To extract histologically relevant biophysical parameters from diffusion data in neocortex using a method combining surface based techniques and a three-compartment diffusion model.Our diffusion model consists of two types of compartment: intraneurite, and extraneurite. By modelling neocortical neurons using two populations of sticks (Figure 1)—`radially' distributed sticks perpendicular to the cortical surface, and `tangential' sticks distributed isotropically parallel to the cortical surface—we separate the volume fraction of the intraneurite compartment into radial and tangential components. Following Zhang, et al.¹, the diffusion tensor of the extraneurite compartment is computed by averaging the relation in Szafer, et al.² over all stick populations. A free diffusivity parameter (assumed to be equal for intra- and extra-neurite diffusion) is also fitted, giving three parameters to be fit: radial neurite volume fraction, tangential neurite volume fraction, and diffusivity.

We test our model using a multi-$$$b$$$-value $$$200~\mu$$$m isotropic resolution dataset of a post-mortem human V1 tissue sample from Kleinnijenhuis, et al.³. Data were preprocessed as described in that publication.

Radial cortical directions were estimated with CBS Tools⁴ as the normal vectors to the cortical depth isosurfaces computed with an equivolume model⁵ with 10 estimated depth layers, based on a GM mask manually delineated inside V1 on a $$$b=0$$$ image. Cortical depth values were estimated at each voxel based upon its distance to the closest two layers.

NODDI toolbox v0.9⁶ was used to implement and fit the model, with the radial direction fixed at the values computed using CBS Tools. Comparison is made to a fit using the NODDI model with standard ex vivo parameters and unfixed intraneurite diffusivity^1,7.

Cortical profiles were constructed by binning fitted parameter values into 20 equally spaced bins according to the cortical depth value of each voxel. This number of bins was chosen to include approximately 1000 voxels in each bin. The mean and standard deviation of each bin were plotted as a function of cortical depth. The cortical depth corresponding to the stria of Gennari^8,9 was demarked along a profile of cortex manually based upon a $$$b=0$$$ image.

Figure 2 shows the cortical depth measures and radial cortical directions computed within the GM mask, along with cortical profiles of the fitted parameters. Diffusivity varies strongly near the pial surface, reflecting partial volume effects.

The stria of Gennari^8,9 can be seen prominently in both volume fractions (Figure 2), in line with previous diffusion studies^3,7,10. Our data also show an increase in tangential volume fraction near the pial surface border, a feature known from histology⁸ and diffusion studies, though here the assumption of isotropic tangential neurite distribution means directionality of these neurites¹⁰ could not be examined.

Figure 4 shows comparison with parameters obtained using the NODDI model, a model containing a similar overall number of fitted parameters to that presented here, where instead of two populations of sticks a single dispersed population of sticks is assumed. Although the NODDI model is not representative of the known crossing-fibre structure of neocortex, it has been shown previously to capture known neocortical features⁷. While quantitative comparison is a subject of further work, the NODDI parameters representing intraneurite volume fraction and dispersion do seem to capture the same cortical features; the parameters generated in this work are however more readily interpretable in terms of intracortical fibre connections.

The model presented here is intentionally very simple, ignoring effects including the known anisotropy of cortical layer I neurites¹⁰, exchange, and oblique neurites^8,9. Given the present model's simplicity, and the rich amount of information contained in the diffusion signal, further work will investigate their inclusion. However, the validation presented here already outlines the interest of this model, in particular for in vivo studies of intracortical anatomy and connectivity.

We have demonstrated that a diffusion model with only three fitted parameters can capture radial and tangential features of neocortical structure. Further studies will interrogate their meaning, particularly how well they represent intracortical collaterals and association fibres.