Voluntary private patients may be admitted in accordance with the regulations to be established by the state board of regents, and their care, nursing, observation, treatment, medicine, and maintenance shall be without expense to the state. However, the charge for such care, nursing, observation, treatment, medicine, and maintenance shall not exceed the cost of the same to the state. The physicians or physician assistants who meet the qualifications set forth in the definition of a mental health professional in section 228.1 on the hospital staff may charge such patients for their medical services under such rules, regulations, and plan therefor as approved by the state board of regents.