In Asia there exists a clear distinction between Eastern and Western medicine and what the strengths of each approach are. In Chinese hospitals you will find the pharmacy divided into an Eastern and Western department, by the type of medication it dispenses — the pharmaceuticals we are used to seeing in the West, or traditional Chinese remedies prepared largely from herbs and natural ingredients (this can include tissue extracts from animals). The Chinese often say that Western medicine is better for surgery, which requires high-tech precision, and Chinese medicine is better for treating holistic conditions. My back pain would fall under the latter category.
1. Center for Traditional Eastern Medicine — metro Pushkinskaya, (495) 694-02-17, doctor-gui.ru
See their treatment programs here — like most Chinese medicine centers in Moscow, their focus is on aesthetics, weight less, skin care, etc.
2. Tibet Clinic — metro Novokuznetskaya, (495) 781-57-57, clinica-tibet.ru
This clinic is more focused on medical treatment of back pain. I like the comprehensive guide to various musculoskeletal conditions on their site. And many of their doctors studied medicine in Mongolia/China, though are from Russia.
3. Great Tree Health Center — metro Taganskaya, Chkalovskaya, (495) 915-58-25, center-qigong.ru
As of 11 June, they are hosting a visiting Chinese doctor, Zhu Ci. They also offer many qigong classes.
This is by no means a comprehensive list