Diffusion-weighted imaging is a non-invasive functional imaging modality for breast tumor characterization through apparent diffusion coefficients. Yet, it has so far been unable to intuitively inform on tissue microstructure. In this IRB-approved prospective study, we applied novel multidimensional diffusion (MDD) encoding across 16 patients with suspected breast cancer to evaluate its potential for tissue characterization in the clinical setting. Data acquired via custom MDD sequences was processed using an algorithm estimating non-parametric diffusion tensor distributions. The statistical descriptors of these distributions allow us to quantify tissue composition in terms of metrics informing on cell densities, shapes, and orientations. Additionally, signal fractions from specific cell types, such as elongated cells (bin1), isotropic cells (bin2), and free water (bin3), were teased apart. Histogram analysis in cancers and healthy breast tissue showed that cancers exhibited lower mean values of “size” (1.43 ± 0.54 × 10⁻³ mm²/s) and higher mean values of “shape” (0.47 ± 0.15) corresponding to bin1, while FGT (fibroglandular breast tissue) presented higher mean values of “size” (2.33 ± 0.22 × 10⁻³ mm²/s) and lower mean values of “shape” (0.27 ± 0.11) corresponding to bin3 (p < 0.001). Invasive carcinomas showed significant differences in mean signal fractions from bin1 (0.64 ± 0.13 vs. 0.4 ± 0.25) and bin3 (0.18 ± 0.08 vs. 0.42 ± 0.21) compared to ductal carcinomas in situ (DCIS) and invasive carcinomas with associated DCIS (p = 0.03). MDD enabled qualitative and quantitative evaluation of the composition of breast cancers and healthy glands.

In biological tissues, typical MRI voxels comprise multiple microscopic environments, the local organization of which can be captured by microscopic diffusion tensors. The measured diffusion MRI signal can, therefore, be written as the multidimensional Laplace transform of an intravoxel diffusion tensor distribution (DTD). Tensor‐valued diffusion encoding schemes have been designed to probe specific features of the DTD, and several algorithms have been introduced to invert such data and estimate statistical descriptors of the DTD, such as the mean diffusivity, the variance of isotropic diffusivities, and the mean squared diffusion anisotropy. However, the accuracy and precision of these estimations have not been assessed systematically and compared across methods. In this article, we perform and compare such estimations in silico for a one‐dimensional Gamma fit, a generalized two‐term cumulant approach, and two‐dimensional and four‐dimensional Monte‐Carlo‐based inversion techniques, using a clinically feasible tensor‐valued acquisition scheme. In particular, we compare their performance at different signal‐to‐noise ratios (SNRs) for voxel contents varying in terms of the aforementioned statistical descriptors, orientational order, and fractions of isotropic and anisotropic components. We find that all inversion techniques share similar precision (except for a lower precision of the two‐dimensional Monte Carlo inversion) but differ in terms of accuracy. While the Gamma fit exhibits infinite‐SNR biases when the signal deviates strongly from monoexponentiality and is unaffected by orientational order, the generalized cumulant approach shows infinite‐SNR biases when this deviation originates from the variance in isotropic diffusivities or from the low orientational order of anisotropic diffusion components. The two‐dimensional Monte Carlo inversion shows remarkable accuracy in all systems studied, given that the acquisition scheme possesses enough directions to yield a rotationally invariant powder average. The four‐dimensional Monte Carlo inversion presents no infinite‐SNR bias, but suffers significantly from noise in the data, while preserving good contrast in most systems investigated.

Purpose: To estimate for each distinct fiber population within voxels containing multiple brain tissue types.Methods: A diffusion‐ correlation experiment was carried out in an in vivo human brain using tensor‐valued diffusion encoding and multiple repetition times. The acquired data were inverted using a Monte Carlo algorithm that retrieves nonparametric distributions of diffusion tensors and longitudinal relaxation rates . Orientation distribution functions (ODFs) of the highly anisotropic components of were defined to visualize orientation‐specific diffusion‐relaxation properties. Finally, Monte Carlo density‐peak clustering (MC‐DPC) was performed to quantify fiber‐specific features and investigate microstructural differences between white matter fiber bundles.Results: Parameter maps corresponding to ’s statistical descriptors were obtained, exhibiting the expected contrast between brain tissue types. Our ODFs recovered local orientations consistent with the known anatomy and indicated differences in between major crossing fiber bundles. These differences, confirmed by MC‐DPC, were in qualitative agreement with previous model‐based works but seem biased by the limitations of our current experimental setup.Conclusions: Our Monte Carlo framework enables the nonparametric estimation of fiber‐specific diffusion‐ features, thereby showing potential for characterizing developmental or pathological changes in within a given fiber bundle, and for investigating interbundle differences.

Characterizing the properties and orientations of sub-voxel fiber populations, although essential to study white-matter architecture, microstructure and connectivity, remains one of the main challenges faced by the MRI microstructure community. While some progress has been made in overcoming this challenge using models, signal representations and tractography algorithms, these approaches are ultimately limited by their key assumptions or by the lack of specificity of the diffusion signal alone. In order to alleviate these limitations, we combine diffusion-relaxation MR acquisitions incorporating tensor-valued diffusion encoding, Monte-Carlo signal inversions that extract non-parametric intra-voxel distributions of diffusion tensors and relaxation rates, and density-based clustering techniques. This new approach, called "Monte-Carlo density-peak clustering" (MC-DPC), first delineates clusters in the diffusion-orientation subspace of the fiber-like diffusion-relaxation components output by Monte-Carlo signal inversions and then draws from the statistical aspect of these inversion algorithms to compute the median and interquartile range of orientation-resolved means of diffusivities and relaxation rates. Evaluating MC-DPC on tensor-valued diffusion-encoded and T2-weighted correlated datasets in silico and in vivo, we demonstrate its ability to simultaneously capture sub-voxel fiber orientations and cones of uncertainty, and measure fiber-specific diffusion-relaxation properties that are consistent with the known anatomy and existing literature. Straightforwardly translatable to other diffusion-relaxation correlation experiments probing $T_1$ and $T_2^*$, MC-DPC shows potential in tracking bundle-specific patient-control group differences and longitudinal microstructural changes, enabling new tools for microstructure-informed tractography, and mapping tract-specific myelination states.

Purpose: To estimate fiber-specific $T_1$ values, i.e. proxies for myelin content, in heterogeneous brain tissue. Methods: A diffusion-$T_1$ correlation experiment was carried out on an in vivo human brain using tensor-valued diffusion encoding and multiple repetition times. The acquired data was inverted using a Monte-Carlo inversion algorithm that retrieves non-parametric distributions $\mathcal{P}(\mathbf{D},R_1)$ of diffusion tensors and longitudinal relaxation rates $R_1 = 1/T_1$. Orientation distribution functions (ODFs) of the highly anisotropic components of $\mathcal{P}(\mathbf{D},R_1)$ were defined to visualize orientation-specific diffusion-relaxation properties. Finally, Monte-Carlo density-peak clustering (MC-DPC) was performed to quantify fiber-specific features and investigate microstructural differences between white-matter fiber bundles. Results: Parameter maps corresponding to $\mathcal{P}(\mathbf{D},R_1)$'s statistical descriptors were obtained, exhibiting the expected $R_1$ contrast between brain-tissue types. Our ODFs recovered local orientations consistent with the known anatomy and indicated possible differences in $T_1$ relaxation between major fiber bundles. These differences, confirmed by MC-DPC, were in qualitative agreement with previous model-based works but seem biased by the limitations of our current experimental setup. Conclusions: Our Monte-Carlo framework enables the non-parametric estimation of fiber-specific diffusion-$T_1$ features, thereby showing potential for characterizing developmental or pathological changes in $T_1$ within a given fiber bundle, and for investigating inter-bundle $T_1$ differences.