Massively Multidimensional Diffusion-Relaxation Correlation MRI

Diverse approaches such as oscillating gradients, tensor-valued encoding, and diffusion-relaxation correlation have been used to study microstructure and heterogeneity in healthy and pathological biological tissues. Recently, acquisition schemes with free gradient waveforms exploring both the frequency-dependent and tensorial aspects of the encoding spectrum b(ω) have enabled estimation of nonparametric distributions of frequency-dependent diffusion tensors. These “D(ω)-distributions” allow investigation of restricted diffusion for each distinct component resolved in the diffusion tensor trace, anisotropy, and orientation dimensions. Likewise, multidimensional methods combining longitudinal and transverse relaxation rates, R1 and R2, with (ω-independent) D-distributions capitalize on the component resolution offered by the diffusion dimensions to investigate subtle differences in relaxation properties of sub-voxel water populations in the living human brain, for instance nerve fiber bundles with different orientations. By measurements on an ex vivo rat brain, we here demonstrate a “massively multidimensional” diffusion-relaxation correlation protocol joining all the approaches mentioned above. Images acquired as a function of the magnitude, normalized anisotropy, orientation, and frequency content of b(ω), as well as the repetition time and echo time, yield nonparametric D(ω)-R1-R2-distributions via a Monte Carlo data inversion algorithm. The obtained per-voxel distributions are converted to parameter maps commonly associated with conventional lower-dimensional methods as well as unique statistical descriptors reporting on the correlations between restriction, anisotropy, and relaxation.

Multidimensional Diffusion Magnetic Resonance Imaging for Characterization of Tissue Microstructure in Breast Cancer Patients: A Prospective Pilot Study

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.

Simulation of elliptic and hypo-elliptic conditional diffusions

Suppose X is a multidimensional diffusion process. Assume that at time zero the state of X is fully observed, but at time $T>0$ only linear combinations of its components are observed. That is, one only observes the vector $L X_T$ for a given matrix L. In this paper we show how samples from the conditioned process can be generated. The main contribution of this paper is to prove that guided proposals, introduced in [35], can be used in a unified way for both uniformly elliptic and hypo-elliptic diffusions, even when L is not the identity matrix. This is illustrated by excellent performance in two challenging cases: a partially observed twice-integrated diffusion with multiple wells and the partially observed FitzHugh–Nagumo model.