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Ronse, Christian; Tajine, Mohamed

doi:10.1023/a:1008366032284

Cited by 32 publications

(1 citation statement)

References 22 publications

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“…The motivation comes from the fact that in comparing two different organisms of the same species and age, we expect some differences between them -the exact length and width of limbs, for example -but the general shapes ought to be similar; limbs should not be growing from different places or missing altogether. Our metric is based off of the Hausdorff distance [44] and the Minkowski metric as defined on the Minkowski spacetime [35]. Indeed, since the definition of biological structures includes cell-birth parameters, we need a notion of spacetime interval.…”

Section: Examples Of Admissible and Inadmissible Sets Of Cell Bodies mentioning

confidence: 99%

Morphogenesis modelization of a fractone-based model

Chyba¹,

Tamura-Sato²

2017

Discrete &Amp; Continuous Dynamical Systems - B

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It has been hypothesized that the generation of new neural cells (neurogenesis) in the developing and adult brain is guided by the extracellular matrix. The extracellular matrix of the neurogenic niches features specialized structures termed fractones, which are scattered in between stem/progenitor cells and bind and activate growth factors at the surface of stem/progenitor cells to influence their proliferation. We present a mathematical control model that considers the role of fractones as captors and activators of growth factors, controlling the rate of proliferation and directing the location of the newly generated neuroepithelial cells in the forming brain. The model is a hybrid control system that incorporates both continuous and discrete dynamics. The continuous dynamics of the model features the diffusion of multiple growth factor concentrations through the mass of cells, with fractones acting as sinks that absorb and hold growth factor. When a sufficient amount has been captured, growth is assumed to occur instantaneously in the discrete dynamics of the model, causing an immediate rearrangement of cells, and potentially altering the dynamics of the diffusion. The fractones in the model are represented by controls that allow for their dynamic placement in and removal from the evolving cell mass.

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Section: Examples Of Admissible and Inadmissible Sets Of Cell Bodies mentioning

confidence: 99%