To maximize your endurance, make your exhalation “dense”—a scaled down power breathing.

The increased pressure in the lungs drives more oxygen into the alveoli. 

Prof. Krestovnikov tells a story of a young scientist unskilled in correct breathing who experienced a number of difficulties and symptoms on a 1,700m (5,500’) climb in the Alps. When he was twenty years older and a lot wiser, he climbed three times higher, 5,500m (18,000’), with no ill effects—“with deep nasal breathing, a slight pause, and a following forceful exhalation.”