Ivana Drobnjak

Conventions and nomenclature for double diffusion encoding NMR and MRI

Stejskal and Tanners ingenious pulsed field gradient design from 1965 has made diffusion NMR and MRI the mainstay of most studies seeking to resolve microstructural information in porous systems in general and biological systems in particular. Methods extending beyond Stejskal and Tanners design, such as double diffusion encoding (DDE) NMR and MRI, may provide novel quantifiable metrics that are less easily inferred from conventional diffusion acquisitions. Despite the growing interest on the topic, the terminology for the pulse sequences, their parameters, and the metrics that can be derived from them remains inconsistent and disparate among groups active in DDE. Here, we present a consensus of those groups on terminology for DDE sequences and associated concepts. Furthermore, the regimes in which DDE metrics appear to provide microstructural information that cannot be achieved using more conventional counterparts (in a model‐free fashion) are elucidated. We highlight in particular DDEs potential for determining microscopic diffusion anisotropy and microscopic fractional anisotropy, which offer metrics of microscopic features independent of orientation dispersion and thus provide information complementary to the standard, macroscopic, fractional anisotropy conventionally obtained by diffusion MR. Finally, we discuss future vistas and perspectives for DDE. Magn Reson Med 75:82–87, 2016.

Optimizing gradient waveforms for microstructure sensitivity in diffusion-weighted MR

Variations in gradient waveforms can provide different levels of sensitivity to microstructure parameters in diffusion-weighted MR. We present a method that identifies gradient waveforms with maximal sensitivity to parameters of a model relating microstructural features to diffusion MR signals. The method optimizes the shape of the gradient waveform, constrained by hardware limits and fixed orientation, to minimize the expected variance of parameter estimates. The waveform is defined discretely and each point optimized independently. The method is illustrated with a biomedical application in which we maximize the sensitivity to microstructural features of white matter such as axon radius, intra-cellular volume fraction and diffusion constants. Simulation experiments find that optimization of the shape of the gradient waveform improves sensitivity to model parameters for both human and animal MR systems. In particular, the optimized waveforms make axon radii smaller than 5 microm more distinguishable than standard pulsed gradient spin-echo (PGSE). The identified class of optimized gradient waveforms have dominant square-wave components with frequency that increases as the radius size decreases.

Development of a functional magnetic resonance imaging simulator for modeling realistic rigid-body motion artifacts.

Functional magnetic resonance imaging (FMRI) is a noninvasive method of imaging brain function in vivo. However, images produced in FMRI experiments are imperfect and contain several artifacts that contaminate the data. These artifacts include rigid‐body motion effects, B0‐field inhomogeneities, chemical shift, and eddy currents. To investigate these artifacts, with the eventual aim of minimizing or removing them completely, a computational model of the FMR image acquisition process was built that can simulate all of the above‐mentioned artifacts. This paper gives an overview of the development of the FMRI simulator. The simulator uses the Bloch equations together with a geometric definition of the object (brain) and a varying T  2* model for the BOLD activations. Furthermore, it simulates rigid‐body motion of the object by solving Bloch equations for given motion parameters that are defined for an object moving continuously in time, including during the read‐out period, which is a novel approach in the area of MRI computer simulations. With this approach it is possible, in a controlled and precise way, to simulate the full effects of various rigid‐body motion artifacts in FMRI data (e.g. spin‐history effects, B0‐motion interaction, and within‐scan motion blurring) and therefore formulate and test algorithms for their reduction. Magn Reson Med, 2006.

PGSE, OGSE, and sensitivity to axon diameter in diffusion MRI: Insight from a simulation study.

To identify optimal pulsed gradient spin‐echo (PGSE) and oscillating gradient spin‐echo (OGSE) sequence settings for maximizing sensitivity to axon diameter in idealized and practical conditions.

Estimation of pore size in a microstructure phantom using the optimised gradient waveform diffusion weighted NMR sequence

There has been increasing interest in nuclear magnetic resonance (NMR) techniques that are sensitive to diffusion of molecules containing NMR visible nuclei for the estimation of microstructure parameters. A microstructure parameter of particular interest is pore radius distribution. A recent in silico study optimised the shape of the gradient waveform in diffusion weighted spin-echo experiments for estimating pore size. The study demonstrated that optimised gradient waveform (GEN) protocols improve pore radius estimates compared to optimised pulse gradient spin-echo (PGSE) protocols, particularly at shorter length scales. This study assesses the feasibility of implementing GEN protocols on a small bore 9.4 T scanner and verifies their additional sensitivity to pore radius. We implement GEN and PGSE protocols optimised for pore radii of 1, 2.5, 5, 7.5, 10 μm and constrained to maximum gradient strengths of 40, 80, 200 mT m(-1). We construct microstructure phantoms, which have a single pore radius for each phantom, using microcapillary fibres. The measured signal shows good agreement with simulated signal, strongly indicating that the GEN waveforms can be implemented on a 9.4 T system. We also demonstrate that GEN protocols provide improved sensitivity to the smaller pore radii when compared to optimised PGSE protocols, particularly at the lower gradient amplitudes investigated in this study. Our results suggest that this improved sensitivity of GEN protocols would be reflected in clinical scenarios.

Realistic simulation of artefacts in diffusion MRI for validating post-processing correction techniques.

In this paper we demonstrate a simulation framework that enables the direct and quantitative comparison of post-processing methods for diffusion weighted magnetic resonance (DW-MR) images. DW-MR datasets are employed in a range of techniques that enable estimates of local microstructure and global connectivity in the brain. These techniques require full alignment of images across the dataset, but this is rarely the case. Artefacts such as eddy-current (EC) distortion and motion lead to misalignment between images, which compromise the quality of the microstructural measures obtained from them. Numerous methods and software packages exist to correct these artefacts, some of which have become de-facto standards, but none have been subject to rigorous validation. In the literature, improved alignment is assessed using either qualitative visual measures or quantitative surrogate metrics. Here we introduce a simulation framework that allows for the direct, quantitative assessment of techniques, enabling objective comparisons of existing and future methods. DW-MR datasets are generated using a process that is based on the physics of MRI acquisition, which allows for the salient features of the images and their artefacts to be reproduced. We apply this framework in three ways. Firstly we assess the most commonly used method for artefact correction, FSLs eddy_correct, and compare it to a recently proposed alternative, eddy. We demonstrate quantitatively that using eddy_correct leads to significant errors in the corrected data, whilst eddy is able to provide much improved correction. Secondly we investigate the datasets required to achieve good correction with eddy, by looking at the minimum number of directions required and comparing the recommended full-sphere acquisitions to equivalent half-sphere protocols. Finally, we investigate the impact of correction quality by examining the fits from microstructure models to real and simulated data.

Gaussian phase distribution approximations for oscillating gradient spin echo diffusion MRI

Oscillating gradients provide an optimal probe of small pore sizes in diffusion MRI. While sinusoidal oscillations have been popular for some time, recent work suggests additional benefits of square or trapezoidal oscillating waveforms. This paper presents analytical expressions of the free and restricted diffusion signal for trapezoidal and square oscillating gradient spin echo (OGSE) sequences using the Gaussian phase distribution (GPD) approximation and generalises existing similar expressions for sinusoidal OGSE. Accurate analytical models are necessary for exploitation of these pulse sequences in imaging studies, as they allow model fitting and parameter estimation in reasonable computation times. We evaluate the accuracy of the approximation against synthesised data from the Monte Carlo (MC) diffusion simulator in Camino and Callaghans matrix method and we show that the accuracy of the approximation is within a few percent of the signal, while providing several orders of magnitude faster computation. Moreover, since the expressions for trapezoidal wave are complex, we test sine and square wave approximations to the trapezoidal OGSE signal. The best approximations depend on the gradient amplitude and the oscillation frequency and are accurate to within a few percent. Finally, we explore broader applications of trapezoidal OGSE, in particular for non-model based applications, such as apparent diffusion coefficient estimation, where only sinusoidal waveforms have been considered previously. We show that with the right apodisation, trapezoidal waves also have benefits by virtue of the higher diffusion weighting they provide compared to sinusoidal gradients.

The matrix formalism for generalised gradients with time-varying orientation in diffusion NMR.

The matrix formalism is a general framework for evaluating the diffusion NMR signal from restricted spins under generalised gradient waveforms. The original publications demonstrate the method for waveforms that vary only in magnitude and have fixed orientation. In this work, we extend the method to allow for variations in the direction of the gradient. This extension is necessary, for example to incorporate the effects of crusher gradients or imaging gradients in diffusion MRI, to characterise signal anisotropy in double pulsed field gradient (dPFG) experiments, or to optimise the gradient waveform for microstructure sensitivity. In particular, we show for primitive geometries (planes, cylinders and spheres), how to express the matrix operators at each time point of the gradient waveform as a linear combination of one or two fundamental matrices. Thus we obtain an efficient implementation with both the storage and CPU demands similar to the fixed-orientation case. Comparison with Monte Carlo simulations validates the implementation on three different sequences: dPFG, helical waveforms and the stimulated echo (STEAM) sequence.

Resolution limit of cylinder diameter estimation by diffusion MRI: The impact of gradient waveform and orientation dispersion

Diffusion MRI has been proposed as a non‐invasive technique for axonal diameter mapping. However, accurate estimation of small diameters requires strong gradients, which is a challenge for the transition of the technique from preclinical to clinical MRI scanners, since these have weaker gradients. In this work, we develop a framework to estimate the lower bound for accurate diameter estimation, which we refer to as the resolution limit. We analyse only the contribution from the intra‐axonal space and assume that axons can be represented by impermeable cylinders. To address the growing interest in using techniques for diffusion encoding that go beyond the conventional single diffusion encoding (SDE) sequence, we present a generalised analysis capable of predicting the resolution limit regardless of the gradient waveform. Using this framework, waveforms were optimised to minimise the resolution limit. The results show that, for parallel cylinders, the SDE experiment is optimal in terms of yielding the lowest possible resolution limit. In the presence of orientation dispersion, diffusion encoding sequences with square‐wave oscillating gradients were optimal. The resolution limit for standard clinical MRI scanners (maximum gradient strength 60–80 mT/m) was found to be between 4 and 8 μm, depending on the noise levels and the level of orientation dispersion. For scanners with a maximum gradient strength of 300 mT/m, the limit was reduced to between 2 and 5 μm.

Optimising time-varying gradient orientation for microstructure sensitivity in diffusion-weighted MR

Here we investigate whether varying the diffusion-gradient orientation during a general waveform single pulsed-field gradient sequence improves sensitivity to the size of coherently oriented pores over having a fixed orientation. The experiment optimises the shape and the orientation of the gradient waveform in each of a set of measurements to minimise the expected variance of estimates of the parameters of a simple model. A key application motivating the work is measuring the size of axons in white matter. Thus, we use a two compartment white matter model with impermeable, single-radius cylinders, and search for waveforms that maximise the sensitivity to axon radius, intra-cellular volume fraction and diffusion constants. Output of the optimisation suggests the only benefit of allowing the gradient orientation to vary in the plane perpendicular to the cylinders is that we can gain perpendicular gradient strength by maximising two orthogonal gradients simultaneously. This suggests that varying orientation in itself does not increase the sensitivity to model parameters. On the other hand, the variation in a plane containing the parallel direction increases the sensitivity significantly because parallel sensitivity improves the diffusion constant estimates. However, we also find that similar improvement in the estimates can be achieved without optimising the orientation, but by having one measurement in the parallel and the rest in the perpendicular direction. The optimisation searches a very large space where it cannot hope to find the global minimum so we cannot make a categorical conclusion. However, given the consistency of the results in multiple reruns and variations of the experiments reported here, we can suggest that for probing coherently oriented systems, pulse sequences with variable orientation, such as double-wave vector sequences, do not offer more advantage than fixed orientation sequences with optimised shape. The advantage of varying orientation is however likely to emerge for more complex systems with dispersed pore orientation.