Polysurface covering sections of a concave mesh

I have concave meshes like in the pictures given below. How can I construct a polysurface covering the inside of the mesh (highlighted red with a pixel graphics tool)? I use Rhino for Mac 5.3.

For convex mesh sections I (1) copied the mesh, (2) split it with a surface constructed between the naked edges (3) converted the convex part into a polysurface. But this approach does not work for concave meshes. What could be a solution?