLING COMPLEX BIOLOGICAL SYSTEMS

2005 ◽  
Vol 15 (11) ◽  
pp. 1639-1666 ◽  
Author(s):  
ABDELGHANI BELLOUQUID ◽  
MARCELLO DELITALA
Keyword(s):  
Kinetic Theory ◽  
Evolution Equations ◽  
Classical Mechanics ◽  
Mathematical Framework ◽  
Mathematical Approach ◽  
Biological Functions ◽  
Mathematical Methods ◽  
Research Perspectives ◽  
Large Systems ◽  
The One

This paper develops a variety of mathematical tools to model the dynamics of large systems of interacting cells. Interactions are ruled not only by laws of classical mechanics, but also by some biological functions. The mathematical approach is the one of kinetic theory and non-equilibrium statistical mechanics. The paper deals both with the derivation of evolution equations and with the design of specific models consistent with the above-mentioned mathematical framework. Various hints for research perspectives are proposed in the last part of the paper.

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.

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.

FROM THE MODELING OF THE IMMUNE HALLMARKS OF CANCER TO A BLACK SWAN IN BIOLOGY

2013 ◽  
Vol 23 (05) ◽  
pp. 949-978 ◽  
Author(s):  
ABDELGHANI BELLOUQUID ◽  
ELENA DE ANGELIS ◽  
DAMIAN KNOPOFF
Keyword(s):  
Immune System ◽  
Kinetic Theory ◽  
Biological Function ◽  
Early Stage ◽  
Black Swan ◽  
Mathematical Approach ◽  
Hallmarks Of Cancer ◽  
Active Particles ◽  
Scalar Variable ◽  
Large Systems

This paper deals with the modeling of the early stage of cancer phenomena, namely mutations, onset, progression of cancer cells, and their competition with the immune system. The mathematical approach is based on the kinetic theory of active particles developed to describe the dynamics of large systems of interacting cells, called active particles. Their microscopic state is modeled by a scalar variable which expresses the main biological function. The modeling focuses on an interpretation of the immune-hallmarks of cancer.

scholarly journals On the Discrete Kinetic Theory for Active Particles. Modelling the Immune Competition

2006 ◽  
Vol 7 (2-3) ◽  
pp. 143-157 ◽  
Author(s):  
I. Brazzoli ◽  
A. Chauviere
Keyword(s):  
Kinetic Theory ◽  
Cancer Cells ◽  
Mathematical Framework ◽  
Research Perspectives ◽  
Active Particles

This paper deals with the application of the mathematical kinetic theory for active particles, with discrete activity states, to the modelling of the immune competition between immune and cancer cells. The first part of the paper deals with the assessment of the mathematical framework suitable for the derivation of the models. Two specific models are derived in the second part, while some simulations visualize the applicability of the model to the description of biological events characterizing the immune competition. A final critical outlines some research perspectives.

scholarly journals What is life? A perspective of the mathematical kinetic theory of active particles

2021 ◽  
pp. 1-46
Author(s):  
Nicola Bellomo ◽  
Diletta Burini ◽  
Giovanni Dosi ◽  
Livio Gibelli ◽  
Damian Knopoff ◽  
...  
Keyword(s):  
Kinetic Theory ◽  
Case Studies ◽  
General Framework ◽  
Living Systems ◽  
Mathematical Approach ◽  
Collective Behaviors ◽  
Research Perspectives ◽  
Active Particles ◽  
Look Ahead

The modeling of living systems composed of many interacting entities is treated in this paper with the aim of describing their collective behaviors. The mathematical approach is developed within the general framework of the kinetic theory of active particles. The presentation is in three parts. First, we derive the mathematical tools, subsequently, we show how the method can be applied to a number of case studies related to well defined living systems, and finally, we look ahead to research perspectives.

A multiscale view of nonlinear diffusion in biology: From cells to tissues

2019 ◽  
Vol 29 (04) ◽  
pp. 791-823 ◽  
Author(s):  
D. Burini ◽  
N. Chouhad
Keyword(s):  
Kinetic Theory ◽  
Nonlinear Diffusion ◽  
Stochastic Game ◽  
Broad Class ◽  
Kinetic Equations ◽  
Classical Mechanics ◽  
Theory Model ◽  
Macroscopic Models ◽  
Research Perspectives ◽  
Stochastic Game Theory

This paper presents a review on the mathematical tools for the derivation of macroscopic models in biology from the underlying description at the scale of cells as it is delivered by a kinetic theory model. The survey is followed by an overview of research perspectives. The derivation is inspired by the Hilbert’s method, known in classic kinetic theory, which is here applied to a broad class of kinetic equations modeling multicellular dynamics. The main difference between this class of equations with respect to the classical kinetic theory consists in the modeling of cell interactions which is developed by theoretical tools of stochastic game theory rather than by laws of classical mechanics. The survey is focused on the study of nonlinear diffusion and source terms.

MATHEMATICAL TOPICS ON THE MODELLING COMPLEX MULTICELLULAR SYSTEMS AND TUMOR IMMUNE CELLS COMPETITION

2004 ◽  
Vol 14 (11) ◽  
pp. 1683-1733 ◽  
Author(s):  
N. BELLOMO ◽  
A. BELLOUQUID ◽  
M. DELITALA
Keyword(s):  
Immune Cells ◽  
Critical Analysis ◽  
Mathematical Theory ◽  
Cellular Level ◽  
Mathematical Framework ◽  
Mathematical Methods ◽  
Microscopic Description ◽  
Macroscopic Equation ◽  
Research Perspectives ◽  
Mathematical Literature

This paper deals with a critical analysis and some developments related to the mathematical literature on multiscale modelling of multicellular systems involving tumor immune cells competition at the cellular level. The analysis is focused on the development of mathematical methods of the classical kinetic theory to model the above physical system and to recover macroscopic equation from the microscopic description. Various hints are given toward research perspectives, with special attention on the modelling of the interplay of microscopic (at the cellular level) biological and mechanical variables on the overall evolution of the system. Indeed the final aim of this paper consists of organizing the various contributions available in the literature into a mathematical framework suitable to generate a mathematical theory for complex biological systems.

FROM THE MATHEMATICAL KINETIC THEORY TO MODELLING COMPLEX SYSTEMS IN APPLIED SCIENCES

2004 ◽  
Vol 18 (04n05) ◽  
pp. 487-500 ◽  
Author(s):  
NICOLA BELLOMO
Keyword(s):  
Applied Sciences ◽  
Kinetic Theory ◽  
Statistical Mechanics ◽  
Complex Systems ◽  
Nonequilibrium Statistical Mechanics ◽  
Classical Mechanics ◽  
Large Complex ◽  
Large Systems

This paper deals with the design of a nonequilibrium statistical mechanics theory developed to model large systems of interacting individuals. Interactions being ruled, not only by laws of classical mechanics, but also by some intelligent or organized behaviour. The paper technically shows, also by reasoning on specific examples, how the theory can be applied to model large complex systems in natural and applied sciences.

The Ultimate Sophistication of Special Theory of Relativity

2021 ◽  
Vol 11 (3) ◽  
pp. 43-49
Author(s):  
Hamdoon A. Khan ◽  
Keyword(s):  
Special Relativity ◽  
Special Theory ◽  
Mathematical Approach ◽  
Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
The Real ◽  
The Past ◽  
The One ◽  
The Universe ◽  
Faster Than Light

With the consideration of the light which carries the photon particles, the Lorentz transformation was constructed with an impressive mathematical approach. But the generalization of that equation for all the velocities of the universe is direct enforcement on other things not to travel faster than light. It has created serious issues in every scientific research that was done in the last century based on the special theory of relativity. This paper replaces the velocity of light with some other velocities and shows us the possible consequences and highlights the issues of special relativity. If I travel through my past or future and was able to see another me there, who would be the real Hamdoon I or the one I see there in the past or future! If the real one is only me, the one I saw, is not me, so, I could not travel through my or someone else's past or future. Therefore, no one can travel through time. If both of us are the same, can the key of personal identity be duplicated or be separated into two or more parts? These are some of the fundamental philosophical arguments that annihilate the concept of time travel which is one of the sequels of special relativity.

Reductions and Solutions of Two Types of Coupled Nonlinear Evolution Equations in Optical Fibers and Fluid Dynamics

2011 ◽  
Vol 66 (8-9) ◽  
pp. 552-558
Author(s):  
Li-Cai Liu ◽  
Bo Tian ◽  
Bo Qin ◽  
Xing Lü ◽  
Zhi-Qiang Lin ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Raman Scattering ◽  
Optical Fibers ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Dark Soliton ◽  
Nonlinear Evolution Equations ◽  
The One ◽  
Gain Loss ◽  
Burgers Type Equations

Abstract Under investigation in this paper are the coupled nonlinear Schrödinger equations (CNLSEs) and coupled Burgers-type equations (CBEs), which are, respectively, a model for certain birefringent optical fibers Raman-scattering, Kerr and gain/loss effects, and a generalized model in fluid dynamics. Special attention should be paid to the existing claim that the solitons for the CNLSEs do not exist. Through certain dependent-variable transformations, the CNLSEs are reduced to a Manakov system and the CBEs are linearized. In that way, some new solutions of the CNLSEs and CBEs are obtained via symbolic computation. Especially the one-dark-soliton-like solutions for the CNLSEs have been found, against the existing claim.

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