From kinetic models of multicellular growing systems to macroscopic biological tissue models

Bellouquid, Abdelghani; Angelis, Elena De

doi:10.1016/j.nonrwa.2010.09.005

Cited by 41 publications

(28 citation statements)

References 60 publications

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“…This approach has been initiated in biology by Othmer, Dunbar and Alt, 156 where the main idea consists in perturbing the transport equation by a velocity jump process, which appears appropriate to model the velocity dynamics of cells modeled as living particles. This method, which leads to hyperbolic transport equation, has been subsequently developed by various authors, among others, 2,13,14,22,46,48,68,76,97,118,157 who contributed to improve the approach and developed various applications in biology. The book by Banasiak and Lachowicz 8 is an important source of additional bibliography.…”

Section: Asymptotic Methods From the Micro-scale To The Macro-scalementioning

confidence: 99%

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Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues

Bellomo

Bellouquid

Tao

et al. 2015

Math. Models Methods Appl. Sci.

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875

818

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This paper proposes a survey and critical analysis focused on a variety of chemotaxis models in biology, namely the classical Keller-Segel model and its subsequent modifications, which, in several cases, have been developed to obtain models that prevent the non-physical blow up of solutions. The presentation is organized in three parts. The first part focuses on a survey of some sample models, namely the original model and some of its developments, such as flux limited models, or models derived according to similar concepts. The second part is devoted to the qualitative analysis of analytic problems, such as the existence of solutions, blow-up and asymptotic behavior. The third part deals with the derivation of macroscopic models from the underlying description, delivered by means of kinetic theory methods. This approach leads to the derivation of classical models as well as that of new models, which might deserve attention as far as 1663

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Section: Asymptotic Methods From the Micro-scale To The Macro-scalementioning

confidence: 99%

“…The contents refer to an already vast literature (see Refs. 2,9,11,[13][14][15]22,51,[46][47][48]68,69,76,97,118,157,173) from which three different techniques are presented/have been chosen. The first one, given in Sec.…”

Section: Aims and Plan Of The Papermentioning

confidence: 99%

Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues

Bellomo

Bellouquid

Tao

et al. 2015

Math. Models Methods Appl. Sci.

Self Cite

875

818

View full text Add to dashboard Cite

show abstract

“…The approaches consist in linking mathematical frameworks to lower and upper scales by means of hydrodynamic limits with the aim to derive macroscopic tissue equations based on the underlying description at the microscopic scale, see, among others, papers [62][63][64][65][66][67][68].…”

Section: The Multiscale Problemmentioning

confidence: 99%

Towards a unified approach in the modeling of fibrosis: A review with research perspectives

Amar

Bianca

2016

Physics of Life Reviews

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Pathological fibrosis is the result of a failure in the wound healing process. The comprehension and the related modeling of the different mechanisms that trigger fibrosis is a challenge of many researchers that work in the field of medicine and biology. The modern scientific analysis of a phenomenon generally consists of three major approaches: theoretical, experimental, and computational. Different theoretical tools coming from mathematics and physics have been proposed for the modeling of the physiological and pathological fibrosis. However a complete framework is missing and the development of a general theory is required. This review aims at finding a unified approach in the modeling of fibrosis diseases that takes into account the different phenomena occurring at each level: molecular, cellular and tissue. Specifically by means of a critical analysis of the different models that have been proposed in the mathematical, computational and physical biology, from molecular to tissue scales, a multiscale approach is proposed, an approach that has been strongly recommended by top level biologists in the past decades.

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“…Bellouquid and Angelis [13] showed how the macroscopic tissue behavior can be described from the underlying cellular description and that this specific biological state modifies the structures of the models obtained by different assumptions using asymptotic analysis. They derived hyperbolic models and focused on the existence of global equilibrium solutions.…”

Section: Recent Work Papers On Soft Tissuementioning

confidence: 99%

Remodeling of soft tissues due to cell activity

Stoffel

Weichert

et al. 2014

Proc Appl Math and Mech

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The continuum mechanical modeling of collagenous biological tissues is of interest in the field of biomedical engineering. Particularly, the change of material properties as a result of cell activity is of great interest, as chondrocyte (cartilage cell) implantation yields significant functional improvement. The aim of the contribution is to present the remodeling phenomenon of a cellular material due to cell activity, which results in synthesis of collagen type‐II fibers. For the experimental study, cellular condensed gel is mechanically stimulated in a bioreactor for four weeks. The change of the stiffness of the gel is measured in a compression test. The remodeling process is theoretically derived by an appropriate evolution law in the framework of continuum mechanics. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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From kinetic models of multicellular growing systems to macroscopic biological tissue models

Cited by 41 publications

References 60 publications

Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues

Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues

Towards a unified approach in the modeling of fibrosis: A review with research perspectives

Remodeling of soft tissues due to cell activity

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