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7Be and 22Na radionuclides for a new therapy for cancer

  • Vladimir I. Kukulin , Anton V. Bibikov , Eugene V. Tkalya , Matteo Ceccarelli and Igor V. Bodrenko EMAIL logo
Published/Copyright: December 31, 2023
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Biomolecular Concepts
From the journal Biomolecular Concepts Volume 14 Issue 1

Abstract

10B isotopes have been almost exclusively used in the neutron-capture radiation therapy (NCT) of cancer for decades. We have identified two other nuclides suitable for radiotherapy, which have ca. ten times larger cross section of absorption for neutrons and emit heavy charged particles. This would provide several key advantages for potential NCT, such as the possibility to use a lower nuclide concentration in the target tissues or a lower neutron irradiation flux. By detecting the characteristic γ radiation from the spontaneous decay of the radionuclides, one can image their biodistribution. These advantages could open up new possibilities for NCT applications as a safer and more efficient cancer therapy.

Keywords: radiotherapy; neutron capture; radionuclides; theranostics

Introduction

The use of ionizing radiation in cancer therapy has a long and successful history [1,2]. It is one of the most remarkable examples of direct medical application of the results of modern physics utilized in more than 50% of patients with cancer [3].

The ionizing radiation can be delivered from outside the patient, a method known as external-beam radiation therapy (EBRT). Heavy charged particles (protons, accelerated nuclei) have an advantage over leptons and photons due to relatively small range straggling and to the sharp Bragg peak in the energy loss vs the path length curve, located at the end of the particle’s range in the tissue [4,5,6]. To access tumors located deep in the body, one needs to accelerate the particles up to the energies of a few hundred MeV/nucleon and to focus the beam onto the target in the human body. This makes the infrastructure for heavy particle radiation therapy very complex, expensive, and limited to large medical/research centers, while a much cheaper γ-ray radiation therapy has come to many common hospitals [5,7].

Alternatively, one may use radioactive nuclides bound into radiopharmaceuticals and selectively transported into the target tissues [8]. The spontaneous decay of a radioactive nucleus may release up to several tens of MeV, converted into the kinetic energy of charged particles producing the ionization within less than a millimeter range. The radionuclide therapy, therefore, replaces the problem of kinematic delivery of the ionizing particle into the target tissue in EBRT with the problem of selective accumulation of radiopharmaceuticals. The radionuclide therapy also brings a new issue – the problematic temporal control. The timescales of the accumulation and of the excretion of the radiopharmaceuticals (which are regulated by the metabolism and are difficult to control) should be in due relation to the lifetime of the isotope so that to maximize the part of the nuclei decayed in the tumor and not on their way into or out of the target.

In neutron capture radiation therapy (NCT), the active isotope undergoes induced radioactive decay following the capture of a neutron. This method combines the local energy deposition properties of the radionuclide therapy and a good temporal control of the beam particle radiation therapy, as the neutron flux may be switched on and off quickly. The idea was suggested in 1936 [9] and then implemented for the first time in 1954 [10] by utilizing the 10B isotope and the reaction 10B(n,αγ)7Li. However, despite more than 60 years of research and development, boron neutron capture therapy (BNCT) is still in the experimental phase [11,12,13,14]. Several issues are cited as the reason for this situation [15]. First, it is often difficult to identify boron-containing compounds that can be selectively accumulated and kept at the necessary concentration in specific tumor cells. Second, besides many successful practical applications, a significant number of adverse side effects due to neutron irradiation of healthy tissues were observed. Third, relatively high neutron fluxes (109–1010 cm−2 s−1) required by the BNCT were available only in nuclear reactors and in large-scale accelerator complexes until recently, thus assuming an infrastructure that is complex, expensive, and not well suited for systematic clinical studies.

The only alternative up to date, gadolinium, in particular, the 157Gd isotope (GdNCT) in the reaction 157Gd(n,γ)158Gd, has been considered for NCT, although to a much lesser extent [16]. The main advantage of the GdNCT, its huge cross section of thermal neutron absorption (by more than 60 times larger than that for 10B), is diminished by the fact that in most cases the 158Gd* excitation energy is taken away from the target tissues by high-energy γ photons, which do not create any local ionization. On average, only a small part of the excitation energy (less than 1%) is radiated in the form of electrons via the internal conversion and Auger mechanisms, which produce ionization within a 0.1 mm range from the source [17]. As a result, GdNCT has no obvious benefits over BNCT and still remains in the experimental phase, mostly focused on the identification of appropriate tumor-selective Gd delivery agents or hybrid B–Gd-containing compounds [18].

Presently, due to the recent developments of compact accelerators for neutron production, there is a growing interest in NCT worldwide [15,19]. The therapy is available in hospital-based facilities, and there is a strong need for novel drugs, which makes this topic extremely hot. In this work, we have identified two new nuclides, 7Be and 22Na, suitable for radiation therapy and analyzed their capabilities to serve in novel NCTs.

Experimental background and estimates

Nuclide properties

Both 7Be and 22Na are unstable radionuclides (Figure 1) and are well-known to physicists. 7Be decays into stable 7Li via the electron capture mechanism with a half-life of 53 days. As the decay rate depends on the electronic density at the nucleus, 7Be has been used to study the effects of the chemical environment in the nuclear processes [22,23,24]. More importantly, 7Be is assumed to play a key role in the lithium yield of the big-bang nucleosynthesis for standard cosmology via the neutron absorption reaction 7Be(n,p)7Li [25,26]. 22Na decays mainly by emitting positrons and γ-radiation into a stable 22Ne isotope and has a half-life of 2.6 years. It is important for the nucleosynthesis problem [27] and also is used in positron emission tomography (PET).

Figure 1 Schematic diagrams of 7Be (a) and 22Na (b) spontaneous decay; the data are from Tilley et al. [20] and Basunia [21], respectively.
Figure 1

Schematic diagrams of 7Be (a) and 22Na (b) spontaneous decay; the data are from Tilley et al. [20] and Basunia [21], respectively.

In Figure 2 and Table 1, we summarize the neutron capture properties of the two radionuclides and compare them with those of 10B. The neutron capture reactions pass via an intermediate compound nucleus in an excited state – 11B, 8Be, or 23Na. The compound nuclei then decay into the daughter nuclei (7Li in the case of B and Be and 22Ne for Na) by emitting a heavy particle – an α-particle for boron and a proton for beryllium and sodium. With a probability of 93.3%, 11B* decays into the first excited state of 7Li emitting the characteristic 478 keV γ-radiation (Figure 1a). Also, 23Na* decays mainly (99.15%) into the first excited state of its daughter nucleus, 22Ne, emitting the 1.275 MeV photon (Figure 1b). In contrast, 8Be* decays predominantly (98.8%) into the ground state of 7Li. The cross section for the 10B(n,αγ)7Li reaction is well determined (see the recent update in the study of Carlson et al. [29]). It follows Bethe’s ∝ 1/v law with an accuracy better than 5% for the neutron incident energies E n < 100 keV so that σ nα √E n = 0.6114 kb eV1/2. The cross section of 7Be(n,p)7Li follows the ∝ 1/v law for a much smaller neutron kinetic energy range, E n < 100 eV [26]. Moreover, there is inconsistency (of more than 20%) between the σ nα values obtained by different research groups. Thus, for the thermal neutrons (E n = 0.0253 eV) the neutron capture cross section varies from 38.4 ± 0.8 kb [31] to 52.3 ± 5.2 kb [26]. This discrepancy is still under debate [30]. We have adopted the latest result [30] so that σnα √E n = 7.0 kb eV1/2 in the abovementioned neutron energy range. The 22Na(n,pγ)22Ne reaction also follows the ∝ 1/v law until the neutron energies, E n < 100 eV, so that σ nα √E n = 5.0 kb eV1/2 [27].

Figure 2 Neutron absorption cross section for NCT-related reactions [28].
Figure 2

Neutron absorption cross section for NCT-related reactions [28].

Table 1

Neutron capture properties [27,29,30]

Nuclide properties
10B(J π = 3+) stable B e 7 3 ‒ 2 ⟶ 53.2 d L i 7 N a 22 ( 3 + ) ⟶ 2.60 y N e 22
Main reaction channels: “0” – the ground state of the daughter nucleus; “1” – the first excited state
10B + n → 11B∗ → 7Be + n → 8Be∗ → 22Na + n → 23Na∗ →
(93.3%) 7Li1 + α1 + γ (1.2%) 7Li1 + p1 + γ (99.15%) 22Ne1 + p1 + γ
(6.7%) 7Li0 + α0 (98.8%) 7Li0 + p0 (0.85%) 22Ne0 + p0
Kinetic energy of heavy particle products in the predominant channel [MeV]
0.84(7Li1) + 1.47(α1) 0.21(7Li0) + 1.44(p0) 0.10(22Ne1) + 2.25(p1)
Total neutron capture cross section σ nX √ E n [kb eV 1/2 ]
0.6114 7.0 5.0
σ nX ( E n [eV]) [kb]
σ nα (0.0253) = 3.844 σ np (0.0253) = 44 σ np (0.0253) = 31
σ nα (1.0) = 0.611 σ np (1.0) = 7.0 σ np (1.0) = 5.0
σ nα (10) = 0.193 σ np (10) = 2.2 σ np (10) = 1.6
σ nα (100) = 0.0611 σ np (100) = 0.7 σ np (100) = 0.5

It is interesting to note that, besides 7Be and 22Na, there are no other reasonably stable nuclides that have the capture cross section for the thermal and the epithermal neutrons larger than that for 10B and emit high linear energy transfer (LET) radiation [29]. There are very strong neutron absorbers like 135Xe and 113Cd but via the (n, γ) reaction, i.e., emitting γ-radiation is not suitable for the NCT.

Neutron capture energy deposition

For a more direct comparison of the BNCT with potential BeNCT and NaNCT, we have estimated the energy deposition after neutron capture in water (Table 2), considering only the predominant reaction channels. The γ-radiation emitted in the predominant channels for BNCT and NaNCT (Table 1) is a low LET radiation. This type of radiation has a low probability to produce ionization in the vicinity of the decaying nuclide but it rather escapes from the tumor region. A part of the decay energy may be transformed into the electronic excitation of the daughter nucleus via different mechanisms (e.g., the internal conversion, the coulomb excitation by the emitting charged particles, the shake-off due to the instant change in the nucleus charge, and of its momentum) and can be released in the form of Auger electrons and photons. However, for the light elements considered here (Be, B, and Na), the energy released in this form and its biological effects may probably be neglected for the NCT, in contrast with the heavy elements like Gd, where internal conversion is important [17]. Thus, only the kinetic energy, E t, transferred to charged heavy particles (high LET radiation) is useful for the NCT and is reported at the top of Table 2.

Table 2

BNCT (left) vs BeNCT (center) vs NaNCT (right): the energy deposition in water

High LET radiation energy, E t [MeV]
2.31 1.65 2.35
Ranges [µm] of the high LET radiation [32,33]
R α = 8, R Li = 5 R p = 44 , R Li = 2 R p = 92, R Ne < 1
Number of reactions per cell ( N r ) required for a dose of 20 Gy
120 170 120
Nuclide concentration, c ( E n ) [µ g g −1 ] (in parenthesis – the number of nuclides per cell, N cell ( E n )) required for a dose of 20 Gy absorbed during 1 h exposition to neutron flux of 10 10 s −1 cm −2
E n = 0.0253 eV
6.5 (0.9 × 109) 0.56 (0.11 × 109) 1.7 (0.11 × 109)
E n = 1.0 eV
41 (5.7 × 109) 3.5 (0.69 × 109) 11 (0.68 × 109)
E n = 10.0 eV
130 (18 × 109) 11 (2.2 × 109) 34 (2.1 × 109)
E n = 100.0 eV
410 (57 × 109) 35 (6.9 × 109) 110 (6.8 × 109)

  1. The values “per cell” stand for per mass, M cell = 2.3 ng; and E n denotes the neutron kinetic energy.

To relate the radiation doses in water in the biological context, we will consider a typical cell linear dimension, L cell = 13 µm, and a typical cell mass, M cell = 2.3 ng; see Appendix A. Also, we will assume D t = 20 Gy in tumor tissues for a typical dose required for the NCT in a single run [5,11]. To compare the nuclides, we use the number of neutron capture reactions per cell N r, required to release locally the absorbed radiation dose D t (see Appendix B). This quantity is independent of the neutron capture probability and reflects only the difference (among the nuclides) in the total energy of high LET radiation following the neutron capture. Only a part of the nuclides in the cell absorbs neutrons and contributes to the radiation dose, depending on the neutron flux, Φ n, the neutron kinetic energy, E n, the absorption cross section, σ n (E n), and the time of the irradiation. Therefore, the required number, N cell, of nuclides per cell to give the absorbed dose D while exposing the cell for time t to neutron flux Φ n is a more relevant quantity to compare NCT properties of nuclides. Alternatively to N cell, the relative concentration, c, of the nuclide in the target (in the units of ppm or µg of the nuclide per 1 g of tissue) is often used. Both N cell and c are shown in Table 2 for D t = 20 Gy, t = 1 h, Φ n = 1010 s−1 cm−2, and for different neutron kinetic energies.

Discussion

BeNCT and NaNCT: advantage and perspective

Based on the data and the estimates shown in the tables, we can discuss the pros and cons of the potential BeNCT and NaNCT in comparison to the existing BNCT. First, the neutron absorption cross section for 7Be is more than ten times (Table 1) larger, and for 22Na it is more than eight times larger than that for 10B for E n < 100 eV. This principal advantage of the 7Be is somewhat counterbalanced by a lower (by 30%) released kinetic energy of the high LET radiation (Table 2). For 22Na, the kinetic energy release is almost the same as for 10B. In the end, the required number of 7Be nuclides per cell, N cell, is the same as for 22Na, and it is at least eight times smaller than that for the boron, at the same neutron flux and the exposition time. For example, for thermal neutrons, one would need 0.9 × 109 10B nuclei per 2.3 ng of water (typical cell) to obtain 20 Gy of the absorbed radiation dose after 1 h of exposition to Φ n = 1010 s−1 cm−2 neutron flux, while only 1.1 × 108 of 7Be or 22Na is required. This ratio remains valid for neutron kinetic energies lower than 100 eV. As the requirement of sufficient concentration of the nuclide is one of the key issues in BNCT [14], the reduction by a factor of 8 in the case of 7Be and of 22Na may be crucial for the success of the NCT. The larger cross section would also make it possible to bring the required dose to the tumors more deeply buried in the body than for BNCT, thus increasing the potential applicability of the therapy.

The main ionizing particles are different for the boron and the new nuclides (α particles and protons, respectively), so the biological effect may be different at the same total kinetic energy. On the one hand, the α-particle has a shorter range and, if 10B is located close to the cell nucleus, it will release its kinetic energy within several microns, creating maximum radiation damage directly to the DNA. The proton radiated by 7Be or 22Na after the neutron capture travels tens of microns and deposits its kinetic energy in several cells, thus reducing the biological damage to each one of them. On the other hand, if the activated nuclide is located in the cell far from the nucleus, the α-particle can stop before reaching the important organelles and produce only a small radiation damage. The proton, however, has a higher probability to hit a cell nucleus while crossing several adjacent cells and also delivers a more uniform dose in the areas containing the radionuclides, than in the case of 10B. The abovementioned contributions that dominate the biological effect of the NCT will also depend on the mode the nuclide is accumulated inside the tumor cells. This is one key question for future experimental studies; it remains to be verified how much is the actual relative biological effect value of the protons compared to that of the α particles emitted in the reaction on 10B.

Another way to profit from the larger neutron capture cross section for the new nuclides is to reduce the intensity of neutron flux, again by a factor of 8, while keeping the nuclide concentration in the tumor the same as for 10B. This will give two advantages to the BeNCT and the NaNCT. First, the probability of activation of the atomic nuclei (also other than Na and Be) as well as of the elastic and inelastic collisions of neutrons in the healthy tissues will be eight times smaller compared to BNCT, thus reducing the neutron irradiation adverse effects (it is assumed that the ratio of the nuclide concentrations in the tumor and in healthy tissues are not smaller than for BNCT). This is especially important, e.g., for the brain glioblastoma where the tumor is embedded deeply inside the brain tissue [12,34]. One needs to apply epithermal neutrons to reach the tumor in this case, and so any significant reduction of the neutron flux would be very beneficial. Second, a lower required intensity (108−9 s−1 cm−2) of the neutron beam would make it possible to use a smaller scale and cheaper accelerator-based neutron sources [35,36]. This would make the NCT economically more efficient and more competitive.

Additionally, as the reaction byproducts, the positrons from the spontaneous decay of 22Na can be used in PET. The same holds for the characteristic γ-radiation (478 keV) from the spontaneous decay of 7Be (Figure 1a) and the γ (1.28 MeV) from the spontaneous decay of 22Na (Figure 1b), which can be utilized very favorably in the standard single photon emission computer tomography (SPECT) [37] to trace the biodistribution of the nuclide before neutron irradiation. This is also an important advantage over the BNCT, where the control of the nuclide accumulation is difficult, and one has to additionally label the boron-containing compound with 18F to utilize PET [38].

Open problems

There are also new challenges in the way of 7Be and 22Na to the successful NCT management. 22Na is used for PET and it is already a commercial product. On the 10–1,000 ng scale necessary for experimental studies, 7Be may be produced as a byproduct on existing accelerator-based neutron sources utilizing, e.g., the proton-induced spallation reaction on 16O [39]. For potential industrial-scale application, a dedicated production infrastructure will be necessary. In this respect, the idea (first suggested in Ref. [40]) of an accelerator for NCT utilizing the reverse reaction, 7Li(p,n)7Be, and an intense (10 mA and more) proton beam to produce neutrons looks especially attractive. Here, the beryllium isotope made during neutron generation can be further utilized for BeNCT, thus also reducing the cost of radioactive waste.

The radiotoxicity problem of these radioactive isotopes is another one. That is, one has to understand and minimize the adverse effects of the spontaneous radiation on the patient, but also on his/her family, the personnel, and the environment during drug production, administration, excretion, and radioactive waste management. To assess the effects of the spontaneous radiation of the 7Be and the 22Na nuclides, we compare them, see Appendix C with the iodine radioisotope, 131I, which emits similar radiation (β and γ), and is widely used in the therapy of thyroid cancer [41]. For radiation therapy, one uses the amount of 131I equivalent to the activity ranging from 0.2 to more than 50 GBq [41]. As 4.6 GBq corresponds to 1 µg of the nuclide, one can take 1 µg as a typical mass per procedure with 131I. The same mass of 7Be in the target is necessary to produce 20 Gy per hour in 1 g of tumor in BeNCT (Table 2). The external dose rate at the distance of 1 m from the source, D ̇ ext , which characterizes the radiation risk for the environment and the personnel, is 2.5 times smaller for 7Be (0.09 mGy/h) than for the typical therapeutic amount of 131I. For 22Na, the necessary mass of the nuclide is 3 µg per 1 g of the tumor, and D ̇ ext = 0.21 mGy/h is similar to that of 1 µg of 131I. The β component of the internal spontaneous dose is absorbed locally, within 2 mm from the source. It produces a therapeutic effect in the tumor and is harmful when the radionuclide is in the healthy tissues. In the case of 131I, the internal dose rate is D ̇ int β = 360 mGy/h for 1 µg of the nuclide; it is eight times lower for 3 µg of 22Na, and it is absent for 7Be. However, the main therapeutic effect of 22Na and 7Be comes from the neutron capture reaction and has an absorbed dose rate of 20 Gy/h, i.e., it is more than 50 times stronger than that for 131I. The γ component of the internal dose is absorbed (by definition) within the sphere of R = 10 cm from the decaying nuclides and, most probably, outside the tumor. Therefore, damages the healthy tissues with the same dose rate of about D ̇ int ϒ = 60 mGy/h per 1 µg of 131I and 3 µg of 22Na; the effect is 2.5 times smaller for 1 µg of 7Be. Therefore, we conclude that if administered in the same amount as 131I for thyroid cancer therapy (i.e., in the range of micrograms), the radiation risk from spontaneous decay of 7Be and 22Na would be at the same level or smaller than that for 131I. Thus, the nuclides can be managed and administered by following a standard security procedure and technologies for radiopharmaceuticals for radioisotope therapy. However, simultaneously, the therapeutic effect for the tumor is much stronger and with better temporal control for NCT than for the standard radionuclide treatment. The assessment of the radio-toxicity of the nuclides also should take into account their biological halftimes. This issue is strongly connected to the properties of the drug containing a nuclide, which should control targeting, bio-distribution, and pharmacokinetics, as discussed in the following paragraphs.

The major challenge for future NCT research is how to provide the targeting, the accumulation, and the pharmacokinetic timescales for 7Be and 22Na at the same level as in the case of 131I therapy. In other words, one needs a substance that binds the radionuclide, transports it selectively into a specific cancerous tissue providing the nuclide concentration of 1–3 ppm for several hours, and then is excreted together with the remaining non-activated nuclides within several days. Of the total administered amount of several (up to a few tens) micrograms of the nuclide per procedure (the amount limited by the spontaneous radiation risk), a substantial part (more than 10%) should pass through the tumor. The abovementioned limitations of the total amount of the nuclide and the required pharmacokinetics will also eliminate (or substantially ease) the problem of chemical toxicity of the pure elements, and in particular, that for beryllium (the median lethal dose, LD50, for animals is more than 10 mg beryllium/kg [42]). Besides, there is a second criterion, the nuclide accumulation selectivity, arising from the requirement to minimize the radiation risk under neutron irradiation – the ratio of the nuclide concentration in the tumor and in the surrounding healthy tissues must be larger than 3 [15].

The earlier approach employed in the BNCT consists of binding the active nuclide into a soluble enough and low-toxic compound administered in large quantities to achieve the desirable concentration in the target tissue, e.g., boronophenylalanine and sodium borocaptate [14]. However, the tumor targeting for these compounds is not sufficient. For example, one had to administer around 10 mg of boron per 1 kg of the patient’s weight [15] to achieve the necessary nuclide concentration in the tumor. Therefore, only a small part of 10B ends up in the tumor, while almost 1 g of that enters the healthy tissues and should be excreted. Obviously, this approach does not fit the BeNCT and NaNCT due to the spontaneous radioactivity. Another method of delivery can be based on recent developments in nanomedicine [14,43] and could be utilized for the new NCT. This modular approach can comprise two or three of the following steps. One first binds the nuclide in a stable compound, then encapsulates it into a nanoparticle having sufficient solubility, pharmacokinetics, and low toxicity, and finally, functionalizes the nanoparticles to target specific cells.

The nanomedicine approach can potentially provide a very high selectivity, and it is especially suitable for NCT. Here, there is no need to release the drug in the target tissues as in the case of chemically acting compounds – the ionizing radiation will exit the nanocage anyway. Moreover, it would be advantageous to keep the non-activated nuclides tightly encapsulated during the whole procedure to eliminate the radiotoxicity risk and control the excretion. A possible way to prevent the nuclide's interaction with the aqueous medium (and thus their toxicity, in particular, beryllium) could be encapsulation in a low-reactivity vessel. Due to their availability and well-studied properties, fullerenes appear as a logical choice but sealed nanotubes could prove useful, as well as derivatives or supramolecular coordination complexes [44,45]. We have shown recently [24,46] that the energetic barrier for beryllium to cross the wall of a C36 fullerene is 1–2 eV, but one may argue that C60 would be a better choice due to its lower reactivity. Then, a poorly soluble fullerene can be functionalized or encapsulated further (into, e.g., a liposome) to improve the pharmacokinetics. From here, we can functionalize the fullerene again to target the specific tissue by following the existing nanomedicine techniques [14,43]. Also, recent developments in beryllium-organic chemistry [47,48] potentially could provide other options for the coordination of beryllium.

Conclusion

We have put forward physical arguments in favor of the potential use of 7Be and 22Na nuclides for neutron capture therapy. We have discussed their advantages vs existing BNCT, limitations, and new challenges arising from the spontaneous radioactivity, and the production issues. The use of new nuclides alone or in combination with traditional 10B and/or 157Gd would open up a new way in neutron capture therapy, unexplored before. There are no other reasonably stable nuclides that have the capture cross section for the thermal and epithermal neutrons larger than that for 10B and emit high LET radiation suitable for NCT. By combining BeNCT and NaNCT with SPECT (or NaNCT with PET), one would obtain real theranostics – simultaneous imaging of the nuclide biodistribution and the targeted therapy of cancerous tissues – an important ingredient of modern personalized medicine.

Acknowledgements

MC and IVB thank Paolo Randaccio for useful discussions, Detlef Gabel for his constructive criticism and suggestions regarding the radiotoxicity issue, and Wolfgang Sauerwein for the critical but encouraging discussions. The authors thank Stefan Milenkovic for his help in the preparation of the manuscript.

  1. Funding information: EVT was supported by a grant from the Russian Science Foundation (Project No. 19-72-30014). This study was funded by bilateral Russian (RFBR) Italian (CNR) research Projects 20-58-7802 (RFBR) and CUP: B55F21000620005 (CNR). We acknowledge a CINECA award under the ISCRA initiative (Project No. IsC92 BeNCTS) for the availability of high performance computing resources and support.

  2. Conflict of interest: The authors state no conflict of interest.

  3. Data availability statement: The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Appendix A Typical cell size and mass

The average volumes of human cells range from 30 to 4 × 106 µm3, depending on the tissue [49]; the corresponding linear dimensions range from 3 to 160 µm. For the estimates, we will assume the typical cancer cell volume, V cell = 2,300 µm3, and the typical cell linear dimension, L cell = 13 µm, which corresponds to HeLa cells often used in cancer in vitro studies [49]. Then, we assume the mass density of the cell, ρ cell = 1 g cm−3, so that the typical cancer cell’s mass, M cell = 2.3 ng.

Appendix B Estimation of the absorbed radiation dose under neutron irradiation

The dose of high LET radiation absorbed in a cell is given by D = E t N r /M cell, where N r is the number of neutron capture reactions occurring. Thus, the required N r to release the absorbed radiation dose D locally into the cell is N r = DM cell /E t. Here, we underline again that we have assumed that the γ-radiation after neutron capture has a small probability to interact and ionize matter within the tumor region (<10 cm) so that the locally deposed energy is only that of the charged particles, E t. The corresponding estimates for the BNCT, the BeNCT, and the NaNCT are shown in Table 2, assuming D = 20 Gy in tumor tissues for a typical dose required for the radiation therapy in a single run [5,11].

The absorbed dose rate in a cell under a constant neutron flux Φ n is Ḋ(t) = E t Ṅ(t)/M cell, where N ̇(t) = N 0 exp(−t/τ n)/τ n is the number of the neutron capture reactions in the cell per second, N 0 is the initial (at t = 0) number of nuclide particles per cell; τ n = 1/(σ n J n) is the reaction time constant; and σ n is the neutron capture cross section. For typical values of σ n (Table 1) and of the neutron flux, Φ n < 1013 s−1 cm−2, the reaction time constant (τ n > 106 s) is much larger than the reasonable duration of the NCT procedure (up to a few hours). Therefore, if N 0 is not changing significantly during the neutron irradiation procedure due to the accumulation and the excretion, the dose rate is time-independent, and the absorbed dose for time t of the neutron exposure is given by D(t) = tE t N 0 σ n J n /M cell. Then, the number of nuclides per cell to have the absorbed dose D while exposing for time t to neutron flux Φ n is N cell = N r /(tσ n J n). The corresponding required mass concentration of the nuclide, c ≡ M (nuclide)/M cell, is c = Dµ/(E t N A σ n J n t), where µ is the molar mass of the nuclide and N A is the Avogadro constant. In Table 2, we show the estimated concentration of nuclide (both N cell and c) required to obtain the absorbed radiation dose of D = 20 Gy in water after 1 h exposure to Φ n = 1010 s−1 cm−2 neutron flux for thermal and epithermal neutron energies.

Once the neutrons enter the target (a water phantom or a human body) with initial energy E n 0 , they start to scatter on the atoms (mainly, elastically and on hydrogens) and slow down. The average neutron energy in the target, E n(x), decreases with the depth x from the initial energy E n(0) at x = 0 until the thermal energy is equal to 3/2k B T at a given temperature T, and the neutron capture cross section is σ n(E n(x)), for the active nuclide increases with x reaching the value for the thermal neutrons. Besides, neutrons change their direction after each collision so that the initially collimated beam will disperse with the distance traveled in the target. Therefore, the neutron flux Φ n(x) along the initial beam direction decreases with the depth x. As the absorbed dose is proportional to the product, D(x) ∝ σ n(E n(x))J n(x), it also depends on the depth x even at a uniform concentration of the active nuclide. If the incident neutrons are already thermalized, their average energy and the capture cross section are constant so that the dose decreases with the depth due to the decrease of the average flux. If the initial neutrons have a higher energy (0.5 eV to 10 keV), the absorbed dose, D(x), first increases with x together with the neutron capture cross section, then reaches its maximum at a certain distance x 0 (1–4 cm) [35], and then decreases due to the flux angular dispersion. The interval of the depth, [x min, x max] around x 0, where the absorbed dose is higher than a certain critical value (e.g., 20 Gy/h) at a given nuclide concentration is suitable for the NCT. For the 7Be and the 22Na nuclides, having the neutron capture cross section larger than that for 10B by a factor of 10, the maximum working depth, x max, can be much larger than x 0 and can reach 10–20 cm required for potential therapy of deep sitting tumors.

Appendix C The absorbed dose from the spontaneous radiation

To estimate the effects of the spontaneous radiation of 7Be and the 22Na nuclides, both for the patient and for the personnel, we compare them with the iodine radioisotope, 131I, which emits similar radiation and also is widely used in the therapy of thyroid cancer [41] (Table A1). There are several standard physical characteristics of spontaneous decay.

Table A1

Comparison of the radiation effects of the spontaneous decay

Nuclide (half-life)
131I (8.0 d) 7Be (53 d) 22Na (2.60 y)
Mass-specific activity, A m [GBq/µg] radiation type, its energy, and the abundance
4.6 13 0.23
γ, 370 keV (average) γ, 478 keV, f = 0.10 γ, 1,280 keV, f = 1
β−, 570 keV (average) β+, 540 keV, f = 0.9, γ, 511 keV, f = 1.8
γ constant at a distance of 1 m, Γ [mGy/h/GBq]
0.05 0.007 0.30
External absorbed dose rate, D ̇ ext [mGy/h] per 1 µg of nuclide at a distance of 1 m
0.23 0.09 0.07
Internal absorbed dose rate per 1 µg of nuclide, D ̇ int [mGy/h] contribution for each radiation type is specified separately
60 – γ 25 – γ 18 – γ
360 – β 15 – β
Total: 420 Total: 33

Iodine isotope has the shortest lifetime, T 1/2, of 8 days, while the sodium isotope’s half-life is the longest among the three nuclides and equals 2.6 years. The activity of a radionuclide (the number of decays per second) of initial mass M, after time t is

(C1) A ( t ) = A m M exp − In ( 2 ) t T 1 / 2 ,

where A m = ln(2)N A /(µT 1/2) is the nuclide-mass-specific activity and µ is the molar mass. Table A1 shows that the mass-specific activity for 7Be is the largest despite the half-life for 131I being shorter; apparently, it is due to the almost 20 times larger isotope mass for the iodine.

To characterize the external (personnel and environmental) radiation risk of a radionuclide, one usually calculates the absorbed radiation dose rate at a certain distance d from a point-like source of activity A. The distance is typically large enough (e.g., 1 m) so that all the β radiation is absorbed well before d, and only γ-radiation contributes to the ionization. The external γ-radiation dose rate is given as

(C2) d D ext d t = Γ A d 2 P s .

Here, the γ constant,

(C3) Γ = 1 4 π μ en ρ ∑ i E ϒ i f i

is a standard characteristic of the external radiation risk of the nuclide at a given activity. The sum in the latter equation runs over the energies of all the emitted γ particles weighted by the corresponding abundance (f i is the average number of photons of type i per decay of the nuclide). The energy attenuation coefficient, µ en, determines the average relative energy loss of the photon beam after passing distance x in the material: E/E 0 = exp(−µ en x). As µ en is approximately proportional to the mass density, ρ, of the material, one often introduces the mass-energy attenuation coefficient, µ en /ρ. In particular, for both air and liquid water, µ en /ρ ≈ 0.03 cm2 g−1 with 20% accuracy for the photon energies from 60 keV to 2 MeV [50]. The γ shielding factor, P s, describes the reduction of the average energy of the emitted photons due to the absorption and the inelastic scattering on the way from the source to the observation point at a distance d. If the energy attenuation coefficient of the shielding material, as discussed above, μ en s , weakly depends on the photon energy. The shielding factor can be estimated as follows: P s = exp(−µ s en L), where L ≤ d is the thickness of the shield. In air, ρ s = 0.001225 g cm−3, and the characteristic energy attenuation length, λ = 1/µ s en is about 270 m so that at a distance below d = 1 m, the shielding factor, P s = exp(−d/λ) ≈ 1. The energies and the corresponding abundances of the radiation are shown in Table A1. For 131I, more than 10 different photons may be emitted [51], and we show only the average (weighted) value, ∑ i E ϒ i f i , in the table. The calculated Γ constants reported in Table A1 agree with the values recommended in the study of Unger and Trubey [51] within 20% accuracy sufficient for the nuclide comparison presented here. This also justifies the approximations accepted for the simplified estimates of the absorbed doses. The calculated external dose rate at 1 m per 1 µg of nuclide, D ̇ ext , is reported in Table A1.

To quantify the possible effect of the spontaneous radiation on the patient, we calculate the average absorbed dose rate within a sphere of water of radius R = 10 cm around a pointlike source. The β-radiation from the spontaneous decay is completely absorbed within less than 2 mm from the source [32], releasing the energy, P i E β i f β i . The photons, on average, lose only a part of their initial energy equal to ( 1 − exp ( − μ en R ) ) ∑ i E ϒ i f i . The internal absorbed dose rate is the sum of the two contributions:

(C4) D int = D int ϒ + D int β ,

(C5) d D int ϒ d t = A ( 1 − exp ( − μ en R ) ) ∑ i E ϒ i f i 3 4 π R 3 ρ d D int β d t = A ∑ i E β i f β i 3 4 π R 3 ρ .

The calculated external dose rate per 1 µg of nuclide, D ̇ int , is reported in Table A1 for the photons and the β-particles, separately.

The half-life, the mass-specific activity, and the Γ constant reflect different physical properties of radioactive nuclides, and, separately, are not sufficient to characterize the risk of spontaneous radiation. The mass-specific internal D ̇ int and external, D ̇ ext , dose rates defined here are more suitable for comparing radionuclides.

For the radiation therapy of thyroid cancer, one uses the amount of 131I equivalent to the activity ranging from 0.2 to >50 GBq [41]. As 4.6 GBq corresponds to 1 µg (Table A1) of the nuclide, we can consider 1 µg as a typical mass per procedure with 131I. The same mass of 7Be in the target would be necessary to produce 20 Gy per hour in 1 g of tumor in BeNCT (Table 2). The external dose rate at 1 m, D ̇ ext , characterizing the radiation risk for the environment and the personnel, is 2.5 times smaller for 7Be (0.09 mGy/h) than for the typical therapeutic amount of 131I. For 22Na, the necessary mass of the nuclide is 3 µg per 1 g of tumor, and D ̇ ext = 0.21 mGy/h is similar to that of 1 µg of 131I.

The β component of the internal spontaneous dose is absorbed locally. It produces a therapeutic effect in the tumor and it is harmful when the radionuclide is in the healthy tissues. In the case of 131I, the dose rate is D ̇ int β = 360 mGy/h for 1 µg of the nuclide. It is 8 times lower for 3 µg of 22Na and it is absent for 7Be. However, the therapeutic effect of 22Na and 7Be comes from the neutron capture reaction and has an absorbed dose rate of 20 Gy/h, i.e., it is more than 50 times stronger than for 131I.

The γ component of the internal dose is absorbed (by definition) within the sphere of R = 10 cm from the decaying nuclides, and most probably, outside the tumor. Therefore, it makes the radiation damage to healthy tissues with the same dose rate of about D ̇ int ϒ =60 mGy/h per 1 µg of 131I or 3 µg of 22Na; the effect is 2.5 times smaller for 1 µg of 7Be.

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Received: 2023-02-02
Revised: 2023-04-17
Accepted: 2023-04-18
Published Online: 2023-12-31

© 2023 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/bmc-2022-0028
Keywords for this article
radiotherapy; neutron capture; radionuclides; theranostics
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