The pilot reported that he had departed from the private airstrip on two previous agricultural aerial application flights. During the next takeoff roll, the airplane veered to the left when it passed the center crown in the runway. He reported that the main wheel "caught" a deep rut at the runway edge. The airplane went off the runway and the left wing impacted a cornfield, which spun the airplane around. The landing gear, propeller, and empennage sustained substantial damage. The airport used by the pilot was a privately owned, paved airstrip used only by agricultural spray aircraft.