In the annals of running history, there are many examples of runners such as Alberto Salazar or Ron Clarke pushing themselves to in races to points far beyond exhaustion to self detriment. While I don't intend to cause this type of harm upon myself (such as Ron Clark who ran so hard he developed a heart condition) I would like to learn to give move even when in excruciating pain. I'm wondering if this is just a mental strength that people like this posses or are there workouts to learn to push through the pain to run faster. I feel like the obvious one would be to run hard until you drop but this could be self destructive to do while only in training. Should one focus on their lactate threshold to do this or structure workouts to attack the mental aspect?
Background: I've ran many competitive races where near the end, my unwillingness to push through the pain has held me back from big personal gains. While I've greatly improved my physical ability, no matter how fast I get, I can't break through this mental/physical wall.
**I would appreciate real answers rather than "grow some balls" or "don't be a p^$$y"**