The introduction of 1-34rhPTH (TPTD) for treatment of individuals with osteoporosis at high risk of fracture changed the paradigm and gave clinicians an agent that has the capacity to correct the underlying architectural defect that is the hallmark of osteoporosis. Our group has a long-standing interest in the effects of TPTD on bone and have an ongoing study designed to look mechanistically at TPTD effects on bone, into which we have recruited 150 women with osteoporosis who were either treatment nave or who had been previously treated with alendronate. These individuals are being followed for 2 yrs (4 three TPTD month cycles or 2 yrs daily treatment). This application is a logical extension of that ongoing study and takes advantage of this unique population of TPTD-treated patients to compare the effects of teriparatide given cyclically (8 three month cycles) over 4 years with teriparatide given daily for 2 years on BMD of the spine and hip by DXA and QCT and BMD and microstructure of the radius and tibia assessed by high resolution pQCT. The specific aims are to determine in treatment nave and alendronate-treated subjects: 1. If TPTD given cyclically (3months on, 3 months off) over a 4 year period produces a clinically meaningful greater increase in BMD by DXA than 2 years of daily TPTD. 2. If QCT (hip, spine, radius and tibia), and FEA modeling of CT data, show enhanced effects of TPTD treatment or simply mirror DXA data. 3. If the tachyphylaxis seen with daily TPTD is caused by depletion of osteoblast precursors, and if it can be obviated by cyclic administration of TPTD. There is no other cohort, and nor will there be, any similar cohort in which these important and clinically relevant aims can be addressed. We believe that our population of subjects treated with TPTD allows us a unique opportunity to determine these clinically important long-term outcomes, since fracture studies with these TPTD regimens are unlikely to be undertaken. The issue of tachyphylaxis to ongoing TPTD administration, will be able to be assessed using the novel technique of an evaluation of the size of the circulating osteoblast pool in cyclic versus daily therapy.