Spatial normalization of diffusion tensor MRI using multiple channels

Diffusion Tensor MRI (DT-MRI) can provide important in vivo information for the detection of brain abnormalities in diseases characterized by compromised neural connectivity. To quantify diffusion tensor abnormalities based on voxel-based statistical analysis, spatial normalization is required to minimize the anatomical variability between studied brain structures. In this article, we used a multiple input channel registration algorithm based on a demons algorithm and evaluated the spatial normalization of diffusion tensor image in terms of the input information used for registration. Registration was performed on 16 DT-MRI data sets using different combinations of the channels, including a channel of T2-weighted intensity, a channel of the fractional anisotropy, a channel of the difference of the first and second eigenvalues, two channels of the fractional anisotropy and the trace of tensor, three channels of the eigenvalues of the tensor, and the six channel tensor components. To evaluate the registration of tensor data, we defined two similarity measures, i.e., the endpoint divergence and the mean square error, which we applied to the fiber bundles of target images and registered images at the same seed points in white matter segmentation. We also evaluated the tensor registration by examining the voxel-by-voxel alignment of tensors in a sample of 15 normalized DT-MRIs. In all evaluations, nonlinear warping using six independent tensor components as input channels showed the best performance in effectively normalizing the tract morphology and tensor orientation. We also present a nonlinear method for creating a group diffusion tensor atlas using the average tensor field and the average deformation field, which we believe is a better approach than a strict linear one for representing both tensor distribution and morphological distribution of the population.     

Brain tissue segmentation based on DTI data

We present a method for automated brain tissue segmentation based on the multi-channel fusion of diffusion tensor imaging (DTI) data. The method is motivated by the evidence that independent tissue segmentation based on DTI parametric images provides complementary information of tissue contrast to the tissue segmentation based on structural MRI data. This has important applications in defining accurate tissue maps when fusing structural data with diffusion data. In the absence of structural data, tissue segmentation based on DTI data provides an alternative means to obtain brain tissue segmentation. Our approach to the tissue segmentation based on DTI data is to classify the brain into two compartments by utilizing the tissue contrast existing in a single channel. Specifically, because the apparent diffusion coefficient (ADC) values in the cerebrospinal fluid (CSF) are more than twice that of gray matter (GM) and white matter (WM), we use ADC images to distinguish CSF and non-CSF tissues. Additionally, fractional anisotropy (FA) images are used to separate WM from non-WM tissues, as highly directional white matter structures have much larger fractional anisotropy values. Moreover, other channels to separate tissue are explored, such as eigenvalues of the tensor, relative anisotropy (RA), and volume ratio (VR). We developed an approach based on the Simultaneous Truth and Performance Level Estimation (STAPLE) algorithm that combines these two-class maps to obtain a complete tissue segmentation map of CSF, GM, and WM. Evaluations are provided to demonstrate the performance of our approach. Experimental results of applying this approach to brain tissue segmentation and deformable registration of DTI data and spoiled gradient-echo (SPGR) data are also provided.     

Comparison of regularization methods for human cardiac diffusion tensor MRI

Diffusion tensor MRI (DT-MRI) is an imaging technique that is gaining importance in clinical applications. However, there is very little work concerning the human heart. When applying DT-MRI to in vivo human hearts, the data have to be acquired rapidly to minimize artefacts due to cardiac and respiratory motion and to improve patient comfort, often at the expense of image quality. This results in diffusion weighted (DW) images corrupted by noise, which can have a significant impact on the shape and orientation of tensors and leads to diffusion tensor (DT) datasets that are not suitable for fibre tracking. This paper compares regularization approaches that operate either on diffusion weighted images or on diffusion tensors. Experiments on synthetic data show that, for high signal-to-noise ratio (SNR), the methods operating on DW images produce the best results; they substantially reduce noise error propagation throughout the diffusion calculations. However, when the SNR is low, Rician Cholesky and Log-Euclidean DT regularization methods handle the bias introduced by Rician noise and ensure symmetry and positive definiteness of the tensors. Results based on a set of sixteen ex vivo human hearts show that the different regularization methods tend to provide equivalent results.     

Mean diffusivity and fractional anisotropy histogram analysis of the cervical cord in MS patients

The spinal cord is frequently involved in multiple sclerosis (MS), and cord damage may be an important contributor to disability. Diffusion tensor magnetic resonance imaging (DT-MRI) provides quantitative information about the structural and orientational features of the central nervous system. In order to assess whether diffusion tensor-derived measures of cord tissue damage are related to clinical disability, mean diffusivity (MD) and fractional anisotropy (FA) histograms from the cervical cord were acquired from a large cohort of MS patients. Diffusion-weighted sensitivity-encoded (SENSE) echo planar images of the cervical cord, and brain dual-echo and diffusion-weighted scans were acquired from 44 patients with MS and 17 healthy controls. Cord and brain MD and FA histograms were produced. An analysis of variance model, adjusting for cord volume and patient age, was used to compare cord DT-MRI parameters from controls and patients. A multivariate linear regression model was used to identify DT-MRI variables independently associated with disability. Average cervical cord FA was significantly lower in MS patients compared to controls. Cord cross-sectional area, average FA and average MD were all significantly correlated with the degree of disability (r values ranging from 0.36 to 0.51). The multivariate linear regression model retained average cord FA and average brain MD as variables independently associated with disability, with a correlation coefficient of 0.73 (P < 0.001). DT-MRI reveals a loss of cervical cord tissue structure in MS patients. The strong correlation found between a composite DT-MRI score and disability suggests that a full and accurate assessment of cervical cord damage in MS provides information that usefully contributes to an explanation of the clinical manifestations of the disease.     

Optic nerve diffusion tensor imaging in optic neuritis

Diffusion tensor magnetic resonance imaging (DT-MRI) provides in vivo information about the pathology of multiple sclerosis lesions. Increases in mean diffusivity (MD) and reductions in fractional anisotropy (FA) have been found and may represent axonal disruption. The optic nerve is an ideal structure for study by DT-MRI but previous clinical studies did not obtain the full diffusion tensor necessary to calculate MD and FA. In this study, a technique that was specifically developed to achieve full diffusion tensor measurements from the optic nerve (zonal oblique multislice (ZOOM) echoplanar imaging) was applied to 25 patients with a single unilateral episode of optic neuritis at least one year previously, and 15 controls. The intraorbital nerves were segmented on non-diffusion-weighted images and the regions of interest transferred to MD, FA, and eigenvalue maps to obtain quantitative data. Quantitative visual testing and electrophysiology were also performed. In affected nerves, mean MD and mean orthogonal eigenvalue lambda( perpendicular) were elevated, and mean FA reduced compared with clinically unaffected contralateral nerves (P < 0.001) and control nerves (P < 0.001). The mean principal eigenvalue lambda\\ was significantly increased in affected nerves compared to contralateral unaffected nerves (P = 0.04) but not compared to control nerves (P = 0.13). There was no association of clinical measures of visual function in affected eyes with the DT-MRI parameters but there was a significant correlation of the whole field visual evoked potential (VEP) amplitude with MD (r = -0.57, P = 0.006) and lambda( perpendicular) (r = -0.56, P = 0.007). These findings suggest that optic nerve DT-MRI measures provide an indication of the structural integrity of axons.     

Processing and visualization for diffusion tensor MRI

This paper presents processing and visualization techniques for Diffusion Tensor Magnetic Resonance Imaging (DT-MRI). In DT-MRI, each voxel is assigned a tensor that describes local water diffusion. The geometric nature of diffusion tensors enables us to quantitatively characterize the local structure in tissues such as bone, muscle, and white matter of the brain. This makes DT-MRI an interesting modality for image analysis. In this paper we present a novel analytical solution to the Stejskal-Tanner diffusion equation system whereby a dual tensor basis, derived from the diffusion sensitizing gradient configuration, eliminates the need to solve this equation for each voxel. We further describe decomposition of the diffusion tensor based on its symmetrical properties, which in turn describe the geometry of the diffusion ellipsoid. A simple anisotropy measure follows naturally from this analysis. We describe how the geometry or shape of the tensor can be visualized using a coloring scheme based on the derived shape measures. In addition, we demonstrate that human brain tensor data when filtered can effectively describe macrostructural diffusion, which is important in the assessment of fiber-tract organization. We also describe how white matter pathways can be monitored with the methods introduced in this paper. DT-MRI tractography is useful for demonstrating neural connectivity (in vivo) in healthy and diseased brain tissue.     

Water Diffusion Changes in Wallerian Degeneration and Their Dependence on White Matter Architecture

This study investigates water diffusion changes in Wallerian degeneration. We measured indices derived from the diffusion tensor (DT) and T2-weighted signal intensities in the descending motor pathways of patients with small chronic lacunar infarcts of the posterior limb of the internal capsule on one side. We compared these measurements in the healthy and lesioned sides at different levels in the brainstem caudal to the primary lesion. We found that secondary white matter degeneration is revealed by a large reduction in diffusion anisotropy only in regions where fibers are arranged in isolated bundles of parallel fibers, such as in the cerebral peduncle. In regions where the degenerated pathway crosses other tracts, such as in the rostral pons, paradoxically there is almost no change in diffusion anisotropy, but a significant change in the measured orientation of fibers. The trace of the diffusion tensor is moderately increased in all affected regions. This allows one to differentiate secondary and primary fiber loss where the increase in trace is considerably higher. We show that DT-MRI is more sensitive than T2-weighted MRI in detecting Wallerian degeneration. Significant diffusion abnormalities are observed over the entire trajectory of the affected pathway in each patient. This finding suggests that mapping degenerated pathways noninvasively with DT-MRI is feasible. However, the interpretation of water diffusion data is complex and requires a priori information about anatomy and architecture of the pathway under investigation. In particular, our study shows that in regions where fibers cross, existing DT-MRI-based fiber tractography algorithms may lead to erroneous conclusion about brain connectivity.     

Feature-based interpolation of diffusion tensor fields and application to human cardiac DT-MRI

Diffusion tensor interpolation is an important issue in the application of diffusion tensor magnetic resonance imaging (DT-MRI) to the human heart, all the more as the points representing the myocardium of the heart are often sparse. We propose a feature-based interpolation framework for the tensor fields from cardiac DT-MRI, by taking into account inherent relationships between tensor components. In this framework, the interpolation consists in representing a diffusion tensor in terms of two tensor features, eigenvalues and orientation, interpolating the Euler angles or the quaternion relative to tensor orientation and the logarithmically transformed eigenvalues, and reconstructing the tensor to be interpolated from the interpolated eigenvalues and tensor orientations. The results obtained with the aid of both synthetic and real cardiac DT-MRI data demonstrate that the feature-based schemes based on Euler angles or quaternions not only maintain the advantages of Log-Euclidean and Riemannian interpolation as for preserving the tensor's symmetric positive-definiteness and the monotonic determinant variation, but also preserve, at the same time, the monotonicity of fractional anisotropy (FA) and mean diffusivity (MD) values, which is not the case with Euclidean, Cholesky and Log-Euclidean methods. As a result, both interpolation schemes remove the phenomenon of FA collapse, and consequently avoid introducing artificial fiber crossing, with the difference that the quaternion is independent of coordinate system while Euler angles have the property of being more suitable for sophisticated interpolations.     

Structure-adaptive sparse denoising for diffusion-tensor MRI

Diffusion tensor magnetic resonance imaging (DT-MRI) is becoming a prospective imaging technique in clinical applications because of its potential for in vivo and non-invasive characterization of tissue organization. However, the acquisition of diffusion-weighted images (DWIs) is often corrupted by noise and artifacts, and the intensity of diffusion-weighted signals is weaker than that of classical magnetic resonance signals. In this paper, we propose a new denoising method for DT-MRI, called structure-adaptive sparse denoising (SASD), which exploits self-similarity in DWIs. We define a similarity measure based on the local mean and on a modified structure-similarity index to find sets of similar patches that are arranged into three-dimensional arrays, and we propose a simple and efficient structure-adaptive window pursuit method to achieve sparse representation of these arrays. The noise component of the resulting structure-adaptive arrays is attenuated by Wiener shrinkage in a transform domain defined by two-dimensional principal component decomposition and Haar transformation. Experiments on both synthetic and real cardiac DT-MRI data show that the proposed SASD algorithm outperforms state-of-the-art methods for denoising images with structural redundancy. Moreover, SASD achieves a good trade-off between image contrast and image smoothness, and our experiments on synthetic data demonstrate that it produces more accurate tensor fields from which biologically relevant metrics can then be computed.     

磁共振弥散张量成像鉴别诊断超急性与急性缺血性脑梗死

目的 评价磁共振弥散张量成像(DTI)在超急性与急性缺血性脑梗死鉴别诊断中的临床应用价值。方法 回顾分析我院经临床及MRI诊断的单侧超急性期(18例)和急性期(27例)缺血性脑梗死患者的DTI图像。分析DTI序列各项异性指数(FA)、容积比各项异性(VRA)、平均弥散系数(DCavg)及衰减指数(Exat)参数图,并选取病灶、近病灶边缘脑组织(BTCI)及相应对侧为ROI,记录各ROI参数值并计算病灶-对侧各参数相对值。同时以病灶及对侧ROI为种子点重建弥散张量纤维束图。比较病灶、BTCI与相应对侧间各参数值的差异,分析病灶-对侧各参数相对值在超急性与急性脑梗死间的差异。结果 急性缺血性脑梗死DTT DCavg、DTT FA图均可观察到纤维束损伤表现;超急性脑梗死仅DTT DCavg图可观察到损伤表现,DTT FA图未见明显改变。超急性和急性脑梗死病灶DCavg值均低于对侧,Exat值均高于对侧(P均<0.05),而FA和VRA值仅在急性期低于对侧(P<0.05)。超急性期脑梗死BTCI区FA、VRA和Exat值较对侧增高(P<0.05),DCavg值较对侧降低(P<0.05)。急性期脑梗死病灶-对侧FA、VRA和DCavg相对值均低于超急性期(P<0.05)。对于鉴别超急性和急性脑梗死,ROC曲线分析示病灶-对侧FA、VRA和DCavg相对值最佳诊断界值分别为0.852、0.886和0.541;对应诊断敏感度均为100%,特异度分别为90.5%、100%和71.4%。结论 临床可将FA、VRA、DCavg及Exat值综合运用于发病时间不明确的超急性与急性缺血性脑梗死的鉴别诊断,从而有助于选择合理的治疗方案。     

Visualization of peripheral nerve degeneration and regeneration: monitoring with diffusion tensor tractography

We applied diffusion tensor tractography (DTT), a recently developed MRI technique that reveals the microstructures of tissues based on its ability to monitor the random movements of water molecules, to the visualization of peripheral nerves after injury. The rat sciatic nerve was subjected to contusive injury, and the data obtained from diffusion tensor imaging (DTI) were used to determine the tracks of nerve fibers (DTT). The DTT images obtained using the fractional anisotropy (FA) threshold value of 0.4 clearly revealed the recovery process of the contused nerves. Immediately after the injury, fiber tracking from the designated proximal site could not be continued beyond the lesion epicenter, but the intensity improved thereafter, returning to its pre-injury level by 3 weeks later. We compared the FA value, a parameter computed from the DTT data, with the results of histological and functional examinations of the injured nerves, during recovery. The FA values of the peripheral nerves were more strongly correlated with axon-related (axon density and diameter) than with myelin-related (myelin density and thickness) parameters, supporting the theories that axonal membranes play a major role in anisotropic water diffusion and that myelination can modulate the degree of anisotropy. Moreover, restoration of the FA value at the lesion epicenter was strongly correlated with parameters of motor and sensory functional recovery. These correlations of the FA values with both the histological and functional changes demonstrate the potential usefulness of DTT for evaluating clinical events associated with Wallerian degeneration and the regeneration of peripheral nerves.     

The influence of complex white matter architecture on the mean diffusivity in diffusion tensor MRI of the human brain

In diffusion tensor magnetic resonance imaging (DT-MRI), limitations concerning complex fiber architecture (when an image voxel contains fiber populations with more than one dominant orientation) are well-known. Fractional anisotropy (FA) values are lower in such areas because of a lower directionality of diffusion on the voxel-scale, which makes the interpretation of FA less straightforward. Moreover, the interpretation of the axial and radial diffusivities is far from trivial when there is more than one dominant fiber orientation within a voxel. In this work, using (i) theoretical considerations, (ii) simulations, and (iii) experimental data, it is demonstrated that the mean diffusivity (or the trace of the diffusion tensor) is lower in complex white matter configurations, compared with tissue where there is a single dominant fiber orientation within the voxel. We show that the magnitude of this reduction depends on various factors, including configurational and microstructural properties (e.g., the relative contributions of different fiber populations) and acquisition settings (e.g., the b-value). These results increase our understanding of the quantitative metrics obtained from DT-MRI and, in particular, the effect of the microstructural architecture on the mean diffusivity. More importantly, they reinforce the growing awareness that differences in DT-MRI metrics need to be interpreted cautiously.     

Early laminar organization of the human cerebrum demonstrated with diffusion tensor imaging in extremely premature infants

Diffusion tensor imaging (DTI) was used to delineate early laminar organization of the cerebrum in two extremely premature infants imaged postnatally at estimated ages of 25 and 27 menstrual weeks. The diffusivity and anisotropy of the cortical plate, subplate zone, intermediate zone, subventricular and periventricular zones, and germinal matrix are examined. Automated segmentation of diffusion tensor images to reveal the laminar architecture of the developing human cerebrum is also demonstrated.     

磁共振扩散张量成像定量分析猪心肌梗死早期离体心肌结构变化

目的 利用磁共振扩散张量成像(DT-MRI)研究急性心肌梗死(AMI)后离体心肌纤维束结构的改变。方法 制作实验用中华小型猪AMI模型并进行离体心脏DT-MRI。纤维束示踪技术(FT)显示梗死与正常心肌纤维结构,定量分析梗死与正常心肌ADC、 FA、心肌纤维束长度和数量。采用配对样本t检验及Wilcoxon检验进行统计学分析。结果 FT显示正常心肌纤维走行规则,排列整齐,梗死心肌纤维结构松散,纤维长短不一。与正常心机相比,梗死心肌ADC值增加,FA值减小,心肌纤维束长度缩短,纤维数目稍减少。结论 AMI后8 h即可在DT-MR图像上显示水分子扩散特性及心肌纤维结构的改变。     

Diffusion imaging of whole, post-mortem human brains on a clinical MRI scanner

Diffusion imaging of post mortem brains has great potential both as a reference for brain specimens that undergo sectioning, and as a link between in vivo diffusion studies and "gold standard" histology/dissection. While there is a relatively mature literature on post mortem diffusion imaging of animals, human brains have proven more challenging due to their incompatibility with high-performance scanners. This study presents a method for post mortem diffusion imaging of whole, human brains using a clinical 3-Tesla scanner with a 3D segmented EPI spin-echo sequence. Results in eleven brains at 0.94 × 0.94 × 0.94 mm resolution are presented, and in a single brain at 0.73 × 0.73 × 0.73 mm resolution. Region-of-interest analysis of diffusion tensor parameters indicate that these properties are altered compared to in vivo (reduced diffusivity and anisotropy), with significant dependence on post mortem interval (time from death to fixation). Despite these alterations, diffusion tractography of several major tracts is successfully demonstrated at both resolutions. We also report novel findings of cortical anisotropy and partial volume effects.     

磁共振弥散加权成像对急性脑梗死的诊断价值

目的：探讨磁共振弥散加权成像(DWI)在急性脑梗死中临床诊断价值和区分多发梗死灶中急性和非急性方面的能力。方法：对56例脑梗死发病时间不同的病例行常规MR及DWI程序检查，对同一层面所有的磁共振成像进行比较，重点分析信号强度及病灶大小，数据做统计分析。结果：DWI对超急性及急性脑梗死可显示T2加权像不能显示的病灶，并随时间延长显影范围逐渐增大，表现弥散系数(ADC值)明显下降。急性后期DWI显示病灶不如T2加权像，ADC值接近或高于正常。结论：脑梗死的DWI信号和ADC值变化具有特征性的时间演变规律，DWI能非常可靠地显示超急性和急性脑梗死，具有区分急性和非急性脑梗死的临床诊断价值。     

Segmentation of fiber tracts based on an accuracy analysis on diffusion tensor software phantoms

Due to its unique sensitivity to tissue microstructure, one of the primary applications of diffusion-weighted magnetic resonance imaging is the reconstruction of neural fiber pathways by means of fiber-tracking algorithms. In this work, we make use of realistic diffusion-tensor software phantoms in order to carry out an analysis of the precision of streamline tractography by systematically varying certain properties of the simulated image data (noise, tensor anisotropy, and image resolution) as well as certain fiber-tracking parameters (number of seed points and step length). Building upon the gained knowledge about the precision of the analyzed fiber-tracking algorithm, we proceed by suggesting a fuzzy segmentation algorithm for diffusion tensor images which better estimates the precise spatial extent of a tracked fiber bundle. The presented segmentation algorithm utilizes information given by the estimated main diffusion direction in a voxel and the respective uncertainty, and its validity is confirmed by both qualitative and quantitative analyses.     

磁共振弥散张量成像在急性腔隙性脑梗死预后评估中的价值

目的探讨磁共振弥散张量成像（DTI）在急性腔隙性脑梗死患者预后评估中的临床价值及相关性。方法急性腔隙性脑梗死患者40例,在MRI常规检查的同时加做DTI检查,得到各向异性分数伪彩图并测量分析梗死灶各向异性分数值,重建双侧皮质脊髓束,以梗死灶在双侧皮质脊髓束的空间位置分为纤维束外、纤维束旁、纤维束内3组;每次磁共振检查之前进行Fugl-Meyer运动功能评分评定,最后分析梗死灶位置与运动功能评分之间的关系。结果康复治疗前后病灶与皮质脊髓束越空间关系越密切的,运动功能评分增加的百分数越低,呈负相关（P<0.01）。结论通过DTI在急性腔隙性脑梗死灶与双侧皮质脊髓束的空间位置关系的水分子扩散各向异性分值及扩散张量纤维束成像分级,可以较准确、直观地显示皮质脊髓束的损伤程度,为脑梗死患者临床治疗及预后提供明确的依据。     

重复时间和场强对脑白质弥散张量成像定量研究的影响

目的 研究重复时间(TR)以及场强对脑白质弥散张量成像(DTI)定量指标有无影响.方法 分别利用1.5T和3.0T MR扫描仪对7只健康成年恒河猴进行DTI数据采集.在其他参数固定的情况下改变TR值(500～6000 ms,共16个采样点),得到一系列DTI数据.选择双侧内囊后肢作为感兴趣区(ROI),并测量该ROI内的平均弥散率(MD),分数各向异性(FA)、纵向本征值(λ1)和横向本征值(λ2、3).运用Pearson相关分析分析这些弥散指标与TR的线性关系,并采用双因素重复资料的方差分析比较两种场强下各指标均值是否有差异.结果 当信噪比(SNR)足够大时(SNR>35),恒河猴白质区ROI各指标与TR无相关性(P＞0.05).与1.5T相比,3.0T的FA值较高,而MD及λ2、3较低(P＜0.001).两场强λ1差异无统计学意义(P＞0.05).结论 场强可能影响DTI定量指标的测量,而TR时间对DTI定量的影响不显著.     

Estradiol treatment altered anticholinergic-related brain activation during working memory in postmenopausal women

Diffusion MRI is used extensively to investigate changes in white matter microstructure related to brain development and pathology. Ageing, however, is also associated with significant white and grey matter loss which in turn can lead to cerebrospinal fluid (CSF) based partial volume artefacts in diffusion MRI metrics. This is especially problematic in regions prone to CSF contamination, such as the fornix and the genu of corpus callosum, structures that pass through or close to the ventricles respectively. The aim of this study was to model the effects of CSF contamination on diffusion MRI metrics, and to evaluate different post-acquisition strategies to correct for CSF-contamination: Controlling for whole brain volume and correcting on a voxel-wise basis using the Free Water Elimination (FWE) approach. Using the fornix as an exemplar of a structure prone to CSF-contamination, corrections were applied to tract-specific and voxel-based [tract based spatial statistics (TBSS)] analyses of empirical DT-MRI data from 39 older adults (53-93 years of age). In addition to significant age-related decreases in whole brain volume and fornix tissue volume fraction, age was also associated with a reduction in mean fractional anisotropy and increase in diffusivity metrics in the fornix. The experimental data agreed with the simulations in that diffusivity metrics (mean diffusivity, axial and radial diffusivity) were more prone to partial volume CSF-contamination errors than fractional anisotropy. After FWE-based voxel-by-voxel partial volume corrections, the significant positive correlations between age and diffusivity metrics, in particular with axial diffusivity, disappeared whereas the correlation with anisotropy remained. In contrast, correcting for whole brain volume had little effect in removing these spurious correlations. Our study highlights the importance of correcting for CSF-contamination partial volume effects in the structures of interest on a voxel-by-voxel basis prior to drawing inferences about underlying changes in white matter structures and have implications for the interpretation of many recent diffusion MRI results in ageing and disease.