There are two main groups of inspiratory muscles: principal and accessory. Principal muscles are used regardless of the level of breathing required, while accessory muscles are only used during forced breathing-when someone has asthma, exercises or has a cold. 

soundersleep.com

The principal (primary) muscles are: the external intercostal, internal intercostal and the diaphragm muscle. Both the external intercostal muscles and the internal intercostal elevate the ribs, thus increasing the width of the thoracic cavity, while the diaphragm contracts to increase the vertical dimensions of the thoracic cavity, and also aids in the elevation of the lower ribs.

The accessory (secondary) muscles of inspiration are: the scalene and sternocleidomastoid  muscles. During inspiration, the external intercostals raise the lower ribs up and out. The sternocleidomastoid and scalene muscles also become involved, serving to raise and push out the upper ribs and the sternum. 

During expiration, the most important muscles are those of the abdominal wall (including the rectus abdominus, internal and external obliques, and transversus abdominus), which drive intra-abdominal pressure up when they contract, and thus push up the diaphragm. The internal intercostals assist with expiration by pulling the ribs down and in. 

Upper ribs move with a “pump-handle” motion about the thoracic (midback) vertebrae.  This elevates the manubrium and rotates it outward to open the chest. Middle ribs move with a “bucket-handle” motion that expands the rib cage laterally. The 11th and 12th ribs move with a “caliper” motion.  
 
When people have asthma they make use of the ribs, thoracic vertebrae and secondary muscles to aid in breathing.  This causes rib restrictions, thoracic vertebrae restrictions (loss of motion) and adhesions/scar tissue in the muscles in the front of the neck, tops of the shoulders, and the diaphragm muscle.  Over time this causes the person to round their shoulders and their head/neck starts to move forward. 
 
We at Back to Health can aid in restoring the motion to the ribs, thoracic vertebrae, breaking up adhesions/scar tissue in the muscles.  When this occurs it is easier to use the proper muscles for breathing!