De-embedding antennas from the channel using Spherical Wave Functions (SWF) is a useful method to reduce the numerical effort in the simulation of wearable antennas. In this paper an analytical solution to the De-embedding problem is presented in form of surface integrals. This new integral solution is helpful on a theoretical level to derive insights and is also well suited for implementation in Finite Difference Time Domain (FDTD) numerical software. The spherical wave function coefficients are calculated directly from near-field values. Furthermore, the presence of a near-field scatterer in the de-embedding problem is discussed on a theoretical level based on the Huygens Equivalence Theorem. This makes it possible to exploit the degrees of freedom in such a way that it is sufficient to only use out-going spherical wave functions and still obtain correct results.