comparison of quantitative diagnostic tests type i error power and sample size for a quantitative laboratory test the 0 975 fractile of the distribution of reference values is commonly used as a discrimination limit and the sensitivity of the test is the proportion of diseased subjects with values exceeding this limit a comparison of the estimates of sensitivity between two tests without taking into account the sampling variation of the discrimination limits can increase the type i error to about seven times the nominal value of 0 05 correct statistical procedures are considered and the power and required sample size are studied for gaussian and log gaussian distributions of diagnostic test values the results may be useful for the planning phase of studies to evaluate quantitative diagnostic tests

spatial normalization of diffusion tensor mri using multiple channels diffusion tensor mri dt mri can provide important in vivo information for the detection of brain abnormalities in diseases characterized by compromised neural connectivity to quantify diffusion tensor abnormalities based on voxel based statistical analysis spatial normalization is required to minimize the anatomical variability between studied brain structures in this article we used a multiple input channel registration algorithm based on a demons algorithm and evaluated the spatial normalization of diffusion tensor image in terms of the input information used for registration registration was performed on 16 dt mri data sets using different combinations of the channels including a channel of t2 weighted intensity a channel of the fractional anisotropy a channel of the difference of the first and second eigenvalues two channels of the fractional anisotropy and the trace of tensor three channels of the eigenvalues of the tensor and the six channel tensor components to evaluate the registration of tensor data we defined two similarity measures i e the endpoint divergence and the mean square error which we applied to the fiber bundles of target images and registered images at the same seed points in white matter segmentation we also evaluated the tensor registration by examining the voxel by voxel alignment of tensors in a sample of 15 normalized dt mris in all evaluations nonlinear warping using six independent tensor components as input channels showed the best performance in effectively normalizing the tract morphology and tensor orientation we also present a nonlinear method for creating a group diffusion tensor atlas using the average tensor field and the average deformation field which we believe is a better approach than a strict linear one for representing both tensor distribution and morphological distribution of the population

unified framework for anisotropic interpolation and smoothing of diffusion tensor images to enhance the performance of diffusion tensor imaging dti based fiber tractography this study proposes a unified framework for anisotropic interpolation and smoothing of dti data the critical component of this framework is an anisotropic sigmoid interpolation kernel which is adaptively modulated by the local image intensity gradient profile the adaptive modulation of the sigmoid kernel permits image smoothing in homogeneous regions and meanwhile guarantees preservation of structural boundaries the unified scheme thus allows piece wise smooth continuous and boundary preservation interpolation of dti data so that smooth fiber tracts can be tracked in a continuous manner and confined within the boundaries of the targeted structure the new interpolation method is compared with conventional interpolation methods on the basis of fiber tracking from synthetic and in vivo dti data which demonstrates the effectiveness of this unified framework

direct estimation of the fiber orientation density function from diffusion weighted mri data using spherical deconvolution diffusion weighted magnetic resonance imaging can provide information related to the arrangement of white matter fibers the diffusion tensor is the model most commonly used to derive the orientation of the fibers within a voxel however this model has been shown to fail in regions containing several fiber populations with distinct orientations a number of alternative models have been suggested such as multiple tensor fitting q space and q ball imaging however each of these has inherent limitations in this study we propose a novel method for estimating the fiber orientation distribution directly from high angular resolution diffusion weighted mr data without the need for prior assumptions regarding the number of fiber populations present we assume that all white matter fiber bundles in the brain share identical diffusion characteristics thus implicitly assigning any differences in diffusion anisotropy to partial volume effects the diffusion weighted signal attenuation measured over the surface of a sphere can then be expressed as the convolution over the sphere of a response function the diffusion weighted attenuation profile for a typical fiber bundle with the fiber orientation density function odf the fiber odf the distribution of fiber orientations within the voxel can therefore be obtained using spherical deconvolution the properties of the technique are demonstrated using simulations and on data acquired from a volunteer using a standard 1 5 t clinical scanner the technique can recover the fiber odf in regions of multiple fiber crossing and holds promise for applications such as tractography

f timer fast tensor image morphing for elastic registration we propose a novel diffusion tensor imaging dti registration algorithm called fast tensor image morphing for elastic registration f timer f timer leverages multiscale tensor regional distributions and local boundaries for hierarchically driving deformable matching of tensor image volumes registration is achieved by utilizing a set of automatically determined structural landmarks via solving a soft correspondence problem based on the estimated correspondences thin plate splines are employed to generate a smooth topology preserving and dense transformation and to avoid arbitrary mapping of nonlandmark voxels to mitigate the problem of local minima which is common in the estimation of high dimensional transformations we employ a hierarchical strategy where a small subset of voxels with more distinctive attribute vectors are first deployed as landmarks to estimate a relatively robust low degrees of freedom transformation as the registration progresses an increasing number of voxels are permitted to participate in refining the correspondence matching a scheme as such allows less conservative progression of the correspondence matching towards the optimal solution and hence results in a faster matching speed compared with its predecessor timer which has been shown to outperform state of the art algorithms experimental results indicate that f timer is capable of achieving comparable accuracy at only a fraction of the computation cost

characterization of all copulas associated with non continuous random variables we introduce a constructive method by means of a doubly stochastic measure to describe all the copulas that in view of sklar s theorem are able to connect a bivariate distribution to its marginals we use this to give the lower and upper optimal bounds for all the copulas that extend a given subcopula

registration of 4d cardiac ct sequences under trajectory constraints with multichannel diffeomorphic demons we propose a framework for the nonlinear spatiotemporal registration of 4d time series of images based on the diffeomorphic demons dd algorithm in this framework the 4d spatiotemporal registration is decoupled into a 4d temporal registration defined as mapping physiological states and a 4d spatial registration defined as mapping trajectories of physical points our contribution focuses more specifically on the 4d spatial registration that should be consistent over time as opposed to 3d registration that solely aims at mapping homologous points at a given time point first we estimate in each sequence the motion displacement field which is a dense representation of the point trajectories we want to register then we perform simultaneously 3d registrations of corresponding time points with the constraints to map the same physical points over time called the trajectory constraints under these constraints we show that the 4d spatial registration can be formulated as a multichannel registration of 3d images to solve it we propose a novel version of the diffeomorphic demons dd algorithm extended to vector valued 3d images the multichannel diffeomorphic demons mdd for evaluation this framework is applied to the registration of 4d cardiac computed tomography ct sequences and compared to other standard methods with real patient data and synthetic data simulated from a physiologically realistic electromechanical cardiac model results show that the trajectory constraints act as a temporal regularization consistent with motion whereas the multichannel registration acts as a spatial regularization finally using these trajectory constraints with multichannel registration yields the best compromise between registration accuracy temporal and spatial smoothness and computation times a prospective example of application is also presented with the spatiotemporal registration of 4d cardiac ct sequences of the same patient before and after radiofrequency ablation rfa in case of atrial fibrillation af the intersequence spatial transformations over a cardiac cycle allow to analyze and quantify the regression of left ventricular hypertrophy and its impact on the cardiac function

fiber tracking from dti using linear state space models detectability of the pyramidal tract abstract diffusiontensor imaging dti is an emerging and promising tool to provide information about the course of white matter fiber tracts in the human brain based on specific acquisition schemes diffusion tensor data resemble local fiber orientations allowing for a reconstruction of the fiber bundles current techniques to calculate fascicles range from simple heuristic tracking solutions to bayesian and differential equations approaches most methods are based only on local diffusion information often resulting in bending or kinking fiber paths in voxels with reduced diffusion properties in this article we present a new tracking approach based on linear state space models encompassing an inherent smoothness criterion to avoid too wiggly tracked fiber bundles the new technique will be described formally and tested on simulated and real data the performance tests are focused on the pyramidal tract where we employed a test retest study and a group comparison in healthy subjects anatomical course was confirmed in a patient with selective degeneration of the pyramidal tract the potential of the presented technique for improved neurosurgical planning is demonstrated by visualization of a tumor induced displacement of the motor pathways the paper closes with a thorough discussion of perspectives and limitations of the new tracking approach

dti segmentation via the combined analysis of connectivity maps and tensor distances we describe a novel approach to extract the neural tracts of interest from a diffusion tensor image dti compared to standard streamline tractography existing probabilistic methods are able to capture fiber paths that deviate from the main tensor diffusion directions at the same time tensor clustering methods are able to more precisely delimit the border of the bundle to the best of our knowledge we propose the first algorithm which combines the advantages supplied by probabilistic and tensor clustering approaches the algorithm includes a post processing step to limit partial volume related segmentation errors we extensively test the accuracy of our algorithm on different configurations of a dti software phantom for which we systematically vary the image noise the number of gradients the geometry of the fiber paths and the angle between adjacent and crossing fiber bundles the reproducibility of the algorithm is supported by the segmentation of the corticospinal tract of nine patients additional segmentations of the corticospinal tract the arcuate fasciculus and the optic radiations are in accordance with anatomical knowledge the required user interaction is comparable to that of streamline tractography which allows for an uncomplicated integration of the algorithm into the clinical routine

constructing a cut off point for a quantitative diagnostic test this paper is concerned with the problem of constructing a suitable cut off point for a quantitative diagnostic test from a sample of diseased and non diseased individuals when the specificity and or sensitivity required for the resulting diagnostic classification rule are specified statistical procedures are discussed which yield an explicit cut off point together with the necessary confidence limits on the true specificity and sensitivity of the test operating at this point by contrast to confidence limits referring to an unknown optimal choice of the cut off point sample size formulae are derived showing a relative efficiency of up to 1 5 for a new procedure introduced in this paper over the usual procedure based on tolerance limits

dt refind diffusion tensor registration with exact finite strain differential in this paper we propose the dt refind algorithm for the diffeomorphic nonlinear registration of diffusion tensor images unlike scalar images deforming tensor images requires choosing both a reorientation strategy and an interpolation scheme current diffusion tensor registration algorithms that use full tensor information face difficulties in computing the differential of the tensor reorientation strategy and consequently these methods often approximate the gradient of the objective function in the case of the finite strain fs reorientation strategy we borrow results from the pose estimation literature in computer vision to derive an analytical gradient of the registration objective function by utilizing the closed form gradient and the velocity field representation of one parameter subgroups of diffeomorphisms the resulting registration algorithm is diffeomorphic and fast we contrast the algorithm with a traditional fs alternative that ignores the reorientation in the gradient computation we show that the exact gradient leads to significantly better registration at the cost of computation time independently of the choice of euclidean or log euclidean interpolation and sum of squared differences dissimilarity measure the exact gradient achieves better alignment over an entire spectrum of deformation penalties alignment quality is assessed with a battery of metrics including tensor overlap fractional anisotropy inverse consistency and closeness to synthetic warps the improvements persist even when a different reorientation scheme preservation of principal directions is used to apply the final deformations

probabilistic diffusion tractography with multiple fibre orientations what can we gain we present a direct extension of probabilistic diffusion tractography to the case of multiple fibre orientations using automatic relevance determination we are able to perform online selection of the number of fibre orientations supported by the data at each voxel simplifying the problem of tracking in a multi orientation field we then apply the identical probabilistic algorithm to tractography in the multi and single fibre cases in a number of example systems which have previously been tracked successfully or unsuccessfully with single fibre tractography we show that multi fibre tractography offers significant advantages in sensitivity when tracking non dominant fibre populations but does not dramatically change tractography results for the dominant pathways

some new characterizations and properties of quasi copulas in this paper we characterize the concept of quasi copula in three different ways as a special subclass of aggregation operators in terms of its associated volume and for the bivariate case in terms of non increasing tracks on 0 1 2 we also provide sufficient conditions and new properties for quasi copulas

a diffusion tensor imaging tractography algorithm based on navier stokes fluid mechanics we introduce a fluid mechanics based tractography method for estimating the most likely connection paths between points in diffusion tensor imaging dti volumes we customize the navier stokes equations to include information from the diffusion tensor and simulate an artificial fluid flow through the dti image volume we then estimate the most likely connection paths between points in the dti volume using a metric derived from the fluid velocity vector field we validate our algorithm using digital dti phantoms based on a helical shape our method segmented the structure of the phantom with less distortion than was produced using implementations of heat based partial differential equation pde and streamline based methods in addition our method was able to successfully segment divergent and crossing fiber geometries closely following the ideal path through a digital helical phantom in the presence of multiple crossing tracts to assess the performance of our algorithm on anatomical data we applied our method to dti volumes from normal human subjects our method produced paths that were consistent with both known anatomy and directionally encoded color images of the dti dataset

reflection invariant copulas abstract in the present paper we study the class of all those copulas that are invariant under a special class of transformations called reflections in particular we focus on the special role played by the independence copula within this class for this purpose we introduce a bijective transformation which turns every copula into a reflection invariant copula and enforces a strong geometric property the n fold composition of this transformation to a d dimensional copula coincides with the independence copula on the mesh 0 1 2 n 2 n 1 2 n 1 d it turns out that the independence copula is the unique fixed point of the introduced transformation

a novel tensor distribution model for the diffusion weighted mr signal diffusion mri is a non invasive imaging technique that allows the measurement of water molecule diffusion through tissue in vivo the directional features of water diffusion allow one to infer the connectivity patterns prevalent in tissue and possibly track changes in this connectivity over time for various clinical applications in this paper we present a novel statistical model for diffusion weighted mr signal attenuation which postulates that the water molecule diffusion can be characterized by a continuous mixture of diffusion tensors an interesting observation is that this continuous mixture and the mr signal attenuation are related through the laplace transform of a probability distribution over symmetric positive definite matrices we then show that when the mixing distribution is a wishart distribution the resulting closed form of the laplace transform leads to a rigaut type asymptotic fractal expression which has been phenomenologically used in the past to explain the mr signal decay but never with a rigorous mathematical justification until now our model not only includes the traditional diffusion tensor model as a special instance in the limiting case but also can be adjusted to describe complex tissue structure involving multiple fiber populations using this new model in conjunction with a spherical deconvolution approach we present an efficient scheme for estimating the water molecule displacement probability functions on a voxel by voxel basis experimental results on both simulations and real data are presented to demonstrate the robustness and accuracy of the proposed algorithms

spatial shrinkage estimation of diffusion tensors on diffusion weighted imaging data diffusion tensor imaging dti based on the diffusion weighted imaging dwi data acquired from magnetic resonance experiments has been widely used to analyze the physical structure of white matter fibers in the human brain in vivo the raw dwi data however carry noise this contaminates the diffusion tensor dt estimates and introduces systematic bias into the induced eigenvalues these bias components affect the effectiveness of fiber tracking algorithms in this article we propose a two stage spatial shrinkage estimation spske procedure to accommodate the spatial information carried in dwi data in dt estimation and to reduce the bias components in the corresponding derived eigenvalues to this end in the framework of the heteroscedastic linear model spske incorporates l 1 type penalization and the locally weighted least square function the theoretical properties of spske are explored the effectiveness of spske is further illustrated by simulation and real data examples supplementary materi

a bayesian approach for stochastic white matter tractography white matter fiber bundles in the human brain can be located by tracing the local water diffusion in diffusion weighted magnetic resonance imaging mri images in this paper a novel bayesian modeling approach for white matter tractography is presented the uncertainty associated with estimated white matter fiber paths is investigated and a method for calculating the probability of a connection between two areas in the brain is introduced the main merits of the presented methodology are its simple implementation and its ability to handle noise in a theoretically justified way theory for estimating global connectivity is also presented as well as a theorem that facilitates the estimation of the parameters in a constrained tensor model of the local water diffusion profile

efficient confidence bounds for roc curves the specificity and sensitivity of a quantitative diagnostic marker depends on the selected cut off point the roc curve is generated by plotting sensitivity against specificity as the cut off point runs through the whole range of possible marker values confidence bounds for roc curves may be constructed by combining two separate confidence intervals for sensitivity and specificity in the present paper a more efficient method which is based on a statistical test introduced by greenhouse and mantel is presented the resulting 95 per cent confidence intervals are up to 40 per cent smaller a formula is given to calculate the sample size necessary to obtain a confidence interval of a stipulated length at a specified point of the roc curve as an example the performance of a tumour marker in the diagnosis of bone marrow metastases is investigated

a constrained variational principle for direct estimation and smoothing of the diffusion tensor field from complex dwi in this paper we present a novel constrained variational principle for simultaneous smoothing and estimation of the diffusion tensor field from complex valued diffusion weighted images dwi the constrained variational principle involves the minimization of a regularization term of l sup p norms subject to a nonlinear inequality constraint on the data the data term we employ is the original stejskal tanner equation instead of the linearized version usually employed in literature the complex valued nonlinear form leads to a more accurate when compared to the linearized version estimate of the tensor field the inequality constraint requires that the nonlinear least squares data term be bounded from above by a known tolerance factor finally in order to accommodate the positive definite constraint on the diffusion tensor it is expressed in terms of cholesky factors and estimated the constrained variational principle is solved using the augmented lagrangian technique in conjunction with the limited memory quasi newton method experiments with complex valued synthetic and real data are shown to depict the performance of our tensor field estimation and smoothing algorithm

spatial normalization and averaging of diffusion tensor mri data sets diffusion tensor magnetic resonance imaging dt mri is unique in providing information about both the structural integrity and the orientation of white matter fibers in vivo and through tractography revealing the trajectories of white matter tracts dt mri is therefore a promising technique for detecting differences in white matter architecture between different subject populations however while studies involving analyses of group averages of scalar quantities derived from dt mri data have been performed as yet there have been no similar studies involving the whole tensor here we present the first step towards realizing such a study i e the spatial normalization of whole tensor data sets the approach is illustrated by spatial normalization of 10 dt mri data sets to a standard anatomical template both qualitative and quantitative approaches are described for assessing the results of spatial normalization techniques are then described for combining the spatially normalized data sets according to three definitions of average i e the mean median and mode of a distribution of tensors the current absence of and hence need for appropriate statistical tests for comparison of results derived from group averaged dt mri data sets is then discussed finally the feasibility of performing tractography on the group averaged dt mri data set is investigated and the possibility and implications of generating a generic map of brain connectivity from a group of subjects is considered

dt mri fiber tracking a shortest paths approach we derive a new fiber tracking algorithm for dt mri that parts with the locally ldquogreedyrdquo paradigm intrinsic to conventional tracking algorithms we demonstrate the ability to precisely reconstruct a diverse range of fiber trajectories in authentic and computer generated dt mri data for which well known conventional tracking algorithms are shown to fail our approach is to pose fiber tracking as a problem in computing shortest paths in a weighted digraph voxels serve as vertices and edges are included between neighboring voxels we assign probabilities weights to edges using a bayesian framework higher probabilities are assigned to edges that are aligned with fiber trajectories in their close proximity we compute optimal paths of maximum probability using computationally scalable shortest path algorithms the salient features of our approach are global optimality unlike conventional tracking algorithms local errors do not accumulate and one ldquowrong turnrdquo does not spell disaster a target point is specified a priori precise reconstruction is demonstrated for extremely low signal to noise ratio impartiality to which of two endpoints is used as a seed and faster computation times than conventional all paths tracking we can use our new tracking algorithm in either a single path tracking mode deterministic tracking or an all paths tracking mode probabilistic tracking

a framework for callosal fiber distribution analysis this paper presents a framework for analyzing the spatial distribution of neural fibers in the brain with emphasis on interhemispheric fiber bundles crossing through the corpus callosum the proposed approach combines methodologies for fiber tracking and spatial normalization and is applied on diffusion tensor images and standard magnetic resonance images

filtered multitensor tractography we describe a technique that uses tractography to drive the local fiber model estimation existing techniques use independent estimation at each voxel so there is no running knowledge of confidence in the estimated model fit we formulate fiber tracking as recursive estimation at each step of tracing the fiber the current estimate is guided by those previous to do this we perform tractography within a filter framework and use a discrete mixture of gaussian tensors to model the signal starting from a seed point each fiber is traced to its termination using an unscented kalman filter to simultaneously fit the local model to the signal and propagate in the most consistent direction despite the presence of noise and uncertainty this provides a causal estimate of the local structure at each point along the fiber using two and three fiber models we demonstrate in synthetic experiments that this approach significantly improves the angular resolution at crossings and branchings in vivo experiments confirm the ability to trace through regions known to contain such crossing and branching while providing inherent path regularization

a hitchhiker s guide to quasi copulas abstract this paper presents a review of the concept of an n quasi copula starting from the characterization of functions that can be derived from operations on random variables we recall several other characterizations and properties that have been proven in the literature highlighting the differences between the bivariate case and the higher dimensional case additionally we recall several applications of n quasi copulas such as their role in the study of bounds on sets of n copulas we also recall various classes of n quasi copulas that have been studied in the literature finally we present some questions that have not yet been answered in the literature

a new parametric method based on s distributions for computing receiver operating characteristic curves for continuous diagnostic tests receiver operating characteristic roc curves provides a method for evaluating the performance of a diagnostic test these curves represent the true positive ratio that is the true positives among those affected by the disease as a function of the false positive ratio that is the false positives among the healthy corresponding to each possible value of the diagnostic variable when the diagnostic variable is continuous the corresponding roc curve is also continuous however estimation of such curve through the analysis of sample data yields a step line unless some assumption is made on the underlying distribution of the considered variable since the actual distribution of the diagnostic test is seldom known it is difficult to select an appropriate distribution for practical use data transformation may offer a solution but also may introduce a distortion on the evaluation of the diagnostic test in this paper we show that the distribution family known as the s distribution can be used to solve this problem the s distribution is defined as a differential equation in which the dependent variable is the cumulative this special form provides a highly flexible family of distributions that can be used as models for unknown distributions it has been shown that classical statistical distributions can be represented accurately as s distributions and that they occur in a definite subspace of the parameter space corresponding to the whole s distribution family consequently many other distributional forms that do not correspond to known distributions are provided by the s distribution this property can be used to model observed data for unknown distributions and is very useful in constructing parametric roc curves in those cases after fitting an s distribution to the observed samples of diseased and healthy populations roc curve computation is straightforward a roc curve can be considered as the solution of a differential equation in which the dependent variable is the ratio of true positives and the independent variable is the ratio of false positives this equation can be easily obtained from the s distributions fitted to observed data using these results we can compute pointwise confidence bands for the roc curve and the corresponding area under the curve we shall compare this approach with the empirical and the binormal methods for estimating a roc curve to show that the s distribution based method is a useful parametric procedure

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

integral curves of noisy vector fields and statistical problems in diffusion tensor imaging nonparametric kernel estimation and hypotheses testing let v be a vector field in a bounded open set g d suppose that v is observed with a random noise at random points x i i 1 n that are independent and uniformly distributed in g the problem is to estimate the integral curve of the differential equation dx t dt q x 0 x 0 g starting at a given point x 0 x 0 g and to develop statistical tests for the hypothesis that the integral curve reaches a specified set r c g we develop an estimation procedure based on a nadaraya watson type kernel regression estimator show the asymptotic normality of the estimated integral curve and derive differential and integral equations for the mean and covariance function of the limit gaussian process this provides a method of tracking not only the integral curve but also the covariance matrix of its estimate we also study the asymptotic distribution of the squared minimal distance from the integral curve to a smooth enough surface r c g building upon this we develop testing procedures for the hypothesis that the integral curve reaches r the problems of this nature are of interest in diffusion tensor imaging a brain imaging technique based on measuring the diffusion tensor at discrete locations in the cerebral white matter where the diffusion of water molecules is typically anisotropic the diffusion tensor data is used to estimate the dominant orientations of the diffusion and to track white matter fibers from the initial location following these orientations our approach brings more rigorous statistical tools to the analysis of this problem providing in particular hypothesis testing procedures that might be useful in the study of axonal connectivity of the white matter

regional confidence bands for roc curves the performance of a diagnostic test is characterized by its specificity and sensitivity for a quantitative diagnostic test these criteria depend on the selected cut off point the receiver operating characteristic roc curve of a quantitative diagnostic test is generated by plotting sensitivity against specificity as the cut off point runs through the whole range of possible test values in practice the roc curve is estimated from clinical data one important goal is to select an optimal cut off point for this purpose the sample variability has to be taken into account recently campbell has introduced non parametric asymptotic simultaneous confidence bands that are valid for the whole roc curve in this paper a non parametric asymptotic approach for the construction of regional confidence bands for roc curves is proposed it can be applied for any specificity interval of interest our approach is based on the asymptotic theory of empirical and quantile processes to investigate the small sample properties of the different approaches a monte carlo study was conducted using normal and log normal data a method for sample size calculation is presented finally the approaches are applied to a tumour marker in the diagnosis of bone marrow metastases

resolution of complex tissue microarchitecture using the diffusion orientation transform dot this article describes an accurate and fast method for fiber orientation mapping using multidirectional diffusion weighted magnetic resonance mr data this novel approach utilizes the fourier transform relationship between the water displacement probabilities and diffusion attenuated mr signal expressed in spherical coordinates the radial part of the fourier integral is evaluated analytically under the assumption that mr signal attenuates exponentially the values of the resulting functions are evaluated at a fixed distance away from the origin the spherical harmonic transform of these functions yields the laplace series coefficients of the probabilities on a sphere of fixed radius alternatively probability values can be computed nonparametrically using legendre polynomials orientation maps calculated from excised rat nervous tissue data demonstrate this technique s ability to accurately resolve crossing fibers in anatomical regions such as the optic chiasm this proposed methodology has a trivial extension to multiexponential diffusion weighted signal decay the developed methods will improve the reliability of tractography schemes and may make it possible to correctly identify the neural connections between functionally connected regions of the nervous system

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

phase vector incompressible registration algorithm for motion estimation from tagged magnetic resonance images tagged magnetic resonance imaging has been used for decades to observe and quantify motion and strain of deforming tissue it is challenging to obtain 3 d motion estimates due to a tradeoff between image slice density and acquisition time typically interpolation methods are used either to combine 2 d motion extracted from sparse slice acquisitions into 3 d motion or to construct a dense volume from sparse acquisitions before image registration methods are applied this paper proposes a new phase based 3 d motion estimation technique that first computes harmonic phase volumes from interpolated tagged slices and then matches them using an image registration framework the approach uses several concepts from diffeomorphic image registration with a key novelty that defines a symmetric similarity metric on harmonic phase volumes from multiple orientations the material property of harmonic phase solves the aperture problem of optical flow and intensity based methods and is robust to tag fading a harmonic magnitude volume is used in enforcing incompressibility in the tissue regions the estimated motion fields are dense incompressible diffeomorphic and inverse consistent at a 3 d voxel level the method was evaluated using simulated phantoms human brain data in mild head accelerations human tongue data during speech and an open cardiac data set the method shows comparable accuracy to three existing methods while demonstrating low computation time and robustness to tag fading and noise

fast local trust region technique for diffusion tensor registration using exact reorientation and regularization diffusion tensor imaging is widely used in brain connectivity research as more and more studies recruit large numbers of subjects it is important to design registration methods which are not only theoretically rigorous but also computationally efficient however the requirement of reorienting diffusion tensors complicates and considerably slows down registration procedures due to the correlated impacts of registration forces at adjacent voxel locations based on the diffeomorphic demons algorithm vercauteren 2009 we propose a fast local trust region algorithm for handling inseparable registration forces for quadratic energy functions the method guarantees that at any time and at any voxel location the velocity is always within its local trust region this local regularization allows efficient calculation of the transformation update with numeric integration instead of completely solving a large linear system at every iteration it is able to incorporate exact reorientation and regularization into the velocity optimization and preserve the linear complexity of the diffeomorphic demons algorithm in an experiment with 84 diffusion tensor images involving both pair wise and group wise registrations the proposed algorithm achieves better registration in comparison with other methods solving large linear systems yeo 2009 at the same time this algorithm reduces the computation time and memory demand tenfold

improved fiber tractography with bayesian tensor regularization diffusion tensor tractography suffers from the effects of noise and partial volume averaging pva for reliable reconstruction of fiber pathways tracking algorithms that are robust to these artifacts are called for to meet this need the present study establishes a novel bayesian regularization framework for fiber tracking that takes into account the effects of noise and pva thereby improving tracking accuracy and precision with this framework the propagation of a fiber path follows an optimal vector determined by bayes decision rule the probability functions involved are modeled on the basis of multivariate normal distributions of diffusion tensor elements which allows the optimal solution with maximum a posteriori probability to be derived analytically parameters for the probability functions are estimated from the uncertainty of tensor elements and the variance among tensors within an oriented sampling volume weighted by fractional anisotropy experiments with monte carlo simulations synthetic and in vivo human diffusion tensor data demonstrate that this specialized scheme enhances the immunity of fiber tracking to noise and pva and hence enables fibers to be more faithfully reconstructed

a large deformation diffeomorphic metric mapping solution for diffusion spectrum imaging datasets spatial transformation for diffusion spectrum imaging dsi is an important step for group analyses of dsi datasets in this study we developed a transformation method for dsi datasets under the framework of large deformation diffeomorphic metric mapping lddmm which is termed lddmm dsi the proposed method made use of the fact that a dsi dataset is 6d and generalized the original 2d 3d lddmm algorithm to the 6d case with some modifications made for the dsi datasets in this manner the conventional reorientation problem that arises from transforming diffusion weighted datasets was avoided by making the dsi datasets capable of being freely deformed in the q space the algorithm treated the data matching task as a variational problem under the lddmm framework and sought optimal velocity fields from which the generated transformations were diffeomorphic and the transformation curve was a geodesic the mathematical materials and numerical implementation are detailed in the paper and experiments were performed to analyze the proposed method on real brain dsi datasets the results showed that the method was capable of registering different dsi datasets in both global structural shapes and local diffusion profiles in conclusion the proposed method can facilitate group analyses of dsi datasets and the generation of a dsi template

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

frequency polygons theory and application abstract in this article i investigate the theoretical properties and applications of the frequency polygon which is constructed by connecting with straight lines the mid bin values of a histogram for estimating an unknown probability density function using a random sample the frequency polygon is shown to dominate the histogram with respect to the criterion of integrated mean squared error achieving the same rate of convergence to zero of the integrated mean squared error as non negative kernel estimators data based algorithms for constructing frequency polygons are discussed and illustrated one is based on a histogram with bin width equal to 2 15sn 1 5 where s is an estimate of the standard deviation from a sample of size n another approach is based on the method of generalized crossvalidation the bivariate frequency polygon is also investigated comparisons are made between the frequency polygon and other density estimators examples with data in one and two dimensions are presented

high dimensional spatial normalization of diffusion tensor images improves the detection of white matter differences an example study using amyotrophic lateral sclerosis spatial normalization of diffusion tensor images plays a key role in voxel based analysis of white matter wm group differences currently it has been achieved using low dimensional registration methods in the large majority of clinical studies this paper aims to motivate the use of high dimensional normalization approaches by generating evidence of their impact on the findings of such studies using an ongoing amyotrophic lateral sclerosis als study we evaluated three normalization methods representing the current range of available approaches low dimensional normalization using the fractional anisotropy fa high dimensional normalization using the fa and high dimensional normalization using full tensor information each method was assessed in terms of its ability to detect significant differences between als patients and controls our findings suggest that inadequate normalization with low dimensional approaches can result in insufficient removal of shape differences which in turn can confound fa differences in a complex manner and that utilizing high dimensional normalization can both significantly minimize the confounding effect of shape differences to fa differences and provide a more complete description of wm differences in terms of both size and tissue architecture differences we also found that high dimensional approaches by leveraging full tensor features instead of tensor derived indices can further improve the alignment of wm tracts

flipping and cyclic shifting of binary aggregation functions we introduce two types of transformations of random variables called flipping and cyclic shifting as these transformations preserve monotonicity at the level of univariate cumulative distribution functions they can be used to develop corresponding coordinate wise transformations of binary aggregation functions we lay bare the admissibility of these transformations i e the necessary and sufficient conditions under which they result in a binary aggregation function we investigate which additional properties such as the 1 lipschitz property and 2 increasingness entail these admissibility conditions moreover we point out which of these properties are preserved under flipping and or cyclic shifting interestingly quasi copulas remain quasi copulas under flipping while copulas remain copulas under flipping as well as under cyclic shifting

multimodal brain warping using the demons algorithm and adaptative intensity corrections this paper presents an original method for three dimensional elastic registrat ion of multimodal images we propose to make use of a scheme that iterates between correcting for intensity differences between images and performing standard monomodal registration the core of our contribution resides in providing a method that finds the transformation that maps the intensities of one image to those of another it makes the assumption that there are at most two functional dependences between the intensities of structures present in the images to register and relies on robust estimation techniques to evaluate these functions we provide results showing successful registratio n between several imaging modalities involving segmentations t1 magnetic resonance mr t2 mr proton density pd mr and computed tomography ct we also argue that our intensity modeling may be more appropriate than mutual information mi in the context of evaluating high dimensional deformations as it puts more constraints on the parameters to be estimated and thus permits a better search of the parameter space

a bayesian framework for global tractography we readdress the diffusion tractography problem in a global and probabilistic manner instead of tracking through local orientations we parameterise the connexions between brain regions at a global level and then infer on global and local parameters simultaneously in a bayesian framework this approach offers a number of important benefits the global nature of the tractography reduces sensitivity to local noise and modelling errors by constraining tractography to ensure a connexion is found and then inferring on the exact location of the connexion we increase the robustness of connectivity based parcellations allowing parcellations of connexions that were previously invisible to tractography the bayesian framework allows a direct comparison of the evidence for connecting and non connecting models to test whether the connexion is supported by the data crucially by explicit parameterisation of the connexion between brain regions we infer on a parameter that is shared with models of functional connectivity this model is a first step toward the joint inference on functional and anatomical connectivity

flipping of multivariate aggregation functions abstract we consider flipping transformations of multivariate aggregation functions and we investigate the closure of these transformations with respect to the class of aggregation functions with annihilator element equal to 0 moreover the consecutive application of flipping transformations is also discussed the results present interesting connections both with quasi copulas and with suitable modifications of the n increasing property of a multivariate probability distribution function

on the construction of radially symmetric copulas in higher dimensions abstract we prove a representation theorem for copulas that are simultaneously symmetric and radially symmetric we use this representation theorem to propose a method to construct an n ary symmetric function that is radially symmetric starting from an n 1 dimensional copula and an n ary auxiliary function we study the necessary and sufficient conditions on this auxiliary function that guarantee our construction method to result in a symmetric and radially symmetric n dimensional copula we examine several options for defining the auxiliary function in the trivariate case inspired by the nesting of copulas the lifting of copulas and product like extensions for each choice of auxiliary function we provide several examples for different families of copulas

binary survival aggregation functions we introduce a transformation that acts on binary aggregation functions and that generalizes the transformation that maps copulas a well studied class of binary aggregation functions with a profound probabilistic interpretation to their associated survival copulas the new transformation called double flipping is the composition of two elementary flipping transformations introduced earlier each operating on one of the arguments of the aggregation function we lay bare the relationships between these elementary flipping operations and double flipping we study invariants under these transformations furthermore we characterize the transformations that preserve flippability most importantly we characterize different subclasses of flippable aggregation functions in particular aggregation functions that have an absorbing element or that have a neutral element in this investigation the key role played by quasi copulas and their dual operations is highlighted these findings support the introduction of the term survival aggregation function

3d stochastic completion fields for mapping connectivity in diffusion mri the 2d stochastic completion field algorithm introduced by williams and jacobs 1 2 uses a directional random walk to model the prior probability of completion curves in the plane this construct has had a powerful impact in computer vision where it has been used to compute the shapes of likely completion curves between edge fragments in visual imagery motivated by these developments we extend the algorithm to 3d using a spherical harmonics basis to achieve a rotation invariant computational solution to the fokker planck equation describing the evolution of the probability density function underlying the model this provides a principled way to compute 3d completion patterns and to derive connectivity measures for orientation data in 3d as arises in 3d tracking motion capture and medical imaging we demonstrate the utility of the approach for the particular case of diffusion magnetic resonance imaging where we derive connectivity maps for synthetic data on a physical phantom and on an in vivo high angular resolution diffusion image of a human brain

a random effects modelling approach to the crossing fibre problem in tractography abstract this paper examines a bayesian random effects modelling approach to the analysis of multiple directions diffusion weighted mr data with a focus on the crossing fibre problem various models were investigated including a spatial markov random field model an exchangeable model and the besag york mollie model which includes both exchangeable and spatial random effect terms each of these models was built around the diffusion weighted signal intensity mixture model outlined in behrens et al behrens t e j johansen berg h jbabdi s rushworth m f s woolrich m w 2007 probabilistic diffusion tractography with multiple fibre orientations what can we gain neuroimage 34 144 155 the analyses were performed using markov chain monte carlo simulation two regions were selected for investigation both of which include distinct non collinear pathways in close proximity resulting in crossing fibre voxels the first region includes the corpus callosum the corona radiata and the superior longitudinal fasciculus the second region is within the pons convincing fibre angular distributions were obtained using diffusion data generated with a low b value 1000 s mm 2 and restricted to 20 directions with only two acquisitions per direction the results indicate that random effects modelling provides a useful alternative to current methods documented in the mr tractography literature

multi contrast large deformation diffeomorphic metric mapping for diffusion tensor imaging diffusion tensor imaging dti can reveal detailed white matter anatomy and has the potential to detect abnormalities in specific white matter structures such detection and quantification are however not straightforward the voxel based analysis after image normalization is one of the most widely used methods for quantitative image analyses to apply this approach to dti it is important to examine if structures in the white matter are well registered among subjects which would be highly dependent on employed algorithms for normalization in this paper we evaluate the accuracy of normalization of dti data using a highly elastic transformation algorithm called large deformation diffeomorphic metric mapping after simulation based validation of the algorithm dti data from normal subjects were used to measure the registration accuracy to examine the impact of morphological abnormalities on the accuracy the algorithm was also tested using data from alzheimer s disease ad patients with severe brain atrophy the accuracy level was measured by using manual landmark based white matter matching and surface based brain and ventricle matching as gold standard to improve the accuracy level cascading and multi contrast approaches were developed the accuracy level for the white matter was 1 88 0 55 and 2 19 0 84 mm for the measured locations in the controls and patients respectively

characterizing brain anatomical connections using diffusion weighted mri and graph theory abstract a new methodology based on diffusion weighted magnetic resonance imaging dw mri and graph theory is presented for characterizing the anatomical connections between brain gray matter areas in a first step brain voxels are modeled as nodes of a non directed graph in which the weight of an arc linking two neighbor nodes is assumed to be proportional to the probability of being connected by nervous fibers this probability is estimated by means of probabilistic tissue segmentation and intravoxel white matter orientational distribution function obtained from anatomical mri and dw mri respectively a new tractography algorithm for finding white matter routes is also introduced this algorithm solves the most probable path problem between any two nodes leading to the assessment of probabilistic brain anatomical connection maps in a second step for assessing anatomical connectivity between k gray matter structures the previous graph is redefined as a k 1 partite graph by partitioning the initial nodes set in k non overlapped gray matter subsets and one subset clustering the remaining nodes three different measures are proposed for quantifying anatomical connections between any pair of gray matter subsets anatomical connection strength acs anatomical connection density acd and anatomical connection probability acp this methodology was applied to both artificial and actual human data results show that nervous fiber pathways between some regions of interest were reconstructed correctly additionally mean connectivity maps of acs acd and acp between 71 gray matter structures for five healthy subjects are presented

tractography from hardi using an intrinsic unscented kalman filter a novel adaptation of the unscented kalman filter ukf was recently introduced in literature for simultaneous multitensor estimation and fiber tractography from diffusion mri this technique has the advantage over other tractography methods in terms of computational efficiency due to the fact that the ukf simultaneously estimates the diffusion tensors and propagates the most consistent direction to track along this ukf and its variants reported later in literature however are not intrinsic to the space of diffusion tensors lack of this key property can possibly lead to inaccuracies in the multitensor estimation as well as in the tractography in this paper we propose a novel intrinsic unscented kalman filter iukf in the space of diffusion tensors which are symmetric positive definite matrices that can be used for simultaneous recursive estimation of multitensors and propagation of directional information for use in fiber tractography from diffusion weighted mr data in addition to being more accurate iukf retains all the advantages of ukf mentioned above we demonstrate the accuracy and effectiveness of the proposed method via experiments publicly available phantom data from the fiber cup challenge miccai 2009 and diffusion weighted mr scans acquired from human brains and rat spinal cords

visual exploration of hardi fibers with probabilistic tracking high angular resolution diffusion imaging hardi is an effective method for characterizing complex neural fiber paths in the human brain however visualizing and analyzing the fibers is often challenging because of the complexity of the fiber orientation distribution function used to describe the crossing kissing and fanning fibers in this paper we propose a novel visual analytics approach to study brain fiber paths that allows users to explore fiber bundles to reveal the probability of fiber paths using a new visual classification method first we use a spherical deconvolution model for diffusion estimation and a bayesian theorem for fiber tractography second each fiber is subjected to a cluster analysis using pixel based visual encoding this result is shown in a pixel based visual representation where each pixel bar maps opacity color and length to the probability direction and length of a fiber fiber bundles can then be acquired via a two step classification routine that uses dbscan to group fibers based on similarities then the user can further refine fiber bundle selection using probabilistic information from the pixel bars therefore the proposed approach shows not only the shape but also the confidence of the fiber paths we demonstrate the resulting hardi fiber bundles and compare a brain with tumor and normal brain using our system experiments and an empirical user study verify the effectiveness of our approach