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

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.

Modeling biological systems with an improved fractional Gompertz law

“…This is usually justified by the assumption that bacterial cells live suspended in the bulk liquid. Nonetheless, it was recently observed that bacteria tend to organize themselves in biofilm form [27], which are aggregates of cells enclosed in a self-produced matrix [28,29]. Then diffusion phenomena at micro-scale turn out to be of paramount importance for such systems.…”

Start-up of a nutrient removal system using Scenedesmus vacuolatus and Chlorella vulgaris biofilms

“…Biofilm accumulation is determined by the balance of attachment, growth and detachment processes (Hunt et al 2004;Kesaano and Sims 2014;D' Acunto et al 2015;Mattei et al 2018). Five phases were defined according to the observed colonization, nutrient removal and the green intensity of the cotton fabric carrier by S. vacuolatus ACUF_053 (Fig.…”

Modeling Heavy Metal Sorption and Interaction in a Multispecies Biofilm

“…These structures, known as multispecies biofilms, include different components, such as living cells, inert materials and extracellular polymeric substances (EPS) [3][4][5][6]. Their structural organization confers to these biological systems enhanced mechanical characteristics and adaptive features to many environmental conditions [7][8][9]. For instance, the protective self-secreted EPS matrix can strongly affect the dynamics of substances within the biofilm and it can also serve as a source of nutrients for bacteria [10,11].…”

“…In this context, mathematical modeling represents an appropriate tool to provide basic information on specific biosorption phenomena and stimulate further research on the multiplicity of mechanisms regulating biosorption process by biofilms [2]. For instance, multidimensional models can be implemented for specific applications when micro-scale outputs are required [7]. The spatial distribution of diffusing compounds and microbial species within the biofilm, and the physical structure of the biofilm at a micro-scale level can be investigated by using complex 2D and 3D mathematical models [23][24][25][26].…”