Bone growth stimulators were developed by Dr. Robert Becker and Dr. Andy Basset, orthopedic surgeons, to prevent the need to amputate limbs because the crushed bones were not healing. The science behind what lead to the discovery of using electrical stimulation is presented in Dr. Becker's book, "The Body Electric - Electromagnetism and The Foundation of LIfe".
In a nutshell version a basic premise of cell growth ( note this is not related only to bones but to cells in general) is you have a physical attraction of opposite charges between cells. With electromagnetism it's similar to having two magnets and placing the north end of one magnet beside the south end of the other magnet. The two magnets will attract each other and if close enough they join together. Reverse the setting so both ends are north and the magnets repel/repulse each other and there is no union occurring. Of course with electrotherapy the terms are the positive and negative charges. Opposite charges attract, and same charges repel.
When a bone is fractured or broken the two ends of the bone facing each other will have one distal end with a positive charge, and the other proximal end with a negative charge. That is normal and in that electromagnetic field the two bones are trying to unionize or heal. Often the actual cellular charges of one end of either bone will "reverse polarity" or simply put both ends have the same charge so there is no unionization, or bone healing. A bone stimulator is applied to reverse the polarity and healing begins again. It is this process that helps non healing bones fuse together and regain form and function.
Some orthopedic surgeons use different types of bone growth stimulators knowing the bone will unionize with nothing being done, but desire a faster healing rate than normal and use bone growth stimulators to advance the healing. This is done by Yale Univ. hospital on many of the neck fracture patients simply because of the fear of further injury in the neck spinal region. It's a safeguard to accelerate bone unionization. The bone stimulators are also used in sports medicine for athletic injuries where a player needs to heal quicker in order to return to competition.
The process of furthering healing with electrotherapy is similar for soft tissue cells, such as bed sores, sprained/strainked ankles etc. as the physics are of cells, not structures.