Which of the following is NOT a possible pathology associated with Little League Elbow?

Volkmann's contracture is primarily associated with severe forearm injuries, particularly those involving vascular compromise or compartment syndrome, rather than with the pathologies typically seen in Little League Elbow. Little League Elbow refers to overuse injuries in young pitchers and is predominantly characterized by growth plate injuries, strains, and stress reactions due to repetitive throwing motions.

The other options listed are directly related to the overuse and stress placed on the elbow joint in young athletes. Osteochondrosis of the humeral capitulum involves degeneration or necrosis of the bone due to repeated stress. Avulsion of the ossification center of the medial epicondyle occurs when the growth plate is pulled away from the bone, a frequent result of excessive throwing. Nonunion stress fractures of the olecranon epiphysis refer to fractures that do not heal properly, also related to the excessive repetitive stresses associated with throwing sports.

Thus, the connection of Volkmann's contracture to Little League Elbow is much weaker, as it is not a consequence of the usual pathology seen in the repetitive strain injuries characteristic of that condition.