Tensor-valued Encoding Research Articles

In vivo rat brain mapping of multiple gray matter water populations using nonparametric D(ω)-R1-R2 distributions MRI.

Massively multidimensional diffusion magnetic resonance imaging combines tensor-valued encoding, oscillating gradients, and diffusion-relaxation correlation to provide multicomponent subvoxel parameters depicting some tissue microstructural features. This method was successfully implemented ex vivo in microimaging systems and clinical conditions with tensor-valued gradient waveform of variable duration giving access to a narrow diffusion frequency (ω) range. We demonstrate here its preclinical in vivo implementation with a protocol of 389 contrast images probing a wide diffusion frequency range of 18 to 92 Hz at b-values up to 2.1ms/μm2 enabled by the use of modulated gradient waveforms and combined with multislice high-resolution and low-distortion echo planar imaging acquisition with segmented and full reversed phase-encode acquisition. This framework allows the identification of diffusion ω-dependence in the rat cerebellum and olfactory bulb gray matter (GM), and the parameter distributions are shown to resolve two water pools in the cerebellum GM with different diffusion coefficients, shapes, ω-dependence, relaxation rates, and spatial repartition whose attribution to specific microstructure could modify the current understanding of the origin of restriction in GM.

Multidimensional encoding of restricted and anisotropic diffusion by double rotation of the qvector.

Diffusion NMR and MRI methods building on the classic pulsed gradient spin-echo sequence are sensitive to many aspects of translational motion, including time and frequency dependence ("restriction"), anisotropy, and flow, leading to ambiguities when interpreting experimental data from complex heterogeneous materials such as living biological tissues. While the oscillating gradient technique specifically targets frequency dependence and permits control of the sensitivity to flow, tensor-valued encoding enables investigations of anisotropy in orientationally disordered materials. Here, we propose a simple scheme derived from the "double-rotation" technique in solid-state NMR to generate a family of modulated gradient waveforms allowing for comprehensive exploration of the 2D frequency-anisotropy space and convenient investigation of both restricted and anisotropic diffusion with a single multidimensional acquisition protocol, thereby combining the desirable characteristics of the oscillating gradient and tensor-valued encoding techniques. The method is demonstrated by measuring multicomponent isotropic Gaussian diffusion in simple liquids, anisotropic Gaussian diffusion in a polydomain lyotropic liquid crystal, and restricted diffusion in a yeast cell sediment.

Stay on the Beat With Tensor-Valued Encoding: Time-Dependent Diffusion and Cell Size Estimation in ex vivo Heart

Diffusion encoding with free gradient waveforms can provide increased microstructural specificity in heterogeneous tissues compared to conventional encoding approaches. This is achieved by considering specific aspects of encoding, such as b-tensor shape, sensitivity to bulk motion and to time-dependent diffusion (TDD). In tensor-valued encoding, different b-tensor shapes are used, such as in linear tensor encoding (LTE) or spherical tensor encoding (STE). STE can be employed for estimation of mean diffusivity (MD) or in combination with LTE to probe average microscopic anisotropy unconfounded by orientation dispersion. While tensor-valued encoding has been successfully applied in the brain and other organs, its potential and limitations have not yet been fully explored in cardiac applications. To avoid artefacts due to motion, which are particularly challenging in cardiac imaging, arbitrary b-tensors can be designed with motion compensation, i.e. gradient moment nulling, while also nulling the adverse effects of concomitant gradients. Encoding waveforms with varying degrees of motion compensation may however have significantly different sensitivities to TDD. This effect can be prominent in tissues with relatively large cell sizes such as in the heart and can be used advantageously to provide further tissue information. To account for TDD in tensor-valued encoding, the interplay between asynchronous gradients simultaneously applied along different directions needs to be considered. As the first step toward in vivo cardiac applications, our overarching goal was to explore the feasibility of acceleration compensated tensor-valued encoding on preclinical and clinical scanners ex vivo. We have demonstrated strong and predictable variation of MD due to TDD in mouse and pig hearts using a wide range of LTE and STE with progressively increasing degrees of motion compensation. Our preliminary data from acceleration compensated STE and LTE at high b-values, attainable on the preclinical scanner, indicate that TDD needs to be considered in experiments with varying b-tensor shapes. We have presented a novel theoretical framework, which enables cell size estimation, helps to elucidate limitations and provides a basis for further optimizations of experiments probing both mean diffusivity and microscopic anisotropy in the heart.

Massively Multidimensional Diffusion-Relaxation Correlation MRI

Diverse approaches such as oscillating gradients, tensor-valued encoding, and diffusion-relaxation correlation have been used to study microstructure and heterogeneity in healthy and pathological biological tissues. Recently, acquisition schemes with free gradient waveforms exploring both the frequency-dependent and tensorial aspects of the encoding spectrum b(ω) have enabled estimation of nonparametric distributions of frequency-dependent diffusion tensors. These “D(ω)-distributions” allow investigation of restricted diffusion for each distinct component resolved in the diffusion tensor trace, anisotropy, and orientation dimensions. Likewise, multidimensional methods combining longitudinal and transverse relaxation rates, R1 and R2, with (ω-independent) D-distributions capitalize on the component resolution offered by the diffusion dimensions to investigate subtle differences in relaxation properties of sub-voxel water populations in the living human brain, for instance nerve fiber bundles with different orientations. By measurements on an ex vivo rat brain, we here demonstrate a “massively multidimensional” diffusion-relaxation correlation protocol joining all the approaches mentioned above. Images acquired as a function of the magnitude, normalized anisotropy, orientation, and frequency content of b(ω), as well as the repetition time and echo time, yield nonparametric D(ω)-R1-R2-distributions via a Monte Carlo data inversion algorithm. The obtained per-voxel distributions are converted to parameter maps commonly associated with conventional lower-dimensional methods as well as unique statistical descriptors reporting on the correlations between restriction, anisotropy, and relaxation.

Probing tissue microstructure by diffusion skewness tensor imaging

Probing the cellular structure of in vivo biological tissue is a fundamental problem in biomedical imaging and medical science. This work introduces an approach for analyzing diffusion magnetic resonance imaging data acquired by the novel tensor-valued encoding technique for characterizing tissue microstructure. Our approach first uses a signal model to estimate the variance and skewness of the distribution of apparent diffusion tensors modeling the underlying tissue. Then several novel imaging indices, such as weighted microscopic anisotropy and microscopic skewness, are derived to characterize different ensembles of diffusion processes that are indistinguishable by existing techniques. The contributions of this work also include a theoretical proof that shows that, to estimate the skewness of a diffusion tensor distribution, the encoding protocol needs to include full-rank tensor diffusion encoding. This proof provides a guideline for the application of this technique. The properties of the proposed indices are illustrated using both synthetic data and in vivo data acquired from a human brain.

Motion-compensated gradient waveforms for tensor-valued diffusion encoding by constrained numerical optimization.

PurposeDiffusion‐weighted MRI is sensitive to incoherent tissue motion, which may confound the measured signal and subsequent analysis. We propose a “motion‐compensated” gradient waveform design for tensor‐valued diffusion encoding that negates the effects bulk motion and incoherent motion in the ballistic regime.MethodsMotion compensation was achieved by constraining the magnitude of gradient waveform moment vectors. The constraint was incorporated into a numerical optimization framework, along with existing constraints that account for b‐tensor shape, hardware restrictions, and concomitant field gradients. We evaluated the efficacy of encoding and motion compensation in simulations, and we demonstrated the approach by linear and planar b‐tensor encoding in a healthy heart in vivo.ResultsThe optimization framework produced asymmetric motion‐compensated waveforms that yielded b‐tensors of arbitrary shape with improved efficiency compared with previous designs for tensor‐valued encoding, and equivalent efficiency to previous designs for linear (conventional) encoding. Technical feasibility was demonstrated in the heart in vivo, showing vastly improved data quality when using motion compensation. The optimization framework is available online in open source.ConclusionOur gradient waveform design is both more flexible and efficient than previous methods, facilitating tensor‐valued diffusion encoding in tissues in which motion would otherwise confound the signal. The proposed design exploits asymmetric encoding times, a single refocusing pulse or multiple refocusing pulses, and integrates compensation for concomitant gradient effects throughout the imaging volume.

Disentangling white-matter damage from physiological fibre orientation dispersion in multiple sclerosis.

Multiple sclerosis leads to diffuse damage of the central nervous system, affecting also the normal-appearing white matter. Demyelination and axonal degeneration reduce regional fractional anisotropy in normal-appearing white matter, which can be routinely mapped with diffusion tensor imaging. However, the standard fractional anisotropy metric is also sensitive to physiological variations in orientation dispersion of white matter fibres. This complicates the detection of disease-related damage in large parts of cerebral white matter where microstructure physiologically displays a high degree of fibre dispersion. To resolve this ambiguity, we employed a novel tensor-valued encoding method for diffusion MRI, which yields a microscopic fractional anisotropy metric that is unaffected by regional variations in orientation dispersion. In 26 patients with relapsing-remitting multiple sclerosis, 14 patients with primary-progressive multiple sclerosis and 27 age-matched healthy controls, we compared standard fractional anisotropy mapping with the novel microscopic fractional anisotropy mapping method, focusing on normal-appearing white matter. Mean microscopic fractional anisotropy and standard fractional anisotropy of normal-appearing white matter were significantly reduced in both patient groups relative to healthy controls, but microscopic fractional anisotropy yielded a better reflection of disease-related white-matter alterations. The reduction in mean microscopic fractional anisotropy showed a significant positive linear relationship with physical disability, as reflected by the expanded disability status scale. Mean reduction of microscopic fractional anisotropy in normal-appearing white matter also scaled positively with individual cognitive dysfunction, as measured with the symbol digit modality test. Mean microscopic fractional anisotropy reduction in normal-appearing white matter also showed a positive relationship with total white-matter lesion load as well as lesion load in specific tract systems. None of these relationships between normal-appearing white-matter microstructure and clinical, cognitive or structural measures emerged when using mean fractional anisotropy. Together, the results provide converging evidence that microscopic fractional anisotropy mapping substantially advances the assessment of cerebral white matter in multiple sclerosis by disentangling microstructure damage from variations in physiological fibre orientation dispersion at the stage of data acquisition. Since tensor-valued encoding can be implemented in routine diffusion MRI, microscopic fractional anisotropy mapping bears considerable potential for the future assessment of disease progression in normal-appearing white matter in both relapsing-remitting and progressive forms of multiple sclerosis as well as other white-matter-related brain diseases.

Tensor-valued diffusion encoding for diffusional variance decomposition (DIVIDE): Technical feasibility in clinical MRI systems.

Microstructure imaging techniques based on tensor-valued diffusion encoding have gained popularity within the MRI research community. Unlike conventional diffusion encoding—applied along a single direction in each shot—tensor-valued encoding employs diffusion encoding along multiple directions within a single preparation of the signal. The benefit is that such encoding may probe tissue features that are not accessible by conventional encoding. For example, diffusional variance decomposition (DIVIDE) takes advantage of tensor-valued encoding to probe microscopic diffusion anisotropy independent of orientation coherence. The drawback is that tensor-valued encoding generally requires gradient waveforms that are more demanding on hardware; it has therefore been used primarily in MRI systems with relatively high performance. The purpose of this work was to explore tensor-valued diffusion encoding on clinical MRI systems with varying performance to test its technical feasibility within the context of DIVIDE. We performed whole-brain imaging with linear and spherical b-tensor encoding at field strengths between 1.5 and 7 T, and at maximal gradient amplitudes between 45 and 80 mT/m. Asymmetric gradient waveforms were optimized numerically to yield b-values up to 2 ms/μm2. Technical feasibility was assessed in terms of the repeatability, SNR, and quality of DIVIDE parameter maps. Variable system performance resulted in echo times between 83 to 115 ms and total acquisition times of 6 to 9 minutes when using 80 signal samples and resolution 2×2×4 mm3. As expected, the repeatability, signal-to-noise ratio and parameter map quality depended on hardware performance. We conclude that tensor-valued encoding is feasible for a wide range of MRI systems—even at 1.5 T with maximal gradient waveform amplitudes of 33 mT/m—and baseline experimental design and quality parameters for all included configurations. This demonstrates that tissue features, beyond those accessible by conventional diffusion encoding, can be explored on a wide range of MRI systems.