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.

scholarly journals Towards a mathematical theory of behavioral human crowds

2022 ◽  
pp. 1-38
Author(s):  
Nicola Bellomo ◽  
Livio Gibelli ◽  
Annalisa Quaini ◽  
Alessandro Reali
Keyword(s):  
Critical Analysis ◽  
Mathematical Theory ◽  
Social Dynamics ◽  
Living Systems ◽  
General Survey ◽  
Multiscale Problems ◽  
Modeling Approach ◽  
Research Perspectives

The first part of our paper presents a general survey on the modeling, analytic problems, and applications of the dynamics of human crowds, where the specific features of living systems are taken into account in the modeling approach. This critical analysis leads to the second part which is devoted to research perspectives on modeling, analytic problems, multiscale topics which are followed by hints towards possible achievements. Perspectives include the modeling of social dynamics, multiscale problems and a detailed study of the link between crowds and swarms modeling.

scholarly journals Multiscale Modeling and Mathematical Problems Related to Tumor Evolution and Medical Therapy

2003 ◽  
Vol 5 (2) ◽  
pp. 111-136 ◽  
Author(s):  
Nicola Bellomo ◽  
Elena De Angelis ◽  
Luigi Preziosi
Keyword(s):  
Immune System ◽  
Mathematical Models ◽  
Multiscale Modeling ◽  
Critical Analysis ◽  
Applied Mathematics ◽  
Tumor Evolution ◽  
Research Perspectives ◽  
Mathematical Problems ◽  
Mathematical Literature ◽  
Characteristic Scales

This paper provides a survey of mathematical models and methods dealing with the analysis and simulation of tumor dynamics in competition with the immune system. The characteristic scales of the phenomena are identified and the mathematical literature on models and problems developed on each scale is reviewed and critically analyzed. Moreover, this paper deals with the modeling and optimization of therapeutical actions. The aim of the critical analysis and review consists in providing the background framework towards the development of research perspectives in this promising new field of applied mathematics.

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.

scholarly journals Hierarchical modeling of mechano-chemical dynamics of epithelial sheets across cells and tissue

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yoshifumi Asakura ◽  
Yohei Kondo ◽  
Kazuhiro Aoki ◽  
Honda Naoki
Keyword(s):  
Wound Healing ◽  
Cell Migration ◽  
Continuum Model ◽  
Tissue Level ◽  
Chemical Signals ◽  
Cellular Level ◽  
Mathematical Framework ◽  
Collective Cell Migration ◽  
The Continuum ◽  
Cell Cell

AbstractCollective cell migration is a fundamental process in embryonic development and tissue homeostasis. This is a macroscopic population-level phenomenon that emerges across hierarchy from microscopic cell-cell interactions; however, the underlying mechanism remains unclear. Here, we addressed this issue by focusing on epithelial collective cell migration, driven by the mechanical force regulated by chemical signals of traveling ERK activation waves, observed in wound healing. We propose a hierarchical mathematical framework for understanding how cells are orchestrated through mechanochemical cell-cell interaction. In this framework, we mathematically transformed a particle-based model at the cellular level into a continuum model at the tissue level. The continuum model described relationships between cell migration and mechanochemical variables, namely, ERK activity gradients, cell density, and velocity field, which could be compared with live-cell imaging data. Through numerical simulations, the continuum model recapitulated the ERK wave-induced collective cell migration in wound healing. We also numerically confirmed a consistency between these two models. Thus, our hierarchical approach offers a new theoretical platform to reveal a causality between macroscopic tissue-level and microscopic cellular-level phenomena. Furthermore, our model is also capable of deriving a theoretical insight on both of mechanical and chemical signals, in the causality of tissue and cellular dynamics.

scholarly journals On the structural connectivity of large-scale models of brain networks at cellular level

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Giuseppe Giacopelli ◽  
Domenico Tegolo ◽  
Emiliano Spera ◽  
Michele Migliore
Keyword(s):  
Large Scale ◽  
Brain Networks ◽  
Structural Connectivity ◽  
Network Models ◽  
Brain Regions ◽  
Cellular Level ◽  
Scale Model ◽  
Mathematical Framework ◽  
Underlying Mechanisms ◽  
Experimental Findings

AbstractThe brain’s structural connectivity plays a fundamental role in determining how neuron networks generate, process, and transfer information within and between brain regions. The underlying mechanisms are extremely difficult to study experimentally and, in many cases, large-scale model networks are of great help. However, the implementation of these models relies on experimental findings that are often sparse and limited. Their predicting power ultimately depends on how closely a model’s connectivity represents the real system. Here we argue that the data-driven probabilistic rules, widely used to build neuronal network models, may not be appropriate to represent the dynamics of the corresponding biological system. To solve this problem, we propose to use a new mathematical framework able to use sparse and limited experimental data to quantitatively reproduce the structural connectivity of biological brain networks at cellular level.

Modeling virus pandemics in a globally connected world a challenge towards a mathematics for living systems

2021 ◽  
pp. 1-7
Author(s):  
N. Bellomo ◽  
F. Brezzi ◽  
M. A. J. Chaplain
Keyword(s):  
Complex System ◽  
Population Dynamics ◽  
Mathematical Models ◽  
Modeling And Simulation ◽  
Critical Analysis ◽  
Living Systems ◽  
Special Issue ◽  
Research Perspectives ◽  
Heterogeneous Features

This editorial paper presents the papers published in a special issue devoted to the modeling and simulation of mutating virus pandemics in a globally connected world. The presentation is proposed in three parts. First, motivations and objectives are presented according to the idea that mathematical models should go beyond deterministic population dynamics by considering the multiscale, heterogeneous features of the complex system under consideration. Subsequently, the contents of the papers in this issue are presented referring to the aforementioned complexity features. Finally, a critical analysis of the overall contents of the issue is proposed, with the aim of providing a forward look to research perspectives.

scholarly journals Critical Analysis of Non-Thermal Plasma-Driven Modulation of Immune Cells from Clinical Perspective

2020 ◽  
Vol 21 (17) ◽  
pp. 6226 ◽  
Author(s):  
Barbora Smolková ◽  
Adam Frtús ◽  
Mariia Uzhytchak ◽  
Mariia Lunova ◽  
Šárka Kubinová ◽  
...  
Keyword(s):  
Immune Cells ◽  
Thermal Plasma ◽  
Critical Analysis ◽  
Cell Function ◽  
Immune Cell ◽  
Real Life ◽  
Research Strategy ◽  
Cellular Mechanisms ◽  
Non Thermal Plasma

The emerged field of non-thermal plasma (NTP) shows great potential in the alteration of cell redox status, which can be utilized as a promising therapeutic implication. In recent years, the NTP field considerably progresses in the modulation of immune cell function leading to promising in vivo results. In fact, understanding the underlying cellular mechanisms triggered by NTP remains incomplete. In order to boost the field closer to real-life clinical applications, there is a need for a critical overview of the current state-of-the-art. In this review, we conduct a critical analysis of the NTP-triggered modulation of immune cells. Importantly, we analyze pitfalls in the field and identify persisting challenges. We show that the identification of misconceptions opens a door to the development of a research strategy to overcome these limitations. Finally, we propose the idea that solving problems highlighted in this review will accelerate the clinical translation of NTP-based treatments.

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.

The mathematical theory of epidemics: a study of the evolution of resistance in microorganisms

1971 ◽  
Vol 3 (2) ◽  
pp. 206-208 ◽  
Author(s):  
V. P. Krus ◽  
L. A. Rvachev
Keyword(s):  
Mathematical Theory ◽  
Modern Medicine ◽  
Mathematical Methods ◽  
Resistance To Antibiotics ◽  
Epidemic Theory ◽  
Evolution Of Resistance

In modern medicine it becomes more and more urgent every year to solve new epidemiological problems. One of these is the evolution of resistance to antibiotics of a large spectrum of microorganisms; this resistance is a consequence of the mass administration of antibiotics. In this problem it becomes necessary to apply the mathematical methods of epidemic theory as here the key lies in a purely epidemiological factor, namely the mass character of the use of antibiotics. A first model of the phenomenon encountered is presented.

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