You'll need to set up some sort of system that periodically checks for such cases of incomplete data entry. If your database is hosted from FileMaker Server, a schedule can be set up to run such a script at regular intervals such as once every evening. The script can perform a find for the records and if any are found, loop through them sending out reminder emails to each surgeon.
If you are not hosting from FileMaker Server, a robot file can be set up to perform this script in your main file each time it is opened. Then you set up an OS based scheduler such as Windows Scheduled Tasks to open that file on a regular schedule. In Windows 7, it looks like this may be more complicated--requireing a batch file that is opened by the utility which then in turn opens the database file.