Comparison of basis functions and q-space sampling schemes for robust compressed sensing reconstruction accelerating diffusion spectrum imaging

Time constraints placed on magnetic resonance imaging often restrict the application of advanced diffusion MRI (dMRI) protocols in clinical practice and in high throughput research studies. Therefore, acquisition strategies for accelerated dMRI have been investigated to allow for the collection of versatile and high quality imaging data, even if stringent scan time limits are imposed. Diffusion spectrum imaging (DSI), an advanced acquisition strategy that allows for a high resolution of intra-voxel microstructure, can be sufficiently accelerated by means of compressed sensing (CS) theory. CS theory describes a framework for the efficient collection of fewer samples of a data set than conventionally required followed by robust reconstruction to recover the full data set from sparse measurements. For an accurate recovery of DSI data, a suitable acquisition scheme for sparse q-space sampling and the sensing and sparsifying bases for CS reconstruction need to be selected. In this work we explore three different types of q-space undersampling schemes and two frameworks for CS reconstruction based on either Fourier or SHORE basis functions. After CS recovery, diffusion and microstructural parameters and orientational information are estimated from the reconstructed data by means of state-of-the-art processing techniques for dMRI analysis. By means of simulation, diffusion phantom and in vivo DSI data, an isotropic distribution of q-space samples was found to be optimal for sparse DSI. The CS reconstruction results indicate superior performance of Fourier-based CS-DSI compared to the SHORE-based approach. Based on these findings we outline an experimental design for accelerated DSI and robust CS reconstruction of the sparse measurements that is suitable for the application within time-limited studies.

Compressed Sensing Diffusion Spectrum Imaging for Accelerated Diffusion Microstructure MRI in Long-Term Population Imaging

Mapping non-invasively the complex microstructural architecture of the living human brain, diffusion magnetic resonance imaging (dMRI) is one of the core imaging modalities in current population studies. For the application in longitudinal population imaging, the dMRI protocol should deliver reliable data with maximum potential for future analysis. With the recent introduction of novel MRI hardware, advanced dMRI acquisition strategies can be applied within reasonable scan time. In this work we conducted a pilot study based on the requirements for high resolution dMRI in a long-term and high throughput population study. The key question was: can diffusion spectrum imaging accelerated by compressed sensing theory (CS-DSI) be used as an advanced imaging protocol for microstructure dMRI in a long-term population imaging study? As a minimum requirement we expected a high level of agreement of several diffusion metrics derived from both CS-DSI and a 3-shell high angular resolution diffusion imaging (HARDI) acquisition, an established imaging strategy used in other population studies. A wide spectrum of state-of-the-art diffusion processing and analysis techniques was applied to the pilot study data including quantitative diffusion and microstructural parameter mapping, fiber orientation estimation and white matter fiber tracking. When considering diffusion weighted images up to the same maximum diffusion weighting for both protocols, group analysis across 20 subjects indicates that CS-DSI performs comparable to 3-shell HARDI in the estimation of diffusion and microstructural parameters. Further, both protocols provide similar results in the estimation of fiber orientations and for local fiber tracking. CS-DSI provides high radial resolution while maintaining high angular resolution and it is well-suited for analysis strategies that require high b-value acquisitions, such as CHARMED modeling and biomarkers from the diffusion propagator.

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