Establishment of BMD reference curves at different skeletal sites in women, using a Cartesian coordinate numeration system

The BMD reference curve is the reference value used for diagnosing osteoporosis and assessing bone mass changes. Its accuracy would affect the correctness of T -score and Z -score values and thus the reliability of diagnostic results. In this paper, we report the use of a new method, a Cartesian coordinate numeration system, to establish BMD reference curves at different skeletal sites in women. In a reference population of 3,919 women ranging in age from 5–85 years, we used the dual X-ray absorptiometry (DXA) bone densitometer to measure BMD at the posteroanterior spine (PA; vertebrae L1–L4), followed by a paired PA/lateral spine scan of the vertebral bodies of L2–L4, expressed in g/cm² and g/cm³, and of the hip and forearm. We chose the cubic regression model to best fit BMD curves that varied with age at different skeletal sites. We then referred the BMD of the fitting curves established by the method of the coordinate numeration system as reference curves, compared them to BMD reference curves derived from the fitting curve equation or age cross-section, and calculated the deflection degrees of the BMD reference curves acquired from the fitting curve equation. At the PA spine, lateral spine (expressed in g/cm³), femoral neck, Ward’s triangle and radius + ulna ultradistal, the reference curves calculated from the equation were significantly lower than those confirmed by the method of the coordinate numeration system; whereas, at the lateral spine (expressed in g/cm²), total hip, and radius + ulna 1/3 sites, the reference curves derived from the equation were markedly higher than those acquired from the coordinate numeration system. The differences in the two kinds of reference curves calculated by these two different methods gradually increased along with the increment in ages of the women. At the peak value of the reference curves, the BMD calculated from the equation deflected from 2.02% to −10.0% from the BMD acquired from the coordinate numeration system at different skeletal sites, and from 21.5% to −121.8% until the age of 85 years. The highest positive deflection of 65.2% existed at the lateral spine (expressed in g/cm²) and the lowest positive deflection of 21.5% at the total hip. The maximum negative deflection of −121.8% was at the radius + ulna ultradistal, and the minimum negative deflection of −32.6% at the PA spine. The BMD curve acquired from age cross-section was highly positive compared with the one derived from the coordinate numeration system ( r =0.955–0.985 p =0.000) with no significant difference between them. Various analysts used such a method to obtain the coefficient of variance (CV) in BMD precision on each curve that was from 0.05–0.19%. Our study shows that the Cartesian coordinate numeration system is an accurate, precise and reliable method and can serve to reveal the serious drawbacks of using the fitting curve equation to calculate BMD. The BMD reference curves established by this coordinate numeration system maintained the authenticity of the fitting curve, whereas, using the fitting curve equation to obtain BMD reference curves at different skeletal sites led to distortion, and resulted in false increases or decreases in T -score and Z -score values.