Treatment with testosterone can improve performance on tests of spatial ability in men with low testosterone levels and Alzheimer's disease. Improved performance on these tests may mean an improved ability to get around in one's environment without getting lost or injured. This could have a positive impact on both patients and those who care for them. We will investigate what areas of the brain are involved in these improvements in spatial ability. This will be done using a PET scan, which creates a 3-dimensional image of the brain that can allow us to see how the brain functions.

Volunteers will be treated with a prescription testosterone gel applied to the shoulder or other body area each day. This treatment will continue for 6 months. Subjects will undergo a PET scan at the beginning of the study and after approximately 2 months of treatment. Subjects will undergo some cognitive testing throughout the study.

Inclusion Criteria:

• Alzheimer's disease diagnosis, based on Diagnostic and Statistical Manual of Mental Disorders (5th ed.; DSM-V)
• Total testosterone < 300 ng/dL and/or calculated free testosterone < 50 pg/ml
• Sufficient English to perform cognitive testing
• Stable on concomitant medications for 1 month prior to starting study

Exclusion Criteria:

• history of prostate cancer
• history of breast cancer
• gonadal endocrine disorders
• current major psychiatric illness (excluding depression)
• significant uncontrolled systemic illness
• recent myocardial infarction (within 6 months)
• renal or hepatic disease, sleep apnea
• history of alcoholism or substance abuse within the past year
• history of head injury with loss of consciousness greater than 1 hour
• testosterone or other androgen treatment within past 3 months
• history of taking other drugs that might interfere with the results of the study (ie, spironolactone, cimetidine, antiandrogens, estrogens, p450 enzyme inducers, barbiturates)
• symptomatic BPH: prostatic symptoms, prostatic masses or induration on rectal examination
• prostate specific antigen (PSA) >4.0 mg/mL
• hemoglobin > 17 mg/dL
• generalized skin disease that could affect the absorption of testosterone gel (ie, psoriasis).
• potentially agitated or uncooperative for procedures