Optimized rectification of fiber orientation density function with background threshold.

PURPOSE: To describe an optimized fiber orientation density function (fODF) rectification procedure that removes negative values and absorbs all features below a specified threshold into a constant background. THEORY AND METHODS: The fODF for a white matter imaging voxel describes the angular density of axons. Because of signal noise and Gibbs ringing, fODFs estimated with diffusion MRI may take on unphysical negative values in some directions and contain spurious peaks. In order to suppress such artifacts, an fODF rectification procedure is proposed that both eliminates all negative values and incorporates all features below a specified threshold, η, into a constant background while at the same time minimizing the mean square deviation from the original, unrectified fODF. Calculating this fODF is straightforward, and the directions and shapes of peaks not absorbed into the background are preserved. The rectification method is illustrated for an analytic fODF model and for experimental diffusion MRI data obtained in healthy human brain, with the original fODFs being obtained from fiber ball imaging. RESULTS: Examples of optimal rectified fODFs are given for three choices of the background threshold referred to as minimal rectification (η = 0), average-level rectification (η ≈ 0.08), and fractional-anisotropy-axonal-based rectification (η ≈ 0.1). As η is increased, artifacts and other small features are more strongly suppressed, but the major fODF peaks are largely unaffected for the range of η values illustrated by these three alternatives. CONCLUSION: Artifactual features of fODFs estimated with diffusion MRI can be effectively suppressed by applying the proposed optimized rectification procedure. Since it minimizes fODF distortion in the mean square sense, it may be useful in the study of how fODF fine structure is affected by aging and disease.

Fiber Ball White Matter Modeling Reveals Microstructural Alterations in Healthy Brain Aging.

Age-related white matter degeneration is characterized by myelin breakdown and neuronal fiber loss that preferentially occur in regions that myelinate later in development. Conventional diffusion MRI (dMRI) has demonstrated age-related increases in diffusivity but provide limited information regarding the tissue-specific changes driving these effects. A recently developed dMRI biophysical modeling technique, Fiber Ball White Matter (FBWM) modeling, offers enhanced biological interpretability by estimating microstructural properties specific to the intra-axonal and extra-axonal spaces. We used FBWM to illustrate the biological mechanisms underlying changes throughout white matter in healthy aging using data from 63 cognitively unimpaired adults ages 45-85 with no radiological evidence of neurodegeneration or incipient Alzheimer's disease. Conventional dMRI and FBWM metrics were computed for two late-myelinating (genu of the corpus callosum and association tracts) and two early-myelinating regions (splenium of the corpus callosum and projection tracts). We examined the associations between age and these metrics in each region and tested whether age was differentially associated with these metrics in late- vs. early-myelinating regions. We found that conventional metrics replicated patterns of age-related increases in diffusivity in late-myelinating regions. FBWM additionally revealed specific intra- and extra-axonal changes suggestive of myelin breakdown and preferential loss of smaller-diameter axons, yielding in vivo corroboration of findings from histopathological studies of aged brains. These results demonstrate that advanced biophysical modeling approaches, such as FBWM, offer novel information about the microstructure-specific alterations contributing to white matter changes in healthy aging. These tools hold promise as sensitive indicators of early pathological changes related to neurodegenerative disease.

Impact of intra-axonal kurtosis on fiber orientation density functions estimated with fiber ball imaging.

PURPOSE: To determine the impact of an intra-axonal kurtosis on estimates of the fiber orientation density function (fODF) obtained with fiber ball imaging (FBI). THEORY AND METHODS: Standard FBI assumes Gaussian diffusion within individual axons and estimates the fODF by applying an inverse generalized Funk transform to diffusion MRI data for b-values of 4000 s/mm2 or higher. However, recent work based on numeric simulations shows that diffusion inside axons is non-Gaussian with an intra-axonal kurtosis of ∼ 0.4. Here, the theory underlying FBI is extended to incorporate an intra-axonal kurtosis. This is done to first order in the intra-axonal kurtosis without making assumptions about the details of the diffusion dynamics and to all orders for a specific model based on a gamma distribution of diffusivities. The first order approximation is used to assess the effect of an intra-axonal kurtosis on FBI estimates for the fODF and axonal water fraction. The gamma distribution model is used to test the validity of the approximation. RESULTS: The first order approximation indicates the estimated fODF is altered by a few percent for an intra-axonal kurtosis of 0.4 in comparison to predictions of standard FBI. If one neglects the intra-axonal kurtosis, the angular resolution of the point spread function for the fODF is changed by <1°, whereas the axonal water fraction is overestimated by ∼ 5%. The gamma distribution model shows that the first order approximation is accurate to within a few percent. CONCLUSION: The intra-axonal kurtosis has a small impact on fODFs estimated with FBI.

High b-value diffusion tractography: Abnormal axonal network organization associated with medication-refractory epilepsy.

Diffusion magnetic resonance imaging (dMRI) tractography has played a critical role in characterizing patterns of aberrant brain network reorganization among patients with epilepsy. However, the accuracy of dMRI tractography is hampered by the complex biophysical properties of white matter tissue. High b-value diffusion imaging overcomes this limitation by better isolating axonal pathways. In this study, we introduce tractography derived from fiber ball imaging (FBI), a high b-value approach which excludes non-axonal signals, to identify atypical neuronal networks in patients with epilepsy. Specifically, we compared network properties obtained from multiple diffusion tractography approaches (diffusion tensor imaging, diffusion kurtosis imaging, FBI) in order to assess the pathophysiological relevance of network rearrangement in medication-responsive vs. medication-refractory adults with focal epilepsy. We show that drug-resistant epilepsy is associated with increased global network segregation detected by FBI-based tractography. We propose exploring FBI as a clinically feasible alternative to quantify topological changes that could be used to track disease progression and inform on clinical outcomes.

High fidelity fiber orientation density functions from fiber ball imaging.

The fiber orientation density function (fODF) in white matter is a primary physical quantity that can be estimated with diffusion MRI. It has often been employed for fiber tracking and microstructural modeling. Requirements for the construction of high fidelity fODFs, in the sense of having good angular resolution, adequate data to avoid sampling errors, and minimal noise artifacts, are described for fODFs calculated with fiber ball imaging. A criterion is formulated for the number of diffusion encoding directions needed to achieve a given angular resolution. The advantages of using large b-values (≥6000 s/mm2 ) are also discussed. For the direct comparison of different fODFs, a method is developed for defining a local frame of reference tied to each voxel's individual axonal structure. The Matusita anisotropy axonal is proposed as a scalar fODF measure for quantifying angular variability. Experimental results, obtained at 3 T from human volunteers, are used as illustrations.

Optimized rectification of fiber orientation density function.

PURPOSE: To demonstrate an optimized rectification strategy for fiber orientation density functions (fODFs). THEORY AND METHODS: In white matter, fODFs can be estimated with diffusion MRI. However, because of signal noise, imaging artifacts and other factors, experimentally determined fODFs may take on unphysical negative values in some directions. Here, we show how to rectify such fODFs to eliminate all negative values while minimizing the mean square difference between the original and rectified fODFs. The method is demonstrated for a mathematical model and for fODFs estimated from experimental human data using both constrained spherical deconvolution and fiber ball imaging. Comparison with an alternative nonoptimized rectification approach is also provided. RESULTS: For the mathematical model, it is found that the optimized rectification procedure removes negative fODF values while at the same time reducing the mean square error. Relative to the alternative rectification approach, the optimized fODFs are substantially more accurate. For the experimental data, the optimized fODFs have a lower average fractional anisotropy axonal and often fewer small peaks than the original, unrectified fODFs. The calculation of optimized fODFs is straightforward where the main step is the finding of the root to an equation in one variable, as may be efficiently accomplished with the bisection method. CONCLUSION: Unphysical negative fODF values can be easily eliminated in a manner that minimizes the mean square difference between the original and rectified fODFs. Optimized fODF rectification may be useful in applications for which negative values are problematic.

Optimization of data acquisition and analysis for fiber ball imaging.

The inverse Funk transform of high angular resolution diffusion imaging (HARDI) data provides an estimate for the fiber orientation density function (fODF) in white matter (WM). Since the inverse Funk transform is a straightforward linear transformation, this technique, referred to as fiber ball imaging (FBI), offers a practical means of calculating the fODF that avoids the need for a response function or nonlinear numerical fitting. Nevertheless, the accuracy of FBI depends on both the choice of b-value and the number of diffusion-encoding directions used to acquire the HARDI data. To inform the design of optimal scan protocols for its implementation, FBI predictions are investigated here with in vivo data from healthy adult volunteers acquired at 3 T for b-values spanning 1000 to 10,000 s/mm2, for diffusion-encoding directions varying in number from 30 to 256 and for TE ranging from 90 to 120 ms. Our results suggest b-values above 4000 s/mm2 with at least 64 diffusion-encoding directions are adequate to achieve reasonable accuracy with FBI for calculating axon-specific diffusion measures and for performing WM fiber tractography (WMFT).

Evaluating kurtosis-based diffusion MRI tissue models for white matter with fiber ball imaging.

In order to quantify well-defined microstructural properties of brain tissue from diffusion MRI (dMRI) data, tissue models are typically employed that relate biological features, such as cell morphology and cell membrane permeability, to the diffusion dynamics. A variety of such models have been proposed for white matter, and their validation is a topic of active interest. In this paper, three different tissue models are tested by comparing their predictions for a specific microstructural parameter to a value measured independently with a recently proposed dMRI method known as fiber ball imaging (FBI). The three tissue models are all constructed with the diffusion and kurtosis tensors, and they are hence compatible with diffusional kurtosis imaging. Nevertheless, the models differ significantly in their details and predictions. For voxels with fractional anisotropies (FAs) exceeding 0.5, all three are reasonably consistent with FBI. However, for lower FA values, one of these, called the white matter tract integrity (WMTI) model, is found to be in much better accord with FBI than the other two, suggesting that the WMTI model has a broader range of applicability.