The treatment is dictated by the principle of early and total evacuation of the pleural content. The most effective treatment method for traumatic pneumohemothorax is intrapleural tube drainage, accomplished in various ways – by thoracostomy; by closed system drainage; by open thoracotomy; by thoracoscopy.
I agree that "treatment is subjected to the principle of" isn't quite right. At minimum, "subjected" should be "subject", but the more usual phrasing would be "treatment is dictated by the principle of". Kafetzou's "follows" is okay too.
Some other comments... "closed system" is too vague; use "closed system drainage". A Google search reveals pneumohemothorax is a minor variant of the term hemopneumothorax. Does the source text specify hemopneumothorax, or just pneumothorax?
Thanks for your help. I changed "subjected to" to your suggestion of "dictated by" and added "drainage" after "closed system". As for "hemopneumothorax", that's what it says in the original.