Benoit Scherrer^{1}, Maxime Taquet^{1,2}, Etienne Saint-Onge^{1}, Gaetan Rensonnet^{2}, and Simon K Warfield^{3}

The DIAMOND diffusion compartment imaging (DCI) model has been recently proposed to model the 3-D diffusivity of each compartment with a statistical distribution of diffusion tensors. This enabled the assessment of compartment-specific diffusion characteristics while also capturing the intra-compartment heterogeneity. The approach, however, could only describe symmetric heterogeneity, while tissue heterogeneity likely differs along and perpendicular to the fascicles' orientation. In this work we propose a new statistical distribution model able to capture the asymmetric nature of tissue heterogeneity. We demonstrate that it captures different axial and radial heterogeneities in presence of dispersion and investigate results with in vivo data.

1. Scherrer, B., A. Schwartzman, M. Taquet, M. Sahin, S.P. Prabhu, and S.K. Warfield, Characterizing brain tissue by assessment of the distribution of anisotropic microstructural environments in diffusion-compartment imaging (DIAMOND). Magn Reson Med, 2016. 76(3): p. 963-977.

2. Zhang, H., T. Schneider, C.A. Wheeler-Kingshott, and D.C. Alexander, NODDI: practical in vivo neurite orientation dispersion and density imaging of the human brain. Neuroimage, 2012. 61(4): p. 1000-16. 3.

3. Efron, B., Estimating the error rate of a prediction rule: improvement on cross-validation. Journal of the American Statistical Association, 1983. 78(382): p. 316-331.

Shown are the symmetric compartment heterogeneity
index (cHEI) of DIAMOND and the asymmetric compartment heterogeneity index
(heiAD,heiRD) of ADIAMOND; the cAD and cRD and the fraction of isotropic
diffusion in presence of increasing dispersion. Results are shown without noise
(top) and with noise (bottom)

(a) Fascicle orientations in each voxel
estimated by ADIAMOND. (b-d) Symmetric
and asymmetric heterogeneity indexes of DIAMOND and ADIAMOND. (e) Fractional
anisotropy of the heterogeneity index of ADIAMOND, showing that the
heterogeneity is asymmetric is most of the brain. The heterogeneity is mostly symmetrical
in the CC, except near the inter-hemispheric plane

Zoom of the
heterogeneity in the CC, showing that the heterogeneity is asymmetric near the
genu of the CC (i) but symmetric in the splenium (ii).

(a) ROIs in which the
generalization error was assesssed, based on the highly asymmetric heterogeneity
in these regions. (a-b) Histograms showing the reduction of the generalization
error when using ADIAMOND instead of DIAMOND (negative result means a lower
generalization error with ADIAMOND).