Measurement of an evaporation coefficient in tissue sections as a correction factor for 10B determination

Boron neutron capture therapy (BNCT) is a cancer treatment option that combines preferential uptake of a boron compound in tumors and irradiation with thermal neutrons. For treatment planning, the boron concentration in different tissues must be considered. Neutron autoradiography using nuclear track detectors (NTD) can be applied to study both the concentration and microdistribution of boron in tissue samples. Histological sections are obtained from frozen tissue by cryosectioning. When the samples reach room temperature, they undergo an evaporation process, which leads to an increase in the boron concentration. To take this effect into account, certain correction factors (evaporation coefficients, CEv) must be applied. With this aim, a protocol was established to register and analyze mass variation of tissue sections, measured with a semimicro scale. Values of ambient temperature, pressure, and humidity were simultaneously recorded. Reproducible results of evaporation curves and CEv values were obtained for different tissue samples, which allowed the systematization of the procedure. This study could contribute to a more precise determination of boron concentration in tissue samples through the neutron autoradiography technique, which is of great relevance to make dosimetric calculations in BNCT.


Introduction
Boron neutron capture therapy (BNCT) is an attractive proposal for cancer treatment. Many advances have been made in basic and clinical research in this field, exploring different targets with a promising outcome (e.g., Chen et al. 2021;Hirose et al. 2021;Kawabata et al. 2021). Unlike conventional treatments, BNCT is a biologically targeted radiation therapy: it allows the irradiation of individual cells or micrometastatic sites with high linear energy transfer (LET) radiation, without affecting the surrounding healthy tissue. It is mainly applied to pathologies that respond poorly to conventional therapies. In many cases, a poor response is due to the high heterogeneity of the treated tumors, the high sensitivity of the surrounding healthy tissue that acts as a dose limiter, or because the lesions are too small to be correctly detected or are distributed in such a way that radiation damage to healthy tissues cannot be avoided (Coderre et al. 2003).
BNCT is considered as a binary therapy. It requires that a nontoxic compound rich in 10 B that preferentially accumulates in tumor cells is infused to the patient. Once the compound is biodistributed in the organism, the region to be treated is irradiated with a thermal or epithermal neutron beam. The charged particles emitted in the boron neutron capture (BNC) reaction deposit a high amount of energy in a range of about a cell diameter. In this way, the tumor cells that have captured 10 B atoms are destroyed, while the healthy ones are ideally preserved.
To calculate the neutron irradiation time according to the dose to be delivered during a BNCT protocol, it is necessary to know the boron concentration in the different tissues involved during the treatment. These data are included in the treatment planning to define the dose to be delivered to the target (Coderre and Morris 1999). A recent approach proposes the use of a neural network-based prediction method to calculate the therapeutic dose in BNCT (Tian et al. 2023). At present, there is no way to routinely determine tissue boron concentrations during neutron irradiation. Instead, 1 3 blood samples are collected during the neutron irradiation, and boron concentrations in the tissues of interest must be inferred from the concentrations measured in blood. Therefore, tumor/blood, tumor/normal tissue, and normal tissue/ blood concentration ratios must be determined previously. This information can be obtained through biodistribution studies prior to treatment, with positron emission tomography (PET) (Imahori et al. 1996;Aihara et al. 2006). Furthermore, to understand the observed response to therapy and study the biological effectiveness of boron carriers, it is necessary to study the boron concentration and distribution at the tissue, cellular, and subcellular level, both in in vitro and in vivo models (Witting 2008). The available techniques in BNCT to study boron spatial distribution at the microscopic level are: secondary ion mass spectrometry (SIMS) (Chandra et al. 2014), laser post-ionization secondary neutral mass spectrometry (laser-SNMS) (Aldossari et al. 2019), electron energy loss spectroscopy (EELS) (Michel et al. 2003), laser-induced breakdown spectroscopy (LIBS) (Kalot et al. 2020), laser ablation inductively coupled mass spectrometry (Reifschneider et al. 2015), matrix-assisted laser desorption/ionization mass spectrometry imaging (MALDI-MSI) (Miyake et al. 2022), and neutron autoradiography with nuclear track detectors. In comparison with the aforementioned techniques, neutron autoradiography allows high-resolution determination at relative low cost. Its accessibility and applicability have made it possible to apply this technique to several biological models (in vitro and in vivo) by different research groups, to evaluate the potential efficacy of 10 B delivery compounds and strategies (Ferrari et al. 2009;Ciani et al. 2013;Pietrangeli et al. 2015;Portu et al. 2015a;Garabalino et al. 2019;Nar et al. 2019) and assess the correlation with BNCT efficacy in radiobiological studies (Molinari et al. 2015;Bortolussi et al. 2017). Moreover, neutron autoradiography has been applied to address boron microdistribution in human liver samples (Altieri et al. 2008;Schütz et al. 2012).
The neutron autoradiography technique using nuclear track detectors (NTD) allows the mapping of heavy particle emitting elements in a sample. Within the framework of BNCT, it means the possibility of knowing the 10 B microdistribution in tissue sections. When a boron-loaded tissue section is placed in contact with an NTD and exposed to a thermal neutron flux, the BNC reaction ( 10B(n, )7Li ) occurs. The α and 7 Li resulting particles impact the detector, generating localized damage in the material, in the surroundings of the ion path (latent tracks). Through a chemical attack process or etching, these latent tracks are revealed and amplified even at the light microscopy level, which enables their observation and quantification (e.g., Fleisher et al. 1975). By measuring the number of tracks per unit area (tracks density) observed on the detector and using a previously established calibration curve (Portu et al. 2011a), it is possible to estimate the concentration of 10 B in the different tissue structures of the original sample (Portu et al. 2011b(Portu et al. , 2013. Regardless of the chosen boron determination technique, the efficacy of BNCT depends on the correct estimation of the boron dose. For that reason, accuracy of absolute boron concentration values becomes essential (Wittig et al. 2008). In the case of neutron autoradiography, the histological sections to be studied using this technique are obtained by freezing using a cryostatic microtome (or cryostat). In the transition to room temperature, the tissue undergoes an evaporation process, which generates an increase in the concentration of 10 B atoms in the sample. Furthermore, in the case of soft tissues, evaporation has a direct influence on the tissue section thickness, which at the time of irradiation will be smaller than the nominal thickness set in the cryostat. The thickness of the sample determines the number of particles arriving at the NTD, and consequently, on the boron quantification (Ceberg et al. 1993). For these reasons, a natural amplification of the final number of tracks in the detector occurs.
To quantify the boron concentration in the original sample, it is necessary to establish correction factors that account for this effect. Since evaporation implies a loss of weight in the sample, and assuming that the quantity of boron atoms does not vary during this process, the concentration can be corrected by an evaporation coefficient (CEv), defined as: where m h corresponds to the "wet" section mass, measured immediately after the tissue is sectioned in the cryostat, and m s is the "dry" section mass, measured when the evaporation process is finished.
The CEv is applied directly to determine [ 10 B] from the calibration curve: where N A −1 is the amount of tracks per unit area, Ord is the ordinate, and S the slope of the calibration curve.
The measurement of mass loss is usually carried out through a thermogravimetric analysis (TGA) (Saadatkhah et al. 2020). However, this method requires special equipment, is a destructive technique, and takes a long time (2 h; Portu et al. 2015a,b), which reduces the possibility of doing several measurements per day. Therefore, it is necessary to develop a protocol that allows weight evaluation using equipment that is widely available, without restrictions on the number of samples to be analyzed.
The problem of tissue evaporation was presented in Gadan et al. (2012) and the evaporation dynamics were extensively studied in our laboratory (Espector et al. 2018).
The proposed correction was applied by Takeno et al. (2021) to consider the effects of water loss on density and elemental composition, and was also employed in alpha spectrometry determinations (Bortolussi and Altieri 2013). The aim of this work was to explore different aspects involved in the setup of the experimental conditions for the sample mass variation measurement, and to establish a protocol to determine the evaporation coefficients corresponding to different tissues. Systematization of the measurement method also made it possible to create specific software for data recording, visualization, and analysis (EVAP v.2.0). Temperature, pressure, and humidity values were registered simultaneously to mass measurements, and correction factors associated to environmental conditions were proposed. The protocol was applied to record mass variation due to evaporation in different tissues of interest for autoradiographic analysis, to obtain reference values of CEv.

Materials and methods
A Sartorius laboratory-scale Cubis line, model MSE125P-000-DU-00 (precision: 10 -5 g) with USB connection to a notebook was used in this work (Sartorius AG Weender Landstrasse 94-108 37,075 Göttingen Germany). Measurements of the mass evolution were taken every 1 s. To characterize the scale drift, 24 h records of mass values as a function of time were made with different standard weights (Gebrüder Bosch Jungingen/Hohenz) of 20, 50, 100, 200, and 500 mg. Simultaneously, temperature, pressure, and humidity readings were monitored at intervals of 1 s, using INGKA environmental sensors. Two correction factors were determined to reduce the error associated with the scale drift.
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 Eqs. 3 and 4, the error of the proposed methodology has been estimated as 5%.
A program designed in Matlab, EVAP v.2.0, was developed to command the whole process of weight determinations over 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 code selects the first significant mass value and defines it as m h . The program plots a graph with the registered values of mass variation over time, normalized to the initial mass (m h ). As the evaporation takes place, the mass measurements stabilize in about 5 min. Thus, an average of the values recorded between 6 and 12 min was used to obtain the m s value and calculate the evaporation coefficient.
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, which are used to correct the original mass values by applying correction factors.
Tissue samples from normal BDIX rats, nude mice, and hamsters were analyzed in this work, all of them being of interest for neutron autoradiography analysis in BNCT. Samples coming from a hamster's cheek pouch oral cancer model were also included in the analysis (Kreimann et al. 2001). All the animals were infused with borofenilalanine combined with fructose (BPA-f) according to protocols previously established in each case: for the BDIX rat (Garabalino et al. 2011) and hamster (Kreimann et al. 2001) with a dose of 300 mg/kg and sacrificed 3 h post boron injection and for nude mice (Carpano et al. 2015) of 350 mg/kg and sacrificed 1 h post boron injection. All samples used in this study come from other research groups at BNCT, approved by the institution's ethics committee. BDIX rat liver samples were used to design the protocol, due to the uniformity of this tissue at the histological level. To analyze the variation of CEv between species, samples of hamsters and nude mice liver were also included. Furthermore, CEvs were determined in reference tissues (liver, kidney, and lung) in BDIX rats.
Sections of the different tissues were obtained by freeze sectioning with a CM 1850 cryostatic microtome from Leica Microsystems (Leica Microsystems Inc., Buffalo Grove, IL, USA). In a previous work, it was proven that differences in the sections thickness modify the evaporation dynamics of the sample but do not affect the CEv final value (Espector et al. 2018). Thus, to reproduce the conditions under which an autoradiography is performed, 30 and 60 µm nominal thickness sections were obtained and extended on square polycarbonate sheets (2 cm side and 250 µm thick). In previous work, the advantages of using polycarbonate as NTD for the quantification of particles from BNC were established (Saint Martin et al. 2011). The assembly tissue section + polycarbonate was transferred to the scale's weighing chamber inside an ice container to prevent the evaporation process from starting before recording. Registration time The evaporation dynamics obtained through the procedure proposed in this work was compared with the one measured by thermogravimetry, considered as the reference method. For that purpose, a Shimadzu DTG-50/Simultaneous TG-DTA (Shimadzu Corporation 1 Nishinokyo Kuwabaracho Nakagyo-ku Kyoto 604-8511 Japan) was set at ambient temperature, without air flux, to assure equivalent conditions to those used for the proposed method. The rolled slices were inserted in quartz weighing pans and the mass was registered for 2 h, every 1 s.
In summary, a measurement protocol was established to standardize the conditions for every sample to be analyzed. Firstly, both registration of the scale and sensors readings are started by the computer. Then, the sample is sliced in the cryostat, mounted on a 250 µm thickness polycarbonate sheet, and immediately placed on the scale plate. At the end of the 30 min acquisition, EVAP v.2.0 calculates the CEv and plots the complete curve of mass as a function of time.

Results and discussion
To characterize the Cubis balance, measurements with standard weights were taken. In all cases, mass fluctuations were found over time, as can be seen in yellow dots in Fig. 1, where the mass oscillates between 100.02 and 99.02 mg in an interval of 3.5 h for a standard weight of 100 mg. For this reason, several correction factors were proposed to compensate for the variations observed, and thus stabilize the recording of the mass of the standard weights.
The application of a correction factor (F af ) associated with the aerostatic driving force is recommended in the bibliography. The aerostatic driving force is the ascending force of the object that is being weighed (Peña Pérez and Becerra Santiago 2010). The F af (Eq. 3) to be applied to the scalerecorded mass value takes into account the air density, which may vary depending on ambient temperature, pressure, and humidity: where ρ a is the air density expressed in kg/m 3 (calculated with Eq. 4), ρ c is the density of the weights used by the manufacturer to calibrate the scale (8000 kg/m 3 , corresponding to stainless steel), and ρ is the density of the objects being weighed (2700 kg/m 3 for aluminum weights).
The air density ρ a is calculated according to the semiempirical formula 1 where p is air pressure in hPa, h is relative moisture (%), and t is temperature (°C).
When the F af 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: where T inst and T average are the instantaneous and mean temperature during measurement, respectively, and m n 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: When applying both the aerostatic and the empirical factors (Eq. 6), records got stable around the nominal value for the different standard weights. An example of the smoothing effect of these corrections on measurements is shown 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 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 cases that extended in time weighing determinations were necessary.
The data obtained with the proposed methodology were compared with the results of measurements using TGA. Representative curves of both types of measurements are shown in Fig. 2. To compare results, the mass values at the i-th instant are normalized to the first value (normalized mass = m i /m h ). Since stabilization using TGA is slower and more variable than in the new procedure, subsequent intervals should be considered for the calculation of m s (1-2 h after the beginning of the measurement). 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 et al. 2015b). The equivalence between CEv values from TGA and the new methodology was also confirmed for lung samples (see Table 2).
Mass values as a function of time were recorded using EVAP v.2.0 for BDIX rat liver samples, as seen in Fig. 3. 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 (6-12 min) was considered to calculate the dry mass m s .
The CEv values of 38 liver sections coming from different animals were determined, obtaining the distribution shown in Fig. 4. 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 determination of 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. 5, when analyzing the same type of tissue from different species, no variations are observed in the final CEv value (see Table 2).
The protocol developed in this work allowed determination of reference CEv values for some tissues, to be used in boron quantification by neutron autoradiography. Table 2 presents the 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, such 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). The reference CEv values reported in the present work could be of interest for other applications apart from BNCT, such as physiologically based pharmacokinetic modeling, physiological studies, or other imaging techniques (e.g., Pethig and Kell 1987;Kim et al. 2017). Table 2 also presents 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 lungs and lungs 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 et al. 2015a), 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.
Given that the new methodology allows measurements with equipment commonly found in a laboratory, it proved to be advantageous to obtain CEv 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, which is essential information in the frame of BNCT (Wittig et al. 2008).

Conclusions
A protocol was established with the aim of studying the mass variation of histological sections due to evaporation, which allows the determination of the CEv with affordable equipment and materials present in a standard laboratory. A code, EVAP v.2.0, was developed to perform the recording, visualization, and analysis of the obtained data. The error of the proposed methodology was estimated at 5%. The influence of environmental parameters on the evaporation process was also studied and correction factors were determined to balance ambient fluctuations. However, it was found that this correction was not necessary for readings carried out under laboratory environmental conditions, at least for studies performed during 30 min, as those presented in this work.
The designed protocol was applied to determine CEv values for different tissues and species. Reproducible and consistent results were obtained, which allowed establishing set of reference values.
The proposed methodology for measuring evaporation coefficients is a high-throughput technology that allows many repetitions, given its practicability compared with other techniques such as TGA, and it can also be applied to samples of human biopsies. In this case, precise information of the boron uptake pattern in tumor and normal tissue obtained by neutron autoradiography will be of great importance when planning a BNCT treatment.