multimodality image registration by maximization of mutual information a new approach to the problem of multimodality medical image registration is proposed using a basic concept from information theory mutual information mi or relative entropy as a new matching criterion the method presented in this paper applies mi to measure the statistical dependence or information redundancy between the image intensities of corresponding voxels in both images which is assumed to be maximal if the images are geometrically aligned maximization of mi is a very general and powerful criterion because no assumptions are made regarding the nature of this dependence and no limiting constraints are imposed on the image content of the modalities involved the accuracy of the mi criterion is validated for rigid body registration of computed tomography ct magnetic resonance mr and photon emission tomography pet images by comparison with the stereotactic registration solution while robustness is evaluated with respect to implementation issues such as interpolation and optimization and image content including partial overlap and image degradation our results demonstrate that subvoxel accuracy with respect to the stereotactic reference solution can be achieved completely automatically and without any prior segmentation feature extraction or other preprocessing steps which makes this method very well suited for clinical applications

co registration and distortion correction of diffusion and anatomical images based on inverse contrast normalization diffusion mri provides quantitative information about microstructural properties which can be useful in neuroimaging studies of the human brain echo planar imaging epi sequences which are frequently used for acquisition of diffusion images are sensitive to inhomogeneities in the primary magnetic b0 field that cause localized distortions in the reconstructed images we describe and evaluate a new method for correction of susceptibility induced distortion in diffusion images in the absence of an accurate b0 fieldmap in our method the distortion field is estimated using a constrained non rigid registration between an undistorted t1 weighted anatomical image and one of the distorted epi images from diffusion acquisition our registration framework is based on a new approach inversion inverse contrast normalization for very simple registration which exploits the inverted contrast relationship between t1 and t2 weighted brain images to define a simple and robust similarity measure we also describe how inversion can be used for rigid alignment of diffusion images and t1 weighted anatomical images our approach is evaluated with multiple in vivo datasets acquired with different acquisition parameters compared to other methods inversion shows robust and consistent performance in rigid registration and shows improved alignment of diffusion and anatomical images relative to normalized mutual information for non rigid distortion correction

enhanced false discovery rate using gaussian mixture models for thresholding fmri statistical maps a typical fmri data analysis proceeds via the generalized linear model glm with gaussian noise using a model based on the experimental paradigm this analysis ultimately results in the production of z statistic images corresponding to the contrasts of interest thresholding such z statistic images at uncorrected thresholds suitable for testing activation at a single voxel results in the problem of multiple comparisons a number of methods which account for the problem of multiple comparisons have been proposed including gaussian random field theory mixture modeling and false discovery rate fdr the focus of this paper is on the development of a generalized version of fdr gfdr in an empirical bayesian framework specially adapted for fmri thresholding that is more robust to modeling violations as compared to traditional fdr we show theoretically as well as by simulation that for real fmri data various factors lead to a mixture of gaussians mog density for the null distribution artificial data was used to systematically study the bias of fdr and gfdr under varying intensity of modeling violations signal to noise ratios and activation fractions for a range of q values gfdr was able to handle modeling violations and produce good results when fdr failed real fmri data was also used to confirm gfdr capabilities our results indicate that it is very important to account for the form and fraction of the null hypothesis adaptively from the data in order to obtain valid inference

multisite longitudinal reliability of tract based spatial statistics in diffusion tensor imaging of healthy elderly subjects large scale longitudinal neuroimaging studies with diffusion imaging techniques are necessary to test and validate models of white matter neurophysiological processes that change in time both in healthy and diseased brains the predictive power of such longitudinal models will always be limited by the reproducibility of repeated measures acquired during different sessions at present there is limited quantitative knowledge about the across session reproducibility of standard diffusion metrics in 3t multi centric studies on subjects in stable conditions in particular when using tract based spatial statistics and with elderly people in this study we implemented a multi site brain diffusion protocol in 10 clinical 3t mri sites distributed across 4 countries in europe italy germany france and greece using vendor provided sequences from siemens allegra trio tim verio skyra biograph mmr philips achieva and ge hdxt scanners we acquired dti data 2 2 2 mm 3 b 700 s mm 2 5 b0 and 30 diffusion weighted volumes of a group of healthy stable elderly subjects 5 subjects per site in two separate sessions at least a week apart for each subject and session four scalar diffusion metrics were considered fractional anisotropy fa mean diffusivity md radial diffusivity rd and axial ad diffusivity the diffusion metrics from multiple subjects and sessions at each site were aligned to their common white matter skeleton using tract based spatial statistics the reproducibility at each mri site was examined by looking at group averages of absolute changes relative to the mean on various parameters i reproducibility of the signal to noise ratio snr of the b0 images in centrum semiovale ii full brain test retest differences of the diffusion metric maps on the white matter skeleton iii reproducibility of the diffusion metrics on atlas based white matter rois on the white matter skeleton despite the differences of mri scanner configurations across sites vendors models rf coils and acquisition sequences we found good and consistent test retest reproducibility white matter b0 snr reproducibility was on average 7 1 with no significant mri site effects whole brain analysis resulted in no significant test retest differences at any of the sites with any of the dti metrics the atlas based roi analysis showed that the mean reproducibility errors largely remained in the 2 4 range for fa and ad and 2 6 for md and rd averaged across rois our results show reproducibility values comparable to those reported in studies using a smaller number of mri scanners slightly different dti protocols and mostly younger populations we therefore show that the acquisition and analysis protocols used are appropriate for multi site experimental scenarios

meaningful design and contrast estimability in fmri optimising the efficiency of an experimental design is known to be of great importance however existing methods for calculating design rank deficiency and contrast estimability an important aspect of experimental design relate to computational precision rather than image noise and are therefore not very meaningful for example a contrast between two experimental conditions may be mathematically estimable while requiring a huge differential bold response for statistical significance to be reached in this paper we formulate standard efficiency equations in terms of required bold effect and use this to generate measures of rank estimability which are meaningful this takes into account the strength and smoothness of the timeseries noise and is applicable to complex contrasts we show how to re express several regressors and an associated contrast vector as a single equivalent regressor so that we can calculate the contrast s effective peak peak height unambiguously we also present some example results on typical designs and characterise noise results from a range of typical fmri acquisitions in order to allow experimenters to apply efficiency estimation in advance of acquiring data

temporal autocorrelation in univariate linear modeling of fmri data in functional magnetic resonance imaging statistical analysis there are problems with accounting for temporal autocorrelations when assessing change within voxels techniques to date have utilized temporal filtering strategies to either shape these autocorrelations or remove them shaping or coloring attempts to negate the effects of not accurately knowing the intrinsic autocorrelations by imposing known autocorrelation via temporal filtering removing the autocorrelation or prewhitening gives the best linear unbiased estimator assuming that the autocorrelation is accurately known for single event designs the efficiency of the estimator is considerably higher for prewhitening compared with coloring however it has been suggested that sufficiently accurate estimates of the autocorrelation are currently not available to give prewhitening acceptable bias to overcome this we consider different ways to estimate the autocorrelation for use in prewhitening after high pass filtering is performed a tukey taper set to smooth the spectral density more than would normally be used in spectral density estimation performs best importantly estimation is further improved by using nonlinear spatial filtering to smooth the estimated autocorrelation but only within tissue type using this approach when prewhitening reduced bias to close to zero at probability levels as low as 1 x 10 5

functional quantitative susceptibility mapping fqsm blood oxygenation level dependent bold functional magnetic resonance imaging fmri is a powerful technique typically based on the statistical analysis of the magnitude component of the complex time series here we additionally interrogated the phase data of the fmri time series and used quantitative susceptibility mapping qsm in order to investigate the potential of functional qsm fqsm relative to standard magnitude bold fmri high spatial resolution data 1 mm isotropic were acquired every 3 seconds using zoomed multi slice gradient echo epi collected at 7 t in single orientation so and multiple orientation mo experiments the latter involving 4 repetitions with the subject s head rotated relative to b0 statistical parametric maps spm were reconstructed for magnitude phase and qsm time series and each was subjected to detailed analysis several fqsm pipelines were evaluated and compared based on the relative number of voxels that were coincidentally found to be significant in qsm and magnitude spms common voxels we found that sensitivity and spatial reliability of fqsm relative to the magnitude data depended strongly on the arbitrary significance threshold defining activated voxels in spms and on the efficiency of spatio temporal filtering of the phase time series sensitivity and spatial reliability depended slightly on whether mo or so fqsm was performed and on the qsm calculation approach used for so data our results present the potential of fqsm as a quantitative method of mapping bold changes we also critically discuss the technical challenges and issues linked to this intriguing new technique

a nonconservative lagrangian framework for statistical fluid registration safira in this paper we used a nonconservative lagrangian mechanics approach to formulate a new statistical algorithm for fluid registration of 3 d brain images this algorithm is named safira acronym for statistically assisted fluid image registration algorithm a nonstatistical version of this algorithm was implemented where the deformation was regularized by penalizing deviations from a zero rate of strain in the terms regularizing the deformation included the covariance of the deformation matrices and the vector fields q here we used a lagrangian framework to reformulate this algorithm showing that the regularizing terms essentially allow nonconservative work to occur during the flow given 3 d brain images from a group of subjects vector fields and their corresponding deformation matrices are computed in a first round of registrations using the nonstatistical implementation covariance matrices for both the deformation matrices and the vector fields are then obtained and incorporated separately or jointly in the nonconservative terms creating four versions of safira we evaluated and compared our algorithms performance on 92 3 d brain scans from healthy monozygotic and dizygotic twins 2 d validations are also shown for corpus callosum shapes delineated at midline in the same subjects after preliminary tests to demonstrate each method we compared their detection power using tensor based morphometry tbm a technique to analyze local volumetric differences in brain structure we compared the accuracy of each algorithm variant using various statistical metrics derived from the images and deformation fields all these tests were also run with a traditional fluid method which has been quite widely used in tbm studies the versions incorporating vector based empirical statistics on brain variation were consistently more accurate than their counterparts when used for automated volumetric quantification in new brain images this suggests the advantages of this approach for large scale neuroimaging studies

on the convergence rate of a quasi newton method for inverse eigenvalue problems in this paper we first note that the proof of the quadratic convergence of the quasi newton method as given in friedland nocedal and overton siam j numer anal 24 1987 pp 634 667 is incorrect then we give a correct proof of the convergence

a quadratically convergent algorithm based on matrix equations for inverse eigenvalue problems abstract we propose a quadratically convergent algorithm for inverse symmetric eigenvalue problems based on matrix equations the basic idea is seen in a recent study by ogita and aishima while they derive an efficient iterative refinement algorithm for symmetric eigenvalue problems using special matrix equations in other words this study is interpreted as a unified view on quadratically convergent algorithms for eigenvalue problems and inverse eigenvalue problems based on matrix equations to the best of our knowledge such a unified development of algorithms is provided for the first time since the proposed algorithm for the inverse eigenvalue problems can be regarded as the newton s method for the matrix equations the quadratic convergence is naturally proved our algorithm is interpreted as an improved version of the cayley transform method for the inverse eigenvalue problems although the cayley transform method is one of the effective iterative methods the cayley transform takes o n 3 arithmetic operations to produce an orthogonal matrix using a skew symmetric matrix in each iteration our algorithm can refine orthogonality without the cayley transform which reduces the operations in each iteration it is worth noting that our approach overcomes the limitation of the cayley transform method to the inverse standard eigenvalue problems resulting in an extension to inverse generalized eigenvalue problems

strong semismoothness of eigenvalues of symmetric matrices and its application to inverse eigenvalue problems it is well known that the eigenvalues of a real symmetric matrix are not everywhere differentiable a classical result of ky fan states that each eigenvalue of a symmetric matrix is the difference of two convex functions which implies that the eigenvalues are semismooth functions based on a recent result of the authors it is further proved in this paper that the eigenvalues of a symmetric matrix are strongly semismooth everywhere as an application it is demonstrated how this result can be used to analyze the quadratic convergence of newton s method for solving inverse eigenvalue problems ieps and generalized ieps with multiple eigenvalues

regression models for identifying noise sources in magnetic resonance images stochastic noise susceptibility artifacts magnetic field and radiofrequency inhomogeneities and other noise components in magnetic resonance images mris can introduce serious bias into any measurements made with those images we formally introduce three regression models including a rician regression model and two associated normal models to characterize stochastic noise in various magnetic resonance imaging modalities including diffusion weighted imaging dwi and functional mri fmri estimation algorithms are introduced to maximize the likelihood function of the three regression models we also develop a diagnostic procedure for systematically exploring mr images to identify noise components other than simple stochastic noise and to detect discrepancies between the fitted regression models and mri data the diagnostic procedure includes goodness of fit statistics measures of influence and tools for graphical display the goodness of fit statistics can assess the key assumptions of the three r

a faster capacity scaling algorithm for minimum cost submodular flow we describe an o n exp 4 h min log u n exp 2 log n capacity scaling algorithm for the minimum cost submodular flow problem our algorithm modifies and extends the edmonds karp capacity scaling algorithm for minimum cost flow to solve the minimum cost submodular flow problem the modification entails scaling a relaxation parameter delta capacities are relaxed by attaching a complete directed graph with uniform arc capacity delta in each scaling phase we then modify a feasible submodular flow by relaxing the submodular constraints so that complementary slackness is satisfied this creates discrepancies between the boundary of the flow and the base polytope of a relaxed submodular function to reduce these discrepancies we use a variant of the successive shortest path algorithm that augments flow along min cost paths of residual capacity at least delta the shortest augmenting path subroutine we use is a variant of dijkstra s algorithm modified to handle exchange capacity arcs efficiently the result is a weakly polynomial time algorithm whose running time is better than any existing submodular flow algorithm when u is small and c is big we also show how to use max mean cuts to make the algorithm strongly polynomial the resulting algorithm is the first capacity scaling algorithm to match the current best strongly polynomial bound for submodular flow

comparing methods of analyzing fmri statistical parametric maps approaches for the analysis of statistical parametric maps spms can be crudely grouped into three main categories in which different philosophies are applied to delineate activated regions these being type i error control thresholding false discovery rate fdr control thresholding and posterior probability thresholding to better understand the properties of these main approaches we carried out a simulation study to compare the approaches as they would be used on real data sets using default settings we find that posterior probability thresholding is the most powerful approach and type i error control thresholding provides the lowest levels of type i error false discovery rate control thresholding performs in between the other approaches for both these criteria although for some parameter settings this approach can approximate the performance of posterior probability thresholding based on these results we discuss the relative merits of the three approaches in an attempt to decide upon an optimal approach we conclude that viewing the problem of delineating areas of activation as a classification problem provides a highly interpretable framework for comparing the methods within this framework we highlight the role of the loss function which explicitly penalizes the types of errors that may occur in a given analysis

the impact of image smoothness on intrinsic functional connectivity and head motion confounds we present a novel method for controlling the effects of group differences in motion on functional connectivity studies resting state functional magnetic resonance imaging rs fmri is a powerful tool that allows for the assessment of whole brain functional organization across a wide range of clinical populations however as highlighted by recent studies many measures commonly used in rs fmri are highly correlated with subject head movement a source of this problem is that motion itself and motion correction algorithms lead to spatial smoothing which is then variable across the brain and across subjects or groups dependent upon the amount of motion present during scanning studies aimed at elucidating differences between populations that have different head motion characteristics e g patients often move more in the scanner than healthy control subjects are significantly confounded by these effects in this work we propose a solution to this problem uniform smoothing which ensures that all subject images in a study have equal effective spatial resolution we establish that differences in the intrinsic smoothness of images across a group can confound connectivity results and link these differences in smoothness to motion we demonstrate that eliminating these smoothness differences via our uniform smoothing solution is successful in reducing confounds related to the differences in head motion between subjects

variational inference of the fiber orientation density using diffusion mr imaging diffusion mr imaging has enabled the in vivo exploration of the connectional architecture in human brain this method particularly reveals the complex system of long range nerve fibers that integrate the functionally distinct areas of the cerebral cortex since the fibers are not directly observed but the diffusion process of water molecules in the underlying material a forward model is established that maps the microgeometry of nervous tissue onto the diffusion weighted signals this article proposes the spherical deconvolution of the fiber orientation density in a reproducing kernel hilbert space thereby generalizing previous approaches that perform a truncated fourier analysis on the sphere the specified inverse problem is solved within a smoothing spline framework which preserves the characteristic properties of a density function namely its normalization and non negativity a gaussian process model allows the specification of confidence bands for the estimated fiber orientation density and the rigorous selection of the hyperparameters here the high frequency content in the density function and the noise variance of the mr observations in addition we weaken the constant diffusivity assumption frequently made in the spherical convolution methodology the novel approach which uncovers the fiber orientation field of white matter is demonstrated with diffusion weighted data sets featuring high angular resolution

multi contrast multi scale surface registration for improved alignment of cortical areas the position of cortical areas can be approximately predicted from cortical surface folding patterns however there is extensive inter subject variability in cortical folding patterns prohibiting a one to one mapping of cortical folds in certain areas in addition the relationship between cortical area boundaries and the shape of the cortex is variable and weaker for higher order cortical areas current surface registration techniques align cortical folding patterns using sulcal landmarks or cortical curvature for instance the alignment of cortical areas by these techniques is thus inherently limited by the sole use of geometric similarity metrics magnetic resonance imaging t1 maps show intra cortical contrast that reflects myelin content and thus can be used to improve the alignment of cortical areas in this article we present a new symmetric diffeomorphic multi contrast multi scale surface registration mmsr technique that works with partially inflated surfaces in the level set framework mmsr generates a more precise alignment of cortical surface curvature in comparison to two widely recognized surface registration algorithms the resulting overlap in gyrus labels is comparable to freesurfer most importantly mmsr improves the alignment of cortical areas further by including t1 maps as a first application we present a group average t1 map at a uniquely high resolution and multiple cortical depths which reflects the myeloarchitecture of the cortex mmsr can also be applied to other mr contrasts such as functional and connectivity data

a reproducing kernel hilbert space approach for q ball imaging diffusion magnetic resonance mr imaging has enabled us to reveal the white matter geometry in the living human brain the q ball technique is widely used nowadays to recover the orientational heterogeneity of the intra voxel fiber architecture this article proposes to employ the funk radon transform in a hilbert space with a reproducing kernel derived from the spherical laplace beltrami operator thus generalizing previous approaches that assume a bandlimited diffusion signal the function estimation problem is solved within a tikhonov regularization framework while a gaussian process model allows for the selection of the smoothing parameter and the specification of confidence bands shortcomings of q ball imaging are discussed

a systematic study of the sensitivity of partial volume correction methods for the quantification of perfusion from pseudo continuous arterial spin labeling mri abstract arterial spin labeling asl mri is a non invasive technique for the quantification of cerebral perfusion and pseudo continuous arterial spin labeling pcasl has been recommended as the standard implementation by a recent consensus of the community due to the low spatial resolution of asl images perfusion quantification is biased by partial volume effects consequently several partial volume correction pvec methods have been developed to reduce the bias in gray matter gm perfusion quantification the efficacy of these methods relies on both the quality of the asl data and the accuracy of partial volume estimates here we systematically investigate the sensitivity of different pvec methods to variability in both the asl data and partial volume estimates using simulated pcasl data and in vivo pcasl data from a reproducibility study we examined the pvec methods in two ways the ability to preserve spatial details and the accuracy of gm perfusion estimation judging by the root mean square error rmse between simulated and estimated gm cbf the spatially regularized method was superior in preserving spatial details compared to the linear regression method rmse of 1 2 vs 5 1 in simulation of gm cbf with short scale spatial variations the linear regression method was generally less sensitive than the spatially regularized method to noise in data and errors in the partial volume estimates rmse 6 3 vs 23 4 for snr 5 simulated data but this could be attributed to the greater smoothing introduced by the method analysis of a healthy cohort dataset indicates that pvec using either method improves the repeatability of perfusion quantification within subject coefficient of variation reduced by 5 after pvec

white matter compartment models for in vivo diffusion mri at 300mt m this paper compares a range of compartment models for diffusion mri data on in vivo human acquisitions from a standard 60mt m system philips 3t achieva and a unique 300mt m system siemens connectom the key aim is to determine whether both systems support broadly the same models or whether the connectom higher gradient system supports significantly more complex models a single volunteer underwent 8h of acquisition on each system to provide uniquely wide and dense sampling of the available space of pulsed gradient spin echo pgse measurements we select a set of promising models from the wide set of possible three compartment models for in vivo white matter wm that previous work and preliminary experiments suggest as strong candidates but extend them to fit for compartmental t2 and diffusivity we focus on the corpus callosum where the wm fibre architecture is simplest and compare their ability to explain the measured data using akaike s information criterion aic and to predict unseen data using cross validation we also compare the stability of parameter estimates in the presence of i noise using bootstrapping and ii spatial variation using visual assessment and comparison with anatomical knowledge broadly similar models emerge from the aic and cross validation experiments in both data sets specifically a three compartment model consisting of either a bingham distribution of sticks or a cylinder for the intracellular compartment an anisotropic diffusion tensor dt model for the extracellular compartment as well as an isotropic csf compartment performs consistently well however various other models also perform well and no single model emerges as clear winner the wm data with virtually no csf contamination do not support compartmental t2 but partially support compartmental diffusivity evaluation of parameter stability favours simpler models than those identified by aic or cross validation they suggest that the level of complexity in models underpinning currently popular microstructure imaging techniques such as noddi charmed or activeax where the number of free parameters is about 4 or 5 rather than 10 or 11 may reflect the level of complexity achievable for a useful technique on current systems although the 300mt m data may support more complex models

recent developments in nonparametric density estimation advances in computation and the fast and cheap computational facilities now available to statisticians have had a significant impact upon statistical research and especially the development of nonparametric data analysis procedures in particular theoretical and applied research on nonparametric density estimation has had a noticeable influence on related topics such as nonparametric regression nonparametric discrimination and nonparametric pattern recognition this article reviews recent developments in nonparametric density estimation and includes topics that have been omitted from review articles and books on the subject the early density estimation methods such as the histogram kernel estimators and orthogonal series estimators are still very popular and recent research on them is described different types of restricted maximum likelihood density estimators including order restricted estimators maximum penalized likelihood estimators and sieve estimators are discussed where restrictions are imposed upon the class of densities or on the form of the likelihood function nonparametric density estimators that are data adaptive and lead to locally smoothed estimators are also discussed these include variable partition histograms estimators based on statistically equivalent blocks nearest neighbor estimators variable kernel estimators and adaptive kernel estimators for the multivariate case extensions of methods of univariate density estimation are usually straightforward but can be computationally expensive a method of multivariate density estimation that did not spring from a univariate generalization is described namely projection pursuit density estimation in which both dimensionality reduction and density estimation can be pursued at the same time finally some areas of related research are mentioned such as nonparametric estimation of functionals of a density robust parametric estimation semiparametric models and density estimation for censored and incomplete data directional and spherical data and density estimation for dependent sequences of observations

a comprehensive review of group level model performance in the presence of heteroscedasticity can a single model control type i errors in the presence of outliers even after thorough preprocessing and a careful time series analysis of functional magnetic resonance imaging fmri data artifact and other issues can lead to violations of the assumption that the variance is constant across subjects in the group level model this is especially concerning when modeling a continuous covariate at the group level as the slope is easily biased by outliers various models have been proposed to deal with outliers including models that use the first level variance or that use the group level residual magnitude to differentially weight subjects the most typically used robust regression implementing a robust estimator of the regression slope has been previously studied in the context of fmri studies and was found to perform well in some scenarios but a loss of type i error control can occur for some outlier settings a second type of robust regression using a heteroscedastic autocorrelation consistent hac estimator which produces robust slope and variance estimates has been shown to perform well with better type i error control but with large sample sizes 500 1000 subjects the type i error control with smaller sample sizes has not been studied in this model and has not been compared to other modeling approaches that handle outliers such as fsl s flame 1 and fsl s outlier de weighting focusing on group level inference with a continuous covariate over a range of sample sizes and degree of heteroscedasticity which can be driven either by the within or between subject variability both styles of robust regression are compared to ordinary least squares ols fsl s flame 1 flame 1 with outlier de weighting algorithm and kendall s tau additionally subject omission using the cook s distance measure with ols and nonparametric inference with the ols statistic are studied pros and cons of these models as well as general strategies for detecting outliers in data and taking precaution to avoid inflated type i error rates are discussed

the connectivity of functional cores reveals different degrees of segregation and integration in the brain at rest the principles of functional specialization and integration in the resting brain are implemented in a complex system of specialized networks that share some degree of interaction recent studies have identified wider functional modules compared to previously defined networks and reported a small world architecture of brain activity in which central nodes balance the pressure to evolve segregated pathways with the integration of local systems the accurate identification of such central nodes is crucial but might be challenging for several reasons e g inter subject variability and physiological pathological network plasticity and recent works reported partially inconsistent results concerning the properties of these cortical hubs here we applied a whole brain data driven approach to extract cortical functional cores and examined their connectivity from a resting state fmri experiment on healthy subjects two main statistically significant cores centered on the posterior cingulate cortex and the supplementary motor area were extracted and their functional connectivity maps thresholded at three statistical levels revealed the presence of two complex systems one system is consistent with the default mode network dmn and gradually connects to visual regions the other centered on motor regions and gradually connects to more sensory specific portions of cortex these two large scale networks eventually converged to regions belonging to the medial aspect of the dmn potentially allowing inter network interactions

partition based mass clustering of tractography streamlines we describe a novel scalable clustering framework for streamlines obtained from diffusion tractography clustering is an attractive means of segmenting a large set of streamlines into anatomically relevant bundles for most existing methods however the large datasets produced in high resolution or multiple subject studies are problematical to achieve good scalability our method repeatedly divides the data into subsets which are then partitioned using hierarchical clustering a final partition is obtained by recombining the subsets in addition the recombination scheme provides a consistency measure for cluster assignment of individual streamlines which is used to clean up the final result the clusters have good anatomical plausibility and we show that three clusters corresponding to the three known segments of the arcuate fasciculus show excellent agreement with literature a major advantage of the method is the fact that it can find clusters in datasets of essentially arbitrary size this fact is exploited to find consistent clusters in concatenated tractography data from multiple subjects we expect the identification of bundles across subjects to be an important application of the method

segmentation of perivascular spaces in 7 t mr image using auto context model with orientation normalized features quantitative study of perivascular spaces pvss in brain magnetic resonance mr images is important for understanding the brain lymphatic system and its relationship with neurological diseases one of the major challenges is the accurate extraction of pvss that have very thin tubular structures with various directions in three dimensional 3d mr images in this paper we propose a learning based pvs segmentation method to address this challenge specifically we first determine a region of interest roi by using the anatomical brain structure and the vesselness information derived from eigenvalues of image derivatives then in the roi we extract a number of randomized haar features which are normalized with respect to the principal directions of the underlying image derivatives the classifier is trained by the random forest model that can effectively learn both discriminative features and classifier parameters to maximize the information gain finally a sequential learning strategy is used to further enforce various contextual patterns around the thin tubular structures into the classifier for evaluation we apply our proposed method to the 7t brain mr images scanned from 17 healthy subjects aged from 25 to 37 the performance is measured by voxel wise segmentation accuracy cluster wise classification accuracy and similarity of geometric properties such as volume length and diameter distributions between the predicted and the true pvss moreover the accuracies are also evaluated on the simulation images with motion artifacts and lacunes to demonstrate the potential of our method in segmenting pvss from elderly and patient populations the experimental results show that our proposed method outperforms all existing pvs segmentation methods

structures of polyhedra determined by submodular functions on crossing families the present paper shows that for any submodular functionf on a crossing family with if the polyhedron is nonempty then there exist a unique distributive lattice with and a unique submodular function with such thatb f coincides with the base polyhedron associated with the submodular system here iff is integer valued thenf 1 is also integer valued based on this fact we also show the relationship between the independent flow problem considered by the author and the minimum cost flow problem considered by j edmonds and r giles

joint reconstruction of white matter pathways from longitudinal diffusion mri data with anatomical priors we consider the problem of reconstructing white matter pathways in a longitudinal study where diffusion weighted and t1 weighted mr images have been acquired at multiple time points for the same subject we propose a method for joint reconstruction of a subject s pathways at all time points given the subject s entire set of longitudinal data we apply a method for unbiased within subject registration to generate a within subject template from the t1 weighted images of the subject at all time points we follow a global probabilistic tractography approach where the unknown pathway is represented in the space of this within subject template and propagated to the native space of the diffusion weighted images at all time points to compute its posterior probability given the images this ensures spatial correspondence of the reconstructed pathway among time points which in turn allows longitudinal changes in diffusion measures to be estimated consistently along the pathway we evaluate the reliability of the proposed method on data from healthy controls scanned twice within a month where no changes in white matter microstructure are expected between scans we evaluate the sensitivity of the method on data from huntington s disease patients scanned repeatedly over the course of several months where changes are expected between scans we show that reconstructing white matter pathways jointly using the data from all time points leads to improved reliability and sensitivity when compared to reconstructing the pathways at each time point independently

predicting ct image from mri data through feature matching with learned nonlinear local descriptors attenuation correction for positron emission tomography pet magnetic resonance mr hybrid imaging systems and dose planning for mr based radiation therapy remain challenging due to insufficient high energy photon attenuation information we present a novel approach that uses the learned nonlinear local descriptors and feature matching to predict pseudo computed tomography pct images from t1 weighted and t2 weighted magnetic resonance imaging mri data the nonlinear local descriptors are obtained by projecting the linear descriptors into the nonlinear high dimensional space using an explicit feature map and low rank approximation with supervised manifold regularization the nearest neighbors of each local descriptor in the input mr images are searched in a constrained spatial range of the mr images among the training dataset then the pct patches are estimated through k nearest neighbor regression the proposed method for pct prediction is quantitatively analyzed on a dataset consisting of paired brain mri and ct images from 13 subjects our method generates pct images with a mean absolute error mae of 75 25 18 05 hounsfield units a peak signal to noise ratio of 30 87 1 15 db a relative mae of 1 56 0 5 in pet attenuation correction and a dose relative structure volume difference of 0 055 0 107 in d 98 as compared with true ct the experimental results also show that our method outperforms four state of the art methods

bayesian deconvolution of corrected fmri data using bilinear dynamical systems abstract in penny et al penny w ghahramani z friston k j 2005 bilinear dynamical systems philos trans r soc lond b biol sci 360 1457 983 993 a particular case of the linear dynamical systems ldss was used to model the dynamic behavior of the bold response in functional mri this state space model called bilinear dynamical system bds is used to deconvolve the fmri time series in order to estimate the neuronal response induced by the different stimuli of the experimental paradigm the bds model parameters are estimated using an expectation maximization em algorithm proposed by ghahramani and hinton ghahramani z hinton g e 1996 parameter estimation for linear dynamical systems technical report department of computer science university of toronto in this paper we introduce modifications to the bds model in order to explicitly model the spatial variations of the haemodynamic response function hrf in the brain using a non parametric approach while in penny et al penny w ghahramani z friston k j 2005 bilinear dynamical systems philos trans r soc lond b biol sci 360 1457 983 993 the relationship between neuronal activation and fmri signals is formulated as a first order convolution with a kernel expansion using basis functions typically two or three in this paper we argue in favor of a spatially adaptive glm in which a local non parametric estimation of the hrf is performed furthermore in order to overcome the overfitting problem typically associated with simple em estimates we propose a full variational bayes vb solution to infer the bds model parameters we demonstrate the usefulness of our model which is able to estimate both the neuronal activity and the haemodynamic response function in every voxel of the brain we first examine the behavior of this approach when applied to simulated data with different temporal and noise features as an example we will show how this method can be used to improve interpretability of estimates from an independent component analysis ica analysis of fmri data we finally demonstrate its use on real fmri data in one slice of the brain

effects of repeatability measures on results of fmri sica a study on simulated and real resting state effects spatial independent components analysis sica has become a widely applied data driven method for fmri data especially for resting state studies these sica approaches are often based on iterative estimation algorithms and there are concerns about accuracy due to noise repeatability measures such as icasso raicar and arabica have been introduced as remedies but information on their effects on estimates is limited the contribution of this study was to provide more of such information and test if the repeatability analyses are necessary we compared fastica based ordinary and repeatability approaches concerning mixing vector estimates comparisons included original fastica fsl4 melodic fastica and original and modified icasso the effects of bootstrapping and convergence threshold were evaluated the results show that there is only moderate improvement due to repeatability measures and only in the bootstrapping case bootstrapping attenuated power from time courses of resting state network related ics at frequencies higher than 0 1 hz and made subsets of low frequency oscillations more emphasized ic wise the convergence threshold did not have a significant role concerning the accuracy of estimates the performance results suggest that repeatability measures or strict converge criteria might not be needed in sica analyses of fmri data consequently the results in existing sica fmri literature are probably valid in this sense a decreased accuracy of original bootstrapping icasso was observed and corrected by using centrotype mixing estimates but the results warrant for thorough evaluations of data driven methods in general also given the fmri specific considerations further development of sica methods is strongly encouraged

nonparametric inference of the hemodynamic response using multi subject fmri data estimation and inferences for the hemodynamic response functions hrf using multi subject fmri data are considered within the context of the general linear model two new nonparametric estimators for the hrf are proposed the first is a kernel smoothed estimator which is used to construct hypothesis tests on the entire hrf curve in contrast to only summaries of the curve as in most existing tests to cope with the inherent large data variance we introduce a second approach which imposes tikhonov regularization on the kernel smoothed estimator an additional bias correction step which uses multi subject averaged information is introduced to further improve efficiency and reduce the bias in estimation for individual hrfs by utilizing the common properties of brain activity shared across subjects this is the main improvement over the standard methods where each subject s data is usually analyzed independently a fast algorithm is also developed to select the optimal regularization and smoothing parameters the proposed methods are compared with several existing regularization methods through simulations the methods are illustrated by an application to the fmri data collected under a psychology design employing the monetary incentive delay mid task

time dependence of graph theory metrics in functional connectivity analysis brain graphs provide a useful way to computationally model the network structure of the connectome and this has led to increasing interest in the use of graph theory to quantitate and investigate the topological characteristics of the healthy brain and brain disorders on the network level the majority of graph theory investigations of functional connectivity have relied on the assumption of temporal stationarity however recent evidence increasingly suggests that functional connectivity fluctuates over the length of the scan in this study we investigate the stationarity of brain network topology using a bayesian hidden markov model hmm approach that estimates the dynamic structure of graph theoretical measures of whole brain functional connectivity in addition to extracting the stationary distribution and transition probabilities of commonly employed graph theory measures we propose two estimators of temporal stationarity the s index and n index these indexes can be used to quantify different aspects of the temporal stationarity of graph theory measures we apply the method and proposed estimators to resting state functional mri data from healthy controls and patients with temporal lobe epilepsy our analysis shows that several graph theory measures including small world index global integration measures and betweenness centrality may exhibit greater stationarity over time and therefore be more robust additionally we demonstrate that accounting for subject level differences in the level of temporal stationarity of network topology may increase discriminatory power in discriminating between disease states our results confirm and extend findings from other studies regarding the dynamic nature of functional connectivity and suggest that using statistical models which explicitly account for the dynamic nature of functional connectivity in graph theory analyses may improve the sensitivity of investigations and consistency across investigations

probabilistic independent component analysis for functional magnetic resonance imaging we present an integrated approach to probabilistic independent component analysis ica for functional mri fmri data that allows for nonsquare mixing in the presence of gaussian noise in order to avoid overfitting we employ objective estimation of the amount of gaussian noise through bayesian analysis of the true dimensionality of the data i e the number of activation and non gaussian noise sources this enables us to carry out probabilistic modeling and achieves an asymptotically unique decomposition of the data it reduces problems of interpretation as each final independent component is now much more likely to be due to only one physical or physiological process we also describe other improvements to standard ica such as temporal prewhitening and variance normalization of timeseries the latter being particularly useful in the context of dimensionality reduction when weak activation is present we discuss the use of prior information about the spatiotemporal nature of the source processes and an alternative hypothesis testing approach for inference using gaussian mixture models the performance of our approach is illustrated and evaluated on real and artificial fmri data and compared to the spatio temporal accuracy of results obtained from classical ica and glm analyses

multilevel linear modelling for fmri group analysis using bayesian inference functional magnetic resonance imaging studies often involve the acquisition of data from multiple sessions and or multiple subjects a hierarchical approach can be taken to modelling such data with a general linear model glm at each level of the hierarchy introducing different random effects variance components inferring on these models is nontrivial with frequentist solutions being unavailable a solution is to use a bayesian framework one important ingredient in this is the choice of prior on the variance components and top level regression parameters due to the typically small numbers of sessions or subjects in neuroimaging the choice of prior is critical to alleviate this problem we introduce to neuroimage modelling the approach of reference priors which drives the choice of prior such that it is noninformative in an information theoretic sense we propose two inference techniques at the top level for multilevel hierarchies a fast approach and a slower more accurate approach we also demonstrate that we can infer on the top level of multilevel hierarchies by inferring on the levels of the hierarchy separately and passing summary statistics of a noncentral multivariate t distribution between them

parametric spherical deconvolution inferring anatomical connectivity using diffusion mr imaging the human brain forms a complex neural network with a connectional architecture that is still far from being known in full detail even at the macroscopic level the advent of diffusion mr imaging has enabled the exploration of the structural properties of white matter in vivo in this article we propose a new forward model that maps the microscopic geometry of nervous tissue onto the water diffusion process and further onto the measured mr signals our spherical deconvolution approach completely parameterizes the fiber orientation density by a finite mixture of bingham distributions in addition we define the term anatomical connectivity taking the underlying image modality into account this neurophysiological metric may represent the proportion of the nerve fibers originating in the source area which intersect a given target region the specified inverse problem is solved by bayesian statistics posterior probability maps denote the probability that the connectivity value exceeds a chosen threshold conditional upon the noisy observations these maps allow us to draw inferences about the structural organization of the cerebral cortex moreover we will demonstrate the proposed approach with diffusion weighted data sets featuring high angular resolution

the impact of study design on pattern estimation for single trial multivariate pattern analysis a prerequisite for a pattern analysis using functional magnetic resonance imaging fmri data is estimating the patterns from time series data which then are input into the pattern analysis here we focus on how the combination of study design order and spacing of trials with pattern estimator impacts the type i error rate of the subsequent pattern analysis when type i errors are inflated the results are no longer valid so this work serves as a guide for designing and analyzing mvpa studies with controlled false positive rates the mvpa strategies examined are pattern classification and similarity utilizing single trial activation patterns from the same functional run primarily focusing on the least squares single and least square all pattern estimators we show that collinearities in the models along with temporal autocorrelation can cause false positive correlations between activation pattern estimates that adversely impact the false positive rates of pattern similarity and classification analyses it may seem intuitive that increasing the interstimulus interval isi would alleviate this issue but remaining weak correlations between activation patterns persist and have a strong influence in pattern similarity analyses pattern similarity analyses using only activation patterns estimated from the same functional run of data are susceptible to inflated false positives unless trials are randomly ordered with a different randomization for each subject in other cases where there is any structure to trial order valid pattern similarity analysis results can only be obtained if similarity computations are restricted to pairs of activation patterns from independent runs likewise for pattern classification false positives are minimized when the testing and training sets in cross validation do not contain patterns estimated from the same run

assessing the repeatability of absolute cmro2 oef and haemodynamic measurements from calibrated fmri abstract as energy metabolism in the brain is largely oxidative the measurement of cerebral metabolic rate of oxygen consumption cmro2 is a desirable biomarker for quantifying brain activity and tissue viability currently pet techniques based on oxygen isotopes are the gold standard for obtaining whole brain cmro2 maps among mri techniques that have been developed as an alternative are dual calibrated fmri dcfmri methods which exploit simultaneous measurements of bold and asl signals during a hypercapnic hyperoxic experiment to modulate brain blood flow and oxygenation in this study we quantified the repeatability of a dcfmri approach developed in our lab evaluating its limits and informing its application in studies aimed at characterising the metabolic state of human brain tissue over time our analysis focussed on the estimates of oxygen extraction fraction oef cerebral blood flow cbf cbf related cerebrovascular reactivity cvr and cmro2 based on a forward model that describes analytically the acquired dual echo gre signal indices of within and between session repeatability are calculated from two different datasets both at a bulk grey matter and at a voxel wise resolution and finally compared with similar indices obtained from previous mri and pet measurements within and between session values of intra subject coefficient of variation cvintra calculated from bulk grey matter estimates 6 7 6 6 mean std and 10 5 9 7 for oef 6 9 6 and 5 5 4 7 for cbf 12 9 7 and 12 3 10 for cmro2 coefficient of variation cv and intraclass correlation coefficient icc maps showed the spatial distribution of the repeatability metrics informing on the feasibility limits of the method in conclusion results show an overall consistency of the estimated physiological parameters with literature reports and a satisfactory level of repeatability considering the higher spatial sensitivity compared to other mri methods with varied performance depending on the specific parameter under analysis on the spatial resolution considered and on the study design

framework for shape analysis of white matter fiber bundles diffusion imaging coupled with tractography algorithms allows researchers to image human white matter fiber bundles in vivo these bundles are three dimensional structures with shapes that change over time during the course of development as well as in pathologic states while most studies on white matter variability focus on analysis of tissue properties estimated from the diffusion data e g fractional anisotropy the shape variability of white matter fiber bundle is much less explored in this paper we present a set of tools for shape analysis of white matter fiber bundles namely 1 a concise geometric model of bundle shapes 2 a method for bundle registration between subjects 3 a method for deformation estimation our framework is useful for analysis of shape variability in white matter fiber bundles we demonstrate our framework by applying our methods on two datasets one consisting of data for 6 normal adults and another consisting of data for 38 normal children of age 11 days to 8 5 years we suggest a robust and reproducible method to measure changes in the shape of white matter fiber bundles we demonstrate how this method can be used to create a model to assess age dependent changes in the shape of specific fiber bundles we derive such models for an ensemble of white matter fiber bundles on our pediatric dataset and show that our results agree with normative human head and brain growth data creating these models for a large pediatric longitudinal dataset may improve understanding of both normal development and pathologic states and propose novel parameters for the examination of the pediatric brain

variational bayes inference of spatial mixture models for segmentation mixture models are commonly used in the statistical segmentation of images for example they can be used for the segmentation of structural medical images into different matter types or of statistical parametric maps into activating and nonactivating brain regions in functional imaging spatial mixture models have been developed to augment histogram information with spatial regularization using markov random fields mrfs in previous work an approximate model was developed to allow adaptive determination of the parameter controlling the strength of spatial regularization inference was performed using markov chain monte carlo mcmc sampling however this approach is prohibitively slow for large datasets in this work a more efficient inference approach is presented this combines a variational bayes approximation with a second order taylor expansion of the components of the posterior distribution which would otherwise be intractable to variational bayes this provides inference on fully adaptive spatial mixture models an order of magnitude faster than mcmc we examine the behavior of this approach when applied to artificial data with different spatial characteristics and to functional magnetic resonance imaging statistical parametric maps

rapid two step dipole inversion for susceptibility mapping with sparsity priors quantitative susceptibility mapping qsm is a post processing technique of gradient echo phase data that attempts to map the spatial distribution of local tissue magnetic susceptibilities to obtain these maps an ill posed field to source inverse problem must be solved to remove non local magnetic field perturbations current state of the art algorithms which aim to solve the dipole inversion problem are plagued by the trade off between reconstruction speed and accuracy a two step dipole inversion algorithm is proposed to bridge this gap our approach first addresses the well conditioned k space region which is reconstructed using a krylov subspace solver then the ill conditioned k space region is reconstructed by solving a constrained l1 minimization problem the proposed pipeline does not incorporate a priori information but utilizes sparsity constraints in the second step we compared our method to well established qsm algorithms with respect to cosmos in in vivo volunteer datasets compared to medi and heidi the proposed algorithm produces susceptibility maps with a lower root mean square error and a higher coefficient of determination with respect to cosmos while being 50 times faster our two step dipole inversion algorithm without a priori information yields improved qsm reconstruction quality at reduced computation times compared to current state of the art methods

a quadratically convergent algorithm for inverse eigenvalue problems with multiple eigenvalues abstract in 2017 for inverse symmetric eigenvalue problems a new quadratically convergent algorithm has been derived from simple matrix equations although this algorithm has some nice features compared with the other quadratically convergent methods it is not applied to multiple eigenvalues in this paper we improve this algorithm with the aid of an optimization problem for the eigenvectors associated with multiple eigenvalues the proposed algorithm is adapted to an arbitrary set of given eigenvalues the main contribution is our convergence theorem formulated in a different manner from previous work for the existing quadratically convergent methods our theorem ensures the quadratic convergence in a neighborhood of the solutions that satisfy a mild condition

a comprehensive analysis of resting state fmri measures to classify individual patients with alzheimer s disease alzheimer s disease ad patients show altered patterns of functional connectivity fc on resting state functional magnetic resonance imaging rsfmri scans it is yet unclear which rsfmri measures are most informative for the individual classification of ad patients we investigated this using rsfmri scans from 77 ad patients mmse 20 4 4 5 and 173 controls mmse 27 5 1 8 we calculated i fc matrices between resting state components as obtained with independent component analysis ica ii the dynamics of these fc matrices using a sliding window approach iii the graph properties e g connection degree and clustering coefficient of the fc matrices and iv we distinguished five fc states and administered how long each subject resided in each of these five states furthermore for each voxel we calculated v fc with 10 resting state networks using dual regression vi fc with the hippocampus vii eigenvector centrality and viii the amplitude of low frequency fluctuations alff these eight measures were used separately as predictors in an elastic net logistic regression and combined in a group lasso logistic regression model we calculated the area under the receiver operating characteristic curve plots auc to determine classification performance the auc values ranged between 0 51 and 0 84 and the highest were found for the fc matrices 0 82 fc dynamics 0 84 and alff 0 82 the combination of all measures resulted in an auc of 0 85 we show that it is possible to obtain moderate to good ad classification using rsfmri scans fc matrices fc dynamics and alff are most discriminative and the combination of all the resting state measures improves classification accuracy slightly

deterministic and probabilistic tractography based on complex fibre orientation distributions we propose an integral concept for tractography to describe crossing and splitting fibre bundles based on the fibre orientation distribution function odf estimated from high angular resolution diffusion imaging hardi we show that in order to perform accurate probabilistic tractography one needs to use a fibre odf estimation and not the diffusion odf we use a new fibre odf estimation obtained from a sharpening deconvolution transform sdt of the diffusion odf reconstructed from q ball imaging qbi this sdt provides new insight into the relationship between the hardi signal the diffusion odf and the fibre odf we demonstrate that the sdt agrees with classical spherical deconvolution and improves the angular resolution of qbi another important contribution of this paper is the development of new deterministic and new probabilistic tractography algorithms using the full multidirectional information obtained through use of the fibre odf an extensive comparison study is performed on human brain datasets comparing our new deterministic and probabilistic tracking algorithms in complex fibre crossing regions finally as an application of our new probabilistic tracking we quantify the reconstruction of transcallosal fibres intersecting with the corona radiata and the superior longitudinal fasciculus in a group of eight subjects most current diffusion tensor imaging dti based methods neglect these fibres which might lead to incorrect interpretations of brain functions

diffeomorphic registration using geodesic shooting and gauss newton optimisation this paper presents a nonlinear image registration algorithm based on the setting of large deformation diffeomorphic metric mapping lddmm but with a more efficient optimisation scheme both in terms of memory required and the number of iterations required to reach convergence rather than perform a variational optimisation on a series of velocity fields the algorithm is formulated to use a geodesic shooting procedure so that only an initial velocity is estimated a gauss newton optimisation strategy is used to achieve faster convergence the algorithm was evaluated using freely available manually labelled datasets and found to compare favourably with other inter subject registration algorithms evaluated using the same data

dynamic multiscale modes of resting state brain activity detected by entropy field decomposition the ability of functional magnetic resonance imaging fmri to noninvasively measure fluctuations in brain activity in the absence of an applied stimulus offers the possibility of discerning functional networks in the resting state of the brain however the reconstruction of brain networks from these signal fluctuations poses a significant challenge because they are generally nonlinear and nongaussian and can overlap in both their spatial and temporal extent moreover because there is no explicit input stimulus there is no signal model with which to compare the brain responses a variety of techniques have been devised to address this problem but the predominant approaches are based on the presupposition of statistical properties of complex brain signal parameters which are unprovable but facilitate the analysis in this article we address this problem with a new method entropy field decomposition for estimating structure within spatiotemporal data this method is based on a general information field theoretic formulation of bayesian probability theory incorporating prior coupling information that allows the enumeration of the most probable parameter configurations without the need for unjustified statistical assumptions this approach facilitates the construction of brain activation modes directly from the spatial temporal correlation structure of the data these modes and their associated spatial temporal correlation structure can then be used to generate space time activity probability trajectories called functional connectivity pathways which provide a characterization of functional brain networks

a two step inexact newton chebyshev like method for inverse eigenvalue problems abstract a two step inexact newton chebyshev like method is proposed to solve inverse eigenvalue problems unlike general newton type methods which need to invert the jacobian matrix that may lead to an unexpected instability the proposed method can guarantee the numerical stability by exploiting the chebyshev method to approximate the inverse of the jacobian matrix theoretically we prove that the proposed method converges cubically numerical examples are given to demonstrate the effectiveness of our method

efficient least squares multimodal registration with a globally exhaustive alignment search there are many image registration situations in which the initial misalignment of the two images is large these registration problems often involving comparison of the two images only within a region of interest roi are difficult to solve most intensity based registration methods perform local optimization of their cost function and often miss the global optimum when the initial misregistration is large the registration of multimodal images makes the problem even more difficult since it limits the choice of available cost functions we have developed an efficient method capable of multimodal rigid body registration within an roi that performs an exhaustive search over all integer translations and a local search over rotations the method uses the fast fourier transform to efficiently compute the sum of squared differences cost function for all possible integer pixel shifts and for each shift models the relationship between the intensities of the two images using linear regression test cases involving medical imaging remote sensing and forensic science applications show that the method consistently brings the two images into close registration so that a local optimization method should have no trouble fine tuning the solution

exploring the 3d geometry of the diffusion kurtosis tensor impact on the development of robust tractography procedures and novel biomarkers diffusion kurtosis imaging dki is a diffusion weighted technique which overcomes limitations of the commonly used diffusion tensor imaging approach this technique models non gaussian behaviour of water diffusion by the diffusion kurtosis tensor kt which can be used to provide indices of tissue heterogeneity and a better characterisation of the spatial architecture of tissue microstructure in this study the geometry of the kt is elucidated using synthetic data generated from multi compartmental models where diffusion heterogeneity between intra and extra cellular media is taken into account as well as the sensitivity of the results to each model parameter and to synthetic noise furthermore based on the assumption that the maxima of the kt are distributed perpendicularly to the direction of well aligned fibres a novel algorithm for estimating fibre direction directly from the kt is proposed and compared to the fibre directions extracted from dki based orientation distribution function odf estimates previously proposed in the literature synthetic data results showed that for fibres crossing at high intersection angles direction estimates extracted directly from the kt have smaller errors than the dki based odf estimation approaches dki odf nevertheless the proposed method showed smaller angular resolution and lower stability to changes of the simulation parameters on real data tractography performed on these kt fibre estimates suggests a higher sensitivity than the dki based odf in resolving lateral corpus callosum fibres reaching the pre central cortex when diffusion acquisition is performed with five b values using faster acquisition schemes kt based tractography did not show improved performance over the dki odf procedures nevertheless it is shown that direct kt fibre estimates are more adequate for computing a generalised version of radial kurtosis maps

approximate cayley transform methods for inverse eigenvalue problems and convergence analysis abstract based on an approximation to cayley transform we propose an approximate cayley transform method and its inexact version for solving inverse eigenvalue problems which has the advantage over other known methods in the sense that it avoids solving systems in obtaining the approximate eigenvectors under the nonsingular condition used in d sun and j sun 29 we show that the proposed methods converge at least superlinearly moreover numerical experiments are given which illustrate that comparing with the cayley transform methods our methods need much less inner iterations and cpu time

functional connectivity and structural covariance between regions of interest can be measured more accurately using multivariate distance correlation studies of brain wide functional connectivity or structural covariance typically use measures like the pearson correlation coefficient applied to data that have been averaged across voxels within regions of interest rois however averaging across voxels may result in biased connectivity estimates when there is inhomogeneity within those rois e g sub regions that exhibit different patterns of functional connectivity or structural covariance here we propose a new measure based on distance correlation a test of multivariate dependence of high dimensional vectors which allows for both linear and non linear dependencies we used simulations to show how distance correlation out performs pearson correlation in the face of inhomogeneous rois to evaluate this new measure on real data we use resting state fmri scans and t1 structural scans from 2 sessions on each of 214 participants from the cambridge centre for ageing neuroscience cam can project pearson correlation and distance correlation showed similar average connectivity patterns for both functional connectivity and structural covariance nevertheless distance correlation was shown to be 1 more reliable across sessions 2 more similar across participants and 3 more robust to different sets of rois moreover we found that the similarity between functional connectivity and structural covariance estimates was higher for distance correlation compared to pearson correlation we also explored the relative effects of different preprocessing options and motion artefacts on functional connectivity because distance correlation is easy to implement and fast to compute it is a promising alternative to pearson correlations for investigating roi based brain wide connectivity patterns for functional as well as structural data

statistical parametric network analysis of functional connectivity dynamics during a working memory task abstract network analysis has become a tool of choice for the study of functional and structural magnetic resonance imaging mri data little research however has investigated connectivity dynamics in relation to varying cognitive load in fmri correlations among slow

a note on the frank tardos bi truncation algorithm for crossing submodular functions recently frank and tardos 1988 presented an algorithm called the bi truncation algorithm for discerning whether a polyhedron defined by q b x x in s forall x subseteq s x x le b x x s b s is nonempty whereb is a crossing submodular function on 2s we point out an error in their algorithm and show how it is corrected

registering a multisensor ensemble of images many registration scenarios involve aligning more than just two images these image sets called ensembles are conventionally registered by choosing one image as a template and every other image is registered to it this pairwise approach is problematic because results depend on which image is chosen as the template the issue is particularly acute for multisensor ensembles because different sensors create images with different features also pairwise methods use only a fraction of the available data at a time in this paper we propose a maximum likelihood clustering method that registers all the images in a multisensor ensemble simultaneously experiments involving rigid body and affine transformations show that the clustering method is more robust and accurate than competing pairwise registration methods moreover the clustering results can be used to form a rudimentary segmentation of the image ensemble

adjusting the effect of nonstationarity in cluster based and tfce inference in nonstationary images cluster inference depends on the local image smoothness as clusters tend to be larger in smoother regions by chance alone in order to correct the inference for such nonstationary cluster sizes can be adjusted according to a local smoothness estimate in this study adjusted cluster sizes are used in a permutation testing framework for both cluster based and threshold free cluster enhancement tfce inference and tested on both simulated and real data we find that tfce inference is already fairly robust to nonstationarity in the data while cluster based inference requires an adjustment to ensure homogeneity a group of possible multi level adjustments are introduced and their results on simulated and real data are assessed using a new performance index we also find that adjusting for local smoothness via a separate resampling procedure is more effective at removing nonstationarity than an adjustment via a random field theory based smoothness estimator

improved optimization for the robust and accurate linear registration and motion correction of brain images linear registration and motion correction are important components of structural and functional brain image analysis most modern methods optimize some intensity based cost function to determine the best registration to date little attention has been focused on the optimization method itself even though the success of most registration methods hinges on the quality of this optimization this paper examines the optimization process in detail and demonstrates that the commonly used multiresolution local optimization methods can and do get trapped in local minima to address this problem two approaches are taken 1 to apodize the cost function and 2 to employ a novel hybrid global local optimization method this new optimization method is specifically designed for registering whole brain images it substantially reduces the likelihood of producing misregistrations due to being trapped by local minima the increased robustness of the method compared to other commonly used methods is demonstrated by a consistency test in addition the accuracy of the registration is demonstrated by a series of experiments with motion correction these motion correction experiments also investigate how the results are affected by different cost functions and interpolation methods

a new method for improving functional to structural mri alignment using local pearson correlation abstract accurate registration of functional magnetic resonance imaging fmri t2 weighted volumes to same subject high resolution t1 weighted structural volumes is important for blood oxygenation level dependent bold fmri and crucial for applications such as cortical surface based analyses and pre surgical planning such registration is generally implemented by minimizing a cost functional which measures the mismatch between two image volumes over the group of proper affine transformations widely used cost functionals such as mutual information mi and correlation ratio cr appear to yield decent alignments when visually judged by matching outer brain contours however close inspection reveals that internal brain structures are often significantly misaligned poor registration is most evident in the ventricles and sulcal folds where csf is concentrated this observation motivated our development of an improved modality specific cost functional which uses a weighted local pearson coefficient lpc to align t2 and t1 weighted images in the absence of an alignment gold standard we used three human observers blinded to registration method to provide an independent assessment of the quality of the registration for each cost functional we found that lpc performed significantly better p

multimodality image registration by maximization of quantitative qualitative measure of mutual information this paper presents a novel image similarity measure referred to as quantitative qualitative measure of mutual information q mi for multimodality image registration conventional information measures e g shannon s entropy and mutual information mi reflect quantitative aspects of information because they only consider probabilities of events in fact each event has its own utility to the fulfillment of the underlying goal which can be independent of its probability of occurrence thus it is important to consider both quantitative i e probability and qualitative i e utility measures of information in order to fully capture the characteristics of events accordingly in multimodality image registration q mi should be used to integrate the information obtained from both the image intensity distributions and the utilities of voxels in the images different voxels can have different utilities for example in brain images two voxels can have the same intensity value but their utilities can be different e g a white matter wm voxel near the cortex can have higher utility than a wm voxel inside a large uniform wm region in q mi the utility of each voxel in an image can be determined according to the regional saliency value calculated from the scale space map of this image since the voxels with higher utility values or saliency values contribute more in measuring q mi of the two images the q mi based registration method is much more robust compared to conventional mi based registration methods also the q mi based registration method can provide a smoother registration function with a relatively larger capture range in this paper the proposed q mi has been validated and applied to the rigid registrations of clinical brain images such as mr ct and pet images

beyond fractional anisotropy extraction of bundle specific structural metrics from crossing fiber models diffusion mri dmri measurements are used for inferring the microstructural properties of white matter and to reconstruct fiber pathways very often voxels contain complex fiber configurations comprising multiple bundles rendering the simple diffusion tensor model unsuitable multi compartment models deliver a convenient parameterization of the underlying complex fiber architecture but pose challenges for fitting and model selection spherical deconvolution in contrast very economically produces a fiber orientation density function fodf without any explicit model assumptions since however the fodf is represented by spherical harmonics a direct interpretation of the model parameters is impossible based on the fact that the fodf can often be interpreted as superposition of multiple peaks each associated to one relatively coherent fiber population bundle we offer a solution that seeks to combine the advantages of both approaches first the fiber configuration is modeled as fodf represented by spherical harmonics and then each of the peaks is parameterized separately in order to characterize the underlying bundle in this work the fodf peaks are approximated by bingham distributions capturing first and second order statistics of the fiber orientations from which we derive metrics for the parametric quantification of fiber bundles we propose meaningful relationships between these measures and the underlying microstructural properties we focus 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 we compare these metrics to the conventionally used fractional anisotropy fa and show how they may help to increase the specificity of the characterization of microstructural properties while metrics relying on the first moments of the bingham distributions provide relatively robust results second order metrics representing the peak spread are only meaningful if the snr is very high and no fiber crossings are present in the voxel

detecting network modules in fmri time series a weighted network analysis approach many network analyses of fmri data begin by defining a set of regions extracting the mean signal from each region and then analyzing the correlations between regions one essential question that has not been addressed in the literature is how to best define the network neighborhoods over which a signal is combined for network analyses here we present a novel unsupervised method for the identification of tightly interconnected voxels or modules from fmri data this approach weighted voxel coactivation network analysis wvcna is based on a method that was originally developed to find modules of genes in gene networks this approach differs from many of the standard network approaches in fmri in that connections between voxels are described by a continuous measure whereas typically voxels are considered to be either connected or not connected depending on whether the correlation between the two voxels survives a hard threshold value additionally instead of simply using pairwise correlations to describe the connection between two voxels wvcna relies on a measure of topological overlap which not only compares how correlated two voxels are but also the degree to which the pair of voxels is highly correlated with the same other voxels we demonstrate the use of wvcna to parcellate the brain into a set of modules that are reliably detected across data within the same subject and across subjects in addition we compare wvcna to ica and show that the wvcna modules have some of the same structure as the ica components but tend to be more spatially focused we also demonstrate the use of some of the wvcna network metrics for assessing a voxel s membership to a module and also how that voxel relates to other modules last we illustrate how wvcna modules can be used in a network analysis to find connections between regions of the brain and show that it produces reasonable results

generalized polymatroids and submodular flows polyhedra related to matroids and sub or supermodular functions play a central role in combinatorial optimization the purpose of this paper is to present a unified treatment of the subject the structure of generalized polymatroids and submodular flow systems is discussed in detail along with their close interrelation in addition to providing several applications we summarize many known results within this general framework

a backward error for the symmetric generalized inverse eigenvalue problem abstract in this paper we discuss the backward error for the symmetric generalized inverse eigenvalue problem which extends the result of sun 1999 10 the optimal backward error is defined for symmetric generalized inverse eigenvalue problem with respect to an approximate solution and the upper and lower bounds are derived for the optimal backward error the expressions may be useful for testing the stability of practical algorithms

segmenting lung fields in serial chest radiographs using both population based and patient specific shape statistics this paper presents a new deformable model using both population based and patient specific shape statistics to segment lung fields from serial chest radiographs there are two novelties in the proposed deformable model first a modified scale invariant feature transform sift local descriptor which is more distinctive than the general intensity and gradient features is used to characterize the image features in the vicinity of each pixel second the deformable contour is constrained by both population based and patient specific shape statistics and it yields more robust and accurate segmentation of lung fields for serial chest radiographs in particular for segmenting the initial time point images the population based shape statistics is used to constrain the deformable contour as more subsequent images of the same patient are acquired the patient specific shape statistics online collected from the previous segmentation results gradually takes more roles thus this patient specific shape statistics is updated each time when a new segmentation result is obtained and it is further used to refine the segmentation results of all the available time point images experimental results show that the proposed method is more robust and accurate than other active shape models in segmenting the lung fields from serial chest radiographs

inexact newton methods for inverse eigenvalue problems in this paper we survey some of the latest development in using inexact newton methods for solving inverse eigenvalue problems these methods require the solutions of nonsymmetric and large linear systems i e the large jacobian equations one can solve these systems by iterative methods inner iterations however iterative methods usually oversolve the problem in the sense that they require far more inner iterations than is required for the convergence of the newton outer iterations the inexact methods can avoid the oversolving problem and hence improve the efficiency the convergence rate of the inexact methods are superlinear and a good tradeoff between the required inner and outer iterations can be obtained

a bayesian model of shape and appearance for subcortical brain segmentation automatic segmentation of subcortical structures in human brain mr images is an important but difficult task due to poor and variable intensity contrast clear well defined intensity features are absent in many places along typical structure boundaries and so extra information is required to achieve successful segmentation a method is proposed here that uses manually labelled image data to provide anatomical training information it utilises the principles of the active shape and appearance models but places them within a bayesian framework allowing probabilistic relationships between shape and intensity to be fully exploited the model is trained for 15 different subcortical structures using 336 manually labelled t1 weighted mr images using the bayesian approach conditional probabilities can be calculated easily and efficiently avoiding technical problems of ill conditioned covariance matrices even with weak priors and eliminating the need for fitting extra empirical scaling parameters as is required in standard active appearance models furthermore differences in boundary vertex locations provide a direct purely local measure of geometric change in structure between groups that unlike voxel based morphometry is not dependent on tissue classification methods or arbitrary smoothing in this paper the fully automated segmentation method is presented and assessed both quantitatively using leave one out testing on the 336 training images and qualitatively using an independent clinical dataset involving alzheimer s disease median dice overlaps between 0 7 and 0 9 are obtained with this method which is comparable or better than other automated methods an implementation of this method called first is currently distributed with the freely available fsl package

constrained linear basis sets for hrf modelling using variational bayes abstract fmri modelling requires flexible haemodynamic response function hrf modelling with the hrf being allowed to vary spatially and between subjects to achieve this flexibility voxelwise parameterised hrfs have been proposed however inference on such models is very slow an alternative approach is to use basis functions allowing inference to proceed in the more manageable general linear model glm framework however a large amount of the subspace spanned by the basis functions produces nonsensical hrf shapes in this work we propose a technique for choosing a basis set and then the means to constrain the subspace spanned by the basis set to only include sensible hrf shapes penny et al neuroimage 2003 showed how variational bayes can be used to infer on the glm for fmri here we extend the work of penny et al to give inference on the glm with constrained hrf basis functions and with spatial markov random fields on the autoregressive noise parameters constraining the subspace spanned by the basis set allows for far superior separation of activating voxels from nonactivating voxels in fmri data we use spatial mixture modelling to produce final probabilities of activation and demonstrate increased sensitivity on an fmri dataset

non parametric model selection for subject specific topological organization of resting state functional connectivity abstract in recent years graph theory has been successfully applied to study functional and anatomical connectivity networks in the human brain most of these networks have shown small world topological characteristics high efficiency in long distance communication between nodes combined with highly interconnected local clusters of nodes moreover functional studies performed at high resolutions have presented convincing evidence that resting state functional connectivity networks exhibits exponentially truncated scale free behavior such evidence however was mostly presented qualitatively in terms of linear regressions of the degree distributions on log log plots even when quantitative measures were given these were usually limited to the r 2 correlation coefficient however the r 2 statistic is not an optimal estimator of explained variance when dealing with truncated power law models recent developments in statistics have introduced new non parametric approaches based on the kolmogorov smirnov test for the problem of model selection in this work we have built on this idea to statistically tackle the issue of model selection for the degree distribution of functional connectivity at rest the analysis performed at voxel level and in a subject specific fashion confirmed the superiority of a truncated power law model showing high consistency across subjects moreover the most highly connected voxels were found to be consistently part of the default mode network our results provide statistically sound support to the evidence previously presented in literature for a truncated power law model of resting state functional connectivity

the effect of global signal regression on dcm estimates of noise and effective connectivity from resting state fmri the influence of global bold fluctuations on resting state functional connectivity in fmri data remains a topic of debate with little consensus in this study we assessed the effects of global signal regression gsr on effective connectivity within and between resting state networks rsns as estimated with dynamic causal modelling dcm for resting state fmri rsfmri dcm incorporates a forward generative model that quantifies the contribution of different types of noise including global measurement noise effective connectivity and neuro vascular processes to functional connectivity measurements dcm analyses were applied to two different designs namely longitudinal and cross sectional designs in the modelling of longitudinal designs we considered four extensive longitudinal resting state fmri datasets with a total number of 20 subjects in the analysis of cross sectional designs we used rsfmri data from 361 subjects from the human connectome project we hypothesized that 1 gsr would have no discernible impact on effective connectivity estimated with dcm and 2 gsr would be reflected in the parameters representing global measurement noise additionally we performed comparative analyses of information gain with and without gsr our results showed negligible to small effects of gsr on effective connectivity within small separately estimated rsns however although the effect sizes were small there was substantial to conclusive evidence for an effect of gsr on connectivity parameters for between network connectivity we found two important effects the effect of gsr on between network effective connectivity averaged over all connections was negligible to small while the effect of gsr on individual connections was non negligible in the cross sectional but not in the longitudinal data some connections showed substantial to conclusive evidence for an effect of gsr contrary to our expectations we found either no effect in the longitudinal designs or a non specific cross sectional design effect of gsr on parameters characterising global measurement noise data without gsr were found to be more informative than data with gsr however in small resting state networks the precision of posterior estimates was greater after gsr in conclusion gsr is a minor concern in dcm studies however quantitative interpretation of between network connections as opposed to average between network connectivity and noise parameters should be treated with some caution the kullback leibler divergence of the posterior from the prior i e information gain together with the precision of posterior estimates might offer a useful measure to assess the appropriateness of gsr in resting state fmri

neural representations of magnitude for natural and rational numbers humans have developed multiple symbolic representations for numbers including natural numbers positive integers as well as rational numbers both fractions and decimals despite a considerable body of behavioral and neuroimaging research it is currently unknown whether different notations map onto a single fully abstract magnitude code or whether separate representations exist for specific number types e g natural versus rational or number representations e g base 10 versus fractions we address this question by comparing brain metabolic response during a magnitude comparison task involving on different trials integers decimals and fractions univariate and multivariate analyses revealed that the strength and pattern of activation for fractions differed systematically within the intraparietal sulcus from that of both decimals and integers while the latter two number representations appeared virtually indistinguishable these results demonstrate that the two major notations formats for rational numbers fractions and decimals evoke distinct neural representations of magnitude with decimals representations being more closely linked to those of integers than to those of magnitude equivalent fractions our findings thus suggest that number representation base 10 versus fractions is an important organizational principle for the neural substrate underlying mathematical cognition

a solution of the affine quadratic inverse eigenvalue problem abstract the quadratic inverse eigenvalue problem qiep is to find the three matrices m c and k given a set of numbers closed under complex conjugations such that these numbers become the eigenvalues of the quadratic pencil p 2 m c k the affine inverse quadratic eigenvalue problem aqiep is the qiep with an additional constraint that the coefficient matrices belong to an affine family that is these matrices are linear combinations of substructured matrices an affine family of matrices very often arise in vibration engineering modeling and analysis research on qiep and aqiep are still at developing stage in this paper we propose three methods and the associated mathematical theories for solving aqiep a newton method an alternating projections method and a hybrid method combining the two validity of these methods are illustrated with results on numerical experiments on a spring mass problem and comparisons are made with these three methods amongst themselves and with another newton method developed by elhay and ram 2002 12 the results of our experiments show that the hybrid method takes much smaller number of iterations and converges faster than any of these methods

radial bias is not necessary for orientation decoding multivariate pattern analysis can be used to decode the orientation of a viewed grating from fmri signals in early visual areas although some studies have reported identifying multiple sources of the orientation information that make decoding possible a recent study argued that orientation decoding is only possible because of a single source a coarse scale retinotopically organized preference for radial orientations here we aim to resolve these discrepant findings we show that there were subtle but critical experimental design choices that led to the erroneous conclusion that a radial bias is the only source of orientation information in fmri signals in particular we show that the reliance on a fast temporal encoding paradigm for spatial mapping can be problematic as effects of space and time become conflated and lead to distorted estimates of a voxel s orientation or retinotopic preference when we implement minor changes to the temporal paradigm or to the visual stimulus itself by slowing the periodic rotation of the stimulus or by smoothing its contrast energy profile we find significant evidence of orientation information that does not originate from radial bias in an additional block paradigm experiment where space and time were not conflated we apply a formal model comparison approach and find that many voxels exhibit more complex tuning properties than predicted by radial bias alone or in combination with other known coarse scale biases our findings support the conclusion that radial bias is not necessary for orientation decoding in addition our study highlights potential limitations of using temporal phase encoded fmri designs for characterizing voxel tuning properties

effects of diffusion weighting schemes on the reproducibility of dti derived fractional anisotropy mean diffusivity and principal eigenvector measurements at 1 5t diffusion tensor imaging dti is used to study tissue composition and architecture in vivo to increase the signal to noise ratio snr of dti contrasts studies typically use more than the minimum of 6 diffusion weighting dw directions or acquire repeated observations of the same set of dw directions simulation based studies have sought to optimize dti acquisitions and suggest that increasing the directional resolution of a dti dataset i e the number of distinct directions is preferable to repeating observations in an equal scan time comparison however it is not always clear how to translate these recommendations into practice when considering physiological noise and scanner stability furthermore the effect of different dw schemes on in vivo dti findings is not fully understood this study characterizes how the makeup of a dw scheme in terms of the number of directions impacts the precision and accuracy of in vivo fractional anisotropy fa mean diffusivity md and principal eigenvector pev findings orientation dependence of dti reliability is demonstrated in vivo and a principled theoretical framework is provided to support and interpret findings with simulation results as long as sampling orientations are well balanced differences in dti contrasts due to different dw schemes are shown to be small relative to intra session variability these differences are accentuated at low snr while minimized at high snr this result suggests that typical clinical studies which use similar protocols but different well balanced dw schemes are readily comparable within the experimental precision

quantitative susceptibility mapping using structural feature based collaborative reconstruction sfcr in the human brain the reconstruction of mr quantitative susceptibility mapping qsm from local phase measurements is an ill posed inverse problem and different regularization strategies incorporating a priori information extracted from magnitude and phase images have been proposed however the anatomy observed in magnitude and phase images does not always coincide spatially with that in susceptibility maps which could give erroneous estimation in the reconstructed susceptibility map in this paper we develop a structural feature based collaborative reconstruction sfcr method for qsm including both magnitude and susceptibility based information the sfcr algorithm is composed of two consecutive steps corresponding to complementary reconstruction models each with a structural feature based l 1 norm constraint and a voxel fidelity based l 2 norm constraint which allows both the structure edges and tiny features to be recovered whereas the noise and artifacts could be reduced in the m step the initial susceptibility map is reconstructed by employing a rm k space based compressed sensing model incorporating magnitude prior in the s step the susceptibility map is fitted in spatial domain using weighted constraints derived from the initial susceptibility map from the m step simulations and in vivo human experiments at 7t mri show that the sfcr method provides high quality susceptibility maps with improved rmse and mssim finally the susceptibility values of deep gray matter are analyzed in multiple head positions with the supine position most approximate to the gold standard cosmos result