Theoretical explanation of the relationship between backscattered electron and x-ray linear attenuation coefficients...

X-ray absorption and backscattered electron (BSE) microscopies are two commonly used techniques for estimating mineral contents in calcified tissues. The resolution in BSE images is usually higher than in x-ray images, but due to the previous lack of good standards to quantify the grey levels in BSE images of bones and teeth, x-ray microtomography (XMT) images of the same specimens have been used for calibration. However, the physics of these two techniques is different: for a specimen with a given composition, the x-ray linear attenuation coefficient is proportional to density, but there is no such relation with the BSE coefficient. To understand the reason that this calibration appears to be valid, the behaviour of simulated bone samples was investigated. In this, the bone samples were modelled as having three phases: hydroxyapatite (Ca10(PO4)6(OH)2), protein, and void (either empty or completely filled with polymethylmethacrylate (PMMA), a resin which is usually used for embedding bones and teeth in microscopic studies). The x-ray linear attenuation coefficients (calculated using published data) and the BSE coefficients (calculated using Monte Carlo simulation) were compared for samples of various phase proportions. It was found that the BSE coefficient correlated only with the x-ray attenuation coefficient for samples with PMMA infiltration. This was attributed to the properties of PMMA (density and mean atomic number) being very similar to those of the protein; therefore, the sample behaves like a two-phase system which allows the establishment of a monotonic relation between density and BSE coefficient. With the newly developed standards (brominated and iodinated dimethacrylate esters) for BSE microscopy of bone, grey levels can be converted to absolute BSE coefficients by linear interpolation, from which equivalent densities can be determined.