Histological preparation
Transverse sections of mouse embryos at stages that bracket major morphogenetic events of diaphragm development (embryonic day 11.5 and day 13 [E11.5 and E13]) have been examined (see footnote 2). Paraffin embedded mouse embryos were prepared in accordance with the standards of the Institutional Animal Care and Use Committee of Columbia University. Five micron transverse serial sections were cut and stained with hematoxylin and eosin.
Image analysis and digitalization
Sections were examined under bright microscopy at 40× magnification. Selected microscopy images were digitally captured, and computer-assisted tracing of key diaphragmatic structures was performed (Fig. 7). Where necessary, images from sequential sections were "stacked" to complete structure outlines – in essence, creating a two-dimensional orthographic projection of structures where the complete structure could not be captured on a single transverse section. Tracings were then imported into image-analysis software (GetData© 2.17, http://getdata.com.ru webcite) and digitized to yield two-dimensional coordinate-space data points. These digital coordinates were imported into the Nudge++™ software environment; the software then regenerated the original tracings as computerized anatomical boundaries within the simulations (Fig. 8).
Computer simulations
Nudge++™ is a robust computer modeling system designed to study the morphogenesis of multi-cellular organisms (see footnote 3). Details of the model have been presented elsewhere [16]. In brief, model cells carry out programmed behaviors based on internal states and external cues. The model successively iterates over the cell population – evaluating cellular conditions and generating cellular activities. Tissues and organs are built from cohorts of these interacting cells. The model can be tailored to a variety of systems (both two- and three-dimensional) and includes an extensive and expandable set of cellular states and environmental cues (Table 1). The model also allows for the description of regions based on anatomical data; regional boundaries can act as constraints to cell movement.
Here, we use Nudge++™ in two-dimensional mode whereby the model tissue is confined to a plane but individual cells are three-dimensional. Cells are modeled as inelastic spheres. Cell cycle time is normally distributed about a set mean (see footnote 4). When a cell divides, two daughter cells are produced, each of volume equal to one-half of that of the original cell. The orientations of cell divisions have been kept random within the plane of the diaphragm. There is no cell death. Active cell movement is used in some simulations (see below). Details of how these model cells interact on a geometric basis have been previously described [16].
Each simulation has been run a minimum of five times and representative runs are figured.
Incorporation of data into simulations
Digitized tissue boundaries for the E11.5 and E13 mouse embryos were introduced into the simulation model as described above. Intermediate time-points for these boundaries were generated in Nudge++™ by a simple morphing of matching structures over embryonic time (Fig. 9).
Model cells were introduced into the initial composite based on the digitized boundaries of the PPF at stage E11.5. In each simulation, the right side is representative of a normal PPF and hemi-diaphragm, while the left side is representative of a CDH. The PPF defect has been described and defined in recent observations in the rat nitrofen CDH model [10]. Transverse sections through the mid-portion of the defective PPF demonstrate a posterolateral defect (Fig. 6). Therefore, at E11.5 the right model PPF is completely filled with cells while the cellular component of the left model PPF has a posterolateral defect (Fig. 10).
As model cells carry out program-directed behaviors within the simulation, they are physically constrained by boundaries representing the body wall and dorsal mesentery. Hence, experimentally-derived boundary data are used both to place the original model cells within the normal and defective PPF, and to modify cell behaviors over simulation time. The initial alignment of boundaries and cells is uniquely determined by the E11.5 data. However, there are options in terms of aligning the data-derived boundaries (which change over time by morphing) and the simulated cell populations (which change over time by growth, division and movement). Here we allow the coordinate space of the cell populations to "stretch" as the body wall grows (see footnote 5).
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