Estimating intensity variance due to noise in registered images: Applications to diffusion tensor MRI

What's new and what's next in diffusion MRI preprocessing

Diffusion MRI (dMRI) provides invaluable information for the study of tissue microstructure and brain connectivity, but suffers from a range of imaging artifacts that greatly challenge the analysis of results and their interpretability if not appropriately accounted for. This review will cover dMRI artifacts and preprocessing steps, some of which have not typically been considered in existing pipelines or reviews, or have only gained attention in recent years: brain/skull extraction, B-matrix incompatibilities w.r.t the imaging data, signal drift, Gibbs ringing, noise distribution bias, denoising, between- and within-volumes motion, eddy currents, outliers, susceptibility distortions, EPI Nyquist ghosts, gradient deviations, B1 bias fields, and spatial normalization. The focus will be on "what's new" since the notable advances prior to and brought by the Human Connectome Project (HCP), as presented in the predecessing issue on "Mapping the Connectome" in 2013. In addition to the development of novel strategies for dMRI preprocessing, exciting progress has been made in the availability of open source tools and reproducible pipelines, databases and simulation tools for the evaluation of preprocessing steps, and automated quality control frameworks, amongst others. Finally, this review will consider practical considerations and our view on "what's next" in dMRI preprocessing.

Longitudinal neuroimaging following combat concussion: sub-acute, 1 year and 5 years post-injury

Questions remain regarding the long-term impact of combat concussive blast exposure. While efforts have begun to highlight the clinical impact, less is known about neuroimaging trajectories that may inform underlying pathophysiological changes post-injury. Through collaborative efforts in combat, following medical evacuation, and at universities in the USA, this study followed service members both with and without blast concussion from the sub-acute to 1-year and 5-year outcomes with quantitative neuroimaging. The following two primary and two exploratory groups were examined: combat-deployed controls without blast exposure history ‘non-blast control’ and concussive blast patients (primary) and combat concussion arising not from blast ‘non-blast concussion’ and combat-deployed controls with blast exposure history ‘blast control’ (exploratory). A total of 575 subjects were prospectively enrolled and imaged; 347 subjects completed further neuroimaging examination at 1 year and 342 subjects completed further neuroimaging examination at 5 years post-injury. At each time point, MRI scans were completed that included high-resolution structural as well as diffusion tensor imaging acquisitions processed for quantitative volumetric and diffusion tensor imaging changes. Longitudinal evaluation of the number of abnormal diffusion tensor imaging and volumetric regions in patients with blast concussion revealed distinct trends by imaging modality. While the presence of abnormal volumetric regions remained quite stable comparing our two primary groups of non-blast control to blast concussion, the diffusion tensor imaging abnormalities were observed to have varying trajectories. Most striking was the fractional anisotropy ‘U-shaped’ curve observed for a proportion of those that, if we had only followed them to 1 year, would look like trajectories of recovery. However, by continuing the follow-up to 5 years in these very same patients, a secondary increase in the number of reduced fractional anisotropy regions was identified. Comparing non-blast controls to blast concussion at each time point revealed significant differences in the number of regions with reduced fractional anisotropy at both the sub-acute and 5-year time points, which held after adjustment for age, education, gender, scanner and subsequent head injury exposure followed by correction for multiple comparisons. The secondary increase identified in patients with blast concussion may be the earliest indications of microstructural changes underlying the ‘accelerated brain aging’ theory recently reported from chronic, cross-sectional studies of veterans following brain injury. These varying trajectories also inform potential prognostic neuroimaging biomarkers of progression and recovery.

Longitudinal Structural and Functional Differences Between Proportional and Poor Motor Recovery After Stroke

BACKGROUND

Evolution of motor function during the first months after stroke is stereotypically bifurcated, consisting of either recovery to about 70% of maximum possible improvement ("proportional recovery, PROP") or in little to no improvement ("poor recovery, POOR"). There is currently no evidence that any rehabilitation treatment will prevent POOR and favor PROP.

OBJECTIVE

To perform a longitudinal and multimodal assessment of functional and structural changes in brain organization associated with PROP.

METHODS

Fugl-Meyer Assessments of the upper extremity and high-density electroencephalography (EEG) were obtained from 63 patients, diffusion tensor imaging from 46 patients, at 2 and 4 weeks (T0) and at 3 months (T1) after stroke onset.

RESULTS

We confirmed the presence of 2 distinct recovery patterns (PROP and POOR) in our sample. At T0, PROP patients had greater integrity of the corticospinal tract (CST) and greater EEG functional connectivity (FC) between the affected hemisphere and rest of the brain, in particular between the ventral premotor and the primary motor cortex. POOR patients suffered from degradation of corticocortical and corticofugal fiber tracts in the affected hemisphere between T0 and T1, which was not observed in PROP patients. Better initial CST integrity correlated with greater initial global FC, which was in turn associated with less white matter degradation between T0 and T1.

CONCLUSIONS

These findings suggest links between initial CST integrity, systems-level cortical network plasticity, reduction of white matter atrophy, and clinical motor recovery after stroke. This identifies candidate treatment targets.

Non-Stationary Rician Noise Estimation in Parallel MRI Using a Single Image: A Variance-Stabilizing Approach

Parallel magnetic resonance imaging (pMRI) techniques have gained a great importance both in research and clinical communities recently since they considerably accelerate the image acquisition process. However, the image reconstruction algorithms needed to correct the subsampling artifacts affect the nature of noise, i.e., it becomes non-stationary. Some methods have been proposed in the literature dealing with the non-stationary noise in pMRI. However, their performance depends on information not usually available such as multiple acquisitions, receiver noise matrices, sensitivity coil profiles, reconstruction coefficients, or even biophysical models of the data. Besides, some methods show an undesirable granular pattern on the estimates as a side effect of local estimation. Finally, some methods make strong assumptions that just hold in the case of high signal-to-noise ratio (SNR), which limits their usability in real scenarios. We propose a new automatic noise estimation technique for non-stationary Rician noise that overcomes the aforementioned drawbacks. Its effectiveness is due to the derivation of a variance-stabilizing transformation designed to deal with any SNR. The method was compared to the main state-of-the-art methods in synthetic and real scenarios. Numerical results confirm the robustness of the method and its better performance for the whole range of SNRs.

5-Year imaging sequelae of concussive blast injury and relation to early clinical outcome

Current imaging diagnostic techniques are often insensitive to the underlying pathological changes following mild traumatic brain injury (TBI) or concussion so much so that the explicit definition of these uncomplicated mild brain injuries includes the absence of radiological findings. In the US military, this is complicated by the natural tendency of service members to down play symptoms for fear of removal from their unit particularly in combat making it challenging for clinicians to definitively diagnose and determine course of treatment. Questions remain regarding the long-term impact of these war-time brain injuries. The objective of the current study was to evaluate the long-term imaging sequelae of blast concussion in active-duty US military and leverage previous longitudinal data collected in these same patients to identify predictors of sustained DTI signal change indicative of chronic neurodegeneration. In total, 50 blast TBI and 44 combat-deployed controls were evaluated at this 5-year follow up by advanced neuroimaging techniques including diffusion tensor imaging and quantitative volumetry. While cross-sectional analysis of regions of white matter on DTI images did not reveal significant differences across groups after statistical correction, an approach flexible to the heterogeneity of brain injury at the single-subject level identified 74% of the concussive blast TBI cohort to have reductions in fractional anisotropy indicative of chronic brain injury. Logistic regression leveraging clinical and demographic data collected in the acute/sub-acute and 1-year follow up to determine predictors of these long-term imaging changes determined that brain injury diagnosis, older age, verbal memory and verbal fluency best predicted the presence of DTI abnormalities 5 years post injury with an AUC of 0.78 indicating good prediction strength. These results provide supporting evidence for the evolution not resolution of this brain injury pathology, adding to the growing body of literature describing imaging signatures of chronic neurodegeneration even after mild TBI and concussion.

•

Design: prospective, observational, longitudinal research study

•

Patients: concussive blast (n = 50), combat-deployed control (n = 44)

•

Diffusion tensor imaging analyzed 5 yr post-injury, highly predicted by 1 yr outcomes.

•

Imaging abnormalities appear to evolve from sub-acute, to 1-year, to 5-year scan.

•

Findings indicate chronic neurodegeneration in majority of blast concussion patients.

Diffusion tensor imaging of the nigrostriatal fibers in Parkinson's disease

BACKGROUND

Parkinson's disease (PD) is histopathologically characterized by the loss of dopamine neurons in the substantia nigra pars compacta. The depletion of these neurons is thought to reduce the dopaminergic function of the nigrostriatal pathway, as well as the neural fibers that link the substantia nigra to the striatum (putamen and caudate), causing a dysregulation in striatal activity that ultimately leads to lack of movement control. Based on diffusion tensor imaging, visualizing this pathway and measuring alterations of the fiber integrity remain challenging. The objectives were to 1) develop a diffusion tensor tractography protocol for reliably tracking the nigrostriatal fibers on multicenter data; 2) test whether the integrities measured by diffusion tensor imaging of the nigrostriatal fibers are abnormal in PD; and 3) test whether abnormal integrities of the nigrostriatal fibers in PD patients are associated with the severity of motor disability and putaminal dopamine binding ratios.

METHODS

Diffusion tensor tractography was performed on 50 drug-naïve PD patients and 27 healthy control subjects from the international multicenter Parkinson's Progression Marker Initiative.

RESULTS

Tractography consistently detected the nigrostriatal fibers, yielding reliable diffusion measures. Fractional anisotropy, along with radial and axial diffusivity of the nigrostriatal tract, showed systematic abnormalities in patients. In addition, variations in fractional anisotropy and radial diffusivity of the nigrostriatal tract were associated with the degree of motor deficits in PD patients.

CONCLUSION

Taken together, the findings imply that the diffusion tensor imaging characteristic of the nigrostriatal tract is potentially an index for detecting and staging of early PD.

A PRELIMINARY STUDY ON THE EFFECT OF MOTION CORRECTION ON HARDI RECONSTRUCTION

Post-acquisition motion correction is widely performed in diffusion-weighted imaging (DWI) to guarantee voxel-wise correspondence between DWIs. Whereas this is primarily motivated to save as many scans as possible if corrupted by motion, users do not fully understand the consequences of different types of interpolation schemes on the final analysis. Nonetheless, interpolation might increase the partial volume effect while not preserving the volume of the diffusion profile, whereas excluding poor DWIs may affect the ability to resolve crossing fibers especially with small separation angles. In this paper, we investigate the effect of interpolating diffusion measurements as well as the elimination of bad directions on the reconstructed fiber orientation diffusion functions and on the estimated fiber orientations. We demonstrate such an effect on synthetic and real HARDI datasets. Our experiments demonstrate that the effect of interpolation is more significant with small fibers separation angles where the exclusion of motion-corrupted directions decreases the ability to resolve such crossing fibers.

On the Expectation-Maximization Algorithm for Rice-Rayleigh Mixtures With Application to Noise Parameter Estimation in Magnitude MR Datasets

Magnitude magnetic resonance (MR) images are noise-contaminated measurements of the true signal, and it is important to assess the noise in many applications. A recently introduced approach models the magnitude MR datum at each voxel in terms of a mixture of upto one Rayleigh and an a priori unspecified number of Rice components, all with a common noise parameter. The Expectation-Maximization (EM) algorithm was developed for parameter estimation, with the mixing component membership of each voxel as the missing observation. This paper revisits the EM algorithm by introducing more missing observations into the estimation problem such that the complete (observed and missing parts) dataset can be modeled in terms of a regular exponential family. Both the EM algorithm and variance estimation are then fairly straightforward without any need for potentially unstable numerical optimization methods. Compared to local neighborhood- and wavelet-based noise-parameter estimation methods, the new EM-based approach is seen to perform well not only on simulation datasets but also on physical phantom and clinical imaging data.

Motion Detection in Diffusion MRI via Online ODF Estimation

The acquisition of high angular resolution diffusion MRI is particularly long and subject motion can become an issue. The orientation distribution function (ODF) can be reconstructed online incrementally from diffusion-weighted MRI with a Kalman filtering framework. This online reconstruction provides real-time feedback throughout the acquisition process. In this article, the Kalman filter is first adapted to the reconstruction of the ODF in constant solid angle. Then, a method called STAR (STatistical Analysis of Residuals) is presented and applied to the online detection of motion in high angular resolution diffusion images. Compared to existing techniques, this method is image based and is built on top of a Kalman filter. Therefore, it introduces no additional scan time and does not require additional hardware. The performance of STAR is tested on simulated and real data and compared to the classical generalized likelihood ratio test. Successful detection of small motion is reported (rotation under 2°) with no delay and robustness to noise.

Plasticity and stability of the visual system in human achiasma

The absence of the optic chiasm is an extraordinary and extreme abnormality in the nervous system. The abnormality produces highly atypical functional responses in the cortex, including overlapping hemifield representations and bilateral population receptive fields in both striate and extrastriate visual cortex. Even in the presence of these large functional abnormalities, the effect on visual perception and daily life is not easily detected. Here, we demonstrate that in two achiasmic humans the gross topography of the geniculostriate and occipital callosal connections remains largely unaltered. We conclude that visual function is preserved by reorganization of intracortical connections instead of large-scale reorganizations of the visual cortex. Thus, developmental mechanisms of local wiring within cortical maps compensate for the improper gross wiring to preserve function in human achiasma.

Nonparametric Bayesian inference of the fiber orientation distribution from diffusion-weighted MR images

Diffusion MR imaging provides a unique tool to probe the microgeometry of nervous tissue and to explore the wiring diagram of the neural connections noninvasively. Generally, a forward model is established to map the intra-voxel fiber architecture onto the observable diffusion signals, which is reformulated in this article by adopting a measure-theoretic approach. However, the inverse problem, i.e., the spherical deconvolution of the fiber orientation density from noisy MR measurements, is ill-posed. We propose a nonparametric representation of the tangential distribution of the nerve fibers in terms of a Dirichlet process mixture. Given a second-order approximation of the impulse response of a fiber segment, the specified problem is solved by Bayesian statistics under a Rician noise model, using an adaptive reversible jump Markov chain Monte Carlo sampler. The density estimation framework is demonstrated by various experiments with a diffusion MR dataset featuring high angular resolution, uncovering the fiber orientation field in the cerebral white matter of the living human brain.

A reproducing kernel hilbert space approach for q-ball imaging

Diffusion magnetic resonance (MR) imaging has enabled us to reveal the white matter geometry in the living human brain. The Q-ball technique is widely used nowadays to recover the orientational heterogeneity of the intra-voxel fiber architecture. This article proposes to employ the Funk-Radon transform in a Hilbert space with a reproducing kernel derived from the spherical Laplace-Beltrami operator, thus generalizing previous approaches that assume a bandlimited diffusion signal. The function estimation problem is solved within a Tikhonov regularization framework, while a Gaussian process model allows for the selection of the smoothing parameter and the specification of confidence bands. Shortcomings of Q-ball imaging are discussed.

Effects of physiological noise in population analysis of diffusion tensor MRI data

The goal of this study is to characterize the potential effect of artifacts originating from physiological noise on statistical analysis of diffusion tensor MRI (DTI) data in a population. DTI derived quantities including mean diffusivity (Trace(D)), fractional anisotropy (FA), and principal eigenvector (ε(1)) are computed in the brain of 40 healthy subjects from tensors estimated using two different methods: conventional nonlinear least-squares, and robust fitting (RESTORE). RESTORE identifies artifactual data points as outliers and excludes them on a voxel-by-voxel basis. We found that outlier data points are localized in specific spatial clusters in the population, indicating a consistency in brain regions affected across subjects. In brain parenchyma RESTORE slightly reduces inter-subject variance of FA and Trace(D). The dominant effect of artifacts, however, is bias. Voxel-wise analysis indicates that inclusion of outlier data points results in clusters of under- and over-estimation of FA, while Trace(D) is always over-estimated. Removing outliers affects ε(1) mostly in low anisotropy regions. It was found that brain regions known to be affected by cardiac pulsation - cerebellum and genu of the corpus callosum, as well as regions not previously reported, splenium of the corpus callosum-show significant effects in the population analysis. It is generally assumed that statistical properties of DTI data are homogenous across the brain. This assumption does not appear to be valid based on these results. The use of RESTORE can lead to a more accurate evaluation of a population, and help reduce spurious findings that may occur due to artifacts in DTI data.

Cortical maps and white matter tracts following long period of visual deprivation and retinal image restoration

Abnormal visual input during development has dramatic effects on the visual system. How does the adult visual system respond when input is corrected? MM lost his left eye and became blind in the right due to corneal damage at the age of 3. At age 46, MM regained his retinal image, but his visual abilities, even seven years following the surgery, remain severely limited, and he does not rely on vision for daily life. Neuroimaging measurements reveal several differences among MM, sighted controls, sighted monocular, and early blind subjects. We speculate that these differences stem from damage during the critical period in development of retinal neurons with small, foveal receptive fields. In this case, restoration of functional vision requires more than improving retinal image contrast. In general, visual restoration will require accounting for the developmental trajectory of the individual and the consequences of the early deprivation on cortical circuitry.

Noise estimation in magnitude MR datasets

Estimating the noise parameter in magnitude magnetic resonance (MR) images is important in a wide range of applications. We propose an automatic noise estimation method that does not rely on a substantial proportion of voxels being from the background. Specifically, we model the magnitude of the observed signal as a mixture of Rice distributions with common noise parameter. The expectation-maximization (EM) algorithm is used to estimate all parameters, including the common noise parameter. The algorithm needs initializing values for which we provide some strategies that work well. The number of components in the mixture model also needs to be estimated en route to noise estimation and we provide a novel approach to doing so. Our methodology performs very well on a range of simulation experiments and physical phantom data. Finally, the methodology is demonstrated on four clinical datasets.

Probabilistic Identification and Estimation of Noise (PIESNO): a self-consistent approach and its applications in MRI

Data analysis in MRI usually entails a series of processing procedures. One of these procedures is noise assessment, which in the context of this work, includes both the identification of noise-only pixels and the estimation of noise variance (standard deviation). Although noise assessment is critical to many MRI processing techniques, the identification of noise-only pixels has received less attention than has the estimation of noise variance. The main objectives of this paper are, therefore, to demonstrate (a) that the identification of noise-only pixels has an important role to play in the analysis of MRI data, (b) that the identification of noise-only pixels and the estimation of noise variance can be combined into a coherent framework, and (c) that this framework can be made self-consistent. To this end, we propose a novel iterative approach to simultaneously identify noise-only pixels and estimate the noise standard deviation from these identified pixels in a commonly used data structure in MRI. Experimental and simulated data were used to investigate the feasibility, the accuracy and the stability of the proposed technique.

Interpolation artifacts in sub-pixel image registration

We consider the problem of registering (aligning) two images to sub-pixel accuracy by optimization of objective functions constructed from the images' intensity values. We show that some widely used interpolation methods can introduce multiple local optima in the energy of the interpolated image which, if not counter-balanced by other terms, can cause local optima in registration objective functions including the sum of squared differences, cross correlation, and mutual information. We discuss different solutions to address the problem based on high degree B-spline interpolation, low pass filtering the images, and stochastic integration. Numerical examples using synthetic and real signals and images are shown.

Identifying the human optic radiation using diffusion imaging and fiber tractography

Measuring the properties of the white matter pathways from retina to cortex in the living human brain will have many uses for understanding visual performance and guiding clinical treatment. For example, identifying the Meyer's loop portion of the optic radiation (OR) has clinical significance because of the large number of temporal lobe resections. We use diffusion tensor imaging and fiber tractography (DTI-FT) to identify the most likely pathway between the lateral geniculate nucleus (LGN) and the calcarine sulcus in sixteen hemispheres of eight healthy volunteers. Quantitative population comparisons between DTI-FT estimates and published postmortem dissections match with a spatial precision of about 1 mm. The OR can be divided into three bundles that are segmented based on the direction of the fibers as they leave the LGN: Meyer's loop, central, and direct. The longitudinal and radial diffusivities of the three bundles do not differ within the measurement noise; there is a small difference in the radial diffusivity between the right and left hemispheres. We find that the anterior tip of Meyer's loop is 28 +/- 3 mm posterior to the temporal pole, and the population range is 1 cm. Hence, it is important to identify the location of this bundle in individual subjects or patients.

ConTrack: finding the most likely pathways between brain regions using diffusion tractography

Magnetic resonance diffusion-weighted imaging coupled with fiber tractography (DFT) is the only non-invasive method for measuring white matter pathways in the living human brain. DFT is often used to discover new pathways. But there are also many applications, particularly in visual neuroscience, in which we are confident that two brain regions are connected, and we wish to find the most likely pathway forming the connection. In several cases, current DFT algorithms fail to find these candidate pathways. To overcome this limitation, we have developed a probabilistic DFT algorithm (ConTrack) that identifies the most likely pathways between two regions. We introduce the algorithm in three parts: a sampler to generate a large set of potential pathways, a scoring algorithm that measures the likelihood of a pathway, and an inferential step to identify the most likely pathways connecting two regions. In a series of experiments using human data, we show that ConTrack estimates known pathways at positions that are consistent with those found using a high quality deterministic algorithm. Further we show that separating sampling and scoring enables ConTrack to identify valid pathways, known to exist, that are missed by other deterministic and probabilistic DFT algorithms.

Diffusion-tensor MR imaging and tractography: exploring brain microstructure and connectivity

Diffusion magnetic resonance (MR) imaging is evolving into a potent tool in the examination of the central nervous system. Although it is often used for the detection of acute ischemia, evaluation of directionality in a diffusion measurement can be useful in white matter, which demonstrates strong diffusion anisotropy. Techniques such as diffusion-tensor imaging offer a glimpse into brain microstructure at a scale that is not easily accessible with other modalities, in some cases improving the detection and characterization of white matter abnormalities. Diffusion MR tractography offers an overall view of brain anatomy, including the degree of connectivity between different regions of the brain. However, optimal utilization of the wide range of data provided with directional diffusion MR measurements requires careful attention to acquisition and postprocessing. This article will review the principles of diffusion contrast and anisotropy, as well as clinical applications in psychiatric, developmental, neurodegenerative, neoplastic, demyelinating, and other types of disease.

Automatic estimation of the noise variance from the histogram of a magnetic resonance image

Estimation of the noise variance of a magnetic resonance (MR) image is important for various post-processing tasks. In the literature, various methods for noise variance estimation from MR images are available, most of which however require user interaction and/or multiple (perfectly aligned) images. In this paper, we focus on automatic histogram-based noise variance estimation techniques. Previously described methods are reviewed and a new method based on the maximum likelihood (ML) principle is presented. Using Monte Carlo simulation experiments as well as experimental MR data sets, the noise variance estimation methods are compared in terms of the root mean squared error (RMSE). The results show that the newly proposed method is superior in terms of the RMSE.

Removal of local and biased global maxima in intensity-based registration

Intensity based registration (e.g., mutual information) suffers from a scalloping artifact giving rise to local maxima and sometimes a biased global maximum in a similarity objective function. Here, we demonstrate that scalloping is principally due to the noise reduction filtering that occurs when image samples are interpolated. Typically at a much smaller scale (100 times less in our test cases), there are also fluctuations in the similarity objective function due to interpolation of the signal and to sampling of a continuous, band-limited image signal. Focusing on the larger problem from noise, we show that this phenomenon can even bias global maxima, giving inaccurate registrations. This phenomenon is readily seen when one registers an image onto itself with different noise realizations but is absent when the same noise realization is present in both images. For linear interpolation, local maxima and global bias are removed if one filters the interpolated image using a new constant variance filter for linear interpolation (cv-lin filter), which equalizes the variance across the interpolated image. We use 2D synthetic and MR images and characterize the effect of cv-lin on similarity objective functions. With a reduction of local and biased maxima, image registration becomes more robust and accurate. An efficient implementation adds insignificant computation time per iteration, and because optimization proceeds more smoothly, sometimes fewer iterations are needed.