Markov models for fMRI correlation structure: is brain functional connectivity small world, or decomposable into networks?

Correlations in the signal observed via functional Magnetic Resonance Imaging (fMRI), are expected to reveal the interactions in the underlying neural populations through hemodynamic response. In particular, they highlight distributed set of mutually correlated regions that correspond to brain networks related to different cognitive functions. Yet graph-theoretical studies of neural connections give a different picture: that of a highly integrated system with small-world properties: local clustering but with short pathways across the complete structure. We examine the conditional independence properties of the fMRI signal, i.e. its Markov structure, to find realistic assumptions on the connectivity structure that are required to explain the observed functional connectivity. In particular we seek a decomposition of the Markov structure into segregated functional networks using decomposable graphs: a set of strongly-connected and partially overlapping cliques. We introduce a new method to efficiently extract such cliques on a large, strongly-connected graph. We compare methods learning different graph structures from functional connectivity by testing the goodness of fit of the model they learn on new data. We find that summarizing the structure as strongly-connected networks can give a good description only for very large and overlapping networks. These results highlight that Markov models are good tools to identify the structure of brain connectivity from fMRI signals, but for this purpose they must reflect the small-world properties of the underlying neural systems

Computerized Analysis of Magnetic Resonance Images to Study Cerebral Anatomy in Developing Neonates

The study of cerebral anatomy in developing neonates is of great importance for the understanding of brain development during the early period of life. This dissertation therefore focuses on three challenges in the modelling of cerebral anatomy in neonates during brain development. The methods that have been developed all use Magnetic Resonance Images (MRI) as source data. To facilitate study of vascular development in the neonatal period, a set of image analysis algorithms are developed to automatically extract and model cerebral vessel trees. The whole process consists of cerebral vessel tracking from automatically placed seed points, vessel tree generation, and vasculature registration and matching. These algorithms have been tested on clinical Time-of- Flight (TOF) MR angiographic datasets. To facilitate study of the neonatal cortex a complete cerebral cortex segmentation and reconstruction pipeline has been developed. Segmentation of the neonatal cortex is not effectively done by existing algorithms designed for the adult brain because the contrast between grey and white matter is reversed. This causes pixels containing tissue mixtures to be incorrectly labelled by conventional methods. The neonatal cortical segmentation method that has been developed is based on a novel expectation-maximization (EM) method with explicit correction for mislabelled partial volume voxels. Based on the resulting cortical segmentation, an implicit surface evolution technique is adopted for the reconstruction of the cortex in neonates. The performance of the method is investigated by performing a detailed landmark study. To facilitate study of cortical development, a cortical surface registration algorithm for aligning the cortical surface is developed. The method first inflates extracted cortical surfaces and then performs a non-rigid surface registration using free-form deformations (FFDs) to remove residual alignment. Validation experiments using data labelled by an expert observer demonstrate that the method can capture local changes and follow the growth of specific sulcus

Fast and accurate Slicewise OutLIer Detection (SOLID) with informed model estimation for diffusion MRI data

The accurate characterization of the diffusion process in tissue using diffusion MRI is greatly challenged by the presence of artefacts. Subject motion causes not only spatial misalignments between diffusion weighted images, but often also slicewise signal intensity errors. Voxelwise robust model estimation is commonly used to exclude intensity errors as outliers. Slicewise outliers, however, become distributed over multiple adjacent slices after image registration and transformation. This challenges outlier detection with voxelwise procedures due to partial volume effects. Detecting the outlier slices before any transformations are applied to diffusion weighted images is therefore required. In this work, we present i) an automated tool coined SOLID for slicewise outlier detection prior to geometrical image transformation, and ii) a framework to naturally interpret data uncertainty information from SOLID and include it as such in model estimators. SOLID uses a straightforward intensity metric, is independent of the choice of the diffusion MRI model, and can handle datasets with a few or irregularly distributed gradient directions. The SOLID-informed estimation framework prevents the need to completely reject diffusion weighted images or individual voxel measurements by downweighting measurements with their degree of uncertainty, thereby supporting convergence and well-conditioning of iterative estimation algorithms. In comprehensive simulation experiments, SOLID detects outliers with a high sensitivity and specificity, and can achieve higher or at least similar sensitivity and specificity compared to other tools that are based on more complex and time-consuming procedures for the scenarios investigated. SOLID was further validated on data from 54 neonatal subjects which were visually inspected for outlier slices with the interactive tool developed as part of this study, showing its potential to quickly highlight problematic volumes and slices in large population studies. The informed model estimation framework was evaluated both in simulations and in vivo human data.Peer reviewe

Joint Total Variation ESTATICS for Robust Multi-Parameter Mapping

Quantitative magnetic resonance imaging (qMRI) derives tissue-specific parameters -- such as the apparent transverse relaxation rate R2*, the longitudinal relaxation rate R1 and the magnetisation transfer saturation -- that can be compared across sites and scanners and carry important information about the underlying microstructure. The multi-parameter mapping (MPM) protocol takes advantage of multi-echo acquisitions with variable flip angles to extract these parameters in a clinically acceptable scan time. In this context, ESTATICS performs a joint loglinear fit of multiple echo series to extract R2* and multiple extrapolated intercepts, thereby improving robustness to motion and decreasing the variance of the estimators. In this paper, we extend this model in two ways: (1) by introducing a joint total variation (JTV) prior on the intercepts and decay, and (2) by deriving a nonlinear maximum \emph{a posteriori} estimate. We evaluated the proposed algorithm by predicting left-out echoes in a rich single-subject dataset. In this validation, we outperformed other state-of-the-art methods and additionally showed that the proposed approach greatly reduces the variance of the estimated maps, without introducing bias.Comment: 11 pages, 2 figures, 1 table, conference paper, accepted at MICCAI 202

Structural Variability from Noisy Tomographic Projections

In cryo-electron microscopy, the 3D electric potentials of an ensemble of molecules are projected along arbitrary viewing directions to yield noisy 2D images. The volume maps representing these potentials typically exhibit a great deal of structural variability, which is described by their 3D covariance matrix. Typically, this covariance matrix is approximately low-rank and can be used to cluster the volumes or estimate the intrinsic geometry of the conformation space. We formulate the estimation of this covariance matrix as a linear inverse problem, yielding a consistent least-squares estimator. For $n$ images of size $N$-by-$N$ pixels, we propose an algorithm for calculating this covariance estimator with computational complexity $\mathcal{O}(nN^4+\sqrt{\kappa}N^6 \log N)$, where the condition number $\kappa$ is empirically in the range $10$--$200$. Its efficiency relies on the observation that the normal equations are equivalent to a deconvolution problem in 6D. This is then solved by the conjugate gradient method with an appropriate circulant preconditioner. The result is the first computationally efficient algorithm for consistent estimation of 3D covariance from noisy projections. It also compares favorably in runtime with respect to previously proposed non-consistent estimators. Motivated by the recent success of eigenvalue shrinkage procedures for high-dimensional covariance matrices, we introduce a shrinkage procedure that improves accuracy at lower signal-to-noise ratios. We evaluate our methods on simulated datasets and achieve classification results comparable to state-of-the-art methods in shorter running time. We also present results on clustering volumes in an experimental dataset, illustrating the power of the proposed algorithm for practical determination of structural variability.Comment: 52 pages, 11 figure

DTI denoising for data with low signal to noise ratios

Low signal to noise ratio (SNR) experiments in diffusion tensor imaging (DTI) give key information about tracking and anisotropy, e. g., by measurements with small voxel sizes or with high b values. However, due to the complicated and dominating impact of thermal noise such data are still seldom analysed. In this paper Monte Carlo simulations are presented which investigate the distributions of noise for different DTI variables in low SNR situations. Based on this study a strategy for the application of spatial smoothing is derived. Optimal prerequisites for spatial filters are unbiased, bell shaped distributions with uniform variance, but, only few variables have a statistics close to that. To construct a convenient filter a chain of nonlinear Gaussian filters is adapted to peculiarities of DTI and a bias correction is introduced. This edge preserving three dimensional filter is then validated via a quasi realistic model. Further, it is shown that for small sample sizes the filter is as effective as a maximum likelihood estimator and produces reliable results down to a local SNR of approximately 1. The filter is finally applied to very recent data with isotropic voxels of the size 1×1×1mm^3 which corresponds to a spatially mean SNR of 2.5. This application demonstrates the statistical robustness of the filter method. Though the Rician noise model is only approximately realized in the data, the gain of information by spatial smoothing is considerable

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

Spatio-temporal wavelet regularization for parallel MRI reconstruction: application to functional MRI

Parallel MRI is a fast imaging technique that enables the acquisition of highly resolved images in space or/and in time. The performance of parallel imaging strongly depends on the reconstruction algorithm, which can proceed either in the original k-space (GRAPPA, SMASH) or in the image domain (SENSE-like methods). To improve the performance of the widely used SENSE algorithm, 2D- or slice-specific regularization in the wavelet domain has been deeply investigated. In this paper, we extend this approach using 3D-wavelet representations in order to handle all slices together and address reconstruction artifacts which propagate across adjacent slices. The gain induced by such extension (3D-Unconstrained Wavelet Regularized -SENSE: 3D-UWR-SENSE) is validated on anatomical image reconstruction where no temporal acquisition is considered. Another important extension accounts for temporal correlations that exist between successive scans in functional MRI (fMRI). In addition to the case of 2D+t acquisition schemes addressed by some other methods like kt-FOCUSS, our approach allows us to deal with 3D+t acquisition schemes which are widely used in neuroimaging. The resulting 3D-UWR-SENSE and 4D-UWR-SENSE reconstruction schemes are fully unsupervised in the sense that all regularization parameters are estimated in the maximum likelihood sense on a reference scan. The gain induced by such extensions is illustrated on both anatomical and functional image reconstruction, and also measured in terms of statistical sensitivity for the 4D-UWR-SENSE approach during a fast event-related fMRI protocol. Our 4D-UWR-SENSE algorithm outperforms the SENSE reconstruction at the subject and group levels (15 subjects) for different contrasts of interest (eg, motor or computation tasks) and using different parallel acceleration factors (R=2 and R=4) on 2x2x3mm3 EPI images.Comment: arXiv admin note: substantial text overlap with arXiv:1103.353