Robust, fast and accurate mapping of diffusional mean kurtosis

Reviewer #1 (Public Review):

Summary:
This study introduces an innovative method for assessing the mean kurtosis, utilizing the mathematical foundation of the sub-diffusion framework. In particular, a new fitting technique that incorporates two different diffusion times is proposed to estimate the parameters of the sub-diffusion model. The evaluation of this technique, which generates kurtosis maps based on the sub-diffusion framework, is conducted through simulations and the examination of data obtained from human subjects.

Strengths:
The utilization of the sub-diffusion model for tissue characterization is a significant conceptual advancement for the field of diffusion MRI. This study adeptly harnesses this approach for an accurate estimation of the parameters of the widely employed diffusion model, DKI, leveraging their established analytical interconnection as evidenced in prior research. Notably, this approach not only proposes a robust, fast, and accurate technique for DKI parameter estimation but also underscores the viability of deploying the sub-diffusion model for tissue characterization, substantiated by both simulated and human subject analyses. The paper is very-well written; well-organized; and coherent. The simulation study included different aspects of water diffusion as captured by diffusion-weighted MRI such as varying diffusion times and different b-value subpopulations, resulting in a comprehensive and thorough discussion.

Weaknesses:
The primary objective of this study is to demonstrate a robust approach for estimating DKI parameters by directly calculating them using the parameters of the sub-diffusion model. This premise, however, relies on the assumption that the sub-diffusion model effectively characterizes the diffusion MRI signal and that its parameters are both robust and accurate. Throughout the manuscript, the term "ground truth kurtosis K" is frequently used to denote the "true K" value in the context of the simulation study. Nonetheless, given that the data is simulated using the new sub-diffusion model - an approximation of the DKI-based signal expression- this value cannot truly be considered the "ground truth K". The simulation study highlights the robustness and accuracy of D* and K*, but it inherently operates under the assumption that the observed data is in the form of the sub-diffusion model.

Reviewer #2 (Public Review):

Summary: The authors present a technique for fitting diffusion magnetic resonance images (dMRI) to a sub-diffusion model of the diffusion process within brain imaging. The authors suggest that their technique provides robust and accurate calculation of diffusional kurtosis imaging parameters from which high quality images can be calculated from short dMRI data acquisitions at two diffusion times.

Strengths: If the authors can show that the dMRI signal in brain tissue follows a sub-diffusion model decay curve then their technique for accurately and robustly calculating diffusional kurtosis parameters from multiple diffusion times would be of benefit for tissue microstructural imaging in research and clinical arenas.

Weaknesses: The applied sub-diffusion model has two parameters that are invariant to diffusion time, D_β and β which are used to calculate the diffusional kurtosis measures of a diffusion time dependent D* and a diffusion time invariant K*. However, the authors do not demonstrate that the D_β, β and K* parameters are invariant to diffusion time in brain tissue. The authors' results visually show that there is time dependence of the K* measure (in Figure 6) that is more apparent in white matter with K* values being higher for diffusion times of ∆=49 ms than ∆ = 19 ms. The diffusion time dependence of K* indicates there is also diffusion time dependence of β. Furthermore, Figure 7 shows that there is a tissue specific root mean squared error in model fitting over the two diffusion times which indicates greater deviation from the model fit in white matter than grey matter. To show that the sub-diffusion model is robust and accurate (and consequently that K* is robust and accurate) the authors would have to demonstrate that there is no diffusion time-dependence in both D_β and β in application to brain imaging data for each diffusion time separately. Simulated data should not be used to demonstrate the robustness and accuracy of the sub-diffusion model or to determine optimization of dMRI acquisition parameters without first demonstrating that D_β and β are invariant to diffusion time. This is because simulated signals calculated by using the sub-diffusion charateristic equation of dMRI signal decay will necessarily have diffusion time invariant D_β and β parameters.

Without further information demonstrating diffusion time invariance of D_β, β and K* it is not possible to determine whether the authors have achieved their aims or that their results support their conclusions.