The Mathematics of Quasi-Diffusion Magnetic Resonance Imaging

Quasi-diffusion imaging (QDI) is a novel quantitative diffusion magnetic resonance imaging (dMRI) technique that enables high quality tissue microstructural imaging in a clinically feasible acquisition time. QDI is derived from a special case of the continuous time random walk (CTRW) model of diffusion dynamics and assumes water diffusion is locally Gaussian within tissue microstructure. By assuming a Gaussian scaling relationship between temporal () and spatial () fractional exponents, the dMRI signal attenuation is expressed according to a diffusion coefficient, (in mm2 s−1), and a fractional exponent, . Here we investigate the mathematical properties of the QDI signal and its interpretation within the quasi-diffusion model. Firstly, the QDI equation is derived and its power law behaviour described. Secondly, we derive a probability distribution of underlying Fickian diffusion coefficients via the inverse Laplace transform. We then describe the functional form of the quasi-diffusion propagator, and apply this to dMRI of the human brain to perform mean apparent propagator imaging. QDI is currently unique in tissue microstructural imaging as it provides a simple form for the inverse Laplace transform and diffusion propagator directly from its representation of the dMRI signal. This study shows the potential of QDI as a promising new model-based dMRI technique with significant scope for further development.

Can MRI measure myelin? Systematic review, qualitative assessment, and meta-analysis of studies validating microstructural imaging with myelin histology

Recent years have seen an increased understanding of the importance of myelination in healthy brain function and neuropsychiatric diseases. Non-invasive microstructural magnetic resonance imaging (MRI) holds the potential to expand and translate these insights to basic and clinical human research, but the sensitivity and specificity of different MR markers to myelination is a subject of debate.To consolidate current knowledge on the topic, we perform a systematic review and meta-analysis of studies that validate microstructural imaging by combining it with myelin histology.We find meta-analytic evidence for correlations between myelin histology and markers from different MRI modalities, including fractional anisotropy, radial diffusivity, macromolecular pool, magnetization transfer ratio, susceptibility and longitudinal relaxation rate, but not mean diffusivity. Meta-analytic correlation effect sizes range widely, between R2 = 0.26 and R2 = 0.82. However, formal comparisons between MRI-based myelin markers are limited by methodological variability, inconsistent reporting and potential for publication bias, thus preventing the establishment of a single most sensitive strategy to measure myelin with MRI.To facilitate further progress, we provide a detailed characterisation of the evaluated studies as an online resource. We also share a set of 12 recommendations for future studies validating putative MR-based myelin markers and deploying them in vivo in humans.HighlightsSystematic review and meta-analysis of studies validating microstructural imaging with myelin histologyWe find many MR markers are sensitive to myelin, including FA, RD, MP, MTR, Susceptibility, R1, but not MDFormal comparisons between MRI-based myelin markers are limited by methodological variability, inconsistent reporting and potential for publication biasResults emphasize the advantage of using multimodal imaging when testing hypotheses related to myelin in vivo in humans.