Fitting curve passing through designated point to data for promoting the reproducibility of peripheral quantitative computed tomography (pQCT)

The Peripheral quantitative computed tomography (pQCT) is increasingly being used to monitor bone mineral density (BMD) change in both research and clinical practice in order to evaluate the fracture susceptibility in old people or the effect following therapeutic intervention^[3]. In follow-up studies, the drift area (change area) of total cross-sectional area (CSA) comparing with that of the baseline measurement (first measurement) was used to control the position as the baseline measurement. To study the interrelationship between the apparent BMD change and CSA change, the nonlinear regression curve was required to pass through a designated point. However, there is no ready-made software that can give the regression model which can pass through a designated point. In this study, BMD at 21 skeletal locations around 4% length of radius were measured by pQCT, then linear and nonlinear regression models passing through designated point were set up based on least square method using Matlab. The results showed the logarithmic model y = 23.4009-5.92491n(x + 51.9140) was suitable to describe the relationship between BMD change and cross-sectional area (CSA) change at the distal radius. This will be helpful to promote the reproducibility of pQCT in follow-up measurements.