On the Interaction Between Soft and Hard Sciences: the Role of Mathematical Sciences

Aylaj, Bouchra; Bellomo, Nicola; Chouhad, Nadia; Knopoff, Damián

doi:10.1007/s10013-019-00381-3

Cited by 6 publications

(5 citation statements)

References 75 publications

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“…Since the behavior of glioma cells as a pattern-forming population is influenced by processes taking place on single-cell and mesoscopic (featuring velocity-dependent cell density; the direction of cell migration in response to the underlying tissue structure seems to be relevant for the shape and extent of the patterns) levels, we consider a multiscale approach in which we start from such lower scale descriptions and then deduce (in a formal way) the macroscopic dynamics leading to the mentioned patterns. (We refer to [33] for a recent review of principle-based modeling in a broader context involving such mathematical structures.) We begin by introducing some notations for the various variables and functions involved in our modeling process:…”

Section: Modelingmentioning

confidence: 99%

A Flux-Limited Model for Glioma Patterning with Hypoxia-Induced Angiogenesis

Kumar

Surulescu

2020

Symmetry

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We propose a model for glioma patterns in a microlocal tumor environment under the influence of acidity, angiogenesis, and tissue anisotropy. The bottom-up model deduction eventually leads to a system of reaction–diffusion–taxis equations for glioma and endothelial cell population densities, of which the former infers flux limitation both in the self-diffusion and taxis terms. The model extends a recently introduced (Kumar, Li and Surulescu, 2020) description of glioma pseudopalisade formation with the aim of studying the effect of hypoxia-induced tumor vascularization on the establishment and maintenance of these histological patterns which are typical for high-grade brain cancer. Numerical simulations of the population level dynamics are performed to investigate several model scenarios containing this and further effects.

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Section: Modelingmentioning

confidence: 99%

A Flux-Limited Model for Glioma Patterning with Hypoxia-Induced Angiogenesis

Kumar

Surulescu

2020

Symmetry

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“…Therefore, an additional dynamics should be inserted in the overall model. Some guide principles towards modeling of endogenous networks have been given in [46] and [5], referring to the KTAP theory, but additional work should still be developed towards a complete theory.…”

Section: On a Mathematical Theory Of Behavioral Swarmsmentioning

confidence: 99%

“…nicola.bellomo@polito.it (2) University of Perugia, Italy., dilettaburini@alice.it (3) Scuola Superiore Sant'Anna, Pisa Italy., giovanni.dosi@santannapisa.it (4) School of Engineering, Inst. for Multiscale Thermofluids, University of Edinburgh, U.K, livio.gibelli@ed.ac.uk (5) BCAM, Basque Center for Applied Mathematics, Spain, and Centro de Investigación y Estudios de Matemática (CONICET) and Famaf (UNC), Córdoba, Argentina., damian.knopoff@unc.edu.ar (6) Cadi Ayyad University, Faculty of Sciences Semlalia, LMDP, Morocco and UMMISCO (IRD-Sorbonne University, France) outada@ljll.math.upmc.fr (7) University of Torino, Torino, Italy, and Fondazione Collegio Carlo Alberto, Torino, Italy., pietro.terna@unito.it (8) Scuola Superiore Sant'Anna, Pisa, Italy., mariaenrica.virgillito@santannapisa.it…”

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confidence: 99%

Active particles methods towards modeling in science and society

Bellomo¹,

Burini²,

Dosi³

et al. 2020

Preprint

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This paper is a first step to chase the ambitious objective of developing a mathematical theory of living systems. The contents refer modeling large systems of interacting living entities with the aim of describing their collective behaviors by differential models.The contents is in three parts. Firstly, we derive the mathematical method; subsequently, we show how the method can be applied in a number of case studies related to well defined living systems and finally, we look ahead to research perspectives focusing both on mathematical methods and further applications.

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“…The mathematical representation of human and animal populations is one of the most interesting modelling challenges of the last century [1]. Over the years, scientists have focused on this aspect of mathematical biology, providing great contributions based on di↵erent mathematical theories.…”

Section: Introductionmentioning

confidence: 99%