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

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

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

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

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

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

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

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

predicting the dynamic postural control response from quiet stance behavior in elderly adults human postural sway as measured by fluctuations of the center of pressure cop under the feet of a quietly standing individual can be characterized as a stochastic process the fluctuation dissipation theorem fdt provides a linear relationship between the fluctuations of a quasi static stochastic system to the same system s relaxation to equilibrium following a perturbation we applied a similar linear relationship based on the fdt to the human postural control system to explore whether anterior posterior ap fluctuations of the cop during quiet stance can be used to predict the ap response of the postural control system to a weak posteriorly directed mechanical perturbation tug or pull at the waist we tested 10 healthy elderly mean age of 69yr and 10 healthy young mean age of 25yr adult subjects we found that this linear relationship was applicable to the postural control system of all 10 young and eight of the 10 elderly adult subjects these results suggest that it is possible to predict an individual s dynamic response to a mild perturbation using quiet stance data regardless of age the existence of this fdt based linear relationship with respect to the human postural control system suggests that for a given individual the postural control system may use the same control mechanisms during quiet stance and mild perturbation conditions regardless of age

measure valued branching processes associated with neumann nonlinear semiflows abstract we construct a measure valued branching markov process associated with a nonlinear boundary value problem where the boundary condition has a nonlinear pseudo monotone branching mechanism term which includes the case u u m with 0 m 1 the process is then used in the probabilistic representation of the solution of the parabolic problem associated with a nonlinear neumann boundary value problem in this way the classical association of the superprocesses to the dirichlet boundary value problems also holds for the nonlinear neumann boundary value problems it turns out that the obtained branching process behaves on the measures carried by the given open set like the linear continuous semiflow induced by the reflected brownian motion while the branching occurs on the measures having non zero traces on the boundary of the open set with the behavior of the superprocess having as spatial motion the process on the boundary associated to the reflected brownian motion

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

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

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

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

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

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

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