Bayesian intravoxel incoherent motion parameter mapping in the human heart

Background: Intravoxel incoherent motion (IVIM) imaging of diffusion and perfusion in the heart suffers from high parameter estimation error. The purpose of this work is to improve cardiac IVIM parameter mapping using Bayesian inference. Methods: A second-order motion-compensated diffusion weighted spin-echo sequence with navigator-based slice tracking was implemented to collect cardiac IVIM data in early systole in eight healthy subjects on a clinical 1.5 T CMR system. IVIM data were encoded along six gradient optimized directions with b-values of 0–300 s/mm2. Subjects were scanned twice in two scan sessions one week apart to assess intra-subject reproducibility. Bayesian shrinkage prior (BSP) inference was implemented to determine IVIM parameters (diffusion D, perfusion fraction F and pseudo-diffusion D*). Results were compared to least-squares (LSQ) parameter estimation. Signal-to-noise ratio (SNR) requirements for a given fitting error were assessed for the two methods using simulated data. Reproducibility analysis of parameter estimation in-vivo using BSP and LSQ was performed. Results: BSP resulted in reduced SNR requirements when compared to LSQ in simulations. In-vivo, BSP analysis yielded IVIM parameter maps with smaller intra-myocardial variability and higher estimation certainty relative to LSQ. Mean IVIM parameter estimates in eight healthy subjects were (LSQ/BSP): 1.63 ± 0.28/1.51 ± 0.14·10−3 mm2/s for D, 13.13 ± 19.81/13.11 ± 5.95% for F and 201.45 ± 313.23/13.11 ± 14.53·10−3 mm2/s for D ∗. Parameter variation across all volunteers and measurements was lower with BSP compared to LSQ (coefficient of variation BSP vs. LSQ: 9% vs. 17% for D, 45% vs. 151% for F and 111% vs. 155% for D ∗). In addition, reproducibility of the IVIM parameter estimates was higher with BSP compared to LSQ (Bland-Altman coefficients of repeatability BSP vs. LSQ: 0.21 vs. 0.26·10−3 mm2/s for D, 5.55 vs. 6.91% for F and 15.06 vs. 422.80·10−3 mm2/s for D*). Conclusion: Robust free-breathing cardiac IVIM data acquisition in early systole is possible with the proposed method. BSP analysis yields improved IVIM parameter maps relative to conventional LSQ fitting with fewer outliers, improved estimation certainty and higher reproducibility. IVIM parameter mapping holds promise for myocardial perfusion measurements without the need for contrast agents

Computational experimental design for quantitative MRI

This thesis presents contributions to the field of quantitative MRI (qMRI) computational experimental design (CED). qMRI experiments are constructed from experimental ‘building blocks’ (e.g. acquisition protocol, model selection, parameter estimation) which, when combined, map tissue properties to quantitative biomarkers. Each of these blocks presents experimental choices: which acquisition protocol, which model, which parameter estimation method. Together, these choices form experimental designs. CED is the in-silico process by which such designs are tailored to suit specific imaging applications. This work addresses three limitations with current CED practices. The first is that they are too narrow in their scope: they are unduly focused on acquisition protocol. qMRI is underpinned by model fitting, which relies on an appropriate choice of signal model and fitting method. This choice cannot be taken for granted: model fitting both depends on and influences the quality of the acquired data. This work argues that CED should not focus on acquisition protocol alone, but rather consider all experimental components in an end-to-end, holistic manner. The second limitation relates to the experimental evaluation metrics currently used in CED. Experiments are assessed on their ability to generate close-to-groundtruth biomarker estimates, rather than on these estimates’ ability to solve real-world tasks (e.g. tissue classification); there is a disconnect between evaluation and application. This work address this by proposing a CED method which assesses experiments on their task performance, and validates its assessments on two clinical datasets. The final limitation relates to the parameter estimation methods available to CED. Existing methods are task-agnostic; they cannot be tailored to the needs of a specific qMRI experiment. This work takes advantage of machine learning techniques to, for the first time, make this possible: by changing training labels, parameter estimation performance is shown to be adjusted in a task-specific manner

Ball and rackets: inferring fiber fanning from diffusion-weighted MRI

A number of methods have been proposed for resolving crossing fibers from diffusion-weighted (DW) MRI. However, other complex fiber geometries have drawn minimal attention. In this study, we focus on fiber orientation dispersion induced by within-voxel fanning. We use a multi-compartment, model-based approach to estimate fiber dispersion. Bingham distributions are employed to represent continuous distributions of fiber orientations, centered around a main orientation, and capturing anisotropic dispersion. We evaluate the accuracy of the model for different simulated fanning geometries, under different acquisition protocols and we illustrate the high SNR and angular resolution needs. We also perform a qualitative comparison between our parametric approach and five popular non-parametric techniques that are based on orientation distribution functions (ODFs). This comparison illustrates how the same underlying geometry can be depicted by different methods. We apply the proposed model on high-quality, post-mortem macaque data and present whole-brain maps of fiber dispersion, as well as exquisite details on the local anatomy of fiber distributions in various white matter regions

Estimation of white matter fiber parameters from compressed multiresolution diffusion MRI using sparse Bayesian learning

We present a sparse Bayesian unmixing algorithm BusineX: Bayesian Unmixing for Sparse Inference-based Estimation of Fiber Crossings (X), for estimation of white matter fiber parameters from compressed (under-sampled) diffusion MRI (dMRI) data. BusineX combines compressive sensing with linear unmixing and introduces sparsity to the previously proposed multiresolution data fusion algorithm RubiX, resulting in a method for improved reconstruction, especially from data with lower number of diffusion gradients. We formulate the estimation of fiber parameters as a sparse signal recovery problem and propose a linear unmixing framework with sparse Bayesian learning for the recovery of sparse signals, the fiber orientations and volume fractions. The data is modeled using a parametric spherical deconvolution approach and represented using a dictionary created with the exponential decay components along different possible diffusion directions. Volume fractions of fibers along these directions define the dictionary weights. The proposed sparse inference, which is based on the dictionary representation, considers the sparsity of fiber populations and exploits the spatial redundancy in data representation, thereby facilitating inference from under-sampled q-space. The algorithm improves parameter estimation from dMRI through data-dependent local learning of hyperparameters, at each voxel and for each possible fiber orientation, that moderate the strength of priors governing the parameter variances. Experimental results on synthetic and in-vivo data show improved accuracy with a lower uncertainty in fiber parameter estimates. BusineX resolves a higher number of second and third fiber crossings. For under-sampled data, the algorithm is also shown to produce more reliable estimates

Contributions to MCMC Methods in Constrained Domains with Applications to Neuroimaging

Markov chain Monte Carlo (MCMC) methods form a rich class of computational techniques that help its user ascertain samples from target distributions when direct sampling is not possible or when their closed forms are intractable. Over the years, MCMC methods have been used in innumerable situations due to their flexibility and generalizability, even in situations involving nonlinear and/or highly parametrized models. In this dissertation, two major works relating to MCMC methods are presented. The first involves the development of a method to identify the number and directions of nerve fibers using diffusion-weighted MRI measurements. For this, the biological problem is first formulated as a model selection and estimation problem. Using the framework of reversible jump MCMC, a novel Bayesian scheme that performs both the above tasks simultaneously using customizable priors and proposal distributions is proposed. The proposed method allows users to set a prior level of spatial separation between the nerve fibers, allowing more crossing paths to be detected when desired or a lower number to potentially only detect robust nerve tracts. Hence, estimation that is specific to a given region of interest within the brain can be performed. In simulated examples, the method has been shown to resolve up to four fibers even in instances of highly noisy data. Comparative analysis with other state-of-the-art methods on in-vivo data showed the method\u27s ability to detect more crossing nerve fibers. The second work involves the construction of an MCMC algorithm that efficiently performs (Bayesian) sampling of parameters with support constraints. The method works by embedding a transformation called inversion in a sphere within the Metropolis-Hastings sampler. This creates an image of the constrained support that is amenable to sampling using standard proposals such as Gaussian. The proposed strategy is tested on three domains: the standard simplex, a sector of an n-sphere, and hypercubes. In each domain, a comparison is made with existing sampling techniques

Resolving Intravoxel White Matter Structures in the Human Brain Using Regularized Regression and Clustering

The human brain is a complex system of neural tissue that varies significantly between individuals. Although the technology that delineates these neural pathways does not currently exist, medical imaging modalities, such as diffusion magnetic resonance imaging (dMRI), can be leveraged for mathematical identification. The purpose of this work is to develop a novel method employing machine learning techniques to determine intravoxel nerve number and direction from dMRI data. The method was tested on multiple synthetic datasets and showed promising estimation accuracy and robustness for multi-nerve systems under a variety of conditions, including highly noisy data and imprecision in parameter assumptions

Bayesian Estimation of White Matter Atlas from High Angular Resolution Diffusion Imaging

We present a Bayesian probabilistic model to estimate the brain white matter atlas from high angular resolution diffusion imaging (HARDI) data. This model incorporates a shape prior of the white matter anatomy and the likelihood of individual observed HARDI datasets. We first assume that the atlas is generated from a known hyperatlas through a flow of diffeomorphisms and its shape prior can be constructed based on the framework of large deformation diffeomorphic metric mapping (LDDMM). LDDMM characterizes a nonlinear diffeomorphic shape space in a linear space of initial momentum uniquely determining diffeomorphic geodesic flows from the hyperatlas. Therefore, the shape prior of the HARDI atlas can be modeled using a centered Gaussian random field (GRF) model of the initial momentum. In order to construct the likelihood of observed HARDI datasets, it is necessary to study the diffeomorphic transformation of individual observations relative to the atlas and the probabilistic distribution of orientation distribution functions (ODFs). To this end, we construct the likelihood related to the transformation using the same construction as discussed for the shape prior of the atlas. The probabilistic distribution of ODFs is then constructed based on the ODF Riemannian manifold. We assume that the observed ODFs are generated by an exponential map of random tangent vectors at the deformed atlas ODF. Hence, the likelihood of the ODFs can be modeled using a GRF of their tangent vectors in the ODF Riemannian manifold. We solve for the maximum a posteriori using the Expectation-Maximization algorithm and derive the corresponding update equations. Finally, we illustrate the HARDI atlas constructed based on a Chinese aging cohort of 94 adults and compare it with that generated by averaging the coefficients of spherical harmonics of the ODF across subjects

Adaptive microstructure-informed tractography for accurate brain connectivity analyses

Human brain has been subject of deep interest for centuries, given it's central role in controlling and directing the actions and functions of the body as response to external stimuli. The neural tissue is primarily constituted of neurons and, together with dendrites and the nerve synapses, constitute the gray matter (GM) which plays a major role in cognitive functions. The information processed in the GM travel from one region to the other of the brain along nerve cell projections, called axons. All together they constitute the white matter (WM) whose wiring organization still remains challenging to uncover. The relationship between structure organization of the brain and function has been deeply investigated on humans and animals based on the assumption that the anatomic architecture determine the network dynamics. In response to that, many different imaging techniques raised, among which diffusion-weighted magnetic resonance imaging (DW-MRI) has triggered tremendous hopes and expectations. Diffusion-weighted imaging measures both restricted and unrestricted diffusion, i.e. the degree of movement freedom of the water molecules, allowing to map the tissue fiber architecture in vivo and non-invasively. Based on DW-MRI data, tractography is able to exploit information of the local fiber orientation to recover global fiber pathways, called streamlines, that represent groups of axons. This, in turn, allows to infer the WM structural connectivity, becoming widely used in many different clinical applications as for diagnoses, virtual dissections and surgical planning. However, despite this unique and compelling ability, data acquisition still suffers from technical limitations and recent studies have highlighted the poor anatomical accuracy of the reconstructions obtained with this technique and challenged its effectiveness for studying brain connectivity. The focus of this Ph.D. project is to specifically address these limitations and to improve the anatomical accuracy of the structural connectivity estimates. To this aim, we developed a global optimization algorithm that exploits micro and macro-structure information, introducing an iterative procedure that uses the underlying tissue properties to drive the reconstruction using a semi-global approach. Then, we investigated the possibility to dynamically adapt the position of a set of candidate streamlines while embedding the anatomical prior of trajectories smoothness and adapting the configuration based on the observed data. Finally, we introduced the concept of bundle-o-graphy by implementing a method to model groups of streamlines based on the concept that axons are organized into fascicles, adapting their shape and extent based on the underlying microstructure