Estimation of diffusion properties in crossing fiber bundles

Towards non-invasive tissue hydration measurements with optical coherence tomography

The attenuation coefficient ( μ OCT ) measured by optical coherence tomography (OCT) has been used to determine tissue hydration. Previous dual-wavelength OCT systems could not attain the needed precision, which we attribute to the absence of wavelength-dependent scattering of tissue in the underlying model. Assuming that scattering can be described using two parameters, we propose a triple/quadrupole-OCT system to achieve clinically relevant precision in water volume fraction. In this study, we conduct a quantitative analysis to determine the necessary precision of μ OCT measurements and compare it with numerical simulation. Our findings emphasize that achieving a clinically relevant assessment of a 2% water fraction requires determining the attenuation coefficient with a remarkable precision of 0.01 m m - 1 . This precision threshold is influenced by the chosen wavelength for attenuation measurement and can be enhanced through the inclusion of a fourth wavelength range.

Optimal experimental design and estimation for q-space trajectory imaging

Tensor-valued diffusion encoding facilitates data analysis by q-space trajectory imaging. By modeling the diffusion signal of heterogeneous tissues with a diffusion tensor distribution (DTD) and modulating the encoding tensor shape, this novel approach allows disentangling variations in diffusivity from microscopic anisotropy, orientation dispersion, and mixtures of multiple isotropic diffusivities. To facilitate the estimation of the DTD parameters, a parsimonious acquisition scheme coupled with an accurate and precise estimation of the DTD is needed. In this work, we create two precision-optimized acquisition schemes: one that maximizes the precision of the raw DTD parameters, and another that maximizes the precision of the scalar measures derived from the DTD. The improved precision of these schemes compared to a naïve sampling scheme is demonstrated in both simulations and real data. Furthermore, we show that the weighted linear least squares (WLLS) estimator that uses the squared reciprocal of the noisy signal as weights can be biased, whereas the iteratively WLLS estimator with the squared reciprocal of the predicted signal as weights outperforms the conventional unweighted linear LS and nonlinear LS estimators in terms of accuracy and precision. Finally, we show that the use of appropriate constraints can considerably increase the precision of the estimator with only a limited decrease in accuracy.

Cerebellar Microstructural Abnormalities in Parkinson's Disease: a Systematic Review of Diffusion Tensor Imaging Studies

Diffusion tensor imaging (DTI) is now having a strong momentum in research to evaluate the neural fibers of the CNS. This technique can study white matter (WM) microstructure in neurodegenerative disorders, including Parkinson's disease (PD). Previous neuroimaging studies have suggested cerebellar involvement in the pathogenesis of PD, and these cerebellum alterations can correlate with PD symptoms and stages. Using the PRISMA 2020 framework, PubMed and EMBASE were searched to retrieve relevant articles. Our search revealed 472 articles. After screening titles and abstracts, and full-text review, and implementing the inclusion criteria, 68 papers were selected for synthesis. Reviewing the selected studies revealed that the patterns of reduction in cerebellum WM integrity, assessed by fractional anisotropy, mean diffusivity, radial diffusivity, and axial diffusivity measures can differ symptoms and stages of PD. Cerebellar diffusion tensor imaging (DTI) changes in PD patients with "postural instability and gait difficulty" are significantly different from "tremor dominant" PD patients. Freezing of the gate is strongly related to cerebellar involvement depicted by DTI. The "reduced cognition," "visual disturbances," "sleep disorders," "depression," and "olfactory dysfunction" are not related to cerebellum microstructural changes on DTI, while "impulsive-compulsive behavior" can be linked to cerebellar WM alteration. Finally, higher PD stages and longer disease duration are associated with cerebellum white matter alteration depicted by DTI. Depiction of cerebellar white matter involvement in PD is feasible by DTI. There is an association with disease duration and severity and several clinical presentations with DTI findings. This clinical-imaging association may eventually improve disease management.

Precision of attenuation coefficient measurements by optical coherence tomography

SIGNIFICANCE

Optical coherence tomography (OCT) is an interferometric imaging modality, which provides tomographic information on the microscopic scale. Furthermore, OCT signal analysis facilitates quantification of tissue optical properties (e.g., the attenuation coefficient), which provides information regarding the structure and organization of tissue. However, a rigorous and standardized measure of the precision of the OCT-derived optical properties, to date, is missing.

AIM

We present a robust theoretical framework, which provides the Cramér -Rao lower bound σμOCT for the precision of OCT-derived optical attenuation coefficients.

APPROACH

Using a maximum likelihood approach and Fisher information, we derive an analytical solution for σμOCT when the position and depth of focus are known. We validate this solution, using simulated OCT signals, for which attenuation coefficients are extracted using a least-squares fitting procedure.

RESULTS

Our analytical solution is in perfect agreement with simulated data without shot noise. When shot noise is present, we show that the analytical solution still holds for signal-to-noise ratios (SNRs) in the fitting window being above 20 dB. For other cases (SNR<20 dB, focus position not precisely known), we show that the numerical calculation of the precision agrees with the σμOCT derived from simulated signals.

CONCLUSIONS

Our analytical solution provides a fast, rigorous, and easy-to-use measure for OCT-derived attenuation coefficients for signals above 20 dB. The effect of uncertainties in the focal point position on the precision in the attenuation coefficient, the second assumption underlying our analytical solution, is also investigated by numerical calculation of the lower bounds. This method can be straightforwardly extended to uncertainty in other system parameters.

Fiber orientation distribution from diffusion MRI: Effects of inaccurate response function calibration

Background and Purpose

Diffusion MRI of the brain enables to quantify white matter fiber orientations noninvasively. Several approaches have been proposed to estimate such characteristics from diffusion MRI data with spherical deconvolution being one of the most widely used methods. Spherical deconvolution requires to define––or derive from the data––a response function, which is used to compute the fiber orientation distribution (FOD). Different characteristics of the response function are expected to affect the FOD computation and the subsequent fiber tracking.

Methods

In this work, we explored the effects of inaccuracies in the shape factors of the response function on the FOD characteristics.

Results

With simulations, we show that the apparent fiber density could be doubled in the presence of underestimated shape factors in the response functions, whereas the overestimation of the shape factor will cause more spurious peaks in the FOD, especially when the signal‐to‐noise ratio is below 15. Moreover, crossing fiber populations with a separation angle smaller than 60° were more sensitive to inaccuracies in the response function than fiber populations with more orthogonal separation angles. Results with in vivo data demonstrate angular deviations in the FODs and spurious peaks as a result of modified shape factors of the response function, while the reconstruction of the main parts of fiber bundles is well preserved.

Conclusions

This work sheds light on how specific aspects of the response function shape can affect the estimated FODs, and highlights the importance of a proper calibration/definition of the response function.

Tract-specific analysis and neurocognitive functioning in sickle cell patients without history of overt stroke

INTRODUCTION

Sickle cell disease (SCD) is a hereditary blood disorder in which the oxygen-carrying hemoglobin molecule in red blood cells is abnormal. SCD patients are at increased risks for strokes and neurocognitive deficit, even though neurovascular screening and treatments have lowered the rate of overt strokes. Tract-specific analysis (TSA) is a statistical method to evaluate microstructural WM damage in neurodegenerative disorders, using diffusion tensor imaging (DTI).

METHODS

We utilized TSA and compared 11 major brain WM tracts between SCD patients with no history of overt stroke, anemic controls, and healthy controls. We additionally examined the relationship between the most commonly used DTI metric of WM tracts and neurocognitive performance in the SCD patients and healthy controls.

RESULTS

Disruption of WM microstructure orientation-dependent metrics for the SCD patients was found in the genu of the corpus callosum (CC), cortico-spinal tract, inferior fronto-occipital fasciculus, right inferior longitudinal fasciculus, superior longitudinal fasciculus, and left uncinate fasciculus. Neurocognitive performance indicated slower processing speed and lower response inhibition skills in SCD patients compared to controls. TSA abnormalities in the CC were significantly associated with measures of processing speed, working memory, and executive functions.

CONCLUSION

Decreased DTI-derived metrics were observed on six tracts in chronically anemic patients, regardless of anemia subtype, while two tracks with decreased measures were unique to SCD patients. Patients with WMHs had more significant FA abnormalities. Decreased FA values in the CC significantly correlated with all nine neurocognitive tests, suggesting a critical importance for CC in core neurocognitive processes.

Analysis of attenuation coefficient estimation in Fourier-domain OCT of semi-infinite media

The attenuation coefficient (AC) is an optical property of tissue that can be estimated from optical coherence tomography (OCT) data. In this paper, we aim to estimate the AC accurately by compensating for the shape of the focused beam. For this, we propose a method to estimate the axial PSF model parameters and AC by fitting a model for an OCT signal in a homogenous sample to the recorded OCT signal. In addition, we employ numerical analysis to obtain the theoretical optimal precision of the estimated parameters for different experimental setups. Finally, the method is applied to OCT B-scans obtained from homogeneous samples. The numerical and experimental results show accurate estimations of the AC and the focus location when the focus is located inside the sample.

Orientation Prior and Consistent Model Selection Increase Sensitivity of Tract-Based Spatial Statistics in Crossing-Fiber Regions

The goal of this paper is to increase the statistical power of crossing-fiber statistics in voxelwise analyses of diffusion-weighted magnetic resonance imaging (DW-MRI) data. In the proposed framework, a fiber orientation atlas and a model complexity atlas were used to fit the ball-and-sticks model to diffusion-weighted images of subjects in a prospective population-based cohort study. Reproducibility and sensitivity of the partial volume fractions in the ball-and-sticks model were analyzed using TBSS (tract-based spatial statistics) and compared to a reference framework. The reproducibility was investigated on two scans of 30 subjects acquired with an interval of approximately three weeks by studying the intraclass correlation coefficient (ICC). The sensitivity to true biological effects was evaluated by studying the regression with age on 500 subjects from 65 to 90 years old. Compared to the reference framework, the ICC improved significantly when using the proposed framework. Higher t-statistics indicated that regression coefficients with age could be determined more precisely with the proposed framework and more voxels correlated significantly with age. The application of a fiber orientation atlas and a model complexity atlas can significantly improve the reproducibility and sensitivity of crossing-fiber statistics in TBSS.

Spatial versus angular resolution for tractography-assisted planning of deep brain stimulation

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Deep brain stimulation (DBS) benefits from precise targeting of white matter tracts.

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Better to increase spatial vs. angular resolution for separating parallel tracts.

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Scanning time trade-off between angular & spatial resolution depends on local anatomy.

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We recommend increased spatial resolution dMRI for tract-guided internal capsule DBS.

Given the restricted total scanning time for clinical neuroimaging, it is unclear whether clinical diffusion MRI protocols would benefit more from higher spatial resolution or higher angular resolution. In this work, we investigated the relative benefit of improving spatial or angular resolution in diffusion MRI to separate two parallel running white matter tracts that are targets for deep brain stimulation: the anterior thalamic radiation and the supero-lateral branch of the medial forebrain bundle. Both these tracts are situated in the ventral anterior limb of the internal capsule, and recent studies suggest that targeting a specific tract could improve treatment efficacy. Therefore, we scanned 19 healthy volunteers at 3T and 7T according to three diffusion MRI protocols with respectively standard clinical settings, increased spatial resolution of 1.4 mm, and increased angular resolution (64 additional gradient directions at b = 2200s/mm²). We performed probabilistic tractography for all protocols and quantified the separability of both tracts. The higher spatial resolution protocol improved separability by 41% with respect to the clinical standard, presumably due to decreased partial voluming. The higher angular resolution protocol resulted in increased apparent tract volumes and overlap, which is disadvantageous for application in precise treatment planning. We thus recommend to increase the spatial resolution for deep brain stimulation planning to 1.4 mm while maintaining angular resolution. This recommendation complements the general advice to aim for high angular resolution to resolve crossing fibers, confirming that the specific application and anatomical considerations are leading in clinical diffusion MRI protocol optimization.

Subdividing the superior longitudinal fasciculus using local quantitative MRI

The association fibers of the superior longitudinal fasciculus (SLF) connect parietal and frontal cortical regions in the human brain. The SLF comprises of three distinct sub-bundles, each presenting a different anatomical trajectory, and specific functional roles. Nevertheless, in vivo studies of the SLF often consider the entire SLF complex as a single entity. In this work, we suggest a data-driven approach that relies on microstructure measurements for separating SLF-III from the rest of the SLF. We apply the SLF-III separation procedure in three independent datasets using parameters of diffusion MRI (fractional anisotropy), as well as relaxometry-based parameters (T1, T2, T2* and T2-weighted/T1-weighted). We show that the proposed procedure is reproducible across datasets and tractography algorithms. Finally, we suggest that differential crossing with different white-matter tracts is the source of the distinct MRI signatures of SLF-II and SLF-III.

Comparison of Multi-Tensor Diffusion Models' Performance for White Matter Integrity Estimation in Chronic Stroke

Better insight into white matter (WM) alterations after stroke onset could help to understand the underlying recovery mechanisms and improve future interventions. MR diffusion imaging enables to assess such changes. Our goal was to investigate the relation of WM diffusion characteristics derived from diffusion models of increasing complexity with the motor function of the upper limb. Moreover, we aimed to evaluate the variation of such characteristics across different WM structures of chronic stroke patients in comparison to healthy subjects. Subjects were scanned with a two b-value diffusion-weighted MRI protocol to exploit multiple diffusion models: single tensor, single tensor with isotropic compartment, bi-tensor model, bi-tensor with isotropic compartment. From each model we derived the mean tract fractional anisotropy (FA), mean (MD), radial (RD) and axial (AD) diffusivities outside the lesion site based on a WM tracts atlas. Asymmetry of these measures was correlated with the Fugl-Meyer upper extremity assessment (FMA) score and compared between patient and control groups. Eighteen chronic stroke patients and eight age-matched healthy individuals participated in the study. Significant correlation of the outcome measures with the clinical scores of stroke recovery was found. The lowest correlation of the corticospinal tract FAasymmetry and FMA was with the single tensor model (r = -0.3, p = 0.2) whereas the other models reported results in the range of r = -0.79 ÷ -0.81 and p = 4E-5 ÷ 8E-5. The corticospinal tract and superior longitudinal fasciculus showed most alterations in our patient group relative to controls. Multiple compartment models yielded superior correlation of the diffusion measures and FMA compared to the single tensor model.

Reliable Dual Tensor Model Estimation in Single and Crossing Fibers Based on Jeffreys Prior

Purpose

This paper presents and studies a framework for reliable modeling of diffusion MRI using a data-acquisition adaptive prior.

Methods

Automated relevance determination estimates the mean of the posterior distribution of a rank-2 dual tensor model exploiting Jeffreys prior (JARD). This data-acquisition prior is based on the Fisher information matrix and enables the assessment whether two tensors are mandatory to describe the data. The method is compared to Maximum Likelihood Estimation (MLE) of the dual tensor model and to FSL’s ball-and-stick approach.

Results

Monte Carlo experiments demonstrated that JARD’s volume fractions correlated well with the ground truth for single and crossing fiber configurations. In single fiber configurations JARD automatically reduced the volume fraction of one compartment to (almost) zero. The variance in fractional anisotropy (FA) of the main tensor component was thereby reduced compared to MLE. JARD and MLE gave a comparable outcome in data simulating crossing fibers. On brain data, JARD yielded a smaller spread in FA along the corpus callosum compared to MLE. Tract-based spatial statistics demonstrated a higher sensitivity in detecting age-related white matter atrophy using JARD compared to both MLE and the ball-and-stick approach.

Conclusions

The proposed framework offers accurate and precise estimation of diffusion properties in single and dual fiber regions.

Analytical performance bounds for multi-tensor diffusion-MRI

PURPOSE

To examine the effects of MR acquisition parameters on brain white matter fiber orientation estimation and parameter of clinical interest in crossing fiber areas based on the Multi-Tensor Model (MTM).

MATERIAL AND METHODS

We compute the Cramér-Rao Bound (CRB) for the MTM and the parameter of clinical interest such as the Fractional Anisotropy (FA) and the dominant fiber orientations, assuming that the diffusion MRI data are recorded by a multi-coil, multi-shell acquisition system. Considering the sum-of-squares method for the reconstructed magnitude image, we introduce an approximate closed-form formula for Fisher Information Matrix that has the simplicity and easy interpretation advantages. In addition, we propose to generalize the FA and the mean diffusivity to the multi-tensor model.

RESULTS

We show the application of the CRB to reduce the scan time while preserving a good estimation precision. We provide results showing how the increase of the number of acquisition coils compensates the decrease of the number of diffusion gradient directions. We analyze the impact of the b-value and the Signal-to-Noise Ratio (SNR). The analysis shows that the estimation error variance decreases with a quadratic rate with the SNR, and that the optimum b-values are not unique but depend on the target parameter, the context, and eventually the target cost function.

CONCLUSION

In this study we highlight the importance of choosing the appropriate acquisition parameters especially when dealing with crossing fiber areas. We also provide a methodology for the optimal tuning of these parameters using the CRB.

Estimation of diffusion properties in three-way fiber crossings without overfitting

Diffusion-weighted magnetic resonance imaging permits assessment of the structural integrity of the brain's white matter. This requires unbiased and precise quantification of diffusion properties. We aim to estimate such properties in simple and complex fiber geometries up to three-way fiber crossings using rank-2 tensor model selection. A maximum a-posteriori (MAP) estimator is employed to determine the parameters of a constrained triple tensor model. A prior is imposed on the parameters to avoid the degeneracy of the model estimation. This prior maximizes the divergence between the three tensor's principal orientations. A new model selection approach quantifies the extent to which the candidate models are appropriate, i.e. a single-, dual- or triple-tensor model. The model selection precludes overfitting to the data. It is based on the goodness of fit and information complexity measured by the total Kullback-Leibler divergence (ICOMP-TKLD). The proposed framework is compared to maximum likelihood estimation on phantom data of three-way fiber crossings. It is also compared to the ball-and-stick approach from the FMRIB Software Library (FSL) on experimental data. The spread in the estimated parameters reduces significantly due to the prior. The fractional anisotropy (FA) could be precisely estimated with MAP down to an angle of approximately 40° between the three fibers. Furthermore, volume fractions between 0.2 and 0.8 could be reliably estimated. The configurations inferred by our method corresponded to the anticipated neuro-anatomy both in single fibers and in three-way fiber crossings. The main difference with FSL was in single fiber regions. Here, ICOMP-TKLD predominantly inferred a single fiber configuration, as preferred, whereas FSL mostly selected dual or triple order ball-and-stick models. The prior of our MAP estimator enhances the precision of the parameter estimation, without introducing a bias. Additionally, our model selection effectively balances the trade-off between the goodness of fit and information complexity. The proposed framework can enhance the sensitivity of statistical analysis of diffusion tensor MRI.

Estimation of optimal b-value sets for obtaining apparent diffusion coefficient free from perfusion in non-small cell lung cancer

The purpose of this study was to determine optimal sets of b-values in diffusion-weighted MRI (DW-MRI) for obtaining monoexponential apparent diffusion coefficient (ADC) close to perfusion-insensitive intravoxel incoherent motion (IVIM) model ADC (ADCIVIM) in non-small cell lung cancer. Ten subjects had 40 DW-MRI scans before and during radiotherapy in a 1.5 T MRI scanner. Respiratory triggering was applied to the echo-planar DW-MRI with TR ≈ 4500 ms, TE  =  74 ms, eight b-values of 0-1000 μs μm(-2), pixel size  =  1.98 × 1.98 mm(2), slice thickness  =  6 mm, interslice gap  =  1.2 mm, 7 axial slices and total acquisition time ≈6 min. One or more DW-MRI scans together covered the whole tumour volume. Monoexponential model ADC values using various b-value sets were compared to reference-standard ADCIVIM values using all eight b-values. Intra-scan coefficient of variation (CV) of active tumour volumes was computed to compare the relative noise in ADC maps. ADC values for one pre-treatment DW-MRI scan of each of the 10 subjects were computed using b-value pairs from DW-MRI images synthesized for b-values of 0-2000 μs μm(-2) from the estimated IVIM parametric maps and corrupted by various Rician noise levels. The square root of mean of squared error percentage (RMSE) of the ADC value relative to the corresponding ADCIVIM for the tumour volume of the scan was computed. Monoexponential ADC values for the b-value sets of 250 and 1000; 250, 500 and 1000; 250, 650 and 1000; 250, 800 and 1000; and 250-1000 μs μm(-2) were not significantly different from ADCIVIM values (p > 0.05, paired t-test). Mean error in ADC values for these sets relative to ADCIVIM were within 3.5%. Intra-scan CVs for these sets were comparable to that for ADCIVIM. The monoexponential ADC values for other sets-0-1000; 50-1000; 100-1000; 500-1000; and 250 and 800 μs μm(-2) were significantly different from the ADCIVIM values. From Rician noise simulation using b-value pairs, there was a wide range of acceptable b-value pairs giving small RMSE of ADC values relative to ADCIVIM. The pairs for small RMSE had lower b-values as the noise level increased. ADC values of a two b-value set-250 and 1000 μs μm(-2), and all three b-value sets with 250, 1000 μs μm(-2) and an intermediate value approached ADCIVIM, with relative noise comparable to that of ADCIVIM. These sets may be used in lung tumours using comparatively short scan and post-processing times. Rician noise simulation suggested that the b-values in the vicinity of these experimental best b-values can be used with error within an acceptable limit. It also suggested that the optimal sets will have lower b-values as the noise level becomes higher.

Detecting statistically significant differences in quantitative MRI experiments, applied to diffusion tensor imaging

In this work we present a framework for reliably detecting significant differences in quantitative magnetic resonance imaging and evaluate it with diffusion tensor imaging (DTI) experiments. As part of this framework we propose a new spatially regularized maximum likelihood estimator that simultaneously estimates the quantitative parameters and the spatially-smoothly-varying noise level from the acquisitions. The noise level estimation method does not require repeated acquisitions. We show that the amount of regularization in this method can be set a priori to achieve a desired coefficient of variation of the estimated noise level. The noise level estimate allows the construction of a Cramér-Rao-lower-bound based test statistic that reliably assesses the significance of differences between voxels within a scan or across different scans. We show that the regularized noise level estimate improves upon existing methods and results in a substantially increased precision of the uncertainty estimates of the DTI parameters. It enables correct specification of the null distribution of the test statistic and with it the test statistic obtains the highest sensitivity and specificity. The source code of the estimation framework, test statistic and experiment scripts are made available to the community.

Toward tract-specific fractional anisotropy (TSFA) at crossing-fiber regions with clinical diffusion MRI

PURPOSE

White matter fractional anisotropy (FA), a measure suggesting microstructure, is significantly underestimated with single diffusion tensor model at crossing-fiber regions (CFR). We propose a tract-specific FA (TSFA), corrected for the effects of crossing-fiber geometry and free water at CFR, and adapted for tract analysis with diffusion MRI (dMRI) in clinical research.

METHODS

At CFR voxels, the proposed technique estimates free water fraction (fiso ) as a linear function of mean apparent diffusion coefficient (mADC), fits the dual tensors and estimates TSFA. Digital phantoms were designed for testing the accuracy of fiso and fitted dual-anisotropies at CFR. The technique was applied to clinical dMRI of normal subjects and hereditary spastic paraplegia (HSP) patients to test the effectiveness of TSFA.

RESULTS

Phantom simulation showed unbiased estimates of dual-tensor anisotropies at CFR and high accuracy of fiso as a linear function of mADC. TSFA at CFR was highly consistent to the single tensor FA at non-CFR within the same tract with normal human dMRI. Additional HSP imaging biomarkers with significant correlation to clinical motor function scores could be identified with TSFA.

CONCLUSION

Results suggest the potential of the proposed technique in estimating unbiased TSFA at CFR and conducting tract analysis in clinical research.

Diffusion tensor MRI of chemotherapy-induced cognitive impairment in non-CNS cancer patients: a review

Patients with non-central nervous system cancers often experience subtle cognitive deficits after treatment with cytotoxic agents. Therapy-induced structural changes to the brain could be one of the possible causes underlying these reported cognitive deficits. In this review, we evaluate the use of diffusion tensor imaging (DTI) for assessing possible therapy-induced changes in the microstructure of the cerebral white matter (WM) and provide a critical overview of the published DTI research on therapy-induced cognitive impairment. Both cross-sectional and longitudinal DTI studies have demonstrated abnormal microstructural properties in WM regions involved in cognition. These findings correlated with cognitive performance, suggesting that there is a link between reduced "WM integrity" and chemotherapy-induced impaired cognition. In this paper, we will also introduce the basics of diffusion tensor imaging and how it can be applied to evaluate effects of therapy on structural changes in cerebral WM. The review concludes with considerations and discussion regarding DTI data interpretation and possible future directions for investigating therapy-induced WM changes in cancer patients. This review article is part of a Special Issue entitled: Neuroimaging Studies of Cancer and Cancer Treatment.

Beyond fractional anisotropy: extraction of bundle-specific structural metrics from crossing fiber models

Diffusion MRI (dMRI) measurements are used for inferring the microstructural properties of white matter and to reconstruct fiber pathways. Very often voxels contain complex fiber configurations comprising multiple bundles, rendering the simple diffusion tensor model unsuitable. Multi-compartment models deliver a convenient parameterization of the underlying complex fiber architecture, but pose challenges for fitting and model selection. Spherical deconvolution, in contrast, very economically produces a fiber orientation density function (fODF) without any explicit model assumptions. Since, however, the fODF is represented by spherical harmonics, a direct interpretation of the model parameters is impossible. Based on the fact that the fODF can often be interpreted as superposition of multiple peaks, each associated to one relatively coherent fiber population (bundle), we offer a solution that seeks to combine the advantages of both approaches: first the fiber configuration is modeled as fODF represented by spherical harmonics and then each of the peaks is parameterized separately in order to characterize the underlying bundle. In this work, the fODF peaks are approximated by Bingham distributions, capturing first and second-order statistics of the fiber orientations, from which we derive metrics for the parametric quantification of fiber bundles. We propose meaningful relationships between these measures and the underlying microstructural properties. We focus on metrics derived directly from properties of the Bingham distribution, such as peak length, peak direction, peak spread, integral over the peak, as well as a metric derived from the comparison of the largest peaks, which probes the complexity of the underlying microstructure. We compare these metrics to the conventionally used fractional anisotropy (FA) and show how they may help to increase the specificity of the characterization of microstructural properties. While metrics relying on the first moments of the Bingham distributions provide relatively robust results, second-order metrics representing the peak spread are only meaningful, if the SNR is very high and no fiber crossings are present in the voxel.

Incorporation of Rician noise in the analysis of biexponential transverse relaxation in cartilage using a multiple gradient echo sequence at 3 and 7 Tesla

PURPOSE

Previous work has evaluated the quality of different analytic methods for extracting relaxation times from magnitude imaging data exhibiting Rician noise. However, biexponential analysis of relaxation in tissue, including cartilage, and materials is of increasing interest. We, therefore, analyzed biexponential transverse relaxation decay in the presence of Rician noise and assessed the accuracy and precision of several approaches to determining component fractions and apparent transverse relaxation times.

THEORY AND METHODS

Comparisons of four different voxel-by-voxel fitting methods were performed using Monte Carlo simulations, and phantom and ex vivo bovine nasal cartilage (BNC) experiments. In each case, preclinical and clinical imaging field strengths of 7 Tesla (T) and 3T, respectively, and parameters, were investigated across a range of signal-to-noise ratios (SNR). Results were compared with Cramér-Rao lower bound calculations.

RESULTS

As expected, at high SNR, all methods performed well. At lower SNR, fits explicitly incorporating the analytic form of the Rician noise maintained performance. The much more efficient correction scheme of Gudbjartsson and Patz performed almost as well in many cases. Ex vivo experiments on phantoms and BNC were consistent with simulation results.

CONCLUSION

Explicit incorporation of Rician noise greatly improves accuracy and precision in the analysis of biexponential transverse decay data.

DTI of human skeletal muscle: the effects of diffusion encoding parameters, signal-to-noise ratio and T2 on tensor indices and fiber tracts

In this study, we have performed simulations to address the effects of diffusion encoding parameters, signal-to-noise ratio (SNR) and T2 on skeletal muscle diffusion tensor indices and fiber tracts. Where appropriate, simulations were corroborated and validated by in vivo diffusion tensor imaging (DTI) of human skeletal muscle. Specifically, we have addressed: (i) the accuracy and precision of the diffusion parameters and eigenvectors at different SNR levels; (ii) the effects of the diffusion gradient direction encoding scheme; (iii) the optimal b value for diffusion tensor estimation; (iv) the effects of changes in skeletal muscle T2; and, finally, the influence of SNR on fiber tractography and derived (v) fiber lengths, (vi) pennation angles and (vii) fiber curvatures. We conclude that accurate DTI of skeletal muscle requires an SNR of at least 25, a b value of between 400 and 500 s/mm(2), and data acquired with at least 12 diffusion gradient directions homogeneously distributed on half a sphere. Furthermore, for DTI studies focusing on skeletal muscle injury or pathology, apparent changes in the diffusion parameters need to be interpreted with great care in view of the confounding effects of T2, particularly for moderate to low SNR values.

Model selection and estimation of multi-compartment models in diffusion MRI with a Rician noise model

Multi-compartment models in diffusion MRI (dMRI) are used to describe complex white matter fiber architecture of the brain. In this paper, we propose a novel multi-compartment estimation method based on the ball-and-stick model, which is composed of an isotropic diffusion compartment ("ball") as well as one or more perfectly linear diffusion compartments ("sticks"). To model the noise distribution intrinsic to dMRI measurements, we introduce a Rician likelihood term and estimate the model parameters by means of an Expectation Maximization (EM) algorithm. This paper also addresses the problem of selecting the number of fiber compartments that best fit the data, by introducing a sparsity prior on the volume mixing fractions. This term provides automatic model selection and enables us to discriminate different fiber populations. When applied to simulated data, our method provides accurate estimates of the fiber orientations, diffusivities, and number of compartments, even at low SNR, and outperforms similar methods that rely on a Gaussian noise distribution assumption. We also apply our method to in vivo brain data and show that it can successfully capture complex fiber structures that match the known anatomy.

Parametric representation of multiple white matter fascicles from cube and sphere diffusion MRI

The characterization of the complex diffusion signal arising from the brain remains an open problem. Many representations focus on characterizing the global shape of the diffusion profile at each voxel and are limited to the assessment of connectivity. In contrast, Multiple Fascicle Models (MFM) seek to represent the contribution from each white matter fascicle and may be useful in the investigation of both white matter connectivity and diffusion properties of each individual fascicle. However, the most appropriate representation of multiple fascicles remains unclear. In particular, a multiple tensor representation of multiple fascicles has frequently been reported to be numerically challenging and unstable. We provide here the first analytical demonstration that when using a diffusion MRI acquisition with only one non-zero b-value, such as in conventional single-shell HARDI acquisition, a co-linearity in model parameters makes the precise model estimation impossible. Motivated by this theoretical result, we propose the novel CUSP (CUbe and SPhere) optimal acquisition scheme to achieve multiple non-zero b-values. It combines the gradients of a single-shell HARDI with gradients in its enclosing cube, in which varying b-values can be acquired by modulation of the gradient strength, without modifying the minimum echo time. Compared to a multi-shell HARDI acquisition, our scheme has significantly increased signal-to-noise ratio. We propose a novel estimation algorithm that enables efficient, robust and accurate estimation of the parameters of a multi-tensor model. In conjunction with a CUSP acquisition, it enables full estimation of the multi-tensor model. We present an evaluation of CUSP-MFM on both synthetic phantoms and invivo data. We report qualitative and quantitative experimental evaluations which demonstrate the ability of CUSP-MFM to characterize multiple fascicles from short duration acquisitions. CUSP-MFM enables rapid and effective investigation of multiple white matter fascicles, in both normal development and in disease and injury, in research and clinical practice.

Quantification of increased cellularity during inflammatory demyelination

Multiple sclerosis is characterized by inflammatory demyelination and irreversible axonal injury leading to permanent neurological disabilities. Diffusion tensor imaging demonstrates an improved capability over standard magnetic resonance imaging to differentiate axon from myelin pathologies. However, the increased cellularity and vasogenic oedema associated with inflammation cannot be detected or separated from axon/myelin injury by diffusion tensor imaging, limiting its clinical applications. A novel diffusion basis spectrum imaging, capable of characterizing water diffusion properties associated with axon/myelin injury and inflammation, was developed to quantitatively reveal white matter pathologies in central nervous system disorders. Tissue phantoms made of normal fixed mouse trigeminal nerves juxtaposed with and without gel were employed to demonstrate the feasibility of diffusion basis spectrum imaging to quantify baseline cellularity in the absence and presence of vasogenic oedema. Following the phantom studies, in vivo diffusion basis spectrum imaging and diffusion tensor imaging with immunohistochemistry validation were performed on the corpus callosum of cuprizone treated mice. Results demonstrate that in vivo diffusion basis spectrum imaging can effectively separate the confounding effects of increased cellularity and/or grey matter contamination, allowing successful detection of immunohistochemistry confirmed axonal injury and/or demyelination in middle and rostral corpus callosum that were missed by diffusion tensor imaging. In addition, diffusion basis spectrum imaging-derived cellularity strongly correlated with numbers of cell nuclei determined using immunohistochemistry. Our findings suggest that diffusion basis spectrum imaging has great potential to provide non-invasive biomarkers for neuroinflammation, axonal injury and demyelination coexisting in multiple sclerosis.