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
Titolo: | A multiscale approach leading to hybrid mathematical models for angiogenesis: the role of randomness |
Autori: | CAPASSO, VINCENZO (Primo) MORALE, DANIELA (Ultimo) |
Settore Scientifico Disciplinare: | Settore MAT/06 - Probabilita' e Statistica Matematica Settore MAT/07 - Fisica Matematica |
Data di pubblicazione: | 2013 |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/978-1-4614-4178-6_4 |
Tipologia: | Book Part (author) |
Appare nelle tipologie: | 03 - Contributo in volume |