Abstract
To estimate microstructure-related parameters from diffusion MRI data, biophysical models make strong, simplifying assumptions about the underlying tissue. The extent to which many of these assumptions are valid remains an open research question. This study was inspired by the disparity between the estimated intra-axonal axial diffusivity from literature and that typically assumed by the Neurite Orientation Dispersion and Density Imaging (NODDI) model (d║ = 1.7μm2/ms). We first demonstrate how changing the assumed axial diffusivity results in considerably different NODDI parameter estimates. Second, we illustrate the ability to estimate axial diffusivity as a free parameter of the model using high b-value data and an adapted NODDI framework. Using both simulated and in vivo data we investigate the impact of fitting to either real-valued or magnitude data, with Gaussian and Rician noise characteristics respectively, and what happens if we get the noise assumptions wrong in this high b-value and thus low SNR regime. Our results from real-valued human data estimate intra-axonal axial diffusivities of ~ 2 – 2.5μm2/ms, in line with current literature. Crucially, our results demonstrate the importance of accounting for both a rectified noise floor and/or a signal offset to avoid biased parameter estimates when dealing with low SNR data.
Competing Interest Statement
The authors have declared no competing interest.
Footnotes
In our initial investigations we aimed to simultaneously estimate the three parameters dax, kappa, and F on a voxelwise basis. However, upon closer examination, the parameters were found to be degenerate, leading to an overestimation of dax. Key changes include: 1) Having discovered an important parameter degeneracy between F and dax, which are highly correlated, we now normalise by the powder averaged signal to avoid needing to estimate F. 2) In addition to real-valued and magnitude in vivo data, we use simulations to investigate the model parameter degeneracy and bias with respect to noise characteristics. Crucially, we found that the parameter degeneracies and bias could be overcome if we fitted to high SNR data (Figure 6) and explicitly model a Rician noise floor in magnitude data. Further, we found that real-valued data could provide more reliable and accurate estimates of dax and kappa (Figures 5 and 6). Consequently, for in vivo data we fitted to the concatenated signal across many voxels to boost SNR, include a noise floor parameter in the model fitting, and present results for both real-valued and magnitude images that were reconstructed from the same complex data of 6 healthy subjects. 3) When inspecting the in vivo data (Figure 2), we observe non-zero signal in the ventricles at high b-value. Here it is compelling that we see a similar offset both in real-valued data - where there is no rectified noise floor and where we typically expect the data to be Gaussian distributed and zero mean - and magnitude data. Consequently, we explicitly account for a signal offset when fitting the model. 4) We now include simulations that demonstrate how mis-estimation of the signal offset and/or Rician noise floor can substantially bias the other parameters (Figure 7). Therefore, we include both signal offset and noise floor as parameters of the model, rather than setting them to values estimated a priori (for example, setting them to values estimated from data in the ventricles, as was done previously). Our new results from in vivo, high b-value, real-valued data estimate axial diffusivities of 2-2.5 μm2/ms, in line with current literature (Figure 8) and substantially above that typically assumed by NODDI (1.7 μm2/ms). These results suggest that conventional NODDI modelling produces biased indices which are dependent on the modelling assumptions; secondarily, our results highlight the importance of incorporating noise characteristics of the data when working in a low-SNR regime.
