Until two years ago, people in China who wanted medical care from Brigham and Women’s Hospital, an affiliate of Harvard University, had to take a 7,000-mile plane ride to Boston. That all changed in 2018, when the Boao Evergrande International Hospital opened on China’s Hainan island. The facility, a Brigham partnership with one of China’s biggest property developers, is focused initially on treating breast cancer.  Brigham is only one of a growing group of world-renowned American hospitals planting their flags in China. They are tapping into one of the world’s fastest growing health-care markets, one that is on track to spend $2.4 trillion annually on medical services by the year 2040, according to China’s National Health and Family Planning Commission. The Cleveland Clinic has struck a deal with Luye Medical, a Singapore-based company, to set up a hospital in Shanghai. Mount Sinai Health System in New York has agreed to advise Taikang Healthcare on a 500-bed hos