THE PNEUMATIC DISTRIBUTION SUPPLY DUCT RUPTURED AS THE AIRPLANE BEGAN ITS TAKEOFF ROLL WITH THE FIRST OFFICER AT THE CONTROLS. THE CAPTAIN FELT A SLIGHT CHANGE IN CABIN PRESSURE AND OBSERVED AN ADVISORY MESSAGE ON THE ELECTRONIC INFORMATION CREW ALARM SYSTEM (EICAS) THAT CAUTIONED OF A LEAK IN THE PNEUMATIC DUCT SYSTEM. THE FIRST FLIGHT ATTENDANT ADVISED THE FLIGHT CREW THAT THERE WAS SMOKE, DUST AND HIGH TEMPERATURES IN THE CABIN. THE CAPTAIN ASSUMED CONTROL OF THE AIRPLANE, ABORTED THE TAKEOFF AND TURNED OFF THE RUNWAY AT A MIDFIELD TAXIWAY. AFTER THE AIRPLANE EXITED THE RUNWAY THE CAPTAIN DISPATCHED THE FIRST OFFICER TO THE CABIN TO SURVEY THE SITUATION. THE FIRST OFFICER CONFIRMED THE FLIGHT ATTENDANT'S REPORT AND ADVISED THAT THE PASSENGERS WERE COUGHING CONTINUOUSLY. THE CAPTAIN ELECTED TO EVACUATE ALL PERSONNEL VIA THE EMERGENCY EGRESS SLIDES. THE EXAMINATION DISCLOSED THE APU SUPPLY DUCT RUPTURED ALONG THE WELDED SEAM AT FUSELAGE STATION (FS) 1219.