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A Multiscale Approach Leading to Hybrid Mathematical Models for Angiogenesis: The Role of Randomness

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Mathematical Methods and Models in Biomedicine

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 [7] and retina angiogenesis [8]. 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 [18, 19].

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Authors and Affiliations

  1. Department of Mathematics, University of Milan, 20133, Milan, Italy

    Vincenzo Capasso & Daniela Morale

  2. CIMAB (Interuniversity Centre for Mathematics Applied to Biology, Medicine and Environmental Sciences), University of Milan, 20133, Milan, Italy

    Vincenzo Capasso & Daniela Morale

Authors
  1. Vincenzo Capasso
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  2. Daniela Morale
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Correspondence to Vincenzo Capasso .

Editor information

Editors and Affiliations

  1. , Mathematics and Statistics, Southern Illinois University Edwardsvill, Edwardsville, 62026, Illinois, USA

    Urszula Ledzewicz

  2. , Electrical and Systems Engineering, Washington University, Brookings Drive 1, Saint Louis, 63130, Missouri, USA

    Heinz Schättler

  3. Mathematical Biosciences Institute, Ohio State University, W. 18th Avenue 231, Columbus, 43210-1292, Ohio, USA

    Avner Friedman

  4. Tel Aviv University, Ramat Aviv, Tel Aviv, 69978, Israel

    Eugene Kashdan

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Capasso, V., Morale, D. (2013). A Multiscale Approach Leading to Hybrid Mathematical Models for Angiogenesis: The Role of Randomness. In: Ledzewicz, U., Schättler, H., Friedman, A., Kashdan, E. (eds) Mathematical Methods and Models in Biomedicine. Lecture Notes on Mathematical Modelling in the Life Sciences. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4178-6_4

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