During vigorous exercise, the anaerobic cellular process occurs when there is not enough oxygen available for the muscles to produce energy aerobically. Instead, the energy production switches to anaerobic metabolism. As a result, the runner may experience the accumulation of lactic acid in their muscles. Lactic acid is produced when glucose is broken down without oxygen, and its buildup can lead to muscle fatigue and soreness. Therefore, the correct answer is the "accumulation of lactic acid".