[Paper Review] Improved reproducibility of diffusion kurtosis imaging using regularized non-linear optimization informed by artificial neural networks

Leevi Kerkelä, Kiran Seunarine+3 more|arXiv (Cornell University)|Mar 14, 2022

Advanced Neuroimaging Techniques and Applications4 citations

TL;DR

This paper proposes a novel regularized non-linear optimization framework for diffusion kurtosis imaging (DKI) that uses artificial neural networks to predict kurtosis metrics (MK, AK, RK) from high-quality dMRI data, which are then used to regularize the fitting process. The method significantly improves reproducibility and robustness—especially in white matter tracts with low radial diffusivity—achieving DKI parameter reproducibility comparable to diffusion tensor imaging (DTI) on clinical scan-rescan data.

ABSTRACT

Diffusion kurtosis imaging is an extension of diffusion tensor imaging that provides scientifically and clinically valuable information about brain tissue microstructure but suffers from poor robustness to noise, especially in voxels containing tightly packed aligned axons. We present a new algorithm for estimating diffusion and kurtosis tensors using regularized non-linear optimization and make it publicly available in an easy-to-use open-source Python software package. Our approach uses fully-connected feed-forward neural networks to predict kurtosis values in voxels where the standard non-linear least squares fit fails. The predicted values are then used in the objective function to avoid implausible kurtosis values. We show that our algorithm is more robust than standard non-linear least squares and a previously proposed regularized non-linear optimization method. The algorithm was then applied on a multi-site scan-rescan dataset acquired using a clinical scan protocol to assess the reproducibility of diffusion kurtosis parameter estimation in human white matter using the proposed algorithm. Our results show that the reproducibility of diffusion kurtosis parameters is similar to diffusion tensor parameters.

Motivation & Objective

• To address the poor robustness of standard non-linear least squares (NLLS) in DKI, especially in voxels with tightly packed axons where kurtosis values become implausible (e.g., negative).
• To improve reproducibility of DKI parameters in clinical settings by reducing noise-induced instability in parameter estimation.
• To develop a generalizable, open-source software solution that enhances DKI reliability without requiring ground truth data.
• To investigate whether regularization using neural network predictions of MK, AK, and RK can outperform existing methods that only regularize MK.
• To validate the method on a multi-site, scan-rescan dataset using a standard clinical protocol.

Proposed method

• Trained fully-connected feed-forward neural networks to predict mean kurtosis (MK), axial kurtosis (AK), and radial kurtosis (RK) from diffusion-weighted imaging (dMRI) data in voxels where standard NLLS produced only non-negative kurtosis values.
• Used the neural network predictions as regularization terms in a non-linear least squares objective function, penalizing deviations from predicted values during optimization.
• Applied the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm to solve the regularized non-linear optimization problem with a hybrid objective combining data fidelity and regularization.
• Constructed a training dataset from high-quality dMRI scans where NLLS produced valid (non-negative) kurtosis values, assuming this subset captures diverse microstructural conditions.
• Integrated the method into an open-source Python package (available at https://github.com/kerkelae/dkmri) for reproducible, accessible use in the research community.
• Used a hyperparameter α to balance the influence of data fit and regularization, which must be tuned per acquisition protocol.

Experimental results

Research questions

• RQ1 Can neural network-predicted kurtosis metrics improve the robustness of DKI parameter estimation compared to standard NLLS and prior regularization methods?
• RQ2 Does regularization using predictions of MK, AK, and RK—rather than only MK—lead to more plausible kurtosis tensor estimates in low-radial-diffusivity regions?
• RQ3 To what extent does the proposed method improve the reproducibility of DKI parameters in a multi-site, scan-rescan clinical dMRI protocol?
• RQ4 How does the reproducibility of DKI parameters estimated with the new method compare to that of DTI parameters under identical acquisition conditions?
• RQ5 Is the method generalizable across different clinical acquisition protocols, and how sensitive is it to data quality and hyperparameter choice?

Key findings

• The proposed method significantly reduced the number of voxels with implausible negative kurtosis values compared to standard NLLS and the prior regularization method that used only MK predictions.
• Reproducibility of DKI parameters (measured by coefficient of variation) was comparable to that of DTI parameters across major white matter tracts in a multi-site scan-rescan dataset.
• The method achieved high prediction accuracy for MK, AK, and RK on the training data, suggesting minimal bias introduction relative to standard NLLS.
• The algorithm demonstrated improved stability in challenging regions such as the splenium and genu of the corpus callosum, where radial diffusivity is low and standard NLLS often fails.
• The open-source software package enables widespread adoption and further methodological development in the neuroimaging community.
• The method remains sensitive to initial parameter values and hyperparameter α, which must be tuned per acquisition protocol to achieve optimal performance.