A nonlinear inverse problem in estimating the polymerization heat source of bone cements by an iterative regularization method

In the present study, the conjugate gradient method (CGM) using an iterative regularization method (IRM) is used to solve the inverse heat conduction problem (IHCP) in order to estimate the unknown heat generated during polymerization of bone cement. The exothermic chain propagation reaction results in a high local temperature and has a deleterious effect on living tissues and extracellular matrices. Only when such a heat source is estimated accurately, can the influences of the production of bone cements on bone cells be analyzed more clearly. Results obtained by using the CGM to solve this IHCP are justified based on the numerical experiments. It is concluded based on the results of the reported numerical experiments that the accurate polymerization heat source can be estimated by the CGM. Finally, the effects of the simulated measurement errors on the inverse solutions are included and discussed. It is found that when considering a real functional form of heat source, the measurement errors of 1% and 3% will yield the relative average errors for the solution of only less than 2% and 4%, respectively.