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Residual analysis reveals variation of the intrinsic diffusivity throughout the brain in neurite orientation dispersion and density imaging (NODDI)
Jose M Guerrero1, Nagesh Adluru2, Steven Kecskemeti2, Richard Davidson3, Hui Zhang4, and Andrew L Alexander5

1Medical Physics, University of Wisconsin - Madison, Madison, WI, United States, 2Waisman Center, University of Wisconsin - Madison, Madison, WI, United States, 3Psychology and Psychiatry, University of Wisconsin - Madison, Madison, WI, United States, 4Department of Computer Science, University College London, London, United Kingdom, 5Medical Physics, Psychiatry, University of Wisconsin - Madison, Madison, WI, United States

Synopsis

NOODI and its widely used estimation toolbox assume the intrinsic diffusivity to a fixed value suitable for healthy adult brains. For broader applicability of the model in neurological diseases it is important to understand the validity of assumed fixed intrinsic diffusivity. Using multi-shell diffusion data we investigated the variability of estimated NODDI indices as well as the model residuals with respect to variations in intrinsic diffusivity. The results suggest significant differences between optimum intrinsic diffusivity for white and gray matter regions as derived from intrinsic diffusivity values that generate smallest model residuals. The variability analysis indicates appreciable differences in the estimated parameters in the range of probable diffusivities predicted by the residual analysis.

Introduction

NODDI1 was developed to better characterize brain tissue microstructure from estimates of neurite volume fraction ($$$V_{ic}$$$), orientation concentration ($$$\kappa$$$), and free water (CSF) volume fraction($$$V_{iso}$$$). Since its publication in 2012, NODDI has been adopted in numerous studies for investigating microstructure in early development and other neurological conditions.2-8 One of the key fixed parameters of the NODDI model that plays a role in both optimizing acquisition protocol9 as well as in the model fitting is the intracellular parallel diffusivity ($$$d_{||}$$$) also referred as the intrinsic diffusivity. It is set to $$$1.7 μm^2ms^{-1}$$$ in the widely distributed estimation toolbox 10 as well as in protocol optimization.9 This value was estimated from the corpus callosum midsagittal plane of a healthy brain. Assuming minimal orientation dispersion, the axial diffusivity averaged over the region was estimated and used to provide an estimate for the intrinsic diffusivity. Although this assumption seems reasonable in the major tissues types of a healthy adult brain,9 as NODDI gets applied in broader settings, $$$d_{||}$$$ can vary between tissue types and pathology conditions. The main purpose of this work is to formally investigate the variability in (1) the estimated NODDI indices and (2) the accuracy of the NODDI model in terms of explaining the multi-shell diffusion data as a function of $$$d_{||}$$$.

Methods

Data acquisition. Multi-shell diffusion weighted data were acquired from 5 groups of healthy volunteers (3 subjects per group, ages 1 month-72 years) on a GE 3.0 T scanner with group specific diffusion imaging parameters. Group 1 (infants): 63 directions, b: 350, 800, 1500. Group 2 (adolescents): 62 directions, b: 320, 800, 2500. Group 3 (adolescents): 57 directions, b: 500, 800, 2000. Group 4 (20-40 years): 57 directions, b: 500, 800, 2000. Group 5 (>45 years) : 105 directions, b: 300, 1200, 2700, 4800, 7500.

Analysis. NODDI indices were estimated for 16 $$$d_{||}$$$ values in the 0.5-2.0 range with a step size of 0.1 $$$μm^2ms^{-1}$$$.

Tissue segmentation. White matter (WM) and gray matter (GM) segmentations and corresponding masks where computed using FSL FAST11 on mean diffusivity and fractional anisotropy maps, which themselves where obtained by estimating the diffusion tensors from the lowest b-value diffusion weighted volumes.

Model accuracy. The relationship between model accuracy, as measured by root mean squared error (RMSE), and $$$d_{||}$$$ was examined for each voxel in all subjects. Mean RMSE values were computed across each tissue type as a function of $$$d_{||}$$$. Then, for each voxel the $$$d_{||}$$$ at which the model had the least RMSE was found, which we refer to as the optimal $$$d_{||}$$$. Optimal intrinsic diffusivity maps were segmented into WM and GM using the previously computed masks. The value of $$$d_{||}$$$ that resulted in the smallest RMSE for most voxels for each tissue type was then found by histogram analysis.

Variability of indices. For each $$$d_{||}$$$, $$$\kappa$$$, $$$V_{ic}$$$, and $$$V_{iso}$$$ maps were segmented into WM and GM. The mean for each parameter across tissue type was calculated as a function of $$$d_{||}$$$.

Results

Except for the infants in Group 1, GM mean RMSE curves (Figure-1) have minima at values of $$$d_{||}$$$ that are considerably lower (<1) than the default. For Group 1, minima for the WM RMSE curves occur at values slightly less than the default. Minima in WM RMSE curves are difficult to assess for the other groups as the model residuals in WM are fairly flat for $$$d_{||}$$$ greater than 1.3. Optimal $$$d_{||}$$$ maps (Figure-2) reveal significant differences between optimum $$$d_{||}$$$ for WM and GM regions. This is confirmed with the histogram analysis (Figure-3). Compared to the default diffusivity, mode values are much lower for all groups in GM and higher in WM, except for the infants in Group 1 which also have lower than default values in WM. Figure-4 demonstrates that there are appreciable differences in the estimated parameters across the range of probable diffusivities predicted by the residual analysis [~0.7,2] for all groups.

Conclusion

Our analysis of variability and model accuracy suggests that the fixed model parameter of $$$d_{||}=1.7μm^2ms^{-1}$$$ may be suboptimal and appears different for GM and WM. Further, the optimum $$$d_{||}$$$ may vary with age and protocol. This hints that, when available, a priori knowledge on $$$d_{||}$$$ should be incorporated in the estimation process by a simple two line modification of the MatLab code.7 Future work will conduct a more thorough evaluation of the effects of age and acquisition parameters on the optimal $$$d_{||}$$$ as obtained with the RMSE analysis and examine the model behavior for larger values of $$$d_{||}$$$ (up to $$$3.0 μm^2ms^{-1}$$$).

Acknowledgements

This work has received support from the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1256259, the Science and Medicine Scholars Graduate Research Fellowship, and NIH grants HD090256, MH100031, and NS091733.

References

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Figures

Mean of RMS residuals as function of intrinsic diffusivity in white and gray matter. At each voxel, the RMS residual was obtained for the 16 equally spaced diffusivities in 0.5-2. The mean RMS residual was obtained for segmented white and gray matter regions. This was done for each of the three subjects in each group.

Voxel-wise maps of the residual-analysis-based optimal intrinsic diffusivity. Sagittal, coronal, and axial views of optimal diffusivity maps are shown from one subject in each of the groups. Each voxel contains the diffusivity value that resulted in the smallest RMS residual between the measured an predicted signals.

Optimal intrinsic diffusivity distributions in white and gray matter. For all subjects, the optimal intrinsic diffusivity maps like those shown in Figure 2 were segmented into white and gray matter and the corresponding distributions were plotted.

Mean NODDI parameters as functions of intrinsic diffusivity in white and gray matter. NODDI estimated parameter maps were segmented into white and gray matter regions. Mean values of each parameter were calculated in each tissue type as a function of intrinsic diffusivity.

Proc. Intl. Soc. Mag. Reson. Med. 26 (2018)
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