Escape from New York

In 1988, following a 400% increase in crime, the United States Government has turned Manhattan into a giant maximum-security prison. A 50-foot (15Â m) containment wall surrounds the island and routes out of Manhattan have been dismantled or mined, while armed helicopters patrol the rivers. In 1997, while travelling to a peace summit between the United States, China and the Soviet Union, Air Force One is hijacked by a terrorist. The President is given a security bracelet, and has a briefcase (containing an audiotape describing a powerful new bomb) handcuffed to his wrist. He makes it to an escape pod, and lands in Manhattan just before Air Force One crashes, killing everyone else aboard.
Police officers are dispatched to rescue the President. However, Romero, the right-hand man of the Duke of New York, the top crime boss in the prison, warns them that the Duke has taken the President hostage, and that he will be killed if the police mount any further rescue attempts. Police Commissioner Bob Hauk offers a deal to "Snake" Plissken, a former Special Forces soldier convicted of attempting to rob the Federal Reserve in Denver, Colorado: if Snake rescues the President and retrieves the cassette tape, Hauk will arrange a presidential pardon. To ensure his compliance, Hauk has him injected with explosives that will rupture Snake's carotid arteries within 22 hours; if Snake returns with the President and the tape in time, Hauk will neutralize the explosives.
Snake is sent into Manhattan in a stealth glider, landing atop the World Trade Center. He tracks the President's life-monitor bracelet to a vaudeville theatre, only to find it on the wrist of an old man. He meets "Cabbie," who takes Snake in his armored taxi cab to Harold "Brain" Hellman, an advisor to the Duke based in the New York Public Library. Brain tells Snake that the Duke plans to unify the gangs in a mass exodus across the heavily-guarded Queensboro Bridge, using the President as a human shield and a map Brain has created to avoid the mines. Snake forces Brain and his girlfriend Maggie to lead him to the Duke's compound at Grand Central Station. He finds the President and tries to free him, but is captured by the Duke's men.
While Snake is forced to fight to the death with Slag, a prisoner, Brain and Maggie trick Romero into letting them see the President, killing him and fleeing with the President. As Snake kills Slag, the Duke learns of Brain's treachery and rallies his gang to chase them down. Snake, Brain, Maggie, and the President attempt to use Snake's glider to escape from New York. After a group of crazies destroy it, the group returns to the street and encounters Cabbie, who offers to take them across the bridge. When Cabbie reveals that he has the secret tape (having traded it to Romero earlier for his hat), the President demands it, but Snake keeps it.
With the Duke chasing in another car, the cab is blown in half by a mine and Cabbie is killed. As they flee on foot, Brain is killed when he steps on another mine. Maggie refuses to leave him, and shoots repeatedly at the Duke; he runs her over. Snake and the President reach the wall and the guards raise the President on a rope. The Duke kills the guards and attacks Snake, but the President, now armed atop the wall, gleefully shoots the Duke dead. Snake is lifted to safety and the implanted explosives are deactivated with seconds to spare.
As the President prepares for a televised speech to the leaders at the summit meeting, he thanks Snake for saving him. Snake asks how he feels about the people who died saving his life, but the President only offers halfhearted regret. Hauk offers Snake a job, but Snake walks away. The President's speech commences, and he offers the contents of the cassette; to his embarrassment, the tape is Cabbie's cassette of the swing song "Bandstand Boogie". As Snake walks away, he tears the magnetic tape out of the real cassette.

Question: How does Brain die?
Answer: Steps on a mine