When you only have one heart remaining, you will be knocked out ( go unconscious ), where you will not be able to move anymore, nor see anything.
You will remain unconscious until either 120 seconds pass and you die, or someone comes and revives you by holding right-click at you.
If you get revived, then you will have five minutes to be operated on if a doctor is online. If the five minutes elapse and you did not get operated on, you will get killed.
However, if you get revived but there is no doctor online at all, the requirement for surgery will be nullified!