What condition causes the human rib cage to swell?

Pagets Disease: I am not quite sure what you mean by swelling of rib cage. Do you mean the bones themselves or over inflation. Paget's is a bone disorder that can cause hyperplasia of bones but usually affects the back. If symptoms are significant, I would start with an X ray of the chest and some basic lab studies.

Emphysema: Emphysema is also on the list that causes a dangerous expansion of the chest. Physician's call this COPD.