Medical Image Computing and Computer-Assisted Intervention – MICCAI 2011

Diffusion tensor magnetic resonance imaging (DT-MRI) tractography allows to probe brain connections

in vivo

. This paper presents a change detection framework that relies on white-matter pathways with application to neuromyelitis optica (NMO). The objective is to detect global or local fiber diffusion property modifications between two longitudinal DT-MRI acquisitions of a patient. To this end, estimation and testing tools on tensors along the white-matter pathways are considered. Two tests are implemented: a pointwise test that compares at each sampling point of the fiber bundle the tensor populations of the two exams in the cross section of the bundle and a fiberwise test that compares paired tensors along all the fiber bundle. Experiments on both synthetic and real data highlight the benefit of considering fiber based statistical tests compared to the standard voxelwise strategy.

In this paper, we propose to use the full diffusion tensor to perform brain-wide score prediction on diffusion tensor imaging (DTI) using the log-Euclidean framework., rather than the commonly used fractional anisotropy (FA). Indeed, scalar values such as the FA do not capture all the information contained in the diffusion tensor. Additionally, full tensor information is included in every step of the pre-processing pipeline: registration, smoothing and feature selection using voxelwise multivariate regression analysis. This approach was tested on data obtained from 30 children and adolescents with autism spectrum disorder and showed some improvement over the FA-only analysis.

DTI tractography allows unprecedented understanding of brain neural connectivity in-vivo by capturing water diffusion patterns in brain white-matter microstructures. However, tractography algorithms often output hundreds of thousands of fibers, rendering the computation needed for subsequent data analysis intractable. A remedy is to group the fibers into bundles using fiber clustering techniques. Most existing fiber clustering methods, however, rely on fiber geometrical information only by viewing fibers as curves in the 3D Euclidean space. The important neuroanatomical aspect of the fibers is mostly ignored. In this paper, neuroanatomical information is encapsulated in a feature vector called the associativity vector, which functions as the “fingerprint” for each fiber and depicts the connectivity of the fiber with respect to individual anatomies. Using the associativity vectors of fibers, we model the fibers as observations sampled from multivariate Gaussian mixtures in the feature space. An expectation-maximization clustering approach is then employed to group the fibers into 16 major bundles. Experimental results indicate that the proposed method groups the fibers into anatomically meaningful bundles, which are highly consistent across subjects.

We present a novel approach for probabilistic clustering of white matter fibre pathways using curve-based regression mixture modelling techniques in 3D curve space. The clustering algorithm is based on a principled method for probabilistic modelling of a set of fibre trajectories as individual sequences of points generated from a finite mixture model consisting of multivariate polynomial regression model components. Unsupervised learning is carried out using maximum likelihood principles. Specifically, conditional mixture is used together with an EM algorithm to estimate cluster membership. The result of clustering is a probabilistic assignment of fibre trajectories to each cluster and an estimate of cluster parameters. A statistical shape model is calculated for each clustered fibre bundle using fitted parameters of the probabilistic clustering. We illustrate the potential of our clustering approach on synthetic and real data.

Existing methods for fiber tracking, interactive bundling and editing from Diffusion Magnetic Resonance Images (DMRI) reconstruct white matter fascicles using groups of virtual pathways. Classical numerical fibers suffer from image noise and cumulative tracking errors. 3D visualization of bundles of fibers reveals structural connectivity of the brain; however, extensive human intervention, tracking variations and errors in fiber sampling make quantitative fascicle comparison difficult. To simplify the process and offer standardized white matter samples for analysis, we propose a new integrated fascicle parcellation and normalization method that combines a generic parametrized volumetric tract model with orientation information from diffusion images. The new technique offers a tract-derived spatial parameter for each voxel within the model. Cross-subject statistics of tract data can be compared easily based on these parameters. Our implementation demonstrated interactive speed and is available to the public in a packaged application.

Study of structural and functional connectivities of the human brain has received significant interest and effort recently. A fundamental question arises when attempting to measure the structural and/or functional connectivities of specific brain networks: how to best identify possible Regions of Interests (ROIs)? In this paper, we present a novel ROI prediction framework that localizes ROIs in individual brains based on learned fiber shape models from multimodal task-based fMRI and diffusion tensor imaging (DTI) data. In the training stage, ROIs are identified as activation peaks in task-based fMRI data. Then, shape models of white matter fibers emanating from these functional ROIs are learned. In addition, ROIs’ location distribution model is learned to be used as an anatomical constraint. In the prediction stage, functional ROIs are predicted in individual brains based on DTI data. The ROI prediction is formulated and solved as an energy minimization problem, in which the two learned models are used as energy terms. Our experiment results show that the average ROI prediction error is 3.45 mm, in comparison with the benchmark data provided by working memory task-based fMRI. Promising results were also obtained on the ADNI-2 longitudinal DTI dataset.

The construction of realistic subject-specific models of the myocardial fiber architecture is relevant to the understanding and simulation of the electro-mechanical behavior of the heart. This paper presents a statistical approach for the prediction of fiber orientation from myocardial morphology based on the Knutsson mapping. In this space, the orientation of each fiber is represented in a continuous and distance preserving manner, thus allowing for consistent statistical analysis of the data. Furthermore, the directions in the shape space which correlate most with the myocardial fiber orientations are extracted and used for subsequent prediction. With this approach and unlike existing models, all shape information is taken into account in the analysis and the obtained latent variables are statistically optimal to predict fiber orientation in new datasets. The proposed technique is validated based on a sample of canine Diffusion Tensor Imaging (DTI) datasets and the results demonstrate marked improvement in cardiac fiber orientation modeling and prediction.

Diffusion magnetic resonance imaging (dMRI) is an important tool that allows non-invasive investigation of neural architecture of the brain. The data obtained from these

in-vivo

scans provides important information about the integrity and connectivity of neural fiber bundles in the brain. A multi-shell imaging (MSI) scan can be of great value in the study of several psychiatric and neurological disorders, yet its usability has been limited due to the long acquisition times required. A typical MSI scan involves acquiring a large number of gradient directions for the 2 (or more) spherical shells (several b-values), making the acquisition time significantly long for clinical application. In this work, we propose to use results from the theory of compressive sampling and determine the minimum number of gradient directions required to attain signal reconstruction similar to a traditional MSI scan. In particular, we propose a generalization of the single shell

spherical ridgelets

basis for sparse representation of multi shell signals. We demonstrate its efficacy on several synthetic and

in-vivo

data sets and perform quantitative comparisons with solid spherical harmonics based representation. Our preliminary results show that around 20-24 directions per shell are enough for robustly recovering the diffusion propagator.

This paper presents a novel tractography algorithm for more accurate reconstruction of fiber trajectories in low SNR diffusion-weighted images, such as neonatal scans. We leverage information from a later-time-point longitudinal scan to obtain more reliable estimates of local fiber orientations. Specifically, we determine the orientation posterior probability at each voxel location by utilizing prior information given by the longitudinal scan, and with the likelihood function formulated based on the Watson distribution. We incorporate this Bayesian model of local orientations into a state-space model for particle-filtering-based probabilistic tracking, catering for the possibility of crossing fibers by modeling multiple orientations per voxel. Regularity of fibers is enforced by encouraging smooth transitions of orientations in subsequent locations traversed by the fiber. Experimental results performed on neonatal scans indicate that fiber reconstruction is significantly improved with less stray fibers and is closer to what one would expect anatomically.

We present a new method for the uncertainty estimation of diffusion parameters for quantitative body DW-MRI assessment. Diffusion parameters uncertainty estimation from DW-MRI is necessary for clinical applications that use these parameters to assess pathology. However, uncertainty estimation using traditional techniques requires repeated acquisitions, which is undesirable in routine clinical use. Model-based bootstrap techniques, for example, assume an underlying linear model for residuals rescaling and cannot be utilized directly for body diffusion parameters uncertainty estimation due to the non-linearity of the body diffusion model. To offset this limitation, our method uses the Unscented transform to compute the residuals rescaling parameters from the non-linear body diffusion model, and then applies the wild-bootstrap method to infer the body diffusion parameters uncertainty. Validation through phantom and human subject experiments shows that our method identify the regions with higher uncertainty in body DWI-MRI model parameters correctly with realtive error of ~36% in the uncertainty values.

This paper proposes a technique for a previously unaddressed problem, namely, mapping axon diameter in crossing fiber regions, using diffusion MRI. Direct measurement of tissue microstructure of this kind using diffusion MRI offers a new class of biomarkers that give more specific information about tissue than measures derived from diffusion tensor imaging. Most existing techniques for axon diameter mapping assume a single axon orientation in the tissue model, which limits their application to only the most coherently oriented brain white matter, such as the corpus callosum, where the single orientation assumption is a reasonable one. However, fiber crossings and other complex configurations are widespread in the brain. In such areas, the existing techniques will fail to provide useful axon diameter indices for any of the individual fiber populations. We propose a novel crossing fiber tissue model to enable axon diameter mapping in voxels with crossing fibers. We show in simulation that the technique can provide robust axon diameter estimates in a two-fiber crossing with the crossing angle as small as 45

o

. Using

ex vivo

imaging data, we further demonstrate the feasibility of the technique by establishing reasonable axon diameter indices in the crossing region at the interface of the cingulum and the corpus callosum.

We derive herein first and second-order differential operators for detecting structure in diffusion tensor MRI (DTI). Unlike existing methods, we are able to generate full first and second-order differentials without dimensionality reduction and while respecting the underlying manifold of the data. Further, we extend corner and curvature feature detectors to DTI using our differential operators. Results using the feature detectors on diffusion tensor MR images show the ability to highlight structure within the image that existing methods cannot.

Background:

In Diffusion Tensor Imaging (DTI), Riemannian framework based on Information Geometry theory has been proposed for processing tensors on estimation, interpolation, smoothing, regularization, segmentation, statistical test and so on. Recently Riemannian framework has been generalized to Orientation Distribution Function (ODF) and it is applicable to any Probability Density Function (PDF) under orthonormal basis representation. Spherical Polar Fourier Imaging (SPFI) was proposed for ODF and Ensemble Average Propagator (EAP) estimation from arbitrary sampled signals without any assumption.

Purpose:

Tensors only can represent Gaussian EAP and ODF is the radial integration of EAP, while EAP has full information for diffusion process. To our knowledge, so far there is no work on how to process EAP data. In this paper, we present a Riemannian framework as a mathematical tool for such task.

Method:

We propose a state-of-the-art Riemannian framework for EAPs by representing the square root of EAP, called wavefunction based on quantum mechanics, with the Fourier dual Spherical Polar Fourier (dSPF) basis. In this framework, the exponential map, logarithmic map and geodesic have closed forms, and weighted Riemannian mean and median uniquely exist. We analyze theoretically the similarities and differences between Riemannian frameworks for EAPs and for ODFs and tensors. The Riemannian metric for EAPs is diffeomorphism invariant, which is the natural extension of the affine-invariant metric for tensors. We propose Log-Euclidean framework to fast process EAPs, and Geodesic Anisotropy (GA) to measure the anisotropy of EAPs. With this framework, many important data processing operations, such as interpolation, smoothing, atlas estimation, Principal Geodesic Analysis (PGA), can be performed on EAP data.

Results and Conclusions:

The proposed Riemannian framework was validated in synthetic data for interpolation, smoothing, PGA and in real data for GA and atlas estimation. Riemannian median is much robust for atlas estimation.

Diffusion Tensor Imaging (DTI) is a Magnetic Resonance Imaging method for measuring water diffusion

in vivo

. One powerful DTI contrast is fractional anisotropy (FA). FA reflects the strength of water’s diffusion directional preference and is a primary metric for neuronal fiber tracking. As with other DTI contrasts, FA measurements are obscured by the well established presence of bias. DTI bias has been challenging to assess because it is a multivariable problem including SNR, six tensor parameters, and the DTI collection and processing method used. SIMEX is a modern statistical technique that estimates bias by tracking measurement error as a function of added noise. Here, we use SIMEX to assess bias in FA measurements and show the method provides; i) accurate FA bias estimates, ii) representation of FA bias that is data set specific and accessible to non-statisticians, and iii) a first time possibility for incorporation of bias into DTI data analysis.

We evaluate the impact of radial and angular sampling on multiple shells (MS) acquisition in diffusion MRI. The validation of our results is based on a new and efficient method to accurately reconstruct the Ensemble Average Propagator (EAP) in term of the Spherical Polar Fourier (SPF) basis from very few diffusion weighted magnetic resonance images (DW-MRI). This approach nicely exploits the duality between SPF and a closely related basis in which one can respectively represent the EAP and the diffusion signal using the same coefficients. We efficiently combine this relation to the recent acquisition and reconstruction technique called Compressed Sensing (CS). Based on results of multi-tensors models reconstruction, we show how to construct a robust acquisition scheme for both neural fibre orientation detection and attenuation signal/EAP reconstruction.

Diffusion-weighted imaging (DWI) enables non-invasive investigation and characterization of the white-matter but suffers from a relatively poor resolution. In this work we propose a super-resolution reconstruction (SRR) technique based on the acquisition of multiple anisotropic orthogonal DWI scans. We address the problem of patient motions by aligning the volumes both in space and in q-space. The SRR is formulated as a maximum

a posteriori

(MAP) problem. It relies on a volume acquisition model which describes the generation of the acquired scans from the unknown high-resolution image. It enables the introduction of image priors that exploit spatial homogeneity and enables regularized solutions. We detail our resulting SRR optimization procedure and report various experiments including numerical simulations, synthetic SRR scenario and real world SRR scenario. Super-resolution reconstruction in DWI may enable DWI to be performed with unprecedented resolution.

White matter fiber tractography plays a key role in the

in vivo

understanding of brain circuitry. For tract-based comparison of a population of images, a common approach is to first generate an atlas by averaging, after spatial normalization, all images in the population, and then perform tractography using the constructed atlas. The reconstructed fiber trajectories form a common geometry onto which diffusion properties of each individual subject can be projected based on the corresponding locations in the subject native space. However, in the case of High Angular Resolution Diffusion Imaging (HARDI), where modeling fiber crossings is an important goal, the above-mentioned averaging method for generating an atlas results in significant error in the estimation of local fiber orientations and causes a major loss of fiber crossings. These limitatitons have significant impact on the accuracy of the reconstructed fiber trajectories and jeopardize subsequent tract-based analysis. As a remedy, we present in this paper a more effective means of performing tractography at a population level. Our method entails determining a bipolar Watson distribution at each voxel location based on information given by all images in the population, giving us not only the local principal orientations of the fiber pathways, but also confidence levels of how reliable these orientations are across subjects. The distribution field is then fed as an input to a probabilistic tractography framework for reconstructing a set of fiber trajectories that are consistent across all images in the population. We observe that the proposed method, called

PopTract

, results in significantly better preservation of fiber crossings, and hence yields better trajectory reconstruction in the atlas space.

The contrast provided by diffusion MRI has been exploited repeatedly for in vivo segmentations of thalamic nuclei. This paper systematically investigates the benefits of high-angular resolution (HARDI) data for this purpose. An empirical analysis of clustering stability reveals a clear advantage of acquiring HARDI data at

b

 = 1000 s/mm

2

. However, based on stability arguments, as well as further visual and statistical evidence and theoretical insights about the impact of parameters, HARDI models such as the q-ball do not exhibit clear benefits over the standard diffusion tensor for thalamus segmentation at this

b

value.

Fiber clustering is a prerequisite step towards tract-based analysis of white mater integrity via diffusion tensor imaging (DTI) in various clinical neuroscience applications. Many methods reported in the literature used geometric or anatomic information for fiber clustering. This paper proposes a novel method that uses functional coherence as the criterion to guide the clustering of fibers derived from DTI tractography. Specifically, we represent the functional identity of a white matter fiber by two resting state fMRI (rsfMRI) time series extracted from the two gray matter voxels to which the fiber connects. Then, the functional coherence or similarity between two white matter fibers is defined as their rsfMRI time series’ correlations, and the data-driven affinity propagation (AP) algorithm is used to cluster fibers into bundles. At current stage, we use the corpus callosum (CC) fibers that are the largest fiber bundle in the brain as an example. Experimental results show that the proposed fiber clustering method can achieve meaningful bundles that are reasonably consistent across different brains, and part of the clustered bundles was validated via the benchmark data provided by task-based fMRI data.

The vast majority of High Angular Resolution Diffusion Imaging (HARDI) modeling methods recover networks of neuronal fibres, using a heuristic extraction of their local orientation. In this paper, we present a method for computing the apparent intravoxel Fibre Population Dispersion (FPD), which conveys the manner in which distinct fibre populations are partitioned within the same voxel. We provide a statistical analysis, without any prior assumptions on the number or size of these fibre populations, using an analytical formulation of the diffusion signal autocorrelation function in the spherical harmonics basis. We also propose to extract features of the FPD obtained in the group of rotations, using several metrics based on unit quaternions. We show results on simulated data and on physical phantoms, that demonstrate the effectiveness of the FPD to reveal regions with crossing tracts, in contrast to the standard anisotropy measures.

In the field of diffusion weighted imaging (DWI), it is common to fit one of many available models to the acquired data. A hybrid diffusion imaging (HYDI) approach even allows to reconstruct different models and measures from a single dataset. Methods for DWI atlas construction (and registration) are as plenty as the number of available models. Therefore, it would be nice if we were able to perform atlas building

before

model reconstruction.

In this work, we present a method for atlas construction of DWI data in q-space: we developed a new multi-subject multi-channel diffeomorphic matching algorithm, which is combined with a recently proposed DWI retransformation method in q-space.

We applied our method to HYDI data of 10 healthy subjects. From the resulting atlas, we also reconstructed some advanced models. We hereby demonstrate the feasibility of q-space atlas building, as well as the quality, advantages and possibilities of such an atlas.

In this paper, we propose a novel method for correcting the geometric distortions in diffusion weighted images (DWI) obtained with echo planar imaging (EPI) protocol. Our EPI distortion correction approach employs a deformable registration framework with the B-splines transformation, where the control point distributions are non-uniform and functions of the expected norm of the spatial distortions. In our framework, the amount of distortions are first computed by estimating the

B

0

fieldmap from an initial segmentation of a distortion–free structural image and tissue susceptibility models. Fieldmap estimates are propagated to obtain expected spatial distortion maps, which are used in the sampling of active B-spline control points. This transformation is flexible in locations with large distortion expectations, yet with relatively few degrees-of-freedom and does not suffer from local optima convergence and hence does not distort anatomically salient locations. Results indicate that with the proposed correction scheme, tensor derived scalar maps and fiber tracts of the same subject computed from data acquired with different phase encoding directions provide better coherency and consistency compared traditional registration based approaches.

High Angular Resolution Diffusion Imaging (HARDI) demands a higher amount of data measurements compared to Diffusion Tensor Imaging (DTI), restricting its use in practice. We propose to represent the probabilistic Orientation Distribution Function (ODF) in the frame of Spherical Wavelets (SW), where it is highly sparse. From a reduced subset of measurements (nearly four times less than the standard for HARDI), we pose the estimation as an inverse problem with sparsity regularization. This allows the fast computation of a positive, unit-mass, probabilistic ODF from 14-16 samples, as we show with both synthetic diffusion signals and real HARDI data with typical parameters.

We introduce an automated and probabilistic method for subject-specific segmentation of sheet-like fiber tracts. In addition to clustering of trajectories into anatomically meaningful bundles, the method provides statistics of diffusion measures by establishing point correspondences on the estimated medial representation of each bundle. We also introduce a new approach for medial surface generation of sheet-like fiber bundles in order too initialize the proposed clustering algorithm. Applying the new method to a population study of brain aging on 24 subjects demonstrates the capabilities and strengths of the algorithm in identifying and visualizing spatial patterns of group differences.

Registration of diffusion tensor (DT) images is indispensible, especially in white-matter studies involving a significant amount of data. This task is however faced with challenging issues such as the generally low SNR of diffusion-weighted images and the relatively high complexity of tensor representation. To improve the accuracy of DT image registration, we design an attribute vector that encapsulates both tract and tensor information to serve as a voxel morphological signature for effective correspondence matching. The attribute vector captures complementary information from both the global connectivity structure given by the fiber tracts and the local anatomical architecture given by the tensor regional descriptors. We incorporate this attribute vector into a multi-scale registration framework where the moving image is warped to the space of the fixed image under the guidance of tract information at a more global level (coarse scales), followed by alignment refinement using regional tensor distribution features at a more local level (fine scales). Experimental results indicate that this framework yields marked improvement over DT image registration using volumetric information alone.

By assuming that orientation information of brain white matter fibers can be inferred from Diffusion Weighted Magnetic Resonance Imaging (DWMRI) measurements, tractography algorithms provide an estimation of the brain connectivity in-vivo. The two key ingredients of tractography are the diffusion model (tensor, high-order tensor, Q-ball, etc.) and the way to deal with uncertainty during the tracking process (deterministic vs probabilistic). In this paper, we investigate the use of an analytical Q-ball model for the diffusion data within a well-formalized particle filtering framework. The proposed method is validated and compared to other tracking algorithms on the MICCAI’09 contest Fiber Cup phantom and on in-vivo brain DWMRI data.

The estimation of the ensemble average propagator (EAP) directly from

q

-space DWI signals is an open problem in diffusion MRI. Diffusion spectrum imaging (DSI) is one common technique to compute the EAP directly from the diffusion signal, but it is burdened by the large sampling required. Recently, several analytical EAP reconstruction schemes for multiple

q

-shell acquisitions have been proposed. One, in particular, is Diffusion Propagator Imaging (DPI) which is based on the Laplace’s equation estimation of diffusion signal for each shell acquisition. Viewed intuitively in terms of the heat equation, the DPI solution is obtained when the heat distribution between temperatuere measurements at each shell is at steady state.

We propose a generalized extension of DPI, Bessel Fourier Orientation Reconstruction (BFOR), whose solution is based on heat equation estimation of the diffusion signal for each shell acquisition. That is, the heat distribution between shell measurements is no longer at steady state. In addition to being analytical, the BFOR solution also includes an intrinsic exponential smootheing term. We illustrate the effectiveness of the proposed method by showing results on both synthetic and real MR datasets.

Parallel MRI leads to magnitude data corrupted by noise described in most cases as following a Rician or a non central

χ

distribution. And yet, very few correction methods perform a non central

χ

noise removal. However, this correction step, adapted to the correct noise model, is of very much importance, especially when working with Diffusion Weighted MR data yielding a low SNR. We propose an extended Linear Minimum Mean Square Error estimator (LMMSE), which is adapted to deal with non central

χ

distributions. We demonstrate on simulated and real data that the extended LMMSE outperforms the original LMMSE on images corrupted by a non central

χ

noise.

The paper presents a method for creating abnormality classifiers from high angular resolution diffusion imaging (HARDI) data. We utilized the fiber orientation distribution (FOD) diffusion model to represent the local WM architecture of each subject. The FOD images are then spatially normalized to a common template using a non-linear registration technique. Regions of homogeneous white matter architecture (ROIs) are determined by applying a parcellation algorithm to the population average FOD image. Orientation invariant features of each ROI’s mean FOD are determined and concatenated into a feature vector to represent each subject. Principal component analysis (PCA) was used for dimensionality reduction and a linear support vector machine (SVM) classifier is trained on the PCA coefficients. The classifier assigns each test subject a probabilistic score indicating the likelihood of belonging to the patient group. The method was validated using a 5 fold validation scheme on a population containing autism spectrum disorder (ASD) patients and typically developing (TD) controls. A clear distinction between ASD patients and controls was obtained with a 77% accuracy.

Spurious temporal drift is abundant in fMRI data, and its removal is a critical preprocessing step in fMRI data assimilation due to the sparse nature and the complexity of the data. Conventional data-driven approaches rest upon specific assumptions of the drift structure and signal statistics, and may lead to inaccurate results. In this paper we present an approach to the assimilation of nonlinear hemodynamic system, with special attention on drift. By treating the drift variation as a random-walk process, the assimilation problem was translated into the identification of a nonlinear system in the presence of time varying bias. We developed two-stage unscented Kalman filter (UKF) to efficiently handle this problem. In this framework the assimilation can implement with original fMRI data without detrending preprocessing. The fMRI responses and drift were estimated simultaneously in an assimilation cycle. The efficacy of this approach is demonstrated in synthetic and real fMRI experiments. Results show that the joint estimation strategy produces more accurate estimation of physiological states, fMRI response and drift than separate processing due to no assumption of structure of the drift that is not available in fMRI data.

Granger causality analysis (GCA) has been well-established in the brain imaging field. However, the structural underpinnings and functional dynamics of Granger causality remain unclear. In this paper, we present fibercentered GCA studies on resting state fMRI and natural stimulus fMRI datasets in order to elucidate the structural substrates and functional dynamics of GCA. Specifically, we extract the fMRI BOLD signals from the two ends of a white matter fiber derived from diffusion tensor imaging (DTI) data, and examine their Granger causalities. Our experimental results showed that Granger causalities on white matter fibers are significantly stronger than the causalities between brain regions that are not fiber-connected, demonstrating the structural underpinning of functional causality seen in resting state fMRI data. Cross-session and cross-subject comparisons showed that our observations are reproducible both within and across subjects. Also, the fiber-centered GCA approach was applied on natural stimulus fMRI data and our results suggest that Granger causalities on DTI-derived fibers reveal significant temporal changes, offering novel insights into the functional dynamics of the brain.

We address the issue of jointly detecting brain activity and estimating underlying brain hemodynamics from functional MRI data. We adopt the so-called Joint Detection Estimation (JDE) framework that takes spatial dependencies between voxels into account. We recast the JDE into a missing data framework and derive a Variational Expectation-Maximization (VEM) algorithm for its inference. It follows a new algorithm that has interesting advantages over the previously used intensive simulation methods (Markov Chain Monte Carlo, MCMC): tests on artificial data show that the VEM-JDE is more robust to model mis-specification while additional tests on real data confirm that it achieves similar performance in much less computation time.

In an event-related functional MRI data analysis, an accurate and robust extraction of the hemodynamic response function (HRF) and its associated statistics (e.g., magnitude, width, and time to peak) is critical to infer quantitative information about the relative timing of the neuronal events in different brain regions. The aim of this paper is to develop a multiscale adaptive smoothing model (MASM) to accurately estimate HRFs pertaining to each stimulus sequence across all voxels. MASM explicitly accounts for both spatial and temporal smoothness information, while incorporating such information to adaptively estimate HRFs in the frequency domain. One simulation study and a real data set are used to demonstrate the methodology and examine its finite sample performance in HRF estimation, which confirms that MASM significantly outperforms the existing methods including the smooth finite impulse response model, the inverse logit model and the canonical HRF.

Mild cognitive impairment (MCI), often an early stage of Alzheimer’s disease (AD), is difficult to diagnose due to the subtlety of cognitive impairment. Recent emergence of reliable network characterization techniques based on diffusion tensor imaging (DTI) and resting-state functional magnetic resonance imaging (rs-fMRI) has made the understanding of neurological disorders at a whole-brain connectivity level possible, providing new avenues for brain classification. Taking a multi-kernel SVM, we attempt to integrate these two imaging modalities for improving classification performance. Our results indicate that the multimodality classification approach performs better than the single modality approach, with statistically significant improvement in accuracy. It was also found that the prefrontal cortex, orbitofrontal cortex, temporal pole, anterior and posterior cingulate gyrus, precuneus, amygdala, thalamus, parahippocampal gyrus and insula regions provided the most discriminant features for classification, in line with the results reported in previous studies. The multimodality classification approach allows more accurate early detection of brain abnormalities with larger sensitivity, and is important for treatment management of potential AD patients.

A growing interest has emerged in studying the correlation structure of spontaneous and task-induced brain activity to elucidate the functional architecture of the brain. In particular, functional networks estimated from resting state (RS) data were shown to exhibit high resemblance to those evoked by stimuli. Motivated by these findings, we propose a novel generative model that integrates RS-connectivity and stimulus-evoked responses under a unified analytical framework. Our model permits exact closed-form solutions for both the posterior activation effect estimates and the model evidence. To learn RS networks, graphical LASSO and the oracle approximating shrinkage technique are deployed. On a cohort of 65 subjects, we demonstrate increased sensitivity in fMRI activation detection using our connectivity-informed model over the standard univariate approach. Our results thus provide further evidence for the presence of an intrinsic relationship between brain activity during rest and task, the exploitation of which enables higher detection power in task-driven studies.

Purpose:

The debate regarding how best to model variability of the hemodynamic response function in fMRI data has focussed on the linear vs. nonlinear nature of the optimal signal model, with few studies exploring the deterministic vs. stochastic nature of the dynamics. We propose a stochastic linear model (SLM) of the hemodynamic signal and noise dynamics to more robustly infer fMRI activation estimates.

Methods:

The SLM models the hemodynamic signal by an exogenous input autoregressive model driven by Gaussian state noise. Activation weights are inferred by a joint state-parameter iterative coordinate descent algorithm based on the Kalman smoother.

Results:

The SLM produced more accurate parameter estimates than the GLM for event-design simulated data. In application to block-design experimental visuo-motor task fMRI data, the SLM resulted in more punctate and well-defined motor cortex activation maps than the GLM, and was able to track variations in the hemodynamics, as expected from a stochastic model.

Conclusions:

We demonstrate in application to both simulated and experimental fMRI data that in comparison to the GLM, the SLM produces more flexible, consistent and enhanced fMRI activation estimates.

The difference between networks has been often assessed by the difference of global topological measures such as the clustering coefficient, degree distribution and modularity. In this paper, we introduce a new framework for measuring the network difference using the Gromov-Hausdorff (GH) distance, which is often used in shape analysis. In order to apply the GH distance, we define the

shape of the brain network

by piecing together the patches of locally connected nearest neighbors using the

graph filtration

. The shape of the network is then transformed to an algebraic form called the single linkage matrix. The single linkage matrix is subsequently used in measuring network differences using the GH distance. As an illustration, we apply the proposed framework to compare the FDG-PET based functional brain networks out of 24 attention deficit hyperactivity disorder (ADHD) children, 26 autism spectrum disorder (ASD) children and 11 pediatric control subjects.

In the context of inter-subject brain surface matching, we present a parameterization of the cortical surface constrained by a model of cortical organization. The parameterization is defined via an harmonic mapping of each hemisphere surface to a rectangular planar domain that integrates a representation of the model. As opposed to previous conformal mapping methods we do not match folds between individuals but instead optimize the fit between cortical sulci and specific iso-coordinate axis in the model. Experiments on both hemispheres of 34 subjects are presented and results are very promising.

Cortical folding patterns are believed to be good predictors of brain cytoarchitecture and function. For instance, neuroscientists frequently apply their domain knowledge to identify brain Regions of Interests (ROIs) based on cortical folding patterns. However, quantitative mapping of cortical folding pattern and brain function has not been established yet in the literature. This paper presents our initial effort in quantification of the regularity and variability of cortical folding pattern features for working memory ROIs identified by taskbased fMRI, which is widely accepted as a standard approach to localize functionally-specialized brain regions. Specifically, we used a set of shape attributes for each ROI base on multiple resolution decomposition of cortical surfaces, and described the meso-scale folding pattern via a polynomial-based approach. We also applied brain atlas label distribution as a global-scale description of ROI folding pattern. Our studies suggest that there is deep-rooted regularity of cortical folding patterns for certain working memory ROIs across subjects, and folding pattern attributes could be useful for the characterization, recognition and prediction of ROIs, if extracted and applied in a proper way.

In this paper we develop a novel technique for surface deformation and mapping in the high-dimensional Laplace-Beltrami embedding space. The key idea of our work is to realize surface deformation in the embedding space via optimization of a conformal metric on the surface. Numerical techniques are developed for computing derivatives of the eigenvalues and eigenfunctions with respect to the conformal metric, which is then applied to compute surface maps in the embedding space by minimizing an energy function. In our experiments, we demonstrate the robustness of our method by applying it to map hippocampal atrophy of multiple sclerosis patients with depression on a data set of 109 subjects. Statistically significant results have been obtained that show excellent correlation with clinical variables. A comparison with the popular SPHARM tool has also been performed to demonstrate that our method achieves more significant results.

In this paper, we propose a novel area-preserving surface flattening method, which is rigorous in theory, efficient in computation, yet general in application domains. Leveraged on the state-of-the-art flattening techniques, an infinitesimal area restoring diffeomorphic flow is constructed as a Lie advection of differential 2-forms on the manifold, which yields strict equality of area elements between the flattened and the original surfaces at its final state. With a surface represented by a triangular mesh, we present how an deterministic algorithm can be faithfully implemented to its continuous counterpart. To demonstrate the utility of this method, we have applied our method to both the cortical hemisphere and the entire cortex. Highly complied results are obtained in a matter of seconds.

Methods to quantify cellular–level phenotypic differences between genetic groups are a key tool in genomics research. In disease processes such as cancer, phenotypic changes at the cellular level frequently manifest in the modification of cell population

profiles

. These changes are hard to detect due the ambiguity in identifying distinct cell phenotypes within a population. We present a methodology which enables the detection of such changes by generating a phenotypic signature of cell populations in a data–derived feature–space. Further, this signature is used to estimate a model for the

redistribution

of phenotypes that was induced by the genetic change. Results are presented on an experiment involving deletion of a tumor–suppressor gene dominant in breast cancer, where the methodology is used to detect changes in nuclear morphology between control and knockout groups.

Hippocampal atrophy and developmental positional variants may co-occur in various neurological disorders. We propose a surface-based framework to analyze independently volume and positioning. After extracting the spherical harmonics combined with point distribution models (SPHARM-PDM) from manual labels, we computed displacement vectors between individual surfaces and the template. Then, we computed surface-based Jacobian determinants (SJD) from these vectors to localize volume changes. To analyze positional variants, we constructed a mean meridian axis (MEMAX), inheriting the shape-constrained point correspondences of SPHARM, on which we compute local curvatures and position vectors. We validated our method on synthetic shapes, and a large database of healthy subjects and patients with temporal lobe epilepsy. Our comprehensive analysis showed that in patients atrophy and positional changes co-occurred at the level of the posterior hippocampus. Indeed, in this region, while SPHARM-PDM showed mirrored deformations, SJD detected atrophy, and shape analysis of MEMAX unveiled medial positioning due to bending.

The trapeziometacarpal joint enables the prehensile function of the thumb. Unfortunately, this joint is vulnerable to osteoarthritis (OA) that typically affects the local shape of the trapezium. A novel, local statistical shape model is defined that employs a differentiable locality measure based on the weighted variance of point coordinates per mode. The simplicity of the function and the smooth derivative enable to quickly determine localized components for densely sampled surfaces.

The method is employed to assess a set of 60 trapezia (38 healthy, 22 with OA). The localized components predominantly model regions affected by OA, contrary to shape variations found with PCA. Furthermore, identification of pathological trapezia based on the localized modes of variation is improved compared to PCA.

An ensemble of biological shapes can be represented and analyzed with a dense set of point correspondences. In previous work, optimal point placement was determined by optimizing an information theoretic criterion that depends on relative spatial locations on different shapes combined with pairwise Euclidean distances between nearby points on the same shape. These choices have prevented such methods from effectively characterizing shapes with complex geometry such as thin or highly curved features. This paper extends previous methods for automatic shape correspondence by taking into account the underlying geometry of individual shapes. This is done by replacing the Euclidean distance for intrashape pairwise particle interactions by the geodesic distance. A novel set of numerical techniques for fast distance computations on curved surfaces is used to extract these distances. In addition, we introduce an intershape penalty term that incorporates surface normal information to achieve better particle correspondences near sharp features. Finally, we demonstrate this new method on synthetic and biological datasets.

Genetic mapping of hippocampal shape, an under-explored area, has strong potential as a neurodegeneration biomarker for AD and MCI. This study investigates the genetic effects of top candidate single nucleotide polymorphisms (SNPs) on hippocampal shape features as quantitative traits (QTs) in a large cohort. FS+LDDMM was used to segment hippocampal surfaces from MRI scans and shape features were extracted after surface registration. Elastic net (EN) and sparse canonical correlation analysis (SCCA) were proposed to examine SNP-QT associations, and compared with multiple regression (MR). Although similar in power, EN yielded substantially fewer predictors than MR. Detailed surface mapping of global and localized genetic effects were identified by MR and EN to reveal multi-SNP-single-QT relationships, and by SCCA to discover multi-SNP-multi-QT associations. Shape analysis identified stronger SNP-QT correlations than volume analysis. Sparse multivariate models have greater power to reveal complex SNP-QT relationships. Genetic analysis of quantitative shape features has considerable potential for enhancing mechanistic understanding of complex disorders like AD.

This paper proposes a novel algorithm to extract feature landmarks on the vestibular system (VS), for the analysis of Adolescent Idiopathic Scoliosis (AIS) disease. AIS is a 3-D spinal deformity commonly occurred in adolescent girls with unclear etiology. One popular hypothesis was suggested to be the structural changes in the VS that induce the disturbed balance perception, and further cause the spinal deformity. The morphometry of VS to study the geometric differences between the healthy and AIS groups is of utmost importance. However, the VS is a genus-3 structure situated in the inner ear. The high-genus topology of the surface poses great challenge for shape analysis. In this work, we present a new method to compute exact geodesic loops on the VS. The resultant geodesic loops are in Euclidean metric, thus characterizing the intrinsic geometric properties of the VS based on the real background geometry. This leads to more accurate results than existing methods, such as the hyperbolic Ricci flow method [13]. Furthermore, our method is fully automatic and highly efficient, e.g., one order of magnitude faster than [13]. We applied our algorithm to the VS of normal and AIS subjects. The promising experimental results demonstrate the efficacy of our method and reveal more statistically significant shape difference in the VS between right-thoracic AIS and normal subjects.

This work presents a statistical model of both the shape and Bone Mineral Density (BMD) distribution of the proximal femur for fracture risk assessment. The shape and density model was built from a dataset of Quantitative Computed Tomography scans of fracture patients and a control group. Principal Component Analysis and Horn’s parallel analysis were used to reduce the dimensionality of the shape and density model to the main modes of variation. The input data was then used to analyze the model parameters for the optimal separation between the fracture and control group. Feature selection using the Fisher criterion determined the parameters with the best class separation, which were used in Fisher Linear Discriminant Analysis to find the direction in the parameter space that best separates the fracture and control group. This resulted in a Fisher criterion value of 6.70, while analyzing the Dual-energy X-ray Absorptiometry derived femur neck areal BMD of the same subjects resulted in a Fisher criterion value of 0.98. This indicates that a fracture risk estimation approach based on the presented model might improve upon the current standard clinical practice.

Longitudinal shape analysis often relies on the estimation of a realistic continuous growth scenario from data sparsely distributed in time. In this paper, we propose a new type of growth model parameterized by acceleration, whereas standard methods typically control the velocity. This mimics the behavior of biological tissue as a mechanical system driven by external forces. The growth trajectories are estimated as smooth flows of deformations, which are twice differentiable. This differs from piecewise geodesic regression, for which the velocity may be discontinuous. We evaluate our approach on a set of anatomical structures of the

same

subject, scanned 16 times between 4 and 8 years of age. We show our acceleration based method estimates smooth growth, demonstrating improved regularity compared to piecewise geodesic regression. Leave-several-out experiments show that our method is robust to missing observations, as well as being less sensitive to noise, and is therefore more likely to capture the underlying biological growth.

In this paper we present a new population-based method for the design of bone fixation plates. Standard pre-contoured plates are designed based on the mean shape of a certain population. We propose a computational process to design implants while reducing the amount of required intra-operative shaping, thus reducing the mechanical stresses applied to the plate. A bending and torsion model was used to measure and minimize the necessary intra-operative deformation. The method was applied and validated on a population of 200 femurs that was further augmented with a statistical shape model. The obtained results showed substantial reduction in the bending and torsion needed to shape the new design into any bone in the population when compared to the standard mean-based plates.

Statistical atlases of bone anatomy are traditionally constructed with point-based models. These methods establish initial point correspondences across the population of shapes and model variations in the shapes using a variety of statistical tools. A drawbacks of such methods is that initial point correspondences are not updated after their first establishment. This paper proposes an iterative method for refining point correspondences for statistical atlases. The statistical model is used to estimate the direction of ”pull” along the surface and consistency checks are used to ensure that illegal shapes are not generated. Our method is much faster that previous methods since it does not rely on computationally expensive deformable registration. It is also generalizable and can be used with any statististical model. We perform experiments on a human pelvis atlas consisting of 110 healthy patients and demonstrate that the method can be used to re-estimate point correspondences which reduce the hausdorff distance from 3.2mm to 2.7mm and the surface error from 1.6mm to 1.4mm for PCA modelling with 20 modes.

In this paper, we exploit spectral shape analysis techniques to detect brain morphological abnormalities. We propose a new shape descriptor able to encode morphometric properties of a brain image or region using diffusion geometry techniques based on the local

Heat Kernel

. Using this approach, it is possible to design a versatile signature, employed in this case to classify between normal subjects and patients affected by schizophrenia. Several diffusion strategies are assessed to verify the robustness of the proposed descriptor under different deformation variations. A dataset consisting of MRI scans from 30 patients and 30 control subjects is utilized to test the proposed approach, which achieves promising classification accuracies, up to 83.33%. This constitutes a drastic improvement in comparison with other shape description techniques.

Despite the growing interest in regression based shape estimation, no study has yet systematically compared different regression methods for shape estimation. We aimed to fill this gap by comparing linear regression methods with a special focus on shapes with landmark position uncertainties. We investigate two scenarios: In the first, the uncertainty of the landmark positions was similar in the training and test dataset, whereas in the second the uncertainty of the training and test data were different. Both scenarios were tested on simulated data and on statistical models of the left ventricle estimating the end-systolic shape from end-diastole with landmark uncertainties derived from the segmentation process, and of the femur estimating the 3D shape from one projection with landmark uncertainties derived from the imaging setup. Results show that in the first scenario linear regression methods tend to perform similar. In the second scenario including estimates of the test shape landmark uncertainty in the regression improved results.

A new type of deformable model is presented that merges meshes and level sets into one representation to provide interoperability between methods designed for either. The key idea is to use a constellation of triangular surface elements (springls) to define a level set. A Spring Level Set (SpringLS) can be interpreted as a mesh or level set and used in place of them in many instances. There is no loss of shape information in the transformation from triangle mesh or level set into SpringLS. As examples, we present results for joint segmentation/spherical mapping of a human brain cortex and atlas/nonatlas segmentation of a pelvis.

Appearance and shape are two key elements exploited in medical image segmentation. However, in some medical image analysis tasks, appearance cues are weak/misleading due to disease/artifacts and often lead to erroneous segmentation. In this paper, a novel deformable model is proposed for robust segmentation in the presence of weak/misleading appearance cues. Owing to the less trustable appearance information, this method focuses on the effective shape modeling with two contributions. First, a shape composition method is designed to incorporate shape prior on-the-fly. Based on two sparsity observations, this method is robust to false appearance information and adaptive to statistically insignificant shape modes. Second, shape priors are modeled and used in a hierarchical fashion. More specifically, by using affinity propagation method, our deformable surface is divided into multiple partitions, on which local shape models are built independently. This scheme facilitates a more compact shape prior modeling and hence a more robust and efficient segmentation. Our deformable model is applied on two very diverse segmentation problems, liver segmentation in PET-CT images and rodent brain segmentation in MR images. Compared to state-of-art methods, our method achieves better performance in both studies.

Voxel based morphometry (VBM) is widely used in the neuroimaging community to infer group differences in brain morphology. VBM is effective in quantifying group differences highly localized in space. However it is not equally effective when group differences might be based on interactions between multiple brain networks. We address this by proposing a new framework called pattern based morphometry (PBM). PBM is a data driven technique. It uses a dictionary learning algorithm to extract global patterns that characterize group differences. We test this approach on simulated and real data obtained from ADNI . In both cases PBM is able to uncover complex global patterns effectively.

Longitudinal measurements of cortical thickness is a current hot topic in medical imaging research. Measuring the thickness of the cortex through time is normally hindered by the presence of noise, partial volume (PV) effects and topological defects, but mainly by the lack of a common directionality in the measurement to ensure consistency. In this paper, we propose a 4D pipeline (3D + time) using the Khalimsky cubic complex for the extraction of a topologically correct Laplacian field in an unbiased temporal group-wise space. The thickness at each time point is then obtained by integrating the probabilistic segmentation (transformed to the group-wise space) modulated by the Jacobian determinant of its deformation field through the group-wise Laplacian field. Experiments performed on digital phantoms show that the proposed method improves the time consistency of the thickness measurements with a statistically significant increase in accuracy when compared to two well established 3D techniques and a 3D version of the same method. Furthermore, quantitative analysis on brain MRI data showed that the proposed algorithm is able to retrieve increasingly significant time consistent consistent group differences between the cortical thickness of AD patients and controls.

The process of brain growth involves the expansion of tissue at different rates at different points within the brain. As the layers within the developing brain evolve they can thicken or increase in area as the brain surface begins to fold. In this work we propose a new spatiotemporal formulation of tensor based volume morphometry that is derived in relation to tissue boundaries. This allows the study of the directional properties of tissue growth by separately characterizing the changes in area and thickness of the adjacent layers. The approach uses temporally weighted, local regression across a population of anatomies with different ages to model changes in components of the growth radial and tangential to the boundary between tissue layers. The formulation is applied to the study of sulcal formation from in-utero MR imaging of human fetal brain anatomy. Results show that the method detects differential growth of tissue layers adjacent to the cortical surface, particularly at sulcal locations, as early as 22 gestational weeks.

This paper presents a fast method for quantifying shape differences/similarities between pairs of magnetic resonance (MR) brain images. Most shape comparisons in the literature require some kind of deformable registration or identification of exact correspondences. The proposed approach relies on an optimal matching of a large collection of features, using a very fast, hierarchical method from the literature, called

spatial pyramid matching

(SPM). This paper shows that edge-based image features in combination with SPM results in a fast similarity measure that captures relevant anatomical information in brain MRI. We present extensive comparisons against known methods for shape-based,

k

-nearest-neighbor lookup to evaluate the performance of the proposed method. Finally, we show that the method compares favorably with more computation-intensive methods in the construction of local atlases for use in brain MR image segmentation.

The Active Shape Model (ASM) is a segmentation algorithm which uses a Statistical Shape Model (SSM) to constrain segmentations to ‘plausible’ shapes. This makes it possible to robustly segment organs with low contrast to adjacent structures. The standard SSM assumes that shapes are Gaussian distributed, which implies that unseen shapes can be expressed by linear combinations of the training shapes. Although this assumption does not always hold true, and several nonlinear SSMs have been proposed in the literature, virtually all applications in medical imaging use the linear SSM. In this work, we investigate 3D ASM segmentation with a nonlinear SSM based on Kernel PCA. We show that a recently published energy minimization approach for constraining shapes with a linear shape model extends to the nonlinear case, and overcomes shortcomings of previously published approaches. Our approach for nonlinear ASM segmentation is applied to vertebra segmentation and evaluated against the linear model.

For segmenting complex structures like vertebrae, a priori knowledge by means of statistical shape models (SSMs) is often incorporated. One of the main challenges using SSMs is the solution of the correspondence problem. In this work we present a generic automated approach for solving the correspondence problem for vertebrae. We determine two closed loops on a reference shape and propagate them consistently to the remaining shapes of the training set. Then every shape is cut along these loops and parameterized to a rectangle. There, we optimize a novel combined energy to establish the correspondences and to reduce the unavoidable area and angle distortion. Finally, we present an adaptive resampling method to achieve a good shape representation. A qualitative and quantitative evaluation shows that using our method we can generate SSMs of higher quality than the ICP approach.

Low-grade gliomas (WHO grade II) are diffusively infiltrative brain tumors arising from glial cells. Spatial classification that is usually based on cerebral lobes lacks accuracy and is far from being able to provide some pattern or statistical interpretation of their appearance. In this paper, we propose a novel approach to understand and infer position of low-grade gliomas using a graphical model. The problem is formulated as a graph topology optimization problem. Graph nodes correspond to extracted tumors and graph connections to the spatial and content dependencies among them. The task of spatial position mapping is then expressed as an unsupervised clustering problem, where cluster centers correspond to centers with position appearance prior, and cluster samples to nodes with strong statistical dependencies on their position with respect to the cluster center. Promising results using leave-one-out cross-validation outperform conventional dimensionality reduction methods and seem to coincide with conclusions drawn in physiological studies regarding the expected tumor spatial distributions and interactions.

In vivo MicroCT imaging of disease models at multiple time points is of great importance for preclinical oncological research, to monitor disease progression. However, the great postural variability between animals in the imaging device complicates data comparison.

In this paper we propose a method for automated registration of whole-body MicroCT follow-up datasets of mice. First, we register the skeleton, the lungs and the skin of an articulated animal atlas (Segars et al. 2004) to MicroCT datasets, yielding point correspondence of these structures over all time points. This correspondence is then used to regularize an intensity-based B-spline registration. This two step approach combines the robustness of model-based registration with the high accuracy of intensity-based registration.

We demonstrate our approach using challenging whole-body in vivo follow-up MicroCT data and obtain subvoxel accuracy for the skeleton and the skin, based on the Euclidean surface distance. The method is computationally efficient and enables high resolution whole-body registration in ≈17 minutes with unoptimized code, mostly executed single-threaded.

In this paper, we propose a pipeline for evaluating the performance of brain image registration methods. Our aim is to compare how well the algorithms align subtle functional/anatomical boundaries that are not easily detectable in T1- or T2-weighted magnetic resonance images (MRI). In order to achieve this, we use structural connectivity information derived from diffusion-weighted MRI data. We demonstrate the approach by looking into how two competing registration algorithms perform at aligning fine-grained parcellations of subcortical structures. The results show that the proposed evaluation framework can offer new insights into the performance of registration algorithms in brain regions with highly varied structural connectivity profiles.

This paper presents an approach for joint segmentation and deformable registration of brain scans of glioma patients to a normal atlas. The proposed method is based on the Expectation Maximization (EM) algorithm that incorporates a glioma growth model for atlas seeding, a process which modifies the normal atlas into one with a tumor and edema. The modified atlas is registered into the patient space and utilized for the posterior probability estimation of various tissue labels. EM iteratively refines the estimates of the registration parameters, the posterior probabilities of tissue labels and the tumor growth model parameters. We have applied this approach to 10 glioma scans acquired with four Magnetic Resonance (MR) modalities (T1, T1-CE, T2 and FLAIR ) and validated the result by comparing them to manual segmentations by clinical experts. The resulting segmentations look promising and quantitatively match well with the expert provided ground truth.

Deformable registration of images obtained from different modalities remains a challenging task in medical image analysis. This paper addresses this problem and proposes a new similarity metric for multi-modal registration, the non-local shape descriptor. It aims to extract the shape of anatomical features in a non-local region. By utilizing the dense evaluation of shape descriptors, this new measure bridges the gap between intensity-based and geometric feature-based similarity criteria. Our new metric allows for accurate and reliable registration of clinical multi-modal datasets and is robust against the most considerable differences between modalities, such as non-functional intensity relations, different amounts of noise and non-uniform bias fields. The measure has been implemented in a non-rigid diffusion-regularized registration framework. It has been applied to synthetic test images and challenging clinical MRI and CT chest scans. Experimental results demonstrate its advantages over the most commonly used similarity metric - mutual information, and show improved alignment of anatomical landmarks.

We present a stochastic optimisation method for intensity-based monomodal image registration. The method is based on a Robbins-Monro stochastic gradient descent method with adaptive step size estimation, and adds a preconditioning matrix. The derivation of the preconditioner is based on the observation that, after registration, the deformed moving image should approximately equal the fixed image. This prior knowledge allows us to approximate the Hessian at the minimum of the registration cost function, without knowing the coordinate transformation that corresponds to this minimum. The method is validated on 3D fMRI time-series and 3D CT chest follow-up scans. The experimental results show that the preconditioning strategy improves the rate of convergence.

We introduce a novel discrete optimization method for nonrigid image registration based on the random walker algorithm. We discretize the space of deformations and formulate registration using a Gaussian MRF where continuous labels correspond to the probability of a point having a certain discrete deformation. The interaction (regularization) term of the corresponding MRF energy is convex and image dependent, thus being able to accommodate different types of tissue elasticity. This formulation results in a fast algorithm that can easily accommodate a large number of displacement labels, has provable robustness to noise and a close to global solution. We experimentally demonstrate the validity of our formulation on synthetic and real medical data.

The identification of anatomical landmarks in medical images is an important task in registration and morphometry. Manual labeling is time consuming and prone to observer errors. We propose a manifold learning procedure, based on Laplacian Eigenmaps, that learns an embedding from patches drawn from multiple brain MR images. The position of the patches in the manifold can be used to predict the location of the landmarks via regression. New images are embedded in the manifold and the resulting coordinates are used to predict the landmark position in the new image. The output of multiple regressors is fused in a weighted fashion to boost the accuracy and robustness. We demonstrate this framework in 3D brain MR images from the ADNI database. We show an accuracy of ~0.5mm, an increase of at least two fold when compared to traditional approaches such as registration or sliding windows.

Accurate slice positioning of diagnostic MR brain images is clinically important due to their inherent anisotropic resolution. Recently, a low-res fast 3D “scout” scan has become popular as a pre-requisite localizer for the positioning of these diagnostic high-res images on relevant anatomies. Automation of this “scout” scan alignment needs to be highly robust, accurate and reproducible, which can not be achieved by existing methods such as voxel-based registration. Although recently proposed “Learning Ensembles of Anatomical Patterns (LEAP)” framework [4] paves the way to high robustness through redundant anatomy feature detections, the “somewhat conflicting”

accuracy

and

reproducibility

goals can not be satisfied simultaneously from the single model-based alignment perspective. Hence, we present a data adaptive multi-structural model based registration algorithm to achieve these joint goals. We validate our system on a large number of clinical data sets (731 adult and 100 pediatric brain MRI scans). Our algorithm demonstrates > 99.5% robustness with high accuracy. The reproducibility is < 0.32° for rotation and < 0.27

mm

for translation on average within multiple follow-up scans for the same patient.

The reconstruction of histology sections into a 3-D volume receives increased attention due to its various applications in modern medical image analysis. To guarantee a geometrically coherent reconstruction, we propose a new way to register histological sections

simultaneously

to previously acquired reference images and to neighboring slices in the stack. To this end, we formulate two potential functions and associate them to the same Markov random field through which we can efficiently find an optimal solution. Due to our simultaneous formulation and the absence of any segmentation step during the reconstruction we can dramatically reduce error propagation effects. This is illustrated by experiments on carefully created synthetic as well as real data sets.

Log-euclidean polyaffine transforms have recently been introduced to characterize the local affine behavior of the deformation in principal anatomical structures. The elegant mathematical framework makes them a powerful tool for image registration. However, their application is limited to large structures since they require the pre-definition of affine regions. This paper extends the polyaffine registration to adaptively fit a log-euclidean polyaffine transform that captures deformations at smaller scales. The approach is based on the sparse selection of matching points in the images and the formulation of the problem as an expectation maximization iterative closest point problem. The efficiency of the algorithm is shown through experiments on inter-subject registration of brain MRI between a healthy subject and patients with multiple sclerosis.

This paper presents a new approach for reconstructing a patient-specific shape model and internal relative intensity distribution of the proximal femur from a limited number (e.g., 2) of calibrated C-arm images or X-ray radiographs. Our approach uses independent shape and appearance models that are learned from a set of training data to encode the

a priori

information about the proximal femur. An intensity-based non-rigid 2D-3D registration algorithm is then proposed to deformably fit the learned models to the input images. The fitting is conducted iteratively by minimizing the dissimilarity between the input images and the associated digitally reconstructed radiographs of the learned models together with regularization terms encoding the strain energy of the forward deformation and the smoothness of the inverse deformation. Comprehensive experiments conducted on images of cadaveric femurs and on clinical datasets demonstrate the efficacy of the present approach.

Registering CT scans in a body atlas is an important technique for aligning and comparing different CT scans. It is also required for navigating automatically to certain regions of a scan or if sub volumes should be identified automatically. Common solutions to this problem employ landmark detectors and interpolation techniques. However, these solutions are often not applicable if the query scan is very small or consists only of a single slice. Therefore, the research community proposed methods being independent from landmark detectors which are using imaging techniques to register the slices in a generalized height scale. In this paper, we propose an improved prediction method for registering single slices. Our solution is based on specialized image descriptors and instance-based learning. The experimental evaluation shows that the new method improves accuracy and stability of comparable registration methods by using only a a single CT slice is required for the registration.

Ultrasound-Fluoroscopy fusion is a key step toward intra-operative dosimetry for prostate brachytherapy. We propose a method for intensity-based registration of fluoroscopy to ultrasound that obviates the need for seed segmentation required for seed-based registration. We employ image thresholding and morphological and Gaussian filtering to enhance the image intensity distribution of ultrasound volume. Finally, we find the registration parameters by maximizing a point-to-volume similarity metric. We conducted an experiment on a ground truth phantom and achieved registration error of 0.7±0.2mm. Our clinical results on 5 patient data sets show excellent visual agreement between the registered seeds and the ultrasound volume with a seed-to-seed registration error of 1.8±0.9mm. With low registration error, high computational speed and no need for manual seed segmentation, our method is promising for clinical application.

MR-guided High Intensity Focused Ultrasound is an emerging non-invasive technique capable of depositing sharply localised energy deep within the body, without affecting the surrounding tissues. This, however, implies exact knowledge of the target’s position when treating mobile organs. In this paper we present an atlas-based prediction technique that trains an atlas from time-resolved 3D volumes using 4DMRI, capturing the full patient specific motion of the organ. Based on a breathing signal, the respiratory state of the organ is then tracked and used to predict the target’s future position. To additionally compensate for the non-periodic slower organ drifts, the static motion atlas is combined with a population-based statistical exhalation drift model. The proposed method is validated on organ motion data of 12 healthy volunteers. Experiments estimating the future position of the entire liver result in an average prediction error of 1.1 mm over time intervals of up to 13 minutes.

Non-linear image registration is an important tool in many areas of image analysis. For instance, in morphometric studies of a population of brains, free-form deformations between images are analyzed to describe the structural anatomical variability. Such a simple deformation model is justified by the absence of an easy expressible prior about the shape changes. Applying the same algorithms used in brain imaging to orthopedic images might not be optimal due to the difference in the underlying prior on the inter-subject deformations. In particular, using an un-informed deformation prior often leads to local minima far from the expected solution. To improve robustness and promote anatomically meaningful deformations, we propose a locally affine and geometry-aware registration algorithm that automatically adapts to the data. We build upon the log-domain demons algorithm and introduce a new type of OBBTree-based regularization in the registration with a natural multiscale structure. The regularization model is composed of a hierarchy of locally affine transformations via their logarithms. Experiments on mandibles show improved accuracy and robustness when used to initialize the demons, and even similar performance by direct comparison to the demons, with a significantly lower degree of freedom. This closes the gap between polyaffine and non-rigid registration and opens new ways to statistically analyze the registration results.

Standard image registration methods do not account for changes in image appearance. Hence, metamorphosis approaches have been developed which jointly estimate a space deformation and a change in image appearance to construct a spatio-temporal trajectory smoothly transforming a source to a target image. For standard metamorphosis, geometric changes are not explicitly modeled. We propose a

geometric metamorphosis

formulation, which explains changes in image appearance by a global deformation, a deformation of a geometric model, and an image composition model. This work is motivated by the clinical challenge of predicting the long-term effects of traumatic brain injuries based on time-series images. This work is also applicable to the quantification of tumor progression (e.g., estimating its infiltrating and displacing components) and predicting chronic blood perfusion changes after stroke. We demonstrate the utility of the method using simulated data as well as scans from a clinical traumatic brain injury patient.

In this paper we propose a novel approach for incorporating measures of spatial uncertainty, which are derived from non-rigid registration, into spatially normalised statistics. Current approaches to spatially normalised statistical analysis use point-estimates of the registration parameters. This is limiting as the registration will rarely be completely accurate, and therefore data smoothing is often used to compensate for the uncertainty of the mapping. We derive localised measurements of spatial uncertainty from a probabilistic registration framework, which provides a principled approach to image smoothing. We evaluate our method using longitudinal deformation features from a set of MR brain images acquired from the Alzheimer’s Disease Neuroimaging Initiative. These images are spatially normalised using our probabilistic registration algorithm. The spatially normalised longitudinal features are adaptively smoothed according to the registration uncertainty. The proposed adaptive smoothing shows improved classification results, (84% correct Alzheimer’s Disease vs. controls), over either not smoothing (79.6%), or using a Gaussian filter with

σ

 = 2mm (78.8%).

Registration of image-time series has so far been accomplished (i) by concatenating registrations between image pairs, (ii) by solving a joint estimation problem resulting in piecewise geodesic paths between image pairs, (iii) by kernel based local averaging or (iv) by augmenting the joint estimation with additional temporal irregularity penalties. Here, we propose a

generative model

extending least squares linear regression to the space of images by using a second-order dynamic formulation for image registration. Unlike previous approaches, the formulation allows for a compact representation of an approximation to the full spatio-temporal trajectory through its initial values. The method also opens up possibilities to design image-based approximation algorithms. The resulting optimization problem is solved using an adjoint method.

Mapping the effects of different clinical conditions on the evolution of the brain structural changes is of central interest in the field of neuroimaging. A reliable description of the cross-sectional longitudinal changes requires the consistent integration of intra and inter-subject variability in order to detect the subtle modifications in populations. In computational anatomy, the changes in the brain are often measured by deformation fields obtained through non rigid registration, and the stationary velocity field (SVF) parametrization provides a computationally efficient registration scheme. The aim of this study is to extend this framework into an efficient and robust multilevel one for accurately modeling the longitudinal changes in populations. This setting is used to investigate the subtle effects of the positivity of the CSF A

β

1 − 42

levels on brain atrophy in healthy aging. Thanks to the higher sensitivity of our framework, we obtain statistically significant results that highlight the relationship between brain damage and positivity to the marker of Alzheimer’s disease and suggest the presence of a presymptomatic pattern of the disease progression.

Accurate and consistent reconstruction of cortical surfaces from longitudinal human brain MR images is of great importance in studying subtle morphological changes of the cerebral cortex. This paper presents a new deformable surface method for consistent and accurate reconstruction of inner, central and outer cortical surfaces from longitudinal MR images. Specifically, the cortical surfaces of the group-mean image of all aligned longitudinal images of the same subject are first reconstructed by a deformable surface method driven by a force derived from the Laplace’s equation. And then the longitudinal cortical surfaces are consistently reconstructed by jointly deforming the cortical surfaces from the group-mean image to all longitudinal images. The proposed method has been successfully applied to both simulated and real longitudinal images, demonstrating its validity.

We present a novel framework for inferring 3D carpal bone kinematics and bone shapes from a single view fluoroscopic sequence. A hybrid statistical model representing both the kinematics and shape variation of the carpal bones is built, based on a number of 3D CT data sets obtained from different subjects at different poses. Given a fluoroscopic sequence, the wrist pose, carpal bone kinematics and bone shapes are estimated iteratively by matching the statistical model with the 2D images. A specially designed cost function enables smoothed parameter estimation across frames. We have evaluated the proposed method on both simulated data and real fluoroscopic sequences. It was found that the relative positions between carpal bones can be accurately estimated, which is potentially useful for detection of conditions such as scapholunate dissociation.