Tractography via the Ensemble Average Propagator in diffusion MRI

International audienceIt's well known that in diffusion MRI (dMRI), fibre crossing is an important problem for most existing diffusion tensor imaging (DTI) based tractography algorithms. To overcome these limitations, High Angular Resolution Diffusion Imaging (HARDI) based tractography has been proposed with a particular emphasis on the the Orientation Distribution Function (ODF). In this paper, we advocate the use of the Ensemble Average Propagator (EAP) instead of the ODF for tractography in dMRI and propose an original and efficient EAP-based tractography algorithm that outperforms the classical ODF-based tractography, in particular, in the regions that contain complex fibre crossing configurations. Various experimental results including synthetic, phantom and real data illustrate the potential of the approach and clearly show that our method is especially efficient to handle regions where fiber bundles are crossing, and still well handle other fiber bundle configurations such as U-shape and kissing fibers

Estimation of Fiber Orientations Using Neighborhood Information

Data from diffusion magnetic resonance imaging (dMRI) can be used to reconstruct fiber tracts, for example, in muscle and white matter. Estimation of fiber orientations (FOs) is a crucial step in the reconstruction process and these estimates can be corrupted by noise. In this paper, a new method called Fiber Orientation Reconstruction using Neighborhood Information (FORNI) is described and shown to reduce the effects of noise and improve FO estimation performance by incorporating spatial consistency. FORNI uses a fixed tensor basis to model the diffusion weighted signals, which has the advantage of providing an explicit relationship between the basis vectors and the FOs. FO spatial coherence is encouraged using weighted l1-norm regularization terms, which contain the interaction of directional information between neighbor voxels. Data fidelity is encouraged using a squared error between the observed and reconstructed diffusion weighted signals. After appropriate weighting of these competing objectives, the resulting objective function is minimized using a block coordinate descent algorithm, and a straightforward parallelization strategy is used to speed up processing. Experiments were performed on a digital crossing phantom, ex vivo tongue dMRI data, and in vivo brain dMRI data for both qualitative and quantitative evaluation. The results demonstrate that FORNI improves the quality of FO estimation over other state of the art algorithms.Comment: Journal paper accepted in Medical Image Analysis. 35 pages and 16 figure

Bayesian Image Quality Transfer with CNNs: Exploring Uncertainty in dMRI Super-Resolution

In this work, we investigate the value of uncertainty modeling in 3D super-resolution with convolutional neural networks (CNNs). Deep learning has shown success in a plethora of medical image transformation problems, such as super-resolution (SR) and image synthesis. However, the highly ill-posed nature of such problems results in inevitable ambiguity in the learning of networks. We propose to account for intrinsic uncertainty through a per-patch heteroscedastic noise model and for parameter uncertainty through approximate Bayesian inference in the form of variational dropout. We show that the combined benefits of both lead to the state-of-the-art performance SR of diffusion MR brain images in terms of errors compared to ground truth. We further show that the reduced error scores produce tangible benefits in downstream tractography. In addition, the probabilistic nature of the methods naturally confers a mechanism to quantify uncertainty over the super-resolved output. We demonstrate through experiments on both healthy and pathological brains the potential utility of such an uncertainty measure in the risk assessment of the super-resolved images for subsequent clinical use.Comment: Accepted paper at MICCAI 201

Infinite Feature Selection on Shore-Based Biomarkers Reveals Connectivity Modulation after Stroke

Connectomics is gaining increasing interest in the scientific and clinical communities. It consists in deriving models of structural or functional brain connections based on some local measures. Here we focus on structural connectivity as detected by diffusion MRI. Connectivity matrices are derived from microstructural indices obtained by the 3D-SHORE. Typically, graphs are derived from connectivity matrices and used for inferring node properties that allow identifying those nodes that play a prominent role in the network. This information can then be used to detect network modulations induced by diseases. In this paper we take a complementary approach and focus on link as opposed to node properties. We hypothesize that network modulation can be better described by measuring the connectivity alteration directly in the form of modulation of the properties of white matter fiber bundles constituting the network communication backbone. The goal of this paper is to detect the paths that are most altered by the pathology by exploiting a feature selection paradigm. Temporal changes on connection weights are treated as features and those playing a leading role in a patient versus healthy controls classification task are detected by the Infinite Feature Selection (Inf-FS) method. Results show that connection paths with high discriminative power can be identified that are shared by the considered microstructural descriptors allowing a classification accuracy ranging between 83% and 89%

Integration of multi-shell diffusion imaging derived metrics in tractography reconstructions of clinical data

Tese de mestrado integrado Engenharia Biomédica e Biofísica (Engenharia Clínica e Instrumentação Médica), Universidade de Lisboa, Faculdade de Ciências, 2019Nos últimos anos, com o rápido avanço das técnicas imagiológicas, a oportunidade de mapear o cérebro humano in vivo com uma resolução sem precedentes tornou-se realidade, permanecendo ainda hoje como uma das áreas de maior interesse da neurociência. Sabendo que o movimento natural das moléculas de água nos tecidos biológicos é altamente influenciado pelo ambiente microestrutural envolvente, e que a anisotropia que este processo aleatório assume na matéria branca pode ser explorada com o intuito de inferir características importantes associadas ao tecido neuronal, a ressonância magnética ponderada por difusão (dMRI, do inglês “Diffusion-Weighted Magnetic Resonance Imaging") afirmou-se como a técnica de imagem mais amplamente utilizada para a investigação in vivo e não invasiva da conectividade cerebral. A primeira técnica padrão de dMRI foi a imagiologia por tensor de difusão (DTI, do inglês "Diffusion Tensor Imaging"). Implementada com a capacidade de fornecer sensibilidade à microestrutura do tecido, esta técnica permite extrair informação acerca da tridimensionalidade da distribuição da difusão de moléculas de água através da aplicação de seis gradientes de difusão não colineares entre si. Além da difusividade média (MD, do inglês "Mean Diffusivity"), é também possível extrair outros índices microestruturais, como a anisotropia fraccional (FA, do inglês "Fractional Anisotropy"), que fornece informação acerca da percentagem de difusão anisotrópica num determinado voxel. Ambas as métricas são amplamente utilizadas como medidas de alterações microestruturais, todavia, apesar da sua sensibilidade, estes marcadores não são específicos quanto às características individuais da microestrutura tecidual. Regiões com reduzida FA podem camuflar regiões de conformação de cruzamento de fibras, ou fibras muito anguladas, que a DTI não consegue resolver. A razão para esta limitação reside no número reduzido de diferentes direções de difusão que são exploradas, assim como no pressuposto de que a distribuição das moléculas de água é gaussiana, o que não é necessariamente verdade. De forma alternativa e com o intuito de tais limitações serem ultrapassadas, é possível implementar uma representação matemática do sinal adquirido de forma a explorar o propagador de difusão, da qual a imagiologia por ressonância magnética do propagador aparente médio (MAP-MRI, do inglês “Mean Apparent Propagator Magnetic Resonance Imaging”) é exemplo. Esta técnica analítica caracteriza-se pelo cálculo da função de densidade de probabilidade associada ao deslocamento de spin, o que permite descrever o caráter não-gaussiano do processo de difusão tridimensional e quantificar índices escalares inerentes ao processo de difusão, os quais sublinham as características complexas intrínsecas à microestrutura do tecido. Estes parâmetros incluem o deslocamento médio quadrático (MSD, em inglês “mean square displacement”), a probabilidade de retorno à origem (RTOP, do inglês “return-to-the origin probability”) e suas variantes de difusão em uma e duas dimensões – a probabilidade de retorno ao plano (RTPP, do inglês “return-to-the plane probability”) e a probabilidade de retorno ao eixo (RTAP, do inglês “return-to-the axis probability”), respetivamente. Em resposta às limitações da DTI associadas à falta de especificidade para distinguir características microestruturais dos tecidos, surgiu ainda o modelo de Dispersão de Orientação de Neurite e Imagem de Densidade (NODDI, do inglês “Neurite Orientation Dispersion and Density Imaging”), o qual utiliza o processo de difusão para estimar a morfologia das neurites. Tendo como premissa subjacente que o sinal de difusão pode ser definido pela soma da contribuição dos sinais de diferentes compartimentos, este modelo biofísico diferencia o espaço intra e extracelular o que, por sua vez, permite quantificar a dispersão e densidade das neurites. Deste modo, dois parâmetros intrínsecos à microestrutura envolvente podem ser calculados: a densidade neurítica e o índice de dispersão da orientação das neurites. No entanto, de forma a garantir a viabilidade clínica do modelo, este pode ser aplicado por meio do método AMICO (do inglês “Accelerated Microstructure Imaging via Convex Optimization”) através do seu ajuste linear, o que permite o cálculo do índice de dispersão da orientação das neurites (ODI, do inglês “Orientation Dispersion Index”), da fração de volume intracelular (ICVF do inglês, “Intracellular Volume Fraction”), e da fração de volume isotrópico (ISOVF, do inglês “Isotropic Volume Fraction”). O estudo da configuração arquitetural das estruturas cerebrais in vivo, por meio da dMRI associada aos métodos de tractografia, permitiu a reconstrução não invasiva das fibras neuronais e a exploração da informação direcional inerente às mesmas, sendo que o seu estudo tem revelado uma enorme expansão por meio do estabelecimento de marcadores biológicos perante a presença de diversas condições patológicas. O objetivo principal desta dissertação prende-se com existência de uma variação proeminentenas métricas de difusão ao longo dos tratos de matéria branca no cérebro humano. Atualmente, a maioriados estudos de tractografia tem por base uma abordagem que se resume à análise do valor escalar médio da métrica de difusão para a estrutura cerebral em estudo, pelo que se tem verificado um crescente interesse na utilização de métodos que considerem a extensão da variabilidade nas métricas de difusão ao longo dos tratos de modo a providenciarem um maior nível de detalhe ao nível do processo de difusão, evitando interpretações erróneas dos parâmetros microestruturais. Desta forma, em primeiro lugar, foi desenvolvido uma análise ao longo dos tratos de matéria branca, tendo por base a variação dos valores assumidos pelos parâmetros microestruturais acima mencionados. No presente estudo foi possível demonstrar a eficácia de tal abordagem ao longo de três tratos de matéria de branca (fascículo arqueado, trato corticoespinhal, e corpo caloso), para além de permitir, através da variância assumida pelos diversos parâmetros microestruturais, o estudo detalhado de regiões anatómicas que assumem uma distribuição complexa de múltiplos conjuntos populacionais de fibras, como é o caso do centro semioval, o qual constitui uma região de cruzamento de fibras provenientes dos três tratos de matéria branca em estudo. De seguida, esta técnica foi utilizada com sucesso na identificação de diferenças microestruturais por meio do estudo dos diversos parâmetros de difusão em pacientes com diagnóstico prévio de epilepsia no lobo temporal (TLE, do inglês “Temporal Lobe Epilepsy”), com foco epiléptico localizado no hemisfério esquerdo, e controlos. O estudo do ambiente microestrutural por meio dos múltiplos mapas escalares permitiu averiguar a alteração do processo de difusão e/ou anisotropia, associadas ao efeito fisiopatológico da TLE na organização da matéria branca. Os resultados revelaram diferenças localizadas, as quais se traduziram num aumento da difusividade e redução da anisotropia do processo de difusão ao longo dos tratos em estudo dos pacientes com TLE, sugerindo deste modo uma perda na organização das diversas estruturas anatómicas e a expansão do espaço extracelular face aos controlos. Verificou-se ainda que pacientes com esta condição neurológica sofrem de alterações microestruturais que afetam redes cerebrais em grande escala, envolvendo regiões temporais e extratemporais de ambos os hemisférios. Adicionalmente, aplicada como técnica capaz de investigar padrões de mudança na matéria branca, procedeu-se à realização de um estudo assente na estatística espacial baseada no trato (TBSS, do inglês “Tract-Based Spatial Statistics”). Após a exploração das diversas métricas de difusão, os pacientes com TLE (com lateralização à esquerda) demonstraram alterações no processo de difusão, ilustradas pelos diversos padrões de mudança microestrutural de cada métrica em estudo, concordantes com os resultados anteriormente aferidos pela análise ao longo do trato. Por fim, uma análise baseada em fixel (FBA, do inglês “Fixel-Based Analysis”) foi realizada, a qual permitiu uma análise estatística abrangente de medidas quantitativas da matéria branca, com o intuito de detetar alterações no volume intra-axonal por variação na densidade intra-voxel e/ou reorganização da morfologia macroscópica. Para identificar tais diferenças entre pacientes e controlos, três parâmetros foram considerados: densidade das fibras (FD, do inglês “Fibre Density”), seção transversal do feixe de fibras (FC, do inglês “Fibre-bundle Cross-section”), e densidade de fibras e seção transversal (FDC, do inglês “Fibre Density and Cross-section). Reduções na FD, FC e FDC foram identificadas em pacientes com TLE (com lateralização à esquerda) em comparação com os controlos, o que está de acordo com as mudanças microestruturais que resultam do processo de degeneração que afeta as estruturas de matéria branca com a perda de axónios na presença de uma condição neuropatológica como a TLE. Apesar do resultado final positivo, tendo em conta a meta previamente estabelecida, está aberto o caminho para o seu aperfeiçoamento, tendo em vista as direções futuras que emergem naturalmente desta dissertação. Como exemplo disso, poder-se-á recorrer ao estudo pormenorizado das metodologias técnicas associadas à abordagem apresentada que tem por base a análise das métricas de difusão ao longo dos tratos de matéria branca, uma vez que o desvio padrão associado a cada valor atribuído pelas diversas métricas foi significativo, o que de alguma forma poderá ter influenciado os resultados e, consequentemente, as conclusões deles extraídas, tendo em vista a sua viabilidade enquanto aplicação clínica. Como nota final, gostaria apenas de salientar que a imagiologia por difusão e, em particular, a tractografia têm ainda muito espaço para progredir. A veracidade desta afirmação traduz-se pela existência de uma grande variedade de modelos e algoritmos implementados, bem como de técnicas e metodologias de análise à informação microestrutural retida tendo por base o perfil de difusão que carateriza cada trato em estudo, sem que no entanto, exista consenso na comunidade científica acerca da melhor abordagem a seguir.Diffusion-weighted magnetic resonance imaging (dMRI) is a non-invasive imaging method which has been successfully applied to study white matter (WM) in order to determine physiological information and infer tissue microstructure. The human body is filled with barriers affecting the mobility of molecules and preventing it from being constant in different directions (anisotropic diffusion). In the brain, the sources for this anisotropy arise from dense packing axons and from the myelin sheath that surrounds them. Diffusion Tensor Imaging (DTI) is widely used to extract fibre directions from diffusion data, but it fails in regions containing multiple fibre orientations. The constrained spherical deconvolution technique had been proposed to address this limitation. It provides an estimate of the fibre orientation distribution that is robust to noise whilst preserving angular resolution. As a noninvasive technique that generates a three-dimensional reconstruction of neuronal fibres, tractography is able to map in vivo the human WM based on the reconstruct of the fibre orientations from the diffusion profile. Most of the tractography studies use a “tract-averaged” approach to analysis, however it is well known that there is a prominent variation in diffusion metrics within WM tracts. In this study we address the challenge of defining a microstructural signature taking into account the potentially rich anatomical variation in diffusion metrics along the tracts. Therefore, a workflow to conduct along-tract analysis of WM tracts (namely, arcuate fasciculus, corticospinal and corpus callosum) and integrate not only DTI derived measures, but also more advanced parameters from Mean Apparent Propagator-Magnetic Resonance Imaging (MAP-MRI) and Neurite Orientation Dispersion and Density Imaging (NODDI) model, was developed across healthy controls and patients with Temporal Lobe Epilepsy (TLE). Beyond the true biological variation in diffusion properties along tracts, this technique was applied to show that it allows a more detailed analysis of small regions-of-interest extracted from the tract in order to avoid fibres from WM pathways in the neighbourhood, which might lead to equivocal biological interpretations of the microstructural parameters. Consequently, the along-tract streamline distribution from the centrum semiovale, which is known to be a complex fibre geometry with multiple fibres populations from arcuate fasciculus, corticospinal and corpus callosum, was investigated. Finally, to validate our approach and highlight the strength of this extensible framework, two other methods were implemented in order to support the conclusions derived from the along-tract analysis computed between-groups. Firstly, a tract-based spatial statistics (TBSS) analysis was performed to study the WM change patterns across the whole brain in patients with TLE, and explore the alteration of multiple diffusion metrics. This voxel-based technique provides a powerful and objective method to perform multi-subject comparison, based on voxel-wise statistics of diffusion metrics but simultaneous aiming to minimize the effects of misalignment using a conventional voxel-based analysis method. With this in mind, the results showed increased diffusivity and reduced diffusion anisotropy, suggesting a loss of structural organization and expansion of the extracellular space in the presence of neuropathological condition as TLE. Secondly, the fixel-based analysis (FBA) was performed allowing a comprehensive statistical analysis of WM quantitative measures in order to have access to changes that may result within WM tracts in the presence of TLE. The microstructural/macrostructural changes in WM tracts of TLE patients were observed in temporal and extratemporal regions of both hemispheres, which agrees with the concept that epilepsy is a network disorder

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

Extraction of Structural Metrics from Crossing Fiber Models

Diffusion MRI (dMRI) measurements allow us to infer the microstructural properties of white matter and to reconstruct fiber pathways in-vivo. High angular diffusion imaging (HARDI) allows for the creation of more and more complex local models connecting the microstructure to the measured signal. One of the challenges is the derivation of meaningful metrics describing the underlying structure from the local models. The aim hereby is to increase the specificity of the widely used metric fractional anisotropy (FA) by using the additional information contained within the HARDI data. A local model which is connected directly to the underlying microstructure through the model of a single fiber population is spherical deconvolution. It produces a fiber orientation density function (fODF), which can often be interpreted as superposition of multiple peaks, each associated to one relatively coherent fiber population (bundle). Parameterizing these peaks one is able to disentangle and characterize these bundles. In this work, the fODF peaks are approximated by Bingham distributions, capturing first and second order statistics of the fiber orientations, from which metrics for the parametric quantification of fiber bundles are derived. Meaningful relationships between these measures and the underlying microstructural properties are proposed. The focus lies 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. These metrics are compared to the conventionally used fractional anisotropy (FA) and it is shown how they may help to increase the specificity of the characterization of microstructural properties. Visualization of the micro-structural arrangement is another application of dMRI. This is done by using tractography to propagate the fiber layout, extracted from the local model, in each voxel. In practice most tractography algorithms use little of the additional information gained from HARDI based local models aside from the reconstructed fiber bundle directions. In this work an approach to tractography based on the Bingham parameterization of the fODF is introduced. For each of the fiber populations present in a voxel the diffusion signal and tensor are computed. Then tensor deflection tractography is performed. This allows incorporating the complete bundle information, performing local interpolation as well as using multiple directions per voxel for generating tracts. Another aspect of this work is the investigation of the spherical harmonic representation which is used most commonly for the fODF by means of the parameters derived from the Bingham distribution fit. Here a strong connection between the approximation errors in the spherical representation of the Dirac delta function and the distribution of crossing angles recovered from the fODF was discovered. The final aspect of this work is the application of the metrics derived from the Bingham fit to a number of fetal datasets for quantifying the brain’s development. This is done by introducing the Gini-coefficient as a metric describing the brain’s age

Denoising and fast diffusion imaging with physically constrained sparse dictionary learning

International audienceDiffusion-weighted imaging (DWI) allows imaging the geometry of water diffusion in biological tissues. However, DW images are noisy at high b-values and acquisitions are slow when using a large number of measurements, such as in Diffusion Spectrum Imaging (DSI). This work aims to denoise DWI and reduce the number of required measurements, while maintaining data quality. To capture the structure of DWI data, we use sparse dictionary learning constrained by the physical properties of the signal: symmetry and positivity. The method learns a dictionary of diffusion profiles on all the DW images at the same time and then scales to full brain data. Its performance is investigated with simulations and two real DSI datasets. We obtain better signal estimates from noisy measurements than by applying mirror symmetry through the q-space origin, Gaussian denoising or state-of- the-art non-local means denoising. Using a high-resolution dictionary learnt on another subject, we show that we can reduce the number of images acquired while still generating high resolution DSI data. Using dictionary learning, one can denoise DW images effectively and perform faster acquisitions. Higher b-value acquisitions and DSI techniques are possible with approximately 40 measurements. This opens important perspectives for the connectomics community using DSI

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