It is attached to the spine, ribs and sternum and is the main muscle of respiration, playing a very important role in the breathing process. The lungs are enclosed in a kind of cage in which the ribs form the sides and the diaphragm, an upwardly arching sheet of muscle,... Click to read more below.The diaphragm in the respiratory system is the dome-shaped sheet of muscle that separates the chest from the abdomen. It is also referred to the thoracic diaphragm because it’s located in the thoracic cavity, or chest.t is attached to the spine, ribs and sternum and is the main muscle of respiration, playing a very important role in the breathing process. The lungs are enclosed in a kind of cage in which the ribs form the sides and the diaphragm, an upwardly arching sheet of muscle,... Click to read more below.