Probabilistic quantification of regional cortical microstructural complexity

(F) (G) (H) (I) (J) (A) (B) (C) (D) (E) (F) (G) (H) (I) (J) . The fiber orientation distribution (FOD) function was generated with 45 spherical harmonics (lmax=8) and was then reconstructed at 8000 equidistant points on the sphere, within each voxel. MBR Bootstrapping: In order to obtain residuals in a given voxel we spherically convolved the spherical harmonics of the FOD generated by CSD with the rotational harmonics of the response function. This gave us recovered HARDI signal, devoid of noise. Residuals were calculated by taking the difference between the recovered HARDI signal and the original HARDI signal. A new image set was created by randomly shuffling the residuals, for any given voxel, amongst all the diffusion-encoding directions and then adding them to the recovered HARDI signals. The image set created by each bootstrap sampling was then processed with CSD to generate new instances of the FODs. To further minimize the effects of noise we set a threshold to only accept those peaks on the FOD, as relating to the principle underlying intravoxel fiber orientations (one or more), whose magnitude was greater than 70% of the maximum peak magnitude on the FOD, in a given voxel. Probability of Number of Fiber Populations: The probability of observing n fiber orientations (n ∈ (1, 2, 3, >3)) was determined from the frequency of finding n fiber orientations over 100 MBR bootstrap iterations. Probability Distribution in Parcellated Regions: The median was calculated as the descriptor of the distribution of probabilities of n fiber orientations amongst all the voxels within each of the cortical and subcortical parcellated regions. In order to demonstrate inter-subject consistency we plotted the parcellation medians for one subject against each of the other subjects, and also plotted the group medians of the parcellation medians across all five subjects for the left hemisphere against the right to assess symmetry of cortical complexity. To obtain a statistical measure of inter-subject similarity we computed correlation coefficient matrices for the parcellation medians between all five subjects for each n and for cortical and subcortical regions separately. Results Various maps for a mid-volume coronal slice in one subject are shown in Figure 1. Fig. 1(A) shows an anisotropy map, followed by voxelwise maps of P(n = 1), P(n = 2), P(n = 3) and P(n > 3) (Fig. 1(B- E), respectively) over 100 MBR bootstrap iterations rendered with the same colormap scaled 0-100%. Color-rendered parcellation regions are overlaid on the corresponding contrast-reduced grayscale T1-weighted image in Fig. 1(F), which is followed by maps of the parcellation medians in this subject for P(n = 1), P(n = 2), P(n = 3) and P(n > 3) (Fig. 1(G-J), respectively) rendered with the same colormap but individually windowed to aid visualization for qualitative comparison. The plots in Fig. 2 have used different marker types and colors to separate cortical and subcortical parcellation regions and median probabilities for each n. The strong correspondence between group medians of parcellation medians in the left and right hemispheres is clearly evident in Fig. 2(A). The parcellation medians in the first subject also correspond well with the parcellation medians in the other four subjects (Fig. 2(B-E)). All of the off-diagonal entries in the matrices of correlation coefficients in Fig. 3 are statistically significant (p<0.01), with correlation coefficients being generally higher for subcortical parcellation regions (Fig. 2(A,C,E,G)) than cortical regions (Fig. 2(B,D,F,H)). Conclusion We have successfully shown consistency in the probability of finding different fiber configurations within parcellated cortical and subcortical regions both between hemispheres and amongst a small group of healthy subjects. This suggests that applying model-based residual bootstrapping to the CSD analysis of clinically- acquirable HARDI data can elucidate information about the underlying microstructural complexity. This information represents a non-invasive measure that is sensitive to cortical cytoarchitecture and that may be useful in cortical parcellation and in the identification of cortical lesions.