Effect of the trabecular bone microstructure on measuring its thermal conductivity: A computer modeling-based study

Abstract

The objective of this work is to quantify the relation between the value of the effective thermal conductivity of trabecular bone and its microstructure and marrow content. The thermal conductivity of twenty bovine trabecular bone samples was measured prior to and after defatting at 37, 47, and 57 °C. Computer models were built including the microstructure geometry and the gap between the tissue and measurement probe. The thermal conductivity (k) measured was 0.39 ± 0.06 W m−1 K−1 at 37 °C, with a temperature dependence of + 0.2%°C−1. Replacing marrow by phosphate-buffered saline (defatting) increased both the computer simulations and measurement results by 0.04 W m−1 K−1. The computer simulations showed that k increases by 0.02–0.04 W m−1 K−1 when the model includes a gap filled by phosphate-buffered saline between the tissue and measurement probe. In the presence of microstructure and fatty red marrow, k varies by ± 0.01 W m−1 K−1 compared with the case considering matrix only, which suggests that there are no significant differences between cortical and trabecular bone in terms of k. The computer results showed that the presence of a gap filled by phosphate-buffered saline around the energy applicator changes maximum temperature by < 0.7 °C, while including the bone microstructure involved a variation of < 0.2 mm in the isotherm location. Future experimental studies on measuring the value of k involving the insertion of a probe into the bone through a drill hole should consider the bias found in the simulations. Thermal models based on a homogeneous geometry (i.e. ignoring the microstructure) could provide sufficient accuracy.