meg beamforming using bayesian pca for adaptive data covariance matrix regularization beamformers are a commonly used method for doing source localization from magnetoencephalography meg data a key ingredient in a beamformer is the estimation of the data covariance matrix when the noise levels are high or when there is only a small amount of data available the data covariance matrix is estimated poorly and the signal to noise ratio snr of the beamformer output degrades one solution to this is to use regularization whereby the diagonal of the covariance matrix is amplified by a pre specified amount however this provides improvements at the expense of a loss in spatial resolution and the parameter controlling the amount of regularization must be chosen subjectively in this paper we introduce a method that provides an adaptive solution to this problem by using a bayesian principle component analysis pca this provides an estimate of the data covariance matrix to give a data driven non arbitrary solution to the trade off between the spatial resolution and the snr of the beamformer output this also provides a method for determining when the quality of the data covariance estimate maybe under question we apply the approach to simulated and real meg data and demonstrate the way in which it can automatically adapt the regularization to give good performance over a range of noise and signal levels

labeling of ambiguous subvoxel fibre bundle configurations in high angular resolution diffusion mri whereas high angular resolution reconstruction methods for diffusion mri can estimate multiple dominant fibre orientations within a single imaging voxel they are fundamentally limited in certain cases of complex subvoxel fibre structures resulting in ambiguous local orientation distribution functions in this article we address the important problem of disambiguating such complex subvoxel fibre tract configurations with the purpose of improving the performance of fibre tractography we do so by extending a curve inference method to distinguish between the cases of curving and fanning fibre bundles using differential geometric estimates in a local neighbourhood the key benefit of this method is the inference of curves instead of only fibre orientations to model the underlying fibre bundles this in turn allows distinct fibre geometries that contain nearly identical sets of fibre orientations at a voxel to be distinguished from one another experimental results demonstrate the ability of the method to successfully label voxels into one of the above categories and improve the performance of a fibre tracking algorithm

manifold regularization a geometric framework for learning from labeled and unlabeled examples we propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution we focus on a semi supervised framework that incorporates labeled and unlabeled data in a general purpose learner some transductive graph learning algorithms and standard methods including support vector machines and regularized least squares can be obtained as special cases we use properties of reproducing kernel hilbert spaces to prove new representer theorems that provide theoretical basis for the algorithms as a result in contrast to purely graph based approaches we obtain a natural out of sample extension to novel examples and so are able to handle both transductive and truly semi supervised settings we present experimental evidence suggesting that our semi supervised algorithms are able to use unlabeled data effectively finally we have a brief discussion of unsupervised and fully supervised learning within our general 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

multi tissue constrained spherical deconvolution for improved analysis of multi shell diffusion mri data constrained spherical deconvolution csd has become one of the most widely used methods to extract white matter wm fibre orientation information from diffusion weighted mri dw mri data overcoming the crossing fibre limitations inherent in the diffusion tensor model it is routinely used to obtain high quality fibre orientation distribution function fodf estimates and fibre tractograms and is increasingly used to obtain apparent fibre density afd measures unfortunately csd typically only supports data acquired on a single shell in q space with multi shell data becoming more and more prevalent there is a growing need for csd to fully support such data furthermore csd can only provide high quality fodf estimates in voxels containing wm only in voxels containing other tissue types such as grey matter gm and cerebrospinal fluid csf the wm response function may no longer be appropriate and spherical deconvolution produces unreliable noisy fodf estimates the aim of this study is to incorporate support for multi shell data into the csd approach as well as to exploit the unique b value dependencies of the different tissue types to estimate a multi tissue odf the resulting approach is dubbed multi shell multi tissue csd msmt csd and is compared to the state of the art single shell single tissue csd ssst csd approach using both simulations and real data we show that msmt csd can produce reliable wm gm csf volume fraction maps directly from the dw data whereas ssst csd has a tendency to overestimate the wm volume in voxels containing gm and or csf in addition compared to ssst csd msmt csd can substantially increase the precision of the fodf fibre orientations and reduce the presence of spurious fodf peaks in voxels containing gm and or csf both effects translate into more reliable afd measures and tractography results with msmt csd compared to ssst csd

variational bayesian inference for a nonlinear forward model variational bayes vb has been proposed as a method to facilitate calculations of the posterior distributions for linear models by providing a fast method for bayesian inference by estimating the parameters of a factorized approximation to the posterior distribution here a vb method for nonlinear forward models with gaussian additive noise is presented in the case of noninformative priors the parameter estimates obtained from this vb approach are identical to those found via nonlinear least squares however the advantage of the vb method lies in its bayesian formulation which permits prior information to be included in a hierarchical structure and measures of uncertainty for all parameter estimates to be obtained via the posterior distribution unlike other bayesian methods vb is only approximate in comparison with the sampling method of mcmc however the vb method is found to be comparable and the assumptions made about the form of the posterior distribution reasonable practically the vb approach is substantially faster than mcmc as fewer calculations are required some of the advantages of the fully bayesian nature of the method are demonstrated through the extension of the noise model and the inclusion of automatic relevance determination ard within the vb algorithm

simultaneous multi scale diffusion estimation and tractography guided by entropy spectrum pathways we have developed a method for the simultaneous estimation of local diffusion and the global fiber tracts based upon the information entropy flow that computes the maximum entropy trajectories between locations and depends upon the global structure of the multi dimensional and multi modal diffusion field computation of the entropy spectrum pathways requires only solving a simple eigenvector problem for the probability distribution for which efficient numerical routines exist and a straight forward integration of the probability conservation through ray tracing of the convective modes guided by a global structure of the entropy spectrum coupled with a small scale local diffusion the intervoxel diffusion is sampled by multi b shell multi q angle diffusion weighted imaging data expanded in spherical waves this novel approach to fiber tracking incorporates global information about multiple fiber crossings in every individual voxel and ranks it in the most scientifically rigorous way this method has potential significance for a wide range of applications including studies of brain connectivity

deconvolution in diffusion spectrum imaging diffusion spectrum magnetic resonance imaging dsi allows the estimation of the displacement probability density function pdf of water molecules which contain valuable information about the microgeometry of the medium where the diffusion process occurs it provides a more general approach to disentangle complex fiber structures in biological tissues because it does not assume any particular model of diffusion even so it has a number of limitations that remain unstudied for instance the theoretical model used to compute the displacement pdf is based on a fourier transformation defined in the whole measurement space however in practice it is computed using discrete signals with a finite support as a consequence the displacement pdf obtained from the experiments is the convolution between the true pdf and a point spread function psf that completely depends on the experimental sampling scheme in this work a general framework to rectify and decontaminate the displacement pdf reconstructed from dsi is introduced this framework is based on model free deconvolution techniques that allow obtaining clearer and sharper dsi estimates the method was tested in synthetic data as well as in real data measured from a healthy human volunteer the results demonstrated that the angular resolution of dsi can be increased potentially revealing new real fiber components and reducing both the artefactual peaks and the uncertainty of the local diffusion orientational distribution furthermore the deconvolution process provides scalar maps of quantities derived from the propagator such as the zero displacement probability with higher tissue contrast

mesh based spherical deconvolution a flexible approach to reconstruction of non negative fiber orientation distributions diffusion weighted mri has enabled the imaging of white matter architecture in vivo fiber orientations have classically been assumed to lie along the major eigenvector of the diffusion tensor but this approach has well characterized shortcomings in voxels containing multiple fiber populations recently proposed methods for recovery of fiber orientation via spherical deconvolution utilize a spherical harmonics framework and are susceptible to noise yielding physically invalid results even when additional measures are taken to minimize such artifacts in this work we reformulate the spherical deconvolution problem onto a discrete spherical mesh we demonstrate how this formulation enables the estimation of fiber orientation distributions which strictly satisfy the physical constraints of realness symmetry and non negativity moreover we analyze the influence of the flexible regularization parameters included in our formulation for tuning the smoothness of the resultant fiber orientation distribution fod we show that the method is robust and reliable by reconstructing known crossing fiber anatomy in multiple subjects finally we provide a software tool for computing the fod using our new formulation in hopes of simplifying and encouraging the adoption of spherical deconvolution techniques

towards quantitative connectivity analysis reducing tractography biases diffusion mri tractography is often used to estimate structural connections between brain areas and there is a fast growing interest in quantifying these connections based on their position shape size and length however a portion of the connections reconstructed with tractography is biased by their position shape size and length thus connections reconstructed are not equally distributed in all white matter bundles quantitative measures of connectivity based on the streamline distribution in the brain such as streamline count density average length and spatial extent volume are biased by erroneous streamlines produced by tractography algorithms in this paper solutions are proposed to reduce biases in the streamline distribution first we propose to optimize tractography parameters in terms of connectivity then we propose to relax the tractography stopping criterion with a novel probabilistic stopping criterion and a particle filtering method both based on tissue partial volume estimation maps calculated from a t1 weighted image we show that optimizing tractography parameters stopping and seeding strategies can reduce the biases in position shape size and length of the streamline distribution these tractography biases are quantitatively reported using in vivo and synthetic data this is a critical step towards producing tractography results for quantitative structural connectivity analysis

transition matrix in acoustic scattering by a strip the transition matrix describing the scalar scattering by a strip has been obtained using a boundary integral equation technique it avoids the procedure of the extended boundary condition taking the strip as the limit of an elliptic cylinder our final results confirm the known results obtained from the extended boundary condition technique the method presented in this paper seems to be very attractive to similar problems in elastodynamic scattering

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

plausibility tracking a method to evaluate anatomical connectivity and microstructural properties along fiber pathways abstract diffusion mri is a non invasive method that potentially gives insight into the brain s white matter structure regarding the pathway of connections and properties of the axons here we propose a novel global tractography method named plausibility tracking that provides the most plausible pathway modeled as a smooth spline curve between two locations in the brain compared to other tractography methods plausibility tracking combines the more complete connectivity pattern of probabilistic tractography with smooth tracks that are globally optimized using the fiber orientation density function and hence is relatively robust against local noise and error propagation it has been tested on phantom and biological data and compared to other methods of tractography plausibility tracking provides reliable local directions all along the fiber pathways which makes it especially interesting for tract based analysis in combination with direction dependent indices of diffusion mri in order to demonstrate this potential of plausibility tracking we propose a framework for the assessment and comparison of diffusion derived tissue properties this framework comprises atlas guided parameterization of tract representation and advanced bundle specific indices describing fiber density fiber spread and white matter complexity we explore the new method using real data and show that it allows for a more specific interpretation of the white matter s microstructure compared to rotationally invariant indices derived from the diffusion tensor

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

brain tractography using q ball imaging and graph theory improved connectivities through fibre crossings via a model based approach brain tractography techniques utilize a set of diffusion weighted magnetic resonance images to reconstruct white matter tracts non invasively and in vivo streamline tracking techniques propagate curves from a seed to imply connectivity to distal voxels alternative approaches have been developed that attempt to quantify connection strength between all voxels and the seed tractography based on graph theory is amongst them despite its potential graph based tracking through complex fibre configurations has not been extensively studied and existing methods have inherent limitations anatomically unlikely connections may be identified in fibre crossing regions by assigning relatively high connection strengths to all crossing populations in this study we discuss these limitations and present a new approach for robustly propagating through fibre crossings as described by the orientation distribution functions odfs derived from q ball imaging each image voxel is treated as a graph node and graph arcs connect neighbouring voxels weights representative of both structural and diffusivity features are assigned to each arc to account for the existence of crossing fibre populations within a voxel complex odfs are decomposed into components representative of single fibre populations and an image multigraph is created the multigraph is searched exhaustively but efficiently to find the strongest paths and assign connectivity strengths between a seed and all the other image voxels a comparison with the existing graph based tractography as well as q ball driven front evolution tractography is performed on simulated data and on human q ball imaging data acquired from five healthy volunteers the new approach improves the connection strengths through fibre crossing regions reducing the strengths of paths that are less anatomically plausible

whole brain diffeomorphic metric mapping via integration of sulcal and gyral curves cortical surfaces and images this paper introduces a novel large deformation diffeomorphic metric mapping algorithm for whole brain registration where sulcal and gyral curves cortical surfaces and intensity images are simultaneously carried from one subject to another through a flow of diffeomorphisms to the best of our knowledge this is the first time that the diffeomorphic metric from one brain to another is derived in a shape space of intensity images and point sets such as curves and surfaces in a unified manner we describe the euler lagrange equation associated with this algorithm with respect to momentum a linear transformation of the velocity vector field of the diffeomorphic flow the numerical implementation for solving this variational problem which involves large scale kernel convolution in an irregular grid is made feasible by introducing a class of computationally friendly kernels we apply this algorithm to align magnetic resonance brain data our whole brain mapping results show that our algorithm outperforms the image based lddmm algorithm in terms of the mapping accuracy of gyral sulcal curves sulcal regions and cortical and subcortical segmentation moreover our algorithm provides better whole brain alignment than combined volumetric and surface registration postelnicu et al 2009 and hierarchical attribute matching mechanism for elastic registration hammer shen and davatzikos 2002 in terms of cortical and subcortical volume segmentation

convergence and divergence of thickness correlations with diffusion connections across the human cerebral cortex cortical thickness correlation across individuals has been observed so far it remains unclear to what extent such a correlation in thickness is a reflection of underlying fiber connection here we explicitly compared the patterns of cortical thickness correlation and diffusion based fiber connection across the entire cerebral cortex in 95 normal adults interregional thickness correlations were extracted by using computational neuroanatomy algorithms based on structural mri and diffusion connections were detected by using diffusion probabilistic tractography approximately 35 40 of thickness correlations showed convergent diffusion connections across the cerebral cortex intriguingly the observed convergences between thickness correlation and diffusion connection are mostly focused on the positive thickness correlations while almost all of the negative correlations 90 did not have a matched diffusion connection suggesting different mechanisms behind the positive and negative thickness correlations the latter not being mediated by a direct fiber pathway furthermore graph theoretic analysis reveals that the thickness correlation network has a more randomized overall topology whereas the nodal characteristics of cortical regions in these two networks are statistically correlated these findings indicate that thickness correlations partly reflect underlying fiber connections but they contains exclusive information and therefore should not be simply taken as a proxy measure for fiber connections

an extended unitary approach for acoustical scattering from elastic shells immersed in a fluid we derive equations using the t matrix approach for acoustical scattering from elastic shells immersed in a fluid the equations contain unitary and symmetry constraints and afford a new procedure for the calculation of the t matrix the technique in addition to satisfying symmetry and unitary conditions proves to be more numerically stable and less time consuming than the conventional method in addition the procedure enables one to determine if convergence has been satisfied and in the limit of no convergence proves to be a better approximation than that of the matrix method we have developed computer codes using the new technique and present comparisons with the conventional procedure a salient feature of the new technique is that convergence is arrived at with a smaller number of expansion terms than the older method and this is particularly true as the aspect ratio of the target is increased

rapid solution of integral equations of scattering theory in two dimensions abstract the present paper describes an algorithm for rapid solution of boundary value problems for the helmholtz equation in two dimensions based on iteratively solving integral equations of scattering theory cpu time requirements of previously published algorithms of this type are of the order n 2 where n is the number of nodes in the discretization of the boundary of the scatterer the cpu time requirements of the algorithm of the present paper are n 4 3 and can be further reduced making it considerably more practical for large scale problems

a bayesian framework to identify principal intravoxel diffusion profiles based on diffusion weighted mr imaging in this paper we introduce a new method to characterize the intravoxel anisotropy based on diffusion weighted imaging dwi the proposed solution under a fully bayesian formalism deals with the problem of joint bayesian model selection and parameter estimation to reconstruct the principal diffusion profiles or primary fiber orientations in a voxel we develop an efficient stochastic algorithm based on the reversible jump markov chain monte carlo rjmcmc method in order to perform the bayesian computation rjmcmc is a good choice for this problem because of its ability to jump between models of different dimensionality this methodology provides posterior estimates of the parameters of interest fiber orientation diffusivities etc unconditional of the model assumed it also gives an empirical posterior distribution of the number of primary nerve fiber orientations given the dwi data different probability maps can be assessed using this methodology 1 the intravoxel fiber orientation map or orientational distribution function that gives the probability of finding a fiber in a particular spatial orientation 2 a three dimensional map of the probability of finding a particular number of fibers in each voxel 3 a three dimensional maxpro maximum probability map that provides the most probable number of fibers for each voxel in order to study the performance and reliability of the presented approach we tested it on synthetic data an ex vivo phantom of intersecting capillaries and dwi data from a human subject

reproducibility of tract segmentation between sessions using an unsupervised modelling based approach abstract this work describes a reproducibility analysis of scalar water diffusion parameters measured within white matter tracts segmented using a probabilistic shape modelling method in common with previously reported neighbourhood tractography nt work the technique optimises seed point placement for fibre tracking by matching the tracts generated using a number of candidate points against a reference tract which is derived from a white matter atlas in the present study no direct constraints are applied to the fibre tracking results an expectation maximisation algorithm is used to fully automate the procedure and make dramatically more efficient use of data than earlier nt methods within subject and between subject variances for fractional anisotropy and mean diffusivity within the tracts are then separated using a random effects model we find test retest coefficients of variation cvs similar to those reported in another study using landmark guided single seed points and subject to subject cvs similar to a constraint based multiple roi method we conclude that our approach is at least as effective as other methods for tract segmentation using tractography whilst also having some additional benefits such as its provision of a goodness of match measure for each segmentation

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

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

apparent fibre density a novel measure for the analysis of diffusion weighted magnetic resonance images this article proposes a new measure called apparent fibre density afd for the analysis of high angular resolution diffusion weighted images using higher order information provided by fibre orientation distributions fods computed using spherical deconvolution afd has the potential to provide specific information regarding differences between populations by identifying not only the location but also the orientations along which differences exist in this work analytical and numerical monte carlo simulations are used to support the use of the fod amplitude as a quantitative measure i e afd for population and longitudinal analysis to perform robust voxel based analysis of afd we present and evaluate a novel method to modulate the fod to account for changes in fibre bundle cross sectional area that occur during spatial normalisation we then describe a novel approach for statistical analysis of afd that uses cluster based inference of differences extended throughout space and orientation finally we demonstrate the capability of the proposed method by performing voxel based afd comparisons between a group of motor neurone disease patients and healthy control subjects a significant decrease in afd was detected along voxels and orientations corresponding to both the corticospinal tract and corpus callosal fibres that connect the primary motor cortices in addition to corroborating previous findings in mnd this study demonstrates the clear advantage of using this type of analysis by identifying differences along single fibre bundles in regions containing multiple fibre populations

symmetric diffeomorphic registration of fibre orientation distributions registration of diffusion weighted images is an important step in comparing white matter fibre bundles across subjects or in the same subject at different time points using diffusion weighted imaging spherical deconvolution enables multiple fibre populations within a voxel to be resolved by computing the fibre orientation distribution fod in this paper we present a novel method that employs fods for the registration of diffusion weighted images registration was performed by optimising a symmetric diffeomorphic non linear transformation model using image metrics based on the mean squared difference and cross correlation of the fod spherical harmonic coefficients the proposed method was validated by recovering known displacement fields using fods represented with maximum harmonic degrees l max of 2 4 and 6 results demonstrate a benefit in using fods at l max 4 compared to l max 2 however a decrease in registration accuracy was observed when l max 6 was used this was likely caused by noise in higher harmonic degrees we compared our proposed method to fractional anisotropy driven registration using an identical code base and parameters fod registration was observed to perform significantly better than fa in all experiments the cross correlation metric performed significantly better than the mean squared difference finally we demonstrated the utility of this method by computing an unbiased group average fod template that was used for probabilistic fibre tractography this work suggests that using crossing fibre information aids in the alignment of white matter and could therefore benefit several methods for investigating population differences in white matter including voxel based analysis tensor based morphometry atlas based segmentation and labelling and group average fibre tractography

locally discriminative topic modeling topic modeling is a powerful tool for discovering the underlying or hidden structure in text corpora typical algorithms for topic modeling include probabilistic latent semantic analysis plsa and latent dirichlet allocation lda despite their different inspirations both approaches are instances of generative model whereas the discriminative structure of the documents is ignored in this paper we propose locally discriminative topic model ldtm a novel topic modeling approach which considers both generative and discriminative structures of the data space different from plsa and lda in which the topic distribution of a document is dependent on all the other documents ldtm takes a local perspective that the topic distribution of each document is strongly dependent on its neighbors by modeling the local relationships of documents within each neighborhood via a local linear model we learn topic distributions that vary smoothly along the geodesics of the data manifold and can better capture the discriminative structure in the data the experimental results on text clustering and web page categorization demonstrate the effectiveness of our proposed approach

group analysis of dti fiber tract statistics with application to neurodevelopment abstract diffusion tensor imaging dti provides a unique source of information about the underlying tissue structure of brain white matter in vivo including both the geometry of major fiber bundles as well as quantitative information about tissue properties represented by derived tensor measures this paper presents a method for statistical comparison of fiber bundle diffusion properties between populations of diffusion tensor images unbiased diffeomorphic atlas building is used to compute a normalized coordinate system for populations of diffusion images the diffeomorphic transformations between each subject and the atlas provide spatial normalization for the comparison of tract statistics diffusion properties such as fractional anisotropy fa and tensor norm along fiber tracts are modeled as multivariate functions of arc length hypothesis testing is performed non parametrically using permutation testing based on the hotelling t 2 statistic the linear discriminant embedded in the t 2 metric provides an intuitive localized interpretation of detected differences the proposed methodology was tested on two clinical studies of neurodevelopment in a study of 1 and 2 year old subjects a significant increase in fa and a correlated decrease in frobenius norm was found in several tracts significant differences in neonates were found in the splenium tract between controls and subjects with isolated mild ventriculomegaly mvm demonstrating the potential of this method for clinical studies

the effect of network thresholding and weighting on structural brain networks in the uk biobank abstract whole brain structural networks can be constructed using diffusion mri and probabilistic tractography however measurement noise and the probabilistic nature of the tracking procedure result in an unknown proportion of spurious white matter connections faithful disentanglement of spurious and genuine connections is hindered by a lack of comprehensive anatomical information at the network level therefore network thresholding methods are widely used to remove ostensibly false connections but it is not yet clear how different thresholding strategies affect basic network properties and their associations with meaningful demographic variables such as age in a sample of 3153 generally healthy volunteers from the uk biobank imaging study aged 44 77 years we constructed whole brain structural networks and applied two principled network thresholding approaches consistency and proportional thresholding these were applied over a broad range of threshold levels across six alternative network weightings streamline count fractional anisotropy mean diffusivity and three novel weightings from neurite orientation dispersion and density imaging and for four common network measures mean edge weight characteristic path length network efficiency and network clustering coefficient we compared network measures against age associations and found that 1 measures derived from unthresholded matrices yielded the weakest age associations 0 033 0 409 and 2 the most commonly used level of proportional thresholding from the literature retaining 68 7 of all possible connections yielded significantly weaker age associations 0 070 0 406 than the consistency based approach which retained only 30 of connections 0 140 0 409 however we determined that the stringency of the threshold was a stronger determinant of the network age association than the choice of threshold method and the two thresholding approaches identified a highly overlapping set of connections icc 0 84 when matched at 70 network sparsity generally more stringent thresholding resulted in more age sensitive network measures in five of the six network weightings except at the highest levels of sparsity 90 where crucial connections were then removed at two commonly used threshold levels the age associations of the connections that were discarded mean 0 068 were significantly smaller in magnitude than the corresponding age associations of the connections that were retained mean 0 219 p

predicting functional connectivity from structural connectivity via computational models using mri an extensive comparison study abstract the relationship between structural connectivity sc and functional connectivity fc in the human brain can be studied using magnetic resonance imaging mri however many of the underlying physiological mechanisms and parameters cannot be directly observed with mri this limitation has motivated the recent use of various computational models meant to bridge the gap however their absolute and relative explanatory power and the properties that actually drive that power remain insufficiently characterized we performed an extensive comparison of seven mainstream computational models predicting fc from sc we investigated the extent to which simulated fc could predict empirical fc we also applied graph theory to the entire set of simulated and empirical fcs in order to further characterize the relationships between the models and the mri data the comparison was performed at three different spatial scales we found that i there were significant effects of scale and model on predictive power ii among all models the simplest model the simultaneous autoregressive sar model was found to consistently perform better than the other models iii the sar also appeared more central from a graph theory perspective and iv empirical fc only appeared weakly correlated with simulated fcs and was featured as peripheral in the graph analysis we conclude that the substantial differences existing between these computational models have little impact on their predictive power for fc and that their capacity to predict fc from sc appears to be both moderate and essentially underlined by a simple core linear process embodied by the sar model

mathematical methods for diffusion mri processing in this article we review recent mathematical models and computational methods for the processing of diffusion magnetic resonance images including state of the art reconstruction of diffusion models cerebral white matter connectivity analysis and segmentation techniques we focus on diffusion tensor images dti and q ball images qbi

rapid solution of integral equations of classical potential theory an algorithm is described for rapid solution of classical boundary value problems dirichlet an neumann for the laplace equation based on iteratively solving integral equations of potential theory cpu time requirements for previously published algorithms of this type are proportional to n2 where n is the number of nodes in the discretization of the boundary of the region the cpu time requirements for the algorithm of the present paper are proportional to n making it considerably more practical for large scale problems

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

image interpolation via graph based bayesian label propagation in this paper we propose a novel image interpolation algorithm via graph based bayesian label propagation the basic idea is to first create a graph with known and unknown pixels as vertices and with edge weights encoding the similarity between vertices then the problem of interpolation converts to how to effectively propagate the label information from known points to unknown ones this process can be posed as a bayesian inference in which we try to combine the principles of local adaptation and global consistency to obtain accurate and robust estimation specially our algorithm first constructs a set of local interpolation models which predict the intensity labels of all image samples and a loss term will be minimized to keep the predicted labels of the available low resolution lr samples sufficiently close to the original ones then all of the losses evaluated in local neighborhoods are accumulated together to measure the global consistency on all samples moreover a graph laplacian based manifold regularization term is incorporated to penalize the global smoothness of intensity labels such smoothing can alleviate the insufficient training of the local models and make them more robust finally we construct a unified objective function to combine together the global loss of the locally linear regression square error of prediction bias on the available lr samples and the manifold regularization term it can be solved with a closed form solution as a convex optimization problem experimental results demonstrate that the proposed method achieves competitive performance with the state of the art image interpolation algorithms

recursive t matrix algorithms for the solution of electromagnetic scattering from strip and patch geometries two recursive t matrix algorithms are presented and their reduced computational complexities and reduced memory requirements are demonstrated these algorithms are applied to the problem of electromagnetic scattering from conducting strips and patches with canonical geometries the geometries are reminiscent of finite sized frequency selective surfaces computational complexities of o n sup 2 and o n sup 7 3 and memory requirements of o n and o n sup 4 3 are shown to be feasible for two dimensional and three dimensional geometries respectively the formulation uses only two components of the electric field therefore the vector electromagnetic problem of scattering from three dimensional patch geometries can be solved using scalar addition theorems for spherical harmonic wave functions for a two dimensional strip problem both tm and te polarizations can be solved simultaneously using this formulation numerical scattering results in the form of radar cross sections rcs are validated by comparison with the method of moments

k space and image space combination for motion induced phase error correction in self navigated multicoil multishot dwi motion during diffusion encodings leads to different phase errors in different shots of multishot diffusion weighted acquisitions phase error incoherence among shots results in undesired signal cancellation when data from all shots are combined motion induced phase error correction for multishot diffusion weighted imaging dwi has been studied extensively and there exist multiple phase error correction algorithms a commonly used correction method is the direct phase subtraction dps dps however can suffer from incomplete phase error correction due to the aliasing of the phase errors in the high spatial resolution phases furthermore improper sampling density compensation is also a possible issue of dps recently motion induced phase error correction was incorporated in the conjugate gradient cg image reconstruction procedure to get a nonlinear phase correction method that is also applicable to parallel dwi although the cg method overcomes the issues of dps its computational requirement is high further cg restricts to sensitivity encoding sense for parallel reconstruction in this paper a new time efficient and flexible k space and image space combination kict algorithm for rigid body motion induced phase error correction is introduced kict estimates the motion induced phase errors in image space using the self navigated capability of the variable density spiral trajectory the correction is then performed in k space the algorithm is shown to overcome the problem of aliased phase errors further the algorithm preserves the phase of the imaging object and receiver coils in the corrected k space data which is important for parallel imaging applications after phase error correction any parallel reconstruction method can be used the kict algorithm is tested with both simulated and in vivo data with both multishot single coil and multishot multicoil acquisitions we show that kict correction results in diffusion weighted images with higher signal to noise ratio snr and fractional anisotropy fa maps with better resolved fiber tracts as compared to dps in peripheral gated acquisitions kict is comparable to the cg method

a fuzzy nonparametric segmentation framework for dti and mri analysis with applications to dti tract extraction this paper presents a novel fuzzy segmentation method for diffusion tensor dt and magnetic resonance mr images typical fuzzy segmentation schemes e g those based on fuzzy c means fcm incorporate gaussian class models that are inherently biased towards ellipsoidal clusters characterized by a mean element and a covariance matrix tensors in fiber bundles however inherently lie on specific manifolds in riemannian spaces unlike fcm based schemes the proposed method represents these manifolds using nonparametric data driven statistical models the paper describes a statistically sound consistent technique for nonparametric modeling in riemannian dt spaces the proposed method produces an optimal fuzzy segmentation by maximizing a novel information theoretic energy in a markov random field framework results on synthetic and real dt and mr images show that the proposed method provides information about the uncertainties in the segmentation decisions which stem from imaging artifacts including noise partial voluming and inhomogeneity by enhancing the nonparametric model to capture the spatial continuity and structure of the fiber bundle we exploit the framework to extract the cingulum fiber bundle typical tractography methods for tract delineation incorporating thresholds on fractional anisotropy and fiber curvature to terminate tracking can face serious problems arising from partial voluming and noise for these reasons tractography often fails to extract thin tracts with sharp changes in orientation such as the cingulum the results demonstrate that the proposed method extracts this structure significantly more accurately as compared to tractography

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

anatomical mapping of functional activation in stereotactic coordinate space numerous applications have been reported for the stereotactic mapping of focal changes in cerebral blood flow during sensory and cognitive activation as measured with positron emission tomography pet subtraction images since these images lack significant anatomical information analysis of these kinds of data has been restricted to an automated search for peaks in the pet subtraction dataset and localization of the peak coordinates within a standardized stereotactic atlas this method is designed to identify isolated foci with dimensions smaller than the image resolution details of activation patterns that may extend over finite distances following the underlying anatomical structures will not be apparent we describe the combined mapping into stereotactic coordinate space of magnetic resonance imaging mri and pet information from each of a set of subjects such that the major features of the activation pattern particularly extended tracts of increased blood flow can be immediately assessed within their true anatomical context as opposed to that presumed using a standard atlas alone near areas of high anatomical variability e g central sulcus or of sharp curvature e g frontal and temporal poles this information can be essential to the localization of a focus to the correct gyrus or for the rejection of extracerebral peaks it also allows for the removal from further analysis of data from cognitively normal subjects with abnormal anatomy such as enlarged ventricles in patients with neuropathology e g alzheimer s disease arteriovenous malformation stroke or neoplasm the use of correlated mri is mandatory for correct localization of functional activation

a dti derived measure of cortico cortical connectivity we arm researchers with a simple method to chart a macroscopic cortico cortical connectivity network in living human subjects the researcher provides a diffusion magnetic resonance imaging mri data set and n cortical regions of interest in return we provide an n times n structural adjacency matrix sam quantifying the relative connectivity between all cortical region pairs we also return a connectivity map for each pair to enable visualization of interconnecting fiber bundles the measure of connectivity we devise is 1 free of length bias 2 proportional to fiber bundle cross sectional area and 3 invariant to an exchange of seed and target we construct a 3 d lattice scaffolding graph for white matter by drawing a link between each pair of voxels in a 26 voxel neighborhood for which their two respective principal eigenvectors form a sufficiently small angle the connectivity between a cortical region pair is then measured as the maximum number of link disjoint paths that can be established between them in the white matter graph we devise an efficient edmonds karp like algorithm to compute a conservative bound on the maximum number of link disjoint paths using both simulated and authentic diffusion tensor imaging data we demonstrate that the number of link disjoint paths as a measure of connectivity satisfies properties 1 3 unlike the fraction of intersecting streamlines the measure intrinsic to most existing probabilistic tracking algorithms finally we present connectivity maps of some notoriously difficult to track longitudinal and contralateral fasciculi

robust subdivision of the thalamus in children based on probability distribution functions calculated from probabilistic tractography virtually all information that enters the cortex must first pass through the thalamus this prominent role has made the human thalamus a target for detailed imaging studies it has previously been shown that probabilistic tractography together with cortical parcellation allowed subdivision of the thalamus into its constituent substructures a new method is presented that allows the subdivision of the thalamus according to its cortical projection targets based on the assumption that any cortical region receives input from the thalamus and calculates the probability of connectivity distribution functions based on probabilistic tractography the feasibility of the method was tested in a data set of 43 healthy children aged between 8 and 13 years a thalamic parcellation pattern similar to that previously found in adults and children below the age of 2 years was obtained however no evidence for an age related change in cortical parcellation volumes were found in line with previously reported studies of thalamic volumes during development lower standard deviations were found for the two smallest projections the sensory and occipital projection using the new method furthermore it was found through comparison with a published thalamic atlas that the method allowed the localization of the center of the different thalamic projection areas within an accuracy of 2 mm

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

connecting and merging fibres pathway extraction by combining probability maps probability mapping of connectivity is a powerful tool to determine the fibre structure of white matter in the brain probability maps are related to the degree of connectivity to a chosen seed area in many applications however it is necessary to isolate a fibre bundle that connects two areas a frequently suggested solution is to select curves which pass only through two or more areas this is very inefficient especially for long distance pathways and small areas in this paper a novel probability based method is presented that is capable of extracting neuronal pathways defined by two seed points a monte carlo simulation based tracking method similar to the probabilistic index of connectivity pico approach was extended to preserve the directional information of the main fibre bundles passing a voxel by combining two of these extended visiting maps arising from different seed points two independent parameters are determined for each voxel the first quantifies the uncertainty that a voxel is connected to both seed points the second represents the directional information and estimates the proportion of fibres running in the direction of the other seed point connecting fibre or face a third area merging fibre both parameters are used to calculate the probability that a voxel is part of the bundle connecting both seed points the performance and limitations of this dti based method are demonstrated using simulations as well as in vivo measurements

the effect and reproducibility of different clinical dti gradient sets on small world brain connectivity measures advances in computational network analysis have enabled the characterization of topological properties in large scale networks including the human brain information on structural networks in the brain can be obtained in vivo by performing tractography on diffusion tensor imaging dti data however little is known about the reproducibility of network properties derived from whole brain tractography data which has important consequences for minimally detectable abnormalities or changes over time moreover acquisition parameters such as the number of gradient directions and gradient strength possibly influence network metrics and the corresponding reproducibility derived from tractography data the aim of the present study is twofold i to determine the effect of several clinically available dti sampling schemes differing in number of gradient directions and gradient amplitude on small world metrics and ii to evaluate the interscan reproducibility of small world metrics dti experiments were conducted on six healthy volunteers scanned twice probabilistic tractography was performed to reconstruct structural connections between regions defined from an anatomical atlas the observed reproducibility of the network measures was high reflected by low values for the coefficient of variation 3 8 advocating the use of graph theoretical measurements to study neurological diseases small world metrics were dependent on the choice of dti gradient scheme and showed stronger connectivity with increasing directional resolution the interscan reproducibility was not dependent on the gradient scheme these findings should be considered when comparing results across studies using different gradient schemes or designing new studies

linear transforms for fourier data on the sphere application to high angular resolution diffusion mri of the brain this paper presents a novel family of linear transforms that can be applied to data collected from the surface of a 2 sphere in three dimensional fourier space this family of transforms generalizes the previously proposed funk radon transform frt which was originally developed for estimating the orientations of white matter fibers in the central nervous system from diffusion magnetic resonance imaging data the new family of transforms is characterized theoretically and efficient numerical implementations of the transforms are presented for the case when the measured data is represented in a basis of spherical harmonics after these general discussions attention is focused on a particular new transform from this family that we name the funk radon and cosine transform fract based on theoretical arguments it is expected that fract based analysis should yield significantly better orientation information e g improved accuracy and higher angular resolution than frt based analysis while maintaining the strong characterizability and computational efficiency of the frt simulations are used to confirm these theoretical characteristics and the practical significance of the proposed approach is illustrated with real diffusion weighted mri brain data these experiments demonstrate that in addition to having strong theoretical characteristics the proposed approach can outperform existing state of the art orientation estimation methods with respect to measures such as angular resolution and robustness to noise and modeling errors

sphere spherical harmonic elastic registration of hardi data abstract in contrast to the more common diffusion tensor imaging dti high angular resolution diffusion imaging hardi allows superior delineation of angular microstructures of brain white matter and makes possible multiple fiber modeling of each voxel for better characterization of brain connectivity however the complex orientation information afforded by hardi makes registration of hardi images more complicated than scalar images in particular the question of how much orientation information is needed for satisfactory alignment has not been sufficiently addressed low order orientation representation is generally more robust than high order representation although the latter provides more information for correct alignment of fiber pathways however high order representation when naively utilized might not necessarily be conducive to improving registration accuracy since similar structures with significant orientation differences prior to proper alignment might be mistakenly taken as non matching structures we present in this paper a hardi registration algorithm called spherical harmonic elastic registration sphere which in a principled means hierarchically extracts orientation information from hardi data for structural alignment the image volumes are first registered using robust relatively direction invariant features derived from the orientation distribution function odf and the alignment is then further refined using spherical harmonic sh representation with gradually increasing orders this progression from non directional single directional to multi directional representation provides a systematic means of extracting directional information given by diffusion weighted imaging coupled with a template subject consistent soft correspondence matching scheme this approach allows robust and accurate alignment of hardi data experimental results show marked increase in accuracy over a state of the art dti registration algorithm

acoustic scattering from a rough sphere the scattering of a plane acoustic wave from a random rough sphere is studied using the null field approach the starting point is an integral representation derived from the helmholtz equation the incident field the scattered field and the free space green s function are all expanded in terms of suitably chosen basis functions in this way a relation between the incident and the scattered fields is obtained which is expressed by the transition matrix t matrix the scattered field is expanded in a power series of a small parameter namely the product of the wave number and the root mean square height of the irregularities analytical expressions for the leading terms of the series have been calculated in particular ensemble averages of the far field amplitude and the scattering cross section have been determined as the analytical results are somewhat complicated some numerical results are presented numerical computations of higher order terms indicate that the convergence of the series is satisfactory as long as the root mean square height is small compared to a correlation length describing the average distance between the peaks of the surface

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

anti plane elastic wave scattering from a rough volumetric crack abstract the scattering of elastic waves from cracks is a field of study which has a number of important applications in nondestructive testing ndt and characterization of materials so far most theoretical studies have concerned smooth cracks there is reason to believe that the influence of roughness will scatter the energy in a more diffuse way thus complicating the interpretation of test results the problem considered here is the scattering of anti plane waves i e horizontally polarized shear waves from a crack in an otherwise homogeneous isotropic elastic solid the geometry is taken to be two dimensional and the scatterer is a curved volumetric crack with a small random roughness which is characterized by the rms height and a correlation length which is related to the average distance between the peaks of the irregularities the term volumetric refers to the fact that the crack surfaces are slightly separated effects due to overall curvature as well as effects due to surface roughness and separation of the crack surfaces are thus included in the analysis the method of solution can be described as an extension of the null field approach where certain matrix elements are expanded in terms of a small parameter describing the deviation from the smooth nonvolumetric crack the ensemble averaged amplitude of the scattered field for an incident plane wave has been computed numerically some results are given for various values of the frequency the rms height the correlation length and the maximum gap between the crack surfaces

laplacian eigenmaps for dimensionality reduction and data representation one of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data we consider the problem of constructing a representation for data lying on a low dimensional manifold embedded in a high dimensional space drawing on the correspondence between the graph laplacian the laplace beltrami operator on the manifold and the connections to the heat equation we propose a geometrically motivated algorithm for representing the high dimensional data the algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering some potential applications and illustrative examples are discussed

probabilistic inference on q ball imaging data diffusion weighted magnetic resonance imaging mri and especially diffusion tensor imaging dti have proven to be useful for the characterization of the microstructure of brain white matter structures in vivo however dti suffers from a number of limitations in characterizing more complex situations the most notable problem occurs when multiple fibre bundles are present within a voxel in this paper we have expanded the existing q ball imaging method to a bayesian framework in order to fully characterize the uncertainty around the fibre directions given the quality of the data we have done this by using a recently proposed spherical harmonics decomposition of the diffusion weighted signal and the resulting q ball orientation distribution function moreover we have incorporated a model selection procedure which determines the appropriate smoothness of the orientation distribution function from the data we show by simulation that our framework can indeed characterize the posterior probability of the fibre directions in cases with multiple fibre populations per voxel and have provided examples of the algorithm s performance on real data where this situation is known to occur

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

some numerical techniques and their use in the extension of t matrix and null field approaches to scattering abstract acoustic electromagnetic and elastic scattering have been described by the t matrix method of waterman high frequency calculations and the description of scattering from general bounded surfaces can give rise to large sets of basis states which in turn necessitate computation of large ill conditioned matrices difficulties in handling these matrices place limitations on the t matrix and null field methods a number of numerical and theoretical techniques are presented which overcome these difficulties and extend the range of applicability of these methods beyond the conventional approach

probabilistic streamline q ball tractography using the residual bootstrap q ball imaging has the ability to discriminate multiple intravoxel fiber populations within regions of complex white matter architecture this information can be used for fiber tracking however diffusion mr is susceptible to noise and multiple other sources of uncertainty affecting the measured orientation of fiber bundles the proposed residual bootstrap method utilizes a spherical harmonic representation for high angular resolution diffusion imaging hardi data in order to estimate the uncertainty in multimodal q ball reconstructions the accuracy of the q ball residual bootstrap technique was examined through simulation the residual bootstrap method was then used in combination with q ball imaging to construct a probabilistic streamline fiber tracking algorithm the residual bootstrap q ball fiber tracking algorithm is capable of following the corticospinal tract and corpus callosum through regions of crossing white matter tracts in the centrum semiovale this fiber tracking algorithm is an improvement upon prior diffusion tensor methods and the q ball data can be acquired in a clinically feasible time frame

improved tractography using asymmetric fibre orientation distributions diffusion mri allows us to make inferences on the structural organisation of the brain by mapping water diffusion to white matter microstructure however such a mapping is generally ill defined for instance diffusion measurements are antipodally symmetric diffusion along x and x are equal whereas the distribution of fibre orientations within a voxel is generally not symmetric therefore different sub voxel patterns such as crossing fanning or sharp bending cannot be distinguished by fitting a voxel wise model to the signal however asymmetric fibre patterns can potentially be distinguished once spatial information from neighbouring voxels is taken into account we propose a neighbourhood constrained spherical deconvolution approach that is capable of inferring asymmetric fibre orientation distributions a fods importantly we further design and implement a tractography algorithm that utilises the estimated a fods since the commonly used streamline tractography paradigm cannot directly take advantage of the new information we assess performance using ultra high resolution histology data where we can compare true orientation distributions against sub voxel fibre patterns estimated from down sampled data finally we explore the benefits of a fods based tractography using in vivo data by evaluating agreement of tractography predictions with connectivity estimates made using different in vivo modalities the proposed approach can reliably estimate complex fibre patterns such as sharp bending and fanning which voxel wise approaches cannot estimate moreover histology based and in vivo results show that the new framework allows more accurate tractography and reconstruction of maps quantifying symmetric and asymmetric fibre complexity

a general learning framework using local and global regularization in this paper we propose a general learning framework based on local and global regularization in the local regularization part our algorithm constructs a regularized classifier for each data point using its neighborhood while the global regularization part adopts a laplacian regularizer to smooth the data labels predicted by those local classifiers we show that such a learning framework can easily be incorporated into either unsupervised learning semi supervised learning and supervised learning paradigm moreover many existing learning algorithms can be derived from our framework finally we present some experimental results to show the effectiveness of our method

investigating white matter fibre density and morphology using fixel based analysis voxel based analysis of diffusion mri data is increasingly popular however most white matter voxels contain contributions from multiple fibre populations often referred to as crossing fibres and therefore voxel averaged quantitative measures e g fractional anisotropy are not fibre specific and have poor interpretability using higher order diffusion models parameters related to fibre density can be extracted for individual fibre populations within each voxel fixels and recent advances in statistics enable the multi subject analysis of such data however investigating within voxel microscopic fibre density alone does not account for macroscopic differences in the white matter morphology e g the calibre of a fibre bundle in this work we introduce a novel method to investigate the latter which we call fixel based morphometry fbm to obtain a more complete measure related to the total number of white matter axons information from both within voxel microscopic fibre density and macroscopic morphology must be combined we therefore present the fbm method as an integral piece within a comprehensive fixel based analysis framework to investigate measures of fibre density fibre bundle morphology cross section and a combined measure of fibre density and cross section we performed simulations to demonstrate the proposed measures using various transformations of a numerical fibre bundle phantom finally we provide an example of such an analysis by comparing a clinical patient group to a healthy control group which demonstrates that all three measures provide distinct and complementary information by capturing information from both sources the combined fibre density and cross section measure is likely to be more sensitive to certain pathologies and more directly interpretable

the null field approach to electromagnetic scattering from composite objects the case of concavo convex constituents time harmonic electromagnetic scattering from a composite body consisting of a dielectric or metallic core plus one or several dielectric coatings was studied using the null field approach previously developed null field approaches to scattering from composite bodies do not apply when these coatings are of concavo convex shapes the authors examine this case and develop alternative null field approaches to such geometries while the scattering problem is usually solved by determination of the total transition matrix referring to spherical waves for the composite scatterer the authors approaches lead to different algebraic expressions for the transition matrix two main alternatives are studied one of these makes use of q matrices for open surfaces while the other is based on a limit procedure applied to a previously developed formalism for layered scatterers the numerical accuracy of the results is less than that obtained for homogeneous scatterers of similar exterior shape and electrical size the convergence of the numerical implementation of the equations is studied in terms of several indicators such as dependence on the truncation order the accuracy with which general constraints such as symmetry and unitarity are fulfilled and the influence of different choices of expansion functions obtained from a moment method solution

multi label segmentation of white matter structures application to neonatal brains accurate and consistent segmentation of brain white matter bundles at neonatal stage plays an important role in understanding brain development and detecting white matter abnormalities for the prediction of psychiatric disorders due to the complexity of white matter anatomy and the spatial resolution of diffusion weighted mr imaging multiple fiber bundles can pass through one voxel the goal of this study is to assign one or multiple anatomical labels of white matter bundles to each voxel to reflect complex white matter anatomy of the neonatal brain for this we develop a supervised multi label k nearest neighbor ml knn classification algorithm in riemannian diffusion tensor spaces our ml knn considers diffusion tensors lying on the log euclidean riemannian manifold of symmetric positive definite spd matrices and their corresponding vector space as feature space the ml knn utilizes the maximum a posteriori map principle to make the prediction of white matter labels by reasoning with the labeling information derived from the neighbors without assuming any probabilistic distribution of the features we show that our approach automatically learns the number of white matter bundles at a location and provides anatomical annotation of the neonatal white matter in addition our approach also provides the binary mask for individual white matter bundles to facilitate tract based statistical analysis in clinical studies we apply this method to automatically segment 13 white matter bundles of the neonatal brain and examine the segmentation accuracy against semi manual labels derived from tractography

learning from normalized local and global discriminative information for semi supervised regression and dimensionality reduction semi supervised dimensionality reduction is one of the important topics in pattern recognition and machine learning during the past decade laplacian regularized least square laprls and semi supervised discriminant analysis sda are the two widely used semi supervised dimensionality reduction methods in this paper we show that sda and laprls can be unified into a constrained manifold regularized least square framework the manifold term however cannot fully utilize the underlying discriminative information we thus introduce a new and effective semi supervised dimensionality reduction method called learning from local and global information llgdi to solve the problem the proposed llgdi method adopts a set of local classification functions to preserve both local geometrical and discriminative information of dataset it also adopts a global classification function to preserve the global discriminative information and an uncorrelated constraint to calculate the projection matrix for simultaneously solving regression and dimensionality reduction problem as a result the llgdi method is able to preserve local discriminative manifold information as well as the global discriminative information theoretical analysis and extensive simulations presented in the paper show the effectiveness of the llgdi algorithm the results also demonstrate llgdi can achieve superior performance compared with other existing methods

diffeomorphic metric mapping of high angular resolution diffusion imaging based on riemannian structure of orientation distribution functions in this paper we propose a novel large deformation diffeomorphic registration algorithm to align high angular resolution diffusion images hardi characterized by orientation distribution functions odfs our proposed algorithm seeks an optimal diffeomorphism of large deformation between two odf fields in a spatial volume domain and at the same time locally reorients an odf in a manner such that it remains consistent with the surrounding anatomical structure to this end we first review the riemannian manifold of odfs we then define the reorientation of an odf when an affine transformation is applied and subsequently define the diffeomorphic group action to be applied on the odf based on this reorientation we incorporate the riemannian metric of odfs for quantifying the similarity of two hardi images into a variational problem defined under the large deformation diffeomorphic metric mapping framework we finally derive the gradient of the cost function in both riemannian spaces of diffeomorphisms and the odfs and present its numerical implementation both synthetic and real brain hardi data are used to illustrate the performance of our registration algorithm

the effect of finite diffusion gradient pulse duration on fibre orientation estimation in diffusion mri abstract an essential step for fibre tracking is the accurate estimation of neuronal fibre orientations within each imaging voxel and a number of methods have been proposed to reconstruct the orientation distribution function based on sampling three dimensional q space in the q space formalism very short infinitesimal gradient pulses are the basic requirement to obtain the true spin displacement probability density function on current clinical mr systems however the diffusion gradient pulse duration is inevitably finite due to the limit on the achievable gradient intensity the failure to satisfy the short gradient pulse sgp requirement has been a recurrent criticism for fibre orientation estimation based on the q space approach in this study the influence of a finite on the dw signal measured as a function of gradient direction is described theoretically and demonstrated through simulations and experimental models our results suggest that the current practice of using long for dw imaging on human clinical mr scanners which is enforced by hardware limitations might in fact be beneficial for estimating fibre orientations for a given b value the prolongation of is advantageous for estimating fibre orientations for two reasons first it leads to a boost in dw signal in the transverse plane of the fibre second it stretches out the shape of the measured diffusion profile which improves the contrast between dw orientations this is especially beneficial for resolving crossing fibres as this contrast is essential to discriminate between different fibre directions

atlas based fiber bundle segmentation using principal diffusion directions and spherical harmonic coefficients abstract purpose to develop an automatic atlas based method for segmentation of fiber bundles using high angular resolution diffusion imaging hardi data hypothesis quantitative evaluation of diffusion characteristics inside specific fiber bundles provides new insights into disease developments evolutions therapy effects and surgical interventions background most of previous segmentation methods use similarity measures and strategies that do not lead to accurate segmentation results they also suffer from subjectivity of initial seeds and regions of interest roi defined by operator materials and methods we propose a novel method that uses spherical harmonic coefficients shc of hardi diffusion signals to compute orientation distribution function odf and to extract principal diffusion directions pdds the proposed method selects most collinear pdd of neighbors of each voxel then based on shc and selected pdd a similarity measure is proposed and used as a speed function in the level set framework that segments fiber bundles to automate the process an atlas based method is used to select initial seeds for fiber bundles to generate data for evaluation of the proposed method an artificial pattern consisting of three crossing bundles intersected by a circular bundle is created also two normal controls are imaged by two different hardi protocols results segmentation results for different fiber bundles in simulated data and normal control data are presented influence of threshold selection on the proposed segmentation method is evaluated using dice coefficient also effect of increasing the number of gradient directions on accuracy of extracted pdds is evaluated conclusion the proposed segmentation method has advantages over previous methods especially those that use similarity measures based on diffusion tensor imaging dti data these advantages are achieved by proper propagation of a hyper surface in fiber crossing areas without making assumptions about diffusivity profile and selection of initial seeds or roi

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

estimation of diffusion properties in crossing fiber bundles there is an ongoing debate on how to model diffusivity in fiber crossings we propose an optimization framework for the selection of a dual tensor model and the set of diffusion weighting parameters b such that both the diffusion shape and orientation parameters can be precisely as well as accurately estimated for that we have adopted the cramer rao lower bound crlb on the variance of the model parameters and performed monte carlo simulations we have found that the axial diffusion needs to be constrained while an isotropic fraction can be modeled by a single parameter fiso under these circumstances the fractional anisotropy fa of both tensors can theoretically be independently estimated with a precision of 9 at snr 25 levenberg marquardt optimization of the maximum likelihood function with a rician noise model approached this precision while the bias was insignificant a two element b vector b 1 0 amp 3 5 103 mm 2 s was found to be sufficient for estimating parameters of heterogeneous tissue with low error this has allowed us to estimate consistent fa profiles along crossing tracts this work defines fundamental limits for comparative studies to correctly analyze crossing white matter structures

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

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

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

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

bootstrap white matter tractography boot trac white matter tractography is a noninvasive method for estimating and visualizing the white matter connectivity patterns in the human brain using diffusion tensor imaging dti data sources of experimental noise may induce errors in the measured fiber directions which will reduce the accuracy of the estimated white matter trajectories in this study a statistical nonparametric bootstrap method is described for estimating the dispersion and other errors in white matter tractography results prior studies have derived models of tractography error using the signal to noise ratio snr and diffusion anisotropy of the dti data tractography errors measured using bootstrap methods were generally consistent with an analytic model of tractography error except in areas where branching was evident white matter tractography with bootstrap resampling is also applied to estimate the probabilities of connection between brain regions the approach was used to generate probabilistic connectivity maps between the cerebral peduncles and specific cortical regions