Experimental and Theoretical Thermal Effects During Cementation of an Endomedullary Infibulum

Abstract

A 1-dimensional mathematical model of a femoral prosthesis implant has been developed. The actual complex geometry has been idealized as a composite cylinder of infinite length having a multishell bone/cement/stem structure. Attention is focused on the cement, which is a polymer that polymerizes “in situ”, inside the medullar channel and generates heat. The “cementation” phenomenon is described by the heat diffusion Fourier equation coupled with the polymerization kinetics. The numerical solution of the model has been accomplished by a finite difference explicit scheme. The experimental kinetic data has been obtained through isothermal polymerization tests, carried out by using a DSC calorimeter and a commercially available Howmedica Simplex P cement. The two most relevant results are:

• 1. The conversion of monomer into polymer is never 100% under the imposed initial and boundary conditions.

• 2. Bone/cement interface temperature is a function of the interface heat transfer coefficient.

Depending on such a parameter, ranging from 10. to 1000. (Wm^{-2 °}K^-1), the temperature may reach the maximum values of 80 °C and 40°C, respectively. In other words, the lower the heat transfer coefficient, the higher the interface temperature. Therefore, the model predicts relatively high temperature values at the bone/cement inteface. Such values confirm the criticality of this type of implant. The mathematical model developed is capable of taking into account both the geometry of the implant and the chemical-physical and kinetic properties of the cement. It represents a useful tool for setting-up the optimal conditions for the new materials developed in this orthopaedic field.

Heat generated within the polymerizing mixture partly diffuses through the bone, causing damages. We have therefore tested bone behaviour before and after thermal treatment in order to find possible mechanical effects.