Principal Investigator/Program Director Williams,Robert W.
Aim 3: Segmentation of the MBL and extraction of quantitative traitsThe final objective of this project is segmentation of the MBL and measurement of quantitative traits. To that end, we propose to develop fiducial-based nonlinear alignment. The algorithms will be tested, implemented as part of the Align software package, and released. Additionally, they will be used to segment the MBL into over 1200 VOIs (see Appendix for complete listing). We will also develop a program to translate coordinates on one brain to another and will add features to NeuroTerrain that will support delineation of VOIs.
Implicit fiducialguided spline alignment.
Fiducial points and surfaces will be used for constructing the atlases (Aim 1) and fine alignment of the MBL. Current image-processing techniques can locate relatively few fiducial structures in the brain (Nissanov and McEacrhon 1991; Schliecher et al. 1999). Manual segmentation is possible, though time-consuming. We propose to identify fiducial location by using local comparison of atlas and MBL regions. A similar concept was used by Bajcsy and Kovacic (1989) and Amit (1997). The general notion is that for each fiducial, we will select a 3D region R in the atlas reference brain, then compare the gray value function in this region with the MBL brain gray values over R at various translations, rotations, and scalings. The comparison process produces a scalar that reaches an extremum (maximum or minimum) when the two gray distributions are most similar. Comparison may be made by cross-correlation (Hibbard and Hawkins 1987; Bajcsy and Kovacic 1989), squared difference (Thevenaz and Unser 1995), conditional variance (Woods et al. 1993), and mutual information (Thevenaz and Unser 1996; Wells et al. 1996; Maes et al. 1997).
We plan to introduce several refinements on the above method. The comparison technique intrinsically identifies a transformation between regions. We will identify a segmentable point in the atlas region and associate the best translation as the displacement of this point: this is what we mean by an implicit fiducial (IF). These data (fiducial point and displacement) are directly applicable for constructing a spline interpolant transformation. Segmenting the same point in the MBL data set allows us to validate the accuracy of the given implicit fiducial. Such validation, on a subset of the MBL brains, will allow us to select stable and reliable implicit fiducials. We will use a multiresolution strategy in the search (Bajcy and Kovacic 1989). An initial approximate alignment will be performed; subsequently, we will look for a few low-resolution IFs that are not sensitive to (moderate) rotations. These will be used to compute an approximate spline transformation. After this is applied, we will use higher-resolution IFs to refine the transformation. These can be applied over smaller search zones. Proper care will be taken to address aliasing problems caused by coarse z-axis sampling and imprecise alignment in the MBL. Some smoothing will be performed in the z direction on the atlas data, to remove possible sensitivity to angular misalignment, and a set of slices through the atlas will be compared with a group of regions in adjacent MBL sections. This set will be stepped along the z axis in the atlas in order to achieve accuracy finer than inter-section spacing. We propose to compare the summed squared difference between the atlas and the MBL, with adaptation for brightness and contrast differences (Thevenaz and Unser 1995). Two strategies will be explored to account for MBL x-y misalignment. The data may be smoothed in the x-y plane to mitigate effects of this jitter. Alternatively, the MBL sections can be translated by different amounts so that each produces a best match, and differences in displacement may be used to refine alignment.
MBL segmentation and quality control
Our main objective in Aim 3 is to use the computed transformation to map the 3D anatomical template onto at least 1200 brains to be stored in the MBL (Project 1). The 4.5-mm/pixel images scanned into the MBL collection will be aligned to standard coordinates. To match the resolution of the atlas, the images will be downsampled to 10 mm/pixel.
For quality control purposes, 5 ROIs will be delineated on each brain, with each region delineated on one section. These ROIs will be compared to the automatic segmentation results. To limit the error associated with manual delineation, we have chosen structures that can easily be segmented using the semiautomatic procedure of thresholding and editing. Our objective is to limit both false positive and false negative pixel assignment to 20% for a 225-mm-diameter circular ROI (this corresponds to roughly 3 times the error on repeated manual delineations of strong edge). In addition to this quantitative performance measure, the quality of the segmentation will also be evaluated by visual inspection. Sections with their anatomical overlap and the corresponding atlas planes will be displayed using NeuroTerrain.
We plan to complete software development, test the alignment algorithm, and begin segmentation of the MBL by the middle of Year 03. Complete delineation of the MBL will require a segmentation throughput of 4 brains per day. With automatic segmentation, we believe that the limiting factor will be availability of brains rather than the alignment algorithm.
TransformerTransformer will be an object (program plus parameters) that evaluates coordinate transformations between data setseither atlases or MBL brains. For the purpose of database access, the physical coordinates of one of the atlases will be selected as the coordinate system (see Aim 1). Using the Internet, an investigator can specify either a region (point, line segment, rectangular window, stack) in the native coordinates (i.e., voxels) of one brain. The transformer will give corresponding coordinates in the native coordinates of another brain. Since considerable care will be taken in establishing the physical location of sections on the slide (Project 1) it will be possible to translate to both image coordinates and to the physical slide coordinates. The coordinate transformations will be computed by composing transformations from one brain to the MBL standard coordinate system and from the coordinate system to another brain. This way, only about 2500 transformations need to be stored. Transformations will be implemented as product cubic splines. Assuming the knot set is on a 10 x 10 x 10 grid, each transformation will require about 12,000 floating point numbers.
Although the above transformation specifications are in the form of product splines, the alignment procedure will compute radial splines from fiducial point data. We use radial splines for alignment because fiducial points range over an irregular grid; product splines, however, are faster to compute. Product splines will be derived from radial splines by sampling these splines over a grid. The grid will be selected to provide adequately accurate approximation of the product spline.
Quantitative informational features
Once segmented, a variety of quantitative information can be extracted and fed to the NTB (Project 4). A straightforward measure is estimate of the volumes of VOIs. Another numerical feature is the magnitude of the nonlinear displacement of a given point in the MBL coordinate system. One can compute point configurations (Amit 1997) or morphological Euclidean invariants as developed by Bookstein (1991). A natural set of features can be derived using tools developed in continuum mechanics (Chandrasekariah and Debnath 1994). Let be a alignment transformation, and let be the deformation gradient tensor.. Then detF is the Jacobian, or local volume ratio, and is an affine invariant, so it is insensitive to difference in (uniform) shrinkage of the brains. Thus one possible set of numerical indices is the values of the Jacobian, indexed by the MBL coordinate system. Mechanical or functional causes for differences between brains can be indicated by regions where the value of the Jacobian is different from unity. If we evaluate the polar decomposition , where V is symmetric and Q is orthogonal, then the eigenvalues of V are Euclidean invariants of the transformation, and differences between eigenvalues and unity indicate non-isotropic growth. In the presence of an intrinsic direction, e.g., the normal to cortex, measures size difference along that axis. If manually segmented information of structures is available, one can compare changes in volume of a given nucleus using either the Jacobian or the overall size difference at that location.
Early in this phase of the project, the facilities to support user-defined VOIs will be incorporated (NeuroTerrain version 3.0, Fig. 1). It will be possible to propagate these VOIs across the entire database. This version of NeuroTerrain will also support manual refinement of the placement of the anatomical template on any given brain, yielding substantially higher segmentation accuracy.
In a later version (NeuroTerrain 3.5), facilities to support visualization of interbrain differences will be added. As described above, we will compute a variety of measures (e.g., non-isotropic compression and expansion and magnitude of displacement relative to the MBL coordinate system). Users will be provided with a number of ways to access that data. One will consist of a point-and-click interface where the variation across strains for the selected coordinate will be retrieved. Another will allow investigators to request a voxel-by-voxel difference map between any two selected strains. Such a map could be displayed as an overlay on any of the eight atlases.We believe that these measures will have considerable ramification for QTL mapping. Statistical techniques to compare these maps and methods to explore these in the context of developmental models will be a major research direction beyond the present grant period.