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I am studying tractography technique which aims to reconstruct bundles of axons in brain by following the diffusion direction of water. It is very interesting because it is non-invasive. It exploits the difference between grey matter and white matter: in white matter (axons) we find an anisotropic environment since there is a preferential direction of diffusivity of water molecules that is along the axons direction, while in grey matter the environment is isotropic since molecules do not move with a preferential direction. The diffusion of molecules is generally given by a difference of concentration of molecules between two points but they should move even though this gradient is not present because of the temperature so because of the fact that they have a certain thermal energy. Therefore my question is: why do molecules move along the axons direction ? Is there a biological aspect that causes like a difference in concentration between the starting point and the ending point ? Maybe the answer is trivial but since I am not a biologist I do not know it :) and I am not able to find something on web . It seems that I find only explanations for diffusion of water molecules from outside the cell to inside... I would like to know the reason why they move in the same direction of the axon.

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The movement is just the thermal energy motion you describe, not due to any concentration difference.

The anisotropy is due to the geometry. White matter tracts are effectively a dense bundle of thick, fatty hoses. Water can freely move in the tubes but cannot move as freely through the dense walls, so you see more movement along the axon length rather than perpendicular to them.

You can read more at https://en.wikipedia.org/wiki/Diffusion_MRI

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