A Mathematical Model for Predicting Ultrasonic Measurement of Total Knee Replacement Contact Areas

A simple mathematical model was developed to characterize diagnostic ultrasound behavior at two-body interfaces of known geometry. The model was based on a 2-D curved-on-flat geometry comprising an infinitely long circular cylinder indenting a flat infinite half-space creating a known contact width W ₀. The effects of indenter radius R _F ultrasound resonance wavelength lambda/2, and ultrasound beam thickness BT on the size of the predicted interfacial contact width W ₁ were investigated. Since the model was purely geometric in nature, material properties of the mating bodies were not considered. A theoretical sensitivity analysis was performed on the model using geometries representative of commercially available orthopedic total knee replacements (TKRs) and typical diagnostic ultrasound resolutions. This investigation was part of an ongoing project to develop an engineering design tool for measuring surface contact areas at the tibio-femoral interfaces of clinically employed TKR prostheses.