recognition of white matter bundles using local and global streamline based registration and clustering virtual dissection of diffusion mri tractograms is cumbersome and needs extensive knowledge of white matter anatomy this virtual dissection often requires several inclusion and exclusion regions of interest that make it a process that is very hard to reproduce across experts having automated tools that can extract white matter bundles for tract based studies of large numbers of people is of great interest for neuroscience and neurosurgical planning the purpose of our proposed method named recobundles is to segment white matter bundles and make virtual dissection easier to perform this can help explore large tractograms from multiple persons directly in their native space recobundles leverages latest state of the art streamline based registration and clustering to recognize and extract bundles using prior bundle models recobundles uses bundle models as shape priors for detecting similar streamlines and bundles in tractograms recobundles is 100 streamline based is efficient to work with millions of streamlines and most importantly is robust and adaptive to incomplete data and bundles with missing components it is also robust to pathological brains with tumors and deformations we evaluated our results using multiple bundles and showed that recobundles is in good agreement with the neuroanatomical experts and generally produced more dense bundles across all the different experiments reported in this paper recobundles was able to identify the core parts of the bundles independently from tractography type deterministic or probabilistic or size thus recobundles can be a valuable method for exploring tractograms and facilitating tractometry studies

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

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

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

flow based fiber tracking with diffusion tensor and q ball data validation and comparison to principal diffusion direction techniques in this study we evaluate the performance of a flow based surface evolution fiber tracking algorithm by means of a physical anisotropic diffusion phantom with known connectivity we introduce a novel speed function for surface evolution that is derived from either diffusion tensor dt data high angular resolution diffusion hard data or a combined dt hard hybrid approach we use the model free q ball imaging qbi approach for hard reconstruction the anisotropic diffusion phantom allows us to compare and evaluate the performance of different fiber tracking approaches in the presence of real imaging artifacts noise and subvoxel partial volume averaging of fiber directions the surface evolution approach using the full diffusion tensor as opposed to the principal diffusion direction pdd only is compared to pdd based line propagation fiber tracking additionally dt reconstruction is compared to hard reconstruction for fiber tracking both using surface evolution we show the potential for surface evolution using the full diffusion tensor to map connections in regions of subvoxel partial volume averaging of fiber directions which can be difficult to map with pdd based methods we then show that the fiber tracking results can be improved by using high angular resolution reconstruction of the diffusion orientation distribution function in cases where the diffusion tensor model fits the data poorly

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

maximum likelihood estimation under order restrictions by the prior feedback method abstract algorithms for deriving isotonic regression estimators in order restricted linear models and more generally restricted maximum likelihood estimators are usually quite dependent on the particular problem considered we propose here an optimization method based on a sequence of formal bayes estimates whose variances converge to zero this method akin to simulated annealing can be applied universally that is as long as these bayes estimators can be derived by exact computation or markov chain monte carlo sampling approximation we then give an illustration of our method for two real life examples

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

estimation of integral curves from high angular resolution diffusion imaging hardi data we develop statistical methodology for a popular brain imaging technique hardi based on the high order tensor model by ozarslan and mareci 10 we investigate how uncertainty in the imaging procedure propagates through all levels of the model signals tensor fields vector fields and fibers we construct asymptotically normal estimators of the integral curves or fibers which allow us to trace the fibers together with confidence ellipsoids the procedure is computationally intense as it blends linear algebra concepts from high order tensors with asymptotical statistical analysis the theoretical results are illustrated on simulated and real datasets this work generalizes the statistical methodology proposed for low angular resolution diffusion tensor imaging by carmichael and sakhanenko 3 to several fibers per voxel it is also a pioneering statistical work on tractography from hardi data it avoids all the typical limitations of the deterministic tractography methods and it delivers the same information as probabilistic tractography methods our method is computationally cheap and it provides well founded mathematical and statistical framework where diverse functionals on fibers directions and tensors can be studied in a systematic and rigorous way

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

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

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

fiber continuity an anisotropic prior for odf estimation the accurate and reliable estimation of fiber orientation distributions based on diffusion sensitized magnetic resonance images is a major prerequisite for tractography algorithms or any other derived statistical analysis in this work we formulate the principle of fiber continuity fc which is based on the simple observation that the imaging of fibrous tissue implies certain expectations for the measured images from this principle we derive a prior for the estimation of fiber orientation distributions based on high angular resolution diffusion imaging hardi we demonstrate on simulated phantom and in vivo data the superiority of the proposed approach further we propose another application of the fc principle named fc flow a method to resolve complex crossing regions solely based on diffusion tensor imaging dti the idea is to infer directional information in crossing regions from adjacent anisotropic areas

estimation of fiber orientation and spin density distribution by diffusion deconvolution a diffusion deconvolution method is proposed to apply deconvolution to the diffusion orientation distribution function dodf and calculate the fiber orientation distribution function fodf which is defined as the orientation distribution of the fiber spin density the dodf can be obtained from q space imaging methods such as q ball imaging qbi diffusion spectrum imaging dsi and generalized q sampling imaging gqi and thus the method can be applied to various diffusion sampling schemes a phantom study was conducted to compare the angular resolution of the fodf with the dodf and the in vivo datasets were acquired using single shell two shell and grid sampling schemes which were then reconstructed by qbi gqi and dsi respectively the phantom study showed that the fodf significantly improved the angular resolution over the dodf at 45 and 60 degree crossing angles the in vivo study showed consistent fodf regardless of the applied sampling schemes and reconstruction methods and the ability to resolve crossing fibers was improved in reduced sampling condition the fiber spin density obtained from deconvolution showed a higher contrast to noise ratio than the fractional anisotropy fa mapping and further application on tractography showed that the fiber spin density can be used to determine the termination of fiber tracts in conclusion the proposed deconvolution method is generally applicable to different q space imaging methods the calculated fodf improves the angular resolution and also provides a quantitative index of fiber spin density to refine fiber tracking

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

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

consistency based thresholding of the human connectome densely seeded probabilistic tractography yields weighted networks that are nearly fully connected hence containing many spurious fibers it is thus necessary to prune spurious connections from probabilistically derived networks to obtain a more reliable overall estimate of the connectivity a standard method is to threshold by weight keeping only the strongest edges here by measuring the consistency of edge weights across subjects we propose a new thresholding method that aims to reduce the rate of false positives in group averaged connectivity matrices close inspection of the relationship between consistency weight and distance suggests that the most consistent edges are in fact those that are strong for their length rather than simply strong overall hence retaining the most consistent edges preserves more long distance connections than traditional weight based thresholding which penalizes long connections for being weak regardless of anatomy by comparing our thresholded networks to mouse and macaque tracer data we also show that consistency based thresholding exhibits the species invariant exponential decay of connection weights with distance while weight based thresholding does not we also show that consistency based thresholding can be used to identify highly consistent and highly inconsistent subnetworks across subjects enabling more nuanced analyses of group level connectivity than just the mean connectivity

reproducibility of superficial white matter tracts using diffusion weighted imaging tractography human brain connection map is far from being complete in particular the study of the superficial white matter swm is an unachieved task its description is essential for the understanding of human brain function and the study of pathogenesis triggered by abnormal connectivity in this work we automatically created a multi subject atlas of swm diffusion based bundles of the whole brain for each subject the complete cortico cortical tractogram is first split into sub tractograms connecting pairs of gyri then intra subject shape based fiber clustering performs compression of each sub tractogram into a set of bundles proceeding further with shape based clustering provides a match of the bundles across subjects bundles found in most of the subjects are instantiated in the atlas to increase robustness this procedure was performed with two independent groups of subjects in order to discard bundles without match across the two independent atlases finally the resulting intersection atlas was projected on a third independent group of subjects in order to filter out bundles without reproducible and reliable projection the final multi subject diffusion based u fiber atlas is composed of 100 bundles in total 50 per hemisphere from which 35 are common to both hemispheres

basis tensor decomposition for restoring intra voxel structure and stochastic walks for inferring brain connectivity in dt mri we present a regularized method for solving an inverse problem in diffusion tensor magnetic resonance imaging dt mri data in the case of brain images dt mr imagery technique produces a tensor field that indicates the local orientation of nerve bundles now days the spatial resolution of this technique is limited by the partial volume effect produced in voxels that contain fiber crossings or bifurcations in this paper we proposed a method for recovering the intra voxel information and inferring the brain connectivity we assume that the observed tensor is a linear combination of a given tensor basis therefore the aim of our approach is the computation of the unknown coefficients of this linear combination by regularizing the problem we introduce the needed prior information about the piecewise smoothness of nerve bundles orientation as a result we recover a multi tensor field moreover for estimating the nerve bundles trajectory we propose a method based on stochastic walks of particles through the computed multi tensor field the performance of the method is demonstrated by experiments in both synthetic and real data

the capacitated max k cut problem we consider a capacitated max k cut problem in which a set of vertices is partitioned into k subsets each edge has a non negative weight and each subset has a possibly different capacity that imposes an upper bound on its size the objective is to find a partition that maximizes the sum of edge weights across all pairs of vertices that lie in different subsets we describe a local search algorithm that obtains a solution with value no smaller than 1 1 k of the optimal solution value this improves a previous bound of 1 2 for the max k cut problem with fixed though possibly different sizes of subsets

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

new formulations for the conflict resolution problem in the scheduling of television commercials we consider the conflict resolution problem arising in the allocation of commercial advertisements to television program breaks because of the competition avoidance requirements issued by advertisers broadcasters aim to allocate any pairs of commercials promoting highly conflicting products to different breaks hence the problem consists of assigning commercials to breaks subject to time capacity constraints with the aim of maximizing a total measure of the conflicts among commercials assigned to different breaks since the existing formulation can hardly be solved via exact methods we introduce three new and efficient mixed integer programming formulations of the problem our computational study is based on two sets of test problems one from the literature and another more challenging data set that we generate numerical results show the excellent performance of the proposed formulations in terms of solution quality and computation times when compared against an existing formulation and an effe

an objective method for regularization of fiber orientation distributions derived from diffusion weighted mri spherical deconvolution is an elegant method by which the orientation of crossing fibers in the brain can be estimated from a diffusion weighted mri measurement however higher resolution of fiber directions comes at the cost of higher susceptibility to noise in this study we describe the use of linear regularization of the fiber orientation distribution function by damped singular value decomposition furthermore the degree of regularization is optimized on a voxel by voxel basis with no user interaction using generalized cross validation we find by simulations that regularization can improve the reliability of fiber orientation determination when the signal to noise ratio is low simulations and in vivo measurements indicate that spurious peaks of the fiber orientation distribution function in regions with low anisotropy largely disappear when regularization is introduced the methods examined are fast enough to be used on a routine basis with diffusion mri data sets and may improve estimation of water diffusion properties in heterogeneous white matter and boost reliability of fiber tracking through regions of brain with complex fiber geometry

conflict resolution in the scheduling of television commercials we extend a previous model for scheduling commercial advertisements during breaks in television programming the proposed extension allows differential weighting of conflicts between pairs of commercials we formulate the problem as a capacitated generalization of the max k cut problem in which the vertices of a graph correspond to commercial insertions and the edge weights to the conflicts between pairs of insertions the objective is to partition the vertices into k capacitated sets to maximize the sum of conflict weights across partitions we note that the problem is np hard we extend a previous local search procedure to allow for the differential weighting of edge weights we show that for problems with equal insertion lengths and break durations the worst case bound on the performance of the proposed algorithm increases with the number of program breaks and the number of insertions per break and that it is independent of the number of conflicts between pairs of insertions simulation results suggest that the algorithm performs well even if the problem size is small

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