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

RECOVERING LOCAL NEURAL TRACT DIRECTIONS AND RECONSTRUCTING NEURAL PATHWAYS IN HIGH ANGULAR RESOLUTION DIFFUSION MRI

Magnetic resonance imaging (MRI) is an imaging technique to visualize internal structures of the body. Diffusion MRI is an MRI modality that measures overall diffusion effect of molecules in vivo and non-invasively. Diffusion tensor imaging (DTI) is an extended technique of diffusion MRI. The major application of DTI is to measure the location, orientation and anisotropy of fiber tracts in white matter. It enables non-invasive investigation of major neural pathways of human brain, namely tractography. As spatial resolution of MRI is limited, it is possible that there are multiple fiber bundles within the same voxel. However, diffusion tensor model is only capable of resolving a single direction. The goal of this dissertation is to investigate complex anatomical structures using high angular resolution diffusion imaging (HARDI) data without any assumption on the parameters. The dissertation starts with a study of the noise distribution of truncated MRI data. The noise is often not an issue in diffusion tensor model. However, in HARDI studies, with many more gradient directions being scanned, the number of repetitions of each gradient direction is often small to restrict total acquisition time, making signal-to-noise ratio (SNR) lower. Fitting complex diffusion models to data with reduced SNR is a major interest of this study. We focus on fitting diffusion models to data using maximum likelihood estimation (MLE) method, in which the noise distribution is used to maximize the likelihood. In addition to the parameters being estimated, we use likelihood values for model selection when multiple models are fit to the same data. The advantage of carrying out model selection after fitting the models is that both the quality of data and the quality of fitting results are taken into account. When it comes to tractography, we extend streamline method by using covariance of the estimated parameters to generate probabilistic tracts according to the uncertainty of local tract orientations

From Diffusion to Tracts

Diffusion of water molecules within the brain tissue can be used to modulate the nuclear magnetic resonance signal that is used to form magnetic resonance images (MRI). As the signal itself can be noisy and its meaning challenging to interpret, mathematical models are generally fitted to these measurements to obtain the more accurate characterization of the brain microstructure. This, of course, requires that the mathematical model itself is sound in respect to the measurement setup. This dissertation focuses on the extensively used tensor models as they have been shown to unravel details of the physical diffusion phenomena along with various applications in the basic neuroscience, the clinical research, and even in the neurosurgery. One of the greatest challenges in the diffusion weighted MRI measurements is subject motion during the image acquisition as that can cause a complete loss of the measurement which is especially highlighted in ill or uncooperative patients studies. Due to the used acquisition technique, this loss extends to multiple measurements simultaneously resulting in an enormous gap in the sampling. Such gaps can be problematic for any model fitting, even for the currently available robust means developed to exclude outlier measurements from affecting the estimate. Hence in this dissertation, a tool coined as SOLID was developed to detect these outliers and to robustly process them during the tensor based model estimation. SOLID was implemented as a part of the widely used ExploreDTI toolbox to allow the rapid international distribution of the tool. Unfortunately, any reduction in the measurement sampling will lead to increasing error propagation during the model estimation. Mathematically this is detailed in terms of a condition number for the matrix inversion in the linear least squares fitting. Previously, the condition number has been used to optimize the diffusion weighted MRI acquisition gradient scheme but in this dissertation it was renovated into a novel quality control tool. The condition number of the matrix inversion that provides the model estimate can be calculated after the outliers are excluded to assess spatially and directionally varying error propagation to obviate any bias in subject or population studies. To motivate the importance of the robust methods and diffusion weighted MRI at large, neurocognitive studies with neonates’ visual abilities and bilinguals’ acquisition age of the second language were conducted as a part of this thesis. The findings in these studies indicated that premature birth affects the white matter structures across the brain whereas the age of acquisition of the second language affects only the speech related brain structures.Aivojen rakenteessa tapahtuvien muutosten mittaaminen on avainasemassa tutkittaessa esimerkiksi keskosena syntyneen lapsen kehitystä tai uusien taitojen, kuten kielten, oppimista. Ihmisaivojen tutkiminen on aiemmin rajoittunut aivojen toiminnan arviointiin aivosähkökäyrän ja neurokognitiivisten testien avulla. Viime vuosikymmenten kehitys magneettikuvaustekniikassa on tuonut mahdollisuuden tutkia kajoamattomasti myös aivojen rakennetta ja jopa seurata sen muutosta lapsen kasvaessa tai ihmisen oppiessa uusia taitoja. Yksi lupaavimmista aivojen tutkimusmenetelmistä on diffuusiopainotettu magneettikuvaus, jolle on löytynyt lukuisia käyttökohteita niin neurotieteessä, lääketieteellisissä tutkimuksissa kuin neurokirurgiassakin. Menetelmä perustuu vesimolekyylien lämpöliikkeen mittaamiseen aivoissa. Molekyylien liike on vapaata muun muassa valkean aineen rakenteiden myötäisesti, mutta lähes mahdotonta kohtisuoraan niiden lävitse. Jäljittämällä nämä reitit voidaan muodostaa tarkka malli aivojen rakenteesta. Mallin pohjalta on mahdollista laskea kuvaavia arvoja, jotka auttavat esimerkiksi määrittämään aivovaurion astetta. Diffuusiopainotetun magneettikuvauksen suurin haaste on menetelmän monimutkaisuus sekä mittauksen että analyysin osalta. Vain hyvin yksinkertaisissa tapauksissa asiantuntija voi arvioida suoraan diffuusiopainotetusta magneettikuvasta poikkeamia aivoissa. Yleensä käytetään matemaattisia menetelmiä kuvan tarkempaan analysointiin. Tällöin keskeistä on inversio-ongelman ratkaisu, missä potilaasta tehdyt mittaukset sovitetaan aivoja kuvaavaan matemaattiseen malliin. Sopivan mallin valinnalla on siis suuri vaikutus lopputuloksen hyödyllisyyteen. Diffuusiopainotettu magneettikuvaus on myös häiriöherkkä ja mittaukset sisältävät luonnostaan paljon kohinaa, jonka vaikutusta vähennetään tekemällä toistomittauksia. Toistomittaukset pidentävät kuvausaikaa, joka puolestaan voi olla haasteellinen potilaalle, koska potilaan pitää olla liikkumatta koko kuvauksen ajan. Potilaan pään pienikin liike voi johtaa huomattaviin mittavirheisiin, koska menetelmällä mitataan vesimolekyylien liikettä, jonka suuruus on vain kymmenien mikrometrien luokkaa. Tässä fysiikan väitöskirjassa keskityttiin diffuusiopainotetun magneettikuvauksen mallintamismenetelmien kehitystyöhön ja niiden käyttöönottoon Helsingin yliopistollisessa sairaalassa. Kehitimme kansainvälistä huomiota herättäneen SOLID-työkalun, jolla voidaan havaita sekä korjata potilaan liikkeestä aiheutuvia virheitä mittaustuloksissa. Tämän lisäksi esitimme laadunvalvonta menetelmän, jolla voidaan arvioida esimerkiksi potilaiden välisten mallinnustulosten vertailukelpoisuutta. Kehitettyjä menetelmiä testattiin ja sovellettiin kahdessa tutkimuksessa: Osoitimme, että vastasyntyneen lapsen kyky seurata katseellaan liikkuvaa kohdetta liittyy laaja-alaisiin muutoksiin aivojen valkean aineen rakenteessa. Lisäksi näytimme, että toisen kielen oppimisajankohta vaikuttaa aivojen puheentuottoon liittyvien aivorakenteiden muodostumiseen

Axonal T₂ estimation using the spherical variance of the strongly diffusion-weighted MRI signal.

In magnetic resonance imaging, the application of a strong diffusion weighting suppresses the signal contributions from the less diffusion-restricted constituents of the brain's white matter, thus enabling the estimation of the transverse relaxation time T <sub>2</sub> that arises from the more diffusion-restricted constituents such as the axons. However, the presence of cell nuclei and vacuoles can confound the estimation of the axonal T <sub>2</sub> , as diffusion within those structures is also restricted, causing the corresponding signal to survive the strong diffusion weighting. We devise an estimator of the axonal T <sub>2</sub> based on the directional spherical variance of the strongly diffusion-weighted signal. The spherical variance T <sub>2</sub> estimates are insensitive to the presence of isotropic contributions to the signal like those provided by cell nuclei and vacuoles. We show that with a strong diffusion weighting these estimates differ from those obtained using the directional spherical mean of the signal which contains both axonal and isotropically-restricted contributions. Our findings hint at the presence of an MRI-visible isotropically-restricted contribution to the signal in the white matter ex vivo fixed tissue (monkey) at 7T, and do not allow us to discard such a possibility also for in vivo human data collected with a clinical 3T system

Incorporating outlier information into diffusion-weighted MRI modeling for robust microstructural imaging and structural brain connectivity analyses

A B S T R A C T The white matter structures of the human brain can be represented using diffusion-weighted MRI tractography. Unfortunately, tractography is prone to find false-positive streamlines causing a severe decline in its specificity and limiting its feasibility in accurate structural brain connectivity analyses. Filtering algorithms have been pro-posed to reduce the number of invalid streamlines but the currently available filtering algorithms are not suitable to process data that contains motion artefacts which are typical in clinical research. We augmented the Con-vex Optimization Modelling for Microstructure Informed Tractography (COMMIT) algorithm to adjust for these signals drop-out motion artefacts. We demonstrate with comprehensive Monte-Carlo whole brain simulations and in vivo infant data that our robust algorithm is capable of properly filtering tractography reconstructions despite these artefacts. We evaluated the results using parametric and non-parametric statistics and our results demonstrate that if not accounted for, motion artefacts can have severe adverse effects in human brain structural connectivity analyses as well as in microstructural property mappings. In conclusion, the usage of robust filtering methods to mitigate motion related errors in tractogram filtering is highly beneficial, especially in clinical stud-ies with uncooperative patient groups such as infants. With our presented robust augmentation and open-source implementation, robust tractogram filtering is readily available.Peer reviewe

On noise, uncertainty and inference for computational diffusion MRI

Diffusion Magnetic Resonance Imaging (dMRI) has revolutionised the way brain microstructure and connectivity can be studied. Despite its unique potential in mapping the whole brain, biophysical properties are inferred from measurements rather than being directly observed. This indirect mapping from noisy data creates challenges and introduces uncertainty in the estimated properties. Hence, dMRI frameworks capable to deal with noise and uncertainty quantification are of great importance and are the topic of this thesis. First, we look into approaches for reducing uncertainty, by de-noising the dMRI signal. Thermal noise can have detrimental effects for modalities where the information resides in the signal attenuation, such as dMRI, that has inherently low-SNR data. We highlight the dual effect of noise, both in increasing variance, but also introducing bias. We then design a framework for evaluating denoising approaches in a principled manner. By setting objective criteria based on what a well-behaved denoising algorithm should offer, we provide a bespoke dataset and a set of evaluations. We demonstrate that common magnitude-based denoising approaches usually reduce noise-related variance from the signal, but do not address the bias effects introduced by the noise floor. Our framework also allows to better characterise scenarios where denoising can be beneficial (e.g. when done in complex domain) and can open new opportunities, such as pushing spatio-temporal resolution boundaries. Subsequently, we look into approaches for mapping uncertainty and design two inference frameworks for dMRI models, one using classical Bayesian methods and another using more recent data-driven algorithms. In the first approach, we build upon the univariate random-walk Metropolis-Hastings MCMC, an extensively used sampling method to sample from the posterior distribution of model parameters given the data. We devise an efficient adaptive multivariate MCMC scheme, relying upon the assumption that groups of model parameters can be jointly estimated if a proper covariance matrix is defined. In doing so, our algorithm increases the sampling efficiency, while preserving accuracy and precision of estimates. We show results using both synthetic and in-vivo dMRI data. In the second approach, we resort to Simulation-Based Inference (SBI), a data-driven approach that avoids the need for iterative model inversions. This is achieved by using neural density estimators to learn the inverse mapping from the forward generative process (simulations) to the parameters of interest that have generated those simulations. By addressing the problem via learning approaches offers the opportunity to achieve inference amortisation, boosting efficiency by avoiding the necessity of repeating the inference process for each new unseen dataset. It also allows inversion of forward processes (i.e. a series of processing steps) rather than only models. We explore different neural network architectures to perform conditional density estimation of the posterior distribution of parameters. Results and comparisons obtained against MCMC suggest speed-ups of 2-3 orders of magnitude in the inference process while keeping the accuracy in the estimates

Local estimation of the noise level in MRI using structural adaptation

We present a method for local estimation of the signal-dependent noise level in magnetic resonance images. The procedure uses a multi-scale approach to adaptively infer on local neighborhoods with similar data distribution. It exploits a maximum-likelihood estimator for the local noise level. The validity of the method was evaluated on repeated diffusion data of a phantom and simulated data using T1-data corrupted with artificial noise. Simulation results are compared with a recently proposed estimate. The method was applied to a high-resolution diffusion dataset to obtain improved diffusion model estimation results and to demonstrate its usefulness in methods for enhancing diffusion data

On noise, uncertainty and inference for computational diffusion MRI

Diffusion Magnetic Resonance Imaging (dMRI) has revolutionised the way brain microstructure and connectivity can be studied. Despite its unique potential in mapping the whole brain, biophysical properties are inferred from measurements rather than being directly observed. This indirect mapping from noisy data creates challenges and introduces uncertainty in the estimated properties. Hence, dMRI frameworks capable to deal with noise and uncertainty quantification are of great importance and are the topic of this thesis. First, we look into approaches for reducing uncertainty, by de-noising the dMRI signal. Thermal noise can have detrimental effects for modalities where the information resides in the signal attenuation, such as dMRI, that has inherently low-SNR data. We highlight the dual effect of noise, both in increasing variance, but also introducing bias. We then design a framework for evaluating denoising approaches in a principled manner. By setting objective criteria based on what a well-behaved denoising algorithm should offer, we provide a bespoke dataset and a set of evaluations. We demonstrate that common magnitude-based denoising approaches usually reduce noise-related variance from the signal, but do not address the bias effects introduced by the noise floor. Our framework also allows to better characterise scenarios where denoising can be beneficial (e.g. when done in complex domain) and can open new opportunities, such as pushing spatio-temporal resolution boundaries. Subsequently, we look into approaches for mapping uncertainty and design two inference frameworks for dMRI models, one using classical Bayesian methods and another using more recent data-driven algorithms. In the first approach, we build upon the univariate random-walk Metropolis-Hastings MCMC, an extensively used sampling method to sample from the posterior distribution of model parameters given the data. We devise an efficient adaptive multivariate MCMC scheme, relying upon the assumption that groups of model parameters can be jointly estimated if a proper covariance matrix is defined. In doing so, our algorithm increases the sampling efficiency, while preserving accuracy and precision of estimates. We show results using both synthetic and in-vivo dMRI data. In the second approach, we resort to Simulation-Based Inference (SBI), a data-driven approach that avoids the need for iterative model inversions. This is achieved by using neural density estimators to learn the inverse mapping from the forward generative process (simulations) to the parameters of interest that have generated those simulations. By addressing the problem via learning approaches offers the opportunity to achieve inference amortisation, boosting efficiency by avoiding the necessity of repeating the inference process for each new unseen dataset. It also allows inversion of forward processes (i.e. a series of processing steps) rather than only models. We explore different neural network architectures to perform conditional density estimation of the posterior distribution of parameters. Results and comparisons obtained against MCMC suggest speed-ups of 2-3 orders of magnitude in the inference process while keeping the accuracy in the estimates