Constrained spherical deconvolution (CSD) of diffusion-weighted MRI (DW-MRI) is a popular analysis method that extracts the full white matter (WM) fiber orientation density function (fODF) in the living human brain, noninvasively. It assumes that the DW-MRI signal on the sphere can be represented as the spherical convolution of a single-fiber response function (RF) and the fODF, and recovers the fODF through the inverse operation. CSD approaches typically require that the DW-MRI data is sampled shell-wise, and estimate the RF in a purely spherical manner using spherical basis functions, such as spherical harmonics (SH), disregarding any radial dependencies. This precludes analysis of data acquired with nonspherical sampling schemes, for example, Cartesian sampling. Additionally, nonspherical sampling can also arise due to technical issues, for example, gradient nonlinearities, resulting in a spatially dependent bias of the apparent tissue densities and connectivity information. Here, we adopt a compact model for the RFs that also describes their radial dependency. We demonstrate that the proposed model can accurately predict the tissue response for a wide range of b-values. On shell-wise data, our approach provides fODFs and tissue densities indistinguishable from those estimated using SH. On Cartesian data, fODF estimates and apparent tissue densities are on par with those obtained from shell-wise data, significantly broadening the range of data sets that can be analyzed using CSD. In addition, gradient nonlinearities can be accounted for using the proposed model, resulting in much more accurate apparent tissue densities and connectivity metrics.

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Diffusion MRI (dMRI) has become an invaluable tool to assess the microstructural organization of brain tissue. Depending on the specific acquisition settings, the dMRI signal encodes specific properties of the underlying diffusion process. In the last two decades, several signal representations have been proposed to fit the dMRI signal and decode such properties. Most methods, however, are tested and developed on a limited amount of data, and their applicability to other acquisition schemes remains unknown. With this work, we aimed to shed light on the generalizability of existing dMRI signal representations to different diffusion encoding parameters and brain tissue types. To this end, we organized a community challenge - named MEMENTO, making available the same datasets for fair comparisons across algorithms and techniques. We considered two state-of-the-art diffusion datasets, including single-diffusion-encoding (SDE) spin-echo data from a human brain with over 3820 unique diffusion weightings (the MASSIVE dataset), and double (oscillating) diffusion encoding data (DDE/DODE) of a mouse brain including over 2520 unique data points. A subset of the data sampled in 5 different voxels was openly distributed, and the challenge participants were asked to predict the remaining part of the data. After one year, eight participant teams submitted a total of 80 signal fits. For each submission, we evaluated the mean squared error, the variance of the prediction error and the Bayesian information criteria. Most predictions predicted either multi-shell SDE data (37%) or DODE data (22%), followed by cartesian SDE data (19%) and DDE (18%). Most submissions predicted the signals measured with SDE remarkably well, with the exception of low and very strong diffusion weightings. The prediction of DDE and DODE data seemed more challenging, likely because none of the submissions explicitly accounted for diffusion time and frequency. Next to the choice of the model, decisions on fit procedure and hyperparameters play a major role in the prediction performance, highlighting the importance of optimizing and reporting such choices. This work is a community effort to highlight strength and limitations of the field at representing dMRI acquired with trending encoding schemes, gaining insights into how different models generalize to different tissue types and fiber configurations over a large range of diffusion encodings.

Tensor‐valued diffusion encoding facilitates data analysis by q‐space trajectory imaging. By modeling the diffusion signal of heterogeneous tissues with a diffusion tensor distribution (DTD) and modulating the encoding tensor shape, this novel approach allows disentangling variations in diffusivity from microscopic anisotropy, orientation dispersion, and mixtures of multiple isotropic diffusivities. To facilitate the estimation of the DTD parameters, a parsimonious acquisition scheme coupled with an accurate and precise estimation of the DTD is needed. In this work, we create two precision‐optimized acquisition schemes: one that maximizes the precision of the raw DTD parameters, and another that maximizes the precision of the scalar measures derived from the DTD. The improved precision of these schemes compared to a naïve sampling scheme is demonstrated in both simulations and real data. Furthermore, we show that the weighted linear least squares (WLLS) estimator that uses the squared reciprocal of the noisy signal as weights can be biased, whereas the iteratively WLLS estimator with the squared reciprocal of the predicted signal as weights outperforms the conventional unweighted linear LS and nonlinear LS estimators in terms of accuracy and precision. Finally, we show that the use of appropriate constraints can considerably increase the precision of the estimator with only a limited decrease in accuracy.

Fitting the diffusion kurtosis imaging free water elimination model (DKI-FWE) to diffusion MRI data represents an ill-conditioned problem. Fortunately, the conditioning of the model fitting can be improved by explicitly modeling the T2 relaxation dependency of the signal. As a benefit, diffusion and kurtosis metrics robust to partial volume effects can be estimated with conventional techniques. In this work, we use Cramér-Rao lower bound (CRLB) theory to identify optimal acquisition settings that maximize the precision of the model parameter estimates.