On the use of the two-pool model to improve the accuracy of axon calibration

Target audience This abstract is intended for microstructure modeling community, in particular for axon diameters inference Purpose We here propose to study the reason for the systematic overestimation of the smaller radius in available axon diameter mapping techniques such as AxCaliber [1] or ActiveAx [2]. In these studies, white matter is decomposed using the CHARMED model relying on the use of two compartments, a restricted compartment corresponding to axons modeled as impermeable cylinders, and an hindered compartment corresponding to the extra-cellular space and glial cells with low residence time modeled using a Gaussian distribution. Recent studies[3] have introduced an alternative model stemming from the assumption of a biphasic behaviour of water molecules in an environment restricted by membranes : water molecules close to the membranes have a slow diffusivity characterized by a high anisotropy while those far from the membranes are characterized by a fast diffusivity and a slower anisotropy, yielding the two-pool model. In [4], we developped the equation of the signal attenuation for a two-pool thick layer cylinder for a PGSE experiment under the Gaussian phase distribution approximation . This model is composed of two pools of water molecules : a layer of molecules with a slow diffusivity (the membrane is in in the middle of this layer) and a cylinder with a fast diffusivity, corresponding to the molecules far from the membranes. This study shows how attenuations for small radii (<=3um) from the two-pool model when varying the thickness of the layer close to axonal membranes can be similar to attenuations from the simple cylinder model with higher radius. Methods The echo attenuation under the Gaussian phase distribution approximation for a PGSE experiment using a two-pool cylinder model of the axon is given for the fast part by the echo attenuation in a cylinder introduced by [4]. The slow attenuation, corresponding to the attenuation of the layer around the membranes (the membrane is in the middle of the slow layer) is developed in [5], assuming no exchange between the pools: