Cats have adapted to conserve energy via long periods of rest and sleep. Purring is a low energy mechanism that stimulates muscles and bones without wasting a lot of energy.
As a result, cats do not display as many muscle and bone abnormalities as the domestic dog. It could be that a cat's purring helps alleviate the dysplasia or osteoporotic conditions that are common in dogs.
Cats purr when inhaling and also when exhaling, with a consistent pattern and frequency between 25 and 150 Hertz. Various investigations have shown that sound frequencies in this range can improve bone density and speed up healing.
This link between the sound frequency of a cat's purr and the accelerated healing of bones and muscles could prove helpful for some humans. Bone density loss and muscle atrophy are a serious concern for astronauts during extended periods at zero gravity.
Cats do not only purr when they are happy. Although cats purr when nursing their kittens, or when being petted by their human, they also do so when recovering from an injury. It is therefore more plausible that cat purring is not only a means of communication, but also a potential source of self-healing.