Spherical demons: fast diffeomorphic landmark-free surface registration

Diffeomorphic sulcal shape analysis on the cortex

We present a diffeomorphic approach for constructing intrinsic shape atlases of sulci on the human cortex. Sulci are represented as square-root velocity functions of continuous open curves in R³, and their shapes are studied as functional representations of an infinite-dimensional sphere. This spherical manifold has some advantageous properties--it is equipped with a Riemannian L² metric on the tangent space and facilitates computational analyses and correspondences between sulcal shapes. Sulcal shape mapping is achieved by computing geodesics in the quotient space of shapes modulo scales, translations, rigid rotations, and reparameterizations. The resulting sulcal shape atlas preserves important local geometry inherently present in the sample population. The sulcal shape atlas is integrated in a cortical registration framework and exhibits better geometric matching compared to the conventional euclidean method. We demonstrate experimental results for sulcal shape mapping, cortical surface registration, and sulcal classification for two different surface extraction protocols for separate subject populations.

Discrete differential geometry: the nonplanar quadrilateral mesh

We consider the problem of constructing a discrete differential geometry defined on nonplanar quadrilateral meshes. Physical models on discrete nonflat spaces are of inherent interest, as well as being used in applications such as computation for electromagnetism, fluid mechanics, and image analysis. However, the majority of analysis has focused on triangulated meshes. We consider two approaches: discretizing the tensor calculus, and a discrete mesh version of differential forms. While these two approaches are equivalent in the continuum, we show that this is not true in the discrete case. Nevertheless, we show that it is possible to construct mesh versions of the Levi-Civita connection (and hence the tensorial covariant derivative and the associated covariant exterior derivative), the torsion, and the curvature. We show how discrete analogs of the usual vector integral theorems are constructed in such a way that the appropriate conservation laws hold exactly on the mesh, rather than only as approximations to the continuum limit. We demonstrate the success of our method by constructing a mesh version of classical electromagnetism and discuss how our formalism could be used to deal with other physical models, such as fluids.

Medical image registration: a review

This paper presents a review of automated image registration methodologies that have been used in the medical field. The aim of this paper is to be an introduction to the field, provide knowledge on the work that has been developed and to be a suitable reference for those who are looking for registration methods for a specific application. The registration methodologies under review are classified into intensity or feature based. The main steps of these methodologies, the common geometric transformations, the similarity measures and accuracy assessment techniques are introduced and described.

Measuring and comparing brain cortical surface area and other areal quantities

Structural analysis of MRI data on the cortical surface usually focuses on cortical thickness. Cortical surface area, when considered, has been measured only over gross regions or approached indirectly via comparisons with a standard brain. Here we demonstrate that direct measurement and comparison of the surface area of the cerebral cortex at a fine scale is possible using mass conservative interpolation methods. We present a framework for analyses of the cortical surface area, as well as for any other measurement distributed across the cortex that is areal by nature. The method consists of the construction of a mesh representation of the cortex, registration to a common coordinate system and, crucially, interpolation using a pycnophylactic method. Statistical analysis of surface area is done with power-transformed data to address lognormality, and inference is done with permutation methods. We introduce the concept of facewise analysis, discuss its interpretation and potential applications.

Brain surface conformal parameterization with the Ricci flow

In brain mapping research, parameterized 3-D surface models are of great interest for statistical comparisons of anatomy, surface-based registration, and signal processing. Here, we introduce the theories of continuous and discrete surface Ricci flow, which can create Riemannian metrics on surfaces with arbitrary topologies with user-defined Gaussian curvatures. The resulting conformal parameterizations have no singularities and they are intrinsic and stable. First, we convert a cortical surface model into a multiple boundary surface by cutting along selected anatomical landmark curves. Secondly, we conformally parameterize each cortical surface to a parameter domain with a user-designed Gaussian curvature arrangement. In the parameter domain, a shape index based on conformal invariants is computed, and inter-subject cortical surface matching is performed by solving a constrained harmonic map. We illustrate various target curvature arrangements and demonstrate the stability of the method using longitudinal data. To map statistical differences in cortical morphometry, we studied brain asymmetry in 14 healthy control subjects. We used a manifold version of Hotelling's T(2) test, applied to the Jacobian matrices of the surface parameterizations. A permutation test, along with the cumulative distribution of p-values, were used to estimate the overall statistical significance of differences. The results show our algorithm's power to detect subtle group differences in cortical surfaces.

FreeSurfer

FreeSurfer is a suite of tools for the analysis of neuroimaging data that provides an array of algorithms to quantify the functional, connectional and structural properties of the human brain. It has evolved from a package primarily aimed at generating surface representations of the cerebral cortex into one that automatically creates models of most macroscopically visible structures in the human brain given any reasonable T1-weighted input image. It is freely available, runs on a wide variety of hardware and software platforms, and is open source.

Cortical surface mapping using topology correction, partial flattening and 3D shape context-based non-rigid registration for use in quantifying atrophy in Alzheimer's disease

Magnetic resonance (MR) provides a non-invasive way to investigate changes in the brain resulting from aging or neurodegenerative disorders such as Alzheimer's disease (AD). Performing accurate analysis for population studies is challenging because of the interindividual anatomical variability. A large set of tools is found to perform studies of brain anatomy and population analysis (FreeSurfer, SPM, FSL). In this paper we present a newly developed surface-based processing pipeline (MILXCTE) that allows accurate vertex-wise statistical comparisons of brain modifications, such as cortical thickness (CTE). The brain is first segmented into the three main tissues: white matter, gray matter and cerebrospinal fluid, after CTE is computed, a topology corrected mesh is generated. Partial inflation and non-rigid registration of cortical surfaces to a common space using shape context are then performed. Each of the steps was firstly validated using MR images from the OASIS database. We then applied the pipeline to a sample of individuals randomly selected from the AIBL study on AD and compared with FreeSurfer. For a population of 50 individuals we found correlation of cortical thickness in all the regions of the brain (average r=0.62 left and r=0.64 right hemispheres). We finally computed changes in atrophy in 32 AD patients and 81 healthy elderly individuals. Significant differences were found in regions known to be affected in AD. We demonstrated the validity of the method for use in clinical studies which provides an alternative to well established techniques to compare different imaging biomarkers for the study of neurodegenerative diseases.

Automated preoperative planning of femoral stem in total hip arthroplasty from 3D CT data: atlas-based approach and comparative study

Atlas-based methods for automated preoperative planning of the femoral stem implant in total hip arthroplasty are described. Statistical atlases are constructed from a number of past preoperative plans prepared by experienced surgeons in order to represent the surgeon's expertise of the planning. Two types of atlases are considered. One is a statistical distance map atlas, which represents surgeon's preference of the contact pattern between the femoral canal (host bone) and stem (implant) surfaces. The other is an optimal reference plan, which is selected as the best representative plan expected to minimize the deviation from the surgeon's preferred contact pattern. These atlases are fitted to the patient data to automatically generate the preoperative plan of the femoral stem. In this paper, we formulate a general framework of atlas-based implant planning, and then describe the methods for construction and utilization of the two proposed atlases. In the experiments, we used 40 cases to evaluate the proposed methods and compare them with previous methods by defining the errors as differences between automated and surgeon's plans. By using the proposed methods, the positional and orientation errors were significantly reduced compared with the previous methods and the size error was superior to inter-surgeon variability in size selection using 2D templates on an X-ray image reported in previous work.

Cortical parcellations of the macaque monkey analyzed on surface-based atlases

Surface-based atlases provide a valuable way to analyze and visualize the functional organization of cerebral cortex. Surface-based registration (SBR) is a primary method for aligning individual hemispheres to a surface-based atlas. We used landmark-constrained SBR to register many published parcellation schemes to the macaque F99 surface-based atlas. This enables objective comparison of both similarities and differences across parcellations. Cortical areas in the macaque vary in surface area by more than 2 orders of magnitude. Based on a composite parcellation derived from 3 major sources, the total number of macaque neocortical and transitional cortical areas is estimated to be about 130-140 in each hemisphere.

Parcellations and hemispheric asymmetries of human cerebral cortex analyzed on surface-based atlases

We report on surface-based analyses that enhance our understanding of human cortical organization, including its convolutions and its parcellation into many distinct areas. The surface area of human neocortex averages 973 cm(2) per hemisphere, based on cortical midthickness surfaces of 2 cohorts of subjects. We implemented a method to register individual subjects to a hybrid version of the FreeSurfer "fsaverage" atlas whose left and right hemispheres are in precise geographic correspondence. Cortical folding patterns in the resultant population-average "fs_LR" midthickness surfaces are remarkably similar in the left and right hemispheres, even in regions showing significant asymmetry in 3D position. Both hemispheres are equal in average surface area, but hotspots of surface area asymmetry are present in the Sylvian Fissure and elsewhere, together with a broad pattern of asymmetries that are significant though small in magnitude. Multiple cortical parcellation schemes registered to the human atlas provide valuable reference data sets for comparisons with other studies. Identified cortical areas vary in size by more than 2 orders of magnitude. The total number of human neocortical areas is estimated to be ∼150 to 200 areas per hemisphere, which is modestly larger than a recent estimate for the macaque.

The organization of the human cerebral cortex estimated by intrinsic functional connectivity

Information processing in the cerebral cortex involves interactions among distributed areas. Anatomical connectivity suggests that certain areas form local hierarchical relations such as within the visual system. Other connectivity patterns, particularly among association areas, suggest the presence of large-scale circuits without clear hierarchical relations. In this study the organization of networks in the human cerebrum was explored using resting-state functional connectivity MRI. Data from 1,000 subjects were registered using surface-based alignment. A clustering approach was employed to identify and replicate networks of functionally coupled regions across the cerebral cortex. The results revealed local networks confined to sensory and motor cortices as well as distributed networks of association regions. Within the sensory and motor cortices, functional connectivity followed topographic representations across adjacent areas. In association cortex, the connectivity patterns often showed abrupt transitions between network boundaries. Focused analyses were performed to better understand properties of network connectivity. A canonical sensory-motor pathway involving primary visual area, putative middle temporal area complex (MT+), lateral intraparietal area, and frontal eye field was analyzed to explore how interactions might arise within and between networks. Results showed that adjacent regions of the MT+ complex demonstrate differential connectivity consistent with a hierarchical pathway that spans networks. The functional connectivity of parietal and prefrontal association cortices was next explored. Distinct connectivity profiles of neighboring regions suggest they participate in distributed networks that, while showing evidence for interactions, are embedded within largely parallel, interdigitated circuits. We conclude by discussing the organization of these large-scale cerebral networks in relation to monkey anatomy and their potential evolutionary expansion in humans to support cognition.

The organization of the human cerebral cortex estimated by intrinsic functional connectivity

Information processing in the cerebral cortex involves interactions among distributed areas. Anatomical connectivity suggests that certain areas form local hierarchical relations such as within the visual system. Other connectivity patterns, particularly among association areas, suggest the presence of large-scale circuits without clear hierarchical relations. In this study the organization of networks in the human cerebrum was explored using resting-state functional connectivity MRI. Data from 1,000 subjects were registered using surface-based alignment. A clustering approach was employed to identify and replicate networks of functionally coupled regions across the cerebral cortex. The results revealed local networks confined to sensory and motor cortices as well as distributed networks of association regions. Within the sensory and motor cortices, functional connectivity followed topographic representations across adjacent areas. In association cortex, the connectivity patterns often showed abrupt transitions between network boundaries. Focused analyses were performed to better understand properties of network connectivity. A canonical sensory-motor pathway involving primary visual area, putative middle temporal area complex (MT+), lateral intraparietal area, and frontal eye field was analyzed to explore how interactions might arise within and between networks. Results showed that adjacent regions of the MT+ complex demonstrate differential connectivity consistent with a hierarchical pathway that spans networks. The functional connectivity of parietal and prefrontal association cortices was next explored. Distinct connectivity profiles of neighboring regions suggest they participate in distributed networks that, while showing evidence for interactions, are embedded within largely parallel, interdigitated circuits. We conclude by discussing the organization of these large-scale cerebral networks in relation to monkey anatomy and their potential evolutionary expansion in humans to support cognition.

Measuring structural-functional correspondence: spatial variability of specialised brain regions after macro-anatomical alignment

The central question of the relationship between structure and function in the human brain is still not well understood. In order to investigate this fundamental relationship we create functional probabilistic maps from a large set of mapping experiments and compare the location of functionally localised regions across subjects using different whole-brain alignment schemes. To avoid the major problems associated with meta-analysis approaches, all subjects are scanned using the same paradigms, the same scanner and the same analysis pipeline. We show that an advanced, curvature driven cortex based alignment (CBA) scheme largely removes macro-anatomical variability across subjects. Remaining variability in the observed spatial location of functional regions, thus, reflects the "true" functional variability, i.e. the quantified variability is a good estimator of the underlying structural-functional correspondence. After localising 13 widely studied functional areas, we found a large variability in the degree to which functional areas respect macro-anatomical boundaries across the cortex. Some areas, such as the frontal eye fields (FEF) are strongly bound to a macro-anatomical location. Fusiform face area (FFA) on the other hand, varies in its location along the length of the fusiform gyrus even though the gyri themselves are well aligned across subjects. Language areas were found to vary greatly across subjects whilst a high degree of overlap was observed in sensory and motor areas. The observed differences in functional variability for different specialised areas suggest that a more complete estimation of the structure-function relationship across the whole cortex requires further empirical studies with an expanded test battery.

Cortical sulci recognition and spatial normalization

Brain mapping techniques pair similar anatomical information across individuals. In this context, spatial normalization is mainly used to reduce inter-subject differences to improve comparisons. These techniques may benefit from anatomically identified landmarks useful to drive the registration. Automatic labeling, classification or segmentation techniques provide such labels. Most of these approaches depend strongly on normalization, as much as normalization depends on landmark accuracy. We propose in this paper a coherent Bayesian framework to automatically identify approximately 60 sulcal labels per hemisphere based on a probabilistic atlas (a mixture of spam models: Statistical Probabilistic Anatomy Map) estimating simultaneously normalization parameters. This way, the labelization method provides also with no extra computational costs a new automatically constrained registration of sulcal structures. We have limited our study to global affine and piecewise affine registration. The suggested global affine approach outperforms significantly standard affine intensity-based normalization techniques in term of sulci alignments. Further, by combining global and local joint labeling, a final mean recognition rate of 86% has been obtained with much more reliable labeling posterior probabilities. The different methods described in this paper have been integrated since the release version 3.2.1 of the BrainVISA software platform (Riviére et al., 2009).

In-vivo measurement of cortical morphology: means and meanings

PURPOSE OF REVIEW

Study of the variability of the cortical mantle thickness is now a key issue in neuroimaging. Here we describe a more recent trend aiming at the study of the variability of the cortical folding morphology.

RECENT FINDINGS

Computerized three-dimensional versions of gyrification index and other morphometric features dedicated to the folding patterns are modified in psychiatric syndromes and neurologic disorders. These observations provide new insights into the mechanisms involved in abnormal development or abnormal aging.

SUMMARY

Quantification of the folding morphology will contribute to the global endeavor aiming at building biomarkers from neuroimaging data, with a specific focus on developmental diseases.

A framework for using diffusion weighted imaging to improve cortical parcellation

Cortical parcellation refers to anatomical labelling of every point in the cortex. An accurate parcellation is useful in many analysis techniques including the study of regional changes in cortical thickness or volume in ageing and neurodegeneration. Parcellation is also key to anatomic apportioning of functional imaging changes. We present preliminary work on a novel algorithm that takes an entire cortical parcellation and iteratively updates it to better match connectivity information derived from diffusion weighted imaging. We demonstrate the algorithm on a cohort of 17 healthy controls. Initial results show the algorithm recovering artificially induced mis-registrations of the parcellation and also converging to a group-wise average. This work introduces a framework to investigate the relationship between structure and function, with no a-priori knowledge of specific regions of interest.

A generative model for image segmentation based on label fusion

We propose a nonparametric, probabilistic model for the automatic segmentation of medical images, given a training set of images and corresponding label maps. The resulting inference algorithms rely on pairwise registrations between the test image and individual training images. The training labels are then transferred to the test image and fused to compute the final segmentation of the test subject. Such label fusion methods have been shown to yield accurate segmentation, since the use of multiple registrations captures greater inter-subject anatomical variability and improves robustness against occasional registration failures. To the best of our knowledge, this manuscript presents the first comprehensive probabilistic framework that rigorously motivates label fusion as a segmentation approach. The proposed framework allows us to compare different label fusion algorithms theoretically and practically. In particular, recent label fusion or multiatlas segmentation algorithms are interpreted as special cases of our framework. We conduct two sets of experiments to validate the proposed methods. In the first set of experiments, we use 39 brain MRI scans-with manually segmented white matter, cerebral cortex, ventricles and subcortical structures-to compare different label fusion algorithms and the widely-used FreeSurfer whole-brain segmentation tool. Our results indicate that the proposed framework yields more accurate segmentation than FreeSurfer and previous label fusion algorithms. In a second experiment, we use brain MRI scans of 282 subjects to demonstrate that the proposed segmentation tool is sufficiently sensitive to robustly detect hippocampal volume changes in a study of aging and Alzheimer's Disease.

Learning task-optimal registration cost functions for localizing cytoarchitecture and function in the cerebral cortex

Image registration is typically formulated as an optimization problem with multiple tunable, manually set parameters. We present a principled framework for learning thousands of parameters of registration cost functions, such as a spatially-varying tradeoff between the image dissimilarity and regularization terms. Our approach belongs to the classic machine learning framework of model selection by optimization of cross-validation error. This second layer of optimization of cross-validation error over and above registration selects parameters in the registration cost function that result in good registration as measured by the performance of the specific application in a training data set. Much research effort has been devoted to developing generic registration algorithms, which are then specialized to particular imaging modalities, particular imaging targets and particular postregistration analyses. Our framework allows for a systematic adaptation of generic registration cost functions to specific applications by learning the "free" parameters in the cost functions. Here, we consider the application of localizing underlying cytoarchitecture and functional regions in the cerebral cortex by alignment of cortical folding. Most previous work assumes that perfectly registering the macro-anatomy also perfectly aligns the underlying cortical function even though macro-anatomy does not completely predict brain function. In contrast, we learn 1) optimal weights on different cortical folds or 2) optimal cortical folding template in the generic weighted sum of squared differences dissimilarity measure for the localization task. We demonstrate state-of-the-art localization results in both histological and functional magnetic resonance imaging data sets.

GRAM: A framework for geodesic registration on anatomical manifolds

Medical image registration is a challenging problem, especially when there is large anatomical variation in the anatomies. Geodesic registration methods have been proposed to solve the large deformation registration problem. However, analytically defined geodesic paths may not coincide with biologically plausible paths of registration, since the manifold of diffeomorphisms is immensely broader than the manifold spanned by diffeomorphisms between real anatomies. In this paper, we propose a novel framework for large deformation registration using the learned manifold of anatomical variation in the data. In this framework, a large deformation between two images is decomposed into a series of small deformations along the shortest path on an empirical manifold that represents anatomical variation. Using a manifold learning technique, the major variation of the data can be visualized by a low-dimensional embedding, and the optimal group template is chosen as the geodesic mean on the manifold. We demonstrate the advantages of the proposed framework over direct registration with both simulated and real databases of brain images.

Quantitative evaluation of LDDMM, FreeSurfer, and CARET for cortical surface mapping

Cortical surface mapping has been widely used to compensate for individual variability of cortical shape and topology in anatomical and functional studies. While many surface mapping methods were proposed based on landmarks, curves, spherical or native cortical coordinates, few studies have extensively and quantitatively evaluated surface mapping methods across different methodologies. In this study we compared five cortical surface mapping algorithms, including large deformation diffeomorphic metric mapping (LDDMM) for curves (LDDMM-curve), for surfaces (LDDMM-surface), multi-manifold LDDMM (MM-LDDMM), FreeSurfer, and CARET, using 40 MRI scans and 10 simulated datasets. We computed curve variation errors and surface alignment consistency for assessing the mapping accuracy of local cortical features (e.g., gyral/sulcal curves and sulcal regions) and the curvature correlation for measuring the mapping accuracy in terms of overall cortical shape. In addition, the simulated datasets facilitated the investigation of mapping error distribution over the cortical surface when the MM-LDDMM, FreeSurfer, and CARET mapping algorithms were applied. Our results revealed that the LDDMM-curve, MM-LDDMM, and CARET approaches best aligned the local curve features with their own curves. The MM-LDDMM approach was also found to be the best in aligning the local regions and cortical folding patterns (e.g., curvature) as compared to the other mapping approaches. The simulation experiment showed that the MM-LDDMM mapping yielded less local and global deformation errors than the CARET and FreeSurfer mappings.

Evaluation of volume-based and surface-based brain image registration methods

Establishing correspondences across brains for the purposes of comparison and group analysis is almost universally done by registering images to one another either directly or via a template. However, there are many registration algorithms to choose from. A recent evaluation of fully automated nonlinear deformation methods applied to brain image registration was restricted to volume-based methods. The present study is the first that directly compares some of the most accurate of these volume registration methods with surface registration methods, as well as the first study to compare registrations of whole-head and brain-only (de-skulled) images. We used permutation tests to compare the overlap or Hausdorff distance performance for more than 16,000 registrations between 80 manually labeled brain images. We compared every combination of volume-based and surface-based labels, registration, and evaluation. Our primary findings are the following: 1. de-skulling aids volume registration methods; 2. custom-made optimal average templates improve registration over direct pairwise registration; and 3. resampling volume labels on surfaces or converting surface labels to volumes introduces distortions that preclude a fair comparison between the highest ranking volume and surface registration methods using present resampling methods. From the results of this study, we recommend constructing a custom template from a limited sample drawn from the same or a similar representative population, using the same algorithm used for registering brains to the template.

DT-REFinD: diffusion tensor registration with exact finite-strain differential

In this paper, we propose the DT-REFinD algorithm for the diffeomorphic nonlinear registration of diffusion tensor images. Unlike scalar images, deforming tensor images requires choosing both a reorientation strategy and an interpolation scheme. Current diffusion tensor registration algorithms that use full tensor information face difficulties in computing the differential of the tensor reorientation strategy and consequently, these methods often approximate the gradient of the objective function. In the case of the finite-strain (FS) reorientation strategy, we borrow results from the pose estimation literature in computer vision to derive an analytical gradient of the registration objective function. By utilizing the closed-form gradient and the velocity field representation of one parameter subgroups of diffeomorphisms, the resulting registration algorithm is diffeomorphic and fast. We contrast the algorithm with a traditional FS alternative that ignores the reorientation in the gradient computation. We show that the exact gradient leads to significantly better registration at the cost of computation time. Independently of the choice of Euclidean or Log-Euclidean interpolation and sum of squared differences dissimilarity measure, the exact gradient achieves better alignment over an entire spectrum of deformation penalties. Alignment quality is assessed with a battery of metrics including tensor overlap, fractional anisotropy, inverse consistency and closeness to synthetic warps. The improvements persist even when a different reorientation scheme, preservation of principal directions, is used to apply the final deformations.