A multi-exponential model of postmenopausal decline in vertebral bone mineral density: a new approach to the BMD reference range.

Although the postmenopausal decline in female bone mineral density (BMD) at the lumbar spine is central to the World Health Organization (WHO) diagnosis of osteoporosis, it has eluded an exact mathematical description. We present a simple mathematical model based on the assumption that bone loss can be described as an exponential decay process that begins at menopause. Women whose menopause begins in the same year of age are assigned a unique exponential function, and results from all women are combined to predict the average cross-sectional BMD on a year-by-year basis. This model has been successfully validated using data from a cross-sectional study of 8,789 female volunteers. No additional "aging" term is required. The normal time-constant was estimated to be 5.8 yr, but natural variation can have a substantial asymmetric effect on the curve. Similarly, variation in the distribution of the age at menopause also has a profound influence and can introduce artifacts when different populations of women are being compared. Using published data from Finland, it was confirmed that a simulation approach can predict the BMD decline observed in typical cross-sectional studies, suggesting the possibility of a cheaper and more convenient way to establish local dual-energy X-ray absorptiometry (DXA) reference curves.