Modelling heat transfer in a bone–cement–prosthesis system

Abstract

The heat transfer in a general bone–cement–prosthesis system was modelled. A quantitative understanding of the heat transfer and the polymerization kinetics in the system is necessary because injury of the bone tissue and the mechanical properties of the cement have been suggested to be effected by the thermal and chemical history of the system. The mathematical model of the heat transfer was based on first principles from polymerization kinetics and heat transfer, rather than certain in vitro observed properties, which has been the common approach. Our model was valid for general three-dimensional geometries and an arbitrary bone cement consisting of an initiator and monomer. The model was simulated for a cross-section of a hip with a potential femoral stem prosthesis and for a cement similar to Palacos R. The simulations were conducted by using the finite element method. These simulations showed that this general model described an auto accelerating heat production and a residual monomer concentration, which are two phenomena suggested to cause bone tissue damage and effect the mechanical properties of the cement.