Isotropic non-white matter partial volume effects in constrained spherical deconvolution

Diffusion-weighted (DW) magnetic resonance imaging (MRI) is a non-invasive imaging method, which can be used to investigate neural tracts in the white matter (WM) of the brain. Significant partial volume effects (PVEs) are present in the DVV signal due to relatively large voxel sizes. These PVEs can be caused by both non-WM tissue, such as gray matter (GM) and cerebrospinal fluid (CSF), and by multiple non-parallel WM fiber populations. High angular resolution diffusion imaging (HARDI) methods have been developed to correctly characterize complex WM fiber configurations, but to date, many of the HARDI methods do not account for non-WM PVEs. In this work, we investigated the isotropic PVEs caused by non-WM tissue in WM voxels on fiber orientations extracted with constrained spherical deconvolution (CSD). Experiments were performed on simulated and real DW-MRI data. In particular, simulations were performed to demonstrate the effects of varying the diffusion weightings, signal-to-noise ratios (SNRs), fiber configurations, and tissue fractions. Our results show that the presence of non-WM tissue signal causes a decrease in the precision of the detected fiber orientations and an increase in the detection of false peaks in CSD. We estimated 35-50% of WM voxels to be affected by non-WM PVEs. For HARDI sequences, which typically have a relatively high degree of diffusion weighting, these adverse effects are most pronounced in voxels with GM PVEs. The non-WM PVEs become severe with 50% GM volume for maximum spherical harmonics orders of 8 and below, and already with 25% GM volume for higher orders. In addition, a low diffusion weighting or SNR increases the effects. The non-WM PVEs may cause problems in connectomics, where reliable fiber tracking at the WM G M interface is especially important. We suggest acquiring data with high diffusion-weighting 2500-3000 s/mm(2), reasonable SNR (similar to 30) and using lower SH orders in GM contaminated regions to minimize the non-WM PVEs in CSD

Spherical deconvolution of multichannel diffusion MRI data with non-Gaussian noise models and spatial regularization

Spherical deconvolution (SD) methods are widely used to estimate the intra-voxel white-matter fiber orientations from diffusion MRI data. However, while some of these methods assume a zero-mean Gaussian distribution for the underlying noise, its real distribution is known to be non-Gaussian and to depend on the methodology used to combine multichannel signals. Indeed, the two prevailing methods for multichannel signal combination lead to Rician and noncentral Chi noise distributions. Here we develop a Robust and Unbiased Model-BAsed Spherical Deconvolution (RUMBA-SD) technique, intended to deal with realistic MRI noise, based on a Richardson-Lucy (RL) algorithm adapted to Rician and noncentral Chi likelihood models. To quantify the benefits of using proper noise models, RUMBA-SD was compared with dRL-SD, a well-established method based on the RL algorithm for Gaussian noise. Another aim of the study was to quantify the impact of including a total variation (TV) spatial regularization term in the estimation framework. To do this, we developed TV spatially-regularized versions of both RUMBA-SD and dRL-SD algorithms. The evaluation was performed by comparing various quality metrics on 132 three-dimensional synthetic phantoms involving different inter-fiber angles and volume fractions, which were contaminated with noise mimicking patterns generated by data processing in multichannel scanners. The results demonstrate that the inclusion of proper likelihood models leads to an increased ability to resolve fiber crossings with smaller inter-fiber angles and to better detect non-dominant fibers. The inclusion of TV regularization dramatically improved the resolution power of both techniques. The above findings were also verified in brain data

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

NODDI-SH: a computational efficient NODDI extension for fODF estimation in diffusion MRI

Diffusion Magnetic Resonance Imaging (DMRI) is the only non-invasive imaging technique which is able to detect the principal directions of water diffusion as well as neurites density in the human brain. Exploiting the ability of Spherical Harmonics (SH) to model spherical functions, we propose a new reconstruction model for DMRI data which is able to estimate both the fiber Orientation Distribution Function (fODF) and the relative volume fractions of the neurites in each voxel, which is robust to multiple fiber crossings. We consider a Neurite Orientation Dispersion and Density Imaging (NODDI) inspired single fiber diffusion signal to be derived from three compartments: intracellular, extracellular, and cerebrospinal fluid. The model, called NODDI-SH, is derived by convolving the single fiber response with the fODF in each voxel. NODDI-SH embeds the calculation of the fODF and the neurite density in a unified mathematical model providing efficient, robust and accurate results. Results were validated on simulated data and tested on \textit{in-vivo} data of human brain, and compared to and Constrained Spherical Deconvolution (CSD) for benchmarking. Results revealed competitive performance in all respects and inherent adaptivity to local microstructure, while sensibly reducing the computational cost. We also investigated NODDI-SH performance when only a limited number of samples are available for the fitting, demonstrating that 60 samples are enough to obtain reliable results. The fast computational time and the low number of signal samples required, make NODDI-SH feasible for clinical application

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

E(3)×SO(3)E(3) \times SO(3)-Equivariant Networks for Spherical Deconvolution in Diffusion MRI

We present Roto-Translation Equivariant Spherical Deconvolution (RT-ESD), an $E(3)\times SO(3)$ equivariant framework for sparse deconvolution of volumes where each voxel contains a spherical signal. Such 6D data naturally arises in diffusion MRI (dMRI), a medical imaging modality widely used to measure microstructure and structural connectivity. As each dMRI voxel is typically a mixture of various overlapping structures, there is a need for blind deconvolution to recover crossing anatomical structures such as white matter tracts. Existing dMRI work takes either an iterative or deep learning approach to sparse spherical deconvolution, yet it typically does not account for relationships between neighboring measurements. This work constructs equivariant deep learning layers which respect to symmetries of spatial rotations, reflections, and translations, alongside the symmetries of voxelwise spherical rotations. As a result, RT-ESD improves on previous work across several tasks including fiber recovery on the DiSCo dataset, deconvolution-derived partial volume estimation on real-world \textit{in vivo} human brain dMRI, and improved downstream reconstruction of fiber tractograms on the Tractometer dataset. Our implementation is available at https://github.com/AxelElaldi/e3so3_convComment: Accepted to Medical Imaging with Deep Learning (MIDL) 2023. Code available at https://github.com/AxelElaldi/e3so3_conv . 19 pages with 6 figure

Empirical comparison of diffusion kurtosis imaging and diffusion basis spectrum imaging using the same acquisition in healthy young adults

As diffusion tensor imaging gains widespread use, many researchers have been motivated to go beyond the tensor model and fit more complex diffusion models, to gain a more complete description of white matter microstructure and associated pathology. Two such models are diffusion kurtosis imaging (DKI) and diffusion basis spectrum imaging (DBSI). It is not clear which DKI parameters are most closely related to DBSI parameters, so in the interest of enabling comparisons between DKI and DBSI studies, we conducted an empirical survey of the interrelation of these models in 12 healthy volunteers using the same diffusion acquisition. We found that mean kurtosis is positively associated with the DBSI fiber ratio and negatively associated with the hindered ratio. This was primarily driven by the radial component of kurtosis. The axial component of kurtosis was strongly and specifically correlated with the restricted ratio. The joint spatial distributions of DBSI and DKI parameters are tissue-dependent and stable across healthy individuals. Our contribution is a better understanding of the biological interpretability of the parameters generated by the two models in healthy individuals

Improving Fiber Alignment in HARDI by Combining Contextual PDE Flow with Constrained Spherical Deconvolution

We propose two strategies to improve the quality of tractography results computed from diffusion weighted magnetic resonance imaging (DW-MRI) data. Both methods are based on the same PDE framework, defined in the coupled space of positions and orientations, associated with a stochastic process describing the enhancement of elongated structures while preserving crossing structures. In the first method we use the enhancement PDE for contextual regularization of a fiber orientation distribution (FOD) that is obtained on individual voxels from high angular resolution diffusion imaging (HARDI) data via constrained spherical deconvolution (CSD). Thereby we improve the FOD as input for subsequent tractography. Secondly, we introduce the fiber to bundle coherence (FBC), a measure for quantification of fiber alignment. The FBC is computed from a tractography result using the same PDE framework and provides a criterion for removing the spurious fibers. We validate the proposed combination of CSD and enhancement on phantom data and on human data, acquired with different scanning protocols. On the phantom data we find that PDE enhancements improve both local metrics and global metrics of tractography results, compared to CSD without enhancements. On the human data we show that the enhancements allow for a better reconstruction of crossing fiber bundles and they reduce the variability of the tractography output with respect to the acquisition parameters. Finally, we show that both the enhancement of the FODs and the use of the FBC measure on the tractography improve the stability with respect to different stochastic realizations of probabilistic tractography. This is shown in a clinical application: the reconstruction of the optic radiation for epilepsy surgery planning

Automatic selection of multiple response functions for generalized Richardson-Lucy spherical deconvolution of diffusion MRI data

Tese de mestrado integrado em Engenharia Biomédica e Biofísica (Sinais e Imagens Médicas), Universidade de Lisboa, Faculdade de Ciências, 2021O processo de desenvolvimento do cérebro humano tem sido objeto de estudo desde há vários anos, levando a avanços significativos no que diz respeito à compreensão das suas diferentes fases e mecanismos. Visto que este desenvolvimento resulta de uma série de complexos processos dinâmicos e adaptativos, existe uma busca contínua de informação sobre a sua organização estrutural e funcional, bem como o seu processo de maturação. A ressonância magnética de difusão (dMRI) é uma técnica bastante completa no que diz respeito à análise do cérebro in vivo. Esta técnica é utilizada para realizar um mapeamento quantitativo, através da aplicação de modelos como o modelo de difusão tensorial (DTI). Estes modelos fornecem medidas que caracterizam o cérebro, tais como a anisotropia fraccional (FA) e difusividade média (MD), permitindo assim a quantificação de microestruturas e consequentemente a reconstrução de feixes de substância branca (WM) que ligam diferentes regiões cerebrais. Dadas as suas propriedades de difusão anisotrópica e a sua constituição fibrosa, as fibras de WM têm sido amplamente estudadas através da dMRI. Além disso, a tractografia tornou-se a abordagem padrão no que diz respeito à avaliação da conectividade cerebral usando dados de dMRI. Os métodos de desconvolução esférica (SD) estão entre os mais utilizados para quantificar a distribuição da orientação das fibras (FOD) a partir de dados dMRI do cérebro, sendo que a forma mais comum de o fazer é com desconvolução esférica limitada (CSD). A ideia original da CSD baseia-se no facto de podermos escolher uma função de resposta (RF) representativa de um determinado tecido presente no cérebro e aplicar a SD para resolver o problema de cruzamento de fibras que o modelo de DTI não consegue resolver. Uma vez que o cérebro possui uma complexa organização de tecidos, múltiplos tecidos devem ser considerados. Não é apropriado usar uma RF de WM em todo o cérebro, pois isso pode levar a reconstruções imprecisas da orientação das fibras e a um mau desempenho durante o processo de tractografia. Ao ter em conta múltiplos tecidos, as propriedades da substância cinzenta (GM) e do líquido céfalo-raquidiano (CSF) podem ser quantificadas, e os efeitos de volume parcial (PVE) podem ser reduzidos. Nos últimos anos, tem sido possível adquirir dados “multi-camada” mais complexos e de elevada resolução, mesmo em recém-nascidos, o que permitiu melhorar a técnica de CSD. Consequentemente, esta aquisição também vai melhorar a reconstrução da FOD no cérebro adulto, pois considera os PVE entre diferentes tipos de tecidos. No cérebro neonatal existem algumas diferenças, pois este é constituído por WM em diferentes fases de maturação, e a GM possui características diferentes em comparação com um cérebro adulto. A possibilidade de distinguir diferentes tipos de fibras apenas com base nas suas características microestruturais deve-se às diferenças presentes no cérebro enquanto este se encontra numa fase de desenvolvimento. Em cérebros adultos, é menos provável conseguir observar tais diferenças. Uma das melhores formas de compreender e estudar estes processos de desenvolvimento cerebral é através do estudo do cérebro de neonatais. Como seria de esperar, o cérebro de um recém-nascido não se encontra completamente maturado, sofrendo por isso diversas alterações até estar totalmente desenvolvido. Estas mudanças vão desde o aumento do tamanho do cérebro a alterações ao nível vascular, levando consequentemente a uma alteração dos processos de cognitivos. Em última análise, a aplicação de CSD a dados de “multi-camada” leva a uma extração mais precisa da FOD que por sua vez irá melhorar o processo de tractografia e levará, consequentemente, a uma melhor compreensão do cérebro humano e do seu desenvolvimento, particularmente se aplicada em recém-nascidos e comparada com adultos. O método Generalized Richardson-Lucy (GRL) pode superar os problemas encontrados pela CSD através da realização de SD robusta, suprimindo picos imprecisos na FOD em dados “multi-camada” de dMRI. Este método pode definir múltiplos tecidos que irão aumentar a precisão da estimativa da FOD. No entanto, no método GRL, as três classes de tecidos representadas (WM, GM e CSF) são pré-definidas com valores FA e MD retirados da literatura. Este estudo consistiu em desenvolver um método que determina automaticamente o número de classes (tecidos) necessárias para aplicar corretamente GRL no cérebro com dados “multi-camada”, utilizando para isso os seus valores de FA e MD. O objetivo é aplicar corretamente o método de GRL no cérebro com as classes obtidas, de forma avaliar se existe uma melhoria no processo de estimação das FOD e por sua vez no processo de tractografia. Os dados utilizados neste trabalho consistem em dados de dMRI de dez neonatais e dez adultos, fornecidos pelo Developing Human Connectome Project (dHCP) e pelo Human Connectome Project (HCP), respetivamente. Estes dados já se encontravam num formato pré-processado, pelo que não foi necessário realizar qualquer etapa adicional neste sentido. A primeira parte do estudo consistiu no desenvolvimento do método de deteção automática do número de tipos de tecidos no cérebro. Para isso, todos os dados foram processados no ExploreDTI, um programa de interface gráfica para dados de dMRI e que permite, por exemplo, a realização de tractografia. Este programa foi também usado para extrair os valores de FA e MD dos dados de dMRI dos cérebros dos neonatais e dos adultos, de modo a analisar a sua distribuição de valores por todo o cérebro através de histogramas. De seguida foi aplicado um gaussian mixture model (GMM) aos histogramas de FA e MD, utilizando o MATLAB R2018a, de forma a decompor os dados em classes. Depois de aplicar o GMM aos dados, foi determinado o número ideal de Gaussianas para os mapas de FA e MD. Para isso foi calculado o Bayesian information criterion (BIC) de cada modelo, em que cada um destes se caracteriza por um certo número de Gaussianas. De seguida, foi calculada a probabilidade do valor de cada voxel pertencer a uma das classes escolhidas de FA e MD, atribuiu-se assim uma classe a cada voxel. Posteriormente selecionaram-se as três melhores combinações de FA e MD de cada classe com base na frequência de ocorrência de cada combinação, sendo que cada classe foi definida pela média e desvio padrão das respetivas Gaussianas. Por fim, foram criados mapas espaciais do cérebro com as classes finais, utilizando o MATLAB R2018a. Na segunda parte do estudo aplicou-se o método GRL aos dados, de forma a estimar a RF de cada um dos tecidos que foram selecionados na primeira parte. Estas duas partes do trabalho integram a nossa abordagem, sendo esta designada por "GRL-auto". No método GRL, a RF da GM e do CSF é baseada em valores de FA e MD retirados da literatura, enquanto que o método GRL-auto desenvolvido neste estudo estima esses valores através da seleção automática dos valores de FA e MD que são característicos de cada um destes tecidos. Obtiveram-se os mapas das frações de sinal da WM, GM, e CSF e foram feitas comparações entre o método GRL e GRL-auto. As FOD da WM obtidas com ambos os métodos foram comparadas entre si em regiões de cruzamento de fibras, tanto para neonatais como para os adultos. Por fim, para ambos os métodos, procedeu-se à tractografia em neonatais. Os resultados indicam que, tanto para recém-nascidos como para adultos, existe consistência em relação aos valores de FA e MD e ao seu respetivo número de classes selecionadas. Além disso, conseguem ser observadas diferentes fases de maturação de WM nos neonatais, mas também algumas imperfeições à volta dos ventrículos e regiões onde ocorre cruzamento de fibras. Todos os mapas espaciais de FA e MD fizeram sentido anatomicamente, sendo consistentes quer nos neonatais quer nos adultos, demonstrando assim a eficácia deste método. Os mapas de sinal das frações de WM, GM, e CSF apresentaram valores plausíveis e concordância com a anatomia esperada, para além de consistência tanto nos recém-nascidos como nos adultos. Os mapas de frações de sinal dos adultos praticamente não apresentaram diferenças entre os dois métodos. No entanto, os neonatais mostraram algumas diferenças notáveis, particularmente nos mapas de GM e CSF. Os resultados relativos às FODs não mostraram diferenças significativas no que diz respeito aos adultos. No entanto, para os neonatais, o método GRL-auto estimou FODs de elevada qualidade na WM, em comparação com o método GRL. Além disso, o método GRL-auto detetou mais picos plausíveis em regiões de cruzamento de fibras par além de uma diferença angular maior entre os principais picos das FOD, em comparação com o método GRL. Por fim, este método demonstrou uma melhoria no processo de tractografia, o que por sua vez levará a uma melhor compreensão do cérebro humano e do seu desenvolvimento. Conclui-se assim que o método desenvolvido neste estudo é eficiente e mostra consistência no que diz respeito ao processo de seleção automática do número de tecidos necessários para efetuar CSD no cérebro. Observou-se uma melhoria na tractografia das fibras, o que permitirá uma melhor compreensão da maturação do cérebro bem como das conexões entre as diversas regiões, tendo-se, assim, cumprido o objetivo principal deste trabalho.To understand the development of the human brain, more detailed information is required regarding the structural and functional cerebral organization and maturation. This development is the product of a complex series of dynamic and adaptive processes, and one of the best ways to understand it is through the study of the neonatal brain. The neonatal brain is not fully developed as it would be expected, so it goes through many changes regarding brain size, vasculature, and cognition. Constrained spherical deconvolution (CSD) is a widely used approach to quantify the fiber orientation distribution (FOD) from diffusion magnetic resonance imaging (dMRI) data of the brain, which allows the reconstruction of more complex white matter (WM) bundles in vivo, including in neonates. However, this method estimates the response function (RF) based on the model of a single fiber population and uses it to try to reconstruct the local WM orientations. Since the brain has a complex tissue organization, multiple tissues must be considered. It is not appropriate to use a WM RF throughout the whole brain because this can lead to spurious fiber orientation reconstructions and bad performance during fiber tractography. By accounting for multiple tissues, properties of grey matter (GM) and cerebrospinal fluid (CSF) can be captured, and partial volume effects (PVE) reduced. The acquisition of more comprehensive high-resolution multi-shell dMRI data offers opportunities to take into account multiple tissue types. Ultimately, these improve fiber tractography and consequently lead to a better understanding of the human brain and its development. The generalized Richardson-Lucy (GRL) method can overcome these challenges by performing robust spherical deconvolution (SD) and suppress spurious FOD peaks on multi-shell dMRI data due to PVE. However, in the GRL method, three tissue classes are typically pre-defined to represent WM, GM, and CSF, using fractional anisotropy (FA) and mean diffusivity (MD) values taken from literature. These two metrics are derived from the diffusion tensor model (DTI), with FA measuring how anisotropic is the tensor in each voxel and MD measuring the average of the diffusion rate at each voxel. This study aims to develop a method that automatically determines the number of tissue types (classes) that are needed to properly perform GRL in each analyzed brain dataset. The dataset used in this work consists of ten neonates and ten adults from the Developing Human Connectome Project (dHCP) and the Human Connectome Project (HCP), respectively. The first part of this study consisted of developing a method for the automatic detection of the number of tissue types in the brain, by applying a gaussian mixture model (GMM) and the Bayesian information criterion (BIC) to automatically extract the number of tissue classes from the histogram of dMRI properties. In the second part, the GRL method was applied to the data to estimate the RF of each tissue that was automatically chosen in the first part, and therefore calculate the FOD and perform fiber tractography. This approach was designated by “GRL-auto”. Lastly, a comparison between the basic GRL formulation and GRL-auto was done. Since GRL uses predefined values calibrated on HCP data, it becomes clear that small differences were expected on such dataset, whereas on dHCP larger differences were expected. Our analysis showed that our method automatically identified three classes in the FA histogram and two classes in the MD histogram when using HCP and dHCP data. Therefore, these results demonstrated consistency regarding the FA and MD values and their respective number of selected classes, for both datasets. Furthermore, different stages of WM maturation were detected in the dHCP data, but also some imperfections around the ventricles and crossing fibers areas. All FA and MD spatial maps were in line with anatomical correspondence and were consistent across all neonatal and adult subjects, demonstrating the efficiency of this method. The values of the WM, GM, and CSF fraction maps were plausible, in line with the expected anatomy, and looked consistent on both HCP and dHCP datasets. The signal fraction maps determined with the HCP data showed almost no difference between GRL and GRL-auto. However, in the dHCP data, we observed notable differences, particularly in the GM and CSF maps. Regarding the FOD estimation, our results showed no difference in the HCP data. Nevertheless, for the dHCP data, GRL-auto estimated high-quality FODs in WM, and detected more peaks in crossing fiber regions and a bigger angular difference between the main FOD peaks, as compared to GRL. Lastly, we showed that GRL-auto led to improvements in fiber tractography, which will likely support gaining a better understanding of the human brain and its development. Therefore, we can conclude that the method developed in this study is efficient and consistent in the automatic selection of the number of tissues needed to properly perform GRL in a brain, given multi-shell data, which was the main goal