What do you want to say?

For it to be understood by an English native speaker who was brought up in a developed English-speaking country, with its long tradition of public and private healthcare and policy debates on such, this will have to be "The importance of a [you need an adjective here: affordable? reasonable? fair?] system of medical fees in [maintaining?promoting?] [healthy? harmonious?] doctor-patient relationships in [public? private? sector] healthcare in [which country]". Some clarification required from you: "管理"是谁管谁啊? "强化" 一词很虚， 究竟怎样才算"强化"? 中文和英文的思维、背后的文化和制度的历史， 都影响着读者的理解和命题者的思维和用字遣词。

From your further explanation, it seems you may need "The importance of an effective regulatory regime for medical fees in the promotion of harmonious and trusting doctor-patient relationships (in China?)"

The importance of the enhancement of management of medical charge to the good physician-patient relationship

Could you post this in the context of the passage you are writing please? This is not a sentence: it does not even have a verb.