Geometrically accurate topology-correction of cortical surfaces using nonseparating loops.

In this paper, we focus on the retrospective topology correction of surfaces. We propose a technique to accurately correct the spherical topology of cortical surfaces. Specifically, we construct a mapping from the original surface onto the sphere to detect topological defects as minimal nonhomeomorphic regions. The topology of each defect is then corrected by opening and sealing the surface along a set of nonseparating loops that are selected in a Bayesian framework. The proposed method is a wholly self-contained topology correction algorithm, which determines geometrically accurate, topologically correct solutions based on the magnetic resonance imaging (MRI) intensity profile and the expected local curvature. Applied to real data, our method provides topological corrections similar to those made by a trained operator.

Cortical surface shape analysis based on spherical wavelets.

In vivo quantification of neuroanatomical shape variations is possible due to recent advances in medical imaging and has proven useful in the study of neuropathology and neurodevelopment. In this paper, we apply a spherical wavelet transformation to extract shape features of cortical surfaces reconstructed from magnetic resonance images (MRIs) of a set of subjects. The spherical wavelet transformation can characterize the underlying functions in a local fashion in both space and frequency, in contrast to spherical harmonics that have a global basis set. We perform principal component analysis (PCA) on these wavelet shape features to study patterns of shape variation within normal population from coarse to fine resolution. In addition, we study the development of cortical folding in newborns using the Gompertz model in the wavelet domain, which allows us to characterize the order of development of large-scale and finer folding patterns independently. Given a limited amount of training data, we use a regularization framework to estimate the parameters of the Gompertz model to improve the prediction performance on new data. We develop an efficient method to estimate this regularized Gompertz model based on the Broyden-Fletcher-Goldfarb-Shannon (BFGS) approximation. Promising results are presented using both PCA and the folding development model in the wavelet domain. The cortical folding development model provides quantitative anatomic information regarding macroscopic cortical folding development and may be of potential use as a biomarker for early diagnosis of neurologic deficits in newborns.

Active-contour-based image segmentation using machine learning techniques.

We introduce a non-linear shape prior for the deformable model framework that we learn from a set of shape samples using recent manifold learning techniques. We model a category of shapes as a finite dimensional manifold which we approximate using Diffusion maps. Our method computes a Delaunay triangulation of the reduced space, considered as Euclidean, and uses the resulting space partition to identify the closest neighbors of any given shape based on its Nyström extension. We derive a non-linear shape prior term designed to attract a shape towards the shape prior manifold at given constant embedding. Results on shapes of ventricle nuclei demonstrate the potential of our method for segmentation tasks.

Cortical Surface Shape Analysis Based on Spherical Wavelet Transformation.

Shape analysis of neuroanatomical structures has proven useful in the study of neuropathology and neurodevelopment. Advances in medical imaging have made it possible to study this shape variation in vivo. In this paper, we propose the use of a spherical wavelet transformation to extract cortical surface shape features, as wavelets can characterize the underlying functions in a local fashion in both space and frequency. Our results demonstrate the utility of the wavelet approach in both detecting the spatial scale and pattern of shape variation in synthetic data, and for quantifying and visualizing shape variations of cortical surface models in subject populations.

An automated labeling system for subdividing the human cerebral cortex on MRI scans into gyral based regions of interest.

In this study, we have assessed the validity and reliability of an automated labeling system that we have developed for subdividing the human cerebral cortex on magnetic resonance images into gyral based regions of interest (ROIs). Using a dataset of 40 MRI scans we manually identified 34 cortical ROIs in each of the individual hemispheres. This information was then encoded in the form of an atlas that was utilized to automatically label ROIs. To examine the validity, as well as the intra- and inter-rater reliability of the automated system, we used both intraclass correlation coefficients (ICC), and a new method known as mean distance maps, to assess the degree of mismatch between the manual and the automated sets of ROIs. When compared with the manual ROIs, the automated ROIs were highly accurate, with an average ICC of 0.835 across all of the ROIs, and a mean distance error of less than 1 mm. Intra- and inter-rater comparisons yielded little to no difference between the sets of ROIs. These findings suggest that the automated method we have developed for subdividing the human cerebral cortex into standard gyral-based neuroanatomical regions is both anatomically valid and reliable. This method may be useful for both morphometric and functional studies of the cerebral cortex as well as for clinical investigations aimed at tracking the evolution of disease-induced changes over time, including clinical trials in which MRI-based measures are used to examine response to treatment.

Quantitative evaluation of automated skull-stripping methods applied to contemporary and legacy images: effects of diagnosis, bias correction, and slice location.

Performance of automated methods to isolate brain from nonbrain tissues in magnetic resonance (MR) structural images may be influenced by MR signal inhomogeneities, type of MR image set, regional anatomy, and age and diagnosis of subjects studied. The present study compared the performance of four methods: Brain Extraction Tool (BET; Smith [2002]: Hum Brain Mapp 17:143-155); 3dIntracranial (Ward [1999] Milwaukee: Biophysics Research Institute, Medical College of Wisconsin; in AFNI); a Hybrid Watershed algorithm (HWA, Segonne et al. [2004] Neuroimage 22:1060-1075; in FreeSurfer); and Brain Surface Extractor (BSE, Sandor and Leahy [1997] IEEE Trans Med Imag 16:41-54; Shattuck et al. [2001] Neuroimage 13:856-876) to manually stripped images. The methods were applied to uncorrected and bias-corrected datasets; Legacy and Contemporary T1-weighted image sets; and four diagnostic groups (depressed, Alzheimer's, young and elderly control). To provide a criterion for outcome assessment, two experts manually stripped six sagittal sections for each dataset in locations where brain and nonbrain tissue are difficult to distinguish. Methods were compared on Jaccard similarity coefficients, Hausdorff distances, and an Expectation-Maximization algorithm. Methods tended to perform better on contemporary datasets; bias correction did not significantly improve method performance. Mesial sections were most difficult for all methods. Although AD image sets were most difficult to strip, HWA and BSE were more robust across diagnostic groups compared with 3dIntracranial and BET. With respect to specificity, BSE tended to perform best across all groups, whereas HWA was more sensitive than other methods. The results of this study may direct users towards a method appropriate to their T1-weighted datasets and improve the efficiency of processing for large, multisite neuroimaging studies.

A genetic algorithm for the topology correction of cortical surfaces.

We propose a technique to accurately correct the spherical topology of cortical surfaces. We construct a mapping from the original surface onto the sphere to detect topological defects as minimal non-homeomorphic regions. A genetic algorithm corrects each defect by finding the maximum-a-posteriori retessellation in a Bayesian framework. During the genetic search, incorrect vertices are iteratively identified and eliminated, while the optimal retessellation is constructed. Applied to synthetic and real data, our method generates optimal topological corrections with only a few iterations.

Metallic electrodes and leads in simultaneous EEG-MRI: specific absorption rate (SAR) simulation studies.

The purpose of this study was to investigate the changes in specific absorption rate (SAR) in human-head tissues while using nonmagnetic metallic electroencephalography (EEG) electrodes and leads during magnetic resonance imaging (MRI). A realistic, high resolution (1 mm(3)) head model from individual MRI data was adopted to describe accurately thin tissues, such as bone marrow and skin. The RF power dissipated in the human head was evaluated using the FDTD algorithm. Both surface and bird cage coils were used. The following numbers of EEG electrodes/leads were considered: 16, 31, 62, and 124. Simulations were performed at 128 and 300 MHz. The difference in SAR between the electrodes/leads and no-electrodes conditions was greater with the bird cage coil than with the surface coil. The peak 1 g averaged SAR values were highest at 124 electrodes, increasing to as much as two orders of magnitude (x172.3) at 300 MHz compared to the original value. At 300 MHz, there was a fourfold (x3.6) increase of SAR averaged over the bone marrow, and a sevenfold (x7.4) increase in the skin. At 128 MHz, there was a fivefold (x5.6) increase of whole head SAR. Head models were obtained from two different subjects, with an inter-subject whole head SAR variability of 3%. .

Sequence-independent segmentation of magnetic resonance images.

We present a set of techniques for embedding the physics of the imaging process that generates a class of magnetic resonance images (MRIs) into a segmentation or registration algorithm. This results in substantial invariance to acquisition parameters, as the effect of these parameters on the contrast properties of various brain structures is explicitly modeled in the segmentation. In addition, the integration of image acquisition with tissue classification allows the derivation of sequences that are optimal for segmentation purposes. Another benefit of these procedures is the generation of probabilistic models of the intrinsic tissue parameters that cause MR contrast (e.g., T1, proton density, T2*), allowing access to these physiologically relevant parameters that may change with disease or demographic, resulting in nonmorphometric alterations in MR images that are otherwise difficult to detect. Finally, we also present a high band width multiecho FLASH pulse sequence that results in high signal-to-noise ratio with minimal image distortion due to B0 effects. This sequence has the added benefit of allowing the explicit estimation of T2* and of reducing test-retest intensity variability.

Automatically parcellating the human cerebral cortex.

We present a technique for automatically assigning a neuroanatomical label to each location on a cortical surface model based on probabilistic information estimated from a manually labeled training set. This procedure incorporates both geometric information derived from the cortical model, and neuroanatomical convention, as found in the training set. The result is a complete labeling of cortical sulci and gyri. Examples are given from two different training sets generated using different neuroanatomical conventions, illustrating the flexibility of the algorithm. The technique is shown to be comparable in accuracy to manual labeling.

Variational, geometric, and statistical methods for modeling brain anatomy and function.

We survey the recent activities of the Odyssée Laboratory in the area of the application of mathematics to the design of models for studying brain anatomy and function. We start with the problem of reconstructing sources in MEG and EEG, and discuss the variational approach we have developed for solving these inverse problems. This motivates the need for geometric models of the head. We present a method for automatically and accurately extracting surface meshes of several tissues of the head from anatomical magnetic resonance (MR) images. Anatomical connectivity can be extracted from diffusion tensor magnetic resonance images but, in the current state of the technology, it must be preceded by a robust estimation and regularization stage. We discuss our work based on variational principles and show how the results can be used to track fibers in the white matter (WM) as geodesics in some Riemannian space. We then go to the statistical modeling of functional magnetic resonance imaging (fMRI) signals from the viewpoint of their decomposition in a pseudo-deterministic and stochastic part that we then use to perform clustering of voxels in a way that is inspired by the theory of support vector machines and in a way that is grounded in information theory. Multimodal image matching is discussed next in the framework of image statistics and partial differential equations (PDEs) with an eye on registering fMRI to the anatomy. The paper ends with a discussion of a new theory of random shapes that may prove useful in building anatomical and functional atlases.