The goal of this study is to determine whether romosozumab will improve bone density in girls and women with functional hypothalamic amenorrhea (cessation of the menstrual period due to intense exercise, stress, or an eating disorder) who have low bone density. Participants will be randomly assigned to receive romosozumab or placebo for 6 months. All participants will receive one IV infusion of zoledronate at the 6 month visit. All participants will also receive transdermal estradiol and cyclic progesterone. We will investigate whether participants who receive active romosozumab will demonstrate greater improvements in bone density at one year than those who receive placebo. We will also compare bone density over a year with healthy controls (girls and women of similar age who have regular menstrual periods).

Inclusion Criteria:

For FHA and controls:

• Female, age 14-30 years, skeletally mature with bone age ≥ 12 years

• For women of reproductive age, agree to use one of the following for the study duration:

  1. an effective non-hormonal contraceptive method
  2. a progestin releasing intrauterine device (no evidence of systemic skeletal effects)
  3. a progestin releasing implant
  4. does not have a history of sexual activity that could lead to pregnancy (i.e., same-sex partners only or total abstinence has been and is their preferred lifestyle)

• Biochemical criteria:

• Negative βHCG (pregnancy test)

• TSH within twice the upper limit of normal; potassium, magnesium within the normal range; prolactin <10 ng/mL above the upper limit of normal; FSH not elevated.

• Serum ALT ≤ 3 times upper limit of normal, LDL ≤ 190 mg/dl

• eGFR ≥ 30ml/minute

• If the diagnosis of FHA is unclear, we may check additional labs (e.g., testosterone and sex hormone binding globulin if there is a suspicion of PCOS based on clinical hyperandrogenism).

Additional inclusion criteria for FHA:

• Less than 3 menses in the preceding 6 months
• BMD Z-score ≤ -1.0 at ≥ 1 skeletal site (for subjects <18 years old, we will use the height Z-score-adjusted BMD Z-score using the pediatric bone density calculator developed by the National Institutes of Health and currently maintained by the Children's Hospital of Philadelphia)
• Dental check-up within the past year
• If the menstrual status of the subject is unclear due to the presence of a progestin-releasing IUD, serum estradiol levels will be checked twice, at least one week apart. Both estradiol levels must be < 50 pg/mL.At the discretion of the study clinician, subjects with a diagnosis of PCOS may undergo one to two serum estradiol levels, at least one week apart. The estradiol level(s) must be < 50 pg/mL

Exclusion Criteria:

For FHA and controls

• Disease other than FHA known to affect bone, including untreated thyroid dysfunction, Cushing's disease, renal failure, diabetes mellitus
• Use of bisphosphonates in the past year
• Use of other medications known to affect bone metabolism within 3 months of the study (other than calcium and vitamin D supplementation).
• Current use of systemic corticosteroids
• Migraine with aura as classified in IHS Classification ICHD-3.
• Personal history of or first-degree relative with unprovoked thromboembolism (unless the subject has been tested and ruled out for a hypercoagulable state).
• Active substance use disorder; currently smokes or vapes
• History of malignancy or Paget disease of bone
• Pregnant, planning to become pregnant within 12 months after the end of treatment and/or breastfeeding

Additional exclusion criteria for FHA

• Cardiovascular: History of myocardial infarction or stroke; history of hypertension or use of anti-hypertensive medications
• Immunodeficiency or taking immunosuppressive therapy
• Other conditions that can cause oligo-amenorrhea such as PCOS, primary ovarian insufficiency. A participant with PCOS may be included if a study clinician determines that missed menstrual periods are more likely a consequence of FHA.
• Dental: Osteonecrosis of the jaw (ONJ) or risk factor for ONJ, such as invasive dental procedures (tooth extraction, dental implants, oral surgery in the past 3 months), poor oral hygiene, periodontal and/or pre-existing dental disease
• Planned invasive dental procedure or other planned major surgery for 18 months after the baseline visit
• Known sensitivity or absolute contraindication to any of the products or components of the medications to be administered (romosozumab, zoledronic acid, transdermal estradiol, micronized progesterone, calcium or vitamin D supplements)
• Concerning EKG findings for ischemia Additional exclusion criteria for normal-weight healthy controls
• BMD Z-score <-2.5 (who we will refer for evaluation)