papillary muscle, any one of the rounded or conical muscular projections attached to the chordae tendineae in the ventricles of the heart. The papillary muscles vary in number. The two main muscles are the anterior papillary muscle and the posterior papillary muscle. The papillary muscles are associated with the atrioventricular valves that they help open and close. Compare chordae tendineae, trabecula carnea.