Investigating the effects of intrinsic diffusivity on neurite orientation dispersion and density imaging (NODDI)
Jose M Guerrero1, Nagesh Adluru2, Steven R Kecskemeti2, Richard J Davidson3, and Andrew L Alexander1

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

Synopsis

NODDI model and its widely used estimation toolbox assume the intracellular (or intrinsic) diffusivity (ID) to a fixed value suitable for healthy adult brains. For broader applicability of the model in neurological diseases it is important to understand the effects of ID. Using multi-shell diffusion data we investigated the variability of estimated NODDI indices as well as the model residuals with respect to variations in ID. Our results suggest that the value for ID cannot simply be set to that offering the least residual since there are appreciable effects on the indices even in a small range of ID values.

Purpose

NODDI1 aims to characterize brain tissue microstructure by estimating indices of neurite volume ($$$V_{ic}$$$), orientation concentration ($$$\kappa$$$), and cerebro-spinal fluid (CSF) volume ($$$V_{iso}$$$). NODDI has been adopted by numerous researchers for investigations of microstructure in early development, brain diseases and disorders.2-5 A key fixed parameter of the NODDI model that plays a role in both optimizing acquisition protocol6 as well as in estimating the indices is the intracellular parallel diffusivity ($$$d_{||}$$$). It is set to $$$1.7\times$$$10$$$^{-9}$$$m$$$^2\cdot$$$s$$$^{-1}$$$ in the widely distributed estimation toolbox.7 Although this assumption seems reasonable for a healthy adult brain,6 as NODDI gets applied in broader settings $$$d_{||}$$$ can vary between tissue types and conditions such as those in ischemic tissue.5,8 The main purpose of this work is to investigate the variability in the estimated NODDI indices and the accuracy of the NODDI model in explaining the multi-shell diffusion data as a function of $$$d_{||}$$$, for fixed acquisition and tissue types.

Methods

Multi-shell diffusion weighted data were acquired from three healthy teenage volunteers with $$$b$$$-values of 0, 350, 800 and 2500 s$$$\cdot$$$mm$$$^{-2}$$$. The analysis was focused on the mid axial slices which covered four major tissue types in the brain (Fig. 1(a)). NODDI indices were estimated for $$$d_{||}$$$ ranging from 0.5 to 3.0 with a step size of 0.1. Variability of indices. For each of the indices (Fig. 1(a)-(c)), its relationship with $$$d_{||}$$$ was modeled in four ROIs (Fig. 2). These dependency models were then tested for validity in all the voxels and the subjects by generating $$$R^2$$$ maps (Fig. 3). Model accuracy. The relationship between model accuracy as measured by root mean squared error (RMS) and $$$d_{||}$$$ was examined for each voxel in all the three subjects. For each voxel we found the $$$d_{||}$$$ at which NODDI model had least RMS (Fig. 4(a.1-3)). Then for each subject we found the most likely $$$d^{\ast}_{||}$$$ that resulted in the least RMS (Fig. 4(b.1-3)). The normalized RMS maps at $$$d^{\ast}_{||}$$$ were then examined qualitatively.

Results

The four ROIs and the NODDI maps (at $$$d_{||}=1.7$$$) are shown in Fig. 1(a-c). The scatter plots and variability models are shown in Fig. 2(a-c). For $$$\kappa$$$, a Gaussian function was the best fitting model, while for $$$V_{ic}$$$ and $$$V_{iso}$$$ linear and simple exponential functions best explained the variability. The voxelwise $$$R^2$$$ maps for these models are shown in Fig. 3 for all the subjects. The results of model accuracy analysis are shown in Fig. 4. The least RMS-$$$d_{||}$$$ maps are shown in Fig. 4(a.1-3). The histograms, corresponding densities, and the maximum likelihood $$$d_{||}$$$ for obtaining lowest RMS are presented in Fig. 4(b.1-3).

Discussion

There is a predictable effect of $$$d_{||}$$$ on the estimated NODDI indices. Specifically for $$$\kappa$$$, there is a Gaussian behavior with peak around $$$d_{||}\sim$$$0.7 and as $$$d_{||}$$$ crosses the 1.5 mark, the $$$\kappa$$$ values get lower and become less variable. This is reasonable as it can be expected that for higher $$$d_{||}$$$ reaching the free water diffusivity range, the dispersion would be isotropic resulting in smaller $$$\kappa$$$. To understand the effects on $$$V_{ic}$$$ and $$$V_{iso}$$$, let us recall the NODDI model $$A = (1-V_{iso})(V_{ic}A_{ic}+(1-V_{ic})A_{ic})+V_{iso}A_{iso},$$where $$$A_{ic}$$$, $$$A_{ec}$$$, and $$$A_{iso}$$$ are the normalized signals contributed by the intra-, extra-cellular, and CSF compartments respectively. For an observed signal $$$A$$$, we expect an inverse relationship between $$$V_{ic}$$$ and $$$V_{iso}$$$. Considering the dependency of $$$A_{ic}$$$ on the fiber response kernel, $$$\texttt{exp}(-b(q\cdot n)^{2}d_{||})$$$, for gradient direction $$$q$$$ and fiber orientation $$$n$$$, we can observe that $$$d_{||}$$$ and $$$A_{ic}$$$ have an inverse relationship implying that $$$d_{||}$$$ and $$$V_{ic}$$$ should be positively correlated. The $$$R^2$$$ maps show that these effects are spatially consistent across the voxels and subjects suggesting that there is an underlying theoretical relationship that needs to be investigated.

The RMS results (Fig. 4) suggest that the NODDI model best explains the multi-shell diffusion data when $$$d_{||}\sim$$$1.58, consistently for all the subjects. The NRMS maps reveal that at $$$d_{||}\sim$$$1.5, the model accuracy is the least in CSF regions. The variability and RMS results suggest that one can not simply set $$$d_{||}$$$ to the lowest RMS achievable since even in the 1.45-1.8 range there are appreciable effects on $$$V_{ic}$$$ and $$$V_{iso}$$$ in white and gray matter.

Conclusion

Our analysis suggests that mis-specifying $$$d_{||}$$$ during the NODDI model fitting could potentially bias the estimated indices. This hints that, when available, a priori knowledge on $$$d_{||}$$$ should be incorporated in the estimation by a simple two-line modification of the toolbox.7 Alternatively, if strong a priori information is unavailable, $$$d_{||}$$$ could be treated as a nuisance variable (random effect) in statistical analysis of the indices.

Acknowledgements

This work was supported in part by the Bill and Melinda Gates Foundation and NIH grants R21 NS091733, P50 NIMH100031, P30 HD003352, and UW ICTR (1UL1RR025011).

References

1. Zhang H, Schneider T, Wheeler-Kingshott C.A.M., et al. NODDI: Practical in vivo neurite orientation dispersion and density imaging of the human brain. NeuroImage 2012; 61: 1000-1016.

2. Eaton-Rosen, Z, Melbourne A, Orasanu E, et al. Longitudinal measurement of the developing thalamus in the preterm brain using multi-modal MRI. MICCAI 2014; Part II, LNCS 8674: 276-283.

3. Figini M, Baselli G, Riva M, et al. NODDI performs better thatn DTI in brain tumors with vasogenic edema. (2014) Proc. Intl. Soc. Mag. Reson. Med. 22 (2014)

4. Winston G. P, Micallef C, Symms M.R, et al. Advanced diffusion imaging sequences could aid assessing patients with focal cortical dysplasia and epilepsy. Epilepsy Res. 2014; 108(2):336-339.

5. Adluru G, Gur Y, Anderson, J.S, et al. Assessment of white matter microstructure in stroke patients using NODDI. Conf Proc IEEE Eng Med Biol Soc. 2014; 742-745.

6. Alexander, D.C. A General framework for experimental design in diffusion MRI and its application in measuring direct tissue-microstructure features. Magnetic Resonance in Medicine 2008; 60: 439-448.

7. http://nitrc.org/projects/noddi_toolbox

8. Beaulieu, C. The basis of anisotropic water diffusion in the nervous system - a technical review. NMR in Biomedicine 2002; 15(7-8):435-455.

Figures

Figure 1. (a) $$$\kappa$$$ map with manually drawn regions of interest (ROIs) encompassing white matter with coherent (WM||) and crossing (WMx) fibers, as well as gray matter (GM) and CSF regions. (b) $$$V_{ic}$$$ and (c) $$$V_{iso}$$$ maps from one of the volunteers.

Figure 2. Variability models relating the mean estimated indices for the subject and ROIs shown in Fig. 1(a) and $$$d_{||}$$$. (a) $$$\kappa$$$, (b) $$$V_{ic}$$$ and (c) $$$V_{iso}$$$. Each graph also shows the best fitting models for each ROI. The units of $$$d_{||}$$$ in this study are in $$$10^{-9}$$$m$$$^2\cdot$$$s$$$^{-1}$$$.

Figure 3. Maps of $$$R^2$$$ values from fitting the variability models deduced by ROI analysis (Fig. 2) at each voxel of the corresponding parameter maps ($$$\kappa$$$, $$$V_{ic}$$$,$$$V_{iso}$$$) for all three subjects (a,b,c).

Figure 4. (a) Maps of $$$d_{||}$$$ values that yielded best model fit per voxel as determined by the root mean squared residual (RMS). (b) Histogram analysis of $$$d_{||}$$$ maps. $$$d^{\ast}_{||}$$$ has the maximum likelihood of producing the smallest RMS. (c) The corresponding normalized RMS map for $$$d^{\ast}_{||}$$$.



Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
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