A time-space model for the growth of microalgae biofilms for biofuel production

Polizzi, Bastien; Bernard, Olivier; Ribot, Magali

doi:10.1016/j.jtbi.2017.08.017

Cited by 24 publications

(19 citation statements)

References 54 publications

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“…We end the time loop by integrating the source term with a semi-implicit Euler method that preserves the positivity. Namely, the negative contributions of the source function are passed on the left hand side and solved semi-implicitly, while the positive contributions are kept in the right-hand side and treated explicitly [31]. The implicitation of the negative term does not involve any linear system inversion: due to the multilinear form of the different terms of the source function, the matrix to be inverted is diagonal.…”

Section: Numerical Implementationmentioning

confidence: 99%

A mathematical model to investigate the key drivers of the biogeography of the colon microbiota

Labarthe

Polizzi

Phan

et al. 2019

Journal of Theoretical Biology

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The gut microbiota, mainly located in the colon, is engaged in a complex dialogue with the large intestinal epithelium through which important regulatory processes for the health and well-being of the host take place. Imbalances of the microbial populations, called dysbiosis, are related to several pathological status, emphasizing the importance of understanding the gut bacterial ecology. Among the ecological drivers of the microbiota, the spatial structure of the colon is of special interest: spatio-temporal mechanisms can lead to the constitution of spatial interactions among the bacterial populations and of environmental niches that impact the overall colonization of the colon. In the present study, we introduce a mathematical model of the colon microbiota in its fluid environment, based on the explicit coupling of a population dynamics model of microbial populations involved in fibre degradation with a fluid dynamics model of the luminal content. This modeling framework is used to study the main drivers of the spatial structure of the microbiota, specially focusing on the dietary fibre inflow, the epithelial motility, the microbial active swimming and viscosity gradients in the digestive track. We found 1) that the viscosity gradients allow the creation of favorable niches in the vicinity of the mucus layer; 2) that very low microbial active swimming in the radial direction is enough to promote bacterial growth, which sheds a new light on microbial motility in the colon and 3) that dietary fibres are the main driver of the spatial structure of the microbiota in the distal bowel whereas epithelial motility is preponderant for the colonization of the proximal colon; in the transverse colon, fibre levels and chemotaxis have the strongest impact on the distribution of the microbial communities.

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Section: Numerical Implementationmentioning

confidence: 99%

A mathematical model to investigate the key drivers of the biogeography of the colon microbiota

Labarthe

Polizzi

Phan

et al. 2019

Journal of Theoretical Biology

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“…conversion between active and inactive material), diffusive or other forms of mobility, etc. [15,16,27], as well as the possibility for different material types to move with different velocities [13,25,38]. Upon summing equations (2), we obtain the volume conservation constraint…”

Section: Biofilm Modelmentioning

confidence: 99%

Flux-Balance Based Modeling of Biofilm Communities

Parker

Carlson

et al. 2018

Preprint

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Models of microbial community dynamics generally rely on a sub-scale model for microbial metabolisms. In systems such as distributed multispecies communities like biofilms, where it is not reasonable to simplify to a small number of limiting substrates, tracking the large number of active metabolites likely requires measurement or estimation of large numbers of kinetic and regulatory parameters. Alternatively, a largely kinetics-free methodology is proposed combining cellular level constrained, steady state metabolic flux analysis with macro scale microbial community models. The methodology easily allows coupling of macroscale information, including measurement data, with cell-scale metabolism. Illustrative examples are included.

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“…For all particulates in the system, the conversion factor remained constant at 80 kgCOD m -3 , however the variation of any of these components could be varied for sensitivity analysis. This value was about 15% greater than that proposed in previous photobiofilm studies [205], and remains a source of uncertainty which could be resolved with experiments, which have been well discussed in the literature [208].…”

Section: Growth Of Particulate Mattermentioning

confidence: 60%

“…However, particulate species must be expressed in terms of volume fractions, α XPB , α XS and α XI . This can be achieved by introducing a conversion term ρ * which is similar to the assumption in previous studies where its value was assumed to be roughly 60-70 kg TS m -3 [136,205]. In this case, we have taken a more systematic approach in converting the COD quantities of the particulate species to volume fractions.…”

Section: Growth Of Particulate Mattermentioning

confidence: 99%

“…In optically thick media, strong scattering effects are observed, including forward scattering [99]. This phototrophic/photosynthetic biofilm mixture model was further developed in subsequent studies [205]. In this study a single functional microbial group This method allows for conservation to be maintained while more accurately capturing the interface between the liquid and biofilm phases.…”

Section: Introductionmentioning

confidence: 99%

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Distributed parameter modelling of phototrophic bioreactor systems

Barry¹

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Purple phototrophic bacteria (PPB) use infrared light to generate microbial energy, with electron, carbon and nitrogen supplied chemically. They have broad applicability for resource recovery from wastes and wastewater, as they have potential value as microbial product and very high growth yields on substrate. Although PPB processes are gaining relevance in the aforementioned industries, reactor design, particularly effective consideration of light in chemical kinetics and hydraulics is a critical issue. This thesis aims to assess key limitations and define their physical behaviour mathematically. The first limitation was that there was no mixed culture PPB process model describing the behaviour of PPB in the presence of ammonia, organic matter and other nutrients. The mixed population models of the International Water Association (IWA) provide a good framework for process modelling and control. As such, a process model for a mixed-culture PPB system was developed based on five key processes: photoheterotrophic growth, photoautotrophic growth, chemoheterotrophic growth, hydrolysis/fermentation, and decay. This model was developed as a set of ordinary differential equations varying in time and lumped in space (as for the IWA models). The second limitation is that the radiative field has not been considered. This can vary spatially and temporally. The radiative field in a PPB system attenuates sharply, which influences the growth domains. A CFD modelling framework was therefore developed in OpenFOAM to describe the spatial variations and interactions between biomass growth, the flow field and the radiative field. It was found that lumped modelling approaches and distributed parameter approaches differed in results based on different reactor domains and behaviours. The deviation from lumped parameter behaviour was greater for a cylindrical stirred reactor than for a flat plate reactor. Therefore, spatial considerations are necessary in the design phase of a photobioreactor. Finally, biofilms are a critical aspect in PPB growth, and a coupled biofilm radiative transfer model has not been previously considered. The model was thus extended to include biofilm formation of a mixed PPB system in the presence of a spatially varying radiative field. A volume-of-fluid approach was used as a basis for this model, considering three particulate species (phototrophic bacteria, biodegradable particulate matter, and inert particulates). The radiative-solid-liquid coupling overall was found to be critical in operation, with traditional lumped parameter approaches to design and analysis not well suited to the emerging challenges of mixed culture photo-bio systems. These aspects should be further considered through model based analysis and experimental validation for future system design.

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A time-space model for the growth of microalgae biofilms for biofuel production

Cited by 24 publications

References 54 publications

A mathematical model to investigate the key drivers of the biogeography of the colon microbiota

A mathematical model to investigate the key drivers of the biogeography of the colon microbiota

Flux-Balance Based Modeling of Biofilm Communities

Distributed parameter modelling of phototrophic bioreactor systems

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