Henrik Lundell

Orientationally invariant metrics of apparent compartment eccentricity from double pulsed field gradient diffusion experiments

Pulsed field gradient diffusion sequences (PFG) with multiple diffusion encoding blocks have been indicated to offer new microstructural tissue information, such as the ability to detect nonspherical compartment shapes in macroscopically isotropic samples, i.e. samples with negligible directional signal dependence on diffusion gradients in standard diffusion experiments. However, current acquisition schemes are not rotationally invariant in the sense that the derived metrics depend on the orientation of the sample, and are affected by the interplay of sampling directions and compartment orientation dispersion when applied to macroscopically anisotropic systems. Here we propose a new framework, the d‐PFG 5‐design, to enable rotationally invariant estimation of double wave vector diffusion metrics (d‐PFG). The method is based on the idea that an appropriate orientational average of the signal emulates the signal from a powder preparation of the same sample, where macroscopic anisotropy is absent by construction. Our approach exploits the theory of exact numerical integration (quadrature) of polynomials on the rotation group, and we exemplify the general procedure with a set consisting of 60 pairs of diffusion wave vectors (the d‐PFG 5‐design) facilitating a theoretically exact determination of the fourth order Taylor or cumulant expansion of the orientationally averaged signal. The d‐PFG 5‐design is evaluated with numerical simulations and ex vivo high field diffusion MRI experiments in a nonhuman primate brain. Specifically, we demonstrate rotational invariance when estimating compartment eccentricity, which we show offers new microstructural information, complementary to that of fractional anisotropy (FA) from diffusion tensor imaging (DTI). The imaging observations are supported by a new theoretical result, directly relating compartment eccentricity to FA of individual pores. Copyright

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.

Interpolation of diffusion weighted imaging datasets

Diffusion weighted imaging (DWI) is used to study white-matter fibre organisation, orientation and structural connectivity by means of fibre reconstruction algorithms and tractography. For clinical settings, limited scan time compromises the possibilities to achieve high image resolution for finer anatomical details and signal-to-noise-ratio for reliable fibre reconstruction. We assessed the potential benefits of interpolating DWI datasets to a higher image resolution before fibre reconstruction using a diffusion tensor model. Simulations of straight and curved crossing tracts smaller than or equal to the voxel size showed that conventional higher-order interpolation methods improved the geometrical representation of white-matter tracts with reduced partial-volume-effect (PVE), except at tract boundaries. Simulations and interpolation of ex-vivo monkey brain DWI datasets revealed that conventional interpolation methods fail to disentangle fine anatomical details if PVE is too pronounced in the original data. As for validation we used ex-vivo DWI datasets acquired at various image resolutions as well as Nissl-stained sections. Increasing the image resolution by a factor of eight yielded finer geometrical resolution and more anatomical details in complex regions such as tract boundaries and cortical layers, which are normally only visualized at higher image resolutions. Similar results were found with typical clinical human DWI dataset. However, a possible bias in quantitative values imposed by the interpolation method used should be considered. The results indicate that conventional interpolation methods can be successfully applied to DWI datasets for mining anatomical details that are normally seen only at higher resolutions, which will aid in tractography and microstructural mapping of tissue compartments.

High angular resolution diffusion imaging with stimulated echoes: compensation and correction in experiment design and analysis

Stimulated echo acquisition mode (STEAM) diffusion MRI can be advantageous over pulsed‐gradient spin‐echo (PGSE) for diffusion times that are long compared with T2. It therefore has potential for biomedical diffusion imaging applications at 7T and above where T2 is short. However, gradient pulses other than the diffusion gradients in the STEAM sequence contribute much greater diffusion weighting than in PGSE and lead to a disrupted experimental design. Here, we introduce a simple compensation to the STEAM acquisition that avoids the orientational bias and disrupted experiment design that these gradient pulses can otherwise produce. The compensation is simple to implement by adjusting the gradient vectors in the diffusion pulses of the STEAM sequence, so that the net effective gradient vector including contributions from diffusion and other gradient pulses is as the experiment intends. High angular resolution diffusion imaging (HARDI) data were acquired with and without the proposed compensation. The data were processed to derive standard diffusion tensor imaging (DTI) maps, which highlight the need for the compensation. Ignoring the other gradient pulses, a bias in DTI parameters from STEAM acquisition is found, due both to confounds in the analysis and the experiment design. Retrospectively correcting the analysis with a calculation of the full B matrix can partly correct for these confounds, but an acquisition that is compensated as proposed is needed to remove the effect entirely.

Diffusion weighted imaging with circularly polarized oscillating gradients.

The short diffusion time regime provides an interesting probe for tissue microstructure and can be investigated with oscillating gradient spin echo (OGSE) experiments. Several studies report new contrasts in preclinical settings and the first in vivo human experiments have recently been presented. One major hurdle in practical implementation is the low effective diffusion weighting provided at high frequency with limited gradient strength.

Commentary on “Microanisotropy imaging: quantification of microscopic diffusion anisotropy and orientation of order parameter by diffusion MRI with magic-angle spinning of the q-vector”

In their recent paper, Lasic et al. describe a parameter termed μFA (microscopic fractional anisotropy) that quantifies microscopic anisotropy independently of macroscopic anisotropy [1]. Specifically such a microstructural parameter makes it possible to detect and characterize anisotropic domains even if they are organized in a macroscopically (i.e., at the level of the voxel) isotropic way—essentially decoupling macroscopic and microscopic anisotropy. Their method is based on the combination of two types of diffusion measurements, a powder average experiment and magic angle spinning of the q vector: The powder average experiment uses a traditional single pulsed field gradient or PGSE acquisition, where the signal along a large number of diffusion directions is averaged, thus emulating an isotropic preparation of the sample. The magic angle spinning of the q vector, the so-called q-MAS, is an approach for isotropic diffusion weighting recently introduced by the same group [2]. A similar parameter of microscopic anisotropy, termed fractional eccentricity (FE), but relying on double pulsed field gradient (dPFG) diffusion experiments was introduced by us recently in Jespersen et al. [3]. In it we extended previous work on indices of microscopic anisotropy in the long diffusion time limit proposed by Lawrenz et al. [4]. The FE terminology was motivated by the existing nomenclature in the dPFG field. However, a simple argument shows that the two metrics μFA and FE are in fact identical in systems consisting of identical pores. First, when all domains are coherently aligned along one direction, it was shown in Jespersen et al. [3] that FE=FA, and similarly in Lasic et al. [1] that μFA=FA: thus FE=μFA in such a system. Secondly, both metrics are independent of the pore orientation distribution function, so both FE and μFA are unaffected when reorganizing the domains to match any anisotropic distribution. Hence the identity FE=μFA is conserved. Nevertheless, a number of observations concerning differences and similarities must be made. Clearly, both approaches presuppose the existence of compartments (pores), in which the bulk of the spins will remain during the relevant time of observation. For the q-MAS approach, this is the duration of the q-MAS modulation, 40 ms in Lasic et al. [1]. For the dPFG approach, the relevant time is the sum of diffusion and exchange times from the onset of the first field pulse to the end of the last field pulse, which was 43 ms in Jespersen et al. [3]. These (comparable) numbers put constraints on the exchange time/permeability of the compartments. Moreover, both approaches involve non-conventional diffusion sequences, requiring programming of gradient modulation waveforms. The qMAS approach requires the combination of two different types of diffusion experiments, and both approaches use data acquired along several diffusion directions. The dPFG experiment can be used to extract also the diffusion tensor. The q-MAS approach assumes that diffusion in the individual pores is Gaussian. This can be a good approximation for example when diffusion weighting is not too strong and diffusion times are large. However, another requirement of the qMAS analysis approach is that the diffusion coefficients in the individual pores are time independent, a condition which may be challenging to balance against the necessity for the spins to experience the pore boundaries, the very source of the μFA. On the other hand, this is presumably a good approximation for the extracellular space in the long diffusion time limit, still assuming no exchange between the intraand extracellular space. The Gaussian approximation can be accurate also when diffusion times are very small, but in this regime μFA will be vanishing as the effect of the confinement is negligible. The dPFG approach to microscopic anisotropy requires long mixing times,

Apparent exchange rate imaging in anisotropic systems

Double‐wave diffusion experiments offer the possibility of probing correlation between molecular diffusion at multiple time points. It has recently been shown that this technique is capable of measuring the exchange of water across cellular membranes. The aim of this study was to investigate the effect of macroscopic tissue anisotropy on the measurement of the apparent exchange rate (AXR) in multicompartment systems.

Fast diffusion tensor imaging and tractography of the whole cervical spinal cord using point spread function corrected echo planar imaging

Diffusion tensor imaging has been used in a number of spinal cord studies, but severe distortions caused by susceptibility induced field inhomogeneities limit its applicability to investigate small volumes within acceptable acquisition times. A way to evaluate image distortions is to map the point spread function of the voxel intensity in a reference scan. In this study, the point spread function was mapped for an echo‐planar imaging sequence in the human cervical spinal cord with isotropic resolution and large field of view. Correction with the point spread function map improved anatomical consistency, and full cervical tractography was thereby possible from a C1 seed region in healthy controls and one individual with spinal cord injury. It is suggested that point spread function mapping of the spinal cord can be used in combination with sequence‐based methods for reduction of susceptibility artifacts or in high‐field imaging settings where off‐resonance effects are pronounced. Magn Reson Med, 2013.

Thalamocortical Connectivity and Microstructural Changes in Congenital and Late Blindness

There is ample evidence that the occipital cortex of congenitally blind individuals processes nonvisual information. It remains a debate whether the cross-modal activation of the occipital cortex is mediated through the modulation of preexisting corticocortical projections or the reorganisation of thalamocortical connectivity. Current knowledge on this topic largely stems from anatomical studies in animal models. The aim of this study was to test whether purported changes in thalamocortical connectivity in blindness can be revealed by tractography based on diffusion-weighted magnetic resonance imaging. To assess the thalamocortical network, we used a clustering method based on the thalamic white matter projections towards predefined cortical regions. Five thalamic clusters were obtained in each group representing their cortical projections. Although we did not find differences in the thalamocortical network between congenitally blind individuals, late blind individuals, and normal sighted controls, diffusion tensor imaging (DTI) indices revealed significant microstructural changes within thalamic clusters of both blind groups. Furthermore, we find a significant decrease in fractional anisotropy (FA) in occipital and temporal thalamocortical projections in both blind groups that were not captured at the network level. This suggests that plastic microstructural changes have taken place, but not in a degree to be reflected in the tractography-based thalamocortical network.

Magnetic resonance temporal diffusion tensor spectroscopy of disordered anisotropic tissue

Molecular diffusion measured with diffusion weighted MRI (DWI) offers a probe for tissue microstructure. However, inferring microstructural properties from conventional DWI data is a complex inverse problem and has to account for heterogeneity in sizes, shapes and orientations of the tissue compartments contained within an imaging voxel. Alternative experimental means for disentangling the signal signatures of such features could provide a stronger link between the data and its interpretation. Double diffusion encoding (DDE) offers the possibility to factor out variation in compartment shapes from orientational dispersion of anisotropic domains by measuring the correlation between diffusivity in multiple directions. Time dependence of the diffusion is another effect reflecting the dimensions and distributions of barriers. In this paper we extend on DDE with a modified version of the oscillating gradient spin echo (OGSE) experiment, giving a basic contrast mechanism closely linked to both the temporal diffusion spectrum and the compartment anisotropy. We demonstrate our new method on post mortem brain tissue and show that we retrieve the correct temporal diffusion tensor spectrum in synthetic data from Monte Carlo simulations of random walks in a range of disordered geometries of different sizes and shapes.