Temporal Diffusion Ratio (TDR) is a recently proposed dMRI technique (Dell'Acqua et al., proc. ISMRM 2019) which provides contrast between areas with restricted diffusion and areas either without restricted diffusion or with length scales too small for characterisation. Hence, it has a potential for informing on pore sizes, in particular the presence of large axon diameters or other cellular structures. TDR employs the signal from two dMRI acquisitions obtained with the same, large, b-value but with different diffusion gradient waveforms. TDR is advantageous as it employs standard acquisition sequences, does not make any assumptions on the underlying tissue structure and does not require any model fitting, avoiding issues related to model degeneracy. This work for the first time introduces and optimises the TDR method in simulation for a range of different tissues and scanner constraints and validates it in a pre-clinical demonstration. We consider both substrates containing cylinders and spherical structures, representing cell soma in tissue. Our results show that contrasting an acquisition with short gradient duration, short diffusion time and high gradient strength with an acquisition with long gradient duration, long diffusion time and low gradient strength, maximises the TDR contrast for a wide range of pore configurations. Additionally, in the presence of Rician noise, computing TDR from a subset (50% or fewer) of the acquired diffusion gradients rather than the entire shell as proposed originally further improves the contrast. In the last part of the work the results are demonstrated experimentally on rat spinal cord. In line with simulations, the experimental data shows that optimised TDR improves the contrast compared to non-optimised TDR. Furthermore, we find a strong correlation between TDR and histology measurements of axon diameter. In conclusion, we find that TDR has great potential and is a very promising alternative (or potentially complement) to model-based approaches for informing on pore sizes and restricted diffusion in general.

To enable application of non-Gaussian diffusion magnetic resonance imaging (dMRI) techniques in large-scale clinical trials and facilitate translation to clinical practice there is a requirement for fast, high contrast, techniques that are sensitive to changes in tissue structure which provide diagnostic signatures at the early stages of disease. Here we describe a new way to compress the acquisition of multi-shell b-value diffusion data, Quasi-Diffusion MRI (QDI), which provides a probe of subvoxel tissue complexity using short acquisition times (1-4 ​min). We also describe a coherent framework for multi-directional diffusion gradient acquisition and data processing that allows computation of rotationally invariant quasi-diffusion tensor imaging (QDTI) maps. QDI is a quantitative technique that is based on a special case of the Continuous Time Random Walk model of diffusion dynamics and assumes the presence of non-Gaussian diffusion properties within tissue microstructure. QDI parameterises the diffusion signal attenuation according to the rate of decay (i.e. diffusion coefficient, D in mm2 s-1) and the shape of the power law tail (i.e. the fractional exponent, α). QDI provides analogous tissue contrast to Diffusional Kurtosis Imaging (DKI) by calculation of normalised entropy of the parameterised diffusion signal decay curve, Hn, but does so without the limitations of a maximum b-value. We show that QDI generates images with superior tissue contrast to conventional diffusion imaging within clinically acceptable acquisition times of between 84 and 228 ​s. We show that QDI provides clinically meaningful images in cerebral small vessel disease and brain tumour case studies. Our initial findings suggest that QDI may be added to routine conventional dMRI acquisitions allowing simple application in clinical trials and translation to the clinical arena.

Gyrification of the human cerebral cortex allows for the surface expansion that accommodates many more cortical neurons in comparison to other mammals. For neuroimaging, however, it forms a feature that complicates analysis. For example, it has long been established that cortical layers do not occupy the same depth in gyri and sulci. Recently, in vivo diffusion imaging has provided insights into the fibre architecture of the cortex, usually showing radial tensor orientations. This makes it relevant to investigate whether cortical diffusion tensor metrics depend on the gyral pattern. High-resolution (1mm isotropic) diffusion weighted MRI of the medial wall of the hemispheres was performed at 7 T. Diffusion data were resampled to surfaces in the cortex and underlying white matter, where the cortical surfaces obeyed the equivolume principle for cortical laminae over the cortical curvature. Diffusion tensor metrics were averaged over bins of curvature to obtain maps of characteristic patterns in the gyrus. Diffusivity, anisotropy and radiality varied with curvature. Radiality was maximal in intermediate layers of the cortex next to the crown of the gyrus, not in white matter or on the crown. In the fundus, the deep cortical layers had tangential tensor orientations. In the white matter, tensor orientation changed from radial on the crown to tangential under the banks and fundus. White matter anisotropy gradually increased from the crown to the fundus. The characteristic pattern in the gyrus demonstrated here is in accordance with ex vivo diffusion MR microscopy and histological studies. The results indicate the necessity of taking into account the gyral pattern when cortical diffusion data is analysed. Additionally, the data suggest a confound for tractography approaches when reaching the gyrus, resulting in a possible bias towards the gyral crown. The implications for mechanisms that could drive cortical folding are discussed.

Anisotropic diffusion MRI techniques using single-shell or multi-shell acquisitions have been proposed as a means to overcome some limitations imposed by diffusion tensor imaging (DTI), especially in complex models of fibre orientation distribution in voxels. A long acquisition time for the angular resolution of diffusion MRI is a major obstacle to practical clinical implementations. In this paper, we propose a novel method to improve angular resolution of diffusion MRI acquisition using given diffusion gradient (DG) directions. First, we define a local diffusion pattern map of diffusion MR signals on a single shell in given DG directions. Using the local diffusion pattern map, we design a prediction scheme to determine the best DG direction to be synthesized within a nearest neighborhood DG directions group. Second, the local diffusion pattern map and the spherical distance on the shell are combined to determine a synthesized diffusion signal in the new DG direction. Using the synthesized and measured diffusion signals on a single sphere, we estimate a spin orientation distribution function (SDF) with human brain data. Although the proposed method is applied to SDF, a basic idea is to increase the angular resolution using the measured diffusion signals in various DG directions. The method can be applicable to different acquired multi-shell data or diffusion spectroscopic imaging (DSI) data. We validate the proposed method by comparing the recovered SDFs using the angular resolution enhanced diffusion signals with the recovered SDF using the measured diffusion data. The developed method provides an enhanced SDF resolution and improved multiple fiber structure by incorporating synthesized signals. The proposed method was also applied neurite orientation dispersion and density imaging (NODDI) using multi-shell acquisitions.

This paper introduces a multi-compartment model for microscopic diffusion anisotropy imaging. The aim is to estimate microscopic features specific to the intra- and extra-neurite compartments in nervous tissue unconfounded by the effects of fibre crossings and orientation dispersion, which are ubiquitous in the brain. The proposed MRI method is based on the Spherical Mean Technique (SMT), which factors out the neurite orientation distribution and thus provides direct estimates of the microscopic tissue structure. This technique can be immediately used in the clinic for the assessment of various neurological conditions, as it requires only a widely available off-the-shelf sequence with two b-shells and high-angular gradient resolution achievable within clinically feasible scan times. To demonstrate the developed method, we use high-quality diffusion data acquired with a bespoke scanner system from the Human Connectome Project. This study establishes the normative values of the new biomarkers for a large cohort of healthy young adults, which may then support clinical diagnostics in patients. Moreover, we show that the microscopic diffusion indices offer direct sensitivity to pathological tissue alterations, exemplified in a preclinical animal model of Tuberous Sclerosis Complex (TSC), a genetic multi-organ disorder which impacts brain microstructure and hence may lead to neurological manifestations such as autism, epilepsy and developmental delay.

High resolution diffusion tensor imaging and tractography of ex vivo brain specimens has the potential to reveal detailed fibre architecture not visible on in vivo images. Previous ex vivo diffusion imaging experiments have focused on animal brains or small sections of human tissue since the unfavourable properties of fixed tissue (including short T(2) and low diffusion rates) demand the use of very powerful gradient coils that are too small to accommodate a whole, human brain. This study proposes the use of diffusion-weighted steady-state free precession (DW-SSFP) as a method of extending the benefits of ex vivo DTI and tractography to whole, human, fixed brains on a clinical 3 T scanner. DW-SSFP is a highly efficient pulse sequence; however, its complicated signal dependence precludes the use of standard diffusion tensor analysis and tractography. In this study, a method is presented for modelling anisotropy in the context of DW-SSFP. Markov Chain Monte Carlo sampling is used to estimate the posterior distributions of model parameters and it is shown that it is possible to estimate a tight distribution on the principal axis of diffusion at each voxel using DW-SSFP. Voxel-wise estimates are used to perform tractography in a whole, fixed human brain. A direct comparison between 3D diffusion-weighted spin echo EPI and 3D DW-SSFP-EPI reveals that the orientation of the principal diffusion axis can be inferred on with a higher degree of certainty using a 3D DW-SSFP-EPI even with a 68% shorter acquisition time.

Diffusion imaging aims to non-invasively characterize the anatomy and integrity of the brain's white matter fibers. We evaluated the accuracy and reliability of commonly used diffusion imaging methods as a function of data quantity and analysis method, using both simulations and highly sampled individual-specific data (927-1442 diffusion weighted images [DWIs] per individual). Diffusion imaging methods that allow for crossing fibers (FSL's BedpostX [BPX], DSI Studio's Constant Solid Angle Q-Ball Imaging [CSA-QBI], MRtrix3's Constrained Spherical Deconvolution [CSD]) estimated excess fibers when insufficient data were present and/or when the data did not match the model priors. To reduce such overfitting, we developed a novel Bayesian Multi-tensor Model-selection (BaMM) method and applied it to the popular ball-and-stick model used in BedpostX within the FSL software package. BaMM was robust to overfitting and showed high reliability and the relatively best crossing-fiber accuracy with increasing amounts of diffusion data. Thus, sufficient data and an overfitting resistant analysis method enhance precision diffusion imaging. For potential clinical applications of diffusion imaging, such as neurosurgical planning and deep brain stimulation (DBS), the quantities of data required to achieve diffusion imaging reliability are lower than those needed for functional MRI.

The combination of diffusion MRI (dMRI) with microscopy provides unique opportunities to study microstructural features of tissue, particularly when acquired in the same sample. Microscopy is frequently used to validate dMRI microstructure models, addressing the indirect nature of dMRI signals. Typically, these modalities are analysed separately, and microscopy is taken as a gold standard against which dMRI-derived parameters are validated. Here we propose an alternative approach in which we combine dMRI and microscopy data obtained from the same tissue sample to drive a single, joint model. This simultaneous analysis allows us to take advantage of the breadth of information provided by complementary data acquired from different modalities. By applying this framework to a spherical-deconvolution analysis, we are able to overcome a known degeneracy between fibre dispersion and radial diffusion. Spherical-deconvolution based approaches typically estimate a global fibre response function to determine the fibre orientation distribution in each voxel. However, the assumption of a 'brain-wide' fibre response function may be challenged if the diffusion characteristics of white matter vary across the brain. Using a generative joint dMRI-histology model, we demonstrate that the fibre response function is dependent on local anatomy, and that current spherical-deconvolution based models may be overestimating dispersion and underestimating the number of distinct fibre populations per voxel.

Diffusion-weighted imaging (DWI), while giving rich information about brain circuitry, is often limited by insufficient spatial resolution and low signal-to-noise ratio (SNR). This paper describes an algorithm that will increase the resolution of DW images beyond the scan resolution, allowing for a closer investigation of fiber structures and more accurate assessment of brain connectivity. The algorithm is capable of generating a dense vector-valued field, consisting of diffusion data associated with the full set of diffusion-sensitizing gradients. The fundamental premise is that, to best preserve information, interpolation should always be performed along axonal fibers. To achieve this, at each spatial location, we probe neighboring voxels in various directions to gather diffusion information for data interpolation. Based on the fiber orientation distribution function (ODF), directions that are more likely to be traversed by fibers will be given greater weights during interpolation and vice versa. This ensures that data interpolation is only contributed by diffusion data coming from fibers that are aligned with a specific direction. This approach respects local fiber structures and prevents blurring resulting from averaging of data from significantly misaligned fibers. Evaluations suggest that this algorithm yields results with significantly less blocking artifacts, greater smoothness in anatomical structures, and markedly improved structural visibility.

Although diffusion tensor imaging (DTI) has provided substantial insights into early brain development, most DTI studies based on fractional anisotropy (FA) and mean diffusivity (MD) may not capitalize on the information derived from the three principal diffusivities (e.g. eigenvalues). In this study, we explored the spatial and temporal evolution of white matter structures during early brain development using two geometrical diffusion measures, namely, linear (Cl) and planar (Cp) diffusion anisotropies, from 71 longitudinal datasets acquired from 29 healthy, full-term pediatric subjects. The growth trajectories were estimated with generalized estimating equations (GEE) using linear fitting with logarithm of age (days). The presence of the white matter structures in Cl and Cp was observed in neonates, suggesting that both the cylindrical and fanning or crossing structures in various white matter regions may already have been formed at birth. Moreover, we found that both Cl and Cp evolved in a temporally nonlinear and spatially inhomogeneous manner. The growth velocities of Cl in central white matter were significantly higher when compared to peripheral, or more laterally located, white matter: central growth velocity Cl=0.0465±0.0273/log(days), versus peripheral growth velocity Cl=0.0198±0.0127/log(days), p<10⁻⁶. In contrast, the growth velocities of Cp in central white matter were significantly lower than that in peripheral white matter: central growth velocity Cp=0.0014±0.0058/log(days), versus peripheral growth velocity Cp=0.0289±0.0101/log(days), p<10⁻⁶. Depending on the underlying white matter site which is analyzed, our findings suggest that ongoing physiologic and microstructural changes in the developing brain may exert different effects on the temporal evolution of these two geometrical diffusion measures. Thus, future studies utilizing DTI with correlative histological analysis in the study of early brain development are warranted.

Diffusion-weighted imaging (DWI) provides a noninvasive tool to probe tissue microstructure. We propose a simplified model of neural cytoarchitecture intended to capture the essential features important for water diffusion as measured by NMR. Two components contribute to the NMR signal in this model: (i) the dendrites and axons, which are modeled as long cylinders with two diffusion coefficients, parallel (D(L)) and perpendicular (D(T)) to the cylindrical axis, and (ii) an isotropic monoexponential diffusion component describing water diffusion within and across all other structures, i.e., in extracellular space and glia cells. The model parameters are estimated from 153 diffusion-weighted images acquired from a formalin-fixed baboon brain. A close correspondence between the data and the signal model is found, with the model parameters consistent with literature values. The model provides an estimate of dendrite density from noninvasive MR diffusion measurements, a parameter likely to be of value for understanding normal as well as abnormal brain development and function.

When investigating connectivity and microstructure of white matter pathways of the brain using diffusion tractography bundle segmentation, it is important to understand potential confounds and sources of variation in the process. While cross-scanner and cross-protocol effects on diffusion microstructure measures are well described (in particular fractional anisotropy and mean diffusivity), it is unknown how potential sources of variation effect bundle segmentation results, which features of the bundle are most affected, where variability occurs, nor how these sources of variation depend upon the method used to reconstruct and segment bundles. In this study, we investigate six potential sources of variation, or confounds, for bundle segmentation: variation (1) across scan repeats, (2) across scanners, (3) across vendors (4) across acquisition resolution, (5) across diffusion schemes, and (6) across diffusion sensitization. We employ four different bundle segmentation workflows on two benchmark multi-subject cross-scanner and cross-protocol databases, and investigate reproducibility and biases in volume overlap, shape geometry features of fiber pathways, and microstructure features within the pathways. We find that the effects of acquisition protocol, in particular acquisition resolution, result in the lowest reproducibility of tractography and largest variation of features, followed by vendor-effects, scanner-effects, and finally diffusion scheme and b-value effects which had similar reproducibility as scan-rescan variation. However, confounds varied both across pathways and across segmentation workflows, with some bundle segmentation workflows more (or less) robust to sources of variation. Despite variability, bundle dissection is consistently able to recover the same location of pathways in the deep white matter, with variation at the gray matter/ white matter interface. Next, we show that differences due to the choice of bundle segmentation workflows are larger than any other studied confound, with low-to-moderate overlap of the same intended pathway when segmented using different methods. Finally, quantifying microstructure features within a pathway, we show that tractography adds variability over-and-above that which exists due to noise, scanner effects, and acquisition effects. Overall, these confounds need to be considered when harmonizing diffusion datasets, interpreting or combining data across sites, and when attempting to understand the successes and limitations of different methodologies in the design and development of new tractography or bundle segmentation methods.

Diffusion tensor imaging (DTI) is a powerful and noninvasive imaging method for characterizing tissue microstructure and white matter organization in the brain. While it has been applied extensively in research studies of the human brain, DTI studies of non-human primates have been performed only recently. The growing application of DTI in rhesus monkey studies would significantly benefit from a standardized framework to compare findings across different studies. A very common strategy for image analysis is to spatially normalize (co-register) the individual scans to a representative template space. This paper presents the development of a DTI brain template, UWRMAC-DTI271, for adolescent Rhesus Macaque (Macaca mulatta) monkeys. The template was generated from 271 rhesus monkeys, collected as part of a unique brain imaging genetics study. It is the largest number of animals ever used to generate a computational brain template, which enables the generation of a template that has high image quality and accounts for variability in the species. The quality of the template is further ensured with the use of DTI-TK, a well-tested and high-performance DTI spatial normalization method in human studies. We demonstrated its efficacy in monkey studies for the first time by comparing it to other commonly used scalar-methods for DTI normalization. It is anticipated that this template will play an important role in facilitating cross-site voxelwise DTI analyses in Rhesus Macaques. Such analyses are crucial in investigating the role of white matter structure in brain function, development, and other psychopathological disorders for which there are well-validated non-human primate models.

We introduce a mathematical framework for computing geometrical properties of white matter fibers directly from diffusion tensor fields. The key idea is to isolate the portion of the gradient of the tensor field corresponding to local variation in tensor orientation, and to project it onto a coordinate frame of tensor eigenvectors. The resulting eigenframe-centered representation then makes it possible to define scalar indices (or measures) that describe the local white matter geometry directly from the diffusion tensor field and its gradient, without requiring prior tractography. We derive new scalar indices of (1) fiber dispersion and (2) fiber curving, and we demonstrate them on synthetic and in vivo data. Finally, we illustrate their applicability to a group study on schizophrenia.

Diffusion tensor imaging (DTI) data at 43 mum isotropic resolution has been acquired on the intact adult mouse brain in 28-h scan time by using a streamlined protocol, including specimen fixation and staining, image acquisition, reconstruction, post-processing, and distribution. An intermediate registration of each component image is required to achieve the desired microscopic resolution. Multiple parameters have been derived, including fractional anisotropy, axial and radial diffusivity, and a color-coded orientation map of the primary eigenvector. Each DTI dataset was mapped to a common reference space to facilitate future standardized analysis. Fiber tracking has also been demonstrated, providing 3D connection information. This protocol to acquire high-resolution DTI data in a robust and repeatable fashion will serve as a foundation to quantitatively study mouse brain integrity and white matter architecture, at what we believe to be the highest spatial resolution yet attained.

The development of a brain template for diffusion tensor imaging (DTI) is crucial for comparisons of neuronal structural integrity and brain connectivity across populations, as well as for the development of a white matter atlas. Previous efforts to produce a DTI brain template have been compromised by factors related to image quality, the effectiveness of the image registration approach, the appropriateness of subject inclusion criteria, and the completeness and accuracy of the information summarized in the final template. The purpose of this work was to develop a DTI human brain template using techniques that address the shortcomings of previous efforts. Therefore, data containing minimal artifacts were first obtained on 67 healthy human subjects selected from an age-group with relatively similar diffusion characteristics (20-40 years of age), using an appropriate DTI acquisition protocol. Non-linear image registration based on mean diffusion-weighted and fractional anisotropy images was employed. DTI brain templates containing median and mean tensors were produced in ICBM-152 space and made publicly available. The resulting set of DTI templates is characterized by higher image sharpness, provides the ability to distinguish smaller white matter fiber structures, contains fewer image artifacts, than previously developed templates, and to our knowledge, is one of only two templates produced based on a relatively large number of subjects. Furthermore, median tensors were shown to better preserve the diffusion characteristics at the group level than mean tensors. Finally, white matter fiber tractography was applied on the template and several fiber-bundles were traced.

The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium can be modeled by the multiple compartment Bloch-Torrey partial differential equation. Under the assumption of negligible water exchange between compartments, the time-dependent apparent diffusion coefficient can be directly computed from the solution of a diffusion equation subject to a time-dependent Neumann boundary condition. This paper describes a publicly available MATLAB toolbox called SpinDoctor that can be used 1) to solve the Bloch-Torrey partial differential equation in order to simulate the diffusion magnetic resonance imaging signal; 2) to solve a diffusion partial differential equation to obtain directly the apparent diffusion coefficient; 3) to compare the simulated apparent diffusion coefficient with a short-time approximation formula. The partial differential equations are solved by P1 finite elements combined with built-in MATLAB routines for solving ordinary differential equations. The finite element mesh generation is performed using an external package called Tetgen. SpinDoctor provides built-in options of including 1) spherical cells with a nucleus; 2) cylindrical cells with a myelin layer; 3) an extra-cellular space enclosed either a) in a box or b) in a tight wrapping around the cells; 4) deformation of canonical cells by bending and twisting; 5) permeable membranes; Built-in diffusion-encoding pulse sequences include the Pulsed Gradient Spin Echo and the Oscillating Gradient Spin Echo. We describe in detail how to use the SpinDoctor toolbox. We validate SpinDoctor simulations using reference signals computed by the Matrix Formalism method. We compare the accuracy and computational time of SpinDoctor simulations with Monte-Carlo simulations and show significant speed-up of SpinDoctor over Monte-Carlo simulations in complex geometries. We also illustrate several extensions of SpinDoctor functionalities, including the incorporation of T2 relaxation, the simulation of non-standard diffusion-encoding sequences, as well as the use of externally generated geometrical meshes.

Head size markedly differs among individuals. To our knowledge, there have been no studies that systematically investigated the effect of head size on diffusion tensor measures of the brain. The purpose of this study was to evaluate the effect of head size or total intracranial volume on diffusion tensor measures (FA and MD). A total of 821 normal subjects (304 females and 517 males) were included in this study. We investigated the effect of total intracranial volume on FA and MD mainly using tract-based spatial statistics (TBSS). There were a number of regions where FA or MD was significantly correlated with total intracranial volume. There was no significant interaction between total intracranial volume and sex. The results indicate that total intracranial volume significantly influences diffusion tensor measures such as FA and MD. The possible explanations of the relationship between diffusion tensor measures and total intracranial volume may be 'partial volume effects' or micro-architectural differences related to head size. When total intracranial volumes are significantly different between groups, it may be necessary to control for total intracranial volume in the statistical analysis, depending on the hypothesis being tested.

Development of a diffusion tensor (DT) template that is representative of the micro-architecture of the human brain is crucial for comparisons of neuronal structural integrity and brain connectivity across populations, as well as for the generation of a detailed white matter atlas. Furthermore, a DT template in ICBM space may simplify consolidation of information from DT, anatomical and functional MRI studies. The previously developed "IIT DT brain template" was produced in ICBM-152 space, based on a large number of subjects from a limited age-range, using data with minimal image artifacts, and non-linear registration. That template was characterized by higher image sharpness, provided the ability to distinguish smaller white matter fiber structures, and contained fewer image artifacts, than several previously published DT templates. However, low-dimensional registration was used in the development of that template, which led to a mismatch of DT information across subjects, eventually manifested as loss of local diffusion information and errors in the final tensors. Also, low-dimensional registration led to a mismatch of the anatomy in the IIT and ICBM-152 templates. In this work, a significantly improved DT brain template in ICBM-152 space was developed, using high-dimensional non-linear registration and the raw data collected for the purposes of the IIT template. The accuracy of inter-subject DT matching was significantly increased compared to that achieved for the development of the IIT template. Consequently, the new template contained DT information that was more representative of single-subject human brain data, and was characterized by higher image sharpness than the IIT template. Furthermore, a bootstrap approach demonstrated that the variance of tensor characteristics was lower in the new template. Additionally, compared to the IIT template, brain anatomy in the new template more accurately matched ICBM-152 space. Finally, spatial normalization of a number of DT datasets through registration to the new and existing IIT templates was improved when using the new template.

Diffusion MRI (dMRI) is a valuable tool in the assessment of tissue microstructure. By fitting a model to the dMRI signal it is possible to derive various quantitative features. Several of the most popular dMRI signal models are expansions in an appropriately chosen basis, where the coefficients are determined using some variation of least-squares. However, such approaches lack any notion of uncertainty, which could be valuable in e.g. group analyses. In this work, we use a probabilistic interpretation of linear least-squares methods to recast popular dMRI models as Bayesian ones. This makes it possible to quantify the uncertainty of any derived quantity. In particular, for quantities that are affine functions of the coefficients, the posterior distribution can be expressed in closed-form. We simulated measurements from single- and double-tensor models where the correct values of several quantities are known, to validate that the theoretically derived quantiles agree with those observed empirically. We included results from residual bootstrap for comparison and found good agreement. The validation employed several different models: Diffusion Tensor Imaging (DTI), Mean Apparent Propagator MRI (MAP-MRI) and Constrained Spherical Deconvolution (CSD). We also used in vivo data to visualize maps of quantitative features and corresponding uncertainties, and to show how our approach can be used in a group analysis to downweight subjects with high uncertainty. In summary, we convert successful linear models for dMRI signal estimation to probabilistic models, capable of accurate uncertainty quantification.