Biomedical subjects
Publications and source records attributed to N Rivier.
We present the first space-filling bearing in three dimensions. It is shown that a packing which contains only loops of an even number of spheres can be constructed in a self-similar way and that it can act as a three-dimensional bearing in which spheres can rotate without slip and with negligible torsion friction.
We give a review of the different models developed recently that describe the renewal of the epidermis. These models, based on concepts borrowed from statistical mechanics, geometry and topology, shed new light on the understanding of the organization and the dynamics of the system. We discuss in detail a topological model of the dynamics of the inner-most layer of the epidermis: the basal layer.
Using a topological approach, we study the dynamics of the basement membrane of the mammalian epidermis when basal cells detach or divide. A theoretical characterization of the steady state of the tissue, in very good agreement with experimental data, includes for the first time the division and the disappearance of cells in a two-dimensional random cellular structure. We predict a strong correlation between the size of the attachment of basal cells to the basement membrane and their biological behavior (division or detachment). This suggests that the main factor determining the fate of basal cells, and thus controlling the renewal of the epidermis, is the cells' surface tension and adhesion.
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A tissue is a geometrical, space-filling, random cellular network; it remains in this steady state while individual cells divide. Cell division is a local, elementary topological transformation which establishes statistical equilibrium of the structure. We describe the physical conditions to maintain stationary the epidermis (of mammals or of the cucumber), in spite of the fact that cells constantly divide and die. Specifically, we study the statistical equilibrium of the basal layer, a corrugated surface filled with cells, constituting a two-dimensional topological froth. Cells divide and detach from the basal layer, and these two topological transformations are responsible for the stationary state of the epidermis. The topological froth is capable of responding rapidly and locally to external constraints, and is a good illustration of the plasticity of random cellular networks. Statistical equilibrium is controlled by entropy, both as a measure of disorder and as information, and is characterized by observable relations between average cell shapes and sizes. The technique can be applied to any random cellular network in dynamical equilibrium. Mitosis as the dominating topological transformation and the fact that the distribution of cell shapes is very narrow are the only inputs specific to biology.
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