Organically Derived Nano-Scale Power
To cut to the chase, there are two organic systems that have already been created by evolution that could be co-opted and modified to provide electrical power to implants that integrates with the patient's natural power generation system. These systems are the mitochondria and the electric organ from electric fish.
Being simpler than a eukaryotic cell, the mitochondria should be much easier to reverse-engineer and modify. It uses glucose, pyruvate, and NADH (Nicotinamide adenine dinucleotide) to transform ADP into ATP. This ATP then goes on to provide energy for most of the processes employed to keep a multicellular organism alive.
On the other side of the coin, the electric organ of electric fish (presumably) use ATP to created macroscopic electric fields. If the functionality of this organ can be reverse-engineered and shrunk, it provides the mechanism to turn organic energy into electric energy.
Putting these two systems together at the interface of an implant and host body would allow the implant to utilize the energy the host acquires naturally from eating to power the device.