We used DosiVox to evaluate the impact of cement thickness on the dose effectively absorbed by the enamel layer. Until now, the thickness of the dental tissues adjacent to the enamel layer was not considered by any of the most widely used combined US-ESR dating programs (DATA and USESR). Instead, if adjacent tissues are present, their thickness is by default assumed to be sufficient to fulfill the infinite matrix conditions.
Our result suggest that such an assumption may represent in first instance a fair approximation of the reality, as even with a thickness of only 1 mm, the cement contributes to at least 98% of the beta dose rate coming from the outer side of the enamel layer. However, when cement is < 1 mm thick, DATA or USESR would overestimate the external beta dose rate and the value should be corrected accordingly by considering the relative contribution of the sediment. The impact of this correction on the total dose rate may vary, as it is directly dependent on the radioactivity of the cement itself, as well as of the sediment or dentine. Our results show that a very thin cement layer (0.1 mm-thick) can significantly contribute to the beta dose rate and should therefore not be neglected. Consequently, based on these results, we recommend the systematic measurement of the thickness of the dental tissues adjacent to the enamel layer during sample preparation, in order to proceed to beta dose rate corrections if necessary. Although this work has been especially focused on the case of fossil teeth showing cement, the conclusions stand for any other geometry involving different dental tissues adjacent to the enamel layer dated by ESR.
- dose rate modelling
- external beta dose rate
- fossil tooth
- ESR dating
One of the main difficulties in Electron Spin Resonance (ESR) dating of fossil teeth lies in the complexity of the system that has to be considered for dose rate evaluation. A tooth is indeed made by various dental tissues of variable thicknesses, densities and radioelement concentrations (Grün and Taylor, 1996; Rink and Hunter, 1997), which may all impact in more or less extent the amount of radiation dose absorbed by the enamel. If the initial and removed thickness of the enamel layer is usually taken into consideration for the alpha and beta dose rate attenuation and self-absorption factors, the thickness of the adjacent tissues (dentine, cement) is in contrast very rarely considered in the dose rate evaluation. Actually, the most widely used combined US-ESR age calculation programs among the community, DATA (Grün, 2009) and USESR (Shao
In order to evaluate to which extent this assumption is correct and how it may impact the external beta dose rate absorbed by the enamel layer, we used DosiVox, a Geant4-based software simulating the interactions of particles within a material for dosimetric purposes (Martin
A tooth is typically made of several tissues (mostly dentine, enamel and cement) that differ in many aspects such as chemical composition, mineralization, density or thickness (see overviews in Driessens, 1980, Elliott, 2002; Hillson, 2012). Tooth structure and geometry is highly variable depending on the type and species considered (Hillson, 2012), and the enamel layer dated by ESR may be surrounded by different materials, such as dental tissues and/or sediment. For example, enamel is the outermost layer in human tooth crown, which means that it is in direct contact with the sediment on its external side. In contrast, fossil equid teeth are notoriously famous for having cement capping the external side of the enamel layer. As a consequence, the sediment is not in direct contact with the enamel. Basically, these two situations have different implications in terms of dose rate evaluation, and especially for the alpha and beta components.
In ESR dating, teeth are typically approximated to a succession of thin layers. Two main geometries can usually be considered, depending on whether the enamel layer is on one side in direct contact with the sediment:
where tissue1 is in most cases the inner tissue, dentine, and tissue2 is the outer dental tissue at the interface between the enamel and the sediment. This tissue is usually cement (e.g. Duval
Dose rate evaluation in fossil teeth is usually based on a series of considerations that may be summarized as follows:
Any dental tissue directly attached to the enamel layer (internal component of the dose rate) contributes to the external alpha and beta dose rate (Grün, 1992), while the gamma dose rate comes from the sediment only (Geometry 1, see
Unlike sediment, dental tissues are assumed to be free of Th-232-series and K-40 elements (Grün and Mc Dermott, 1994; Grün and Taylor 1996). Consequently, the alpha and beta dose rate components in dental tissues come from the U-238 decay chain alone.
As part of the standard sample preparation procedure, the external alpha dose rate contribution is usually removed (or at least significant minimized) by cleaning the enamel layer on both side by > 20 μm (e.g. Duval
In contrast, because the standard penetration depth of the beta particles (about 2 mm) is in the same order of magnitude of the usual thickness of dental tissues (typically around 1.0–1.5 mm), the beta dose rate component cannot be eliminated. Instead, the attenuation of the beta particles has to be considered, together with the thickness of the enamel layer removed on both sides.
A succession of thin and homogeneous layers is considered for the external beta dose rate evaluation. In order to meet the infinite matrix conditions, the thickness of the layers adjacent to the enamel is assumed to be > 2 mm, and an isotropic and homogeneous spatial distribution of U-238 series elements is typically assumed within each dental tissue.
Dental tissues are known to behave as open systems for U-series elements (Grün and Mc Dermott, 1994). Disequilibrium in the U-238 decay chain is commonly observed in fossil teeth, and U-series have to be combined with ESR data to provide a single combined US-ESR age result for a given tooth (Grün
DATA (Grün, 2009) and USESR (Shao
As mentioned above, if the enamel layer is surrounded on both sides by other dental tissues, these adjacent tissues are assumed by DATA and USESR to be thick enough (>2 mm) to meet the infinite matrix conditions. However, this assumption may sometimes be wrong. For example, the thickness of the cement layer in equid teeth is known to be highly variable depending on the type of tooth, the age at the death of the animal, as well as longitudinally, from the occlusal surface to the roots (e.g. Burke and Castanet, 1995). Consequently, it is not unusual to have an outer adjacent dental tissue with a thickness of < 2 mm. However, it is simply unknown in which extent it may impact the final age result. Considering a thickness that fulfills the infinite matrix conditions would lead to the calculation of an overestimated beta dose rate value (and thus an underestimated US-ESR age) if the tissue thickness is thinner than 2 mm. In contrast, considering no dental tissue on the outer side of the enamel layer would underestimate the true beta dose rate and yield thus an overestimated US-ESR age. In first instance, the true age of the sample would be located somewhere in between those two calculations. Consequently, the use of Geometry 1 and 2 may be used in first instance to roughly estimate the impact of a thin (< 2 mm) adjacent tissue on the final age results. However, this evaluation cannot be considered as fully satisfactory given the magnitude of the uncertainty involved (see example above with sample 3546B).
Modelling beta dose rates is in first instance not so straightforward, as complex beta emitter spectra derived from K-40 as well as progeny of U-238 and Th-232 have to be considered (see Guérin
Beta dose rate modelling was carried out with DosiVox program (version 1.04; Martin
In our study, sample geometry was approximated to the stratified-sediment case presented in Martin
Simulations were based on considering a standard sandy sediment with 1 ppm U-238, 3 ppm Th-232 and 1% K-40. In comparison, uranium concentration in the enamel, dentine and cement was assumed to be of 1, 50 and 10–30 ppm. The characteristics of each material (chemical composition, density, water content) used in the simulations are provided in Supplementary material, Table S1. In order to avoid too complex simulations and obtain results that can be directly compared with those from DATA and USESR programs, a couple of assumptions were considered:
Equilibrium in the U-238 decay chain for both dental tissues and sediment was assumed. We are aware that this assumption is most likely incorrect for dental tissues, but DosiVox does not presently contemplate U-series disequilibrium. We acknowledge this may result in some approximation for the beta emitter spectra and the mean path length of beta particles. However, we believe this does not affect the purpose of this work, as the resulting dose overestimation potentially induced by considering equilibrium in dental tissues can in any case be indirectly addressed by diminishing the uranium concentration in the corresponding tissue or adjusting the dose rate conversion factors accordingly.
Each material modelled (sediment and dental tissues) is assumed to display an isotropically homogenous spatial distribution of radionuclides in order to mimic the conditions offered by both DATA and USESR. We are aware the reality is undoubtedly more complex (e.g. Duval
For each case, U-238, Th-232 and K-40 beta spectra were simulated, and a total beta dose rate distribution was calculated according to the conversion factors from Guérin
Numerical values extracted for the enamel layer and derived from the 5 sets of simulations are provided in Supplementary material, Table S2 and graphically displayed in
- the values may increase by ~9 to ~45% for 0 to 2 mm-thick cement with 10 and 30 ppm of U-238, respectively.
- for a cement with uranium concentration > 20 ppm, the relative increase in the total dose rate is already significant (5 to 10 %) with only a 0.1 mm-thick cement.
These simulation shows the non-negligible weight of a thin layer (
Logically, the relative contribution of the cement to the total beta dose rate increases with the thickness and reaches a maximum at 2 mm (
weight of the cement is directly dependent on the radioelement concentration of the dental tissues and sediment. Nevertheless, previous observations made on horse teeth dated by ESR showed that is the large majority of the cases (88%) the cement displays lower uranium concentration values than in the corresponding dentine of a given tooth (Duval
In contrast, the relative contribution of the sediment is minimum (1.3%) as soon as the cement has a thickness > 0.5 mm. U-238 concentrations of 10 and 30 ppm in cement would have virtually no impact on this relative contribution: it would remain within 1.1–1.4 % for a 0.5 mm-thick cement.
We also tested the impact of a “particle reflection” algorithm process on the simulated dose rates with a modified version of DosiVox (Martin, 2015). This algorithm was specifically designed to ensure infinite matrix conditions during the simulations: basically, the beta particles are emitted homogeneously and isotopically, and they are reflected in the opposite direction (
Using this algorithm, resulting beta dose rate no longer display those edge effects,
As mentioned by Guérin and Mercier (2012), one of the main interests of the ‘Reflection algorithm’ is the increased statistical counting by avoiding the loss of beta particle beyond the edge of the parallelepiped. As a consequence, it may thus lead to a significant decrease of calculation times. However, one may be aware that the use of this algorithm results in the creation of a virtual infinite matrix by reflection. Consequently, it can only be applied to planar geometries and must be employed with caution in other cases for which the reflected geometry at the edges of the considered volume would result asymmetrical (considering the range of the beta particles).
The DosiVox simulations show that there is a clear correlation between the cement thickness and the amount of beta dose absorbed by the enamel layer. However, in which extent cement thickness significantly impact the dose rate evaluation?
This work illustrates the great potential of DosiVox to address very simple questions that may be of importance in ESR or Luminescence dating, but require some modelling. Until now, the thickness of the dental tissues adjacent to the enamel layer was not considered. When present, adjacent tissues were assumed to be sufficient to fulfill the infinite matrix conditions. Our result suggests that in first instance such an assumption may represent a fair approximation of the reality, as even with a thickness of only 1 mm, the cement contributes to at least 98% of the beta dose rate coming from the outer side of the enamel layer. When cement is < 1 mm thick, the beta dose rate derived from DATA or USESR should be corrected accordingly by considering the additional contribution of the sediment. The correction factors may be found in
Finally, DosiVox simulations were performed with a given set of experimental conditions, and we do acknowledge that reality is, as per usual, more complex than the modelled scenarios. The values of some parameters such as water content, density, chemical compositions of the sediment and dental tissues may vary among tooth samples and sites, which would have in more or less extent an impact on the modelled beta dose rate values. These aspects will be further investigated in the future in order to quantify the resulting uncertainty.
Although the work has been especially focused on the case of fossil teeth showing cement, the conclusions of this work stand for any other geometry involving different dental tissues adjacent to the enamel layer dated by ESR. Sometimes, multi-folded inner enamel layers may indeed be surrounded by a succession thin dentine and enamel layers (e.g. Grün