Robust tensor estimation in diffusion tensor imaging

The signal response measured in diffusion tensor imaging is subject to detrimental influences caused by noise. Noise fields arise due to various contributions such as thermal and physiological noise and sources related to the hardware imperfection. As a result, diffusion tensors estimated by different linear and non-linear least squares methods in absence of a proper noise correction tend to be substantially corrupted. In this work, we propose an advanced tensor estimation approach based on the least median squares method of the robust statistics. Both constrained and non-constrained versions of the method are considered. The performance of the developed algorithm is compared to that of the conventional least squares method and of the alternative robust methods proposed in the literature. Two examples of simulated diffusion attenuations and experimental in vivo diffusion data sets were used as a basis for comparison. The robust algorithms were shown to be advantageous compared to the least squares method in the cases where elimination of the outliers is desirable. Additionally, the constraints were applied in order to prevent generation of the non-positive definite tensors and reduce related artefacts in the maps of fractional anisotropy. The developed method can potentially be exploited also by other MR techniques where a robust regression or outlier localisation is required.     

Estimation of mutual information objective function based on Fourier shift theorem: an application to eddy current distortion correction in diffusion tensor imaging

Diffusion tensor imaging requires correction of eddy current distortion in diffusion-weighted images. An effective retrospective correction approach is to transform a diffusion-weighted image to maximize the mutual information (MI) between the transformed diffusion-weighted image and the corresponding T2-weighted image. In the literature, either linear interpolation or partial volume interpolation is applied to estimate the MI objective function. However, these interpolation methods induce artifacts to the MI objective function, thus compromising correction results. In this work, the MI objective function is estimated based on interpolation using Fourier shift theorem. This method eliminates the artifacts incurred with the aforementioned interpolation methods. The algorithm is further improved by approximating pixel values using their nearest neighbors in the up-sampled spatial domain, resulting in dramatically increased computational efficiency without compromising the correction results. The effects of varying the number of quantization levels and using Parzen window filtering to smooth the MI objective function are also investigated to obtain optimized algorithm parameters. The diffusion tensor image quality after applying the proposed distortion correction method is significantly improved visually.     

Optimal real-time estimation in diffusion tensor imaging

Diffusion tensor imaging (DTI) constitutes the most used paradigm among the diffusion-weighted magnetic resonance imaging (DW-MRI) techniques due to its simplicity and application potential. Recently, real-time estimation in DW-MRI has deserved special attention, with several proposals aiming at the estimation of meaningful diffusion parameters during the repetition time of the acquisition sequence. Specifically focusing on DTI, the underlying model of the noise present in the acquired data is not taken into account, leading to a suboptimal estimation of the diffusion tensor. In this paper, we propose an optimal real-time estimation framework for DTI reconstruction in single-coil acquisitions. By including an online estimation of the time-changing noise variance associated to the acquisition process, the proposed method achieves the sequential best linear unbiased estimator. Results on both synthetic and real data show that our method outperforms those so far proposed, reaching the best performance of the existing proposals by processing a substantially lower number of diffusion images.     

A diffusion gradient optimization framework for spinal cord diffusion tensor imaging

The uncertainty in the estimation of diffusion model parameters in diffusion tensor imaging (DTI) can be reduced by optimally selecting the diffusion gradient directions utilizing some prior structural information. This is beneficial for spinal cord DTI, where the magnetic resonance images have low signal-to-noise ratio and thus high uncertainty in diffusion model parameter estimation. Presented is a gradient optimization scheme based on D-optimality, which reduces the overall estimation uncertainty by minimizing the Rician Cramer-Rao lower bound of the variance of the model parameter estimates. The tensor-based diffusion model for DTI is simplified to a four-parameter axisymmetric DTI model where diffusion transverse to the principal eigenvector of the tensor is assumed isotropic. Through simulations and experimental validation, we demonstrate that an optimized gradient scheme based on D-optimality is able to reduce the overall uncertainty in the estimation of diffusion model parameters for the cervical spinal cord and brain stem white matter tracts.     

On the effects of dephasing due to local gradients in diffusion tensor imaging experiments: relevance for diffusion tensor imaging fiber phantoms

The effect of susceptibility differences between fluid and fibers on the properties of DTI fiber phantoms was investigated. Thereto, machine-made, easily producible and inexpensive DTI fiber phantoms were constructed by winding polyamide fibers of 15 microm diameter around a circular acrylic glass spindle. The achieved fractional anisotropy was 0.78+/-0.02. It is shown by phantom measurements and Monte Carlo simulations that the transversal relaxation time T(2) strongly depends on the angle between the fibers and the B(0) field if the susceptibilities of the fibers and fluid are not identical. In the phantoms, the measured T(2) time at 3 T decreased by 60% for fibers running perpendicular to B(0). Monte Carlo simulations confirmed this result and revealed that the exact relaxation time depends strongly on the exact packing of the fibers. In the phantoms, the measured diffusion was independent of fiber orientation. Monte Carlo simulations revealed that the measured diffusion strongly depends on the exact fiber packing and that field strength and -orientation dependencies of measured diffusion may be minimal for hexagonal packing while the diffusion can be underestimated by more than 50% for cubic packing at 3 T. To overcome these effects, the susceptibilities of fibers and fluid were matched using an aqueous sodium chloride solution (83 g NaCl per kilogram of water). This enables an orientation independent and reliable use of DTI phantoms for evaluation purposes.     

Correcting power and p-value calculations for bias in diffusion tensor imaging

Diffusion tensor imaging (DTI) provides quantitative parametric maps sensitive to tissue microarchitecture (e.g., fractional anisotropy, FA). These maps are estimated through computational processes and subject to random distortions including variance and bias. Traditional statistical procedures commonly used for study planning (including power analyses and p-value/alpha-rate thresholds) specifically model variability, but neglect potential impacts of bias. Herein, we quantitatively investigate the impacts of bias in DTI on hypothesis test properties (power and alpha-rate) using a two-sided hypothesis testing framework. We present theoretical evaluation of bias on hypothesis test properties, evaluate the bias estimation technique SIMEX for DTI hypothesis testing using simulated data, and evaluate the impacts of bias on spatially varying power and alpha rates in an empirical study of 21 subjects. Bias is shown to inflame alpha rates, distort the power curve, and cause significant power loss even in empirical settings where the expected difference in bias between groups is zero. These adverse effects can be attenuated by properly accounting for bias in the calculation of power and p-values.     

Comparison of compressed sensing diffusion spectrum imaging and diffusion tensor imaging in patients with intracranial masses

PurposeTo compare compressed diffusion spectrum imaging (CS-DSI) with diffusion tensor imaging (DTI) in patients with intracranial masses. We hypothesized that CS-DSI would provide superior visualization of the motor and language tracts.Materials and methodsWe retrospectively analyzed 25 consecutive patients with intracranial masses who underwent DTI and CS-DSI for preoperative planning. Directionally-encoded anisotropy maps, and streamline hand corticospinal motor tracts and arcuate fasciculus language tracts were graded according to a 3-point scale. Tract counts, anisotropy, and lengths were also calculated. Comparisons were made using exact marginal homogeneity, McNemar's and Wilcoxon signed-rank tests.ResultsReaders preferred the CS-DSI over DTI anisotropy maps in 92% of the cases, and the CS-DSI over DTI tracts in 84%. The motor tracts were graded as excellent in 80% of cases for CS-DSI versus 52% for DTI; 58% of the motor tracts graded as acceptable in DTI were graded as excellent in CS-DSI (p = 0.02). The language tracts were graded as excellent in 68% for CS-DSI versus none for DTI; 78% of the language tracts graded as acceptable by DTI were graded as excellent by CS-DSI (p < 0.001). CS-DSI demonstrated smaller normalized mean differences than DTI for motor tract counts, anisotropy and language tract counts (p ≤ 0.01).ConclusionCS-DSI was preferred over DTI for the evaluation of motor and language white matter tracts in patients with intracranial masses. Results suggest that CS-DSI may be more useful than DTI for preoperative planning purposes.     

Correlation of proton MR spectroscopy and diffusion tensor imaging

Proton magnetic resonance spectroscopy ((1)H-MRS) provides indices of neuronal damage. Diffusion tensor imaging (DTI) relates to water diffusivity and fiber tract orientation. A method to compare (1)H-MRS and DTI findings was developed, tested on phantom and applied on normal brain. Point-resolved spectroscopy (T(R)/T(E)=1500/135) was used for chemical shift imaging of a supraventricular volume of interest of 8 x 8 x 2 cm(3) (64 voxels). In DTI, a segmental spin-echo sequence (T(R)/T(E)=5500/91) was used and slices were stacked to reproduce the slab used in MRS. The spatial distributions of choline and N-acetylaspartate (NAA) correlated to mean fractional anisotropy and apparent diffusion coefficient (ADC) for the inner 6 x 6=36 voxels defined in MRS, most notably NAA and ADC value (r=-.70, P<.00001; correlation across four subjects, 144 data pairs). This is the first association of neuron metabolite contents in volunteers with structure as indicated by DTI.     

Correction for fast pseudo-diffusive fluid motion contaminations in diffusion tensor imaging

In this prospective study, we quantified the fast pseudo-diffusion contamination by blood perfusion or cerebrospinal fluid (CSF) intravoxel incoherent movements on the measurement of the diffusion tensor metrics in healthy brain tissue.Diffusion-weighted imaging (TR/TE = 4100 ms/90 ms; b-values: 0, 5, 10, 20, 35, 55, 80, 110, 150, 200, 300, 500, 750, 1000, 1300 s/mm², 20 diffusion-encoding directions) was performed on a cohort of five healthy volunteers at 3 Tesla. The projections of the diffusion tensor along each diffusion-encoding direction were computed using a two b-value approach (2b), by fitting the signal to a monoexponential curve (mono), and by correcting for fast pseudo-diffusion compartments using the biexponential intravoxel incoherent motion model (IVIM) (bi). Fractional anisotropy (FA) and mean diffusivity (MD) of the diffusion tensor were quantified in regions of interest drawn over white matter areas, gray matter areas, and the ventricles.A significant dependence of the MD from the evaluation method was found in all selected regions. A lower MD was computed when accounting for the fast-diffusion compartments. A larger dependence was found in the nucleus caudatus (bi: median 0.86 10⁻³ mm²/s, Δ2b: −11.2%, Δmono: −14.4%; p = 0.007), in the anterior horn (bi: median 2.04 10⁻³ mm²/s, Δ2b: −9.4%, Δmono: −11.5%, p = 0.007) and in the posterior horn of the lateral ventricles (bi: median 2.47 10⁻³ mm²/s, Δ2b: −5.5%, Δmono: −11.7%; p = 0.007). Also for the FA, the signal modeling affected the computation of the anisotropy metrics. The deviation depended on the evaluated region with significant differences mainly in the nucleus caudatus (bi: median 0.15, Δ2b: +39.3%, Δmono: +14.7%; p = 0.022) and putamen (bi: median 0.19, Δ2b: +3.1%, Δmono: +17.3%; p = 0.015).Fast pseudo-diffusive regimes locally affect diffusion tensor imaging (DTI) metrics in the brain. Here, we propose the use of an IVIM-based method for correction of signal contaminations through CSF or perfusion.     

Keyhole and zero-padding approaches for reduced-encoding diffusion tensor imaging of the mouse brains

Keyhole diffusion tensor imaging (keyhole DTI) was previously proposed in cardiac imaging to reconstruct DTI maps from the reduced phase-encoding images. To evaluate the feasibility of keyhole DTI in brain imaging, keyhole and zero-padding DTI algorithms were employed on in vivo mouse brain. The reduced phase-encoding portion, also termed as the sharing rate, was varied from 50% to 90% of the full k-space. Our data showed that zero-padding DTI resulted in decreased fractional anisotropy (FA) and decreased mean apparent diffusion coefficient (mean ADC) in white matter (WM) regions. Keyhole DTI showed a better edge preservation on mean ADC maps but not on FA maps as compared to the zero-padding DTI. When increasing the sharing rate in keyhole approach, an underestimation of FA and an over- or underestimation of mean ADC were measured in WM depending on the selected reference image. The inconsistency of keyhole DTI may add a challenge for the wide use of this modality. However, with a carefully selected directive diffusion-weighted image to serve as the reference image in the keyhole approach, this study demonstrated that one may obtain DTI indices of reduced-encoding images with high consistency to those derived with full k-space DTI.     

Reduced anisotropy of water diffusion in structural cerebral abnormalities demonstrated with diffusion tensor imaging

We used diffusion tensor imaging (DTI) to investigate the behavior of water diffusion in cerebral structural abnormalities. The fractional anisotropy, a measure of directionality of the molecular motion of water, and the mean diffusivity, a measure of the magnitude of the molecular motion of water, were measured in 18 patients with longstanding partial epilepsy and structural abnormalities on standard magnetic resonance imaging and the results compared with measurements in the white matter of 10 control subjects. Structural abnormalities were brain damage (postsurgical brain damage, nonspecific brain damage, perinatal brain damage, perinatal infarct, ischemic infarct, perinatal hypoxia, traumatic brain damage (n = 3), mitochondrial cytopathy and mesiotemporal sclerosis), dysgenesis (cortical dysplasia (n = 2) and heterotopia) and tumors (meningioma (n = 2), hypothalamic hamartoma and glioma). Anisotropy was reduced in all structural abnormalities. In the majority of abnormalities this was associated with an increased mean diffusivity; however, 30% of all structural abnormalities (some patients with brain damage and dysgenesis) had a normal mean diffusivity in combination with a reduced anisotropy. There was no correlation between fractional anisotropy and mean diffusivity measurements in structural abnormalities (r = -0.1). Our findings suggest that DTI is sensitive for the detection of a variety of structural abnormalities, that a reduced anisotropy is the common denominator in structural cerebral abnormalities of different etiologies and that mean diffusivity and fractional anisotropy may be, in part, independent. Combined measurements of mean diffusivity and fractional anisotropy are likely to increase the specificity of DTI.     

A comparative study of acquisition schemes for diffusion tensor imaging using MRI

This study has investigated the effects of the selection of the diffusion-weighted (DW) gradient directions on the precision of a diffusion tensor imaging (DTI) experiment. The theoretical analysis provided a quantitative framework in which the noise performance of DTI schemes could be assessed objectively and for the development of novel DTI schemes, which employ multiple DW gradient directions. This generic framework was first applied to the examination of two commonly used DTI schemes, which employed 6 DW gradient directions and hitherto were used indiscriminately under the sole condition of noncollinearity. It was then used to design and assess a novel 12-DW-gradient-direction DTI protocol, which employed the same total number of DW acquisitions as the two conventional schemes (12). This theoretical investigation was then corroborated using rigorous simulation and DTI experiments on both an isotropic phantom and a healthy human brain. Both the theoretical and the experimental analysis demonstrated that the two conventional schemes showed a significantly different noise performance and that use of the new multiple-DW-gradient-direction scheme clearly improved the precision of the DTI measurements.     

Evaluation of diffusion models of fiber tracts using diffusion tensor magnetic resonance imaging

Modeling of water diffusion in white matter is useful for revealing microstructure of the brain tissue and hence diagnosis and evaluation of white matter diseases. Researchers have modeled diffusion in white matter using mathematical and mechanical analysis at the cellular level. However, less work has been devoted to evaluate these models using macroscopic real data such as diffusion tensor magnetic resonance imaging (DTMRI) data. DTMRI is a noninvasive tool for evaluating white matter microstructure by measuring random motion of water molecules referred to as diffusion. It reflects directional information of microscopic structures such as fibers. Thus, it is applicable for evaluation and modification of mathematical models of white matter. Nevertheless, a realistic relation between a fiber model and imaging data does not exist. This work opens a promising avenue for relating DTMRI data to microstructural parameters of white matter. First, we propose a strategy for relating DTMRI and fiber model parameters to evaluate mathematical models in light of real data. The proposed strategy is then applied to evaluate and extend an existing model of white matter based on clinically available DTMRI data. Next, the proposed strategy is used to estimate microstructural characteristics of fiber tracts. We illustrate this approach through its application to approximation of myelin sheath thickness and fraction of volume occupied by fibers. Using sufficiently small imaging voxels, the proposed approach is capable of estimating model parameters with desirable precision.     

Estimation and application of spatially variable noise fields in diffusion tensor imaging

Optimal interpretation of magnetic resonance image content often requires an estimate of the underlying image noise, which is typically realized as a spatially invariant estimate of the noise distribution. This is not an ideal practice in diffusion tensor imaging because the noise distribution is usually spatially varying due to the use of fast imaging and noise suppression techniques. A new estimation approach for spatially varying noise fields (NFs) is proposed in this article. The approach is based on a noise invariance property in scenarios in which more than one image, each with potentially different signal levels, is acquired on each slice, as in diffusion-weighted MRI. This technique leads to improved NF estimates in simulations, phantom experiments and in vivo studies when compared to traditional NF estimators that use regional variability or background intensity histograms. The proposed method reduces the NF estimation error by a factor of 100 in simulations, shows a strong linear correlation (R²=0.99) between theoretical and estimated noise changes in phantoms and demonstrates consistent (<5% variability) NF estimates in vivo. The advantages of spatially varying NF estimation are demonstrated for power analysis, outlier detection and tensor estimation.     

磁共振扩散张量成像中扩散敏感梯度磁场方向分布方案的研究进展

磁共振扩散张量成像可以定量无创研究人体内水分子在三维空间中的各向异性扩散规律,进而获取重要的病理及生理信息.为了得到水分子各向异性扩散信息,需要按照一定的方案依次施加不同方向的扩散敏感梯度磁场,测量水分子在这些方向上的扩散系数用以估算扩散张量.扩散张量成像测量结果的准确程度受梯度磁场方向分布方案的影响,本文对扩散敏感梯度磁场方向分布方案进行综述,包括完全随机方案、启发式方案、规则多面体式方案和数值优化方案等,分析这些方案的优势与局限性,并提出需进一步研究的问题.     

Quantitative evaluation for brain CT/MRI coregistration based on maximization of mutual information in patients with focal epilepsy investigated with subdural electrodes

Patients with drug-resistant focal epilepsy may require intracranial investigations with subdural electrodes. These must be correctly localized with respect to the brain cortical surface and require appropriate monitoring. For this purpose, coregistration techniques, which fuse preimplantation 3D magnetic resonance imaging scans with postimplantation computed tomography scans, have been implemented. In order to reduce localization errors due to the fusion process, we used a coregistration method based on the maximization of mutual information (MI) in 11 patients with extratemporal epilepsy who were invasively investigated. Our registration method is based on three processing steps: rigid-body transformation for coregistration, computation of MI as a similarity measure and the use of the Downhill Simplex optimization method. After consistency analysis, the shift of the registration method reached 0.14+/-0.27 mm in translation and 0.03+/-0.14 degrees in rotation, and the accuracies assessed on voxels of skull surface and voxels of the center of the brain volume were 1.42+/-0.61 and 1.15+/-0.53 mm, respectively. The accuracy of the fusion process reached submillimeter range, and results were considered reliable for surgical planning in all studied patients.     

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 (相似文献   

A Monte Carlo simulation of image misalignment effects in diffusion tensor imaging

Diffusion tensor imaging (DTI) and tractography are noninvasive MRI methods, providing an insight on microscopic structural information of anisotropic tissues in vivo. The success of this technique stems on a watchful choice of imaging parameters and post-acquisition reconstruction. In the present work, we have focused on the problem of residual linear image misalignment in the DTI data and its effects on the parameters of the diffusion tensor and fiber tracking in human brain. We demonstrate substantial sensitivity of the reconstructed diffusion tensor and fiber tractography on increasing amplitude of artificially induced random image misalignment in the DTI. We show that already a submillimeter image misalignment in the DTI is an important source of error, which may potentially mask pathological presentations of the diseases and may partially explain variations in the results obtained from the DTI. Finally, we evaluated four implementations of image registrations and demonstrate their variable performance. This further supports the fact that a robust image registration must be performed to ensure reliable and reproducible diffusion tensor mapping and reconstruction of white matter (WM) fibers.     

Importance of exactb-tensor calculation for quantitative diffusion tensor imaging and tracking of neuronal fiber bundles

Quantitative diffusion tensor imaging (DTI) is a novel method of magnetic resonance (MR) imaging providing information on the brain’s microstructure in vivo. DTI can be effectively measured with modern clinical MR scanners. However, imaging sequence details required for accurateb matrix calculation and for following DTI quantification are normally unknown to the user. In this work, we investigated the accuracy ofb value approximation if theb matrix is calculated without taking into account the effect of imaging gradients. It was found that an error of more than 4% in DTI estimation arises for a quite typical brain imaging protocol. The errors in mean diffusivity and fractional anisotropy index depend on diffusion tensor shape and eigenvectors orientation and exceed noise level in DTI quantification. These errors however have a strong impact on fiber tracking — up to 30% difference was found between the fiber tracks corresponding to exact and approximate calculated DTI data. Since these errors are dependent on imaging parameters and sequence implementation, accurateb matrix calculations are important for adequate comparison between data acquired on different MR scanners and also for data measured with the different imaging protocols.