## 4 Discussion  
Even though the estimation of quality parameters of our human bone samples was based on a 2D imaging technique, the calibration through the gold-reference measurements in both bone an a sample of porous material (such as sandstone) allowed to achieve a low bias in the estimation (below 5%). We believe this is important, as the cost-benefit of these studies has to be pondered between having accurate porosity values through equipment with limited access, against estimated values obtained through low-cost technology that can be calibrated to minimize error, then allowing a more all-inclusive characterization of bone samples.  
Given its low bias, our approximations of porosity values using 2D images are valid estimators and can be used for further analyzing our bone samples (as well as other porous materials), the reason for which we decided to put our results in terms of those estimated values and proceeded with a comparison between quality and quantity parameters of our samples. However, a similar approximation for less porous materials is not possible due to the known non-linear relationship between specific surface and porosity. In [35], such behavior is represented as a parabolic curve that comprises the range from very compact to least dense material, showing a maximum in medium porosity levels. In our case, due to osteoporosis, all samples belong to the right-tail of such curve (least dense and more porous bone) in which the behavior can be well approximated as a linear function that models a rapid decay of the specific surface of the bone as porosity increases. More details on this can be found in [36].  
Our work adds up to previous studies regarding the comparison among bone-specific surface (BS/TV) against the bone volume fraction (BV/TV). For example, [35] initially proposed a \"dome-shaped\" curve behavior within a fifth-order polynomial. Later, other studies improved the approximation on the relationship among those variables, for example, by analyzing 3D images of cortical femurs with synchrotron radiation [37], or through the development of a computational model of bone remodeling that integrates bone cell interactions based on bone porosity and stiffness [38]. Another example is the work of [39],  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample** & \(\sigma_{max}\) **(MPa)** & \(\sigma_{y}\) **(MPa)** & \(E\) **(MPa)** \\ \hline \multirow{2}{*}{M25} & 66.6 & 57.9 & 2994.9 \\  & 66 & 48.1 & 2918.5 \\ \hline \multirow{2}{*}{F45} & 34.7 & 24.2 & 1764.3 \\  & 34.1 & 26.5 & 557.1 \\ \hline \multirow{2}{*}{M50} & 30 & 21.6 & 1391.4 \\ \hline \multirow{2}{*}{F52} & 29.8 & 23.3 & 1052.2 \\  & 22.7 & 21.4 & 282.7 \\  & 21.3 & 16.5 & 865.1 \\  & 30.2 & 27.1 & 1444 \\ \hline \multirow{2}{*}{M57} & 11.2 & 9.6 & 174.4 \\  & 20.1 & 15.6 & 541 \\ \hline \multirow{2}{*}{M64} & 23.5 & 20.1 & 460.7 \\  & 22.9 & 19.5 & 762.7 \\  & 39.3 & 27.4 & 1429.6 \\ \hline \multirow{2}{*}{F68} & 1.8 & 1.4 & 127.6 \\  & 1.8 & 1.4 & 56 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Results of mechanical tests for each sample cube.  
where bone remodeling equations are proposed for the evaluation of the existing risks of osteoporosis fractures by taking into consideration the microstructure and magnitude of a specific surface. In that context, our work highlights the effectiveness of a comparison between two-dimensional and three-dimensional modalities in bone tissue. We show that it is possible to analyze two-dimensional images in trabecular sections through a binarization process and with comparable results as those obtained through technologies such as X-ray computed microtomography. More details on our preliminary findings are discussed next.