Fundamental radiation limitations for in-body or implantable antennas provide valuable insights into the feasibility of certain systems. Previous work has shown that near-field effects and the distance from the body-to-freespace boundary are critical factors, giving good approximate formulas for the power density obtained at body interface. In this paper, we extend this analysis by examining the effect of the body curvature on the system radiation pattern and gain, by introducing a model for a cylindrical body phantom and comparing it to the planar and spherical cases. To accomplish this, we developed an analysis model based on a cylindrical mode expansion of the electromagnetic fields. This expansion was used to analyze various scenarios, offering the insights needed to extract key information about the EM fields radiated by the implant. Furthermore, from this analysis model, we derived simple analytical expressions that provide estimates for gain and power density reaching free space, aiding in the design of implanted antenna devices.