The board may appoint panels from its members for the purpose of fulfilling the obligations established in subdivision (c) of Section 2004. Any panel appointed under this section shall at no time be comprised of less than four members and the number of public members assigned to the panel shall not exceed the number of licensed physician and surgeon members assigned to the panel. The president of the board shall not be a member of any panel unless there is a vacancy in the membership of the board. Each panel shall annually elect a chair and a vice chair.