Feature Grid for Correlating Data
The spatial-temporal data collected in the above steps are obtained from a variety of sources, and each has a different natural coordinate system. To combine these data we devised a surface coordinate system, or feature grid. The grid and its attendant interpolation software serve as a vehicle through which element-specific data can be obtained for the whole-embryo finite element model.
Biologists generally divide the surface of a neurulation-stage embryo into three main regions: the neural plate region, the neural fold region, and the non-neural ectoderm region (Fig. 7). Potential feature grids devised for the neural plate are shown in Figure 8. The “parabolic” grid (Fig. 8a) was chosen for the neural plate region, and grid systems compatible with it were chosen for the other two regions.
Figure 9. Parametric coordinates shown from a variety of viewing angles
In the feature grid system, each surface point has unique u and v coordinate values, and the grid is mapped onto the 3D embryo surface reconstruction (Fig. 9) using a mathematical mapping (u, v) ^ (x, y, z). Mappings to other data sets are accomplished in a similar way. Details of the process [Bootsma, 2003] are beyond the scope of the present paper. All data are stored in both their raw form and in a feature grid form (Figure. 10).
The finite element mesh generator uses the feature grid as a basis for data inquiry and interpolation, and uses it to determine on an element-by-element basis, tissue geometry and thickness, cellular fabric and mechanical properties.