The Department of Health and Human Services or the Director of Correctional Services may order the temporary transfer of any person committed to the Department of Health and Human Services or the Department of Correctional Services to the University of Nebraska Medical Center with the concurrence of the chancellor thereof for special diagnosis and treatment of any illness such person may suffer which cannot be properly diagnosed or treated by the medical facilities of the institution of which he or she is a patient or inmate. The responsibility of guarding any such patient or inmate transferred shall remain with the institution of which he or she is a patient or inmate. The Department of Health and Human Services or the Department of Correctional Services shall pay, out of the proper account, all expenses incurred by the University of Nebraska Medical Center on behalf of any patient or inmate so transferred by the respective department.