Geometrically constrained two-tensor model for crossing tracts in DWI

MR diffusion tensor imaging (DTI) of the brain and spine provides a unique tool for both visualizing directionality and assessing intactness of white matter fiber tracts in vivo. At the spatial resolution of clinical MRI, much of primate white matter is composed of interdigitating fibers. Analyses based on an assumed single diffusion tensor per voxel yield important information about the average diffusion in the voxel but fail to reveal structure in the presence of crossing tracts. Until today, all clinical scans assume only one tensor, causing potential serious errors in tractography. Since high angular resolution imaging remains, so far, untenable for routine clinical use, a method is proposed whereby the single-tensor field is augmented with additional information gleaned from standard clinical DTI. The method effectively resolves two distinct tract directions within voxels, in which only two tracts are assumed to exist. The underlying constrained two-tensor model is fitted in two stages, utilizing the information present in the single-tensor fit. As a result, the necessary MRI time can be drastically reduced when compared with other approaches, enabling widespread clinical use. Upon evaluation in simulations and application to in vivo human brain DTI data, the method appears to be robust and practical and, if correctly applied, could elucidate tract directions at critical points of uncertainty.     

Fitting of two-tensor models without ad hoc assumptions to detect crossing fibers using clinical DWI data

Analysis of crossing fibers is a challenging topic in recent diffusion-weighted imaging (DWI). Resolving crossing fibers is expected to bring major changes to present tractography results based on the standard tensor model. Model free approaches, like Q-ball or diffusion spectrum imaging, as well as multi-tensor models are used to unfold the different diffusion directions mixed in a voxel of DWI data. Due to its seeming simplicity, the two-tensor model (TTM) is applied frequently to provide two positive-definite tensors and the relative population fraction modeling two crossing fiber branches. However, problems with uniqueness and noise instability are apparent. To stabilize the fit, several of the 13 physical parameters are fixed ad hoc, before fitting the model to the data. Our analysis of the TTM aims at fitting procedures where ad hoc parameters are avoided. Revealing sources of instability, we show that the model's inherent ambiguity can be reduced to one scalar parameter which only influences the fraction and the eigenvalues of the TTM, whereas the diffusion directions are not affected. Based on this, two fitting strategies are proposed: the parsimonious strategy detects the main diffusion directions without extra parameter fixation, to determine the eigenvalues and the population fraction an empirically motivated condition must be added. The expensive strategy determines all 13 physical parameters of the TTM by a fit to DWIs alone; no additional assumption is necessary. Ill-posedness of the model in case of noisy data is cured by denoising of the data and by L-curve regularization combined with global minimization performing a least-squares fit of the full model. By model simulations and real data applications, we demonstrate the feasibility of our fitting strategies and achieve convincing results. Using clinically affordable diffusion acquisition paradigms (encoding numbers: 21, 2*15, 2*21) and b values (b = 500–1500 s/mm²), this methodology can place the TTM parameters involved in crossing fibers on a more empirical basis than fitting procedures with technical assumptions.     

Water diffusion-exchange effect on the paramagnetic relaxation enhancement in off-resonance rotating frame

The off-resonance rotating frame technique based on the spin relaxation properties of off-resonance T1rho can significantly increase the sensitivity of detecting paramagnetic labeling at high magnetic fields by MRI. However, the in vivo detectable dimension for labeled cell clusters/tissues in T1rho-weighted images is limited by the water diffusion-exchange between mesoscopic scale compartments. An experimental investigation of the effect of water diffusion-exchange between compartments on the paramagnetic relaxation enhancement of paramagnetic agent compartment is presented for in vitro/in vivo models. In these models, the size of paramagnetic agent compartment is comparable to the mean diffusion displacement of water molecules during the long RF pulses that are used to generate the off-resonance rotating frame. The three main objectives of this study were: (1) to qualitatively correlate the effect of water diffusion-exchange with the RF parameters of the long pulse and the rates of water diffusion, (2) to explore the effect of water diffusion-exchange on the paramagnetic relaxation enhancement in vitro, and (3) to demonstrate the paramagnetic relaxation enhancement in vivo. The in vitro models include the water permeable dialysis tubes or water permeable hollow fibers embedded in cross-linked proteins gels. The MWCO of the dialysis tubes was chosen from 0.1 to 15 kDa to control the water diffusion rate. Thin hollow fibers were chosen to provide sub-millimeter scale compartments for the paramagnetic agents. The in vivo model utilized the rat cerebral vasculatures as a paramagnetic agent compartment, and intravascular agents (Gd-DTPA)30-BSA were administrated into the compartment via bolus injections. Both in vitro and in vivo results demonstrate that the paramagnetic relaxation enhancement is predominant in the T1rho-weighted image in the presence of water diffusion-exchange. The T1rho contrast has substantially higher sensitivity than the conventional T1 contrast in detecting paramagnetic agents, especially at low paramagnetic agent volumetric fractions, low paramagnetic agent concentrations, and low RF amplitudes. Short pulse duration, short pulse recycle delay and efficient paramagnetic relaxation can reduce the influence of water diffusion-exchange on the paramagnetic enhancement. This study paves the way for the design of off-resonance rotating experiments to detect labeled cell clusters/tissue compartments in vivo at a sub-millimeter scale.     

Simultaneous magnetic resonance imaging of diffusion anisotropy and diffusion gradient

The theory of diffusion gradient-weighted MRI (DGWI) is presented in this paper. The Bloch-Torrey equation was modified to include the effect of intravoxel spatial-location variation of water diffusion (diffusion gradient) on MRI signal, in addition to the effect of intravoxel spatial-direction variation of water diffusion (diffusion anisotropy). An analytical solution for a diffusion-encoding spin-echo pulse sequence was derived. Unlike water diffusion which attenuates the image signal intensity, this newly derived solution relates the spatial gradient of the water diffusion with the phase of the image signal. This novel MRI technique directly measures both the water diffusion and its spatial gradient, and thus offers a noninvasive imaging tool to simultaneously investigate the intravoxel inhomogeneity and anisotropy of tissue structures. In addition, as demonstrated with our preliminary data, this new method may be utilized to delineate the interfaces of tissues with different diffusion. This method is an extension of the successful diffusion tensor MRI (DTI), but requires no additional data acquisition. In addition to the measured diffusion tensor, this new method provides measurements of the spatial derivatives of the three principal diffusivities of the tensor, thereby providing additional information for improving white matter fiber tractography.     

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.     

Novel multisection design of anisotropic diffusion phantoms

Diffusion-weighted magnetic resonance imaging provides access to fiber pathways and structural integrity in fibrous tissues such as white matter in the brain. In order to enable better access to the sensitivity of the diffusion indices to the underlying microstructure, it is important to develop artificial model systems that exhibit a well-known structure, on the one hand, but benefit from a reduced complexity on the other hand. In this work, we developed a novel multisection diffusion phantom made of polyethylene fibers tightly wound on an acrylic support. The phantom exhibits three regions with different geometrical configuration of fibers: a region with fibers crossing at right angles, a region with parallel fibers and homogeneous density, and, finally, a region with parallel fibers but with a gradient of fiber density along the axis of symmetry. This gives rise to a gradual change of the degree of anisotropy within the same phantom. In this way, the need to construct several phantoms with different fiber densities is avoided, and one can access different fractional anisotropies in the same experiment under the same physical conditions. The properties of the developed phantom are demonstrated by means of diffusion tensor imaging and diffusion kurtosis imaging. The measurements were performed using a diffusion-weighted spin-echo and a diffusion-weighted stimulated-echo pulse sequence programmed in-house. The influence of the fiber density packing on the diffusion parameters was analyzed. We also demonstrate how the novel phantom can be used for the validation of high angular resolution diffusion imaging data analysis.     

Efficient cardiac diffusion tensor MRI by three-dimensional reconstruction of solenoidal tensor fields

Tensor tomography is being investigated as a technique for reconstruction of in vivo diffusion tensor fields that can potentially be used to reduce the number of magnetic resonance imaging (MRI) measurements. Specifically, assessments are being made of the reconstruction of cardiac diffusion tensor fields from 3D Radon planar projections using a filtered backprojection algorithm in order to specify the helical fiber structure of myocardial tissue. Helmholtz type decomposition is proposed for 3D second order tensor fields. Using this decomposition a Fourier projection theorem is formulated in terms of the solenoidal and irrotational components of the tensor field. From the Fourier projection theorem, two sets of Radon directional measurements, one that reconstructs the solenoidal component and one that reconstructs the irrotational component of the tensor field, are prescribed. Based on these observations filtered backprojection reconstruction formulae are given for the reconstruction of a 3D second order tensor field and its solenoidal and irrotational components from Radon projection measurements. Computer simulations demonstrate the validity of the mathematical formulations and demonstrate that a realistic model of the helical fiber structure of the myocardial tissue specifies a diffusion tensor field for which the first principal vector (the vector associated with the maximum eigenvalue) of the solenoidal component accurately approximates the first principal vector of the diffusion tensor. A priori knowledge of this allows the orientation of the myocardial fiber structure to be specified utilizing one half of the number of MRI measurements of a normal diffusion tensor field study.     

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.     

Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. 1996

Quantitative-diffusion-tensor MRI consists of deriving and displaying parameters that resemble histological or physiological stains, i.e., that characterize intrinsic features of tissue microstructure and microdynamics. Specifically, these parameters are objective, and insensitive to the choice of laboratory coordinate system. Here, these two properties are used to derive intravoxel measures of diffusion isotropy and the degree of diffusion anisotropy, as well as intervoxel measures of structural similarity, and fiber-tract organization from the effective diffusion tensor, D, which is estimated in each voxel. First, D is decomposed into its isotropic and anisotropic parts, 〈D〉 I and D – 〈D〉 I, respectively (where 〈D〉 = Trace(D)/3 is the mean diffusivity, and I is the identity tensor). Then, the tensor (dot) product operator is used to generate a family of new rotationally and translationally invariant quantities. Finally, maps of these quantitative parameters are produced from high-resolution diffusion tensor images (in which D is estimated in each voxel from a series of 2D-FT spin-echo diffusion-weighted images) in living cat brain. Due to the high inherent sensitivity of these parameters to changes in tissue architecture (i.e., macromolecular, cellular, tissue, and organ structure) and in its physiologic state, their potential applications include monitoring structural changes in development, aging, and disease.     

An MRI perfusion model incorporating nonequilibrium exchange between vascular and extravascular compartments

A model of MRI signal intensity which is a function of perfusion is developed based upon the assumption that biological tissue can be represented by a blood and tissue compartment. The longitudinal magnetization is derived from the Bloch equations which are modified to model the magnetization in both the blood and tissue as a function of the following physiological parameters: blood flow velocity; perfusion fraction, which in the model is parameterized in terms of the ratio of the cross-sectional areas of the tissue and blood compartments; diffusion; rate of exchange between the blood and extravascular tissue compartments. Simulations of slice profiles excited by a repetitive sequence of 90 degrees slice-selective pulses show that the signal intensity in the blood and tissue compartments are modulated by the physiological parameters. A key factor in the modulation of the MRI signal is a time-of-flight effect whereby unexcited spins perfuse the excited region and exchange with blood and tissue compartments, thus immediately increasing the slice signal intensity but also delaying the spin exits from the slice, thereby decreasing their contribution to slice signal intensity in future repetitive pulse measurements.     

MRI diffusion tensor reconstruction with PROPELLER data acquisition

MRI diffusion imaging is effective in measuring the diffusion tensor in brain, cardiac, liver, and spinal tissue. Diffusion tensor tomography MRI (DTT MRI) method is based on reconstructing the diffusion tensor field from measurements of projections of the tensor field. Projections are obtained by appropriate application of rotated diffusion gradients. In the present paper, the potential of a novel data acquisition scheme, PROPELLER (Periodically Rotated Overlapping ParallEL Lines with Enhanced Reconstruction), is examined in combination with DTT MRI for its capability and sufficiency for diffusion imaging. An iterative reconstruction algorithm is used to reconstruct the diffusion tensor field from rotated diffusion weighted blades by appropriate rotated diffusion gradients. DTT MRI with PROPELLER data acquisition shows significant potential to reduce the number of weighted measurements, avoid ambiguity in reconstructing diffusion tensor parameters, increase signal-to-noise ratio, and decrease the influence of signal distortion.     

基于非局部约束球面反卷积模型的纤维追踪算法

基于扩散磁共振成像的纤维追踪技术为非侵入性观测脑白质结构提供了有力的手段，约束球面反卷积作为一种多纤维追踪模型，能够对体素内纤维的方向信息进行建模，进而实现脑纤维的重构.针对约束球面反卷积模型的不适定性以及细节信息丢失问题，本文在约束球面反卷积的基础上，结合邻域信息和分数阶正则化，提出了一种基于非局部约束球面反卷积模型的确定型纤维追踪算法，分数阶的非局部特性使得纤维方向分布模型估计的误差更小，而邻域信息的引入保证了空间一致性，可以减少噪声的影响.分别利用模拟数据、人脑实际数据对本文算法及基于约束球面反卷积的确定型纤维追踪算法作对比实验，结果表明，利用本文算法追踪的纤维不仅整体视觉效果上较整洁，而且对交叉纤维的重建结果更完整准确.     

A practical approach to in vivo high-resolution diffusion tensor imaging of rhesus monkeys on a 3-T human scanner

The nonhuman primate brain study provides important supplemental means for human brain exploration since the two species share close anatomical and functional similarities. MR diffusion tensor imaging (DTI) in human brain has revealed exquisite details of brain structures especially in the brain white matter. However, most previous monkey brain DTI results lack the spatial resolution in comparison to the conventional tracing and postmortem imaging methods, especially when it is acquired in commonly available human MRI scanners of field strength of 3 T or lower. To meet the increasing demands for nonhuman primate DTI studies, we proposed an in vivo high-resolution monkey DTI acquisition protocol that is practically feasible and combined it with an improved postprocessing procedure for a 3-T human scanner. The acquisition protocol, susceptibility distortion correction method with phase reversal acquisition, and postprocessing steps were proved to be effective in our study of rhesus monkeys. Results from diffusion tensor estimations and fiber tractography at 1 x 1 x 1 mm(3) resolution were found to be comparable to previous ex vivo DTI studies with much longer acquisition times. Effects of image resolution were evaluated and it was confirmed that the partial volume effect due to the larger voxel size in low-resolution data biased the diffusion tensor estimation and produced erroneous fiber tractography. Our results suggest that in vivo high-resolution monkey brain DTI can be achieved within practical time, which allows accurate diffusion tensor estimation and fiber tractography in monkey brains, so that the complex anatomical structures within many small but important anatomic structures can be delineated.     

Optimal estimation of the diffusion coefficient from non-averaged and averaged noisy magnitude data

The magnitude operation changes the signal distribution in MRI images from Gaussian to Rician. This introduces a bias that must be taken into account when estimating the apparent diffusion coefficient. Several estimators are known in the literature. In the present paper, two novel schemes are proposed. Both are based on simple least squares fitting of the measured signal, either to the median (MD) or to the maximum probability (MP) value of the Probability Density Function (PDF). Fitting to the mean (MN) or a high signal-to-noise ratio approximation to the mean (HS) is also possible. Special attention is paid to the case of averaged magnitude images. The PDF, which cannot be expressed in closed form, is analyzed numerically. A scheme for performing maximum likelihood (ML) estimation from averaged magnitude images is proposed. The performance of several estimators is evaluated by Monte Carlo (MC) simulations. We focus on typical clinical situations, where the number of acquisitions is limited. For non-averaged data the optimal choice is found to be MP or HS, whereas uncorrected schemes and the power image (PI) method should be avoided. For averaged data MD and ML perform equally well, whereas uncorrected schemes and HS are inadequate. MD provides easier implementation and higher computational efficiency than ML. Unbiased estimation of the diffusion coefficient allows high resolution diffusion tensor imaging (DTI) and may therefore help solving the problem of crossing fibers encountered in white matter tractography.     

Evaluation of diffusional anisotropy and microscopic structure in skeletal muscles using magnetic resonance

The pulsed-gradient spin-echo (PGSE) nuclear magnetic resonance (NMR) method is used for detecting the diffusion of water molecules in biological tissues. Because tissues generally have diffusional anisotropy, their diffusion properties are denoted by a tensor. In this study, we evaluated the diffusional anisotropy and microscopic structure in atrophied skeletal muscles using the PGSE NMR method. The left sciatic nerve was severed in twelve 9-week-old rats. Neurotomy caused neurogenic muscular atrophy at the left gastrocnemius. At 2, 4 and 8 weeks after neurotomy, magnetic resonance signals were selectively acquired from a 2 x 2 x 2 mm(3) voxel, which was located on the left gastrocnemius. The diffusion tensor, the mean diffusivity (MD) and the fractional anisotropy (FA) were calculated from the signals. A theoretical model of the diffusion in muscles was derived from Tanner's equation. The muscle fiber diameter was estimated by fitting the model to the measured signals. The measurements were also performed for normal rats as controls. No significant difference was found in the MD and the estimated intracellular diffusion coefficient between the control group and the denervated group. The denervated group had significantly higher FA compared with the control group (P<.05). The estimated muscle fiber diameter of the denervated group was significantly smaller than the estimated value of the control group (P<.05). These differences were found at 8 weeks after neurotomy. The proposed method is effective for evaluating changes in the microscopic structure of skeletal muscles.     

Recollections about our 1996 JMR paper on diffusion anisotropy

We provide scientific background information and personal accounts relating to our publication of “Microstructural and Physiological Features of Tissues Elucidated by Quantitative-Diffusion-Tensor MRI” in the Journal of Magnetic Resonance B. This paper provided a framework for measuring and mapping intrinsic features of diffusion anisotropy obtained from diffusion tensor MRI (DTI) data.     

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.     

A continuous tensor field approximation of discrete DT-MRI data for extracting microstructural and architectural features of tissue

The effective diffusion tensor of water, D, measured by diffusion tensor MRI (DT-MRI), is inherently a discrete, noisy, voxel-averaged sample of an underlying macroscopic effective diffusion tensor field, D(x). Within fibrous tissues this field is presumed to be continuous and smooth at a gross anatomical length scale. Here a new, general mathematical framework is proposed that uses measured DT-MRI data to produce a continuous approximation to D(x). One essential finding is that the continuous tensor field representation can be constructed by repeatedly performing one-dimensional B-spline transforms of the DT-MRI data. The fidelity and noise-immunity of this approximation are tested using a set of synthetically generated tensor fields to which background noise is added via Monte Carlo methods. Generally, these tensor field templates are reproduced faithfully except at boundaries where diffusion properties change discontinuously or where the tensor field is not microscopically homogeneous. Away from such regions, the tensor field approximation does not introduce bias in useful DT-MRI parameters, such as Trace(D(x)). It also facilitates the calculation of several new parameters, particularly differential quantities obtained from the tensor of spatial gradients of D(x). As an example, we show that they can identify tissue boundaries across which diffusion properties change rapidly using in vivo human brain data. One important application of this methodology is to improve the reliability and robustness of DT-MRI fiber tractography.     

On high b diffusion imaging in the human brain: ruminations and experimental insights

Interest in the manner in which brain tissue signal decays with b factor in diffusion imaging schemes has grown in recent years following the observation that the decay curves depart from purely monoexponential decay behavior. Regardless of the model or fitting function proposed for characterizing sufficiently sampled decay curves (vide infra), the departure from monoexponentiality spells increased tissue characterization potential. The degree to which this potential can be harnessed to improve specificity, sensitivity and spatial localization of diseases in brain, and other tissues, largely remains to be explored. Furthermore, the degree to which currently popular diffusion tensor imaging methods, including visually impressive white matter fiber “tractography” results, have almost completely ignored the nonmonoexponential nature of the basic signal decay with b factor is worthy of communal introspection. Here we limit our attention to a review of the basic experimental features associated with brain water signal diffusion decay curves as measured over extended b-factor ranges, the simple few parameter fitting functions that have been proposed to characterize these decays and the more involved models, e.g.,“ruminations,” which have been proposed to account for the nonmonoexponentiality to date.     

Diffusion-direction-dependent imaging: a novel MRI approach for peripheral nerve imaging

A novel magnetic resonance imaging approach, called diffusion-direction-dependent imaging (DDI), is introduced. Due to inherent anisotropic diffusion properties, peripheral nerves can be visualized on diffusion tensor imaging (DTI). The largest signal attenuation on DTI correlates with the direction of a nerve fiber, and the least signal attenuation correlates with the direction perpendicular to the nerve fiber. Since low signal-to-noise ratio is a concern in peripheral nerve DTI, we explored a new approach focusing on the perpendicular diffusion direction. A 36-gradient diffusion direction scheme was used. A mean expected curve specific for peripheral nerves was calculated based on the sciatic nerve and its division into the common peroneal nerve and the tibial nerve in three healthy volunteers. By a simple postprocessing method, a comparison of the mean expected curve and the measured curve was made voxel by voxel, and the sciatic nerve and its division were reconstructed, excluding other tissues. More studies are needed to investigate whether other postprocessing methods or other diffusion direction schemes are more suited for peripheral nerve imaging with DDI. Further studies may also be of interest to investigate whether DDI can be a complementary method to conventional T(1)-weighted and T(2)-weighted sequences in the imaging of peripheral nerve pathology or even in the visualization of other tissues, possibly with different diffusion direction schemes.