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The scale of bony fish, such as goldfish or carp, has layer structure of two layers; the upper one is the calcified layer, and the lower the fibrous layer. The fibrous layer is formed by a large number of stratified thin sheets of collagen fibers with no cell inside. The collagen fibers are produced as molecules by the osteoblasts (bone formative cells) located at the floor of the fibrous layer, associate after secretion, and then align to form thin sheets; but the mechanisms are unknown.
We present a model of autonomous association and alignment system of fiber molecules. The distribution of molecules is approximated by continuously distributed dipoles, and is assumed to form some potential fields for self-attraction and orientation. We then describe the model by a system of parabolic and elliptic PDEs like chemotaxis systems. Some mathematical analysis and numerical simulation will be also demonstrated in the presentation. |
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