3D numerical simulation of orientated growth of axons in the nervous system
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    Abstract:

    Objective To study the orientated growth of axons in three-dimensional (3D) tissues, and to explore the effects on the rates of advancing, bundling and de-bundling of the axonal growth on an uneven surface of the extracellular matrices (ECM). Methods Based on the experimental observations, it is assumed that the traction for the axonal growth is proportional to the gradient of concentration of the diffusible attractants secreted by the target cells, and the lateral bundling or de-bundling force of the axons is proportional to the gradient of concentration which is the diffusible attractants or repellents secreted by the growth cones. The attractive force points to the uphill direction of the concentration field, the repulsive force points to the downhill direction, and the concentration itself satisfies the diffusion equation. When the growth cones crawl on an uneven surface of the ECM, only the tangential components of the above mentioned forces are helpful for the migration. In this numerical computing, 3D finite difference method and the improved Euler method were employed. Results (1) The basic characteristics of the orientated growth of axons in 3D tissues are similar to those in the 2D medium that were observed by the experiments, it is merely that they are morphologically termed by 2D or 3D problems. (2) The uneven of the ECM does affect the axonal growth. With the slope increasing, the advancing speed of the growth decreases and the lateral speed increases. Conclusions (1) Many mechanisms of the axonal growth revealed by the 2D culture experiments may be still valid in the corresponding 3D cases; (2) The geometry of the ECM is one of the key factors that have impacts on the rate of the axonal growth.

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.3D numerical simulation of orientated growth of axons in the nervous system[J]. Journal of medical biomechanics,2008,23(2):153-157

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