How background noise shifts eigenvectors and increases eigenvalues in DTI

The effect of elimination of gibbs ringing, noise and systematic errors on the DTI metrics and tractography in a rat brain

Diffusion tensor imaging (DTI) metrics and tractography can be biased due to low signal-to-noise ratio (SNR) and systematic errors resulting from image artifacts and imperfections in magnetic field gradients. The imperfections include non-uniformity and nonlinearity, effects caused by eddy currents, and the influence of background and imaging gradients. We investigated the impact of systematic errors on DTI metrics of an isotropic phantom and DTI metrics and tractography of a rat brain measured at high resolution. We tested denoising and Gibbs ringing removal methods combined with the B matrix spatial distribution (BSD) method for magnetic field gradient calibration. The results showed that the performance of the BSD method depends on whether Gibbs ringing is removed and the effectiveness of stochastic error removal. Region of interest (ROI)-based analysis of the DTI metrics showed that, depending on the size of the ROI and its location in space, correction methods can remove systematic bias to varying degrees. The preprocessing pipeline proposed and dedicated to this type of data together with the BSD method resulted in an even - 90% decrease in fractional anisotropy (FA) (globally and locally) in the isotropic phantom and - 45% in the rat brain. The largest global changes in the rat brain tractogram compared to the standard method without preprocessing (sDTI) were noticed after denoising. The direction of the first eigenvector obtained from DTI after denoising, Gibbs ringing removal and BSD differed by an average of 56 and 10 degrees in the ROI from sDTI and from sDTI after denoising and Gibbs ringing removal, respectively. The latter can be identified with the amount of improvement in tractography due to the elimination of systematic errors related to imperfect magnetic field gradients. Based on the results, the systematic bias for high resolution data mainly depended on SNR, but the influence of non-uniform gradients could also be seen. After denoising, the BSD method was able to further correct both the metrics and tractography of the diffusion tensor in the rat brain by taking into account the actual distribution of magnetic field gradients independent of the examined object and uniquely dependent on the scanner and sequence. This means that in vivo studies are also subject to this type of errors, which should be taken into account when processing such data.

In vivo disentanglement of diffusion frequency-dependence, tensor shape, and relaxation using multidimensional MRI

Diffusion MRI with free gradient waveforms, combined with simultaneous relaxation encoding, referred to as multidimensional MRI (MD-MRI), offers microstructural specificity in complex biological tissue. This approach delivers intravoxel information about the microstructure, local chemical composition, and importantly, how these properties are coupled within heterogeneous tissue containing multiple microenvironments. Recent theoretical advances incorporated diffusion time dependency and integrated MD-MRI with concepts from oscillating gradients. This framework probes the diffusion frequency,ω $$ \omega $$ , in addition to the diffusion tensor,D $$ \mathbf{D} $$ , and relaxation,R 1 $$ {R}_1 $$ ,R 2 $$ {R}_2 $$ , correlations. AD ω - R 1 - R 2 $$ \mathbf{D}\left(\omega \right)-{R}_1-{R}_2 $$ clinical imaging protocol was then introduced, with limited brain coverage and 3 mm3 voxel size, which hinder brain segmentation and future cohort studies. In this study, we introduce an efficient, sparse in vivo MD-MRI acquisition protocol providing whole brain coverage at 2 mm3 voxel size. We demonstrate its feasibility and robustness using a well-defined phantom and repeated scans of five healthy individuals. Additionally, we test different denoising strategies to address the sparse nature of this protocol, and show that efficient MD-MRI encoding design demands a nuanced denoising approach. The MD-MRI framework provides rich information that allows resolving the diffusion frequency dependence into intravoxel components based on theirD ω - R 1 - R 2 $$ \mathbf{D}\left(\omega \right)-{R}_1-{R}_2 $$ distribution, enabling the creation of microstructure-specific maps in the human brain. Our results encourage the broader adoption and use of this new imaging approach for characterizing healthy and pathological tissues.

DENOISING DIFFUSION MRI: CONSIDERATIONS AND IMPLICATIONS FOR ANALYSIS

Development of diffusion MRI (dMRI) denoising approaches has experienced considerable growth over the last years. As noise can inherently reduce accuracy and precision in measurements, its effects have been well characterised both in terms of uncertainty increase in dMRI-derived features and in terms of biases caused by the noise floor, the smallest measurable signal given the noise level. However, gaps in our knowledge still exist in objectively characterising dMRI denoising approaches in terms of both of these effects and assessing their efficacy. In this work, we reconsider what a denoising method should and should not do and we accordingly define criteria to characterise the performance. We propose a comprehensive set of evaluations, including i) benefits in improving signal quality and reducing noise variance, ii) gains in reducing biases and the noise floor and improving, iii) preservation of spatial resolution, iv) agreement of denoised data against a gold standard, v) gains in downstream parameter estimation (precision and accuracy), vi) efficacy in enabling noise-prone applications, such as ultra-high-resolution imaging. We further provide newly acquired complex datasets (magnitude and phase) with multiple repeats that sample different SNR regimes to highlight performance differences under different scenarios. Without loss of generality, we subsequently apply a number of exemplar patch-based denoising algorithms to these datasets, including Non-Local Means, Marchenko-Pastur PCA (MPPCA) in the magnitude and complex domain and NORDIC, and compare them with respect to the above criteria and against a gold standard complex average of multiple repeats. We demonstrate that all tested denoising approaches reduce noise-related variance, but not always biases from the elevated noise floor. They all induce a spatial resolution penalty, but its extent can vary depending on the method and the implementation. Some denoising approaches agree with the gold standard more than others and we demonstrate challenges in even defining such a standard. Overall, we show that dMRI denoising performed in the complex domain is advantageous to magnitude domain denoising with respect to all the above criteria.

In vivo disentanglement of diffusion frequency-dependence, tensor shape, and relaxation using multidimensional MRI

Diffusion MRI with free gradient waveforms, combined with simultaneous relaxation encoding, referred to as multidimensional MRI (MD-MRI), offers microstructural specificity in complex biological tissue. This approach delivers intravoxel information about the microstructure, local chemical composition, and importantly, how these properties are coupled within heterogeneous tissue containing multiple microenvironments. Recent theoretical advances incorporated diffusion time dependency and integrated MD-MRI with concepts from oscillating gradients. This framework probes the diffusion frequency, ω , in addition to the diffusion tensor, D , and relaxation, R 1 , R 2 , correlations. A D ( ω ) - R 1 - R 2 clinical imaging protocol was then introduced, with limited brain coverage and 3 mm3 voxel size, which hinder brain segmentation and future cohort studies. In this study, we introduce an efficient, sparse in vivo MD-MRI acquisition protocol providing whole brain coverage at 2 mm3 voxel size. We demonstrate its feasibility and robustness using a well-defined phantom and repeated scans of five healthy individuals. Additionally, we test different denoising strategies to address the sparse nature of this protocol, and show that efficient MD-MRI encoding design demands a nuanced denoising approach. The MD-MRI framework provides rich information that allows resolving the diffusion frequency dependence into intravoxel components based on their D ( ω ) - R 1 - R 2 distribution, enabling the creation of microstructure-specific maps in the human brain. Our results encourage the broader adoption and use of this new imaging approach for characterizing healthy and pathological tissues.

Diffusion Breast MRI: Current Standard and Emerging Techniques

The role of diffusion weighted imaging (DWI) as a biomarker has been the subject of active investigation in the field of breast radiology. By quantifying the random motion of water within a voxel of tissue, DWI provides indirect metrics that reveal cellularity and architectural features. Studies show that data obtained from DWI may provide information related to the characterization, prognosis, and treatment response of breast cancer. The incorporation of DWI in breast imaging demonstrates its potential to serve as a non-invasive tool to help guide diagnosis and treatment. In this review, current technical literature of diffusion-weighted breast imaging will be discussed, in addition to clinical applications, advanced techniques, and emerging use in the field of radiomics.

Adaptive phase correction of diffusion-weighted images

Phase correction (PC) is a preprocessing technique that exploits the phase of images acquired in Magnetic Resonance Imaging (MRI) to obtain real-valued images containing tissue contrast with additive Gaussian noise, as opposed to magnitude images which follow a non-Gaussian distribution, e.g. Rician. PC finds its natural application to diffusion-weighted images (DWIs) due to their inherent low signal-to-noise ratio and consequent non-Gaussianity that induces a signal overestimation bias that propagates to the calculated diffusion indices. PC effectiveness depends upon the quality of the phase estimation, which is often performed via a regularization procedure. We show that a suboptimal regularization can produce alterations of the true image contrast in the real-valued phase-corrected images. We propose adaptive phase correction (APC), a method where the phase is estimated by using MRI noise information to perform a complex-valued image regularization that accounts for the local variance of the noise. We show, on synthetic and acquired data, that APC leads to phase-corrected real-valued DWIs that present a reduced number of alterations and a reduced bias. The substantial absence of parameters for which human input is required favors a straightforward integration of APC in MRI processing pipelines.

Complex diffusion-weighted image estimation via matrix recovery under general noise models

We propose a patch-based singular value shrinkage method for diffusion magnetic resonance image estimation targeted at low signal to noise ratio and accelerated acquisitions. It operates on the complex data resulting from a sensitivity encoding reconstruction, where asymptotically optimal signal recovery guarantees can be attained by modeling the noise propagation in the reconstruction and subsequently simulating or calculating the limit singular value spectrum. Simple strategies are presented to deal with phase inconsistencies and optimize patch construction. The pertinence of our contributions is quantitatively validated on synthetic data, an in vivo adult example, and challenging neonatal and fetal cohorts. Our methodology is compared with related approaches, which generally operate on magnitude-only data and use data-based noise level estimation and singular value truncation. Visual examples are provided to illustrate effectiveness in generating denoised and debiased diffusion estimates with well preserved spatial and diffusion detail.

Diffusion MRI of the breast: Current status and future directions

Diffusion-weighted imaging (DWI) is increasingly being incorporated into routine breast MRI protocols in many institutions worldwide, and there are abundant breast DWI indications ranging from lesion detection and distinguishing malignant from benign tumors to assessing prognostic biomarkers of breast cancer and predicting treatment response. DWI has the potential to serve as a noncontrast MR screening method. Beyond apparent diffusion coefficient (ADC) mapping, which is a commonly used quantitative DWI measure, advanced DWI models such as intravoxel incoherent motion (IVIM), non-Gaussian diffusion MRI, and diffusion tensor imaging (DTI) are extensively exploited in this field, allowing the characterization of tissue perfusion and architecture and improving diagnostic accuracy without the use of contrast agents. This review will give a summary of the clinical literature along with future directions. Level of Evidence: 5 Technical Efficacy: Stage 2 J. Magn. Reson. Imaging 2020;52:70-90.

Temperature and concentration calibration of aqueous polyvinylpyrrolidone (PVP) solutions for isotropic diffusion MRI phantoms

To use the "apparent diffusion coefficient" (Dapp) as a quantitative imaging parameter, well-suited test fluids are essential. In this study, the previously proposed aqueous solutions of polyvinylpyrrolidone (PVP) were examined and temperature calibrations were obtained. For example, at a temperature of 20°C, Dapp ranged from 1.594 (95% CI: 1.593, 1.595) μm2/ms to 0.3326 (95% CI: 0. 3304, 0.3348) μm2/ms for PVP-concentrations ranging from 10% (w/w) to 50% (w/w) using K30 polymer lengths. The temperature dependence of Dapp was found to be so strong that a negligence seems not advisable. The temperature dependence is descriptively modelled by an exponential function exp(c2 (T - 20°C)) and the determined c2 values are reported, which can be used for temperature calibration. For example, we find the value 0.02952 K-1 for 30% (w/w) PVP-concentration and K30 polymer length. In general, aqueous PVP solutions were found to be suitable to produce easily applicable and reliable Dapp-phantoms.

Impact of MR Acquisition Parameters on DTI Scalar Indexes: A Tractography Based Approach

Acquisition parameters play a crucial role in Diffusion Tensor Imaging (DTI), as they have a major impact on the values of scalar measures such as Fractional Anisotropy (FA) or Mean Diffusivity (MD) that are usually the focus of clinical studies based on white matter analysis. This paper presents an analysis on the impact of the variation of several acquisition parameters on these scalar measures with a novel double focus. First, a tractography-based approach is employed, motivated by the significant number of clinical studies that are carried out using this technique. Second, the consequences of simultaneous changes in multiple parameters are analyzed: number of gradient directions, b-value and voxel resolution. Results indicate that the FA is most affected by changes in the number of gradients and voxel resolution, while MD is specially influenced by variations in the b-value. Even if the choice of a tractography algorithm has an effect on the numerical values of the final scalar measures, the evolution of these measures when acquisition parameters are modified is parallel.

Analysis and correction of gradient nonlinearity bias in apparent diffusion coefficient measurements

PURPOSE

Gradient nonlinearity of MRI systems leads to spatially dependent b-values and consequently high non-uniformity errors (10-20%) in apparent diffusion coefficient (ADC) measurements over clinically relevant field-of-views. This work seeks practical correction procedure that effectively reduces observed ADC bias for media of arbitrary anisotropy in the fewest measurements.

METHODS

All-inclusive bias analysis considers spatial and time-domain cross-terms for diffusion and imaging gradients. The proposed correction is based on rotation of the gradient nonlinearity tensor into the diffusion gradient frame where spatial bias of b-matrix can be approximated by its Euclidean norm. Correction efficiency of the proposed procedure is numerically evaluated for a range of model diffusion tensor anisotropies and orientations.

RESULTS

Spatial dependence of nonlinearity correction terms accounts for the bulk (75-95%) of ADC bias for FA = 0.3-0.9. Residual ADC non-uniformity errors are amplified for anisotropic diffusion. This approximation obviates need for full diffusion tensor measurement and diagonalization to derive a corrected ADC. Practical scenarios are outlined for implementation of the correction on clinical MRI systems.

CONCLUSIONS

The proposed simplified correction algorithm appears sufficient to control ADC non-uniformity errors in clinical studies using three orthogonal diffusion measurements. The most efficient reduction of ADC bias for anisotropic medium is achieved with non-lab-based diffusion gradients.

Effect of increasing diffusion gradient direction number on diffusion tensor imaging fiber tracking in the human brain

Objective

To assess the effects of varying the number of diffusion gradient directions (NDGDs) on diffusion tensor fiber tracking (FT) in human brain white matter using tract characteristics.

Materials and Methods

Twelve normal volunteers underwent diffusion tensor imaging (DTI) scanning with NDGDs of 6, 11, 15, 21, and 31 orientations. Three fiber tract groups, including the splenium of the corpus callosum (CC), the entire CC, and the full brain tract, were reconstructed by deterministic DTI-FT. Tract architecture was first qualitatively evaluated by visual observation. Six quantitative tract characteristics, including the number of fibers (NF), average length (AL), fractional anisotropy (FA), relative anisotropy (RA), mean diffusivity (MD), and volume ratio (VR) were measured for the splenium of the CC at the tract branch level, for the entire CC at tract level, and for the full brain tract at the whole brain level. Visual results and those of NF, AL, FA, RA, MD, and VR were compared among the five different NDGDs.

Results

The DTI-FT with NDGD of 11, 15, 21, and 31 orientations gave better tracking results compared with NDGD of 6 after the visual evaluation. NF, FA, RA, MD, and VR values with NDGD of six were significantly greater (smallest p = 0.001 to largest p = 0.042) than those with four other NDGDs (11, 15, 21, or 31 orientations), whereas AL measured with NDGD of six was significantly smaller (smallest p = 0.001 to largest p = 0.041) than with four other NDGDs (11, 15, 21, or 31 orientations). No significant differences were observed in the results among the four NDGD groups of 11, 15, 21, and 31 directions (smallest p = 0.059 to largest p = 1.000).

Conclusion

The main fiber tracts were detected with NDGD of six orientations; however, the use of larger NDGD (≥ 11 orientations) could provide improved tract characteristics at the expense of longer scanning time.

Quantitative comparison of reconstruction methods for intra-voxel fiber recovery from diffusion MRI

Validation is arguably the bottleneck in the diffusion magnetic resonance imaging (MRI) community. This paper evaluates and compares 20 algorithms for recovering the local intra-voxel fiber structure from diffusion MRI data and is based on the results of the "HARDI reconstruction challenge" organized in the context of the "ISBI 2012" conference. Evaluated methods encompass a mixture of classical techniques well known in the literature such as diffusion tensor, Q-Ball and diffusion spectrum imaging, algorithms inspired by the recent theory of compressed sensing and also brand new approaches proposed for the first time at this contest. To quantitatively compare the methods under controlled conditions, two datasets with known ground-truth were synthetically generated and two main criteria were used to evaluate the quality of the reconstructions in every voxel: correct assessment of the number of fiber populations and angular accuracy in their orientation. This comparative study investigates the behavior of every algorithm with varying experimental conditions and highlights strengths and weaknesses of each approach. This information can be useful not only for enhancing current algorithms and develop the next generation of reconstruction methods, but also to assist physicians in the choice of the most adequate technique for their studies.

Diffusion tensor imaging fiber tracking with reliable tracking orientation and flexible step size

We propose a method of reliable tracking orientation and flexible step size fiber tracking. A new directional strategy was defined to select one optimal tracking orientation from each directional set, which was based on the single-tensor model and the two-tensor model. The directional set of planar voxels contained three tracking directions: two from the two-tensor model and one from the single-tensor model. The directional set of linear voxels contained only one principal vector. In addition, a flexible step size, rather than fixable step sizes, was implemented to improve the accuracy of fiber tracking. We used two sets of human data to assess the performance of our method; one was from a healthy volunteer and the other from a patient with low-grade glioma. Results verified that our method was superior to the single-tensor Fiber Assignment by Continuous Tracking and the two-tensor eXtended Streamline Tractography for showing detailed images of fiber bundles.

DTI BASED STRUCTURAL DAMAGE CHARACTERIZATION FOR DISORDERS OF CONSCIOUSNESS

MRI Diffusion Tensor Imaging (DTI) has been recently proposed as a highly discriminative measurement to detect structural damages in Disorders of Consciousness patients (Vegetative State/Unresponsive Wakefulness Syndrome-(VS/UWS) and Minimally Consciousness State-MCS). In the DTI analysis, certain tensor features are often used as simplified scalar indices to represent these alterations. Those characteristics are mathematically and statistically more tractable than the full tensors. Nevertheless, most of these quantities are based on a tensor diffusivity estimation, the arithmetic average among the different strengths of the tensor orthogonal directions, which is supported on a symmetric linear relationship among the three directions, an unrealistic assumption for severely damaged brains. In this paper, we propose a new family of scalar quantities based on Generalized Ordered Weighted Aggregations (GOWA) to characterize morphological damages. The main idea is to compute a tensor diffusitivity estimation that captures the deviations in the water diffusivity associated to damaged tissue. This estimation is performed by weighting and combining differently each tensor orthogonal strength. Using these new scalar quantities we construct an affine invariant DTI tensor feature using regional tissue histograms. An evaluation of these new scalar quantities on 48 patients (23 VS/UWS and 25 MCS) was conducted. Our experiments demonstrate that this new representation outperforms state-of-the-art tensor based scalar representations for characterization and classification problems.

Manifestation and post hoc correction of gradient cross-term artifacts in DTI

Cross-terms between imaging and diffusion gradients, unaccounted for during tensor calculations, can lead to erroneous estimation of diffusivity and fractional anisotropy (FA) in regions of isotropic and anisotropic diffusion. Cross-term of magnitude 136.8±1.6 s/mm(2), artificially introduced in the slice-encode direction, caused an increase in FA in isotropic phantom from 0.0546±0.0001 to 0.0996±0.0001, while the change in chimpanzee brain depended on the orientation of the white matter (WM). Mean diffusivity (MD) remained unchanged in isotropic phantom, but increased by ∼20% in the WM due to cross-terms. A bias was observed in the principal eigenvectors in both phantom and chimpanzee brain, resulting in significant increase in midline crossing fibers along the bias than perpendicular to it in tractography in chimpanzee brain. Post hoc correction of these artifacts was achieved by estimating the cross-term factors using calibration scans on an isotropic phantom and modifying the b-matrix before tensor calculation. Upon correction, the FA and MD values closely resembled the values obtained from sequence without cross-terms, and the bias in principal eigenvectors was eliminated. Customized sequences involving large b-values, high-resolution imaging, or long diffusion or echo times should therefore be evaluated and any residual cross-terms corrected before implementation.

[Introduction to the basic principles and techniques of diffusion-weighted imaging]

This article gives an overview of the many different technical aspects of diffusion-weighted imaging and a review of the physical and mathematical background. Specific terms, such as free and restricted diffusion are introduced and elucidated. The measurement of diffusion by magnetic resonance imaging (MRI) and which phenomena can occur are described. Finally, an overview of current developments in diffusion imaging and its application in research is presented.

Love songs, bird brains and diffusion tensor imaging

The song control system of songbirds displays a remarkable seasonal neuroplasticity in species in which song output also changes seasonally. Thus far, this song control system has been extensively analyzed by histological and electrophysiological methods. However, these approaches do not provide a global view of the brain and/or do not allow repeated measurements, which are necessary to establish causal correlations between alterations in neural substrate and behavior. Research has primarily been focused on the song nuclei themselves, largely neglecting their interconnections and other brain regions involved in seasonally changing behavior. In this review, we introduce and explore the song control system of songbirds as a natural model for brain plasticity. At the same time, we point out the added value of the songbird brain model for in vivo diffusion tensor techniques and its derivatives. A compilation of the diffusion tensor imaging (DTI) data obtained thus far in this system demonstrates the usefulness of this in vivo method for studying brain plasticity. In particular, it is shown to be a perfect tool for long-term studies of morphological and cellular changes of specific brain circuits in different endocrine/photoperiod conditions. The method has been successfully applied to obtain quantitative measurements of seasonal changes of fiber tracts and nuclei from the song control system. In addition, outside the song control system, changes have been discerned in the optic chiasm and in an interhemispheric connection. DTI allows the detection of seasonal changes in a region analogous to the mammalian secondary auditory cortex and in regions of the 'social behavior network', an interconnected group of structures that controls multiple social behaviors, including aggression and courtship. DTI allows the demonstration, for the first time, that the songbird brain in its entirety exhibits an extreme seasonal plasticity which is not merely limited to the song control system as was generally believed.