Iterative Subspace Screening for Rapid Sparse Estimation of Brain Tissue Microstructural Properties

Robust and fast nonlinear optimization of diffusion MRI microstructure models

Advances in biophysical multi-compartment modeling for diffusion MRI (dMRI) have gained popularity because of greater specificity than DTI in relating the dMRI signal to underlying cellular microstructure. A large range of these diffusion microstructure models have been developed and each of the popular models comes with its own, often different, optimization algorithm, noise model and initialization strategy to estimate its parameter maps. Since data fit, accuracy and precision is hard to verify, this creates additional challenges to comparability and generalization of results from diffusion microstructure models. In addition, non-linear optimization is computationally expensive leading to very long run times, which can be prohibitive in large group or population studies. In this technical note we investigate the performance of several optimization algorithms and initialization strategies over a few of the most popular diffusion microstructure models, including NODDI and CHARMED. We evaluate whether a single well performing optimization approach exists that could be applied to many models and would equate both run time and fit aspects. All models, algorithms and strategies were implemented on the Graphics Processing Unit (GPU) to remove run time constraints, with which we achieve whole brain dataset fits in seconds to minutes. We then evaluated fit, accuracy, precision and run time for different models of differing complexity against three common optimization algorithms and three parameter initialization strategies. Variability of the achieved quality of fit in actual data was evaluated on ten subjects of each of two population studies with a different acquisition protocol. We find that optimization algorithms and multi-step optimization approaches have a considerable influence on performance and stability over subjects and over acquisition protocols. The gradient-free Powell conjugate-direction algorithm was found to outperform other common algorithms in terms of run time, fit, accuracy and precision. Parameter initialization approaches were found to be relevant especially for more complex models, such as those involving several fiber orientations per voxel. For these, a fitting cascade initializing or fixing parameter values in a later optimization step from simpler models in an earlier optimization step further improved run time, fit, accuracy and precision compared to a single step fit. This establishes and makes available standards by which robust fit and accuracy can be achieved in shorter run times. This is especially relevant for the use of diffusion microstructure modeling in large group or population studies and in combining microstructure parameter maps with tractography results.

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Evaluate robustness of fit, accuracy, precision for diffusion microstructure models

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Test three optimization algorithms and three parameter initialization strategies

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GPU implementation removes run time constraints; whole brain fit within minutes

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Powell conjugate-direction algorithm has superior fit, accuracy, precision

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Initialization approaches are important for crossing fiber microstructure models

Multi-Tissue Decomposition of Diffusion MRI Signals via Sparse-Group Estimation

Sparse estimation techniques are widely utilized in diffusion magnetic resonance imaging (DMRI). In this paper, we present an algorithm for solving the ℓ₀ sparse-group estimation problem and apply it to the tissue signal separation problem in DMRI. Our algorithm solves the ℓ₀ problem directly, unlike existing approaches that often seek to solve its relaxed approximations. We include the mathematical proofs showing that the algorithm will converge to a solution satisfying the firstorder optimality condition within a finite number of iterations. We apply this algorithm to DMRI data to tease apart signal contributions from white matter, gray matter, and cerebrospinal fluid with the aim of improving the estimation of the fiber orientation distribution function (FODF). Unlike spherical deconvolution approaches that assume an invariant fiber response function (RF), our approach utilizes an RF group to span the signal subspace of each tissue type, allowing greater flexibility in accounting for possible variations of the RF throughout space and within each voxel. Our ℓ₀ algorithm allows for the natural groupings of the RFs to be considered during signal decomposition. Experimental results confirm that our method yields estimates of FODFs and volume fractions of tissue compartments with improved robustness and accuracy. Our ℓ₀ algorithm is general and can be applied to sparse estimation problems beyond the scope of this paper.