Volumetric 3D Reconstruction of Tissues in C. elegans: Part 2
This is the second part in a series of articles about a research project I’m working on in The Zhirong Bao Developmental Biology Lab at the Sloan-Kettering Institute (for part one, go here).
As illustrated in part 1, the goal of this project is to reconstruct the shape of tissues in C. elegans. During embryogenesis, the largest and most pronounced tissues are the pharynx, muscle, and hypoderm. Generating shape models from 2D cellular microscopy images will allow us to expand our ever-growing model of C. elegans embryogenesis, which we present in 4D atlas form in WormGUIDES (source code available here).
A specification for this project has now been developed, so I thought I’d share the starting state in its more technical form as I begin to develop solutions. We will use three different techniques for the three tissues respectively, with some reusability of methods among them.
The pharynx presents the easiest of cases in generating these models, as its cellular connectivity can be formulated as a graph connectivity problem. We will use preexisting 3D nuclear positional data to generate a connectivity graph based on proximal connections and other heuristics. The resulting convex hull will be used to generate a shape model which will be smoothed between vertices to better represent the ground truth biological structure.
The muscle will require a more robust approach. For this tissue, we will fully segment images that highlight muscle development using the gene cnd-1. At left, the muscle (green) begins to form on the boundary of the embryo. This data driven approach will rely on the behavior of the muscle. At each time point of embryogenesis, we will generate an isocontour in volume to capture the shape of the forming muscle. Then, given that we know the cells that make up the muscle tissue, we will warp this shape to the atlas i.e. warp the shape to fit the positional data model presented in WormGUIDES.
The shape generated by the 2D image at left (including those above and below it in the stack) will then be warped to the model below.
The second tier of this model, as a result of the warping based on cellular position data, is a sectioning of the muscle model into the the cells it’s comprised of for another layer of granularity.
The hypoderm is the most challenging tissue. To generate reliable shape models during embryogenesis, given the challenges this tissue presents (see part 1), we will employ a 3-tier validation method. At each time point, we will first generate a binary shell of some arbitrary thinness by applying a thresholding approach to membrane images such as active contours, or a watershed algorithm, that will identify the boundary of the embryo (by definition, where the hypoderm is).
Next, each nuclear position, generated by nuclear position images will be matched to its nearest point on this shell. When this point is found, we will ray trace/walk/shoot out in all directions from the nuclear position in the membrane images until we reach an intensity above a certain threshold, or more reliably, a zero crossing in a derivative image. This point is the membrane. The membrane positions will then be marked on the shell model, and everything contained within will be marked as intercellular. After the shell is fully marked with all membrane data, portions of the shell that are not marked will be cut away, resulting in an accurate model of the hypoderm.
Earlier in development, before the portions of the hypoderm have formed, this method will generate disconnected components. At left, the membranes of hypodermal cells are seen beginning to form toward the head (left), and are still disconnected toward the tail (right).
Later in development, as the components interlace, the result of the method will be a single shape representing the hypoderm.
At this stage, research into existing methods and approaches is critical as we search for an optimal solution. Research I will be doing in the coming days include data driven shape modeling that allow for defining constraints for minimization techniques, non-parametric modeling, mathematical representations for shapes that are manipulable, splat rendering, and mathematical frameworks for generating low energy shapes from voronoi tessellations.
I hope to have some initial feedback from this process in the coming weeks to share for part 3!
