Robust and fast nonlinear optimization of diffusion MRI microstructure models

Abstract

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.

VERDICT‐AMICO: Ultrafast fitting algorithm for non‐invasive prostate microstructure characterization

“…VERDICT‐AMICO can fit the whole volume of interest (30 976 voxels) in less than 1 minute. Improvement in computation time could also potentially be achieved using large GPUs . However, AMICO provides an entirely complementary and direct reduction in computational cost.…”

“…Recently, ultrafast‐fitting algorithms have been developed to address the high computational cost of model‐based microstructure‐imaging techniques . Graphical processing units (GPUs) provide a brute‐force solution, using a parallelized approach, to reduce the computational time as in References and .…”

“…18,19 Recently, ultrafast-fitting algorithms have been developed to address the high computational cost of model-based microstructure-imaging techniques. [20][21][22] Graphical processing units (GPUs) provide a brute-force solution, using a parallelized approach, to reduce the computational time as in References 20 and 22. Although some overhead lies in GPU-based design and implementation, once adapted for GPU platforms the fitting time can be reduced by several orders of magnitude compared with standard central processing units, and is limited only by the number of cores on the GPU.…”

Ultra-high resolution blood volume fMRI and BOLD fMRI in humans at 9.4 T: Capabilities and challenges

“…The code implementing STARC is open source and can be downloaded from Github for Matlab https://github.com/diangraw/STARC-OptimalCoilCombo. In C++ https://github.com/layerfMRI/repository/tree/master/MYCOILCOMBINE and with GPU acceleration in Python https://github.com/cbclab/MCT (Harms et al, 2017; Kashyap et al, 2018). …”

SHORE‐based detection and imputation of dropout in diffusion MRI

“…For 5-20% of outliers in the simulation data, wL1 SHORE performs the best across all metrics in detecting signal dropout Figure 4 show the effect of signal imputation on diffusion and microstructural measures (FA: fractional anisotropy, MD: mean diffusivity, AK: axial kurtosis, ND: neurite density) obtained by means of stateof-the-art dMRI model fitting. 25 NMSE values are shown between the ground truth and the motion corrupted data set, as well as for data corrected via wL1 SHORE, REKINDLE, and GP. All imputation methods improved accuracy when estimating dMRI measures from corrupted data.…”