The radiating mechanism of a class of implanted antennas is investigated. The patch like antennas are bent on a titanium-based alloy made artificial bone that acts as a ground plane. For this investigation, the antennas are embedded in two different bio-compatible materials, namely polydimethylsiloxane and hydroxyapatite, respectively, that circumscribe the artificial bone. The dielectric layers act as a support for surface waves that influence the radiation pattern of the antenna. The relationship between the dielectric properties of the substrates and the electric path of the outgoing electric field is discussed: the explanation of the dissimilar radiation efficiencies of the two antennas is based on the different directions of the refraction at the dielectric-muscle interface, that will influence both the length of the surface waves and the paths in the lossy muscle tissue. The analysis is carried out at the Industrial, Scientific and Medical (ISM) band (2.4-2.5 GHz).