Homogenized model for diffusion and heterogeneous reaction in porous media: Numerical study and validation.

Bourbatache, Mohamed Khaled; Millet, Olivier; Lê, Thạch Ngọc; Moyne, Christian

doi:10.1016/j.apm.2022.07.001

Cited by 5 publications

(2 citation statements)

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“…We test to what extent Fgf8a gradient shape can be explained by an effective porous medium. For this, we compare simulations in fully resolved ECS geometries with simulations in upscaled homogenizations [14, 45, 56]. In these homogenizations, the geometry is simplified to a spherical shell filled with a uniform porous material (see Fig.…”

Section: Resultsmentioning

confidence: 99%

“…Our model resolves the porous medium explicitly by resolving geometry and binding reactions at the “pore scale”. To test whether Fgf8a gradient shape can be explained by an effective porous medium, we compare simulations in a fully resolved ECS geometry with simulations in an upscaled homogenization [19, 54, 68]. In this homogenization, the geometry is simplified to a spherical shell by extracting the outer surfaces of our ECS geometry model at 60% epiboly, filled with a uniform porous material (see Fig.…”

Section: Resultsmentioning

confidence: 99%

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Morphogen gradients are regulated by porous media characteristics of the developing tissue

Stark,

Harish,

Sbalzarini

et al. 2024

Preprint

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Long-range morphogen gradients have been proposed to form by morphogen diffusion from a localized source to distributed sinks in the target tissue. The role of complex embryo geometries in this process is less well understood and ignored by most mathematical models. We address this by numerically reconstructing pore-scale 3D geometries of zebrafish embryos during epiboly from light-sheet microscopy images. In these high-resolution 3D geometries, we simulate Fgf8a gradient formation. The simulations show that when realistic embryo geometries are considered, a source-diffusion-degradation mechanism with additional binding to polymers of the extracellular matrix (HSPG) is sufficient to explain self-organized emergence and robust maintenance of Fgf8a gradients. The predicted normalized gradient is robust against changes in source and sink rates but sensitive to changes in the pore connectivity of the extracellular space, demonstrating the importance of considering realistic geometries when studying morphogen gradients.

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Section: Resultsmentioning

confidence: 99%