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Continuum and discrete approach in modeling biofilm development and structure: a review

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Abstract

The scientific community has recognized that almost 99% of the microbial life on earth is represented by biofilms. Considering the impacts of their sessile lifestyle on both natural and human activities, extensive experimental activity has been carried out to understand how biofilms grow and interact with the environment. Many mathematical models have also been developed to simulate and elucidate the main processes characterizing the biofilm growth. Two main mathematical approaches for biomass representation can be distinguished: continuum and discrete. This review is aimed at exploring the main characteristics of each approach. Continuum models can simulate the biofilm processes in a quantitative and deterministic way. However, they require a multidimensional formulation to take into account the biofilm spatial heterogeneity, which makes the models quite complicated, requiring significant computational effort. Discrete models are more recent and can represent the typical multidimensional structural heterogeneity of biofilm reflecting the experimental expectations, but they generate computational results including elements of randomness and introduce stochastic effects into the solutions.

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Acknowledgements

The authors would like to thank the European Commission for providing financial support through the Erasmus Mundus Joint Doctorate Programme ETeCoS3 (Environmental Technologies for Contaminated Solids, Soils and Sediments) under the Grant agreement FPA n2010-0009. Two of the authors (M. R. Mattei and L. Frunzo) would also like to acknowledge Progetto Giovani GNFM 2016 Comportamenti emergenti ed auto-organizzazione in sistemi iperbolici di reazione-diffusione in ambito biologico ed ecologico.

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  1. Department of Mathematics and Applications “Renato Caccioppoli”, University of Naples Federico II, Via Cintia, Monte S. Angelo, 80126, Naples, Italy

    M. R. Mattei, L. Frunzo & B. D’Acunto

  2. Laboratoire Géomatériaux et Environnement (LGE) EA 4508, Université Paris-Est, Boulevard Descartes 5, 77454, Marne-la-vallée Cedex, France

    Y. Pechaud

  3. Department of Civil, Architectural and Environmental Engineering, University of Naples Federico II, Via Claudio 21, 80125, Naples, Italy

    F. Pirozzi

  4. Department of Civil and Mechanical Engineering, University of Cassino and Souther Lazio, Via di Biasio, 43, 03043, Cassino, FR, Italy

    G. Esposito

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Mattei, M.R., Frunzo, L., D’Acunto, B. et al. Continuum and discrete approach in modeling biofilm development and structure: a review. J. Math. Biol. 76, 945–1003 (2018). https://doi.org/10.1007/s00285-017-1165-y

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