Diffusion magnetic resonance imaging (diffusion MRI) is widely employed to probe the diffusive motion of water molecules within the tissue. Numerous diseases and processes affecting the central nervous system can be detected and monitored via diffusion MRI thanks to its sensitivity to microstructural alterations in tissue. The latter has prompted interest in quantitative mapping of the microstructural parameters, such as the fiber orientation distribution function (fODF), which is instrumental for noninvasively mapping the underlying axonal fiber tracts in white matter through a procedure known as tractography. However, such applications demand repeated acquisitions of MRI volumes with varied experimental parameters demanding long acquisition times and/or limited spatial resolution. In this work, we present a deep-learning-based approach for increasing the spatial resolution of diffusion MRI data in the form of fODFs obtained through constrained spherical deconvolution. The proposed approach is evaluated on high quality data from the Human Connectome Project, and is shown to generate upsampled results with a greater correspondence to ground truth high-resolution data than can be achieved with ordinary spline interpolation methods. Furthermore, we employ a measure based on the earth mover’s distance to assess the accuracy of the upsampled fODFs. At low signal-to-noise ratios, our super-resolution method provides more accurate estimates of the fODF compared to data collected with 8 times smaller voxel volume.

Q-space trajectory imaging (QTI) allows non-invasive estimation of microstructural features of heterogeneous porous media via diffusion magnetic resonance imaging performed with generalised gradient waveforms. A recently proposed constrained estimation framework, called QTI+, improved QTI’s resilience to noise and data sparsity, thus increasing the reliability of the method by enforcing relevant positivity constraints. In this work we consider expanding the set of constraints to be applied during the fitting of the QTI model. We show that the additional conditions, which introduce an upper bound on the diffusivity values, further improve the retrieved parameters on a publicly available human brain dataset as well as on data acquired from healthy volunteers using a scanner-ready protocol.

Porous or biological materials comprise a multitude of micro-domainscontaining water. Diffusion-weighted magnetic resonance measurements are sensitive to the anisotropy of the thermal motion of such water. This anisotropy can bedue to the domain shape, as well as the (lack of) dispersion in their orientations.Averaging over measurements that span all orientations is a trick to suppress thelatter, thereby untangling it from the influence of the domains’ anisotropy on thesignal. Here, we consider domains whose anisotropy is modeled as being the resultof a Hookean (spring) force, which has the advantage of having a Gaussian diffusionpropagator while still confining the spatial range for the diffusing particles. In fact,this confinement model is the effective model of restricted diffusion when diffusion isencoded via gradients of long durations, making the model relevant to a broad rangeof studies aiming to characterize porous media with microscopic subdomains. In thisstudy, analytical expressions for the powder-averaged signal under this assumptionare given for so-called single and double diffusion encoding schemes, which sensitize the MR signal to the diffusive displacement of particles in, respectively, one ortwo consecutive time intervals. The signal for one-dimensional diffusion is shownto exhibit power-law dependence on the gradient strength while its coefficient bearssignatures of restricted diffusion.

Diffusion MRI (dMRI) is a valuable tool in the assessment of tissue microstructure. By fitting a model to the dMRI signal it is possible to derive various quantitative features. Several of the most popular dMRI signal models are expansions in an appropriately chosen basis, where the coefficients are determined using some variation of least-squares. However, such approaches lack any notion of uncertainty, which could be valuable in e.g. group analyses. In this work, we use a probabilistic interpretation of linear least-squares methods to recast popular dMRI models as Bayesian ones. This makes it possible to quantify the uncertainty of any derived quantity. In particular, for quantities that are affine functions of the coefficients, the posterior distribution can be expressed in closed-form. We simulated measurements from single- and double-tensor models where the correct values of several quantities are known, to validate that the theoretically derived quantiles agree with those observed empirically. We included results from residual bootstrap for comparison and found good agreement. The validation employed several different models: Diffusion Tensor Imaging (DTI), Mean Apparent Propagator MRI (MAP-MRI) and Constrained Spherical Deconvolution (CSD). We also used in vivo data to visualize maps of quantitative features and corresponding uncertainties, and to show how our approach can be used in a group analysis to downweight subjects with high uncertainty. In summary, we convert successful linear models for dMRI signal estimation to probabilistic models, capable of accurate uncertainty quantification.

Neuronal and glial projections can be envisioned to be tubes of infinitesimal diameter as far as diffusion magnetic resonance (MR) measurements via clinical scanners are concerned. Recent experimental studies indicate that the decay of the orientationally-averaged signal in white-matter may be characterized by the power-law, Ē(q) ∝ q−1, where q is the wavenumber determined by the parameters of the pulsed field gradient measurements. One particular study by McKinnon et al. [1] reports a distinctively faster decay in gray-matter. Here, we assess the role of the size and curvature of the neurites and glial arborizations in these experimental findings. To this end, we studied the signal decay for diffusion along general curves at all three temporal regimes of the traditional pulsed field gradient measurements. We show that for curvy projections, employment of longer pulse durations leads to a disappearance of the q−1 decay, while such decay is robust when narrow gradient pulses are used. Thus, in clinical acquisitions, the lack of such a decay for a fibrous specimen can be seen as indicative of fibers that are curved. We note that the above discussion is valid for an intermediate range of q-values as the true asymptotic behavior of the signal decay is Ē(q) ∝ q−4 for narrow pulses (through Debye-Porod law) or steeper for longer pulses. This study is expected to provide insights for interpreting the diffusion-weighted images of the central nervous system and aid in the design of acquisition strategies.

The signature of diffusive motion on the NMR signal has been exploited to characterize the mesoscopic structure of specimens in numerous applications. For compartmentalized specimens comprising isolated subdomains, a representation of individual pores is necessary for describing restricted diffusion within them. When gradient waveforms with long pulse durations are employed, a quadratic potential profile is identified as an effective energy landscape for restricted diffusion. The dependence of the stochastic effective force on the center-of-mass position is indeed found to be approximately linear (Hookean) for restricted diffusion even when the walls are sticky. We outline the theoretical basis and practical advantages of our picture involving effective potentials.

We present a novel approach to investigate the properties of diffusion weighted magnetic resonance imaging (dMRI). The process of restricted diffusion of spin particles in the presence of a magnetic field is simulated by an iterated complex matrix multiplication approach. The approach is based on first principles and provides a flexible, transparent and fast simulation tool. The experiments carried out reveals fundamental features of the dMRI process. A particularly interesting observation is that the induced speed of the local spatial spin angle rate of change is highly shift variant. Hence, the encoding basis functions are not the complex exponentials associated with the Fourier transform as commonly assumed. Thus, reconstructing the signal using the inverse Fourier transform leads to large compartment estimation errors, which is demonstrated in a number of 1D and 2D examples. In accordance with previous investigations the compartment size is under-estimated. More interestingly, however, we show that the estimated shape is likely to be far from the true shape using state of the art clinical MRI scanners.

Detection of moving objects concealed behind a concrete wall corner has been demonstrated, using Doppler-based techniques with a stepped-frequency radar centered at 10 GHz, in a reduced-scale model of a street scenario. Micro-Doppler signatures have been traced in the return from a human target, both for walking and for breathing. Separate material measurements of the reflection and transmission of the concrete in the wall have showed that wall reflections are the dominating wave propagation mechanism for producing target detections, while wave components transmitted through the walls could be neglected. Weaker detections have been made of target returns via diffraction in the wall corner. A simple and fast algorithm for the detection and generation of detection tracks in down range has been developed, based on moving target indication technique.