Researchers and Clinicians developing and using diffusion imaging methods to study tissue microstructureDiffusion imaging is an established technique that provides in vivo information about the architecture of the brain and allows extraction of measures of its integrity. Several methods have been used to characterize the diffusion signal, and recently novel multi-shell methods have allowed analytical and continuous reconstruction of the diffusion propagator. The Simple Harmonic Oscillator based Reconstruction and Estimation (SHORE)¹ is one such method, and has been shown to provide better tissue contrast in propagator-based metrics than inherently incomplete discrete methods like DSI². However, existing metrics reduce the rich information present in the diffusion propagator to single scalar maps and discard potentially useful information about microstructure at the different scales probed by the propagator. In this study, we propose two new metrics to better characterize the diffusion propagator at different displacement radii, the Angular Complexity Index (ACI), as a measure of propagator anisotropy, and the Fractional Displacement Probability (FDP), as index of relative mean displacement probability within fixed displacement bands. Preliminary results are here presented on healthy in-vivo data.

Data acquisition: Diffusion MRI data were acquired from a single healthy normal volunteer using a 3T GE Signa HDx and consisted of sampling q-space on 6 different shells defined by b-values: 500, 750, 1000, 1500, 2000 and 3000 mm²/s. The number of directions for each shell was {20;20;40;40;60;60} respectively, and an additional {2;2;4;4;6;6} non-diffusion weighted volumes were collected alongside each shell. Acquisition parameters were the following for all shells: voxel size 2x2x2 mm, matrix = 128x128, FOV=256x56 mm, 70 slices, 1 average, TE=78 ms, using a single-shot spin-echo echo-planar imaging (EPI) sequence with an ASSET (parallel imaging) factor of 2. Peripheral gating was applied with effective TR of 12 R-R intervals. Additionally, an inversion recovery prepared spoiled gradient echo (IR-SPGR) structural image was acquired and used to perform EPI distortions correction of all diffusion data with ExploreDTI³, combined with motion and eddy current distortion correction.

Data Processing: After pre-processing, all shells were used to fit the coefficients of the 3D-SHORE basis, as implemented in dipy⁴, and the diffusion propagator was computed at a maximum displacement of 40$$$\mu m$$$, in a volume of 35x35x35 points, yielding a resolution of approximately 2$$$\mu m$$$. The ACI was then calculated as the “angular” standard deviation of the propagator over the sphere at displacement ($$$r$$$), normalized by the integral of the overall displacement probability:$$$ACI(r)=std(Propagator(r))/\int_{}^{} Propagator$$$. FDP maps were computed as the ratio between the integral defined within a displacement band demarcated by two radii $$$(r_{1},r_{2})$$$ and the total propagator integral as:$$$FDP(B) = \int_{r_{1}}^{r_{2}}Propagator /\int_{}^{} Propagator$$$. For both ACI and FDP maps, radii and bands can be chosen as required by the experiment. In this study we computed ACI at 2,10,16,22 and 28$$$\mu m$$$; the radii chosen for ACI computation defined the upper and lower limits of four different FDP bands, [A,B,C,D], respectively from 2-10,10-16,16-22 and 22-28$$$\mu m$$$.

Figure 1 shows that by measuring ACI at different ranges it is possible to extract different anisotropy contrasts from the diffusion propagator enabling the retrieval of anisotropic information that is characteristic of specific displacements ranges. In the enlarged region, different ACI contrasts can be identified in the region of the corona radiata (Fig1 red arrows) suggesting a different sensitivity to microstructural organisation at different displacement scales. Similarly, Figure 2 shows that with FDP maps it is possible to identify different probability of displacement within different displacement bands. For smaller displacement bands (Fig2.A), higher probabilities are confined to tissue with high restriction like white matter while for higher bands we see contribution only from CSF tissue (Fig2.D). While still preserving a model independent approach it was possible to identify and classify different tissues by looking at their characteristic displacement pattern in the different bands. These maps can potentially be used for new segmentations approaches and may also be able to better inform tractography algorithms in areas of complex microstructural configurations.In this study we have presented a new set of model independent diffusion metrics that extent the amount of information that can be extracted from the diffusion propagator. The additional contrast provided by ACI and FDP maps is complementary to currently existing and more global propagator metrics, such as return-to-origin probability (RT0P) and Mean squared Displacement (MSD) since they are specific only to selected ranges of diffusion displacements¹. These maps have the potential to provide further insight and facilitate exploration of brain microstructure organisation even when no a-priori biophysical model is available.