Comprehensive approach for correction of motion and distortion in diffusion-weighted MRI

Regression Models for Identifying Noise Sources in Magnetic Resonance Images

Stochastic noise, susceptibility artifacts, magnetic field and radiofrequency inhomogeneities, and other noise components in magnetic resonance images (MRIs) can introduce serious bias into any measurements made with those images. We formally introduce three regression models including a Rician regression model and two associated normal models to characterize stochastic noise in various magnetic resonance imaging modalities, including diffusion-weighted imaging (DWI) and functional MRI (fMRI). Estimation algorithms are introduced to maximize the likelihood function of the three regression models. We also develop a diagnostic procedure for systematically exploring MR images to identify noise components other than simple stochastic noise, and to detect discrepancies between the fitted regression models and MRI data. The diagnostic procedure includes goodness-of-fit statistics, measures of influence, and tools for graphical display. The goodness-of-fit statistics can assess the key assumptions of the three regression models, whereas measures of influence can isolate outliers caused by certain noise components, including motion artifacts. The tools for graphical display permit graphical visualization of the values for the goodness-of-fit statistic and influence measures. Finally, we conduct simulation studies to evaluate performance of these methods, and we analyze a real dataset to illustrate how our diagnostic procedure localizes subtle image artifacts by detecting intravoxel variability that is not captured by the regression models.

Diffusion tensor imaging in psychiatric disorders

OBJECTIVES

Since the development of diffusion tensor imaging (DTI) nearly a decade ago, it has been extensively applied to a number of different psychiatric disorders. Its rapid assimilation into psychiatric research has stemmed from its unique property to measure the coherence and direction of neuronal fiber tracts. The goal of this article is to provide an overview of DTI and its application to psychiatric disorders.

METHODS

We performed an extensive literature review of articles using DTI to study psychiatric disorders. To date, most DTI studies have been performed on individuals with schizophrenia. However, recent studies have emerged that evaluate white matter (WM) integrity in major depressive disorder, anxiety disorders, obsessive-compulsive disorder, attention deficit disorder, autism, and personality disorders.

RESULTS

There is tremendous heterogeneity in the results of DTI studies of patients with psychiatric disorders. In schizophrenia, which currently has more than 50 studies using DTI, brain regions such as the cingulate bundle, corpus callosum, and regions within the frontal and temporal WM have a proportionally larger number of positive findings across the studies. Studies of other psychiatric disorders have findings that overlap with those seen in schizophrenia.

CONCLUSIONS

There is converging evidence that a number of psychiatric disorders are associated with WM abnormalities. However, the considerable heterogeneity of results, both within and between existing studies, will require future work within and across psychiatric disorders to better delineate the neurobiological underpinnings of these white matter abnormalities.

A variational image-based approach to the correction of susceptibility artifacts in the alignment of diffusion weighted and structural MRI

This paper presents a method for correcting the geometric and greyscale distortions in diffusion-weighted MRI that result from inhomogeneities in the static magnetic field. These inhomogeneities may due to imperfections in the magnet or to spatial variations in the magnetic susceptibility of the object being imaged--so called susceptibility artifacts. Echo-planar imaging (EPI), used in virtually all diffusion weighted acquisition protocols, assumes a homogeneous static field, which generally does not hold for head MRI. The resulting distortions are significant, sometimes more than ten millimeters. These artifacts impede accurate alignment of diffusion images with structural MRI, and are generally considered an obstacle to the joint analysis of connectivity and structure in head MRI. In principle, susceptibility artifacts can be corrected by acquiring (and applying) a field map. However, as shown in the literature and demonstrated in this paper, field map corrections of susceptibility artifacts are not entirely accurate and reliable, and thus field maps do not produce reliable alignment of EPIs with corresponding structural images. This paper presents a new, image-based method for correcting susceptibility artifacts. The method relies on a variational formulation of the match between an EPI baseline image and a corresponding T2-weighted structural image but also specifically accounts for the physics of susceptibility artifacts. We derive a set of partial differential equations associated with the optimization, describe the numerical methods for solving these equations, and present results that demonstrate the effectiveness of the proposed method compared with field-map correction.

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.

Diffusion tensor fiber tracking in patients with central post-stroke pain; correlation with efficacy of repetitive transcranial magnetic stimulation

Central post-stroke pain (CPSP) is one of the most common types of intractable pain. We reported that repetitive transcranial magnetic stimulation (rTMS) of primary motor cortex relieves pain for patients who were refractory to medical treatment. But the mechanism is unclear. In the present study, we investigated relations between the characteristics of CPSP and the results of fiber tracking, which is the only noninvasive method of evaluating the anatomical connectivity of white matter pathways. Fiber tracking of the corticospinal tract (CST) and thalamocortical tract (TCT) was investigated in 17 patients with CPSP. The stroke lesion was located in a supratentorial region in all cases (corona radiata, one case; thalamus, seven cases; putamen, nine cases). Relations between the delineation ratio (defined as the ratio of the cross section of the affected side to that of the unaffected side) of the CST and of the TCT, manual muscle test score, pain score, region of pain, and efficacy of rTMS were evaluated. Fiber tracking was successful in 13 patients with the stroke lesion involving the TCT. The rTMS-effective group had higher delineation ratio of the CST (p=0.02) and the TCT (p=0.005) than the rTMS-ineffective group. Previous studies suggested that an intact CST allows pain control but did not discuss the TCT. Our results suggest that the TCT also plays a role in pain reduction by rTMS of the primary motor cortex and that the efficacy of rTMS for patients with CPSP is predictable by fiber tracking.

Tractography gone wild: probabilistic fibre tracking using the wild bootstrap with diffusion tensor MRI

Diffusion tensor magnetic resonance imaging (DT-MRI) permits the noninvasive assessment of tissue microstructure and, with fibre-tracking algorithms, allows for the 3-D trajectories of white matter fasciculi to be reconstructed noninvasively. Probabilistic algorithms allow one to assign a "confidence" to a given reconstructed pathway--but often rely on a priori assumptions about sources of uncertainty in the data. Bootstrap methods have been proposed as a way of circumventing this problem, deriving the uncertainty from the data themselves--but acquisition times for data amenable to precise and robust bootstrapping are clinically prohibitive. By combining the wild bootstrap, recently introduced to the DT-MRI literature, with tractography, we show how confidence can be assigned to reconstructed trajectories using data collected in a fraction of the time required for regular bootstrapping. We compare in vivo wild bootstrap tracking results with regular tracking results and show that results are comparable. This approach therefore allows users who have collected data sets for use with deterministic tracking algorithms, rather than those specifically designed for bootstrapping, to be able to apply bootstrap analyses and retrospectively assign confidence to their reconstructed trajectories with minimum additional effort.

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.

Three-dimensional mapping of lingual myoarchitecture by diffusion tensor MRI

This study was performed to assess the feasibility of investigating the complex lingual myoarchitecture through segmentation of muscles from diffusion tensor imaging (DTI) data. The primary eigenvectors were found to be adequate for delineating the superior and inferior longitudinalis, genioglossus, and hyoglossus. The tertiary eigenvector orientations effectively revealed the homogeneous and systematic change of muscle orientation in the tongue core. In the longitudinalis near the tongue tip, the secondary eigenvectors were oriented in the radial direction. Lingual muscles were segmented using two methods: modified directional correlation (DC) and tensor coherence (TC) methods. The DC method, based on one eigenvector, was found to be inadequate for lingual muscle segmentation, whereas the TC method, based on the tensor shape and orientation, was used successfully to segment most lingual muscles. The segmentation result was used to report the diffusion tensor properties of individual lingual muscles. Also found was a continuous change in skewness of the intrinsic tongue core from negative in the anterior region to positive in the posterior region. DTI and the proposed segmentation method provide an adequate means of imaging and visualizing the complex, compartmentalized musculature of the tongue. The potential for in vivo research and clinical applications is demonstrated.

Single-step nonlinear diffusion tensor estimation in the presence of microscopic and macroscopic motion

Patient motion can cause serious artifacts in diffusion tensor imaging (DTI), diminishing the reliability of the estimated diffusion tensor information. Studies in this field have so far been limited mainly to the correction of miniscule physiological motion. In order to correct for gross patient motion it is not sufficient to correct for misregistration between successive shots; the change in the diffusion-encoding direction must also be accounted for. This becomes particularly important for multishot sequences, whereby-in the presence of motion-each shot is encoded with a different diffusion weighting. In this study a general mathematical framework to correct for gross patient motion present in a multishot and multicoil DTI scan is presented. A signal model is presented that includes the effect of rotational and translational motion in the patient frame of reference. This model was used to create a nonlinear least-squares formulation, from which the diffusion tensors were obtained using a nonlinear conjugate gradient algorithm. Applications to both phantom simulations and in vivo studies showed that in the case of gross motion the proposed algorithm performs superiorly compared to conventional methods used for tensor estimation.

Comparison of EPI distortion correction methods in diffusion tensor MRI using a novel framework

Diffusion weighted images (DWIs) are commonly acquired with Echo-planar imaging (EPI). B0 inhomogeneities affect EPI by producing spatially nonlinear image distortions. Several strategies have been proposed to correct EPI distortions including B0 field mapping (B0M) and image registration. In this study, an experimental framework is proposed to evaluation the performance of different EPI distortion correction methods in improving DT-derived quantities. A deformable registration based method with mutual information metric and cubic B-spline modeled constrained deformation field (BSP) is proposed as an alternative when B0 mapping data are not available. BSP method is qualitatively and quantitatively compared to B0M method using the framework. Both methods can successful reduce EPI distortions and significantly improve the quality of DT-derived quantities. Overall, B0M was clearly superior in infratentorial regions including brainstem and cerebellum, as well as in the ventral areas of the temporal lobes while BSP was better in all rostral brain regions.

Integrated SENSE DTI with correction of susceptibility- and eddy current-induced geometric distortions

Diffusion tensor imaging (DTI) is vulnerable to geometric distortions caused by subject-dependent susceptibility effects and diffusion-weighting direction-dependent eddy currents. Although the introduction of sensitivity encoding (SENSE) has reduced the overall distortions for the same imaging matrix size, this benefit is offset by the increasing demand for higher spatial resolution. Thus, significant distortions remain or are exacerbated in high-resolution SENSE DTI acquisitions. While the susceptibility-induced distortions cause global spatial misregistration, the direction-dependent eddy current-induced distortions cause misregistration among different diffusion-weighted images, leading to errors in the derivation of the diffusion tensor in virtually all voxels, and consequently in resulting diffusion parameters as well as in fiber tracking. Here, we apply a comprehensive approach that corrects for both susceptibility- and eddy current-induced distortions to high-resolution SENSE DTI acquisitions, and demonstrate its effectiveness, efficiency, and reliability in vivo as well as its advantages over a twice-refocused spin-echo sequence. This method should find increased use in modern DTI experiments where SENSE acquisitions are commonly used.

Correction of susceptibility artifacts in diffusion tensor data using non-linear registration

Diffusion tensor imaging can be used to localize major white matter tracts within the human brain. For surgery of tumors near eloquent brain areas such as the pyramidal tract this information is of importance to achieve an optimal resection while avoiding post-operative neurological deficits. However, due to the small bandwidth of echo planar imaging, diffusion tensor images suffer from susceptibility artifacts resulting in positional shifts and distortion. As a consequence, the fiber tracts computed from echo planar imaging data are spatially distorted. We present an approach based on non-linear registration using Bézier functions to efficiently correct distortions due to susceptibility artifacts. The approach makes extensive use of graphics hardware to accelerate the non-linear registration procedure. An improvement presented in this paper is a more robust and efficient optimization strategy based on simultaneous perturbation stochastic approximation (SPSA). Since the accuracy of non-linear registration is crucial for the value of the presented correction method, two techniques were applied in order to prove the quality of the proposed framework. First, the registration accuracy was evaluated by recovering a known transformation with non-linear registration. Second, landmark-based evaluation of the registration method for anatomical and diffusion tensor data was performed. The registration was then applied to patients with lesions adjacent to the pyramidal tract in order to compensate for susceptibility artifacts. The effect of the correction on the pyramidal tract was then quantified by measuring the position of the tract before and after registration. As a result, the distortions observed in phase encoding direction were most prominent at the cortex and the brainstem. The presented approach allows correcting fiber tract distortions which is an important prerequisite when tractography data are integrated into a stereotactic setup for intra-operative guidance.

Accounting for signal loss due to dephasing in the correction of distortions in gradient-echo EPI via nonrigid registration

Gradient-echo (GE) echo planar imaging (EPI) is susceptible to both geometric distortions and signal loss. This paper presents a retrospective correction approach based on nonrigid image registration. A new physics-based intensity correction factor derived to compensate for intravoxel dephasing in GE EPI images is incorporated into a previously reported nonrigid registration algorithm. Intravoxel dephasing causes signal loss and thus intensity attenuation in the images. The new rephasing factor we introduce, which changes the intensity of a voxel in images during the registration, is used to improve the accuracy of the intensity-based nonrigid registration method and mitigate the intensity attenuation effect. Simulation-based experiments are first used to evaluate the method. A magnetic resonance (MR) simulator and a real field map are used to generate a realistic GE EPI image. The geometric distortion computed from the field map is used as the ground truth to which the estimated nonrigid deformation is compared. We then apply the algorithm to a set of real human brain images. The results show that, after registration, alignment between EPI and multi-shot, spin-echo images, which have relatively long acquisition times but negligible distortion, is improved and that signal loss caused by dephasing can be recovered.

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.

Genetic contributions to white matter architecture revealed by diffusion tensor imaging in Williams syndrome

Little is known about genetic regulation of the development of white matter. This knowledge is critical in understanding the pathophysiology of neurodevelopmental syndromes associated with altered cognition as well as in elucidating the genetics of normal human cognition. The hemideletion of approximately 25 genes on chromosome 7q11.23 that causes Williams syndrome (WS) includes genes that regulate cytoskeletal dynamics in neurons, especially LIMK1 and CYLN2, and therefore offers the opportunity to investigate the role of these genes in the formation of white matter tracts. We used diffusion tensor imaging to demonstrate alteration in white matter fiber directionality, deviation in posterior fiber tract course, and reduced lateralization of fiber coherence in WS. These abnormalities are consistent with an alteration of the late stages of neuronal migration, define alterations of white matter structures underlying dissociable behavioral phenotypes in WS, and provide human in vivo information about genetic control of white matter tract formation.

Diffusion tensor imaging of the brain

Diffusion tensor imaging (DTI) is a promising method for characterizing microstructural changes or differences with neuropathology and treatment. The diffusion tensor may be used to characterize the magnitude, the degree of anisotropy, and the orientation of directional diffusion. This review addresses the biological mechanisms, acquisition, and analysis of DTI measurements. The relationships between DTI measures and white matter pathologic features (e.g., ischemia, myelination, axonal damage, inflammation, and edema) are summarized. Applications of DTI to tissue characterization in neurotherapeutic applications are reviewed. The interpretations of common DTI measures (mean diffusivity, MD; fractional anisotropy, FA; radial diffusivity, D(r); and axial diffusivity, D(a)) are discussed. In particular, FA is highly sensitive to microstructural changes, but not very specific to the type of changes (e.g., radial or axial). To maximize the specificity and better characterize the tissue microstructure, future studies should use multiple diffusion tensor measures (e.g., MD and FA, or D(a) and D(r)).

A quantitative comparison of two methods to correct eddy current-induced distortions in DT-MRI

Eddy current-induced geometric distortions of single-shot, diffusion-weighted, echo-planar (DW-EP) images are a major confounding factor to the accurate determination of water diffusion parameters in diffusion tensor MRI (DT-MRI). Previously, it has been suggested that these geometric distortions can be removed from brain DW-EP images using affine transformations determined from phantom calibration experiments using iterative cross-correlation (ICC). Since this approach was first described, a number of image-based registration methods have become available that can also correct eddy current-induced distortions in DW-EP images. However, as yet no study has investigated whether separate eddy current calibration or image-based registration provides the most accurate way of removing these artefacts from DT-MRI data. Here we compare how ICC phantom calibration and affine FLIRT (http://www.fmrib.ox.ac.uk), a popular image-based multi-modal registration method that can correct both eddy current-induced distortions and bulk subject motion, perform when registering DW-EP images acquired with different slice thicknesses (2.8 and 5 mm) and b-values (1000 and 3000 s/mm(2)). With the use of consistency testing, it was found that ICC was a more robust algorithm for correcting eddy current-induced distortions than affine FLIRT, especially at high b-value and small slice thickness. In addition, principal component analysis demonstrated that the combination of ICC phantom calibration (to remove eddy current-induced distortions) with rigid body FLIRT (to remove bulk subject motion) provided a more accurate registration of DT-MRI data than that achieved by affine FLIRT.

Variance of estimated DTI-derived parameters via first-order perturbation methods

In typical applications of diffusion tensor imaging (DTI), DT-derived quantities are used to make a diagnostic, therapeutic, or scientific determination. In such cases it is essential to characterize the variability of these tensor-derived quantities. Parametric and empirical methods have been proposed to estimate the variance of the estimated DT, and quantities derived from it. However, the former method cannot be generalized since a parametric distribution cannot be found for all DT-derived quantities. Although powerful empirical methods, such as the bootstrap, are available, they require oversampling of the diffusion-weighted imaging (DWI) data. Statistical perturbation methods represent a hybrid between parametric and empirical approaches, and can overcome the primary limitations of both methods. In this study we used a first-order perturbation method to obtain analytic expressions for the variance of DT-derived quantities, such as the trace, fractional anisotropy (FA), eigenvalues, and eigenvectors, for a given experimental design. We performed Monte Carlo (MC) simulations of DTI experiments to test and validate these formulae, and to determine their range of applicability for different experimental design parameters, including the signal-to-noise ratio (SNR), diffusion gradient sampling scheme, and number of DWI acquisitions. This information should be useful for designing DTI studies and assessing the quality of inferences drawn from them.

Solitary fibrous tumor of the pleura: Apparent diffusion coefficient (ADC) value and ADC map to predict malignant transformation

Solitary fibrous tumors (SFTs) of the pleura are rare soft-tissue tumors that are presumed to be of mesenchymal origin. Most SFTs are histologically benign, but up to 20% of SFTs may be malignant. In addition, malignant transformation may occur within histologically benign SFTs, though it is rare. However, it is difficult to diagnose malignant SFTs of the pleura by means of conventional computed tomography and magnetic resonance imaging (MRI). In this article we present the first case of malignant SFT of the pleura in an 81-year-old man in which the apparent diffusion coefficient (ADC) value and ADC map based on diffusion-weighted MRI were very useful for identifying malignant transformation.

Retrospective distortion correction for 3D MR diffusion tensor microscopy using mutual information and Fourier deformations

Magnetic resonance diffusion tensor imaging (DTI) can be complicated by distortions that contribute to errors in tissue characterization and loss of fine structures. This work presents a correction scheme based on retrospective registration via mutual information (MI), using Fourier transform (FT)-based deformations to enhance the reliability of the entropy-based image registration. The registration methodology is applied to correct distortions in 3D high-resolution DTI datasets, incorporating a complete set of affine deformations. The results demonstrate that the proposed methodology can consistently and significantly reduce the number of misregistered pixels, leading to marked improvement in the visualization of internal brain white matter (WM) structure via DTI. Post-registration analysis revealed that eddy-current effects cannot fully account for the observed image distortions. Combined, these findings support the non-model-based, postprocessing approach for correcting distortions, and demonstrate the advantages of combining FT-based deformations and MI registration to enhance the practical utility of DTI.

How does distortion correction correlate with anisotropic indices? A diffusion tensor imaging study

PURPOSE

The purpose of this study was to determine a suitable registration algorithm for diffusion tensor imaging (DTI) using conventional preprocessing tools [statistical parametric mapping (SPM) and automated image registration (AIR)] and to investigate how anisotropic indices for clinical assessments are affected by these distortion corrections.

MATERIALS AND METHODS

Brain DTI data from 15 normal healthy volunteers were used to evaluate four spatial registration schemes within subjects to correct image distortions: noncorrection, SPM-based affine registration, AIR-based affine registration and AIR-based nonlinear polynomial warping. The performance of each distortion correction was assessed using: (a) quantitative parameters: tensor-fitting error (Ef), mean dispersion index (MDI), mean fractional anisotropy (MFA) and mean variance (MV) within 11 regions of interest (ROI) defined from homogeneous fiber bundles; and (b) fiber tractography through the uncinate fasciculus and the corpus callosum. Fractional anisotropy (FA) and mean diffusivity (MD) were calculated to demonstrate the effects of distortion correction. Repeated-measures analysis of variance was used to investigate differences among the four registration paradigms.

RESULTS

AIR-based nonlinear registration showed the best performance for reducing image distortions with respect to smaller Ef (P<.02), MDI (P<.01) and MV (P<.01) with larger MFA (P<.01). FA was decreased to correct distortions (P<.0001) whether the applied registration was linear or nonlinear and was lowest after nonlinear correction (P<.001). No significant differences were found in MD.

CONCLUSION

In conventional DTI processing, anisotropic indices of FA can be misestimated by noncorrection or inappropriate distortion correction, which leads to an erroneous increase in FA. AIR-based nonlinear distortion correction would be required for a more accurate measurement of this diffusion parameter.

Multiscale white matter fiber tract coregistration: a new feature-based approach to align diffusion tensor data

In this paper an automatic multiscale feature-based rigid-body coregistration technique for diffusion tensor imaging (DTI) based on the local curvature kappa and torsion tau of the white matter (WM) fiber pathways is presented. As a similarity measure, the mean squared difference (MSD) of corresponding fiber pathways in (kappa, tau)-space is chosen. After the MSD is minimized along the arc length of the curve, principal component analysis is applied to calculate the transformation parameters. In addition, a scale-space representation of the space curves is incorporated, resulting in a multiscale robust coregistration technique. This fully automatic technique inherently allows one to apply region of interest (ROI) coregistration, and is adequate for performing both global and local transformations. Simulations were performed on synthetic DT data to evaluate the coregistration accuracy and precision. An in vivo coregistration example is presented and compared with a voxel-based coregistration approach, demonstrating the feasibility and advantages of the proposed technique to align DT data of the human brain.

A unifying theoretical and algorithmic framework for least squares methods of estimation in diffusion tensor imaging

A unifying theoretical and algorithmic framework for diffusion tensor estimation is presented. Theoretical connections among the least squares (LS) methods, (linear least squares (LLS), weighted linear least squares (WLLS), nonlinear least squares (NLS) and their constrained counterparts), are established through their respective objective functions, and higher order derivatives of these objective functions, i.e., Hessian matrices. These theoretical connections provide new insights in designing efficient algorithms for NLS and constrained NLS (CNLS) estimation. Here, we propose novel algorithms of full Newton-type for the NLS and CNLS estimations, which are evaluated with Monte Carlo simulations and compared with the commonly used Levenberg-Marquardt method. The proposed methods have a lower percent of relative error in estimating the trace and lower reduced chi2 value than those of the Levenberg-Marquardt method. These results also demonstrate that the accuracy of an estimate, particularly in a nonlinear estimation problem, is greatly affected by the Hessian matrix. In other words, the accuracy of a nonlinear estimation is algorithm-dependent. Further, this study shows that the noise variance in diffusion weighted signals is orientation dependent when signal-to-noise ratio (SNR) is low (<or=5). A new experimental design is, therefore, proposed to properly account for the directional dependence in diffusion weighted signal variance.

Echoplanar diffusion tensor imaging of the lower leg musculature using eddy current nulled stimulated echo preparation

A sequence for echoplanar diffusion tensor imaging of musculature was developed using a stimulated echo preparation. The strategy was optimized in order to obtain reliable diffusion tensor data in a short measuring time. Image distortion problems due to eddy currents arising from long-lasting diffusion sensitizing gradients could be overcome by insertion of additional gradient pulses in the TM interval of the stimulated echo preparation. In contrast to former approaches with similar intention, the proposed strategy does not influence the stimulated echo signal itself and does not lead to prolonged echo time as in the case of spin echo methods. Phantom measurements were performed to compare eddy current induced distortion effects in diffusion weighted images. The diffusion tensor in the musculature of the lower leg was investigated in four healthy subjects and maps of the trace and the three eigenvalues of the diffusion tensor, fractional anisotropy maps, and angle maps were calculated.

Regional distribution of measurement error in diffusion tensor imaging

The characterization of measurement error is critical in assessing the significance of diffusion tensor imaging (DTI) findings in longitudinal and cohort studies of psychiatric disorders. We studied 20 healthy volunteers, each one scanned twice (average interval between scans of 51 +/- 46.8 days) with a single shot echo planar DTI technique. Intersession variability for fractional anisotropy (FA) and Trace (D) was represented as absolute variation (standard deviation within subjects: SDw), percent coefficient of variation (CV) and intra-class correlation coefficient (ICC). The values from the two sessions were compared for statistical significance with repeated measures analysis of variance or a non-parametric equivalent of a paired t-test. The results showed good reproducibility for both FA and Trace (CVs below 10% and ICCs at or above 0.70 in most regions of interest) and evidence of systematic global changes in Trace between scans. The regional distribution of reproducibility described here has implications for the interpretation of regional findings and for rigorous pre-processing. The regional distribution of reproducibility measures was different for SDw, CV and ICC. Each one of these measures reveals complementary information that needs to be taken into consideration when performing statistical operations on groups of DT images.

Quantification of mechanical vibration during diffusion tensor imaging at 3 T

Subjects sense clear mechanical vibrations during diffusion tensor imaging (DTI). These vibrations, likely resulting from diffusion-sensitizing gradients, have been assumed to be of the same strength and phase in all parts of the magnetic resonance imaging (MRI) scanner so that they could be ignored. However, our measurements, carried out from several parts of the MRI scanner and its surroundings using an optical laser-based interferometer, demonstrate an uneven distribution of mechanical vibrations within the scanner. The measurements were performed during DT scanning at 3 T, with various diffusion-weighting parameters, by positioning a phantom in the head coil and/or a human subject on the patient bed. The vibration-related movement was caused by the diffusion-sensitizing gradients and was maximally 0.5 mm with typical settings used in brain imaging. The compensation for eddy currents, done with gradients in our DTI sequence, increased the vibration level by a factor of 1.5 or more with diffusion-weighting parameter b = 1000 s/mm(2) and by a factor of 3 or more with b = 3000 s/mm(2). Mechanical vibrations stayed at an acceptable level with b < or = 1000 s/mm(2), resulting in additional signal losses of 5-17%. Vibration levels might be reduced by adjusting imaging parameters, by modifying the gradient waveforms in the DTI sequence, and by redesigning the mechanics of patient bed to effectively dampen the movements.

Correction for direction-dependent distortions in diffusion tensor imaging using matched magnetic field maps

Diffusion tensor imaging (DTI) has seen increased usage in clinical and basic science research in the past decade. By assessing the water diffusion anisotropy within biological tissues, e.g. brain, researchers can infer different fiber structures important for neural pathways. A typical DTI data set contains at least one base image and six diffusion-weighted images along non-collinear encoding directions. The resultant images can then be combined to derive the three principal axes of the diffusion tensor and their respective cross terms, which can in turn be used to compute fractional anisotropy (FA) maps, apparent diffusion coefficient (ADC) maps, and to construct axonal fibers. The above operations all assume that DTI images along different diffusion-weighting directions for the same brain register to each other without spatial distortions. This assumption is generally false, as the large diffusion-weighting gradients would usually induce eddy currents to generate diffusion-weighting direction-dependent field gradients, leading to mis-registration within the DTI data set. Traditional methods for correcting magnetic field-induced distortions do not usually take into account these direction-dependent eddy currents unique for DTI, and they are usually time-consuming because multiple phase images need to be acquired. In this report, we describe our theory and implementation of an efficient and effective method to correct for the main field and eddy current-induced direction-dependent distortions for DTI images under a unified framework to facilitate the daily practice of DTI acquisitions.

The NIH MRI study of normal brain development

MRI is increasingly used to study normal and abnormal brain development, but we lack a clear understanding of "normal". Previous studies have been limited by small samples, narrow age ranges and few behavioral measures. This multi-center project conducted epidemiologically based recruitment of a large, demographically balanced sample across a wide age range, using strict exclusion factors and comprehensive clinical/behavioral measures. A mixed cross-sectional and longitudinal design was used to create a MRI/clinical/behavioral database from approximately 500 children aged 7 days to 18 years to be shared with researchers and the clinical medicine community. Using a uniform acquisition protocol, data were collected at six Pediatric Study Centers and consolidated at a Data Coordinating Center. All data were transferred via a web-network into a MYSQL database that allowed (i) secure data transfer, (ii) automated MRI segmentation, (iii) correlation of neuroanatomical and clinical/behavioral variables as 3D statistical maps and (iv) remote interrogation and 3D viewing of database content. A population-based epidemiologic sampling strategy minimizes bias and enhances generalizability of the results. Target accrual tables reflect the demographics of the U.S. population (2000 Census data). Enrolled subjects underwent a standardized protocol to characterize neurobehavioral and pubertal status. All subjects underwent multi-spectral structural MRI. In a subset, we acquired T1/T2 relaxometry, diffusion tensor imaging, single-voxel proton spectroscopy and spectroscopic imaging. In the first of three cycles, successful structural MRI data were acquired in 392 subjects aged 4:6-18:3 years and in 72 subjects aged 7 days to 4:6 years. We describe the methodologies of MRI data acquisition and analysis, using illustrative results. This database will provide a basis for characterizing healthy brain maturation in relationship to behavior and serve as a source of control data for studies of childhood disorders. All data described here will be available to the scientific community from July, 2006.

Characterization of displaced white matter by brain tumors using combined DTI and fMRI

In vivo white matter tractography by diffusion tensor imaging (DTI) has become a popular tool for investigation of white matter architecture in the normal brain. Despite some unresolved issues regarding the accuracy of DTI, recent studies applied DTI for delineating white matter organization in the vicinity of brain lesions and especially brain tumors. Apart from the intrinsic limitations of DTI, the tracking of fibers in the vicinity or within lesions is further complicated due to changes in diseased tissue such as elevated water content (edema), tissue compression and degeneration. These changes deform the architecture of the white matter and in some cases prevent definite selection of the seed region of interest (ROI) from which fiber tracking begins. We show here that for displaced fiber systems, the use of anatomical approach for seed ROI selection yields insufficient results. Alternatively, we propose to select the seed points based on functional MRI activations which constrain the subjective seed ROI selection. The results are demonstrated on two major fiber systems: the pyramidal tract and the superior longitudinal fasciculus that connect critical motor and language areas, respectively. The fMRI based seed ROI selection approach enabled a more comprehensive mapping of these fiber systems. Furthermore, this procedure enabled the characterization of displaced white matter using the eigenvalue decomposition of DTI. We show that along the compressed fiber system, the diffusivity parallel to the fiber increases, while that perpendicular to the fibers decreases, leading to an overall increase in the fractional anisotropy index reflecting the compression of the fiber bundle. We conclude that definition of the functional network of a subject with deformed white matter should be done carefully. With fMRI, one can more accurately define the seed ROI for DTI based tractography and to provide a more comprehensive, functionally related, white matter mapping, a very important tool used in pre-surgical mapping.

Artifacts and pitfalls in diffusion MRI

Although over the last 20 years diffusion MRI has become an established technique with a great impact on health care and neurosciences, like any other MRI technique it remains subject to artifacts and pitfalls. In addition to common MRI artifacts, there are specific problems that one may encounter when using MRI scanner gradient hardware for diffusion MRI, especially in terms of eddy currents and sensitivity to motion. In this article we review those artifacts and pitfalls on a qualitative basis, and introduce possible strategies that have been developed to mitigate or overcome them.

PASTA: pointwise assessment of streamline tractography attributes

Diffusion tensor MRI tractography aims to reconstruct noninvasively the 3D trajectories of white matter fasciculi within the brain, providing neuroscientists and clinicians with a potentially useful tool for mapping brain architecture. While this technique is widely used to visualize white matter pathways, the associated uncertainty in fiber orientation and artifacts have, to date, not been visualized in conjunction with the trajectory data. In this work, the bootstrap method was used to determine the distributions of diffusion indices such as trace and anisotropy, together with the uncertainty in fiber orientation. A novel visualization scheme was developed to encode this information at each point along reconstructed trajectories. By integrating these schemes into a graphical user interface, a new tool which we call PASTA (Pointwise Assessment of Streamline Tractography Attributes) was created to facilitate identification of artifacts in tractography that would otherwise go undetected.

Confidence mapping in diffusion tensor magnetic resonance imaging tractography using a bootstrap approach

The bootstrap technique is an extremely powerful nonparametric statistical procedure for determining the uncertainty in a given statistic. However, its use in diffusion tensor MRI tractography remains virtually unexplored. This work shows how the bootstrap can be used to assign confidence to results obtained with deterministic tracking algorithms. By invoking the concept of a "tract-propagator," it also underlines the important effect of local fiber architecture or architectural milieu on tracking reproducibility. Finally, the practical advantages and limitations of the technique are discussed. Not only does the bootstrap allow any deterministic tractography algorithm to be used in a probabilistic fashion, but also its model-free inclusion of all sources of variability (including those that cannot be modeled) means that it provides the most realistic approach to probabilistic tractography.

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

Image registration techniques which require image interpolation are widely used in neuroimaging research. We show that signal variance in interpolated images differs significantly from the signal variance of the original images in native space. We describe a simple approach to compute the signal variance in registered images based on the signal variance and covariance of the original images, the spatial transformations computed by the registration procedure, and the interpolation or approximation kernel chosen. The method is general and could handle various sources of signal variability, such as thermal noise and physiological noise, provided that their effects can be assessed in the original images. Our approach is applied to diffusion tensor (DT) MRI data, assuming only thermal noise as the source of variability in the data. We show that incorrect noise variance estimates in registered diffusion-weighted images can affect DT parameters, as well as indices of goodness of fit such as chi-square maps. In addition to DT-MRI, we believe that this methodology would be useful any time parameter extraction methods are applied to registered or interpolated data, such as in relaxometry and functional MRI studies.

Affine and polynomial mutual information coregistration for artifact elimination in diffusion tensor imaging of newborns

We have investigated the use of two different image coregistration algorithms for identifying local regions of erroneously high fractional anisotropy (FA) as derived from diffusion tensor imaging (DTI) data sets in newborns. The first algorithm uses conventional affine registration of each of the diffusion-weighted images to the unweighted (b = 0) image for each slice, while the second algorithm uses second-order polynomial warping. Similarity between images was determined using the mutual information (MI) criterion, which is the preferred 'cost' criterion for coregistration of images with significantly different image intensity distributions. We have found that subtle differences exist in the FA values resulting from affine and second-order polynomial coregistration and demonstrate that nonlinear distortions introduce artifacts of spatial extent similar to real white matter structures in the newborn subcortex. We show that polynomial coregistration systematically reduces the presence of erroneous regions of high FA and that such artifacts can be identified by visual inspection of FA maps resulting from affine and polynomial coregistrations. Furthermore, we show that nonlinear distortions may be particularly pronounced when acquiring image slices of axial orientation at the height of the nasal cavity. Finally, we show that third-order polynomial MI coregistration (using the images resulting from second-order coregistration as input) has no observable effect on the resulting FA maps.

k-space correction of eddy-current-induced distortions in diffusion-weighted echo-planar imaging

This paper describes a method for correcting eddy-current (EC)-induced distortions in diffusion-weighted echo-planar imaging (DW-EPI). First, reference measurements of EC fields within the EPI acquisition window are performed for DW gradient pulses applied separately along each physical axis of the gradient set and for a range of gradient amplitudes. EC fields caused by the DW gradients of the DW-MRI protocol are then calculated using the reference EC measurements. Finally, these calculated fields are used to correct the respective DW-EPI raw (k-space) data during image reconstruction. The technique was implemented in a small-bore MRI scanner with no digital preemphasis. It corrected EC-induced image distortions in both phantom and in vivo brain diffusion tensor imaging (DTI) data more effectively than commonly used image-based techniques. The method did not increase imaging time, since the same reference EC measurements were used to correct data acquired from different phantoms, subjects, and DTI protocols. Because of the simplicity of the reference EC measurements, the method can easily be implemented in clinical scanners.

RESTORE: Robust estimation of tensors by outlier rejection

Signal variability in diffusion weighted imaging (DWI) is influenced by both thermal noise and spatially and temporally varying artifacts such as subject motion and cardiac pulsation. In this paper, the effects of DWI artifacts on estimated tensor values, such as trace and fractional anisotropy, are analyzed using Monte Carlo simulations. A novel approach for robust diffusion tensor estimation, called RESTORE (for robust estimation of tensors by outlier rejection), is proposed. This method uses iteratively reweighted least-squares regression to identify potential outliers and subsequently exclude them. Results from both simulated and clinical diffusion data sets indicate that the RESTORE method improves tensor estimation compared to the commonly used linear and nonlinear least-squares tensor fitting methods and a recently proposed method based on the Geman-McClure M-estimator. The RESTORE method could potentially remove the need for cardiac gating in DWI acquisitions and should be applicable to other MR imaging techniques that use univariate or multivariate regression to fit MRI data to a model.

Geometric distortion correction of high-resolution 3 T diffusion tensor brain images

Diffusion-weighted images based on echo planar sequences suffer from distortions due to field inhomogeneities from susceptibility differences as well as from eddy currents arising from diffusion gradients. In this paper, a novel approach using nonlinear warping based on optic flow to correct distortions of baseline and diffusion weighted echo planar images (EPI) acquired at 3 T is presented. The distortion correction was estimated by warping the echo planar images to the anatomically correct T2-weighted fast spin echo images (T2-FSE). A global histogram intensity matching of the T2-FSE precedes the base line EPI image distortion correction. A local intensity-matching algorithm was used to transform labeled T2-FSE regions to match intensities of diffusion-weighted EPI images prior to distortion correction of these images. Evaluation was performed using three methods: (i) visual comparison of overlaid contours, (ii) a global mutual information index, and (iii) a local distance measure between homologous points. Visual assessment and the global index demonstrated a decrease in geometrical distortion and the distance measure showed that distortions are reduced to a subvoxel level. In conclusion, the warping algorithm is effective in reducing geometric distortions, enabling generation of anatomically correct diffusion tensor images at 3 T.

Quantitative evaluation of image-based distortion correction in diffusion tensor imaging

A statistical method for the evaluation of image registration for a series of images based on the assessment of consistency properties of the registration results is proposed. Consistency is defined as the residual error of the composition of cyclic registrations. By combining the transformations of different algorithms the consistency error allows a quantitative comparison without the use of ground truth, specifically, it allows a determination as to whether the algorithms are compatible and hence provide comparable registrations. Consistency testing is applied to evaluate retrospective correction of eddy current-induced image distortion in diffusion tensor imaging of the brain. In the literature several image transformations and similarity measures have been proposed, generally showing a significant reduction of distortion in side-by-side comparison of parametric maps before and after registration. Transformations derived from imaging physics and a three-dimensional affine transformation as well as mutual information (MI) and local correlation (LC) similarity are compared to each other by means of consistency testing. The dedicated transformations could not demonstrate a significant difference for more than half of the series considered. LC similarity is well-suited for distortion correction providing more consistent registrations which are comparable to MI.