Fig. 12.

Using porosity profiles along the AV axis for upscaling in a 1D model. (A) Comparison of the ECS porosity (plus symbols, right y-axis) and [Fgf8a-total] profiles (lines, left y-axis) along the AV axis at different stages of epiboly (see key). In the first 100 μm from the margin, where the profile has a kink, ψ_ECS approximately doubles. All profiles are computed at . (B) AV profiles of the ECS porosity, ψ_ECS (black symbols); the source, ψ_source (solid light-blue line); and the sink, ψ_[Fgfr] (dashed pink line). All profiles are computed according to Eqn 15 by dividing the volume of the respective phase of interest by the total volume of the embedding spherical shell. (C) Upscaling SDD in porous ECS geometries. To disentangle the role of porous ECS heterogeneity in source, diffusion and sink on the formation of the AV gradient kink, we accounted for the AV profiles of ψ_ECS, ψ_source and ψ_[Fgfr] by linearly scaling (1) D_Fgf8a and with ψ_ECS (light-green line) and (2) f_source with ψ_source (light-blue line), and by (3) combining (1) and (2) (dark-green line), and (4) combining (3) with scaling [Fgfr] with ψ_[Fgfr] (pink line). The kink at the source is partly recovered when upscaling D_Fgf8a and f_source (case 3, dark-green line). All profiles are normalized by their maximum concentration and shown at .