Spherical demons: fast diffeomorphic landmark-free surface registration

Spatial Patterns, Longitudinal Development, and Hemispheric Asymmetries of Cortical Thickness in Infants from Birth to 2 Years of Age

Cortical thickness (CT) is related to normal development and neurodevelopmental disorders. It remains largely unclear how the characteristic patterns of CT evolve in the first 2 years. In this paper, we systematically characterized for the first time the detailed vertex-wise patterns of spatial distribution, longitudinal development, and hemispheric asymmetries of CT at 0, 1, and 2 years of age, via surface-based analysis of 219 longitudinal magnetic resonance images from 73 infants. Despite the dynamic increase of CT in the first year and the little change of CT in the second year, we found that the overall spatial distribution of thin and thick cortices was largely present at birth, and evolved only modestly during the first 2 years. Specifically, the precentral gyrus, postcentral gyrus, occipital cortex, and superior parietal region had thin cortices, whereas the prefrontal, lateral temporal, insula, and inferior parietal regions had thick cortices. We revealed that in the first year thin cortices exhibited low growth rates of CT, whereas thick cortices exhibited high growth rates. We also found that gyri were thicker than sulci, and that the anterior bank of the central sulcus was thicker than the posterior bank. Moreover, we showed rightward hemispheric asymmetries of CT in the lateral temporal and posterior insula regions at birth, which shrank gradually in the first 2 years, and also leftward asymmetries in the medial prefrontal, paracentral, and anterior cingulate cortices, which expanded substantially during this period. This study provides the first comprehensive picture of early patterns and evolution of CT during infancy.

Reconstruction of four-dimensional computed tomography lung images by applying spatial and temporal anatomical constraints using a Bayesian model

Current four-dimensional computed tomography (4-D CT) lung image reconstruction methods rely on respiratory gating, such as surrogate, to sort the large number of axial images captured during multiple breathing cycles into serial three-dimensional CT images of different respiratory phases. Such sorting methods may be subject to external surrogate signal noises due to poor reproducibility of breathing cycles. New image-matching-based reconstruction algorithms refine the 4-D CT reconstruction by matching neighboring image slices, and they generally work better for the cine mode of 4-D CT acquisition than the helical mode due to different table positions of axial images in the helical mode. We propose a Bayesian model (BM) based automated 4-D CT lung image reconstruction for helical mode scans. BM allows for applying new spatial and temporal anatomical constraints in the optimization procedure. Using an iterative optimization procedure, each axial image is assigned to a respiratory phase to make sure the anatomical structures are spatially and temporally smooth based on the BM framework. In experiments, we visually and quantitatively compared the results of the proposed BM-based 4-D CT reconstruction with the respiratory surrogate and the normalized cross-correlation based image matching method using both simulated and actual 4-D patient scans. The results indicated that the proposed algorithm yielded more accurate reconstruction and fewer artifacts in the 4-D CT image series.

Quantitative analysis of 3-dimensional facial soft tissue photographic images: technical methods and clinical application

BACKGROUND

The recent advent of 3D photography has created the potential for comprehensive facial evaluation. However, lack of practical true 3D analysis of the information collected from 3D images has been the factor limiting widespread utilization in orthodontics. Current evaluation of 3D facial soft tissue images relies on subjective visual evaluation and 2D distances to assess facial disharmony. The objectives of this project strive to map the surface and define boundaries of 3D facial soft tissue, modify mathematical functions to average multiple 3D facial images, and mathematically average 3D facial images allowing generation of color-coded surface deviation relative to a true average.

METHODS

Collaboration headed by UCLA Orthodontics with UCLA Neuroimaging was initiated to modify advanced brain mapping technology to accurately map the facial surface in 3D. 10 subjects were selected as a sample for development of the technical protocol. 3dMD photographic images were segmented, corrected using a series of topology correcting algorithms, and process to create close meshes. Shapes were mapped to a sphere using conformal and area preserving maps, and were then registered using a spherical patch mapping approach. Finally an average was created using 7-parameter procrustes alignment.

RESULTS

Size-standardized average facial images were generated for the sample population. A single patient was then superimposed on the average and color-coded displacement maps were generated to demonstrate the clinical applicability of this protocol. Further confirmation of the methods through 3D superimposition of the initial (T0) average to the 4 week (T4) average was completed and analyzed.

CONCLUSIONS

The results of this investigation suggest that it is possible to average multiple facial images of highly variable topology. The immediate application of this research will be rapid and detailed diagnostic imaging analysis for orthodontic and surgical treatment planning. There is great potential for application to anthropometrics and genomics. This investigation resulted in establishment of a protocol for mapping the surface of the human face in three dimensions.

Exploration of the Brain's White Matter Structure through Visual Abstraction and Multi-Scale Local Fiber Tract Contraction

We present a visualization technique for brain fiber tracts from DTI data that provides insight into the structure of white matter through visual abstraction. We achieve this abstraction by analyzing the local similarity of tract segment directions at different scales using a stepwise increase of the search range. Next, locally similar tract segments are moved toward each other in an iterative process, resulting in a local contraction of tracts perpendicular to the local tract direction at a given scale. This not only leads to the abstraction of the global structure of the white matter as represented by the tracts, but also creates volumetric voids. This increase of empty space decreases the mutual occlusion of tracts and, consequently, results in a better understanding of the brain's three-dimensional fiber tract structure. Our implementation supports an interactive and continuous transition between the original and the abstracted representations via various scale levels of similarity. We also support the selection of groups of tracts, which are highlighted and rendered with the abstracted visualization as context.

Robust estimation of group-wise cortical correspondence with an application to macaque and human neuroimaging studies

We present a novel group-wise registration method for cortical correspondence for local cortical thickness analysis in human and non-human primate neuroimaging studies. The proposed method is based on our earlier template based registration that estimates a continuous, smooth deformation field via sulcal curve-constrained registration employing spherical harmonic decomposition of the deformation field. This pairwise registration though results in a well-known template selection bias, which we aim to overcome here via a group-wise approach. We propose the use of an unbiased ensemble entropy minimization following the use of the pairwise registration as an initialization. An individual deformation field is then iteratively updated onto the unbiased average. For the optimization, we use metrics specific for cortical correspondence though all of these are straightforwardly extendable to the generic setting: The first focused on optimizing the correspondence of automatically extracted sulcal landmarks and the second on that of sulcal depth property maps. We further propose a robust entropy metric and a hierarchical optimization by employing spherical harmonic basis orthogonality. We also provide the detailed methodological description of both our earlier work and the proposed method with a set of experiments on a population of human and non-human primate subjects. In the experiment, we have shown that our method achieves superior results on consistency through quantitative and visual comparisons as compared to the existing methods.

Construction of a fetal spatio-temporal cortical surface atlas from in utero MRI: Application of spectral surface matching

In this study, we construct a spatio-temporal surface atlas of the developing cerebral cortex, which is an important tool for analysing and understanding normal and abnormal cortical development. In utero Magnetic Resonance Imaging (MRI) of 80 healthy fetuses was performed, with a gestational age range of 21.7 to 38.9 weeks. Topologically correct cortical surface models were extracted from reconstructed 3D MRI volumes. Accurate correspondences were obtained by applying a joint spectral analysis to cortices for sets of subjects close to a specific age. Sulcal alignment was found to be accurate in comparison to spherical demons, a state of the art registration technique for aligning 2D cortical representations (average Fréchet distance≈0.4 mm at 30 weeks). We construct consistent, unbiased average cortical surface templates, for each week of gestation, from age-matched groups of surfaces by applying kernel regression in the spectral domain. These were found to accurately capture the average cortical shape of individuals within the cohort, suggesting a good alignment of cortical geometry. Each spectral embedding and its corresponding cortical surface template provide a dual reference space where cortical geometry is aligned and a vertex-wise morphometric analysis can be undertaken.

Landmark constrained registration of high-genus surfaces applied to vestibular system morphometry

The analysis of the vestibular system (VS) is an important research topic in medical image analysis. VS is a sensory structure in the inner ear for the perception of spatial orientation. It is believed several diseases, such as the Adolescent Idiopathic Scoliosis (AIS), are due to the impairment of the VS function. The morphology of the VS is thus of great research significance. A major challenge is that the VS is a genus-3 surface. The high-genus topology of the VS poses great challenges to find accurate pointwise correspondences between the surfaces and whereby perform accurate shape analysis. In this paper, we present a method to obtain the landmark constrained diffeomorphic registration between the VS surfaces based on the quasi-conformal theory. Given a set of corresponding landmarks on the VS surfaces, a diffeomorphism between the VS surfaces that matches the features consistently can be obtained. The basic idea is to iteratively search for an admissible Beltrami coefficient, which is associated to our desired landmark matching registration. With the obtained surface registrations, vertex-wise morphometric analysis can be carried out. Two types of geometric features are used for shape comparison. One is the collection of homotopic loops on each canals of the VS, which can be used to measure the local thickness of the canals. From the homotopic loops, centerlines can be extracted. By examining the deviations of the centerlines from the best fit planes, bendings of the canals can be detected. The second geometric feature is the minimal surface enclosed by the homotopic loop. From the minimal surfaces of each homotopic loops, cross-sectional area of the canals can be evaluated. To study the local shape difference more comprehensively, a complete shape index, which is defined using the Beltrami coefficients and surface curvatures, is used. We test proposed registration method on 15 VS of normal control subjects and 12 VS of patients suffering from AIS. Experimental results show the efficacy and accuracy of the proposed algorithm to compute the VS surface registration. Shape analysis has also been carried out using the proposed geometric features and shape index, which reveals shape differences in the posterior canal between normal and diseased AIS groups.

Landmark constrained genus-one surface Teichmüller map applied to surface registration in medical imaging

We address the registration problem of genus-one surfaces (such as vertebrae bones) with prescribed landmark constraints. The high-genus topology of the surfaces makes it challenging to obtain a unique and bijective surface mapping that matches landmarks consistently. This work proposes to tackle this registration problem using a special class of quasi-conformal maps called Teichmüller maps (T-Maps). A landmark constrained T-Map is the unique mapping between genus-1 surfaces that minimizes the maximal conformality distortion while matching the prescribed feature landmarks. Existence and uniqueness of the landmark constrained T-Map are theoretically guaranteed. This work presents an iterative algorithm to compute the T-Map. The main idea is to represent the set of diffeomorphism using the Beltrami coefficients (BC). The BC is iteratively adjusted to an optimal one, which corresponds to our desired T-Map that matches the prescribed landmarks and satisfies the periodic boundary condition on the universal covering space. Numerical experiments demonstrate the effectiveness of our proposed algorithm. The method has also been applied to register vertebrae bones with prescribed landmark points and curves, which gives accurate surface registrations.

Medial Demons Registration Localizes The Degree of Genetic Influence Over Subcortical Shape Variability: An N= 1480 Meta-Analysis

We present a multi-cohort shape heritability study, extending the fast spherical demons registration to subcortical shapes via medial modeling. A multi-channel demons registration based on vector spherical harmonics is applied to medial and curvature features, while controlling for metric distortion. We registered and compared seven subcortical structures of 1480 twins and siblings from the Queensland Twin Imaging Study and Human Connectome Project: Thalamus, Caudate, Putamen, Pallidum, Hippocampus, Amygdala, and Nucleus Accumbens. Radial distance and tensor-based morphometry (TBM) features were found to be highly heritable throughout the entire basal ganglia and limbic system. Surface maps reveal subtle variation in heritability across functionally distinct parts of each structure. Medial Demons reveals more significantly heritable regions than two previously described surface registration methods. This approach may help to prioritize features and measures for genome-wide association studies.

AUTOMATIC PARCELLATION OF CORTICAL SURFACES USING RANDOM FORESTS

Automatic and accurate parcellation of cortical surfaces into anatomically and functionally meaningful regions is of fundamental importance in brain mapping. In this paper, we propose a new method leveraging random forests and graph cuts methods to parcellate cortical surfaces into a set of gyral-based regions, using multiple surface atlases with manual labels by experts. Specifically, our method first takes advantage of random forests and auto-context methods to learn the optimal utilization of cortical features for rough parcellation and then the graph cuts method to further refine the parcellation for improved accuracy and spatial consistency. Particularly, to capitalize on random forests, we propose a novel definition of Haar-like features on cortical surfaces based on spherical mapping. The proposed method has been validated on cortical surfaces from 39 adult brain MR images, each with 35 regions manually labeled by a neuroanatomist, achieving the average Dice ratio of 0.902, higher than the-state-of-art methods.

Predicting anatomical landmarks and bone morphology of the femur using local region matching

PURPOSE

Anatomical landmarks and bony features are frequently used in biomechanical and surgical applications. The purpose of this study was to develop a local region matching-based anatomical landmark prediction method.

METHODS

A reference femur model with anatomical landmarks and a surface division map was prepared. Initial registration between the reference femur model and a target femur model was performed in three-dimensional Cartesian space, and closest point pairs were determined by the initial surface correspondence. The models were mapped to unit spheres through spherical parameterization. Spherical registration using the closest point pairs in the spherical parametric space enabled the application of a division map from the reference model to the target model. The reference and target models were divided into local regions defined in the division map, and the corresponding regions were again registered in Cartesian space. Anatomical landmarks in the local regions were identified in the target model.

RESULTS

The accuracy of the proposed method was tested for anatomical landmarks marked by a clinician on 35 femoral models. The effectiveness of local region matching was demonstrated by automatic measurements of the femoral neck-shaft angle. The average prediction error for all eight anatomical landmarks of the femur was 2.74 (±1.78) mm. The average of the predicted neck-shaft angle for our Korean subjects was 126.41° (±4.92°), which was comparable to previous studies in Japanese and Chinese populations.

CONCLUSION

Anatomical landmarks and features could be accurately predicted using the proposed local region matching method. This method offers robustness and accuracy in determining anatomical bony landmarks and bone morphology for clinical and biomechanical applications.

Validation of a nonrigid registration error detection algorithm using clinical MRI brain data

Identification of error in nonrigid registration is a critical problem in the medical image processing community. We recently proposed an algorithm that we call "Assessing Quality Using Image Registration Circuits" (AQUIRC) to identify nonrigid registration errors and have tested its performance using simulated cases. In this paper, we extend our previous work to assess AQUIRC's ability to detect local nonrigid registration errors and validate it quantitatively at specific clinical landmarks, namely the anterior commissure and the posterior commissure. To test our approach on a representative range of error we utilize five different registration methods and use 100 target images and nine atlas images. Our results show that AQUIRC's measure of registration quality correlates with the true target registration error (TRE) at these selected landmarks with an R(2)=0.542. To compare our method to a more conventional approach, we compute local normalized correlation coefficient (LNCC) and show that AQUIRC performs similarly. However, a multi-linear regression performed with both AQUIRC's measure and LNCC shows a higher correlation with TRE than correlations obtained with either measure alone, thus showing the complementarity of these quality measures. We conclude the paper by showing that the AQUIRC algorithm can be used to reduce registration errors for all five algorithms.

A Riemannian Framework for Intrinsic Comparison of Closed Genus-Zero Shapes

We present a framework for intrinsic comparison of surface metric structures and curvatures. This work parallels the work of Kurtek et al. on parameterization-invariant comparison of genus zero shapes. Here, instead of comparing the embedding of spherically parameterized surfaces in space, we focus on the first fundamental form. To ensure that the distance on spherical metric tensor fields is invariant to parameterization, we apply the conjugation-invariant metric arising from the L2 norm on symmetric positive definite matrices. As a reparameterization changes the metric tensor by a congruent Jacobian transform, this metric perfectly suits our purpose. The result is an intrinsic comparison of shape metric structure that does not depend on the specifics of a spherical mapping. Further, when restricted to tensors of fixed volume form, the manifold of metric tensor fields and its quotient of the group of unitary diffeomorphisms becomes a proper metric manifold that is geodesically complete. Exploiting this fact, and augmenting the metric with analogous metrics on curvatures, we derive a complete Riemannian framework for shape comparison and reconstruction. A by-product of our framework is a near-isometric and curvature-preserving mapping between surfaces. The correspondence is optimized using the fast spherical fluid algorithm. We validate our framework using several subcortical boundary surface models from the ADNI dataset.

Studying ventricular abnormalities in mild cognitive impairment with hyperbolic Ricci flow and tensor-based morphometry

Mild Cognitive Impairment (MCI) is a transitional stage between normal aging and dementia and people with MCI are at high risk of progression to dementia. MCI is attracting increasing attention, as it offers an opportunity to target the disease process during an early symptomatic stage. Structural magnetic resonance imaging (MRI) measures have been the mainstay of Alzheimer's disease (AD) imaging research, however, ventricular morphometry analysis remains challenging because of its complicated topological structure. Here we describe a novel ventricular morphometry system based on the hyperbolic Ricci flow method and tensor-based morphometry (TBM) statistics. Unlike prior ventricular surface parameterization methods, hyperbolic conformal parameterization is angle-preserving and does not have any singularities. Our system generates a one-to-one diffeomorphic mapping between ventricular surfaces with consistent boundary matching conditions. The TBM statistics encode a great deal of surface deformation information that could be inaccessible or overlooked by other methods. We applied our system to the baseline MRI scans of a set of MCI subjects from the Alzheimer's Disease Neuroimaging Initiative (ADNI: 71 MCI converters vs. 62 MCI stable). Although the combined ventricular area and volume features did not differ between the two groups, our fine-grained surface analysis revealed significant differences in the ventricular regions close to the temporal lobe and posterior cingulate, structures that are affected early in AD. Significant correlations were also detected between ventricular morphometry, neuropsychological measures, and a previously described imaging index based on fluorodeoxyglucose positron emission tomography (FDG-PET) scans. This novel ventricular morphometry method may offer a new and more sensitive approach to study preclinical and early symptomatic stage AD.

Localization of specific language pathways using diffusion-weighted imaging tractography for presurgical planning of children with intractable epilepsy

OBJECTIVE

To examine whether diffusion-weighted imaging (DWI) tractography can detect multiple white matter pathways connected to language cortices, we employed a maximum a posteriori probability (MAP) classification method, which has been recently validated for the corticospinal tract.

METHODS

DWI was performed in 12 normally developing children and 17 children with intractable focal epilepsy who underwent subsequent two-stage epilepsy surgery with intracranial functional mapping. First, whole-brain DWI tractography was performed to identify unique pathways originating from Broca's area, premotor area, and Wernicke's area on functional magnetic resonance imaging (fMRI) of normal children and intracranial electrical stimulation mapping (ESM) of children with epilepsy. Group averaging of these pathways based on fMRI was performed to construct the probability maps of language areas in standard MRI space. These maps were finally used to design a DWI-MAP classifier, which can automatically sort individual fibers originating from fMRI language areas as well as ESM language areas.

RESULTS

In normally developing children, the DWI-MAP classifier predicted language-activation areas on fMRI with up to 77% accuracy. In children with focal epilepsy, the DWI-MAP classifier also showed high accuracy (up to 82%) for the fibers terminating in proximity to essential language areas determined by ESM. Decreased volumes in DWI-MAP-defined pathways after epilepsy surgery were associated with postoperative language deficits.

SIGNIFICANCE

This study encourages further investigations to determine if DWI-MAP analysis can serve as a noninvasive diagnostic tool during pediatric presurgical planning by estimating not only the location of essential language cortices, but also the underlying fibers connecting these cortical areas.

Simultaneous and consistent labeling of longitudinal dynamic developing cortical surfaces in infants

The human cerebral cortex develops extremely dynamically in the first 2years of life. Accurate and consistent parcellation of longitudinal dynamic cortical surfaces during this critical stage is essential to understand the early development of cortical structure and function in both normal and high-risk infant brains. However, directly applying the existing methods developed for the cross-sectional studies often generates longitudinally-inconsistent results, thus leading to inaccurate measurements of the cortex development. In this paper, we propose a new method for accurate, consistent, and simultaneous labeling of longitudinal cortical surfaces in the serial infant brain MR images. The proposed method is explicitly formulated as a minimization problem with an energy function that includes a data fitting term, a spatial smoothness term, and a temporal consistency term. Specifically, inspired by multi-atlas based label fusion, the data fitting term is designed to integrate the contributions from multi-atlas surfaces adaptively, according to the similarities of their local cortical folding with that of the subject cortical surface. The spatial smoothness term is then designed to adaptively encourage label smoothness based on the local cortical folding geometries, i.e., allowing label discontinuity at sulcal bottoms (which often are the boundaries of cytoarchitecturally and functionally distinct regions). The temporal consistency term is to adaptively encourage the label consistency among the temporally-corresponding vertices, based on their similarity of local cortical folding. Finally, the entire energy function is efficiently minimized by a graph cuts method. The proposed method has been applied to the parcellation of longitudinal cortical surfaces of 13 healthy infants, each with 6 serial MRI scans acquired at 0, 3, 6, 9, 12 and 18months of age. Qualitative and quantitative evaluations demonstrated both accuracy and longitudinal consistency of the proposed method. By using our method, for the first time, we reveal several hitherto unseen properties of the dynamic and regionally heterogeneous development of the cortical surface area in the first 18months of life.

Constructing 4D infant cortical surface atlases based on dynamic developmental trajectories of the cortex

Cortical surface atlases play an increasingly important role for analysis, visualization, and comparison of results across different neuroimaging studies. As the first two years of life is the most dynamic period of postnatal structural and functional development of the highly-folded cerebral cortex, longitudinal (4D) cortical surface atlases for the infant brains during this period is highly desired yet still lacking for early brain development studies. In this paper, we construct the first longitudinal (4D) cortical surface atlases for the dynamic developing infant cortical structures at 1, 3, 6, 9, 12, 18 and 24 months of age, based on 202 serial MRI scans from 35 healthy infants. To ensure longitudinal consistency and unbiasedness of the 4D infant cortical surface atlases, we first compute the within-subject mean cortical folding geometries by groupwise registration of longitudinal surfaces of each infant. Then we establish intersubject cortical correspondences by groupwise registration of the within-subject mean cortical folding geometries of all infants. More importantly, for the first time, we further parcellate the 4D infant surface atlases into developmentally and functionally distinctive regions based solely on the dynamic developmental trajectories of the cortical thickness, by using the spectral clustering method. Specifically, to deal with the problem that each infant has different number of scans, we first compute the within-subject affinity matrix of vertices' cortical thickness trajectories of each infant, and then we use the averaged affinity matrix of all infants for parcellation. Our constructed 4D infant cortical surface atlases with developmental trajectories based parcellation will greatly facilitate the surface-based analysis of dynamic brain development in infants.

Exact surface registration of retinal surfaces from 3-D optical coherence tomography images

Nonrigid registration of optical coherence tomography (OCT) images is an important problem in studying eye diseases, evaluating the effect of pharmaceuticals in treating vision loss, and performing group-wise cross-sectional analysis. High dimensional nonrigid registration algorithms required for cross-sectional and longitudinal analysis are still being developed for accurate registration of OCT image volumes, with the speckle noise in images presenting a challenge for registration. Development of algorithms for segmentation of OCT images to generate surface models of retinal layers has advanced considerably and several algorithms are now available that can segment retinal OCT images into constituent retinal surfaces. Important morphometric measurements can be extracted if accurate surface registration algorithm for registering retinal surfaces onto corresponding template surfaces were available. In this paper, we present a novel method to perform multiple and simultaneous retinal surface registration, targeted to registering surfaces extracted from ocular volumetric OCT images. This enables a point-to-point correspondence (homology) between template and subject surfaces, allowing for a direct, vertex-wise comparison of morphometric measurements across subject groups. We demonstrate that this approach can be used to localize and analyze regional changes in choroidal and nerve fiber layer thickness among healthy and glaucomatous subjects, allowing for cross-sectional population wise analysis. We also demonstrate the method's ability to track longitudinal changes in optic nerve head morphometry, allowing for within-individual tracking of morphometric changes. This method can also, in the future, be used as a precursor to 3-D OCT image registration to better initialize nonrigid image registration algorithms closer to the desired solution.

Comparative evaluation of registration algorithms in different brain databases with varying difficulty: results and insights

Evaluating various algorithms for the inter-subject registration of brain magnetic resonance images (MRI) is a necessary topic receiving growing attention. Existing studies evaluated image registration algorithms in specific tasks or using specific databases (e.g., only for skull-stripped images, only for single-site images, etc.). Consequently, the choice of registration algorithms seems task- and usage/parameter-dependent. Nevertheless, recent large-scale, often multi-institutional imaging-related studies create the need and raise the question whether some registration algorithms can 1) generally apply to various tasks/databases posing various challenges; 2) perform consistently well, and while doing so, 3) require minimal or ideally no parameter tuning. In seeking answers to this question, we evaluated 12 general-purpose registration algorithms, for their generality, accuracy and robustness. We fixed their parameters at values suggested by algorithm developers as reported in the literature. We tested them in 7 databases/tasks, which present one or more of 4 commonly-encountered challenges: 1) inter-subject anatomical variability in skull-stripped images; 2) intensity homogeneity, noise and large structural differences in raw images; 3) imaging protocol and field-of-view (FOV) differences in multi-site data; and 4) missing correspondences in pathology-bearing images. Totally 7,562 registrations were performed. Registration accuracies were measured by (multi-)expert-annotated landmarks or regions of interest (ROIs). To ensure reproducibility, we used public software tools, public databases (whenever possible), and we fully disclose the parameter settings. We show evaluation results, and discuss the performances in light of algorithms' similarity metrics, transformation models and optimization strategies. We also discuss future directions for the algorithm development and evaluations.

Functional Specialization and Flexibility in Human Association Cortex

The association cortex supports cognitive functions enabling flexible behavior. Here, we explored the organization of human association cortex by mathematically formalizing the notion that a behavioral task engages multiple cognitive components, which are in turn supported by multiple overlapping brain regions. Application of the model to a large data set of neuroimaging experiments (N = 10 449) identified complex zones of frontal and parietal regions that ranged from being highly specialized to highly flexible. The network organization of the specialized and flexible regions was explored with an independent resting-state fMRI data set (N = 1000). Cortical regions specialized for the same components were strongly coupled, suggesting that components function as partially isolated networks. Functionally flexible regions participated in multiple components to different degrees. This heterogeneous selectivity was predicted by the connectivity between flexible and specialized regions. Functionally flexible regions might support binding or integrating specialized brain networks that, in turn, contribute to the ability to execute multiple and varied tasks.

Metric optimization for surface analysis in the Laplace-Beltrami embedding space

In this paper, we present a novel approach for the intrinsic mapping of anatomical surfaces and its application in brain mapping research. Using the Laplace-Beltrami eigen-system, we represent each surface with an isometry invariant embedding in a high dimensional space. The key idea in our system is that we realize surface deformation in the embedding space via the iterative optimization of a conformal metric without explicitly perturbing the surface or its embedding. By minimizing a distance measure in the embedding space with metric optimization, our method generates a conformal map directly between surfaces with highly uniform metric distortion and the ability of aligning salient geometric features. Besides pairwise surface maps, we also extend the metric optimization approach for group-wise atlas construction and multi-atlas cortical label fusion. In experimental results, we demonstrate the robustness and generality of our method by applying it to map both cortical and hippocampal surfaces in population studies. For cortical labeling, our method achieves excellent performance in a cross-validation experiment with 40 manually labeled surfaces, and successfully models localized brain development in a pediatric study of 80 subjects. For hippocampal mapping, our method produces much more significant results than two popular tools on a multiple sclerosis study of 109 subjects.

Spatial distribution and longitudinal development of deep cortical sulcal landmarks in infants

Sulcal pits, the locally deepest points in sulci of the highly convoluted and variable cerebral cortex, are found to be spatially consistent across human adult individuals. It is suggested that sulcal pits are genetically controlled and have close relationships with functional areas. To date, the existing imaging studies of sulcal pits are mainly focused on adult brains, yet little is known about the spatial distribution and temporal development of sulcal pits in the first 2 years of life, which is the most dynamic and critical period of postnatal brain development. Studying sulcal pits during this period would greatly enrich our limited understandings of the origins and developmental trajectories of sulcal pits, and would also provide important insights into many neurodevelopmental disorders associated with abnormal cortical foldings. In this paper, by using surface-based morphometry, for the first time, we systemically investigated the spatial distribution and temporal development of sulcal pits in major cortical sulci from 73 healthy infants, each with three longitudinal 3T MR scans at term birth, 1 year, and 2 years of age. Our results suggest that the spatially consistent distributions of sulcal pits in major sulci across individuals have already existed at term birth and this spatial distribution pattern keeps relatively stable in the first 2 years of life, despite that the cerebral cortex expands dramatically and the sulcal depth increases considerably during this period. Specially, the depth of sulcal pits increases regionally heterogeneously, with more rapid growth in the high-order association cortex, including the prefrontal and temporal cortices, than the sensorimotor cortex in the first 2 years of life. Meanwhile, our results also suggest that there exist hemispheric asymmetries of the spatial distributions of sulcal pits in several cortical regions, such as the central, superior temporal and postcentral sulci, consistently from birth to 2 years of age, which likely has close relationships with the lateralization of brain functions of these regions. This study provides detailed insights into the spatial distribution and temporal development of deep sulcal landmarks in infants.

MSM: a new flexible framework for Multimodal Surface Matching

Surface-based cortical registration methods that are driven by geometrical features, such as folding, provide sub-optimal alignment of many functional areas due to variable correlation between cortical folding patterns and function. This has led to the proposal of new registration methods using features derived from functional and diffusion imaging. However, as yet there is no consensus over the best set of features for optimal alignment of brain function. In this paper we demonstrate the utility of a new Multimodal Surface Matching (MSM) algorithm capable of driving alignment using a wide variety of descriptors of brain architecture, function and connectivity. The versatility of the framework originates from adapting the discrete Markov Random Field (MRF) registration method to surface alignment. This has the benefit of being very flexible in the choice of a similarity measure and relatively insensitive to local minima. The method offers significant flexibility in the choice of feature set, and we demonstrate the advantages of this by performing registrations using univariate descriptors of surface curvature and myelination, multivariate feature sets derived from resting fMRI, and multimodal descriptors of surface curvature and myelination. We compare the results with two state of the art surface registration methods that use geometric features: FreeSurfer and Spherical Demons. In the future, the MSM technique will allow explorations into the best combinations of features and alignment strategies for inter-subject alignment of cortical functional areas for a wide range of neuroimaging data sets.

Group-wise cortical correspondence via sulcal curve-constrained entropy minimization

We present a novel cortical correspondence method employing group-wise registration in a spherical parametrization space for the use in local cortical thickness analysis in human and non-human primate neuroimaging studies. The proposed method is unbiased registration that estimates a continuous smooth deformation field into an unbiased average space via sulcal curve-constrained entropy minimization using spherical harmonic decomposition of the spherical deformation field. We initialize a correspondence by our pair-wise method that establishes a surface correspondence with a prior template. Since this pair-wise correspondence is biased to the choice of a template, we further improve the correspondence by employing unbiased ensemble entropy minimization across all surfaces, which yields a deformation field onto the iteratively updated unbiased average. The specific entropy metric incorporates two terms: the first focused on optimizing the correspondence of automatically extracted sulcal landmarks and the second on that of sulcal depth maps. We also propose an encoding scheme for spherical deformation via spherical harmonics as well as a novel method to choose an optimal spherical polar coordinate system for the most efficient deformation field estimation. The experimental results show evidence that the proposed method improves the correspondence quality in non-human primate and human subjects as compared to the pair-wise method.

Conformal mapping via metric optimization with application for cortical label fusion

In this paper we develop a novel approach for computing conformal maps between anatomical surfaces with the ability of aligning anatomical features and achieving greatly reduced metric distortion. In contrast to conventional approaches that focused on conformal maps to the sphere or plane, our method computes the conformal map between surfaces in the embedding space formed the intrinsically defined Laplace-Beltrami (LB) eigenfunctions. Utilizing the power of LB eigenfunctions as informative descriptors of global geometry, the conformal maps computed by our method can effectively align anatomical features on cortical surfaces. By computing such feature-aware conformal maps to a group-wisely optimal atlas surface, which is also computed with metric optimization in the LB embedding space, we develop a fully automated system for cortical labeling with the fusion of labels on a large number of atlas surfaces. In our experiments, we build our system with 40 labeled surfaces and demonstrate its excellent performance with leave-one-out cross validation. We also applied the automated labeling system to cortical surfaces reconstructed from MR scans of 50 patients with Alzheimer's disease (AD) and 50 normal controls (NC) to illustrate its robustness and effectiveness in clinical data analysis.

Mapping longitudinal development of local cortical gyrification in infants from birth to 2 years of age

Human cortical folding is believed to correlate with cognitive functions. This likely correlation may have something to do with why abnormalities of cortical folding have been found in many neurodevelopmental disorders. However, little is known about how cortical gyrification, the cortical folding process, develops in the first 2 years of life, a period of dynamic and regionally heterogeneous cortex growth. In this article, we show how we developed a novel infant-specific method for mapping longitudinal development of local cortical gyrification in infants. By using this method, via 219 longitudinal 3T magnetic resonance imaging scans from 73 healthy infants, we systemically and quantitatively characterized for the first time the longitudinal cortical global gyrification index (GI) and local GI (LGI) development in the first 2 years of life. We found that the cortical GI had age-related and marked development, with 16.1% increase in the first year and 6.6% increase in the second year. We also found marked and regionally heterogeneous cortical LGI development in the first 2 years of life, with the high-growth regions located in the association cortex, whereas the low-growth regions located in sensorimotor, auditory, and visual cortices. Meanwhile, we also showed that LGI growth in most cortical regions was positively correlated with the brain volume growth, which is particularly significant in the prefrontal cortex in the first year. In addition, we observed gender differences in both cortical GIs and LGIs in the first 2 years, with the males having larger GIs than females at 2 years of age. This study provides valuable information on normal cortical folding development in infancy and early childhood.

Automatic alignment of genus-zero surfaces

A new algorithm is presented that provides a constructive way to conformally warp a triangular mesh of genus zero to a destination surface with minimal metric deformation, as well as a means to compute automatically a measure of the geometric difference between two surfaces of genus zero. The algorithm takes as input a pair of surfaces that are topological 2-spheres, each surface given by a distinct triangulation. The algorithm then constructs a map $(f)$ between the two surfaces. First, each of the two triangular meshes is mapped to the unit sphere using a discrete conformal mapping algorithm. The two mappings are then composed with a Möbius transformation to generate the function $(f)$. The Möbius transformation is chosen by minimizing an energy that measures the distance of $(f)$ from an isometry. We illustrate our approach using several "real life" data sets. We show first that the algorithm allows for accurate, automatic, and landmark-free nonrigid registration of brain surfaces. We then validate our approach by comparing shapes of proteins. We provide numerical experiments to demonstrate that the distances computed with our algorithm between low-resolution, surface-based representations of proteins are highly correlated with the corresponding distances computed between high-resolution, atomistic models for the same proteins.

The evolution of a disparity decision in human visual cortex

We used fMRI-informed EEG source-imaging in humans to characterize the dynamics of cortical responses during a disparity-discrimination task. After the onset of a disparity-defined target, decision-related activity was found within an extended cortical network that included several occipital regions of interest (ROIs): V4, V3A, hMT+ and the Lateral Occipital Complex (LOC). By using a response-locked analysis, we were able to determine the timing relationships in this network of ROIs relative to the subject's behavioral response. Choice-related activity appeared first in the V4 ROI almost 200 ms before the button press and then subsequently in the V3A ROI. Modeling of the responses in the V4 ROI suggests that this area provides an early contribution to disparity discrimination. Choice-related responses were also found after the button-press in ROIs V4, V3A, LOC and hMT+. Outside the visual cortex, choice-related activity was found in the frontal and temporal poles before the button-press. By combining the spatial resolution of fMRI-informed EEG source imaging with the ability to sort out neural activity occurring before, during and after the behavioral manifestation of the decision, our study is the first to assign distinct functional roles to the extra-striate ROIs involved in perceptual decisions based on disparity, the primary cue for depth.

Fast Geodesic Active Fields for Image Registration Based on Splitting and Augmented Lagrangian Approaches

In this paper, we present an efficient numerical scheme for the recently introduced geodesic active fields (GAF) framework for geometric image registration. This framework considers the registration task as a weighted minimal surface problem. Hence, the data-term and the regularization-term are combined through multiplication in a single, parametrization invariant and geometric cost functional. The multiplicative coupling provides an intrinsic, spatially varying and data-dependent tuning of the regularization strength, and the parametrization invariance allows working with images of nonflat geometry, generally defined on any smoothly parametrizable manifold. The resulting energy-minimizing flow, however, has poor numerical properties. Here, we provide an efficient numerical scheme that uses a splitting approach; data and regularity terms are optimized over two distinct deformation fields that are constrained to be equal via an augmented Lagrangian approach. Our approach is more flexible than standard Gaussian regularization, since one can interpolate freely between isotropic Gaussian and anisotropic TV-like smoothing. In this paper, we compare the geodesic active fields method with the popular Demons method and three more recent state-of-the-art algorithms: NL-optical flow, MRF image registration, and landmark-enhanced large displacement optical flow. Thus, we can show the advantages of the proposed FastGAF method. It compares favorably against Demons, both in terms of registration speed and quality. Over the range of example applications, it also consistently produces results not far from more dedicated state-of-the-art methods, illustrating the flexibility of the proposed framework.

Assessment of brain damage and plasticity in the visual system due to early occipital lesion: comparison of FDG-PET with diffusion MRI tractography

PURPOSE

To determine the relation between glucose metabolic changes of the primary visual cortex, structural abnormalities of the corresponding visual tracts, and visual symptoms in children with Sturge-Weber syndrome (SWS).

MATERIALS AND METHODS

In 10 children with unilateral SWS (ages 1.5-5.5 years), a region-of-interest analysis was applied in the bilateral medial occipital cortex on positron emission tomography (PET) and used to track diffusion-weighted imaging (DWI) streamlines corresponding to the central visual pathway. Normalized streamline volumes of individual SWS patients were compared with values from age-matched control groups as well as correlated with normalized glucose uptakes and visual field deficit.

RESULTS

Lower glucose uptake and lower corresponding streamline volumes were detected in the affected occipital lobe in 9/10 patients, as compared to the contralateral side. Seven of these 9 patients had visual field deficit and normal or decreased streamline volumes on the unaffected side. The two other children had no visual symptoms and showed high contralateral visual streamline volumes. There was a positive correlation between the normalized ratios on DWI and PET, indicating that lower glucose metabolism was associated with lower streamline volume in the affected hemisphere (R = 0.70, P = 0.024).

CONCLUSION

We demonstrated that 18F-flurodeoxyglucose (FDG)-PET combined with DWI tractography can detect both brain damage on the side of the lesion and contralateral plasticity in children with early occipital lesions.

Reconstruction of the human cerebral cortex robust to white matter lesions: method and validation

Cortical atrophy has been reported in a number of diseases, such as multiple sclerosis and Alzheimer's disease, that are also associated with white matter (WM) lesions. However, most cortical reconstruction techniques do not account for these pathologies, thereby requiring additional processing to correct for the effect of WM lesions. In this work, we introduce CRUISE(+), an automated process for cortical reconstruction from magnetic resonance brain images with WM lesions. The process extends previously well validated methods to allow for multichannel input images and to accommodate for the presence of WM lesions. We provide new validation data and tools for measuring the accuracy of cortical reconstruction methods on healthy brains as well as brains with multiple sclerosis lesions. Using this data, we validate the accuracy of CRUISE(+) and compare it to another state-of-the-art cortical reconstruction tool. Our results demonstrate that CRUISE(+) has superior performance in the cortical regions near WM lesions, and similar performance in other regions.

Borders, map clusters, and supra-areal organization in visual cortex

V1 is a canonical cortical area with clearly delineated architectonic boundaries and a continuous topographic representation of the visual hemifield. It thus serves as a touchstone for understanding what new mapping methods can tell us about cortical organization. By parcellating human cortex using local gradients in functional connectivity, Wig et al. (2014--in this issue) detected the V1 border with V2. By contrast, previously-published clustering methods that focus on global similarity in connectivity reveal a supra-areal organization that emphasizes eccentricity bands spanning V1 and its neighboring extrastriate areas; i.e. in the latter analysis, the V1 border is not evident. Thus the focus on local connectivity gradients emphasizes qualitatively different features of cortical organization than are captured by global similarity measures. What is intriguing to consider is that each kind of information might be telling us something unique about cortical organization. Global similarity measures may be detecting map clusters and other supra-areal arrangements that reflect a fundamental level of organization.

Measuring the dynamic longitudinal cortex development in infants by reconstruction of temporally consistent cortical surfaces

Quantitative measurement of the dynamic longitudinal cortex development during early postnatal stages is of great importance to understand the early cortical structural and functional development. Conventional methods usually reconstruct the cortical surfaces of longitudinal images from the same subject independently, which often generate longitudinally-inconsistent cortical surfaces and thus lead to inaccurate measurement of cortical changes, especially for vertex-wise mapping of cortical development. This paper aims to address this problem by presenting a method to reconstruct temporally-consistent cortical surfaces from longitudinal infant brain MR images, for accurate and consistent measurement of the dynamic cortex development in infants. Specifically, the longitudinal development of the inner cortical surface is first modeled by a deformable growth sheet with elasto-plasticity property to establish longitudinally smooth correspondences of the inner cortical surfaces. Then, the modeled longitudinal inner cortical surfaces are jointly deformed to locate both inner and outer cortical surfaces with a spatial-temporal deformable surface method. The method has been applied to 13 healthy infants, each with 6 serial MR scans acquired at 2 weeks, 3 months, 6 months, 9 months, 12 months and 18 months of age. Experimental results showed that our method with the incorporated longitudinal constraints can reconstruct the longitudinally-dynamic cortical surfaces from serial infant MR images more consistently and accurately than the previously published methods. By using our method, for the first time, we can characterize the vertex-wise longitudinal cortical thickness development trajectory at multiple time points in the first 18 months of life. Specifically, we found the highly age-related and regionally-heterogeneous developmental trajectories of the cortical thickness during this period, with the cortical thickness increased most from 3 to 6 months (16.2%) and least from 9 to 12 months (less than 0.1%). Specifically, the central sulcus only underwent significant increase of cortical thickness from 6 to 9 months and the occipital cortex underwent significant increase from 0 to 9 months, while the frontal, temporal and parietal cortices grew continuously in this first 18 months of life. The adult-like spatial patterns of cortical thickness were generally present at 18 months of age. These results provided detailed insights into the dynamic trajectory of the cortical thickness development in infants.

Dynamics and cortical distribution of neural responses to 2D and 3D motion in human

The perception of motion-in-depth is important for avoiding collisions and for the control of vergence eye-movements and other motor actions. Previous psychophysical studies have suggested that sensitivity to motion-in-depth has a lower temporal processing limit than the perception of lateral motion. The present study used functional MRI-informed EEG source-imaging to study the spatiotemporal properties of the responses to lateral motion and motion-in-depth in human visual cortex. Lateral motion and motion-in-depth displays comprised stimuli whose only difference was interocular phase: monocular oscillatory motion was either in-phase in the two eyes (lateral motion) or in antiphase (motion-in-depth). Spectral analysis was used to break the steady-state visually evoked potentials responses down into even and odd harmonic components within five functionally defined regions of interest: V1, V4, lateral occipital complex, V3A, and hMT+. We also characterized the responses within two anatomically defined regions: the inferior and superior parietal cortex. Even harmonic components dominated the evoked responses and were a factor of approximately two larger for lateral motion than motion-in-depth. These responses were slower for motion-in-depth and were largely independent of absolute disparity. In each of our regions of interest, responses at odd-harmonics were relatively small, but were larger for motion-in-depth than lateral motion, especially in parietal cortex, and depended on absolute disparity. Taken together, our results suggest a plausible neural basis for reduced psychophysical sensitivity to rapid motion-in-depth.

Cartography and connectomes

The past 25 years have seen great progress in parcellating the cerebral cortex into a mosaic of many distinct areas in mice, monkeys, and humans. Quantitative studies of interareal connectivity have revealed unexpectedly many pathways and a wide range of connection strengths in mouse and macaque cortex. In humans, advances in analyzing "structural" and "functional" connectivity using powerful but indirect noninvasive neuroimaging methods are yielding intriguing insights about brain circuits, their variability across individuals, and their relationship to behavior.

Automated parcellation of the brain surface generated from magnetic resonance images

We have developed a fast and reliable pipeline to automatically parcellate the cortical surface into sub-regions. The pipeline can be used to study brain changes associated with psychiatric and neurological disorders. First, a genus zero cortical surface for one hemisphere is generated from the magnetic resonance images at the parametric boundary of the white matter and the gray matter. Second, a hemisphere-specific surface atlas is registered to the cortical surface using geometry features mapped in the spherical domain. The deformation field is used to warp statistic labels from the atlas to the subject surface. The Dice index of the labeled surface area is used to evaluate the similarity between the automated labels with the manual labels on the subject. The average Dice across 24 regions on 14 testing subjects is 0.86. Alternative evaluations have also chosen to show the accuracy and flexibility of the present method. The point-wise accuracy of 14 testing subjects is above 86% in average. The experiment shows that the present method is highly consistent with FreeSurfer (>99% of the surface area), using the same set of labels.

3D time series analysis of cell shape using Laplacian approaches

Background

Fundamental cellular processes such as cell movement, division or food uptake critically depend on cells being able to change shape. Fast acquisition of three-dimensional image time series has now become possible, but we lack efficient tools for analysing shape deformations in order to understand the real three-dimensional nature of shape changes.

Results

We present a framework for 3D+time cell shape analysis. The main contribution is three-fold: First, we develop a fast, automatic random walker method for cell segmentation. Second, a novel topology fixing method is proposed to fix segmented binary volumes without spherical topology. Third, we show that algorithms used for each individual step of the analysis pipeline (cell segmentation, topology fixing, spherical parameterization, and shape representation) are closely related to the Laplacian operator. The framework is applied to the shape analysis of neutrophil cells.

Conclusions

The method we propose for cell segmentation is faster than the traditional random walker method or the level set method, and performs better on 3D time-series of neutrophil cells, which are comparatively noisy as stacks have to be acquired fast enough to account for cell motion. Our method for topology fixing outperforms the tools provided by SPHARM-MAT and SPHARM-PDM in terms of their successful fixing rates. The different tasks in the presented pipeline for 3D+time shape analysis of cells can be solved using Laplacian approaches, opening the possibility of eventually combining individual steps in order to speed up computations.

Surface fluid registration of conformal representation: application to detect disease burden and genetic influence on hippocampus

In this paper, we develop a new automated surface registration system based on surface conformal parameterization by holomorphic 1-forms, inverse consistent surface fluid registration, and multivariate tensor-based morphometry (mTBM). First, we conformally map a surface onto a planar rectangle space with holomorphic 1-forms. Second, we compute surface conformal representation by combining its local conformal factor and mean curvature and linearly scale the dynamic range of the conformal representation to form the feature image of the surface. Third, we align the feature image with a chosen template image via the fluid image registration algorithm, which has been extended into the curvilinear coordinates to adjust for the distortion introduced by surface parameterization. The inverse consistent image registration algorithm is also incorporated in the system to jointly estimate the forward and inverse transformations between the study and template images. This alignment induces a corresponding deformation on the surface. We tested the system on Alzheimer's Disease Neuroimaging Initiative (ADNI) baseline dataset to study AD symptoms on hippocampus. In our system, by modeling a hippocampus as a 3D parametric surface, we nonlinearly registered each surface with a selected template surface. Then we used mTBM to analyze the morphometry difference between diagnostic groups. Experimental results show that the new system has better performance than two publicly available subcortical surface registration tools: FIRST and SPHARM. We also analyzed the genetic influence of the Apolipoprotein E[element of]4 allele (ApoE4), which is considered as the most prevalent risk factor for AD. Our work successfully detected statistically significant difference between ApoE4 carriers and non-carriers in both patients of mild cognitive impairment (MCI) and healthy control subjects. The results show evidence that the ApoE genotype may be associated with accelerated brain atrophy so that our work provides a new MRI analysis tool that may help presymptomatic AD research.

Ricci Flow-based Spherical Parameterization and Surface Registration

This paper presents an improved Euclidean Ricci flow method for spherical parameterization. We subsequently invent a scale space processing built upon Ricci energy to extract robust surface features for accurate surface registration. Since our method is based on the proposed Euclidean Ricci flow, it inherits the properties of Ricci flow such as conformality, robustness and intrinsicalness, facilitating efficient and effective surface mapping. Compared with other surface registration methods using curvature or sulci pattern, our method demonstrates a significant improvement for surface registration. In addition, Ricci energy can capture local differences for surface analysis as shown in the experiments and applications.

Computational analysis of LDDMM for brain mapping

One goal of computational anatomy (CA) is to develop tools to accurately segment brain structures in healthy and diseased subjects. In this paper, we examine the performance and complexity of such segmentation in the framework of the large deformation diffeomorphic metric mapping (LDDMM) registration method with reference to atlases and parameters. First we report the application of a multi-atlas segmentation approach to define basal ganglia structures in healthy and diseased kids' brains. The segmentation accuracy of the multi-atlas approach is compared with the single atlas LDDMM implementation and two state-of-the-art segmentation algorithms-Freesurfer and FSL-by computing the overlap errors between automatic and manual segmentations of the six basal ganglia nuclei in healthy subjects as well as subjects with diseases including ADHD and Autism. The high accuracy of multi-atlas segmentation is obtained at the cost of increasing the computational complexity because of the calculations necessary between the atlases and a subject. Second, we examine the effect of parameters on total LDDMM computation time and segmentation accuracy for basal ganglia structures. Single atlas LDDMM method is used to automatically segment the structures in a population of 16 subjects using different sets of parameters. The results show that a cascade approach and using fewer time steps can reduce computational complexity as much as five times while maintaining reliable segmentations.

Deformable medical image registration: a survey

Deformable image registration is a fundamental task in medical image processing. Among its most important applications, one may cite: 1) multi-modality fusion, where information acquired by different imaging devices or protocols is fused to facilitate diagnosis and treatment planning; 2) longitudinal studies, where temporal structural or anatomical changes are investigated; and 3) population modeling and statistical atlases used to study normal anatomical variability. In this paper, we attempt to give an overview of deformable registration methods, putting emphasis on the most recent advances in the domain. Additional emphasis has been given to techniques applied to medical images. In order to study image registration methods in depth, their main components are identified and studied independently. The most recent techniques are presented in a systematic fashion. The contribution of this paper is to provide an extensive account of registration techniques in a systematic manner.

Automatic detection of primary motor areas using diffusion MRI tractography: comparison with functional MRI and electrical stimulation mapping

PURPOSE

As an alternative tool to identify cortical motor areas for planning surgical resection in children with focal epilepsy, the present study proposed a maximum a posteriori probability (MAP) classification of corticospinal tract (CST) visualized by diffusion MR tractography.

METHODS

Diffusion-weighted imaging (DWI) was performed in 17 normally developing children and 20 children with focal epilepsy. An independent component analysis tractography combined with ball-stick model was performed to identify unique CST pathways originating from mouth/lip, finger, and leg areas determined by functional magnetic resonance imaging (fMRI) in healthy children and electrical stimulation mapping (ESM) in children with epilepsy. Group analyses were performed to construct stereotaxic probability maps of primary motor pathways connecting precentral gyrus and posterior limb of internal capsule, and then utilized to design a novel MAP classifier that can sort individual CST fibers associated with three classes of interest: mouth/lip, fingers, and leg. A systematic leave-one-out approach was applied to train an optimal classifier. A match was considered to occur if classified fibers contacted or surrounded true areas localized by fMRI and ESM.

KEY FINDINGS

It was found that the DWI-MAP provided high accuracy for the CST fibers terminating in proximity to the localization of fMRI/ESM: 78%/77% for mouth/lip, 77%/76% for fingers, 78%/86% for leg (contact), and 93%/89% for mouth/lip, 91%/89% for fingers, and 92%/88% for leg (surrounded within 2 cm).

SIGNIFICANCE

This study provides preliminary evidence that in the absence of fMRI and ESM data, the DWI-MAP approach can effectively retrieve the locations of cortical motor areas and underlying CST courses for planning epilepsy surgery.

Inter-subject alignment of human cortical anatomy using functional connectivity

Inter-subject alignment of functional MRI (fMRI) data is necessary for group analyses. The standard approach to this problem matches anatomical features of the brain, such as major anatomical landmarks or cortical curvature. Precise alignment of functional cortical topographies, however, cannot be derived using only anatomical features. We propose a new inter-subject registration algorithm that aligns intra-subject patterns of functional connectivity across subjects. We derive functional connectivity patterns by correlating fMRI BOLD time-series, measured during movie viewing, between spatially remote cortical regions. We validate our technique extensively on real fMRI experimental data and compare our method to two state-of-the-art inter-subject registration algorithms. By cross-validating our method on independent datasets, we show that the derived alignment generalizes well to other experimental paradigms.

Model-driven harmonic parameterization of the cortical surface: HIP-HOP

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 landmark-based registration methods we do not match folds between individuals but instead optimize the fit between cortical sulci and specific iso-coordinate axis in the model. This strategy overcomes some limitation to sulcus-based registration techniques such as topological variability in sulcal landmarks across subjects. Experiments on 62 subjects with manually traced sulci are presented and compared with the result of the Freesurfer software. The evaluation involves a measure of dispersion of sulci with both angular and area distortions. We show that the model-based strategy can lead to a natural, efficient and very fast (less than 5 min per hemisphere) method for defining inter subjects correspondences. We discuss how this approach also reduces the problems inherent to anatomically defined landmarks and open the way to the investigation of cortical organization through the notion of orientation and alignment of structures across the cortex.

Cortical Correspondence via Sulcal Curve-Constrained Spherical Registration with Application to Macaque Studies

In this work, we present a novel cortical correspondence method with application to the macaque brain. The correspondence method is based on sulcal curve constraints on a spherical deformable registration using spherical harmonics to parameterize the spherical deformation. Starting from structural MR images, we first apply existing preprocessing steps: brain tissue segmentation using the Automatic Brain Classification tool (ABC), as well as cortical surface reconstruction and spherical parametrization of the cortical surface via Constrained Laplacian-based Automated Segmentation with Proximities (CLASP). Then, initial correspondence between two cortical surfaces is automatically determined by a curve labeling method using sulcal landmarks extracted along sulcal fundic regions. Since the initial correspondence is limited to sulcal regions, we use spherical harmonics to extrapolate and regularize this correspondence to the entire cortical surface. To further improve the correspondence, we compute a spherical registration that optimizes the spherical harmonic parameterized deformation using a metric that incorporates the error over the sulcal landmarks as well as the normalized cross correlation of sulcal depth maps over the whole cortical surface. For evaluation, a normal 18-months-old macaque brain (for both left and right hemispheres) was matched to a prior macaque brain template with 9 manually labeled, major sulcal curves. The results show successful registration using the proposed registration approach. Evaluation results for optimal parameter settings are presented as well.

Applying tensor-based morphometry to parametric surfaces can improve MRI-based disease diagnosis

Many methods have been proposed for computer-assisted diagnostic classification. Full tensor information and machine learning with 3D maps derived from brain images may help detect subtle differences or classify subjects into different groups. Here we develop a new approach to apply tensor-based morphometry to parametric surface models for diagnostic classification. We use this approach to identify cortical surface features for use in diagnostic classifiers. First, with holomorphic 1-forms, we compute an efficient and accurate conformal mapping from a multiply connected mesh to the so-called slit domain. Next, the surface parameterization approach provides a natural way to register anatomical surfaces across subjects using a constrained harmonic map. To analyze anatomical differences, we then analyze the full Riemannian surface metric tensors, which retain multivariate information on local surface geometry. As the number of voxels in a 3D image is large, sparse learning is a promising method to select a subset of imaging features and to improve classification accuracy. Focusing on vertices with greatest effect sizes, we train a diagnostic classifier using the surface features selected by an L1-norm based sparse learning method. Stability selection is applied to validate the selected feature sets. We tested the algorithm on MRI-derived cortical surfaces from 42 subjects with genetically confirmed Williams syndrome and 40 age-matched controls, multivariate statistics on the local tensors gave greater effect sizes for detecting group differences relative to other TBM-based statistics including analysis of the Jacobian determinant and the largest eigenvalue of the surface metric. Our method also gave reasonable classification results relative to the Jacobian determinant, the pair of eigenvalues of the Jacobian matrix and volume features. This analysis pipeline may boost the power of morphometry studies, and may assist with image-based classification.