What is one of the pathognomonic features of Lhermitte-Duclos disease?

Lhermitte-Duclos disease is characterized by a specific alteration in the brain, known as cerebellar dysplastic gangliocytoma, which is a type of tumor derived from cerebellar neurons. This condition is often associated with Cowden syndrome, a genetic disorder that increases the risk of developing various types of tumors. The hallmark of Lhermitte-Duclos disease is the presence of this cerebellar dysplastic gangliocytoma, which typically manifests as a mass in the cerebellum leading to symptoms such as headaches and seizures, as well as problems with balance due to its location and effect on cerebellar function.

The other options presented do not represent pathognomonic features of Lhermitte-Duclos disease. While cleft lip, breast cancer, and thyroid nodules can be seen in the context of Cowden syndrome, they do not specifically indicate the presence of Lhermitte-Duclos disease itself. Instead, cerebellar dysplastic gangliocytoma is uniquely associated with this condition, making it the correct response.