  The main respiratory muscle, the diaphragm, is an example of a thin
structure. We aim to perform detailed numerical simulations of the muscle
mechanics based on individual patient data. This requires a representation of
the diaphragm geometry extracted from medical image data. We design an adaptive
reconstruction method based on a least-squares radial basis function partition
of unity method. The method is adapted to thin structures by subdividing the
structure rather than the surrounding space, and by introducing an anisotropic
scaling of local subproblems. The resulting representation is an infinitely
smooth level set function, which is stabilized such that there are no spurious
zero level sets. We show reconstruction results for 2D cross sections of the
diaphragm geometry as well as for the full 3D geometry. We also show solutions
to basic PDE test problems in the reconstructed geometries.
