From my own experience having to exhale at the end of a phrase is an indication of excessive tension, holding air back, not letting it flow relaxed through the horn allowing the CO2 build up to the point where exhalation is necessary before inhalation. I will leave the physiology to the more qualified. Once I learned to play relaxed with breathing no more than mild exertion ie a medium pace walk I can play a mix of 1st and 2nd parts in big band for a 3 hour dance playing sets of 30-45 min with only time between numbers to turn the page to the next, otherwise the dancers go and sit down. There is no magic, if as a 75 year old I can do it but it takes time. Regards, Stuart.