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

Hierarchical particle optimization for cortical shape correspondence in temporal lobe resection

BACKGROUND

Anterior temporal lobe resection is an effective treatment for temporal lobe epilepsy. The post-surgical structural changes could influence the follow-up treatment. Capturing post-surgical changes necessitates a well-established cortical shape correspondence between pre- and post-surgical surfaces. Yet, most cortical surface registration methods are designed for normal neuroanatomy. Surgical changes can introduce wide ranging artifacts in correspondence, for which conventional surface registration methods may not work as intended.

METHODS

In this paper, we propose a novel particle method for one-to-one dense shape correspondence between pre- and post-surgical surfaces with temporal lobe resection. The proposed method can handle partial structural abnormality involving non-rigid changes. Unlike existing particle methods using implicit particle adjacency, we consider explicit particle adjacency to establish a smooth correspondence. Moreover, we propose hierarchical optimization of particles rather than full optimization of all particles at once to avoid trappings of locally optimal particle update.

RESULTS

We evaluate the proposed method on 25 pairs of T1-MRI with pre- and post-simulated resection on the anterior temporal lobe and 25 pairs of patients with actual resection. We show improved accuracy over several cortical regions in terms of ROI boundary Hausdorff distance with 4.29 mm and Dice similarity coefficients with average value 0.841, compared to existing surface registration methods on simulated data. In 25 patients with actual resection of the anterior temporal lobe, our method shows an improved shape correspondence in qualitative and quantitative evaluation on parcellation-off ratio with average value 0.061 and cortical thickness changes. We also show better smoothness of the correspondence without self-intersection, compared with point-wise matching methods which show various degrees of self-intersection.

CONCLUSION

The proposed method establishes a promising one-to-one dense shape correspondence for temporal lobe resection. The resulting correspondence is smooth without self-intersection. The proposed hierarchical optimization strategy could accelerate optimization and improve the optimization accuracy. According to the results on the paired surfaces with temporal lobe resection, the proposed method outperforms the compared methods and is more reliable to capture cortical thickness changes.

Statistical shape analysis of the tricuspid valve in hypoplastic left heart sydrome

Hypoplastic left heart syndrome (HLHS) is a congenital heart disease characterized by incomplete development of the left heart. Children with HLHS undergo a series of operations which result in the tricuspid valve (TV) becoming the only functional atrioventricular valve. Some of those patients develop tricuspid regurgitation which is associated with heart failure and death and necessitates further surgical intervention. Repair of the regurgitant TV, and understanding the connections between structure and function of this valve remains extremely challenging. Adult cardiac populations have used 3D echocardiography (3DE) combined with computational modeling to better understand cardiac conditions affecting the TV. However, these structure-function analyses rely on simplistic point-based techniques that do not capture the leaflet surface in detail, nor do they allow robust comparison of shapes across groups. We propose using statistical shape modeling and analysis of the TV using Spherical Harmonic Representation Point Distribution Models (SPHARM-PDM) in order to generate a reproducible representation, which in turn enables high dimensional low sample size statistical analysis techniques such as principal component analysis and distance weighted discrimination. Our initial results suggest that visualization of the differences in regurgitant vs. non-regurgitant valves can precisely locate populational structural differences as well as how an individual regurgitant valve differs from the mean shape of functional valves. We believe that these results will support the creation of modern image-based modeling tools, and ultimately increase the understanding of the relationship between valve structure and function needed to inform and improve surgical planning in HLHS.

Labeling lateral prefrontal sulci using spherical data augmentation and context-aware training

The inference of cortical sulcal labels often focuses on deep (primary and secondary) sulcal regions, whereas shallow (tertiary) sulcal regions are largely overlooked in the literature due to the scarcity of manual/well-defined annotations and their large neuroanatomical variability. In this paper, we present an automated framework for regional labeling of both primary/secondary and tertiary sulci of the dorsal portion of lateral prefrontal cortex (LPFC) using spherical convolutional neural networks. We propose two core components that enhance the inference of sulcal labels to overcome such large neuroanatomical variability: (1) surface data augmentation and (2) context-aware training. (1) To take into account neuroanatomical variability, we synthesize training data from the proposed feature space that embeds intermediate deformation trajectories of spherical data in a rigid to non-rigid fashion, which bridges an augmentation gap in conventional rotation data augmentation. (2) Moreover, we design a two-stage training process to improve labeling accuracy of tertiary sulci by informing the biological associations in neuroanatomy: inference of primary/secondary sulci and then their spatial likelihood to guide the definition of tertiary sulci. In the experiments, we evaluate our method on 13 deep and shallow sulci of human LPFC in two independent data sets with different age ranges: pediatric (N=60) and adult (N=36) cohorts. We compare the proposed method with a conventional multi-atlas approach and spherical convolutional neural networks without/with rotation data augmentation. In both cohorts, the proposed data augmentation improves labeling accuracy of deep and shallow sulci over the baselines, and the proposed context-aware training offers further improvement in the labeling of shallow sulci over the proposed data augmentation. We share our tools with the field and discuss applications of our results for understanding neuroanatomical-functional organization of LPFC and the rest of cortex (https://github.com/ilwoolyu/SphericalLabeling).

Validation of Group-wise Registration for Surface-based Functional MRI Analysis

Resting-state functional MRI (rsfMRI) provides important information for studying and mapping the activities and functions of the brain. Conventionally, rsfMRIs are often registered to structural images in the Euclidean space without considering cortical surface geometry. Meanwhile, a surface-based representation offers a relaxed coordinate chart, but this still requires surface registration for group-wise data analysis. In this work, we investigate the performance of two existing surface registration methods in a surface-based rsfMRI analysis framework: FreeSurfer and Hierarchical Spherical Deformation (HSD). To minimize registration bias, we establish shape correspondence using both methods in a group-wise manner that estimates the unbiased average of a given cohort. To evaluate their performance, we focus on neuroanatomical alignment as well as the amount of distortion that can potentially bias surface tessellation for secondary level rsfMRI data analyses. In the pilot analysis, we examine a single timepoint of imaging data from 100 subjects out of an aging cohort. Overall, HSD establishes improved shape correspondence with reduced mean curvature deviation (10.94% less on average per subject, paired t-test: p <10-10) and reduced registration distortion (FreeSurfer: average 41.91% distortion per subject, HSD: 18.63%, paired t-test: p <10-10). Furthermore, HSD introduces less distortion than FreeSurfer in the areas identified in the individual components that were extracted by surface-based independent component analysis (ICA) after spatial smoothing and time series normalization. Consequently, we show that FreeSurfer capture individual components with globally similar but locally different patterns in ICA in visual inspection.

Establishing Surface Correspondence for Post-surgical Cortical Thickness Changes in Temporal Lobe Epilepsy

In pre- and post-surgical surface shape analysis, establishing shape correspondence is necessary to investigate the postoperative surface changes. However, structural absence after the operation accompanies focal non-rigid changes, which leads to challenges in existing surface registration methods. In this paper, we present a fully automatic particle-based method to establish surface correspondence that can handle partial structural abnormality in the temporal lobe resection. Our method optimizes the coordinates of points which are modeled as particles on surfaces in a hierarchical way to reduce a chance of being trapped in a local minimum during the optimization. In the experiments, we evaluate the effectiveness of our method in comparison with conventional spherical registration (FreeSurfer) on two scenarios: cortical thickness changes in healthy controls within a short scan-rescan time window and patients with temporal lobe resection. The post-surgical scan is acquired at least 1 year after the presurgical scan. In region of interest-wise (ROI-wise) analysis, no changes on cortical thickness are found in both methods on the healthy control group. In patients, since there is no ground truth available, we instead investigated the disagreement between our method and FreeSurfer. We see poorly matched ROIs and large cortical thickness changes using FreeSurfer. On the contrary, our method shows well-matched ROIs and subtle cortical thickness changes. This suggests that the proposed method can establish a stable shape correspondence, which is not fully captured in a conventional spherical registration.

Registration quality filtering improves robustness of voxel-wise analyses to the choice of brain template

Motivation:

Many clinical and scientific conclusions that rely on voxel-wise analyses of neuroimaging depend on the accurate comparison of corresponding anatomical regions. Such comparisons are made possible by registration of the images of subjects of interest onto a common brain template, such as the Johns Hopkins University (JHU) template. However, current image registration algorithms are prone to errors that are distributed in a template-dependent manner. Therefore, the results of voxel-wise analyses can be sensitive to template choice. Despite this problem, the issue of appropriate template choice for voxel-wise analyses is not generally addressed in contemporary neuroimaging studies, which may lead to the reporting of spurious results.

Results:

We present a novel approach to determine the suitability of a brain template for voxel-wise analysis. The approach is based on computing a “distance” between automatically-generated atlases of the subjects of interest and templates that is indicative of the extent of subject-to-template registration errors. This allows for the filtering of subjects and candidate templates based on a quantitative measure of registration quality. We benchmark our approach by evaluating alternative templates for a voxel-wise analysis that reproduces the well-known decline in fractional anisotropy (FA) with age. Our results show that filtering registrations minimizes errors and decreases the sensitivity of voxel-wise analysis to template choice. In addition to carrying important implications for future neuroimaging studies, the developed framework of template induction can be used to evaluate robustness of data analysis methods to template choice.

Hierarchical spherical deformation for cortical surface registration

We present hierarchical spherical deformation for a group-wise shape correspondence to address template selection bias and to minimize registration distortion. In this work, we aim at a continuous and smooth deformation field to guide accurate cortical surface registration. In conventional spherical registration methods, a global rigid alignment and local deformation are independently performed. Motivated by the composition of precession and intrinsic rotation, we simultaneously optimize global rigid rotation and non-rigid local deformation by utilizing spherical harmonics interpolation of local composite rotations in a single framework. To this end, we indirectly encode local displacements by such local composite rotations as functions of spherical locations. Furthermore, we introduce an additional regularization term to the spherical deformation, which maximizes its rigidity while reducing registration distortion. To improve surface registration performance, we employ the second order approximation of the energy function that enables fast convergence of the optimization. In the experiments, we validate our method on healthy normal subjects with manual cortical surface parcellation in registration accuracy and distortion. We show an improved shape correspondence with high accuracy in cortical surface parcellation and significantly low registration distortion in surface area and edge length. In addition to validation, we discuss parameter tuning, optimization, and implementation design with potential acceleration.

Improving human cortical sulcal curve labeling in large scale cross-sectional MRI using deep neural networks

BACKGROUND

Human cortical primary sulci are relatively stable landmarks and commonly observed across the population. Despite their stability, the primary sulci exhibit phenotypic variability.

NEW METHOD

We propose a fully automated pipeline that integrates both sulcal curve extraction and labeling. In this study, we use a large normal control population (n = 1424) to train neural networks for accurately labeling the primary sulci. Briefly, we use sulcal curve distance map, surface parcellation, mean curvature and spectral features to delineate their sulcal labels. We evaluate the proposed method with 8 primary sulcal curves in the left and right hemispheres compared to an established multi-atlas curve labeling method.

RESULTS

Sulcal labels by the proposed method reasonably well agree with manual labeling. The proposed method outperforms the existing multi-atlas curve labeling method.

COMPARISON WITH EXISTING METHOD

Significantly improved sulcal labeling results are achieved with over 12.5 and 20.6 percent improvement on labeling accuracy in the left and right hemispheres, respectively compared to that of a multi-atlas curve labeling method in eight curves (p≪0.001, two-sample t-test).

CONCLUSION

The proposed method offers a computationally efficient and robust labeling of major sulci.

SlicerSALT: Shape AnaLysis Toolbox

SlicerSALT is an open-source platform for disseminating state-of-the-art methods for performing statistical shape analysis. These methods are developed as 3D Slicer extensions to take advantage of its powerful underlying libraries. SlicerSALT itself is a heavily customized 3D Slicer package that is designed to be easy to use for shape analysis researchers. The packaged methods include powerful techniques for creating and visualizing shape representations as well as performing various types of analysis.

Hierarchical Spherical Deformation for Shape Correspondence

We present novel spherical deformation for a landmark-free shape correspondence in a group-wise manner. In this work, we aim at both addressing template selection bias and minimizing registration distortion in a single framework. The proposed spherical deformation yields a non-rigid deformation field without referring to any particular spherical coordinate system. Specifically, we extend a rigid rotation represented by well-known Euler angles to general non-rigid local deformation via spatial-varying Euler angles. The proposed method employs spherical harmonics interpolation of the local displacements to simultaneously solve rigid and non-rigid local deformation during the optimization. This consequently leads to a continuous, smooth, and hierarchical representation of the deformation field that minimizes registration distortion. In addition, the proposed method is group-wise registration that requires no specific template to establish a shape correspondence. In the experiments, we show an improved shape correspondence with high accuracy in cortical surface parcellation as well as significantly low registration distortion in surface area and edge length compared to the existing registration methods while achieving fast registration in 3 mins per subject.

TRACE: A Topological Graph Representation for Automatic Sulcal Curve Extraction

A proper geometric representation of the cortical regions is a fundamental task for cortical shape analysis and landmark extraction. However, a significant challenge has arisen due to the highly variable, convoluted cortical folding patterns. In this paper, we propose a novel topological graph representation for automatic sulcal curve extraction (TRACE). In practice, the reconstructed surface suffers from noise influences introduced during image acquisition/surface reconstruction. In the presence of noise on the surface, TRACE determines stable sulcal fundic regions by employing the line simplification method that prevents the sulcal folding pattern from being significantly smoothed out. The sulcal curves are then traced over the connected graph in the determined regions by the Dijkstra's shortest path algorithm. For validation, we used the state-of-the-art surface reconstruction pipelines on a reproducibility data set. The experimental results showed higher reproducibility and robustness to noise in TRACE than the existing method (Li et al. 2010) with over 20% relative improvement in error for both surface reconstruction pipelines. In addition, the extracted sulcal curves by TRACE were well-aligned with manually delineated primary sulcal curves. We also provided a choice of parameters to control quality of the extracted sulcal curves and showed the influences of the parameter selection on the resulting curves.

A cortical shape-adaptive approach to local gyrification index

The amount of cortical folding, or gyrification, is typically measured within local cortical regions covered by an equidistant geodesic or nearest neighborhood-ring kernel. However, without careful design, such a kernel can easily cover multiple sulcal and gyral regions that may not be functionally related. Furthermore, this can result in smoothing out details of cortical folding, which consequently blurs local gyrification measurements. In this paper, we propose a novel kernel shape to locally quantify cortical gyrification within sulcal and gyral regions. We adapt wavefront propagation to generate a spatially varying kernel shape that encodes cortical folding patterns: neighboring gyral crowns, sulcal fundi, and sulcal banks. For this purpose, we perform anisotropic wavefront propagation that runs fast along gyral crowns and sulcal fundi by solving a static Hamilton-Jacobi partial differential equation. The resulting kernel adaptively elongates along gyral crowns and sulcal fundi, while keeping a uniform shape over flat regions like sulcal banks. We then measure local gyrification within the proposed spatially varying kernel. The experimental results show that the proposed kernel-based gyrification measure achieves a higher reproducibility than the conventional method in a multi-scan dataset. We further apply the proposed kernel to a brain development study in the early postnatal phase from neonate to 2 years of age. In this study we find that our kernel yields both positive and negative associations of gyrification with age, whereas the conventional method only captures positive associations. In general, our method yields sharper and more detailed statistical maps that associate cortical folding with sex and gestational age.

Constructing Statistically Unbiased Cortical Surface Templates Using Feature-Space Covariance

The choice of surface template plays an important role in cross-sectional subject analyses involving cortical brain surfaces because there is a tendency toward registration bias given variations in inter-individual and inter-group sulcal and gyral patterns. In order to account for the bias and spatial smoothing, we propose a feature-based unbiased average template surface. In contrast to prior approaches, we factor in the sample population covariance and assign weights based on feature information to minimize the influence of covariance in the sampled population. The mean surface is computed by applying the weights obtained from an inverse covariance matrix, which guarantees that multiple representations from similar groups (e.g., involving imaging, demographic, diagnosis information) are down-weighted to yield an unbiased mean in feature space. Results are validated by applying this approach in two different applications. For evaluation, the proposed unbiased weighted surface mean is compared with un-weighted means both qualitatively and quantitatively (mean squared error and absolute relative distance of both the means with baseline). In first application, we validated the stability of the proposed optimal mean on a scan-rescan reproducibility dataset by incrementally adding duplicate subjects. In the second application, we used clinical research data to evaluate the difference between the weighted and unweighted mean when different number of subjects were included in control versus schizophrenia groups. In both cases, the proposed method achieved greater stability that indicated reduced impacts of sampling bias. The weighted mean is built based on covariance information in feature space as opposed to spatial location, thus making this a generic approach to be applicable to any feature of interest.

Group-wise Shape Correspondence of Variable and Complex Objects

We present a group-wise shape correspondence method for analyzing variable and complex objects in a population study. The proposed method begins with the standard spherical harmonics (SPHARM) point distribution models (PDM) with their spherical mappings. In case of complex and variable objects, the equal area spherical mapping based SPHARM correspondence is imperfect. For such objects, we present here a novel group-wise correspondence. As an example dataset, we use 12 second mandibular molars representing 6 living or fossil euarchontan species. To improve initial correspondence of the SPHARM-PDM representation, we first apply a rigid transformation on each subject using five well-known landmarks (molar cusps). We further enhance the correspondence by optimizing landmarks (local) and multidimensional geometric property (global) over each subject with spherical harmonic representation. The resulting average shape model better captures sharp landmark representation in quantitative evaluation as well as a nice separation of different species compared with that of the SPHARM-PDM method.

Multimodal surface matching with higher-order smoothness constraints

In brain imaging, accurate alignment of cortical surfaces is fundamental to the statistical sensitivity and spatial localisation of group studies, and cortical surface-based alignment has generally been accepted to be superior to volume-based approaches at aligning cortical areas. However, human subjects have considerable variation in cortical folding, and in the location of functional areas relative to these folds. This makes alignment of cortical areas a challenging problem. The Multimodal Surface Matching (MSM) tool is a flexible, spherical registration approach that enables accurate registration of surfaces based on a variety of different features. Using MSM, we have previously shown that driving cross-subject surface alignment, using areal features, such as resting state-networks and myelin maps, improves group task fMRI statistics and map sharpness. However, the initial implementation of MSM's regularisation function did not penalize all forms of surface distortion evenly. In some cases, this allowed peak distortions to exceed neurobiologically plausible limits, unless regularisation strength was increased to a level which prevented the algorithm from fully maximizing surface alignment. Here we propose and implement a new regularisation penalty, derived from physically relevant equations of strain (deformation) energy, and demonstrate that its use leads to improved and more robust alignment of multimodal imaging data. In addition, since spherical warps incorporate projection distortions that are unavoidable when mapping from a convoluted cortical surface to the sphere, we also propose constraints that enforce smooth deformation of cortical anatomies. We test the impact of this approach for longitudinal modelling of cortical development for neonates (born between 31 and 43 weeks of post-menstrual age) and demonstrate that the proposed method increases the biological interpretability of the distortion fields and improves the statistical significance of population-based analysis relative to other spherical methods.