The aerostatic driving force is the ascending force of the object that is being weighed (Peña Pérez & Becerra Santiago, 2010). The application of a correction factor (Faf) associated with the aerostatic driving force is recommended in the bibliography. The Faf (Eq. 2) to be applied to the scale recorded mass value takes into account the air density, which may vary depending on ambient temperature, pressure and humidity:
$${F}_{af}=\frac{1-\frac{{\rho }_{a}}{{\rho }_{c}}}{1-\frac{{\rho }_{a}}{\rho }}$$
2
where ρa is the air density expressed in kg/m3 (calculated with Eq. 3), ρc is the density of the weights used by the manufacturer to calibrate the scale (8000 kg/m3, corresponding to stainless steel) and ρ is the density of the objects being weighed (2700 kg/m3for aluminum weights).
The air density ρa is calculated according to the semi-empirical formula
$${\rho }_{a}=\frac{0.348444p-h(0.00252t-0.020582)}{273.15+t}$$
3
where p is air pressure in hPa, h is relative moisture (%), and t is temperature (ºC).
When the Faf correction was applied to the standard weights measurements, a minor difference was observed between the measured value and the weight’s nominal mass. On the other hand, fluctuations observed during the measurement remained.
These fluctuations turned out to be temperature dependent, moreover each temperature increase detected by the temperature sensor implied a mass decrease, and vice versa. From this observation, an empirical factor related to temperature (T) could be determined:
$${F}_{e}={\left(\frac{{T}_{inst}}{{T}_{average}}\right)}^{5/{m}_{n}}$$
4
where Tinst and Taverage are the instantaneous and mean temperature during measurement, respectively, and mn is the nominal mass of standard weights expressed in mg.
Thus, the value of corrected mass (m) is given by the simultaneous application of the factors proposed to the scale reading (W), in the form:
$$m={F}_{af}*{F}_{e}*W$$
5
When applying both the aerostatic and the empirical factors (Eq. 5), records got stable around the nominal value, for the different standard weights. An example of the smoothing effect of these corrections on measurements is presented in Fig. 1.
On the other hand, when analyzing modifications introduced by the correction factors on the CEv calculation, it was observed that only the third decimal place is affected. Therefore, this correction would not be essential in order to obtain a representative CEv. Nevertheless, the corresponding calculation routine was incorporated in the protocol and in the EVAP v.2.0 code, since it could be useful in future measurements, i.e., in case that extended in time weighing determinations were necessary.
The analysis of measurement uncertainties is essential to estimate the error of the proposed new methodology. Nominal uncertainty of each instrument (Table 1) as well as typical values of every magnitude involved in the process (mass, temperature, pressure and humidity) were considered, and relative errors were calculated. Taking into account Eq. 1, and the correction factors of Equations 3 and 4, the error of the proposed methodology has been estimated as 5%.
Table 1
Instrumental ranges and nominal uncertainties.
Instrument | Range | Nominal uncertainty |
Semimicro Scale (Cubis) | 0–60/120 g | 10− 5 g / 10− 4 g |
Temperature Sensor (INGKA) | 0 - +65°C | 0.1°C |
Pressure Sensor (INGKA) | 300–1100 hPa | 0.01 hPa |
Humidity Sensor (INGKA) | 0–100% RH | 10− 6% RH |
Figure 2 shows a screenshot of the EVAP v.2.0 display. The program was developed to record and analyze mass values as a function of time. It allows the input of the sample identification data, and the duration of the time that the recording will last, which was set as 30 min for all the tissue sections measured in this work. The program plots a graph with the registered values, normalized to the initial mass (mh). It displays both the starting and the ending times of the record, as well as the calculated CEv value together with a historical value that serves as a reference. Finally, it offers the possibility of loading a file containing a record with the environmental conditions record, that are used to correct the original mass values by applying the previously explained correction factors.
Liver tissue samples were used to establish the new CEv measurement protocol. The data obtained with the proposed methodology was compared with the results of measurements using TGA. Representative curves of both types of measurements are shown in Fig. 3. In order to compare results, the mass values at the i-th instant are normalized to the first value (Normalized Mass = mi ⁄ mh). Since stabilization using TGA is slower and more variable than in the new procedure, subsequent intervals should be considered for the calculation of ms. The variation in the time elapsed until stabilization is associated with the fact that the geometry of the slice required by the TGA equipment is different from that used in this method. Although the dynamics of the two mass curves as a function of time were different, the final value of the CEv in both cases was equivalent to the historical value of 0.31 ± 0.02 (Portu, Postuma, et al., 2015). The equivalence between CEv values from TGA and the new methodology was also confirmed for lung samples (see Table II).
Mass values as a function of time were recorded using EVAP v.2.0 for BDIX rat liver samples, as it can be seen in Fig. 4. The measurements correspond to tissue sections from the same animal, but under different conditions: (I) different moments along the day, (II) different days, (III) different tissue blocks. The obtained curves were reproducible for the same type of tissue and species, even though the tissue sections had been obtained under different experimental conditions. In every case, it was found that from 0.1 h on, the mass value remains approximately stable. Consequently, the average of mass values recorded in a lapse between 0.1 and 0.2 h (6 to 12 min) was considered to calculate the dry mass ms.
The CEv values of 38 liver sections coming from different animals were determined, obtaining the distribution shown in Fig. 5. In order to evaluate the normal distribution of this data, a Kolmogorov-Smirnov test was performed, showing that the hypothesis is not rejected at a 5% significance level (with a p-value of 0.20). This indicates consistency in CEv values of tissues from different animals and allows to determine a reference value for liver samples. Therefore, the CEv corresponding to this tissue was established as 0.30 ± 0.02 (mean ± standard deviation), which coincides with the historical value determined by TGA (see Table 2).
The new methodology was then applied to study the evaporation dynamics of liver sections from nude mice and hamsters, besides BDIX rats. As shown in Fig. 6, when analyzing the same type of tissue from different species, no variations are observed in the evaporation dynamics and in the final CEv value (see Table 2).
The protocol developed in this work allowed to determine reference CEv values for some tissues, in order to be used in boron quantification by Neutron Autoradiography. Table 2 shows values obtained for tissues of interest, such as liver, lung and kidney. The measurements were taken from n samples from different animals and each dataset showed a normal distribution, as the one presented in Fig. 5. CEv ranges for liver samples from different species overlap, and the calculated values for rat liver and kidney are equivalent to those reported in Takeno et al., 2021. Furthermore, rat tissue CEvs are consistent with the characteristic water content measured by desiccation in lung, liver and kidney reported in the literature (Reinoso et al., 1997).
Table 2
CEv reference values for different types of tissues, to be applied in boron quantification using Neutron Autoradiography.
Tissue | Species | CEv | Water Content |
Liver | NUDE | 0.27 ± 0.03 (n = 16) | |
Liver | Hamster | 0.27 ± 0.03 (n = 17) | |
Liver | BDIX | 0.30 ± 0.02 (n = 33)ᵃ | 0.705ᵈ |
Kidney | BDIX | 0.23 ± 0.02 (n = 19) | 0.771ᵈ |
Lung | BDIX | 0.20 ± 0.02 (n = 24)ᵇ | 0.790ᵈ |
Metastatic lung | BDIX | 0.20 ± 0.03 (n = 16)ᶜ | |
a The value coincides with that obtained through TGA (0.32 ± 0.02). |
ᵇ The value coincides with that obtained through TGA (0.20 ± 0.03).
ᶜ Reported by Espain et al., 2020.
ᵈ Reported by Reinoso et al., 1997.
Table 2 also shows the CEv value of samples from the experimental model of disseminated lung metastases of colon carcinoma in BDIX rats (Trivillin et al., 2014). Despite the histological heterogeneities observed in metastatic lung, the CEv values obtained for these cases did not show statistically significant differences. Furthermore, as discussed in Espain et al., 2020, the CEv value of normal lung and lung with metastases are equivalent.
Because of the interest in studying boron microdistribution in different types of tissue coming from a hamster’s cheek pouch oral cancer model (Portu, Molinari, et al., 2015), CEv values of samples of tumor, normal pouch tissue and precancerous tissue were measured. The results are presented in Table 3. Although the histology of precancer and tumor tissue may vary between each section, this was not reflected in an increased dispersion. Moreover, normal, precancer and tumor tissue showed similar CEv values.
Table 3
CEv reference values for samples coming from a hamster’s cheek pouch oral cancer
Tissue | Species | CEv |
Normal Cheek Pouch | Hamster | 0.23 ± 0.02 (n = 15) |
Precancer | Hamster | 0.19 ± 0.01 (n = 12) |
Tumor | Hamster | 0.18 ± 0.01 (n = 8) |
Given that the new methodology allows measurements with equipment commonly found in a laboratory, it proved to be advantageous to obtain reference values. Besides, as it is not a destructive technique, it allows the determination of the CEv corresponding to the same section that will later be used to quantify boron content by Neutron Autoradiography. This advantage is of special interest for the quantification of heterogeneous tissues that could present differences in their evaporation coefficients. Currently, CEv is used not only to take into account the effects of water evaporation on tissue thickness, but also to study the variation in density and elemental composition between dry and wet tissue samples (Takeno et al., 2021). Having an established and reproducible protocol that allows the systematization of the procedure will contribute to a more precise determination of boron concentration in tissue samples through the Neutron Autoradiography technique.