Three-dimensional visualization of protein expression in mouse brain structures using imaging mass spectrometry

We have developed a method to visualize matrix-assisted laser desorption ionization imaging mass spectrometry (MALDI IMS) data aligned with optically determinable tissue structures in three dimensions. Details of the methodology are exemplified using the 3-D reconstruction of myelin basic protein (MBP) in the corpus callosum of a mouse brain. In this procedure, optical images obtained from serial coronal sections are first aligned to each other to reconstruct a surface of the corpus callosum from segmented contours of the aligned images. The MALDI IMS data are then coregistered to the optical images and superimposed into the surface to create the final 3-D visualization. Correlating proteomic data with anatomical structures provides a more comprehensive understanding of healthy and pathological brain functions, and holds promise to be utilized in more complex anatomical arrangements.     

A nonrigid registration algorithm for longitudinal breast MR images and the analysis of breast tumor response

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) can estimate parameters relating to blood flow and tissue volume fractions and therefore may be used to characterize the response of breast tumors to treatment. To assess treatment response, values of these DCE-MRI parameters are observed at different time points during the course of treatment. We propose a method whereby DCE-MRI data sets obtained in separate imaging sessions can be co-registered to a common image space, thereby retaining spatial information so that serial DCE-MRI parameter maps can be compared on a voxel-by-voxel basis. In performing inter-session breast registration, one must account for patient repositioning and breast deformation, as well as changes in tumor shape and volume relative to other imaging sessions. One challenge is to optimally register the normal tissues while simultaneously preventing tumor distortion. We accomplish this by extending the adaptive bases algorithm through adding a tumor-volume preserving constraint in the cost function. We also propose a novel method to generate the simulated breast magnetic resonance (MR) images, which can be used to evaluate the proposed registration algorithm quantitatively. The proposed nonrigid registration algorithm is applied to both simulated and real longitudinal 3D high resolution MR images and the obtained transformations are then applied to lower resolution physiological parameter maps obtained via DCE-MRI. The registration results demonstrate the proposed algorithm can successfully register breast MR images acquired at different time points and allow for analysis of the registered parameter maps.     

Characterizing changes in MR images with color-coded Jacobians

Image registration is the process of establishing spatial correspondence between two images or between two image volumes. Registration can be achieved by rigid, elastic, or a combination of rigid and elastic transforms that attempt to bring the two images into coincidence. A rigid transform accounts for differences in positioning and an elastic transform describes deformations due to differences in tissue properties, temporal changes due to growth or atrophy, or differences between individuals. Deformation-based morphometry uses the resulting deformation fields from these transforms to evaluate differences between the images being registered. Three methods of registration were evaluated: rigid (affine) transformation, elastic optical flow transformation, and elastic spline transformation. All three methods produce vector deformation fields that map each point in one image to a point in the other image. A 12-color map of the transformation Jacobian was used to represent local volume changes. Using the three registration methods, color-mapped Jacobians were determined using a simulated three-dimensional block with known translation, rotation, expansion, contraction, and intensity modulations. Color-coded Jacobians were also generated for experimentally measured magnetic resonance image volumes of water-filled balloons and 7-year-old twin boys. Color-coded Jacobians overlaid on anatomical images provide a convenient method to identify regional tissue expansion and contraction.     

The discretized flow on domains of attraction: a structural stability result

It is well known that, for stepsize sufficiently small, compactattractors of ordinary differential equations persist underdiscretization. The present paper describes the structure ofthe discrete-time dynamical system obtained via discretizationon A(M_h)\M_h where M_h is the approximate attractor and A(M_h)is its domain of attraction. The existence of a smooth embeddinginto a continuous-time parallelizable flow is proved. The constructioncan be used to define sections for discretizations and can beinterpreted as a justification of the method of modified equations.     

Effect of nonrigid registration algorithms on deformation-based morphometry: a comparative study with control and Williams syndrome subjects

Deformation-based morphometry (DBM) is a widely used method for characterizing anatomical differences across groups. DBM is based on the analysis of the deformation fields generated by nonrigid registration algorithms, which warp the individual volumes to a DBM atlas. Although several studies have compared nonrigid registration algorithms for segmentation tasks, few studies have compared the effect of the registration algorithms on group differences that may be uncovered through DBM. In this study, we compared group atlas creation and DBM results obtained with five well-established nonrigid registration algorithms using 13 subjects with Williams syndrome and 13 normal control subjects. The five nonrigid registration algorithms include the following: (1) the adaptive bases algorithm, (2) the image registration toolkit, (3) The FSL nonlinear image registration tool, (4) the automatic registration tool, and (5) the normalization algorithm available in Statistical Parametric Mapping (SPM8). Results indicate that the choice of algorithm has little effect on the creation of group atlases. However, regions of differences between groups detected with DBM vary from algorithm to algorithm both qualitatively and quantitatively. Some regions are detected by several algorithms, but their extent varies. Others are detected only by a subset of the algorithms. Based on these results, we recommend using more than one algorithm when performing DBM studies.     

Enhancement of histological volumes through averaging and their use for the analysis of magnetic resonance images

Magnetic resonance imaging (MRI) of small animals is routinely performed in research centers. But despite its many advantages, MR still suffers from limited spatial resolution which makes the interpretation and quantitative analysis of the images difficult, particularly for small structures of interest within areas of significant heterogeneity. One possibility to address this issue is to complement the MR images with histological data, which requires reconstructing 3D volumes from a series of 2D images. A number of methods have been proposed recently in the literature to address this issue, but deformation or tearing during the slicing process often produces reconstructed volumes with visible artifacts and imperfections. In this paper, we show that a possible solution to this problem is to work with several histological volumes, reconstruct each of these separately and then compute an average. The resulting histological atlas shows structures and substructures more clearly than any individual volume. We also propose an original approach to normalize intensity values across slices, a required preprocessing step when reconstructing histological volumes. We show that the histological atlas we have created can be used to localize structures and substructures, which cannot be seen easily in MR images. We also create an MR atlas that is associated with the histological atlas. We show that using the histological volumes to create the MR atlas is better than using the MR volumes only. Finally, we validate our approach quantitatively on MR image volumes by comparing volumetric measurements obtained manually and obtained automatically with our atlases.     

Computer-generated fMRI phantoms with motion-distortion interaction

As an extension of previous work on computer-generated phantoms, more accurate, realistic phantoms are generated by integrating image distortion and signal loss caused by susceptibility variations. With the addition of real motions and activations determined from actual functional MRI studies, these phantoms can be used by the fMRI community to assess with higher fidelity pre-processing algorithms such as motion correction, distortion correction and signal-loss compensation. These phantoms were validated by comparison to real echo-planar images. Specifically, studies have shown the effects of motion–distortion interactions on fMRI. We performed motion correction and activation analysis on these phantoms based on a block paradigm design using SPM2, and the results demonstrate that interactions between motion and distortion affect both motion correction and activation detection and thus represent a critical component of phantom generation.     

Relation between brain architecture and mathematical ability in children: A DBM study

Population-based studies indicate that between 5 and 9 percent of US children exhibit significant deficits in mathematical reasoning, yet little is understood about the brain morphological features related to mathematical performances. In this work, deformation-based morphometry (DBM) analyses have been performed on magnetic resonance images of the brains of 79 third graders to investigate whether there is a correlation between brain morphological features and mathematical proficiency. Group comparison was also performed between Math Difficulties (MD-worst math performers) and Normal Controls (NC), where each subgroup consists of 20 age and gender matched subjects. DBM analysis is based on the analysis of the deformation fields generated by non-rigid registration algorithms, which warp the individual volumes to a common space. To evaluate the effect of registration algorithms on DBM results, five nonrigid registration algorithms have been used: (1) the Adaptive Bases Algorithm (ABA); (2) the Image Registration Toolkit (IRTK); (3) the FSL Nonlinear Image Registration Tool; (4) the Automatic Registration Tool (ART); and (5) the normalization algorithm available in SPM8. The deformation field magnitude (DFM) was used to measure the displacement at each voxel, and the Jacobian determinant (JAC) was used to quantify local volumetric changes. Results show there are no statistically significant volumetric differences between the NC and the MD groups using JAC. However, DBM analysis using DFM found statistically significant anatomical variations between the two groups around the left occipital-temporal cortex, left orbital-frontal cortex, and right insular cortex. Regions of agreement between at least two algorithms based on voxel-wise analysis were used to define Regions of Interest (ROIs) to perform an ROI-based correlation analysis on all 79 volumes. Correlations between average DFM values and standard mathematical scores over these regions were found to be significant. We also found that the choice of registration algorithm has an impact on DBM-based results, so we recommend using more than one algorithm when conducting DBM studies. To the best of our knowledge, this is the first study that uses DBM to investigate brain anatomical features related to mathematical performance in a relatively large population of children.     

Geometric distortion correction for echo planar images using nonrigid registration with spatially varying scale

One method used to correct geometric and intensity distortions in echo planar images is to register them to undistorted images via nonrigid deformations. However, some areas in the echo planar images are more distorted than others, thus suggesting the use of deformations whose characteristics are adapted spatially. In this article, we incorporate into our previously developed registration algorithm a spatially varying scale mechanism, which adapts the local scale properties of the transformation by means of a scale map. To compute the scale map, a technique is proposed that relies on an estimate of the expected deformation field. This estimate is generated using knowledge of the physical processes that induce distortions in echo planar images. We evaluate the method of spatially varying scale on both simulated and real data. We find that, in comparison with our earlier method using fixed scale, our new method finds deformation fields that are smoother and finds them faster without sacrificing accuracy.