Emission of β⁺ Particles Via Internal Pair Production in the 0⁺ – 0⁺ Transition of ⁹⁰Zr: Historical Background and Current Applications in Nuclear Medicine Imaging

Abstract

⁹⁰Y is traditionally considered as a pure β^– emitter. However, the decay of this radionuclide has a minor branch to the 0⁺ first excited state of ⁹⁰Zr at 1.76 MeV, that is followed by a β⁺/β^– emission. This internal pair production has been largely studied in the past because it is generated by a rare electric monopole transition (E0) between the states 0⁺/0⁺ of ⁹⁰Zr. The positronic emission has been recently exploited for nuclear medicine applications, i.e. positron emission tomography (PET) acquisitions of ⁹⁰Y-labelled radiopharmaceuticals, widely used as therapeutic agents in internal radiation therapy. To date, this topic is gaining increasing interest in the radiation dosimetry community, as the possibility of detecting β⁺ emissions from ⁹⁰Y by PET scanners may pave the way for an accurate patient-specific dosimetry. This could lead to an explosion in scientific production in this field. In the present paper the historical background behind the study of the internal pair production of the 0⁺/0⁺ transition of ⁹⁰Zr is presented along with most up to date measured branch ratio values. An overview of most recent studies that exploit β⁺ particles emitted from ⁹⁰Y for PET acquisitions is also provided.

1. Introduction

⁹⁰Y is one of the radionuclides most widely used in nuclear medicine therapeutic applications. Thanks to its long β particle range, ⁹⁰Y allows a uniform irradiation of large tumors commonly expressing heterogeneous perfusion and hypoxia. The average energy of β^- emissions from ⁹⁰Y is 0.9367 MeV, with a mean tissue penetration of 2.5 mm and a maximum of 11 mm. However, although ⁹⁰Y has been traditionally considered as a pure β^– emitter, the decay of this radionuclide has a minor branch to the 0⁺ first excited state of stable ⁹⁰Zr at 1.76 MeV, which is followed by a β⁺/β^– emission with an extremely small branching ratio. For decades this transition was not exploited in nuclear medicine. Recently, it was proposed to use this pair production in molecular radiation therapy in order to assess ⁹⁰Y biodistribution by positron emission tomography (PET) acquisitions, especially in regions that may show a high ⁹⁰Y concentration during internal radiotherapy procedures. This is because PET imaging allows high-resolution images to be obtained if compared to bremsstrahlung SPECT, alternatively used to monitor ⁹⁰Y biodistribution following therapeutic administration of ⁹⁰Y-labelled radiopharmaceuticals.

In the last few years, there has been growing interest in liver radioembolization with ⁹⁰Y microspheres for the treatment of unresectable hepatocellular carcinoma and liver metastases. It consists of ⁹⁰Y embedded into non-biodegradable glass or resin microspheres selectively administered by intra-arterial hepatic injection giving high doses of radiation to the tumor and sparing the liver parenchyma. With this technique, a high activity of ⁹⁰Y is likely to be accumulated in a small region of the body (i.e. the liver), thus allowing a sufficient number of positrons to be detected by most commercial PET scanners.

In the present paper the historical background behind the study of the internal pair production of the 0⁺/0⁺ transition of ⁹⁰Zr is presented along with the most recent branch ratio measurements. A precise knowledge of the branch ratio is important for an accurate quantification of ⁹⁰Y accumulated inside the target region. An overview of most recent studies that exploit β⁺ particles emitted from ⁹⁰Y for PET acquisitions is also provided.

2. Internal Pair Production Following the 0⁺ – 0⁺ Transition of ⁹⁰Zr

In the past there has been a great interest in so-called electric monopole transitions (E0) in certain nuclei. This may occur when there is no angular momentum change between initial and final nuclear states and no parity change (in particular, electromagnetic transition between states with J=0). For spin-zero to spin-zero transitions, single gamma emission is strictly forbidden, hence three alternative processes may occur: a) transitions give rise to transfer of radiation energy to an atomic electron in the orbital cloud by internal conversion b) if the energy of the process is greater than (1.022 MeV, where m_e is the mass of the electron), transition can occur via electron-positron internal pair creation. c) two-photon emission, which is generally negligibly small.

The electric monopole transition takes place entirely in the nuclear volume, corresponding classically to a radially oscillating spherical charge distribution that does not give rise to a time-varying field outside the charged region. This may be visualized as a “breathing” mode without change of shape, that is only possible in a compressible nucleus. Past literature studies focused on a number of nuclei that undergo electric monopole transition. Among these, ¹⁶O, ⁴⁰Ca, ⁷²Ge, ⁹⁰Zr have been studied. The importance behind these transitions lies in the fact that the analysis of the small branch ratio associated with two-photon decay provided useful information on the nuclear structure. A surprising result of these researches was that the angular correlation between the two gamma rays was asymmetric about 90^°. This was interpreted as arising from interference between the 2E1 and the 2M1 contributions to the transitions which were found to be of comparable strength [1].

Figure 1. a) Approximate level pattern for protons derived from the shell model. The spin-orbit coupling is adjusted in such a way that the empirical level sequence is represented. Round brackets (2), (4) etc. and square brackets [2], [6], etc. denote the level degeneracies and the total occupation number, respectively. b) Experimental energy levels of ⁹⁰Zr (MeV). The total energies are reported.

Figure 1. a) Approximate level pattern for protons derived from the shell model. The spin-orbit coupling is adjusted in such a way that the empirical level sequence is represented. Round brackets (2), (4) etc. and square brackets [2], [6], etc. denote the level degeneracies and the total occupation number, respectively. b) Experimental energy levels of ⁹⁰Zr (MeV). The total energies are reported.

In particular, a number of past literature studies were dedicated to the analysis of the electric monopole transition (E0) occurring during the decay of ⁹⁰Y nucleus to the fundamental level of ⁹⁰Zr. Figure 1a shows the approximate level pattern for protons derived from the shell model of ⁹⁰Zr, while Figure 1b) shows the associated low-lying excitations. ⁹⁰Zr has 40 protons and 50 neutrons. 50 neutrons form a close shell, filling up to . 28 of 40 protons fill first four shells, while the remaining 12 fill , and . If one of the protons in is excited to , the remaining proton in and the proton in can form states with odd parity and and 5. There are indeed 4^- and 5^- states. ^- State 5 is lower presumably because two protons are closer in space by lining up the orbital angular momenta. If both protons are excited from to , it could give Nevertheless, the anti-symmetry of the wave function allows only states with .They should all have even parity. Indeed, 0⁺, 2⁺, 4⁺, 6⁺, 8⁺ are observed in this order (Figure 1b).

The radioactive decay of ⁹⁰Y nucleus by beta emission to the fundamental level of ⁹⁰Zr with a half-life of 64 hours has been widely studied in the past. However, in 1955 in a letter to the editor of the Physical Review, Ford predicted an excited state (0⁺ state) of ⁹⁰Zr [2]. For the aforementioned reasons, the evidence of the 0⁺ state of ⁹⁰Zr could be proved with the detection of positrons emitted from a ⁹⁰Y source beta decaying to ⁹⁰Zr. As a matter of fact, the predicted state was discovered by Johnson et al. at the same laboratory in the same period and was described in a letter to the editor of the same journal issue [3]. The authors discovered a transition at 1.76 MeV followed by positron emission by using a strong source of ⁹⁰Y in a 40-cm radius of curvature magnetic spectrometer. Very precise measurements of the beta spectrum of ⁹⁰Y gave no indication of any other group of beta rays between 0.5 MeV and the end point at 2.26 MeV. Further, the authors observed no gamma ray line in the region of 1.76 MeV and they concluded that this energetic transition was to be imputable to that of a monopole between two 0⁺ states of the even-even nucleus of ⁹⁰Zr. They observed an internal conversion line whose intensity relative to that of the 2.26 MeV beta spectrum was . These authors also reported the probability of pair creation per beta decay as: .

One year later Greenberg and Deutsch in a new experiment evaluated the entity of internal pair creation by assessing the number of positron emission relative to the main beta spectrum [4]. They used a magnetic focus arrangement combined with coincidence counting of the annihilation radiation to allow the detection of very low positron intensities in the presence of other radiations. In their paper, the authors noted that in the assessment of the pair production probabilities three types of virtual intermediate states have to be considered. Indicating with the nuclear wave function one has [4]:

(1)

with the prime denoting the virtual intermediate state. They noted that the process (a) and (c) contribute about equally to pair creation, i.e. the pairs are formed by the field of the beta ray and of the residual nucleus.

In order to compare their findings with those obtained by other authors, Greenberg and Deutsch evaluated the internal pair production probability following the theoretical formulation proposed by Thomas [5]. According to this formalism, the E0 transition strength from the initial excited state to state is defined by:

(2)

Where represents a summation over all nuclear protons at positions and the parameter is the nuclear radius. Therefore the internal pair production probability, , depends on the relevant matrix [4,5]. Most notably, they observed that the evaluation of this matrix element could only be estimated from some nuclear models. On the other hand, the relative probabilities for the emission of conversion electrons, , or of a positron electron pair involve only an evaluation of the electron wave functions at the nuclear surface. Using the Thomas formulation for and no specific nuclear property, not even the nuclear radius, enter the ratio of internal conversion to internal pair creation.

According to Thomas’ formalism the internal pair production probability is given by the following analytic formula [5]:

(3)

where:

(4)

with:

, α=1/137 fine structure constant, R nuclear radius, Z atomic number of the element and denotes the gamma function. In Equation 3, units have been chosen such that m, c, are equal to unity.

On the other hand, the probability for the emission of conversion electrons, , is:

(5)

Where is the energy of the outgoing electron, E is the transition energy and is its momentum of the electron. For large Z (>60), so that , the following useful approximation may be inserted into Equation (5):

(6)

which also includes the expansion in power of , good for all nuclei with . Then one immediately obtains the relative probability of the emission of conversion electrons to that of a positron electron pair creation:

(7)

where:

(8)

Following this formalism and resolving Equation (7) for the appropriate energy and atomic number, Greenberg and Deutsch obtained for the ratio of the K-conversion to pair creation:

(9)

On the other hand, one year before, Johnson and colleagues reported an internal conversion intensity relative to that beta spectrum and a probability of pair creation per beta decay . As a consequence, using the experimental data obtained by Johnson, one would obtain:

(10)

uncertain to about a factor of two. In view of this substantial discrepancy of the ratio obtained by the two authors, Greenberg and Deutsch decided to measure the number of positrons per beta decay of ⁹⁰Y with their apparatus.

The experimental problem Greenberg and Deutsch had to face consisted of the detection of a very small number of primary positrons in the presence of an overwhelmingly larger number of other radiations (beta rays, internal/external bremsstrahlung radiations and secondary positrons produced by the impact of photons and beta rays). The low relative intensity of the effect sought, made it imperative to use a very selective detection method. Such a method was allowed by the annihilation radiation produced when the positrons were stopped in a beryllium target (referred to as the “catcher”). The two annihilation gammas arising in the target were detected coincidently using two sodium iodide (NaI) detectors. To minimize the formation of positrons by energetic electrons or photons striking the catcher, the latter was located in a magnetic field in such a position that about one-half of all the positrons emitted by the source in the interesting energy interval would strike it while all trajectories of electrons with energy greater than 1 MeV either missed the catcher or were intercepted by the collimator (Figure 2).

Figure 2. Experimental apparatus used by Greenberg and Deutsch for the detection of positrons emitted from a ⁹⁰Y source due to 1.75 MeV electric monopole transition to ⁹⁰Zr. Image reproduced from reference [4].

Figure 2. Experimental apparatus used by Greenberg and Deutsch for the detection of positrons emitted from a ⁹⁰Y source due to 1.75 MeV electric monopole transition to ⁹⁰Zr. Image reproduced from reference [4].

From their experiment, the positron branch ratio was determined to be . Combined with the data for the intensity of the conversion line obtained by from Johnson and colleagues, they obtained an experimental value for the probability of pair creation per beta decay as , in moderate agreement with the calculation of Thomas.

Later on, in 1961, in an attempt to quantify a predicted two gamma emission in the 0+/0+ transition of ⁹⁰Zr by Ryde et al. [6], Langhoff and Hennies [7] determined with a scintillation coincidence spectrometer the positron branch ratio to be and a relative probability of the emission of conversion electrons to that of total beta decays to be .

Figure 3. Decay scheme of ⁹⁰Y

Figure 3. Decay scheme of ⁹⁰Y

In recent years, Selwyn and colleagues [8] used a high-purity germanium detector to determine the internal pair production branch ratio of the 0⁺ – 0⁺ transition of ⁹⁰Zr. The basic measurement technique consisted in counting the gross number of gammas detected within a 511 keV (annihilation) peak and subtracting the bremsstrahlung continuum, environmental continuum, and environmental peak at 511 keV. The germanium detector was selected over other detectors (i.e., NaI and CdTe) based on its superior energy resolution. In the measurement, it is fundamental to quantify the extremely small 511 keV peak observed above the large bremsstrahlung spectrum and environmental 511 keV background. The authors found the branch ratio to be . Figure 3 shows the decay scheme of ⁹⁰Y, while in Table 1 the experimental values for the internal pair production branch ratio of the 0⁺/0⁺ transition of ⁹⁰Zr are reported.

Table 1. Probability of pair creation per beta decay measured in earlier and more recent literature studies.

Reference		Detector
Johnson et al.(1955)		NaI
Greenberg and Deutsch (1955)		NaI
Langhoff and Hennies (1961)		NaI
Selwyn et al. (2006)		HPGe

Table 1. Probability of pair creation per beta decay measured in earlier and more recent literature studies.

Reference		Detector
Johnson et al.(1955)		NaI
Greenberg and Deutsch (1955)		NaI
Langhoff and Hennies (1961)		NaI
Selwyn et al. (2006)		HPGe

Table 2, Table 3 report the most updated properties of ⁹⁰Y beta decay, from LNHB/CEA [9].

Table 2. Beta minus transitions of ⁹⁰Y

	Energy (keV)	Probability (x 100)	Nature
	93.5 (17)	0.0000014 (3)	1st forbidden
	519,1 (17)	0,017 (6)	Unique first forbidden
	2279,8 (17)	99,983 (6)	Unique first forbidden

Table 2. Beta minus transitions of ⁹⁰Y

	Energy (keV)	Probability (x 100)	Nature
	93.5 (17)	0.0000014 (3)	1st forbidden
	519,1 (17)	0,017 (6)	Unique first forbidden
	2279,8 (17)	99,983 (6)	Unique first forbidden

Table 3. Gamma transitions of ⁹⁰Y, including conversion electron (ce)

	Energy (keV)	Probability γ+ce (x 100)	Multipolarity
	1760,7 (2)	0.0000014 (3)	E0
	2186,282 (10)	0,017 (6)	E2

Table 3. Gamma transitions of ⁹⁰Y, including conversion electron (ce)

	Energy (keV)	Probability γ+ce (x 100)	Multipolarity
	1760,7 (2)	0.0000014 (3)	E0
	2186,282 (10)	0,017 (6)	E2

3. Exploitation in Nuclear Medicine of the β⁺/β^–Emission from the 0⁺ – 0⁺ Transition of ⁹⁰Zr

⁹⁰Y is one of the most widely used radionuclide for internal radiotherapy as the long range of the β particles allows more uniform irradiation in large tumours [10]. Therefore, ⁹⁰Y labelling is currently adopted for preparation of compounds belonging to various classes of therapeutic agents: peptides, antibodies, microspheres and citrate. In addition, ⁹⁰Y is also used to label resin or glass microspheres for liver radioembolization, an interventional radiology procedure in which millions of ⁹⁰Y microspheres are infused through a catheter into the hepatic artery. According to this procedure, the microspheres become embedded in the liver, and the therapeutic dose is delivered over a period of about two weeks allowing ⁹⁰Y to irradiate the tumor while sparing healthy liver tissue.

Different authors have used the small positronic emission of ⁹⁰Y to obtain high-resolution positron emission tomography (PET) images of ⁹⁰Y-labelled radiopharmaceuticals. In 2004, Nickles et al. assessed ⁹⁰Y distribution on a Derenzo phantom using a micro-PET scanner provided with bismuth germanate (BGO) crystals showing the remarkable resolution and quantitative accuracy of positron tomography [11]. In the same paper they concluded that ⁹⁰Y provide a “clear picture of the regional dose delivered by the therapy”.

However, the issue associated with ⁹⁰Y PET imaging is the extremely small emission probability of the β⁺ particles. In order to visualize (and properly measure) the activity taken up by a region of interest, a high ⁹⁰Y concentration is required. In liver radioembolization the typically injected activity ranges from one to several GBq and the total amount of radioactivity is concentrated in the liver or in small regions inside it. Hence high ⁹⁰Y concentration regions may be obtained with this technique and PET imaging of ⁹⁰Y is possible.

Recently, accurate biodistribution assessment after microsphere administration by direct ⁹⁰Y-PET scan after liver radioembolization was proven feasible by Lhommel et al. [12,13] and Werner et al. [14] which used a TOF-PET equipped with lutetium-yttrium-oxyorthosilicate (LYSO) crystals and a non-TOF PET/CT with lutetium oxyorthosilicate (LSO) detectors, respectively. The results obtained by these authors pioneered further studies about the possibility of detecting the β⁺ particles emitted by ⁹⁰Y during internal radiotherapy treatments. In another work, Gates et al. [15] showed the feasibility of hepatic localization of microsphere using routine PET on three patients concluding that ⁹⁰Y microspheres can be visualized with a simple 20-min PET/CT scan acquired using universally available technology. Bagni et al. confirmed the feasibility of ⁹⁰Y PET imaging for the assessment of microsphere biodistribution (Figure 4) using a routine PET/CT scanner provided with BGO crystals [16]. Recent studies performed by D’Arienzo et al. [17] and Willowson et al. [18] confirmed the feasibility of dosimetry and quantitative image reconstruction following ⁹⁰Y PET, respectively.

Figure 4. PET acquisition of β⁺ particles emitted in the 0⁺/0⁺ transition of ⁹⁰Zr. The biodistribution of resin microspheres after liver radioembolization is shown (courtesy of Dr. Oreste Bagni).

Figure 4. PET acquisition of β⁺ particles emitted in the 0⁺/0⁺ transition of ⁹⁰Zr. The biodistribution of resin microspheres after liver radioembolization is shown (courtesy of Dr. Oreste Bagni).

Finally, it is worth mentioning that another study by Fabbri et al. [18] considered clinical applications of ⁹⁰Y PET scans in locoregional therapies other than liver radioembolization.

4. Conclusions

Precise knowledge of the branch ratio of the 0^+– 0⁺ transition of ⁹⁰Zr is important for an accurate quantification of ⁹⁰Y accumulated inside the target region and detected via PET acquisition. Most recent literature findings report an internal pair production branch ratio as large as , measured by Selwyn and colleagues using a HPGe detector. Different studies indicate that the high-resolution images attainable with ⁹⁰Y PET may allow for accurate patient dosimetry after locoregional administration of ⁹⁰Y for therapeutic purposes.