The role of the diaphragm and inter costal muscles in breathing :

Mechanism of inspiration : Inspiration or inhaling is taking in of fresh air into lungs. It occurs in following steps :

1. The external intercostal muscles or inspiratory muscles contract and pull the ribs forward and upward thus increasing the volume of thoracic cavity.

2. The radial muscles of diaphragm contract. The diaphragm becomes flat. It also increases volume of thoracic cavity.

3. The abdominal muscles relax. Thus, the organs present in abdominal cavity get compressed to accommodate the flat diaphragm.

All this reduces the pressure of thoracic cavity, the lungs being closely applied to thoracic cavity expand. Thus, pressure of lungs is reduced as compared to the atmospheric pressure. The atmospheric air rushes into lungs via respiratory tract to make the pressure equal. Thus, air is inspired. 

Mechanism of expiration : Expiration is the exhaling of  air. It involves the following steps :

1. The peripheral muscles of the diaphragm relax and push the diaphragm upwards making it convex.

2. Intercostal muscles relax. This reduces the area of the thoracic cavity.

3. Abdominal muscles contract and decrease the thoracic cavity further.

Decrease in thoracic cavity reduces the volume of the lungs. The pressure is increased and the air is expired.