Abstract-New medical procedures promise continuous patient monitoring and drug delivery through implanted sensors and actuators. When over the air wireless radio frequency (OTA-RF) links are used for intra-body implant communication, the network incurs heavy energy costs owing to absorption within the human tissue. With this motivation, we explore an alternate form of intra-body communication that relies on weak electrical signals, instead of OTA-RF. To demonstrate the feasibility of this new paradigm for enabling communication between sensors and actuators embedded within the tissue, or placed on the surface of the skin, we develop a rigorous analytical model based on galvanic coupling of low energy signals. The main contributions in this paper are: (i) developing a suite of analytical expressions for modeling the resulting communication channel for weak electrical signals in a three dimensional multi-layered tissue structure, (ii) validating and verifying the model through extensive finite element simulations, published measurements in existing literature, and experiments conducted with porcine tissue, (iii) designing the communication framework with safety considerations, and analyzing the influence of different network and hardware parameters such as transmission frequency and electrode placements. Our results reveal a close agreement between theory, simulation, literature and experimental findings, pointing to the suitability of the model for quick and accurate channel characterization and parameter estimation for networked and implanted sensors.