Apparently the American Society of Anesthesiologists has advised doctors not to participate:

Gaitan, who was appointed by President George H.W. Bush, told state officials that, among other things, a board-certified anesthesiologist had to ensure that inmates were sedated enough during execution that they would not feel unnecessary pain . . .

. . . Missouri officials sent letters to 298 board-certified anesthesiologists in Missouri and southern Illinois “inquiring of their willingness to participate in execution,” according to the court filing by two assistant attorneys general, Michael E. Pritchett and Stephen D. Hawke. “To this date, no one has accepted.”