What is the manner in which a doctor performs his prayer — after its time has elapsed — due to his engagement in emergency surgeries?

A Muslim must perform the prayer at its prescribed time, except in cases of an overwhelming necessity where there is no alternative, such as saving a drowning person, extinguishing a fire, or repelling an enemy. In such instances, it is permissible to delay the prayer, even if its time expires, because these grave matters cannot be addressed otherwise. The Prophet, peace and blessings be upon him, delayed the Dhuhr and Asr prayers on the Day of Al-Ahzab due to his engagement in fighting, and the Companions delayed the Fajr prayer during the siege of Tuster until it was conquered for them.