To minimize the time necessary to compute the Neurite Orientation Dispersion and Density Index (NODDI) model parametric maps in stroke studies. We compare the accuracy of and computation time required for two implementations of the NODDI model, the original non-linear fitting method [1] and the Accelerated Microstructure Imagine via Convex Optimization (AMICO) approach [2]. The latter model reduces the computation time markedly and here we investigate to what extent the maps of ‘Restricted Diffusion Index (RDI)’ (originally termed Neurite Density), ‘Orientation Dispersion Index (ODI)’, and isotropic Cerebrospinal Fluid (CSF) are of a comparable quality in stroke and normal subjects for the diffusion spectrum imaging acquisitions.

Data Acquisition: Diffusion spectrum imaging data with a b-max of 4000 and 203 directions [3] was acquired in 5 stroke studies and 4 normal studies on a Siemens 3T Verio scanner using a 32 channel head coil. A simultaneous multi-slice blipped CAIPI sequence [4] was used with a slice acceleration factor of three. The scan parameters were TR=3.7 sec, TE=114.2 msec, number of slices=51, slice thickness=2.1mm, total data acquisition time = 13 minutes.

Data Processing: Eddy current distortion correction of the images was first done using eddy in FSL [5]. The NODDI fitting to the acquired data was performed in Matlab [6,7]. The original and AMICO NODDI were computed for 5 stroke studies and for 4 normal studies. The absolute difference between the original and AMICO models was calculated for each of the parameter maps. Their difference was quantified for each case using the Kullback-Leibler divergence (KLD) as well as the Hellinger distance (HD) as in the following equations. $$KLD(F,G) = \int_{R}\ln\frac{f(x)}{g(x)}f(x)dx$$ $$HD(F,G) = \frac{1}{\sqrt{2}}\int_{R}(\sqrt{f(x)}-\sqrt{g(x)})^{2}dx$$ Both are methods to compute the distances between distributions f and g, where f is the original NODDI model (considered the ground truth here). The larger the value of the KLD, or HD the greater the difference in the maps generated by the two methods. The HD was computed so that its value was between 0 and 1. The AMICO NODDI contains three regularization parameters called λ1, λ2, and tolerance, which can be empirically tuned to data as needed. We calculated the HD and KLD statistics and the computation time from manipulating these three variables for one of our stroke study data sets. HD and KLD trends were in agreement so we chose to report only HD.

Figure 1 shows results comparing microstructure maps from a single slice from a stroke study and from a normal study respectively using both the original and AMICO NODDI. The absolute difference images show bigger differences in CSF maps in regions affected by stroke than in normal subjects. The KLD and HD measures showed similar trends and support the image based visual evidence that the AMICO NODDI model is comparable to the original NODDI. Figure 2 shows that overall for all studies, the models varied in the degree of similarity for normal and stroke studies depending on the microstructure map being observed. The HD values and standard deviations in normals were lower in CSF and ODI than in the stroke studies, but actually higher in RDI. The results summary found in Table 1 from tests of regularization parameters, shows that in some cases (RDI, Set 5), it is possible to reduce computation time and increase the similarity between the NODDI models for certain maps of interest. For Set 5, each of the regularization parameters were reduced by an order of magnitude.

The fast NODDI using AMICO provides results in much less time. Total computation time is reduced from 24-28 hours to 6-7 hours. In addition, because the AMICO is a two-step process that linearizes the computations, after kernels are calculated, parameters can be tuned to focus on a map of interest and produce those results in <80 minutes of computation. As evidenced by the HD values given in Figure 1 and Figure 2, there is less difference between the original and AMICO NODDI models for the CSF and ODI microstructure maps, and normal studies tend to show slightly less difference between methods overall than stroke studies except for in the RDI case. However, it was also demonstrated that the similarity of the RDI map can be tuned. Since the AMICO NODDI gives parameters comparable to the original NODDI, it is likely to make monitoring changes in brain microstructures over time more feasible and may contribute to a better understanding of the effects of medication on ischemic stroke recovery.