Pompe disease: An inherited deficiency of the enzyme alpha-glucosidase which helps the body break down glycogen, a complex carbohydrate that is converted to glucose for energy. Without the enzyme, glycogen builds up in the heart and other muscles, causing extensive damage. There are several different forms of Pompe disease which vary in severity. Pompe disease is inherited in an autosomal recessive manner. Also known as type 2 glycogen storage disease.