Diagnosed with terminal brain cancer, Vermont woman vowed to run the Boston Marathon. This week, she did.

This must be a stroke, she thought before she collapsed on the cold trail. Two years ago, Mary Beth Williams was running through the Vermont woods with a friend, their breath forming misty clouds in the January air. Suddenly, she began to slur her words. Her body froze. Her running partner, Eric Brigham, called for an ambulance, which rushed her to the University of Vermont Medical Center in Burlington. After a series of tests and scans, a doctor told her the devastating news. She had suffered a seizure caused by...