We use a single restricted compartment of unknown orientation as a model for our phantoms. All microcapillaries (representing axons) are parallel and non-abutting cylinders, with equal radii and impermeable walls. The parameters of the model are (1) intrinsic diffusivity, D_{j}, (2) microcapillary diameter, a and (3) microcapillary direction, n.

The restricted diffusion signal, S_{r}, can be written as the product of components arising from displacements parallel, S_{r}y, and perpendicular, S_{r}?, to the long axis of the microcapillary as described in [20]. The model for S_{r}? is calculated using the Gaussian phase distribution approximation (GPD) [21] for a diffusion gradient perpendicular to the microcapillary with strength |G| sin в, where в is the angle between n and G. S_{r}|| describes free diffusion with D_{j} for a diffusion gradient parallel to the microcapillary with strength |G| cos в, and is calculated using S_{r}|| = exp(—b cos^{2}вD_{j}/, where the b-value for trapezoidal OGSE is from [22].

The total signal accounting for both components (S_{r}|| and S_{r}?) is:

where So is the MR signal without diffusion weighting.