Bayesian uncertainty quantification in linear models for diffusion MRI

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.Comment: Added results from a group analysis and a comparison with residual bootstra

Fuzzy Fibers: Uncertainty in dMRI Tractography

Fiber tracking based on diffusion weighted Magnetic Resonance Imaging (dMRI) allows for noninvasive reconstruction of fiber bundles in the human brain. In this chapter, we discuss sources of error and uncertainty in this technique, and review strategies that afford a more reliable interpretation of the results. This includes methods for computing and rendering probabilistic tractograms, which estimate precision in the face of measurement noise and artifacts. However, we also address aspects that have received less attention so far, such as model selection, partial voluming, and the impact of parameters, both in preprocessing and in fiber tracking itself. We conclude by giving impulses for future research

Doctor of Philosophy

dissertationDiffusion magnetic resonance imaging (dMRI) has become a popular technique to detect brain white matter structure. However, imaging noise, imaging artifacts, and modeling techniques, etc., create many uncertainties, which may generate misleading information for further analysis or applications, such as surgical planning. Therefore, how to analyze, effectively visualize, and reduce these uncertainties become very important research questions. In this dissertation, we present both rank-k decomposition and direct decomposition approaches based on spherical deconvolution to decompose the fiber directions more accurately for high angular resolution diffusion imaging (HARDI) data, which will reduce the uncertainties of the fiber directions. By applying volume rendering techniques to an ensemble of 3D orientation distribution function (ODF) glyphs, which we call SIP functions of diffusion shapes, one can elucidate the complex heteroscedastic structural variation in these local diffusion shapes. Furthermore, we quantify the extent of this variation by measuring the fraction of the volume of these shapes, which is consistent across all noise levels, the certain volume ratio. To better understand the uncertainties in white matter fiber tracks, we propose three metrics to quantify the differences between the results of diffusion tensor magnetic resonance imaging (DT-MRI) fiber tracking algorithms: the area between corresponding fibers of each bundle, the Earth Mover's Distance (EMD) between two fiber bundle volumes, and the current distance between two fiber bundle volumes. Based on these metrics, we discuss an interactive fiber track comparison visualization toolkit we have developed to visualize these uncertainties more efficiently. Physical phantoms, with high repeatability and reproducibility, are also designed with the hope of validating the dMRI techniques. In summary, this dissertation provides a better understanding about uncertainties in diffusion magnetic resonance imaging: where and how much are the uncertainties? How do we reduce these uncertainties? How can we possibly validate our algorithms

An error analysis of probabilistic fibre tracking methods: average curves optimization

Fibre tractography using diffusion tensor imaging is a promising method for estimating the pathways of white matter tracts in the human brain. The success of fibre tracking methods ultimately depends upon the accuracy of the fibre tracking algorithms and the quality of the data. Uncertainty and its representation have an important role to play in fibre tractography methods to infer useful information from real world noisy diffusion weighted data. Probabilistic fibre tracking approaches have received considerable interest recently for resolving orientational uncertainties. In this study, an average curves approach was used to investigate the impact of SNR and tensor field geometry on the accuracy of three different types of probabilistic tracking algorithms. The accuracy was assessed using simulated data and a range of tract geometries. The average curves representations were employed to represent the optimal fibre path of probabilistic tracking curves. The results are compared with streamline tracking on both simulated and in vivo data

Evaluating the accuracy of diffusion MRI models in white matter

Models of diffusion MRI within a voxel are useful for making inferences about the properties of the tissue and inferring fiber orientation distribution used by tractography algorithms. A useful model must fit the data accurately. However, evaluations of model-accuracy of some of the models that are commonly used in analyzing human white matter have not been published before. Here, we evaluate model-accuracy of the two main classes of diffusion MRI models. The diffusion tensor model (DTM) summarizes diffusion as a 3-dimensional Gaussian distribution. Sparse fascicle models (SFM) summarize the signal as a linear sum of signals originating from a collection of fascicles oriented in different directions. We use cross-validation to assess model-accuracy at different gradient amplitudes (b-values) throughout the white matter. Specifically, we fit each model to all the white matter voxels in one data set and then use the model to predict a second, independent data set. This is the first evaluation of model-accuracy of these models. In most of the white matter the DTM predicts the data more accurately than test-retest reliability; SFM model-accuracy is higher than test-retest reliability and also higher than the DTM, particularly for measurements with (a) a b-value above 1000 in locations containing fiber crossings, and (b) in the regions of the brain surrounding the optic radiations. The SFM also has better parameter-validity: it more accurately estimates the fiber orientation distribution function (fODF) in each voxel, which is useful for fiber tracking

Anisotropy Across Fields and Scales

This open access book focuses on processing, modeling, and visualization of anisotropy information, which are often addressed by employing sophisticated mathematical constructs such as tensors and other higher-order descriptors. It also discusses adaptations of such constructs to problems encountered in seemingly dissimilar areas of medical imaging, physical sciences, and engineering. Featuring original research contributions as well as insightful reviews for scientists interested in handling anisotropy information, it covers topics such as pertinent geometric and algebraic properties of tensors and tensor fields, challenges faced in processing and visualizing different types of data, statistical techniques for data processing, and specific applications like mapping white-matter fiber tracts in the brain. The book helps readers grasp the current challenges in the field and provides information on the techniques devised to address them. Further, it facilitates the transfer of knowledge between different disciplines in order to advance the research frontiers in these areas. This multidisciplinary book presents, in part, the outcomes of the seventh in a series of Dagstuhl seminars devoted to visualization and processing of tensor fields and higher-order descriptors, which was held in Dagstuhl, Germany, on October 28–November 2, 2018

A new method to study energy-dependent arrival delays on photons from astrophysical sources

Correlations between the arrival time and the energy of photons emitted in outbursts of astrophysical objects are predicted in quantum and classical gravity scenarios and can appear as well as a result of complex acceleration mechanisms responsible for the photon emission at the source. This paper presents a robust method to study such correlations that overcomes some limitations encountered in previous analysis, and is based on a Likelihood function built from the physical picture assumed for the emission, propagation and detection of the photons. The results of the application of this method to a flare of Markarian 501 observed by the MAGIC telescope are presented. The method is also applied to a simulated dataset based on the flare of PKS 2155-304 recorded by the H.E.S.S. observatory to proof its applicability to complex photon arrival time distributions.Comment: 18 pages, 7 figure

On the Reliability of Diffusion Neuroimaging

Over the last years, diffusion imaging techniques like DTI, DSI or Q-Ball received increasin

Anisotropy Across Fields and Scales

This open access book focuses on processing, modeling, and visualization of anisotropy information, which are often addressed by employing sophisticated mathematical constructs such as tensors and other higher-order descriptors. It also discusses adaptations of such constructs to problems encountered in seemingly dissimilar areas of medical imaging, physical sciences, and engineering. Featuring original research contributions as well as insightful reviews for scientists interested in handling anisotropy information, it covers topics such as pertinent geometric and algebraic properties of tensors and tensor fields, challenges faced in processing and visualizing different types of data, statistical techniques for data processing, and specific applications like mapping white-matter fiber tracts in the brain. The book helps readers grasp the current challenges in the field and provides information on the techniques devised to address them. Further, it facilitates the transfer of knowledge between different disciplines in order to advance the research frontiers in these areas. This multidisciplinary book presents, in part, the outcomes of the seventh in a series of Dagstuhl seminars devoted to visualization and processing of tensor fields and higher-order descriptors, which was held in Dagstuhl, Germany, on October 28–November 2, 2018