|
Figure 1. a: Equatorial cross-section through a SIM dataset of a gastrula stage Xenopus laevis embryo. b: Enlargement of the region outlined in red in (a) demonstrating the spherical shell organization of cells in surface ectoderm, ectoderm, and mesendoderm. This study was motivated by the desire to digitally image, analyze, and visualize the morphology of cells within these concentric cell layers, while preserving as much of the normal curved geometry of the tissue as possible.
|
|
Figure 2. a: Geometry of the plane projection along the viewing direction of a domain on the surface of a sphere onto the equatorial plane. b: Orthographic projection of equal area circles on the surface of a sphere onto a 2D plane with the north pole at center. Note the reduction in apparent area with decreasing latitude expressed as a percentage of actual surface area. c: Example boundary circle defined by three points (green) and spline boundary for the blastopore (red). The corrected surface area occupied by the blastopore can be estimated from the boundary circle geometry as described in the text. d: Reprojection of the embryo surface and blastopore boundary in c from 2D to 3D using the boundary circle center and radius. e: Naive measurement based directly on the minimum enclosing rectangle (white) for the domain in the planar image gives a length-width ratio of 7.4. f: Use of geometric correction to estimate the length-width ratio from the same image. The boundary (green line) has been defined as before and points on the Xnot boundary are estimated manually (red circles) and interpolated using a closed natural cubic spline (red line). The long axis is defined manually by two points (white circles) and the connecting great circle representing the long-axis of the expression domain calculated (white line). g: The spline boundary is rotated to lie along the equator of a new coordinate system and the corrected minimum enclosing rectangle calculated. The length and width of the domain can then be defined in angular units or length units using the boundary circle radius as an estimate of the sphere radius. The corrected length to maximum width ratio in this example is 8.8, implying a 16% underestimation of the true length of the domain compared to e.
|
|
Figure 3. Semi-automated processing sequence defining the embryonic spherical coordinate system. a: The data is down-sampled and smoothed prior to segmentation. b: Otsu thresholding is used to segment embryonic tissue from non-embryonic material. c: Internal spaces completely bounded by tissue are then filled, completing the mask for regions within the embryo. d: A mesh representing the embryonic surface is then derived from the mask and (e) the mesh vertices used to derive a best-fit sphere. f: The blastopore center is identified by the operator (red crosshair) and combined with the best-fit sphere center to define the latitude origin (equator) for the spherical coordinate system. g: Finally, the dorsal midline is identified by the operator (red crosshair), fixing the longitudinal origin (prime meridian).
|
|
Figure 4. Extraction of anatomical planes from 3D digital images of a spherical embryo. The three columns demonstrate azimuthal (r-z planes passing through a given azimuth or longitude, θ), parasagittal (x-z planes passing through a given azimuth or longitude, θ), and axial (x-y planes passing through a given latitude, ϕ) plane extraction. The position of the extracted plane is indicated by a colored dashed line. For each plane type, two images at different angle values have been extracted from the same SIM dataset of a late gastrula Xenopus laevis embryo.
|
|
Figure 5. a: Schematic of the transformation of a spherical coordinate system corresponding to the original digital Cartesian sampling scheme (xyz) to the anatomic spherical coordinate system, which defines the south pole as the blastopore center. The original coordinate frame is (1) rotated about the y-axis (latitude rotation by ϕy) to place the south pole on the same latitude as the blastopore center, then (2) rotated about the z-axis (longitude rotation by θz) to place the new south pole at the blastopore center. This two-rotation scheme is then combined with the new prime meridian defined by the dorsal midline to complete the coordinate transform, allowing extraction of data from the sampled data using embryonic coordinates. b: Location of the shell (green circle) with a normalized radius of 0.9 shown on an extracted mid-sagittal section. c: Orthographic projection of the extracted shell in b centered over (60°S,0°E) showing the blastopore and dorsal midline. d: Equidistant cylindrical projection of the dorsal axis in the same shell between 80°S and the equator. Cartographic visualization provides a convenient way to compare corresponding regions between different embryos using the normalized radius, latitude, and longitude to specify location.
|
|
Figure 6. To visualize the progression of gastrulation below the surface of the Xenopus laevis embryo, a series of spherical shells were extracted from different radii within a normal series of embryos. Examples were selected of early gastrula (a), mid-gastrula (b), late gastrula (c), and neurula (d). Each dataset was transformed to the standard coordinate system and then a virtual sagittal section (a–d) and a spherical shell in the region of the prospective (e,f) or actual notochord (g,h) was extracted. The resulting spherical shells were visualized as an orthographic projection (e,h), which is equivalent to the view achieved when looking at an image of a frog embryo through a microscope. The difference is that these shells are revealing subsurface features. Enlargements of subregions of the orthographic projections in e,h are shown in (e′–h′). To highlight the relevant anatomy, individual cells and cellular features have been traced and overlaid on a low contrast version of the enlarged region. The blastopore, notochord, and somitic field are all readily apparent. Cell boundaries are on the edge of the contrast and resolution of the underlying image data, and so some regions are clearer than others. The software is presenting all of the resolution of the image data and so improvements in contrast or resolution on the acquisition end would result in clearer cell boundaries. Representative cells in different regions are highlighted, and show a clear medial-lateral polarization within the notochord. In the neurula stage embryo, the archenteron's lateral edges are penetrating into the lateral plate mesoderm. To visualize the changes in cell shape as a function of depth within the embryo, we constructed a stack of orthographic projections, over a range of radii, for each of the pictured embryos (see Supplementary Movies 1–4, embryos from a–d, respectively). Abbreviations in both figures and movies: dbpl, dorsal blastopore lip; bp, blastopore; n, notochord; ar, archenteron; s, somitic field.
|
|
Figure 7. Example extraction and visualization of a virtual dorsal explant from SIM datasets of early (a), middle (b), and late (c) gastrula embryos of Xenopus laevis. For each embryo, virtual mid-sagittal sections (a–c) and virtual dorsal explants (d–f) were extracted computationally from 3D digital volumes. The explant region was defined between latitudes 90°S and 90°N, longitudes 45°E and 45°W, and normalized radii of 0.6 and 1.0 indicated by the green outline in a–c. The progress of the migration of the mesendoderm on the blastocoel roof is evident in the early gastrula explant (d). The dorsal leading edge has almost reached the animal pole in the mid-gastrula embryo (e), and the mesendoderm has met in the late gastrula embryo (f). We noticed in the late gastrula that the roof of the archenteron was thinner along the midline than in the more lateral regions (white arrowhead in f). [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]
|
