Effect of the trabecular bone microstructure on measuring its thermal conductivity: A computer modeling-based study
Introduction
Computer modeling is widely employed to solve problems involving the thermal response of biological tissues in general and bone in particular. Computer models have been proposed to evaluate the heat transfer in bone tissues resulting from thermal ablation (Irastorza et al., 2016, Matschek et al., 2017), mechanical drilling (Davidson and James, 2003), or associated with bone cement in joint prosthesis (Hansen, 2003, Li et al., 2003 Jun). To improve the accuracy of these models, it is crucial to thermally characterize the bone tissues as far as possible, with special attention to their thermal conductivity (k), which determines the ability of the tissue to conduct heat. The models generally use data from different databases (Hasgall et al., 2016), which in turn, review the available scientific literature. Most of these databases consider that tissues are homogeneous. While this assumption may be valid for certain tissues, the porosity of trabecular bone (also known as cancellous bone) could significantly affect its thermal conductivity, as is the case with its electrical properties (Sierpowska et al., 2006, Sierpowska et al., 2007). As the thermal conductivity of trabecular bone and its relationship with its microstructure and marrow content is still poorly understood, our objective was to study the effects of the microstructure and marrow content on its thermal conductivity. In particular: 1) to measure the conductivity in samples of bovine trabecular bone and study their temperature dependence within a broad range (37–57 °C); 2) to use computer simulations to study the effects of bone marrow content and microstructure on the values of thermal conductivity; and 3) to quantify the error associated with the gap between the tissue sample and the thermistor-based conductivity measurement probe.
Section snippets
Samples preparation
Twenty approximately cylindrical bovine trabecular bone samples (10 mm long, 16 mm diameter) were obtained from the femur head of five animals from the local slaughterhouse within less than 24 h post-mortem (stored at 4 °C). The samples were machined using ad hoc tools. During the cutting process, they were moistened with phosphate-buffered saline (PBS) to avoid high temperatures and then kept at 4 °C overnight in sealed plastic tubes containing PBS. The next day they were thawed immediately
Experimental results
Table 3 shows the values of the measured thermal conductivity (kmeas) at three temperatures for two conditions. The mean value of k for non-defatted samples at 37 °C was 0.39 ± 0.06 W m−1 K−1. Regardless of the conditions (defatted vs. non-defatted), kmeas increased with temperature. The best-fit line showed a slope of + 0.2% °C−1 (see Fig. 2). When fat was replaced by PBS, kmeas increased from ~ 0.39 to ~ 0.43 W m−1 K−1.
Computational results
The sensitivity analysis resulted in an outer dimension of ro = 3.8 mm.
Discussion
This study explored the effect of microstructure and marrow content on the thermal conductivity of trabecular bone. Firstly, we measured the thermal conductivity in samples of bovine trabecular bone and studied their temperature dependence within a broad range (37–57 °C). The value found at 37 °C (0.39 ± 0.06 W m−1 K−1) is slightly above the range reported in Hasgall et al. (2016): 0.29 − 0.36 W m−1 K−1. The computer results (discussed below) suggest that this discrepancy may be partially due
Conclusions
The measurement and computer results suggest that: 1) including a gap filled with PBS increases thermal conductivity (k) of trabecular bone by 0.02–0.04 W m−1 K−1, 2) the value of k is possibly around 0.36 W m−1 K−1 at 37 °C, with a temperature dependence of + 0.2%°C−1, 3) the defatting process (i.e. replacing marrow by PBS) increases k by 0.04 W m−1 K−1, and 4) the presence of microstructure and fatty or red marrow has practically no effect on either maximum temperature or the position of the
Acknowledgements
We thank Marisa Orzuza and Marcos Silbestro for assistance with the sample preparation and the circuit design.
Financial support
This work was supported by a grant from the “Agencia Nacional de Promoción Científica y Tecnológica de Argentina” (Ref. PICT-2016–2303), by the National Scientific and Technical Research Council of Argentina (Grant PIO CONICET-UNAJ 0001), and by the Spanish “Programa Estatal de Investigación, Desarrollo e Innovación Orientada a los Retos de la Sociedad" under Grant TEC2014–52383-C3-R (TEC2014–52383-C3-1-R).
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