Filip Szczepankiewicz

Microanisotropy imaging: quantification of microscopic diffusion anisotropy and orientational order parameter by diffusion MRI with magic-angle spinning of the q-vector

Diffusion tensor imaging (DTI) is the method of choice for non-invasive investigations of the structure of human brain white matter. The results are conventionally reported as maps of the fractional anisotropy (FA), which is a parameter related to microstructural features such as axon density, diameter, and myelination. The interpretation of FA in terms of microstructure becomes ambiguous when there is a distribution of axon orientations within the image voxel. In this paper, we propose a procedure for resolving this ambiguity by determining a new parameter, the microscopic fractional anisotropy (µFA), which corresponds to the FA without the confounding influence of orientation dispersion. In addition, we suggest a method for measuring the orientational order parameter (OP) for the anisotropic objects. The experimental protocol is capitalizing on a recently developed diffusion NMR pulse sequence based on magic-angle spinning of the q-vector. Proof-of-principle experiments are carried out on microimaging and clinical MRI equipment using lyotropic liquid crystals and plant tissues as model materials with high µFA and low FA on account of orientation dispersion. We expect the presented method to be especially fruitful in combination with DTI and high angular resolution acquisition protocols for neuroimaging studies of grey and white matter.

Neurite density imaging versus imaging of microscopic anisotropy in diffusion MRI : A model comparison using spherical tensor encoding

ABSTRACT In diffusion MRI (dMRI), microscopic diffusion anisotropy can be obscured by orientation dispersion. Separation of these properties is of high importance, since it could allow dMRI to non‐invasively probe elongated structures such as neurites (axons and dendrites). However, conventional dMRI, based on single diffusion encoding (SDE), entangles microscopic anisotropy and orientation dispersion with intra‐voxel variance in isotropic diffusivity. SDE‐based methods for estimating microscopic anisotropy, such as the neurite orientation dispersion and density imaging (NODDI) method, must thus rely on model assumptions to disentangle these features. An alternative approach is to directly quantify microscopic anisotropy by the use of variable shape of the b‐tensor. Along those lines, we here present the ‘constrained diffusional variance decomposition’ (CODIVIDE) method, which jointly analyzes data acquired with diffusion encoding applied in a single direction at a time (linear tensor encoding, LTE) and in all directions (spherical tensor encoding, STE). We then contrast the two approaches by comparing neurite density estimated using NODDI with microscopic anisotropy estimated using CODIVIDE. Data were acquired in healthy volunteers and in glioma patients. NODDI and CODIVIDE differed the most in gray matter and in gliomas, where NODDI detected a neurite fraction higher than expected from the level of microscopic diffusion anisotropy found with CODIVIDE. The discrepancies could be explained by the NODDI tortuosity assumption, which enforces a connection between the neurite density and the mean diffusivity of tissue. Our results suggest that this assumption is invalid, which leads to a NODDI neurite density that is inconsistent between LTE and STE data. Using simulations, we demonstrate that the NODDI assumptions result in parameter bias that precludes the use of NODDI to map neurite density. With CODIVIDE, we found high levels of microscopic anisotropy in white matter, intermediate levels in structures such as the thalamus and the putamen, and low levels in the cortex and in gliomas. We conclude that accurate mapping of microscopic anisotropy requires data acquired with variable shape of the b‐tensor. HIGHLIGHTSNeuroimaging was performed with linear and spherical tensor encoding (LTE and STE) at 3 T and 7 T.Microscopic anisotropy was quantified by two methods: NODDI and CODIVIDE.NODDI predictions of microscopic anisotropy were not supported by STE data.Levels of microscopic anisotropy were low in the cortex and high in the white matter.

Q-space trajectory imaging for multidimensional diffusion MRI of the human brain.

This work describes a new diffusion MR framework for imaging and modeling of microstructure that we call q-space trajectory imaging (QTI). The QTI framework consists of two parts: encoding and modeling. First we propose q-space trajectory encoding, which uses time-varying gradients to probe a trajectory in q-space, in contrast to traditional pulsed field gradient sequences that attempt to probe a point in q-space. Then we propose a microstructure model, the diffusion tensor distribution (DTD) model, which takes advantage of additional information provided by QTI to estimate a distributional model over diffusion tensors. We show that the QTI framework enables microstructure modeling that is not possible with the traditional pulsed gradient encoding as introduced by Stejskal and Tanner. In our analysis of QTI, we find that the well-known scalar b-value naturally extends to a tensor-valued entity, i.e., a diffusion measurement tensor, which we call the b-tensor. We show that b-tensors of rank 2 or 3 enable estimation of the mean and covariance of the DTD model in terms of a second order tensor (the diffusion tensor) and a fourth order tensor. The QTI framework has been designed to improve discrimination of the sizes, shapes, and orientations of diffusion microenvironments within tissue. We derive rotationally invariant scalar quantities describing intuitive microstructural features including size, shape, and orientation coherence measures. To demonstrate the feasibility of QTI on a clinical scanner, we performed a small pilot study comparing a group of five healthy controls with five patients with schizophrenia. The parameter maps derived from QTI were compared between the groups, and 9 out of the 14 parameters investigated showed differences between groups. The ability to measure and model the distribution of diffusion tensors, rather than a quantity that has already been averaged within a voxel, has the potential to provide a powerful paradigm for the study of complex tissue architecture.

Variability in diffusion kurtosis imaging: Impact on study design, statistical power and interpretation.

Diffusion kurtosis imaging (DKI) is an emerging technique with the potential to quantify properties of tissue microstructure that may not be observable using diffusion tensor imaging (DTI). In order to help design DKI studies and improve interpretation of DKI results, we employed statistical power analysis to characterize three aspects of variability in four DKI parameters; the mean diffusivity, fractional anisotropy, mean kurtosis, and radial kurtosis. First, we quantified the variability in terms of the group size required to obtain a statistical power of 0.9. Second, we investigated the relative contribution of imaging and post-processing noise to the total variance, in order to estimate the benefits of longer scan times versus the inclusion of more subjects. Third, we evaluated the potential benefit of including additional covariates such as the size of the structure when testing for differences in group means. The analysis was performed in three major white matter structures of the brain: the superior cingulum, the corticospinal tract, and the mid-sagittal corpus callosum, extracted using diffusion tensor tractography and DKI data acquired in a healthy cohort. The results showed heterogeneous variability across and within the white matter structures. Thus, the statistical power varies depending on parameter and location, which is important to consider if a pathogenesis pattern is inferred from DKI data. In the data presented, inter-subject differences contributed more than imaging noise to the total variability, making it more efficient to include more subjects rather than extending the scan-time per subject. Finally, strong correlations between DKI parameters and the structure size were found for the cingulum and corpus callosum. Structure size should thus be considered when quantifying DKI parameters, either to control for its potentially confounding effect, or as a means of reducing unexplained variance.

The link between diffusion MRI and tumor heterogeneity: Mapping cell eccentricity and density by diffusional variance decomposition (DIVIDE).

The structural heterogeneity of tumor tissue can be probed by diffusion MRI (dMRI) in terms of the variance of apparent diffusivities within a voxel. However, the link between the diffusional variance and the tissue heterogeneity is not well-established. To investigate this link we test the hypothesis that diffusional variance, caused by microscopic anisotropy and isotropic heterogeneity, is associated with variable cell eccentricity and cell density in brain tumors. We performed dMRI using a novel encoding scheme for diffusional variance decomposition (DIVIDE) in 7 meningiomas and 8 gliomas prior to surgery. The diffusional variance was quantified from dMRI in terms of the total mean kurtosis (MKT), and DIVIDE was used to decompose MKT into components caused by microscopic anisotropy (MKA) and isotropic heterogeneity (MKI). Diffusion anisotropy was evaluated in terms of the fractional anisotropy (FA) and microscopic fractional anisotropy (μFA). Quantitative microscopy was performed on the excised tumor tissue, where structural anisotropy and cell density were quantified by structure tensor analysis and cell nuclei segmentation, respectively. In order to validate the DIVIDE parameters they were correlated to the corresponding parameters derived from microscopy. We found an excellent agreement between the DIVIDE parameters and corresponding microscopy parameters; MKA correlated with cell eccentricity (r=0.95, p<10-7) and MKI with the cell density variance (r=0.83, p<10-3). The diffusion anisotropy correlated with structure tensor anisotropy on the voxel-scale (FA, r=0.80, p<10-3) and microscopic scale (μFA, r=0.93, p<10-6). A multiple regression analysis showed that the conventional MKT parameter reflects both variable cell eccentricity and cell density, and therefore lacks specificity in terms of microstructure characteristics. However, specificity was obtained by decomposing the two contributions; MKA was associated only to cell eccentricity, and MKI only to cell density variance. The variance in meningiomas was caused primarily by microscopic anisotropy (mean±s.d.) MKA=1.11±0.33 vs MKI=0.44±0.20 (p<10-3), whereas in the gliomas, it was mostly caused by isotropic heterogeneity MKI=0.57±0.30 vs MKA=0.26±0.11 (p<0.05). In conclusion, DIVIDE allows non-invasive mapping of parameters that reflect variable cell eccentricity and density. These results constitute convincing evidence that a link exists between specific aspects of tissue heterogeneity and parameters from dMRI. Decomposing effects of microscopic anisotropy and isotropic heterogeneity facilitates an improved interpretation of tumor heterogeneity as well as diffusion anisotropy on both the microscopic and macroscopic scale.

Extrapolation-Based References Improve Motion and Eddy-Current Correction of High B-Value DWI Data: Application in Parkinson’s Disease Dementia

Purpose Conventional motion and eddy-current correction, where each diffusion-weighted volume is registered to a non diffusion-weighted reference, suffers from poor accuracy for high b-value data. An alternative approach is to extrapolate reference volumes from low b-value data. We aim to compare the performance of conventional and extrapolation-based correction of diffusional kurtosis imaging (DKI) data, and to demonstrate the impact of the correction approach on group comparison studies. Methods DKI was performed in patients with Parkinson’s disease dementia (PDD), and healthy age-matched controls, using b-values of up to 2750 s/mm2. The accuracy of conventional and extrapolation-based correction methods was investigated. Parameters from DTI and DKI were compared between patients and controls in the cingulum and the anterior thalamic projection tract. Results Conventional correction resulted in systematic registration errors for high b-value data. The extrapolation-based methods did not exhibit such errors, yielding more accurate tractography and up to 50% lower standard deviation in DKI metrics. Statistically significant differences were found between patients and controls when using the extrapolation-based motion correction that were not detected when using the conventional method. Conclusion We recommend that conventional motion and eddy-current correction should be abandoned for high b-value data in favour of more accurate methods using extrapolation-based references.

Optimal experimental design for filter exchange imaging: Apparent exchange rate measurements in the healthy brain and in intracranial tumors

Filter exchange imaging (FEXI) is sensitive to the rate of diffusional water exchange, which depends, eg, on the cell membrane permeability. The aim was to optimize and analyze the ability of FEXI to infer differences in the apparent exchange rate (AXR) in the brain between two populations.

Constrained optimization of gradient waveforms for generalized diffusion encoding.

Diffusion MRI is a useful probe of tissue microstructure. The conventional diffusion encoding sequence, the single pulsed field gradient, has recently been challenged as more general gradient waveforms have been introduced. Out of these, we focus on q-space trajectory imaging, which generalizes the scalar b-value to a tensor valued entity. To take full advantage of its capabilities, it is imperative to respect the constraints imposed by the hardware, while at the same time maximizing the diffusion encoding strength. We provide a tool that achieves this by solving a constrained optimization problem that accommodates constraints on maximum gradient amplitude, slew rate, coil heating and positioning of radio frequency pulses. The methods efficacy and flexibility is demonstrated both experimentally and by comparison with previous work on optimization of isotropic diffusion sequences.

Measurement Tensors in Diffusion MRI: Generalizing the Concept of Diffusion Encoding

In traditional diffusion MRI, short pulsed field gradients (PFG) are used for the diffusion encoding. The standard Stejskal-Tanner sequence uses one single pair of such gradients, known as single-PFG (sPFG). In this work we describe how trajectories in q-space can be used for diffusion encoding. We discuss how such encoding enables the extension of the well-known scalar b-value to a tensor-valued entity we call the diffusion measurement tensor. The new measurements contain information about higher order diffusion propagator covariances not present in sPFG. As an example analysis, we use this new information to estimate a Gaussian distribution over diffusion tensors in each voxel, described by its mean (a diffusion tensor) and its covariance (a 4th order tensor).

Assessment of Global and Regional Diffusion Changes along White Matter Tracts in Parkinsonian Disorders by MR Tractography.

Purpose The aim of the study was to determine the usefulness of diffusion tensor tractography (DTT) in parkinsonian disorders using a recently developed method for normalization of diffusion data and tract size along white matter tracts. Furthermore, the use of DTT in selected white matter tracts for differential diagnosis was assessed. Methods We quantified global and regional diffusion parameters in major white matter tracts in patients with multiple system atrophy (MSA), progressive nuclear palsy (PSP), idiopathic Parkinson’s disease (IPD) and healthy controls). Diffusion tensor imaging data sets with whole brain coverage were acquired at 3 T using 48 diffusion encoding directions and a voxel size of 2×2×2 mm3. DTT of the corpus callosum (CC), cingulum (CG), corticospinal tract (CST) and middle cerebellar peduncles (MCP) was performed using multiple regions of interest. Regional evaluation comprised projection of fractional anisotropy (FA), mean diffusivity (MD), radial diffusivity (RD) and the apparent area coefficient (AAC) onto a calculated mean tract and extraction of their values along each structure. Results There were significant changes of global DTT parameters in the CST (MSA and PSP), CC (PSP) and CG (PSP). Consistent tract-specific variations in DTT parameters could be seen along each tract in the different patient groups and controls. Regional analysis demonstrated significant changes in the anterior CC (MD, RD and FA), CST (MD) and CG (AAC) of patients with PSP compared to controls. Increased MD in CC and CST, as well as decreased AAC in CG, was correlated with a diagnosis of PSP compared to IPD. Conclusions DTT can be used for demonstrating disease-specific regional white matter changes in parkinsonian disorders. The anterior portion of the CC was identified as a promising region for detection of neurodegenerative changes in patients with PSP, as well as for differential diagnosis between PSP and IPD.