There's an interesting related mouse study on pubmed: Sildenafil restores cognitive function without affecting β-amyloid burden in a mouse model of Alzheimer's disease (https://pubmed.ncbi.nlm.nih.gov/21627640/)

From the abstract:

>>...sildenafil also increased levels of brain-derived neurotrophic factor (BDNF) and the activity-regulated cytoskeletal-associated protein (Arc) in the hippocampus without any detectable modification of brain amyloid burden.

I ran across this as I was looking to see if there were any studies involving sildenafil citrate and BDNF.