The Larmor frequency shift of a white matter magnetic microstructure model with multiple sources.

Magnetic susceptibility imaging may provide valuable information about chemical composition and microstructural organization of tissue. However, its estimation from the MRI signal phase is particularly difficult as it is sensitive to magnetic tissue properties ranging from the molecular to the macroscopic scale. The MRI Larmor frequency shift measured in white matter (WM) tissue depends on the myelinated axons and other magnetizable sources such as iron-filled ferritin. We have previously derived the Larmor frequency shift arising from a dense medium of cylinders with scalar susceptibility and arbitrary orientation dispersion. Here, we extend our model to include microscopic WM susceptibility anisotropy as well as spherical inclusions with scalar susceptibility to represent subcellular structures, biologically stored iron, and so forth. We validate our analytical results with computer simulations and investigate the feasibility of estimating susceptibility using simple iterative linear least squares without regularization or preconditioning. This is done in a digital brain phantom synthesized from diffusion MRI measurements of an ex vivo mouse brain at ultra-high field.

Effects of power training in older patients with multiple sclerosis on neurodegeneration, neuromuscular function, and physical function. A study protocol for the "power training in older multiple sclerosis patients (PoTOMS) randomized control trial.

Introduction: Approximately one-third of all persons with multiple sclerosis (pwMS) are older, i.e., having an age ≥60 years. Whilst ageing and MS separately elicit deteriorating effects on brain morphology, neuromuscular function, and physical function, the combination of ageing and MS may pose a particular challenge. To counteract such detrimental changes, power training (i.e., a type of resistance exercise focusing on moderate-to-high loading at maximal intended movement velocity) presents itself as a viable and highly effective solution. Power training is known to positively impact physical function, neuromuscular function, as well as brain morphology. Existing evidence is promising but limited to young and middle-aged pwMS, with the effects of power training remaining to be elucidated in older pwMS. Methods: The presented 'Power Training in Older MS patients (PoTOMS)' trial is a national, multi-center, parallel-group, randomized controlled trial. The trial compares 24 weeks of usual care(n = 30) to 24 weeks of usual care and power training (n = 30). The primary outcome is whole brain atrophy rate. The secondary outcomes include changes in brain micro and macro structures, neuromuscular function, physical function, cognitive function, bone health, and patient-reported outcomes. Ethics and dissemination: The presented study is approved by The Regional Ethics Committee (reference number 1-10-72-222-20) and registered at the Danish Data Protection Agency (reference number 2016-051-000001). All study findings will be published in scientific peer-reviewed journals and presented at relevant scientific conferences independent of the results. The www.clinicaltrials.gov identifier is NCT04762342.

To mask or not to mask? Investigating the impact of accounting for spatial frequency distributions and susceptibility sources on QSM quality.

PURPOSE: Estimating magnetic susceptibility using MRI depends on inverting a forward relationship between the susceptibility and measured Larmor frequency. However, an often-overlooked constraint in susceptibility fitting is that the Larmor frequency is only measured inside the sample, and after successful background field removal, susceptibility sources should only reside inside the same sample. Here, we test the impact of accounting for these constraints in susceptibility fitting. THEORY AND METHODS: Two different digital brain phantoms with scalar susceptibility were examined. We used the MEDI phantom, a simple phantom with no background fields, to examine the effect of the imposed constraints for various levels of SNR. Next, we considered the QSM reconstruction challenge 2.0 phantom with and without background fields. We estimated the parameter accuracy of openly-available QSM algorithms by comparing fitting results to the ground truth. Next, we implemented the mentioned constraints and compared to the standard approach. RESULTS: Including the spatial distribution of frequencies and susceptibility sources decreased the RMS-error compared to standard QSM on both brain phantoms when background fields were absent. When background field removal was unsuccessful, as is presumably the case in most in vivo conditions, it is better to allow sources outside the brain. CONCLUSION: Informing QSM algorithms about the location of susceptibility sources and where Larmor frequency was measured improves susceptibility fitting for realistic SNR levels and efficient background field removal. However, the latter remains the bottleneck of the algorithm. Allowing for external sources regularizes unsuccessful background field removal and is currently the best strategy in vivo.

Larmor frequency shift from magnetized cylinders with arbitrary orientation distribution.

The magnetic susceptibility of tissue can provide valuable information about its chemical composition and microstructural organization. However, the relation between the magnetic microstructure and the measurable Larmor frequency shift is understood only for a few idealized cases. Here we analyze the microstructure formed by magnetized, NMR-invisible infinite cylinders suspended in an NMR-reporting fluid. Through simulations, we scrutinize various geometries of mesoscopic Lorentz cavities and inclusions, and show that the cavity size should be approximately one order of magnitude larger than the width of the inclusions. We also analytically derive the Larmor frequency shift for a population of cylinders with arbitrary orientation dispersion and show that it is determined by the l = 2 Laplace expansion coefficients p 2 m of the cylinders' orientation distribution function. Our work underscores the need to account for microstructural organization when estimating magnetic tissue properties.

Correlation tensor magnetic resonance imaging.

Diffusional Kurtosis Magnetic Resonance Imaging (DKI) quantifies the extent of non-Gaussian water diffusion, which has been shown to be a sensitive biomarker for microstructure in health and disease. However, DKI is not specific to any microstructural property per se since kurtosis may emerge from several different sources. Q-space trajectory encoding schemes have been proposed for decoupling kurtosis arising from the variance of mean diffusivities (isotropic kurtosis) from kurtosis driven by microscopic anisotropy (anisotropic kurtosis). Still, these methods assume that the system is comprised of multiple Gaussian diffusion components with vanishing intra-compartmental kurtosis (associated with restricted diffusion). Here, we develop a more general framework for resolving the underlying kurtosis sources without relying on the multiple Gaussian diffusion approximation. We introduce Correlation Tensor MRI (CTI) - an approach harnessing the versatility of double diffusion encoding (DDE) and its sensitivity to displacement correlation tensors capable of explicitly decoupling isotropic and anisotropic kurtosis components from intra-compartmental kurtosis effects arising from restricted (and time-dependent) diffusion. Additionally, we show that, by subtracting these isotropic and anisotropic kurtosis components from the total diffusional kurtosis, CTI provides an index that is potentially sensitive to intra-compartmental kurtosis. The theoretical foundations of CTI, as well as the first proof-of-concept CTI experiments in ex vivo mouse brains at ultrahigh field of 16.4 T, are presented. We find that anisotropic and isotropic kurtosis can decouple microscopic anisotropy from substantial partial volume effects between tissue and free water. Our intra-compartmental kurtosis index exhibited positive values in both white and grey matter tissues. Simulations in different synthetic microenvironments show, however, that our current CTI protocol for estimating intra-compartmental kurtosis is limited by higher order terms that were not taken into account in this study. CTI measurements were then extended to in vivo settings and used to map heathy rat brains at 9.4 T. These in vivo CTI results were found to be consistent with our ex vivo findings. Although future studies are still required to assess and mitigate the higher order effects on the intra-compartmental kurtosis index, our results show that CTI's more general estimates of anisotropic and isotropic kurtosis contributions are already ripe for future in vivo studies, which can have significant impact our understanding of the mechanisms underlying diffusion metrics extracted in health and disease.

Diffusion Kurtosis Imaging maps neural damage in the EAE model of multiple sclerosis.

Diffusion kurtosis imaging (DKI) is an imaging modality that yields novel disease biomarkers and in combination with nervous tissue modeling, provides access to microstructural parameters. Recently, DKI and subsequent estimation of microstructural model parameters has been used for assessment of tissue changes in neurodegenerative diseases and associated animal models. In this study, mouse spinal cords from the experimental autoimmune encephalomyelitis (EAE) model of multiple sclerosis (MS) were investigated for the first time using DKI in combination with biophysical modeling to study the relationship between microstructural metrics and degree of animal dysfunction. Thirteen spinal cords were extracted from animals with varied grades of disability and scanned in a high-field MRI scanner along with five control specimen. Diffusion weighted data were acquired together with high resolution T2* images. Diffusion data were fit to estimate diffusion and kurtosis tensors and white matter modeling parameters, which were all used for subsequent statistical analysis using a linear mixed effects model. T2* images were used to delineate focal demyelination/inflammation. Our results reveal a strong relationship between disability and measured microstructural parameters in normal appearing white matter and gray matter. Relationships between disability and mean of the kurtosis tensor, radial kurtosis, radial diffusivity were similar to what has been found in other hypomyelinating MS models, and in patients. However, the changes in biophysical modeling parameters and in particular in extra-axonal axial diffusivity were clearly different from previous studies employing other animal models of MS. In conclusion, our data suggest that DKI and microstructural modeling can provide a unique contrast capable of detecting EAE-specific changes correlating with clinical disability.

Effects of nongaussian diffusion on "isotropic diffusion" measurements: An ex-vivo microimaging and simulation study.

Designing novel diffusion-weighted pulse sequences to probe tissue microstructure beyond the conventional Stejskal-Tanner family is currently of broad interest. One such technique, multidimensional diffusion MRI, has been recently proposed to afford model-free decomposition of diffusion signal kurtosis into terms originating from either ensemble variance of isotropic diffusivity or microscopic diffusion anisotropy. This ability rests on the assumption that diffusion can be described as a sum of multiple Gaussian compartments, but this is often not strictly fulfilled. The effects of nongaussian diffusion on single shot isotropic diffusion sequences were first considered in detail by de Swiet and Mitra in 1996. They showed theoretically that anisotropic compartments lead to anisotropic time dependence of the diffusion tensors, which causes the measured isotropic diffusivity to depend on gradient frame orientation. Here we show how such deviations from the multiple Gaussian compartments assumption conflates orientation dispersion with ensemble variance in isotropic diffusivity. Second, we consider additional contributions to the apparent variance in isotropic diffusivity arising due to intracompartmental kurtosis. These will likewise depend on gradient frame orientation. We illustrate the potential importance of these confounds with analytical expressions, numerical simulations in simple model geometries, and microimaging experiments in fixed spinal cord using isotropic diffusion encoding waveforms with 7.5 ms duration and 3000 mT/m maximum amplitude.

Differential microstructural alterations in rat cerebral cortex in a model of chronic mild stress depression.

Chronic mild stress leads to depression in many cases and is linked to several debilitating diseases including mental disorders. Recently, neuronal tracing techniques, stereology, and immunohistochemistry have revealed persistent and significant microstructural alterations in the hippocampus, hypothalamus, prefrontal cortex, and amygdala, which form an interconnected system known as the stress circuit. Most studies have focused only on this circuit, however, some studies indicate that manipulation of sensory and motor systems may impact genesis and therapy of mood disorders and therefore these areas should not be neglected in the study of brain microstructure alterations in response to stress and depression. For this reason, we explore the microstructural alterations in different cortical regions in a chronic mild stress model of depression. The study employs ex-vivo diffusion MRI (d-MRI) to assess cortical microstructure in stressed (anhedonic and resilient) and control animals. MRI is followed by immunohistochemistry to substantiate the d-MRI findings. We find significantly lower extracellular diffusivity in auditory cortex (AC) of stress groups and a significantly higher fractional anisotropy in the resilient group. Neurite density was not found to be significantly higher in any cortical ROIs in the stress group compared to control, although axonal density is higher in the stress groups. We also report significant thinning of motor cortex (MC) in both stress groups. This is in agreement with recent clinical and preclinical studies on depression and similar disorders where significant microstructural and metabolic alterations were found in AC and MC. Our findings provide further evidence that the AC and MC are sensitive towards stress exposure and may extend our understanding of the microstructural effects of stress beyond the stress circuit of the brain. Progress in this field may provide new avenues of research to help in diagnosis and treatment intervention for depression and related disorders.

Diffusion MRI and MR spectroscopy reveal microstructural and metabolic brain alterations in chronic mild stress exposed rats: A CMS recovery study.

Chronic mild stress (CMS) induced depression elicits several debilitating symptoms and causes a significant economic burden on society. High variability in the symptomatology of depression poses substantial impediment to accurate diagnosis and therapy outcome. CMS exposure induces significant metabolic and microstructural alterations in the hippocampus (HP), prefrontal cortex (PFC), caudate-putamen (CP) and amygdala (AM), however, recovery from these maladaptive changes are limited and this may provide negative effects on the therapeutic treatment and management of depression. The present study utilized anhedonic rats from the unpredictable CMS model of depression to study metabolic recovery in the ventral hippocampus (vHP) and microstructural recovery in the HP, AM, CP, and PFC. The study employed 1H MR spectroscopy (1H MRS) and in-vivo diffusion MRI (d-MRI) at the age of week 18 (week 1 post CMS exposure) week 20 (week 3 post CMS) and week 25 (week 8 post CMS exposure) in the anhedonic group, and at the age of week 18 and week 22 in the control group. The d-MRI data have provided an array of diffusion tensor metrics (FA, MD, AD, and RD), and fast kurtosis metrics (MKT, WL and WT). CMS exposure induced a significant metabolic alteration in vHP, and significant microstructural alterations were observed in the HP, AM, and PFC in comparison to the age match control and within the anhedonic group. A significantly high level of N-acetylaspartate (NAA) was observed in vHP at the age of week 18 in comparison to age match control and week 20 and week 25 of the anhedonic group. HP and AM showed significant microstructural alterations up to the age of week 22 in the anhedonic group. PFC showed significant microstructural alterations only at the age of week 18, however, most of the metrics showed significantly higher value at the age of week 20 in the anhedonic group. The significantly increased NAA concentration may indicate impaired catabolism due to astrogliosis or oxidative stress. The significantly increased WL in the AM and HP may indicate hypertrophy of AM and reduced volume of HP. Such metabolic and microstructural alterations could be useful in disease diagnosis and follow-up treatment intervention in depression and similar disorders.

Diffusion time dependence of microstructural parameters in fixed spinal cord.

Biophysical modelling of diffusion MRI is necessary to provide specific microstructural tissue properties. However, estimating model parameters from data with limited diffusion gradient strength, such as clinical scanners, has proven unreliable due to a shallow optimization landscape. On the other hand, estimation of diffusion kurtosis (DKI) parameters is more robust, and its parameters may be connected to microstructural parameters, given an appropriate biophysical model. However, it was previously shown that this procedure still does not provide sufficient information to uniquely determine all model parameters. In particular, a parameter degeneracy related to the relative magnitude of intra-axonal and extra-axonal diffusivities remains. Here we develop a model of diffusion in white matter including axonal dispersion and demonstrate stable estimation of all model parameters from DKI in fixed pig spinal cord. By employing the recently developed fast axisymmetric DKI, we use stimulated echo acquisition mode to collect data over a two orders of magnitude diffusion time range with very narrow diffusion gradient pulses, enabling finely resolved measurements of diffusion time dependence of both net diffusion and kurtosis metrics, as well as model intra- and extra-axonal diffusivities, and axonal dispersion. Our results demonstrate substantial time dependence of all parameters except volume fractions, and the additional time dimension provides support for intra-axonal diffusivity to be larger than extra-axonal diffusivity in spinal cord white matter, although not unambiguously. We compare our findings for the time-dependent compartmental diffusivities to predictions from effective medium theory with reasonable agreement.

Precision and accuracy of diffusion kurtosis estimation and the influence of b-value selection.

Diffusion kurtosis imaging (DKI) is an extension of diffusion tensor imaging that accounts for leading non-Gaussian diffusion effects. In DKI studies, a wide range of different gradient strengths (b-values) is used, which is known to affect the estimated diffusivity and kurtosis parameters. Hence there is a need to assess the accuracy and precision of the estimated parameters as a function of b-value. This work examines the error in the estimation of mean of the kurtosis tensor (MKT) with respect to the ground truth, using simulations based on a biophysical model for both gray (GM) and white (WM) matter. Model parameters are derived from densely sampled experimental data acquired in ex vivo rat brain and in vivo human brain. Additionally, the variability of MKT is studied using the experimental data. Prevalent fitting protocols are implemented and investigated. The results show strong dependence on the maximum b-value of both net relative error and standard deviation of error for all of the employed fitting protocols. The choice of b-values with minimum MKT estimation error and standard deviation of error was found to depend on the protocol type and the tissue. Protocols that utilize two terms of the cumulant expansion (DKI) were found to achieve minimum error in GM at b-values less than 1 ms/µm2 , whereas maximal b-values of about 2.5 ms/µm2 were found to be optimal in WM. Protocols including additional higher order terms of the cumulant expansion were found to provide higher accuracy for the more commonly used b-value regime in GM, but were associated with higher error in WM. Averaged over multiple voxels, a net average error of around 15% for both WM and GM was observed for the optimal b-value choice. These results suggest caution when using DKI generated metrics for microstructural modeling and when comparing results obtained using different fitting techniques and b-values.

Fast imaging of mean, axial and radial diffusion kurtosis.

Diffusion kurtosis imaging (DKI) is being increasingly reported to provide sensitive biomarkers of subtle changes in tissue microstructure. However, DKI also imposes larger data requirements than diffusion tensor imaging (DTI), hence, the widespread adaptation and exploration of DKI would benefit from more efficient acquisition and computational methods. To meet this demand, we recently developed a method capable of estimating mean kurtosis with only 13 diffusion weighted images. This approach was later shown to provide very accurate mean kurtosis estimates and to be more efficient in terms of contrast to noise per unit time. However, insofar, the computation of two other critical DKI parameters, radial and axial kurtosis, has required the estimation of all 22 variables parameterizing the full DKI signal expression. Here, we present two strategies for estimating all of DKI's principal parameters - mean kurtosis, radial kurtosis, and axial kurtosis - using only 19 diffusion weighted images, compared to the current state-of-the-art acquisitions typically requiring about 60 images. The first approach is based on axially symmetric diffusion and kurtosis tensors, presented here for the first time, and referred to as axially symmetric DKI. The second approach is applicable in tissues with a priori known principal diffusion direction, and does not require fitting of any kind. The approaches are evaluated in human brain in vivo as well as in fixed rat spinal cord, and are demonstrated to provide metrics in good agreement with their full DKI counterparts estimated with nonlinear least squares. For small data sets and in white matter, axially symmetric DKI provides more accurate and robust estimates than unconstrained DKI. The significant acceleration achieved further paves the way to routine application of the technique.

Data for evaluation of fast kurtosis strategies, b-value optimization and exploration of diffusion MRI contrast.

Here we describe and provide diffusion magnetic resonance imaging (dMRI) data that was acquired in neural tissue and a physical phantom. Data acquired in biological tissue includes: fixed rat brain (acquired at 9.4 T) and spinal cord (acquired at 16.4 T) and in normal human brain (acquired at 3 T). This data was recently used for evaluation of diffusion kurtosis imaging (DKI) contrasts and for comparison to diffusion tensor imaging (DTI) parameter contrast. The data has also been used to optimize b-values for ex vivo and in vivo fast kurtosis imaging. The remaining data was obtained in a physical phantom with three orthogonal fiber orientations (fresh asparagus stems) for exploration of the kurtosis fractional anisotropy. However, the data may have broader interest and, collectively, may form the basis for image contrast exploration and simulations based on a wide range of dMRI analysis strategies.

Summary of high field diffusion MRI and microscopy data demonstrate microstructural aberration in chronic mild stress rat brain.

This data article describes a large, high resolution diffusion MRI data set from fixed rat brain acquired at high field strength. The rat brain samples consist of 21 adult rat brain hemispheres from animals exposed to chronic mild stress (anhedonic and resilient) and controls. Histology from amygdala of the same brain hemispheres is also included with three different stains: DiI and Hoechst stained microscopic images (confocal microscopy) and ALDH1L1 antibody based immunohistochemistry. These stains may be used to evaluate neurite density (DiI), nuclear density (Hoechst) and astrocytic density (ALDH1L1). This combination of high field diffusion data and high resolution images from microscopy enables comparison of microstructural parameters derived from diffusion MRI to histological microstructure. The data provided here is used in the article (Jespersen, 2016) [1].

Biophysical modeling of high field diffusion MRI demonstrates micro-structural aberration in chronic mild stress rat brain.

Depression is one of the leading causes of disability worldwide. Immense heterogeneity in symptoms of depression causes difficulty in diagnosis, and to date, there are no established biomarkers or imaging methods to examine depression. Unpredictable chronic mild stress (CMS) induced anhedonia is considered to be a realistic model of depression in studies of animal subjects. Stereological and neuronal tracing techniques have demonstrated persistent remodeling of microstructure in hippocampus, prefrontal cortex and amygdala of CMS brains. Recent developments in diffusion MRI (d-MRI) analyses, such as neurite density and diffusion kurtosis imaging (DKI), are able to capture microstructural changes and are considered to be robust tools in preclinical and clinical imaging. The present study utilized d-MRI analyzed with a neurite density model and the DKI framework to investigate microstructure in the hippocampus, prefrontal cortex, caudate putamen and amygdala regions of CMS rat brains by comparison to brains from normal controls. To validate findings of CMS induced microstructural alteration, histology was performed to determine neurite, nuclear and astrocyte density. d-MRI based neurite density and tensor-based mean kurtosis (MKT) were significantly higher, while mean diffusivity (MD), extracellular diffusivity (Deff) and intra-neurite diffusivity(DL) were significantly lower in the amygdala of CMS rat brains. Deff was also significantly lower in the hippocampus and caudate putamen in stressed groups. Histological neurite density corroborated the d-MRI findings in the amygdala and reductions in nuclear and astrocyte density further buttressed the d-MRI results. The present study demonstrated that the d-MRI based neurite density and MKT can reveal specific microstructural changes in CMS rat brains and these parameters might have value in clinical diagnosis of depression and for evaluation of treatment efficacy.

Kurtosis fractional anisotropy, its contrast and estimation by proxy.

The diffusion kurtosis observed with diffusion magnetic resonance imaging (dMRI) may vary with direction. This directional variation is summarized in the scalar kurtosis fractional anisotropy (KFA). Recent studies suggest that kurtosis anisotropy offers microstructural contrast not contained in other commonly used dMRI markers. We compare KFA to other dMRI contrasts in fixed rat brain and in human brain. We then investigate the observed contrast differences using data obtained in a physical phantom and simulations based on data from the phantom, rat spinal cord, and human brain. Lastly, we assess a strategy for rapid estimation of a computationally modest KFA proxy by evaluating its correlation to true KFA for varying number of sampling directions and signal-to-noise ratio (SNR) levels. We also map this proxy's b-value dependency. We find that KFA supplements the contrast of other dMRI metrics - particularly fractional anisotropy (FA) which vanishes in near orthogonal fiber arrangements where KFA does not. Simulations and phantom data support this interpretation. KFA therefore supplements FA and could be useful for evaluation of complex tissue arrangements. The KFA proxy is strongly correlated to true KFA when sampling is performed along at least nine directions and SNR is high.

Effect of electrical forepaw stimulation on capillary transit-time heterogeneity (CTH).

Functional hyperemia reduces oxygen extraction efficacy unless counteracted by a reduction of capillary transit-time heterogeneity of blood. We adapted a bolus tracking approach to capillary transit-time heterogeneity estimation for two-photon microscopy and then quantified changes in plasma mean transit time and capillary transit-time heterogeneity during forepaw stimulation in anesthetized mice (C57BL/6NTac). In addition, we analyzed transit time coefficient of variance = capillary transit-time heterogeneity/mean transit time, which we expect to remain constant in passive, compliant microvascular networks. Electrical forepaw stimulation reduced, both mean transit time (11.3% ± 1.3%) and capillary transit-time heterogeneity (24.1% ± 3.3%), consistent with earlier literature and model predictions. We observed a coefficient of variance reduction (14.3% ± 3.5%) during functional activation, especially for the arteriolar-to-venular passage. Such coefficient of variance reduction during functional activation suggests homogenization of capillary flows beyond that expected as a passive response to increased blood flow by other stimuli. This finding is consistent with an active neurocapillary coupling mechanism, for example via pericyte dilation. Mean transit time and capillary transit-time heterogeneity reductions were consistent with the relative change inferred from capillary hemodynamics (cell velocity and flux). Our findings support the important role of capillary transit-time heterogeneity in flow-metabolism coupling during functional activation.

Experimental considerations for fast kurtosis imaging.

PURPOSE: The clinical use of kurtosis imaging is impeded by long acquisitions and postprocessing. Recently, estimation of mean kurtosis tensor W¯ and mean diffusivity ( D¯) was made possible from 13 distinct diffusion weighted MRI acquisitions (the 1-3-9 protocol) with simple postprocessing. Here, we analyze the effects of noise and nonideal diffusion encoding, and propose a new correction strategy. We also present a 1-9-9 protocol with increased robustness to experimental imperfections and minimal additional scan time. This refinement does not affect computation time and also provides a fast estimate of fractional anisotropy (FA). THEORY AND METHODS: 1-3-9/1-9-9 data are acquired in rat and human brains, and estimates of D¯, FA, W¯ from human brains are compared with traditional estimates from an extensive diffusion kurtosis imaging data set. Simulations are used to evaluate the influence of noise and diffusion encodings deviating from the scheme, and the performance of the correction strategy. Optimal b-values are determined from simulations and data. RESULTS: Accuracy and precision in D¯ and W¯ are comparable to nonlinear least squares estimation, and is improved with the 1-9-9 protocol. The compensation strategy vastly improves parameter estimation in nonideal data. CONCLUSION: The framework offers a robust and compact method for estimating several diffusion metrics. The protocol is easily implemented. Magn Reson Med 76:1455-1468, 2016. © 2015 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.