In biology and medicine we may observe a wide spectrum of formation of patterns, usually due to self-organization phenomena. This may happen at any scale; from the cellular scale of embryonic tissue formation, wound healing or tumor growth, and angiogenesis to the much larger scale of animal grouping. Patterns are usually explained in terms of a collective behavior driven by “forces,” either external and/or internal, acting upon individuals (cells or organisms). In most of these organization phenomena, randomness plays a major role; here we wish to address the issue of the relevance of randomness as a key feature for producing nontrivial geometric patterns in biological structures. As working examples we offer a review of two important case studies involving angiogenesis, i.e., tumor-driven angiogenesis and retina angiogenesis. In both cases the reactants responsible for pattern formation are the cells organizing as a capillary network of vessels, and a family of underlying fields driving the organization, such as nutrients, growth factors, and alike.

A multiscale approach leading to hybrid mathematical models for angiogenesis: the role of randomness / V. Capasso, D. Morale - In: Mathematical methods and models in biomedicine / [a cura di] U. Ledzewicz, H. Schättler, A. Friedman, E. Kashdan. - [s.l] : Springer, 2013. - ISBN 978-1-4614-4177-9. - pp. 87-115 [10.1007/978-1-4614-4178-6_4]

A multiscale approach leading to hybrid mathematical models for angiogenesis: the role of randomness

V. Capasso
Primo
;
D. Morale
Ultimo
2013

Abstract

In biology and medicine we may observe a wide spectrum of formation of patterns, usually due to self-organization phenomena. This may happen at any scale; from the cellular scale of embryonic tissue formation, wound healing or tumor growth, and angiogenesis to the much larger scale of animal grouping. Patterns are usually explained in terms of a collective behavior driven by “forces,” either external and/or internal, acting upon individuals (cells or organisms). In most of these organization phenomena, randomness plays a major role; here we wish to address the issue of the relevance of randomness as a key feature for producing nontrivial geometric patterns in biological structures. As working examples we offer a review of two important case studies involving angiogenesis, i.e., tumor-driven angiogenesis and retina angiogenesis. In both cases the reactants responsible for pattern formation are the cells organizing as a capillary network of vessels, and a family of underlying fields driving the organization, such as nutrients, growth factors, and alike.
Settore MAT/06 - Probabilita' e Statistica Matematica
Settore MAT/07 - Fisica Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/202544
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