nonperturbative tricritical exponents of trails i exact enumeration on a triangular lattice as the fugacity of intersections in trails intersecting but non overlapping lattice walks is increased the configurations change from swollen ones with the scaling exponents of self avoiding walks to compact ones separating the two regimes is a potentially new tricritical point with no perturbative renormalisation fixed point associated with it supporting evidence for the existence of a tricritical point its likely location and exponents are computed for the first time from exact enumeration of all trails up to length of fifteen lattice constants on the triangular lattice the divergence of the specific heat indicates the location of the tricritical point generalised ratio and pade methods are used to extract the scaling exponents for the number of configurations and their end to end distance

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

stanley symmetric functions and quiver varieties abstract we prove that the coefficients obtained when stanley symmetric functions are expanded in the basis of schur functions are special cases of the coefficients in the formula for quiver varieties given by the author and w fulton 1999 invent math 135 665 687 and we discuss the relations of this with a conjectured littlewood richardson rule for these quiver coefficients in addition we generalize a factorization formula for schubert polynomials of a product of two permutations

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

chern class formulas for quiver varieties our goal in this paper is to prove a formula for the general degeneracy locus xr associated to an oriented quiver of type an if we are given a sequence of vector bundles and vector bundle maps e0 1 e1 2 e2 y y eny1 n en on an algebraic variety x and a collection r rij 0 i j n of non negative integers there is a degeneracy locus xr xr e xr e de ned by xr fx 2 x j rank ei x ej x rij 8 i jg 1 1

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

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

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

semi flexible interacting self avoiding trails on the square lattice abstract self avoiding walks self interacting via nearest neighbours isaw and self avoiding trails interacting via multiply visited sites isat are two models of the polymer collapse transition of a polymer in a dilute solution on the square lattice it has been established numerically that the collapse transition of each model lies in a different universality class it has been shown that by adding stiffness to the isaw model a second low temperature phase eventuates and a more complicated phase diagram ensues with three types of transition that meet at a multi critical point for large enough stiffness the collapse transition becomes first order interestingly a phase diagram of a similar structure has been seen to occur in an extended isat model on the triangular lattice without stiffness it is therefore of interest to see the effect of adding stiffness to the isat model we have studied by computer simulation a generalised model of self interacting self avoiding trails on the square lattice with a stiffness parameter added intriguingly we find that stiffness does not change the order of the collapse transition for isat on the square lattice for a very wide range of stiffness weights while at the lengths considered there are clear bimodal distributions for very large stiffness our numerical evidence strongly suggests that these are simply finite size effects associated with a crossover to a first order phase transition at infinite stiffness

manhattan lattice theta point exponents from kinetic growth walks and exact results from the nienhuis o n model kinetic growth walks kgw on the manhattan lattice have previously been shown to be equivalent to the static problem of interacting self avoiding walks on that lattice at the theta temperature here we illustrate how a complete set of exponents for the static problem including the crossover exponent phi and surface exponents at the ordinary and special transition points may be obtained from simulations of kinetic walks in the process we find that phi m 0 430 or 0 006 which encompasses the conjectured value 3 7 approximately 0 42857 for the theta point on an isotropic lattice our numerics confirm a predicted set of exponents for both the bulk and surface transitions in addition to results such as the exact internal energy at the bulk transition furthermore we point out that a recently examined variant of the nienhuis o n model can be mapped onto theta point walks on the manhattan lattice which allows identification of the scaling dimensions for that problem and thereby provides a method for proving all the numerical conjectures

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

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

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

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

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

smart self avoiding trails and the collapse of chain polymers in three dimensions recently it was shown that certain smart self avoiding trails have end to end distances in three dimensions also the corrections to scaling of and the specific heat are qualitatively very similar to those for polymers exactly at the point the question was thus posed whether they are in the same universality class as linear polymers at the temperature we show that this is not the case since these trails show a first order transition instead of the second order transition at the usual point we argue that this is due to the fact that the smartness of these trails implies that the renormalized n body interactions vanish identically for any finite we conjecture that the qualitative similarity with recent simulations of polymers indicates that for n body interactions the renormalized three body interaction is small in real polymers

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

a scaling theory of the collapse transition in geometric cluster models of polymers and vesicles much effort has been expended in the past decade to calculate numerically the exponents at the collapse transition point in walk polygon and animal models the crossover exponent phi has been of special interest and sometimes is assumed to obey the relation 2 alpha 1 phi with the alpha the canonical thermodynamic exponent that characterizes the divergence of the specific heat the reasons for the validity of this relation are not widely known the authors present a scaling theory of collapse transitions in such models the free energy and canonical partition functions have finite length scaling forms whilst the grand partition function has a tricritical scaling form the link between the grand and canonical ensembles leads to the above scaling relation they then comment on the validity of current estimates of the crossover exponent for interacting self avoiding walks in two dimensions and propose a test involving the scaling relation which may be used to check these values

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

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

a 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

schubert polynomials and quiver formulas fulton s universal schubert polynomials f3 represent degeneracy loci for morphisms of vector bundles with rank conditions coming from a permutation the quiver formula of buch and fulton bf expresses these polynomials as an integer linear combination of products of schur determinants we present a positive nonrecursive combinatorial formula for the coefficients our result is applied to obtain new expansions for the schubert polynomials of lascoux and schutzenberger ls1 and explicit giambelli formulas in the classical and quantum cohomology ring of any partial flag variety

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

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

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

identification of a polymer growth process with an equilibrium multicritical collapse phase transition the meeting point of swollen collapsed and crystalline polymers we have investigated a polymer growth process on the triangular lattice where the configurations produced are self avoiding trails we show that the scaling behavior of this process is similar to the analogous process on the square lattice however while the square lattice process maps to the collapse transition of the canonical interacting self avoiding trail isat model on that lattice the process on the triangular lattice model does not map to the canonical equilibrium model on the other hand we show that the collapse transition of the canonical isat model on the triangular lattice behaves in a way reminiscent of the point of the interacting self avoiding walk isaw model which is the standard model of polymer collapse this implies an unusual lattice dependency of the isat collapse transition in two dimensions by studying an extended isat model we demonstrate that the growth process maps to a multicritical point in a larger parameter space in this extended parameter space the collapse phase transition may be either point like second order or first order and these two are separated by a multicritical point it is this multicritical point to which the growth process maps furthermore we provide evidence that in addition to the high temperature gaslike swollen polymer phase coil and the low temperature liquid drop like collapse phase globule there is also a maximally dense crystal like phase crystal at low temperatures dependent on the parameter values the multicritical point is the meeting point of these three phases our hypothesized phase diagram resolves the mystery of the seemingly differing behaviors of the isaw and isat models in two dimensions as well as the behavior of the trail growth process

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

collapse transition of self avoiding trails on the square lattice abstract the collapse transition of an isolated polymer has been modelled by many different approaches including lattice models based on self avoiding walks and self avoiding trails in two dimensions previous simulations of kinetic growth trails which map to a particular temperature of interacting self avoiding trails showed markedly different behaviour for what was argued to be the collapse transition than that which has been verified for models based of self avoiding walks on the other hand it has been argued that kinetic growth trails represent a special simulation that does not give the correct picture of the standard equilibrium model in this work we simulate the standard equilibrium interacting self avoiding trail model on the square lattice up to lengths over 2 000 000 steps and show that the results of the kinetic growth simulations are in fact entirely in accord with standard simulations of the temperature dependent model in this way we verify that the collapse transition of interacting self avoiding walks and trails are indeed in different universality classes in two dimensions

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

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

grothendieck polynomials and quiver formulas fulton s universal schubert polynomials give cohomology formulas for a class of degeneracy loci which generalize schubert varieties the k theoretic quiver formula of buch expresses the structure sheaves of these loci as integral linear combinations of products of stable grothendieck polynomials we prove an explicit combinatorial formula for the coefficients which shows that they have alternating signs our result is applied to obtain new expansions for the grothendieck polynomials of lascoux and schutzenberger

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

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

walks trials and polymers with loops lattice models interpolating between free and self avoiding random walks are investigated generating functions are constructed for k tolerant walks various trail problems etc for trail problems the effective field theory describing the global behaviour is analysed in the vicinity of the upper critical dimension dc 4 their asymptotic large scale behaviours are the same as those of the self avoiding walk arguments are presented to support the same conclusion for much more general classes of walks including k tolerant walks one of the models exhibits a new tricritical point of order epsilon 1 2 if the fugacity for crossing is increased

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

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

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

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

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

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

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

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