How can one reconcile performing the five daily prayers at their appointed times with the demands of the surgical profession, which may take a long time and require constant concentration?

The fundamental principle is that prayers should be performed on time. If a surgical operation is lengthy, the doctor can begin the operation after performing the prayer at the beginning of its designated time, or arrange the operation schedules to avoid overlapping with prayer times, or rotate duties with the surgical team.

If that is not possible, then he is permitted to combine two prayers. In very rare cases, if the operation extends for a long time, exceeding the time of the two combined prayers, and he is unable to leave, he should pray according to his situation by gesturing, for indeed, religion is ease and there is no hardship in it.