Ultrasonic measurement of the reaction kinetics of the setting of calcium sulfate cements using implicit calibration

Injectable bone cements based on calcium sulfate and calcium phosphates are being developed for use as bone defect filling and reinforcement of osteoporotic bones. For developers and end-users, kinetic properties of the setting reaction of such cements are of great interest. Existing standards for setting time measurement are based on visual examination of the cement surface and thus suffer from poor repeatability and subjectivity. Implicit calibration provides the means of determining parameters of a physical model at the same time as a calibration based on regression. This enables the use of indirect observations for the determination of implicit model parameters. In this paper, we study the hydration of calcium sulfate hemihydrate into calcium sulfate dihydrate, by combining multivariate calibration with a physical model of the reaction kinetics. The physical model contains three parameters, the reaction rate, the reaction order and a time delay. These parameters are estimated from ultrasound amplitude spectra. The resulting model fit has an R 2 value of 99.9%. Copyright © 2008 John Wiley & Sons, Ltd.