Molybdenum-99 production pathways and the sorbents for ⁹⁹Mo/^99mTc generator systems using (n, γ) ⁹⁹Mo: a review

Abstract

Technetiun-99 m (^99mTc) is a widely used and versatile radioisotope obtained from the beta decay of molybdenum (⁹⁹Mo). ⁹⁹Mo can be produced by thermal fission or neutron activation process. Production of ⁹⁹Mo via the neutron capture method draws attention as an alternative to fission derived ⁹⁹Mo due to non-proliferation issues. The main concern with neutron capture-produced ⁹⁹Mo (n, γ) over the common fission-produced involves both lower Curie yield and lower specific activity. In this work, different adsorbents using low specific activity ⁹⁹Mo for ^99mTc generator have been discussed.

1 Introduction

Commercially prepared radioisotope generators are vital for the supply of short-lived radioisotopes. The radioisotope generators contain relatively long-lived parent radioisotopes that continually replenish the supply of a shorter-lived daughter nuclide through radioactive decay. This daughter nuclide can then be chemically extracted for conversion into a useful radiopharmaceutical to be used as either treatment or diagnostic tool. The radionuclides that are used in radiopharmaceuticals should [1, 2]:

• Possess sufficient half-life, decay mode.

• Be pure gamma emitter with sufficient energy for physiological study of interest.

• Have high radiochemical and chemical purities.

• Possess suitable chemical properties for labeling.

• Be carrier-free or no-carrier added in order to limit the toxicity.

• Follow or be trapped by the metabolic process of interest.

• Have a short effective biological half-life so that it is eliminated from the body as quickly as possible.

• Have a high target to non-target ratio so that the resulting image has a high contrast.

Among all radioisotopes, ^99mTc is the most widely used medical isotope in the world. It is the “daughter” isotope of molybdenum (Mo-99), which used in 80–85% of approximately 30 million diagnostic nuclear medical procedures performed each year [3]. The first ⁹⁹Mo/^99mTc generator was developed in 1958 at Brookhaven National Laboratory. A process called column chromatography is utilized in most ⁹⁹Mo/^99mTc generators for chemical separation of the parent and daughter isotopes [4]. Molydbenum-99 in the form of molybdate, MoO₄²⁻, is absorbed onto aluminum oxide, Al₂O₃ (alumina) as an adsorbent, so that when it decays the resulting pertechnetate, TcO₄⁻, is less tightly bound to the alumina and can be removed via saline flush [5].

The ⁹⁹Mo/^99mTc generator that is used in nuclear medicine today follows the decay scheme in which ⁹⁹Mo decays into a meta-stable isomer of ⁹⁹Tc through emission of a beta particle with a 66 h half-life (Fig. 1).

Fig. 1

Decay scheme of ⁹⁹Mo and ^99mTc [3]

Technetium-99 m then (6 h half-life) decays into ⁹⁹Tc, which is also unstable but has a long half-life (2.13 E5 years). The daughter product of this generator type, ^99mTc, is a pure gamma-emitter (~ 0.14 meV) ideal for use in medical applications. The ideal characteristics of ^99mTc such as proper decay mode, half-life, adequate penetrating power, and minimal biological damage from absorbed doses, make it a useful radiopharmaceutical that is used in several diagnostic procedures [6]. The nuclear properties of ^99mTc are ideal for medical imaging as it emits readily available photon energy (~ 140 keV) that is sufficient to determine the exact molecular structure of the coordination compounds by scintillation instruments such as gamma cameras [7]. The data collected by the camera are analyzed to produce detailed structural and functional images of certain human organs that are otherwise difficult or impossible to image.

The problem now shifts toward obtaining significant quantities of ⁹⁹Mo at low cost and reliable availability. Since ⁹⁹Mo does not occur naturally, it can be produced by thermal fission or neutron activation of stable ⁹⁸Mo (24.1 percent abundance). A particle accelerator is also considered an important technique to produce medical radioisotope such as ^99mTc [8]. Currently, the majority of the world’s ⁹⁹Mo supply comes from the thermal fission of highly enriched uranium (HEU, approximately 97 percent ²³⁵U) as a target material. This process, however, generates large quantities of radioactive waste and does not permit reprocessing of the unused uranium targets due to proliferation concerns [9]. Low enriched uranium (LEU, 20 percent ²³⁵U or less) could be used as a substitute but would yield large volumes of waste due to the large quantities of un-useable ²³⁸U present [10]. The cyclotron-based ¹⁰⁰Mo (p, 2n) ^99mTc transformation has been proposed as a viable alternative to the reactor based ²³⁵U (n, f) ⁹⁹Mo → ^99mTc strategy for production of ^99mTc [11]. However, the abundance of other molybdenum isotopes other than ¹⁰⁰Mo in the target and beam energy is the main factor that determines the impurities in the final ^99mTc product [12]. Many of these problems could be reconciled by a net production change to the neutron activation method, but the presence of large quantities of ⁹⁸Mo in the samples would serve to act as a contaminant and yield product of low specific activity [12].

Production of ⁹⁹Mo via the neutron capture method draws attention as an alternative of fission-derived ⁹⁹Mo due to non-proliferation issues. The main concern with neutron capture-produced ⁹⁹Mo (n, γ) over the common fission-produced involves both lower Curie yield and lower specific activity [13] which has impacts on the efficiency, functionality and size of the ⁹⁹Mo/^99mTc generator. These limitations, however, can be overcome by the use of adsorbent with higher capacity for molybdenum. Generators that utilize neutron capture-produced ⁹⁹Mo will need to be larger or equipped with a more efficient absorbent to accommodate the large quantity of ⁹⁸Mo. The purpose of this paper is to review the major technologies associated with this unique radioisotope and its production as well as possible ion-exchange resin based ⁹⁹Mo/^99mTc generator systems.

2 Methods of ⁹⁹Mo production

2.1 Some basic aspects of radionuclide production

Nuclear data plays an important role for the production of medical isotopes [14]. The basic concern in the production of radioisotopes is to minimize radioactive impurities while maximizing product yield. Therefore, it is necessary to investigate all the possible factors such as physical form of target material, energy range, and time of irradiation etc., to achieve the best results. In general, charge particle induced reactions, nuclear fission, neutron activation processes, and radionuclidic generator (chemical method) are the four principle methods of radionuclide production [15]. Each method of radionuclide production process provides useful isotopes with differing characteristics for nuclear imaging and therapy. In this attempt, ⁹⁹Mo production by charge particle induced reactions, nuclear fission, and neutron activation processes are discussed.

2.1.1 Fission

Radioisotope production via the fission route is accomplished through irradiation of special uranium targets rather than by direct irradiation of the reactor fuel. The majority of ⁹⁹Mo produced for medical use comes from the fission of highly enriched uranium (HEU) based target such as uranium-aluminum alloy. Production of ⁹⁹Mo is also possible from low-enriched uranium (LEU) based target. However, it would reduce the ⁹⁹Mo yield to approximately 20% of that generated from HEU with respect to target mass. The ²³⁵U content in the enriched uranium is given in the Table 1.

Table 1 Uranium enriched grade

In a nuclear reactor, the thermal energies and fission neutron spectrum are important to produce ⁹⁹Mo, as the ²³⁵U nuclei absorb thermal neutrons to induce fission. The fission of the ²³⁵U nucleus produces two to three lower mass nuclei referred to as fission fragments. The target is monitored to determine optimum time to remove from the reactor, which is based on the build-up of ⁹⁹Mo from the fission of ²³⁵U. In practice, the uranium targets are inserted into a research reactor and exposed to a high neutron flux for five to seven days in which ⁹⁹Mo is created from approximately six percent of the fission. The amount of ⁹⁹Mo produced in a target is a function of irradiation time, the thermal neutron fission cross section for ²³⁵U, the thermal neutron flux on the target, the mass of ²³⁵U in the target, and the half-life of ⁹⁹Mo. Figure 2 shows the example of fission fragments and the fission yield as a function of mass number of the fission product.

Fig. 2

a example of fission fragments, and b the fission yield as a function of mass number of the fission product

The most common radioisotopes produced by fission are ⁹⁹Mo (which decays to ^99mTc), ¹³¹I, and ¹³³Xe where the pertinent fission reaction for this work is

$${}^{235}U + {}^{1}n_{thermal} \to {}^{236}U \to {}^{99}Mo + {}^{134}Sn + 3^{1} n$$

(1)

Per Eq. (1) ⁹⁹Mo will accumulate at a rate proportional to both the amount of target material present (in this case, ²³⁵U) and thermal neutron flux. During the irradiation process, some of the ⁹⁹Mo is also lost due to radioactive decay so that a simplified expression for the amount present with respect to time can be developed (assuming a thin target)

$$N_{Mo - 99} = \frac{{\varphi \sigma_{U - 235,f} \gamma_{Mo - 99} N_{U - 235,0} }}{{\lambda_{Mo - 99} }}\left[ {1 - e^{{ - \lambda_{Mo - 99} t}} } \right]$$

(2)

where $\varphi$ is the neutron flux, $\lambda_{Mo - 99}$ is the decay constant, $N_{U - 235,0}$ is the amount of target initially present in the system, $\gamma_{Mo - 99}$ is the fission production probability, and $\sigma_{U - 235,f}$ is the fission cross-section. A detailed derivation of Eq. (2) is provided in “Appendix A”. Note that reaction cross-sections are generally given in ‘barn’ (abbreviated by the letter b) and describe the effective cross-sectional area of a target nucleus as seen by an incoming projectile where 1 barn is $10^{ - 24}$ cm². These values are energy-dependent and reaction-specific so that ratio of any particular cross-section (i.e., scattering or absorption) to the sum of all cross-sections denotes the probability of occurrence per collision.

2.1.2 Neutron activation

The neutron activation of molybdenum is another route for ⁹⁹Mo production. Seven out of 35 known isotopes of molybdenum occur naturally. Of these naturally occurring isotopes, five are stable, with atomic masses from 94 to 98. Molybdenum-98 (natural molybdenum) is the most common isotope, comprising approximately 24% of all molybdenum on earth. Table 2 shows isotopic composition of natural and enriched molybdenum.

Table 2 Isotopic composition of natural and enriched molybdenum [8, 16]

In this process, ⁹⁹Mo is produced by the irradiation of molybdenum (⁹⁸Mo) in a thermal neutron flux, {⁹⁸Mo(n,γ)⁹⁹Mo}. The thermal (~ 0.025 eV) or epithermal (0.025–1.0 eV) neutrons produced by the fission of uranium in a nuclear reactor can be used to generate ⁹⁹Mo radionuclide by bombarding stable ⁹⁸Mo target material placed in the reactor [17, 18]. In this process, the ⁹⁸Mo nuclei capture neutron and transform into ⁹⁹Mo isotope as shown in Fig. 3. The excitation function of a typical neutron capture reaction is shown in Fig. 4. Reaction cross-sections such as the plot (Fig. 4) depict how the probability of a particular reaction occurrence changes with respect to projectile energy (in this case neutron energy). It can be divided into a number of regions, with the most important being: thermal (~ 0.025 eV), resonance, and fast [18].

Fig. 3

The neutron activation of ⁹⁸Mo to generate ⁹⁹Mo [19]

Fig. 4

Excitation function of the ⁹⁸Mo (n,γ) ^99Mo reaction

Neutrons are produced by nuclear fission in the fast region (1–2 meV) and pass through the resonance region toward the thermal region as they lose energy from collisions. As the neutrons enter the resonance region, they may experience resonance absorption. The resonance absorption occurs when a neutron is captured by the nucleus and the energy of the resulting compound nucleus is equal to the excited state of the nucleus. Note that this region appears exaggerated in Fig. 4 due to the use of a log scale.

The major interest is in the thermal energy region where both the cross-section and the neutron flux are high. In the thermal region, microscopic cross-section of ⁹⁸Mo is approximately 0.13b and the target containing ⁹⁸Mo are irradiated with neutron flux of 10¹³ to 10¹⁴ n cm⁻² s⁻¹. Irradiation of molybdenum (natural or enriched) with thermal neutron fluxes greater than 10¹³ n cm⁻² s⁻¹ in a nuclear reactor are necessary to produce ⁹⁹Mo with certain specific activities of practical importance [12]. Note that enrichment refers to artificially increasing the amount of ⁹⁸Mo present in the target relative to the approximate 24 percent found in natural molybdenum. The enriched ⁹⁸Mo usually has 4 times higher ⁹⁸Mo atoms (up to fourfold for > 98% enrichment) compared to the natural Mo. It is reported that the specific activity of ⁹⁹Mo production with 8-day irradiation in a reactor with thermal flux 1.0 × 10¹⁴ ncm⁻² s⁻¹ can reach the value of about 1.6 Ci ⁹⁹Mo/ g of natural and 6 Ci ⁹⁹Mo/g of enriched molybdenum target at the end of bombardment (EOB) [20].

In the epithermal region, the cross-section has a resonance character and the integrated cross-section (resonance integral) has a high value for ⁹⁸Mo. For instance, the resonance integral ⁹⁸Mo is of 0.7b. Therefore, the effective cross-section by resonance neutrons is 50 times higher than the thermal neutron cross-section. Several studies investigated the thermal and resonance neutrons input into the ⁹⁹Mo activation process.[16, 17, 21]. Ryabchikov et al. [21] reported that the resonance part of the neutron spectra enhance the yield of ⁹⁹Mo significantly by increasing the effective cross-section of ⁹⁸Mo(n, γ)⁹⁹Mo reaction from 0.14b to 0.7b. These experiments were carried out in a reactor with neutron flux of 1.7 × 10¹⁴ n⁻² s⁻¹. Due to the contribution of resonance integral, after irradiation of MoO₃ sample for 120 h, the specific activity of ⁹⁹Mo was reported to be 3.4 Ci/g for natural molybdenum and 15 Ci/g for enriched ⁹⁸Mo. Matyskin et al. [16] investigated the effect of thermal and resonance neutrons input into ⁹⁸Mo activation process. It was reported that the effective cross-section of ⁹⁸Mo(n, γ)⁹⁹Mo reaction, for the activation of ⁹⁸Mo in a reactor with total fluxes of 7.5 × 10¹¹ n cm⁻² s⁻¹, found to be 0.4–0.5b, compared to 0.136b for thermal neutrons. After 120 h of irradiation, the specific activity of ⁹⁹Mo was reported to be 16 GBq/g (~ 0.432 Ci/g) for enriched sample and 5 GBq/g (0.135 Ci/g) for natural sample. Yields of ⁹⁹Mo can be significantly enhanced by the epithermal neutron activation, hence the selection of the irradiation position is critical particularly in lower flux reactors [12, 20]. Toth et al. [22] reported that there are several factors such as self-shielding, parasitic absorption, and depletion of the product that must be accounted to identify the effective cross-section as these factors may change the results by 10 to 50%. Blaauw et al. [17] reported that the careful estimation of the epithermal neutron contribution and neutron self-shielding correction can provide specific saturation activity of ⁹⁹Mo with good accuracy for the ⁹⁸Mo(n, γ)⁹⁹Mo reaction. It is reported that the use of enriched Mo has a minor effect of the activation rate through the self-shielding of epithermal neutron by the other Mo isotopes [17, 21]. In (n, γ) process, the targets are not irradiated indefinitely as Mo decays while in the reactor. Therefore, a balance must be struck between specific activity, processing cost, and reactor operation cost [12]. The high energy components of the neutron spectrum contributions to the formation of the (n, γ) product are often neglected since both the reaction cross-section and the neutron flux have low values compared to the fission (n, f)-based product.

The ⁹⁹Mo produced by the neutron capture method is not “carrier free” as it contains some unreacted ⁹⁸Mo which is chemically identical with ⁹⁹Mo. Thus, the specific radioactivity (defined as radioactivity per unit mass) achieved in an (n,γ) (neutron capture) reaction is about 4 to 5 orders of magnitude lower than fission ⁹⁹Mo. Note that the use of highly enriched ⁹⁸Mo enhance the yield of ⁹⁹Mo and its specific activity by a factor of about 4. In comparison to the fission process, the radionuclide ⁹⁹Mo produced by neutron capture process would require a larger generator system in order to produce the same activity required for medical procedure. For the production of considerable quantities of ⁹⁹Mo, a very large target is required. Note that the specific activity cannot be artificially increased by ⁹⁹Mo isotopic enrichment (i.e., removal of the ⁹⁸Mo) as current methods require long time periods in which large quantities of ⁹⁹Mo would be lost to decay.

As with fission production, the amount of ⁹⁹Mo produced in a target is a function of irradiation time, the thermal neutron capture cross section for ⁹⁸Mo, the thermal neutron flux on the target, the mass of ⁹⁸Mo in the target, and the half-life of ⁹⁹Mo. Molybdenum-99 will accumulate at a rate proportional to both the amount of target material present (in this case, ⁹⁸Mo) and thermal neutron flux. During the irradiation process, some of the ⁹⁹Mo is also lost due to radioactive decay so that a simplified expression for the amount present with respect to time can be developed (assuming a thin target)

$$N_{Mo - 99} = \frac{{\varphi \sigma_{Mo - 98} N_{Mo - 98,0} }}{{\lambda_{Mo - 99} }}\left[ {1 - e^{{ - \lambda_{Mo - 99} t}} } \right]$$

(3)

where $\varphi$ is the neutron flux, $\lambda_{Mo - 99}$ is the decay constant, $N_{Mo - 98,0}$ is the amount of target initially present in the system, and $\sigma_{Mo - 98}$ is the neutron absorption cross-section. A detailed derivation is provided in “Appendix B”. Equation (3) can be changed to express the sample activity by multiplying both sides by the decay constant

$$Act_{Mo - 99} = \varphi \sigma_{Mo - 98} N_{Mo - 98,0} \left[ {1 - e^{{ - \lambda_{Mo - 99} t}} } \right]$$

(4)

In where, the reaction cross section for ${}^{98}Mo\left( {n,\gamma } \right){}^{99}Mo$ is approximately 0.13 barns so that

$$\sigma = \left( {0.13\,b} \right)\left( {\frac{{10^{ - 24\,} {\text{cm}}^{{2}} }}{1\,b}} \right) = 1.3 \times 10^{ - 25\,} \;{\text{cm}}^{{2}}$$

(5)

And the decay constant for ⁹⁹Mo (66 h half-life) is determined by

$$\lambda = \frac{\ln \left( 2 \right)}{{t_{\frac{1}{2}} }} = \frac{0.693}{{66\,{\text{hours}}}} = 0.0105\;{\text{h}}^{ - 1}$$

(6)

It is important to note that ⁹⁹Mo will accumulate during target exposure to a neutron flux while simultaneously decaying via beta emission. After removal from the flux, no more ⁹⁹Mo is created so that the only change in its population is due to radioactive decay.

2.1.3 Accelerator

Particle accelerators are generally used to study the nature of matter and energy. It is also considered as an important technique to produce medical radioisotopes such as ^99mTc. The most widely discussed accelerator-based routes of ⁹⁹Mo or ^99mTc production are summarized in Fig. 5 [23].

Fig. 5

Summary of potential accelerator-based ⁹⁹Mo/^99mTc production technologies

In a linear accelerator (linac), an alternating voltage of high magnitude is applied to push particles along in a straight line. A cyclotron is somewhat like a linac wrapped into a tight spiral. In accelerator-based technologies, the isotope ^99mTc or its parent ⁹⁹Mo can be produced directly by the interaction of bombarding particles with the target material. The primary accelerated charged particles (electrons, protons, deuterons, etc.) can also be used to produce energetic secondary particles (photons, neutrons) which are then interacted with the target material to produce ⁹⁹Mo. The binding energy of a nucleon is roughly 8 MeV and the Coulomb barrier for the incoming proton is approximately 1.75 meV. Based on the binding energy of nucleon and Coulomb barrier for incoming proton, it is reported that the bombardment energy of 22–24 meV is sufficient to irradiate a 500-micron thick target foil [24]. Ruth [25]. reported that a photon of around 14 meV is needed to knock out a neutron efficiently. Thus, electron energy of 35–50 meV can provide photons that cover the energy region of 10–20 meV with sufficient intensity. In Proton accelerator [Reaction of ¹⁰⁰Mo (p, 2n)^99mTc] route, ^99mTc is directly produced for immediate use via the reaction of an accelerated proton with a ¹⁰⁰Mo nucleus yielding ^99mTc and two neutrons [26]. This technology is useful for small-scale local production because ^99mTc is a short-lived radioisotope. In electron accelerator [Reaction of ¹⁰⁰Mo (γ,n)⁹⁹Mo], ⁹⁹Mo can be produced through the photon-to-neutron reaction (γ, n) on a molybdenum target with enriched ¹⁰⁰Mo [27]. The isotope ¹⁰⁰Mo, which is mostly used in accelerator or cyclotron to produce ⁹⁹Mo or ^99mTc, comprises about 9.6% of the isotopic composition of naturally-occurring molybdenum (Table 2). An electron accelerator is used to irradiate a special target made of purified ¹⁰⁰Mo to produce ⁹⁹Mo using the photo-neutron reaction. Photons for this reaction are provided from the electron deceleration radiation. This technology uses high-energy X-rays produced by a 30–35 meV, 100 kW electron beam to irradiate a ¹⁰⁰Mo target. The induced X-rays, from incident electrons on a specific target, transmute the ¹⁰⁰Mo into ⁹⁹Mo.

Ruth, T. reported that high-energy photons produced at accelerators has the potential to be used for the production of high specific activity ⁹⁹Mo via photo-fission of ^natU [28]. The photo-fission cross-section of ^natU is 0.16b. The yield of ⁹⁹Mo would be several orders of magnitude lower than that in the neutron induced fission of ²³⁵U. A high intensity beam is needed to overcome the smaller cross-section factor for this reaction versus neutron fission of ²³⁵U but this has yet to be demonstrated [9, 29]. In deuteron accelerators [Reaction of ¹⁰⁰Mo(n, 2n)⁹⁹Mo] ⁹⁹Mo is produced through the ¹⁰⁰Mo (n, 2n) ⁹⁹Mo reaction using an enriched ¹⁰⁰Mo target [24, 30]. High energy neutrons for this reaction are provided by energetic deuterons bombarding a natural carbon target.

2.2 Comparison of ⁹⁹Mo production process

The current demand of medical isotopes in the diagnostic area has increased the interest for an economically feasible production technology for medical isotopes. The production of ⁹⁹Mo from the fission of highly enriched uranium (HEU) enables the supply of high specific activity ⁹⁹Mo. This has been threatened by reactor closings, concern over the safety of processing and waste disposal, and the use of HEU targets as approximately 97 percent of the uranium is unused during the process and handled as waste. Significant work has been done to lower the uranium enrichment present in the targets to lower the proliferation concerns, but this simply results in the need for more targets to obtain the same Curie content and therefore larger quantities of hazardous waste for the same amount of end-product.

Neutron capture of stable ⁹⁸Mo can be accomplished using either a natural molybdenum target, or in one which the ⁹⁸Mo content has been enriched to provide higher probabilities of interaction. The specific activity of enriched ⁹⁹Mo is factor of about 4 times more than the natural molybdenum source. Therefore, it is possible to conceive of an approach using enriched ⁹⁸Mo targets to produce (n, γ) ⁹⁹Mo in reactors with a neutron flux of 8 × 10¹³ to 2 × 10¹⁴ n cm⁻² s⁻¹ for alumina column generators and recovery of enriched ⁹⁸Mo from spent generators for recycling [31].

Direct ^99mTc production using cyclotrons has potential advantages in terms of cost, waste management, proliferation resistance, and ease of approval, but can only provide local needs. The technology also needs significant amounts of highly enriched molybdenum (¹⁰⁰Mo). As a result, a large number of cyclotrons would be required to meet the US demand. The technology based on the photonuclear reaction ¹⁰⁰Mo (γ, n) ⁹⁹Mo has high production yield, but has the same difficulties as the reactor-based neutron activation technology. This technology requires highly enriched molybdenum targets and would require recycling to improve economics. The predicted specific activity of molybdenum from this route is not sufficiently high to use in existing technetium generators. Rather, a gel generator or other types of generators would be needed as in the neutron activation route.

Although, all the accelerator-based strategies are under development as major alternatives but the issues related to the practical limits of irradiation volumes and low cross-sections of the reaction routes need careful assessment [3]. For example, the direct ^99mTc production from proton-bombarded ¹⁰⁰Mo-enriched targets using cyclotron is considered as reliable and cost-effective alternative production routes [32]. Qaim et al. [33] reported that the ratio of atoms of long-lived ^99gTc and ⁹⁸Tc to those of ^99mTc is appreciably higher in cyclotron production than in generator production of ^99mTc. This may adversely affect the preparation of ^99mTc-chelates, affect the image resolution and contrast, and moreover additional radiation dose to patient [34].

It is reported that the number of isotopes produces during proton-bombarded ¹⁰⁰Mo-enriched target depends on isotopic composition of the target, cross-section of each isotope, beam energy, and irradiation time [35, 36]. Therefore, controlling isotopic composition of the starting material together with irradiation parameters may improve the radioisotopic purity of the final product [34]. Several studies investigated the effect of isotopic composition of the target and irradiation parameters for the radionuclidic purity of cyclotron-produced ^99mTc [34,35,36,37]. Selivanova et al. [35] reported cyclotron-produced ^99mTc-pertechnetate by the irradiation of enriched ¹⁰⁰Mo (99.815%; 0.17% ⁹⁸Mo; 0.003% each ⁹²Mo-⁹⁷Mo) at 24 meV for 2 h. They demonstrated that the cyclotron-produced ^99mTc-pertechnetate obtained at 17 meV was safe in humans. Uzunov et al. [38] investigated cyclotron-produced ^99mTc using ¹⁰⁰Mo(p,2n)^99mTc reaction at a proton beam energy in the range 15.7–19.4 meV. The isotopic composition of the enriched molybdenum material that was used in these experiments was ¹⁰⁰Mo (99.05%), ⁹⁸Mo (0.54%), ⁹⁷Mo (0.07%), ⁹⁶Mo (0.11%), ⁹⁵Mo(0.10%), ⁹⁴Mo (0.05%), and ⁹²Mo (0.08%). It was reported that the energy region of 15–20 MeV is the best operative solution for the accelerator production of ^99mTc. It was further noted that the image properties obtained using cyclotron-produced ^99mTc are comparable with those from the generator eluted ^99mTc. In order to make ^99mTc production effective by cyclotron, following basic requirements are suggested [29]:

• Use of highly enriched ¹⁰⁰Mo target, including efficient recycling of enriched ¹⁰⁰Mo,

• Radiochemical separation immediately after irradiation,

• Daily production schedule,

• Good logistics.

A summary of the methods discussed in this section is shown in Table 3.

Table 3 Summary of ⁹⁹Mo production methods [2, 3, 39]

3 Separation of ^99mTc radionuclide in a ⁹⁹Mo/^99mTc generator

High elution yield and low breakthrough of ⁹⁹Mo [40] are the two basic requirements for a good generator system. Several studies reviewed the separation technologies that have been traditionally used for the fabrication of ⁹⁹Mo/^99mTc generator systems. A detail discussion on comparative advantage, disadvantage, and technical challenges toward adapting the emerging requirements are discussed in these studies [20, 41]. A number of methods including column chromatography, solvent extraction, sublimation and elution of metallic molybdenum gel [42] have been reported for the separation of daughter ^99mTc nuclide from the parents with a varying degree of success. Among these techniques, the alumina based chromatographic column are used most widely in ⁹⁹Mo/^99mTc generator systems.

3.1 Column chromatography

In a typical column chromatography, ⁹⁹Mo in the form of molybdate, $MoO_{4}^{2 - }$ is adsorbed onto acid alumina (Al₂O₃) as an adsorbent in a column. In ⁹⁹Mo loaded alumina column, when the ⁹⁹Mo decays it forms pertechnetate ($TcO_{4}^{ - }$) which, because of its single charge, is less tightly bound and has very limited interaction to the alumina. When saline (0.9% NaCl) is passed through the column, an ion exchange process takes place between the chloride and pertechnetate ions so that the ^99mTc is washed off or eluted, from the column containing ⁹⁹Mo loaded alumina as sodium pertechnetate, which should be crystal clear in appearance. With a pH of 4.5–7.5, hydrochloric acid and/or sodium hydroxide may have been used for pH adjustment. Over the life of the generator, an elution will contain a yield of > 80% of the theoretical amount of ^99mTc available from the molybdenum ⁹⁹Mo on the generator column. A typical elution profile is given in Fig. 6.

Fig. 6

Typicssor

3.1.1 The chemistry of molybdenum in aqueous solution

Molydbenum-99 in the form of molybdate, MoO₄²⁻, is highly soluble in alkaline than acidic solution. The degree of molybdenum ionization in an aqueous solution depends on the equilibrium concentration as well as the pH value of the solution [43]. Figure 7 shows that at pH of approximately 3, ${Mo}_{7}{O}_{23}{\left(OH\right)}^{5-}$ is the predominant species primarily at higher concentrations [approximately 50% of the molybdate species with approximately 22% of both ${Mo}_{7}{O}_{24}^{6-}$ and${Mo}_{7}{O}_{22}{\left(OH\right)}_{2}^{4-}$] [44]. It is reported that at relatively high and low pH values both the $MoO_{4}^{2 - }$ and various isopolyanions (mainly${Mo}_{7}{O}_{24}^{6-}$) predominate [45].

Fig. 7

Typical example of species distribution of the hydrolysis products formed in the H⁺-Mo(VI) system in the pH range 1.0–6.0 [44]

The $MoO_{4}^{2 - }$ anion undergoes formation of many different polyanions in acidic solutions where the presence of both para $Mo_{7} O_{24}^{6 - }$ molybdate and octa $Mo_{8} O_{26}^{4 - }$ molybdate anions in the solution at acidic pH values (pH ~ 4) [46,47,48]. The formation of polyanions may be represented by the following equations:

$$7MoO_{4}^{2 - } + 8H^{ + } \Leftrightarrow Mo_{7} O_{24}^{6 - } + 4H_{2} O$$

(7)

$$8MoO_{4}^{2 - } + 12H^{ + } \Leftrightarrow Mo_{8} O_{26}^{4 - } + 6H_{2} O$$

(8)

Figure 7 shows that ${Mo}_{7}{O}_{24}^{6-}$ is present in the solution in the pH range of 2–6. Saptima et al. [49] reported that the Mo anions, both $Mo{O}_{4}^{2-}$ and ${Mo}_{7}{O}_{24}^{6-}$ are commonly found in the pH range of 6–8, whereas $Mo{O}_{4}^{2-}$ predominates at a higher pH than 8. It is reported that even if the polyanion is present in the solution the adsorption still occurs via $MoO_{4}^{2 - }$ formation [45, 50]. The degradation of polyanions in the solution occurs due to an increased local pH close to the adsorbent surface [50].

3.1.2 Properties of alumina

In general alumina is used for radiochemical separation of isotopes due to its high radiation resistance and affinity for certain inorganic ions [51]. Alumina can exhibit both anion and cation exchange characteristics based on the surface treatment and chemical environment.[52]. Depending on the solution pH, the surface sites of alumina can undergo protonation, and the extent of protonation will be dependent on the solution pH. Therefore, the surface charge on the alumina will determine the type of bond formed between the metal ion and the surface sites of alumina. It is suggested [47, 53] that surface charge of alumina appears due to dissociation at surface of AlOH groups and detachment of either H⁺ or OH⁻. In simplest term this can be represented by dissociation equilibria equations [53, 54]:

$$Al - O - H \leftrightarrow Al^{ + } + OH^{ - }$$

(9)

$$Al - O - H \leftrightarrow Al - O^{ - } + H^{ + }$$

(10)

3.1.3 Reaction mechanism of Mo with alumina

Acid treatment of alumina in a technetium generator is common practice so it is assumed that at acidic pH < 4, the surface sites of alumina become protonated. The anions can then be adsorbed onto the surface of aluminum oxides either by ion-pair formation with positively charged surface sites or ligand exchange with surface hydroxyl groups [55]. Steigman [48] concluded that acid treated aluminum ions on the surface will complex with some octahedral polymeric variety of MoO₃, most likely via hydroxyl group displacement. Based on the hydroxyl group surface protonation of alumina, the molybdenum species can undergo different chemical reactions with the alumina surface. It is suggested that the adsorption of $MoO_{4}^{2 - }$ on the surface of alumina is either monofunctional or bifunctional type [45, 56, 57]. The chemical structures that may form are shown in Fig. 8.

Fig. 8

Chemical reaction structure of MoO₃ with alumina surface [50]

3.1.4 Chromatographic column preparation

It is important to note that the preparation of column using alumina is very important. The adsorbent should be packed very carefully into the column in order to avoid any channeling or disruption in the bed. Failure to do so will result in excessive amounts of breakthrough. The preparation procedures of a typical chromatographic generator (100 mCi generator) from ⁹⁹Mo produced by irradiating ⁹⁸Mo and adsorbing it on alumina are as follows [58]: In this process, approximately 10 g of acid alumina (80–100 mesh) was transferred to a glass column containing a glass frit at the end and a Teflon disc was placed on top of the alumina bed. The column was then washed with sterile pyrogen free 0.1 N HCl or 0.1 N HNO₃ until the effluent is strongly acidic (pH ~ 1–2). In another attempt, a solution containing predetermined concentration of ⁹⁹Mo with solution pH ~ 3.0 was prepared. The solution was then passed through the alumina column slowly and allowed to drain. The column was then washed with pyrogen free 0.1 N HCl. The column was further washed with isotonic (0.9% NaCl) solution. In order to check the ⁹⁹Mo breakthrough, a few drops of isotonic wash solution (effluent) was collected in a vial containing a few mg of potassium ethyl xanthate. To this, about two drops of 2 N HCl was added. No red color should be observed. If a red color is observed, ⁹⁹Mo is breaking through the column and the column should be rejected. A final check for ⁹⁹Mo should be made on this spot test sample by γ-ray spectrometry. The column is then sealed at both ends with septa and placed in a shield and autoclaved. It is reported [59] that the procedure for preparing a fission product ⁹⁹Mo/^99mTc generator is significantly less complex than the (n,γ) ⁹⁹Mo generator described above as the fission product ⁹⁹Mo is carrier-free and therefore a much smaller alumina column can be used for the same activity. A schematic and cross-section of a commercial ^99mTc- ⁹⁹Mo generator is shown in Fig. 9.

Fig. 9

Schematic diagram of a typical ⁹⁹Mo/^99mTc Generator [59]

3.1.5 ^99mTc accumulation and ⁹⁹Mo decay kinetics

Since ^99mTc is produced from the decay of ⁹⁹Mo and lost through its own decay to ⁹⁹Tc, its kinetics can be described with the following rate equation.

$$N_{Tc - 99m} = \frac{{\lambda_{Mo - 99} }}{{\lambda_{Tc - 99m} - \lambda_{Mo - 99} }}N_{Mo - 99,0} \left[ {e^{{ - \lambda_{Mo - 99} t}} - e^{{ - \lambda_{Tc - 99m} t}} } \right]$$

(11)

Derivation of Eq. 11 is presented in the “Appendix C”. To determine the time at which the maximum amount of ^99mTc is present in the system, it is necessary to take the derivative of Eq. (11) with respect to time and setting it equal to zero so that

$$t_{\max } = \frac{{\ln \left( {\frac{{\lambda_{Mo - 99} }}{{\lambda_{Tc - 99m} }}} \right)}}{{\left( {\lambda_{Mo - 99} - \lambda_{Tc - 99m} } \right)}}$$

(12)

It is important to realize that while this maximum time value is constant, the maximum amount of available activity will decrease with time due to the constant decay of the parent isotope. A good rule of thumb to follow is that Eq. (12) can be approximated by four daughter half-lives. As with previous Eq. 11, a detailed derivation of Eq. (12) is shown in Appendix C.

The activity of ^99mTc is maximum after approximately 23 h as shown in Appendix C. As shown in Fig. 10, the production rate of daughter (^99mTc) and the decay rate of Parent (⁹⁹Mo) are equal after approximately 23 h and the parent and daughter are said to be in transient equilibrium. The daughter (^99mTc) can be repeatedly eluted (extracted) from the parent/daughter pair in a column (Fig. 9) as pertechnetate (^99mTcO₄ ⁻) using saline (0.9% NaCl) solution.

Fig. 10

Profile of transient equilibrium in ^99mTc-⁹⁹Mo generator

3.1.6 Different adsorbents for molybdenum in the generator

The chemical structure mentioned in the Fig. 8 depends on several factors:

• pH of the solution that defines the dominant species present in the solution

• Concentration of Mo in the solution

• The surface charge of the adsorbent

• The pore structure of the adsorbent materials

Molybdate in acid forms quite stable heteropoly complexes with a large number of cations, including Al³⁺ [48]. The adsorption capacity of alumina for molybdenum is reported to be in the range of 2–26 mg/gram of alumina [60, 61]. Several studies described processes to enhance adsorption capacity of alumina for molybdenum [51, 62, 63]. Takahashi et al. [51] studied molybdenum adsorption capacity for commercially available alumina. They found that molybdenum uptake capacity of alumina increases when it was heated at 400 °C for 10 h and subsequent treatment with boiling hydrochloric acid (2 N) for 1 h. The adsorption capacity of treated alumina for molybdenum is reported to be pH dependent. They also observed that the dissolution of treated alumina is least in sodium chloride solution compared to sodium hydroxide, hydrochloric acid, nitric acid, and ammonium hydroxide. Suzuki et al. [62] studied the effect of sintering temperature on molybdenum uptake by Gibbsite-Al₂O₃, P-Boehmite- Al₂O₃, and Bayerite- Al₂O₃. They reported that the molybdenum adsorption properties are influenced by the crystal structure and specific surface area of the alumina. The average adsorption of molybdenum on Gibbsite- Al₂O₃, P-Boehmite- Al₂O₃, and Bayerite- Al₂O₃ samples sintered at 300 °C was reported to be 67.5, 82.4, and 91.1 mg/g of, respectively. Guides-Silva et al. [63] investigated effect of sintering temperature on alumina phases and their subsequent molybdenum uptake capacity. They reported that the alumina powder calcined at 900 °C for 5 h had high chemical stability. The molybdenum adsorption capacity of the alumina heated at 900 °C was reported to be 92.45 mg Mo/g alumina.

Chakravarty et al. [60] studied molybdenum uptake on to nanocrystalline Al₂O₃ that was prepared by solid state mechanochemical reaction of aluminum nitrate with ammonium bicarbonate. It was reported that the sorbent possessed selectivity properties for ⁹⁹Mo and demonstrated a maximum sorption capacity of 200 ± 5 mg Mo/g, which is  ~ 10 times higher than that of ordinary acidic alumina. In this work, a tandem columns generator concept has been proposed using two columns containing ⁹⁹Mo loaded mesoporous alumina that were connected in series. A 26 GBq (700 mCi) ⁹⁹Mo/^99mTc generator was developed using (n,γ)⁹⁹Mo having specific activity of ∼18.5 GBq (500 mCi)/g of Mo. In this method ^99mTc eluted from the first column was fed to the second column to achieve higher radioactive concentration (RAC) as well as the purity of ^99mTc. It was reported that the double tandem column generator provided consistently high yields (> 82% of the theoretical yields) of ^99mTc over a period of 1 week while the single column generator gave low yields (∼50% of the theoretical yields). The ^99mTc eluted from the generator possessed high radionuclidic, radiochemical, and chemical purity and was amenable for the preparation of ^99mTc-labeled radiopharmaceuticals.

Several studies investigated the adsorption characteristics of enriched molybdenum-98 on to alumina [64,65,66]. Skurudin et al. [64] investigated the effect of acid treatment on the adsorption capacity of aluminum oxides for enriched molybdenum-98. It was reported that the adsorption of molybdenum occurs through chemisorption on to the active surface sites of acid treated alumina instead of weak physical adsorption. The maximum adsorption capacity of enriched molybdenum was 23.5 mg/ g of activated alumina. The adsorption of ^99mTc under static and dynamic conditions was also carried out on acid treated aluminum oxides [65]. Upon reduction of ^99mTc with bivalent tin, approximately 93% ^99mTc was reported to be adsorbed on to aluminum oxide. It was envisaged that ^99mTc with high specific activity can be obtained by concentrating ^99mTc onto nanosized colloidal particles of aluminum oxide. In another work Skurudin et al. [66] investigated the factors that influence the elution characteristics of ^99mTc in a generator column. The chromatographic generator column was prepared from ⁹⁹Mo produced by irradiating enriched ⁹⁸Mo and adsorbing it on alumina. The ^99mTc elution profile of the generator is reported to be dependent on the adsorbed mass of molybdenum. It was suggested that a higher yield of ^99mTc can be obtained from a pretreated alumina column filled with molybdenum approximately 85% of its uptake capacity. It was noted that a generator column loaded with 50–60% of its capacity requires additional volume of normal saline to complete ^99mTc elution. At lower uptake, ^99mTc can occupy the vacant active sites of aluminum oxide thus reduce the yield.

A review article by Le, V.S [20]. provided a detail description of available ⁹⁹Mo sources and also the technical aspect of ^99mTc generators. This review discussed technical solution for overcoming the shortage of ⁹⁹Mo supply and various technologies to recover ^99mTc from high and low specific activity ⁹⁹Mo/^99mTc generators systems. Various processes using selective sorbents used to purify and concentrate ^99mTc from low specific activity ⁹⁹Mo are also discussed. Chattapadhya et al. [67] reported a ^99mTc delivery system using (n, γ)⁹⁹Mo adsorbed onto a large alumina column tandem with Dowex-1, a strong base anion-exchange resin, column and column with AgCl. In their work, a ^99mTc generators containing as much as 80–100 g alumina for holding 14.8–18.5 GBq (400–500 mCi) ⁹⁹Mo (at the reference time) has been discussed. A large volume of saline solution (50–70 mL) was used to elute pertechnetate from the ⁹⁹Mo loaded alumina column. The eluate with low specific activity ^99mTc was then passed through the Dowex-1 column to concentrate the ^99mTc in it. About 5–6 mL of 0.2 M NaI solution was used to elute pertechnetate from the Dowex-1 column followed by washing with 1.5–1.8 mL water. Iodide was removed from the pertechnetate eluate by passing it through a 1 g AgCl column. The average yield of ^99mTc was 70–80% compared to the yield of 80–90% from the conventional chromatographic generator systems. In another attempt, Chattopadhyay et al. [68] discussed the possibility of using Dowex-1 column to separate ^99mTc from ⁹⁹Mo. In their work, low to medium specific activity ⁹⁹Mo-molybdate solution of 7.4–18.5 GBq (200–500 mCi) in sodium hydroxide was passed through a tiny Dowex-1 column (25 mg) to separate the ^99mTc from the ⁹⁹Mo. ^99mTc was then eluted using tetrabutylammonium bromide (TBAB) solution (1 mg/5 ml methylene chloride). The TBAB solution containing ^99mTc was then passed through a small alumina column where ^99mTc retained in the column. ^99mTc was finally eluted with 5 mL saline solution. The average separating yield was reported to be 90% (n = 10).

Xu et al. [69] reported mesoporous alumina materials prepared from the precursors of aluminum isopropoxide/HNO₃ in the presence of glucose in aqueous system. In another study Chakravarty et al. [70] prepared mesoporous alumina using the process given by Xu et al. [69] and developed clinical scale ⁹⁹Mo/^99mTc generator. The molybdenum adsorption capacity of the prepared mesoporous alumina was reported to be 225 ± 20 and 168 ± 12 mg Mo/g of sorbent under static and dynamic process. It was reported that the ⁹⁹Mo strongly and selectively retained by mesoporous alumina at acidic pH condition. ^99mTc was obtained from the generator in > 80% yields with high radionuclidic (> 99.99%) and radiochemical purity (> 99%). The compatibility of the product in the preparation of ^99mTc-radiopharmaceuticals was evaluated by radiolabeling standard kits with > 95% yield. Saptiama et al. [71] investigated the calcination temperature, surface area, and crystallinity of mesoporous alumina preparation and their effect on molybdenum uptake capacity. They found that the molybdenum uptake capacity was 12.5 mg/g, 31 mg/g, and 17.5 mg/ g of alumina sample that was prepared at 600 °C, 700 °C and 900 °C, respectively. Denkova et al. [72] have investigated the potential of mesoporous aluminum oxides as adsorbent materials for ⁹⁹Mo/^99mTc generators utilized in nuclear medicine. It was reported that the maximum adsorption capacity of the mesoporous alumina sample was 112 mg/g. Furthermore, they added that approximately 40–50% of ^99mTc could be removed from the molybdenum loaded sorbents in a single elution with negligible loss of ⁹⁹Mo but the aluminum breakthrough was reported to be higher than the NRC accepted limit (10 mg/L).

In another study, Saptiama et al. [58, 73] reports the fabrication of alumina-embedded mesoporous silica (MPS) particles by solution-phase method. In this work different ratio of Al/ Si and calcination temperature was chosen to prepare the adsorbent material. The Mo adsorption experiments conducted using the batch method show the following trend in Mo adsorption capacity in relation to the calcination temperature: 750 °C > 600 °C > 900 °C > 1050 °C and Al/Si molar ratio: Al0.1-MPS < Al0.3-MPS < Al0.5-MPS < Al0.6-MPS. Among all the studied samples, the Al0.6-MPS sample calcined at 750 °C shows the highest Mo adsorption capacity (16.8 mg Mo/g of adsorbent).

Lee et al. [74] reported that Sulfated alumina or alumina-sulfated Zirconia exhibits adsorption capacity that is superior to that of conventional alumina adsorbents, and is stable and is thus loaded in a dry state in an adsorption column. The molybdenum adsorption capacity of sulfated alumina was reported to be 392 mg/g from a solution of 10,500 mg/L molybdenum solution under dynamic condition and subsequent ^99mTc elution efficiency was reported to be 60–80%. Qazi and Mushtaq [75] studied hydrous titanium oxide as an adsorbent for ^99mTc generator. Adsorption behavior of molybdate on hydrous titanium oxide was evaluated at boiling water bath temperature (∼100 °C) using radiotracer technique. The effect of pH, molybdenum concentration in solution, incubation time etc., on molybdenum uptake by the titanium oxide were evaluated. The performance of a generator loaded with 230 mg of ⁹⁹Mo (∼14 mCi) on 1 g of hydrous titanium oxide column showed that the elution efficiency of ^99mTc was 85–90% and more than 90% of the activity was obtained in the first 2 mL of saline. In order to comply with US Pharmacopoeia, an additional mini column of alumina for the removal of excess ⁹⁹Mo was suggested. In another work, Chakaravarty et al. [76] reported polymer embedded nano crystalline titania based adsorbent for ⁹⁹Mo/^99mTc generator. The surface area of this polymer was 30 m²/g with an average pore size of 40 nm. The adsorption capacity of molybdenum for this adsorbent was found to be 100 mg/g. A ⁹⁹Mo/^99mTc generator with 30 mCi ⁹⁹Mo activity level demonstrated 80% ^99mTc recovery and the data was reported to be consistent over a period of one week using this adsorbent. Toth et al. [22] has proposed the use of self-absorbed monolayers on mesoporous support (SAMMS) materials for its proven ability to selectively remove ionic species from aqueous solutions and complex liquids as a potential separation mechanism for ⁹⁹Mo/^99mTc. It was reported that SAMMS material can adsorb almost 70 mg molybdenum/gram of resin.

Le [77] described a process for the synthesis of polymer compound of Zirconium (PZC) based adsorbent and its use in chromatographic ⁹⁹Mo/^99mTc (n,γ) generators with low specific activity. It was reported that a PZC based generator with specific activity ranging from 200 to 1000 mCi Mo-99 can be satisfactorily used in the clinical nuclear medicine application. Tanase et al. [78] reported an inorganic polymer adsorbent (PZC) for use in low specific activity ⁹⁹Mo generators synthesized from heating a solution of zirconium chloride and isopropyl alcohol. It was reported that about 200 mg ⁹⁹Mo(Mo) was adsorbed on to per gram of PZC resin from a molybdenum solution containing ⁹⁹Mo (1.8 mCi/mL). Meta-stable technetium-99 was eluted with a small volume of saline solution for 80% yields. In addition, the ⁹⁹Mo breakthrough was reported to be less than 0.5% in good test conditions.

A US patent is reported by Hasan [79] described an alternative adsorbent of alumina in neutron activation (n,γ) ⁹⁹Mo based ^99mTc/⁹⁹Mo generator. This work describes a method of preparing biopolymer based microporous composite material (MPCM) resin. It is reported that the MPCM resin, porous in nature, is found to be resistant to radiation exposure (50 MRad), extreme pH conditions, strong oxidizing agents, and temperatures exceeding 100 degrees Celsius without substantial physical degradation of the resin [79]. Molydbenum-99 in the form of molybdate, MoO₄²⁻, is absorbed onto resin, so that when it decays the resulting pertechnetate, TcO₄⁻, is less tightly bound to the resin surface and can be removed via saline flush [80]. Figure 11 shows possible reaction mechanism of molybdenum uptake on to MPCM resin. Figure 12 shows the surface charge pattern for Mo (VI) loaded MPCM sample with or without oxidization. It was reported that the chitosan-based composite (MPCM) resin requires further surface charge conditioning by oxidation to facilitate ^99mTc release from the column [79]. A detailed description of the adsorption mechanism of ⁹⁹Mo on to resin and simultaneous release of ^99mTc from the column has been described based on surface charge analysis of the MPCM resin [79].

Fig. 11

Reactions mechanism for the adsorption of Mo (VI) on to composite resin from aqueous solution [79]

Fig. 12

Surface charge of a MPCM and MPCM exposed to 1% of Mo (VI) in solution in the presence of 1 M NaNO₃, respectively and b oxidized and non-oxidized MPCM exposed 1% of Mo(VI) in solution in presence of 1 N NaNO₃, respectively [79]

Chattopadhyay et al. [81] reproduced Hasan’s work and reported that the molybdenum adsorption efficiency of the resin is approximately 50–60% (500–600 mg Mo/g of resin) of the loaded activity. A column prepared with the resin was evaluated for routine elution of ^99mTc with 30 mL saline. The Na[^99mTc]TcO₄⁻ eluates obtained were clear solutions with pH 5–6 and the radiochemical (RC) purities of 99%. The ⁹⁹Mo breakthrough in the ^99mTc fraction with alumina guard column (0.5 g) was 0.002 ± 0.003 (n = 9). The Al and Mo content in the eluted ^99mTc was less than 10 µg/mL. The RC purity of the labeled compounds was greater than 95%. The radionuclidic purity of ^99mTcO₄ ⁻ was more than 99.99%. It was concluded that chitosan resin based ⁹⁹Mo/^99mTc generator using low-specific activity (n, γ)⁹⁹Mo may find an application in nuclear medicine.

In case of molybdenum (Mo) uptake onto MPCM resin, Hasan [79] reported that the adsorption follows Type-1 isotherm and the Mo adsorption mostly occurs at the monolayer of active surface sites of the resin. Based on the above findings [79], Hasan [82] pointed out that the critical structures of the resin that absorb irradiated molybdenum needs to be protected from the negative impact of higher radiation dose. In order to address this issue, following points are considered [82]:

• Since the active region of the resin structure is assumed to be thin, due to range consideration; a new type of shielding concept can be used to protect the critical structure of the resin from the negative impact of absorbed dose.

• The possibility of micro-shielding on the critical surface of the resin needs to be investigated which may reduce the impact of high radiation flux and minimize the radiolytic effect on to the resin surface.

• High Z elements, for instance Hf, can be used as micro-shielding candidate which, may cut down the dose on the active surface sites of the resin.

• Other high Z elements with higher stopping power are also good candidates as micro-shielding materials.

• Since the main constituents of MPCM resin are low Z elements (with less stopping power), the negative impact of high energy particles can also be minimized by maintaining a proper aspect ratio of the column.

It was reported that the radiation tolerance limit and selectivity of the MPCM resin for certain isotopes, was further enhanced by the high Z element crosslinked MPCM resin as it was not being limited by the radiolytic driven reaction [82]. The micro-shielded resin was termed as MPCM-Z resin. The performance of the MPCM-Z resin for molybdenum was evaluated using batch process. It was found that the resin is capable of adsorbing > 95% of available molybdenum (500–600 mg Mo/gram resin) within an hour from 1% solution at solution pH ~ 3.0, when the solid to liquid ratio was 2:100. A generator consisting of MPCM-Z resin loaded with low specific activity (n, γ)⁹⁹Mo was prepared. The ^99mTc recovery was ± 70% when sodium nitrate (1 g/L) as an additive was used with saline solution. The breakthrough of ⁹⁹Mo and the pH of the eluent that pass through an alumina guard column were within the US Pharmacopeia limit.

Several studies reported technetium selective resin such as Dowex, TEVA (TetraValent Actinides), ABEC (aqueous biphasic extraction chromatographic) resin for the selective adsorption of pertechnetate from aqueous solution [83,84,85]. The possible uses of these technetium selective resins in the integrated production of ^99mTc-generator are promising provided that ^99mTc can be collected and concentrated in a small column and then eluted easily with saline, water or any suitable solvents. Keiko et al. [84] described a method for separating and purifying technetium from technetium-containing molybdenum using TEVA resin. However, the strong acidic solution (8 M HNO₃) required for recovery of TcO₄⁻ ions from the TEVA resin. In practice, pertechnetae in strong acid solution is not preferred on the basis of daily use in nuclear medicine [20]. Wojdowska et al. [86] studied the separation of ^99mTc from large excess of molybdenum using column containing Dowex-1 and AnaLig Tc-02 resin, respectively. It was reported that ^99mTc is quantitatively bound to both Dowex-1 × 8 and AnaLig Tc-02 resin whereas molybdenum was found to be retained slightly and that can be rinsed out with 2 M NaOH. ^99mTc was eluted with TBAB solution from the Dowex-1 column and the elution yield amounted to 78%. In case of AnaLig Tc-02 resin, ^99mTc was eluted using small volume of water. The recovery was equal to about 85%. A US patent by Le VS et al. [87] described the preparation process for silica-based multifunctional resin. The molybdenum adsorption capacity of this multifunctional resin was reported to be 456–692 mg Mo/g and 313–445 mg Mo/g of sorbent under static and dynamic process. Due to its high capacity for molybdenum uptake, this multifunctional resin can be considered as a potential candidate for ⁹⁹Mo/^99mTc (n, γ) generator. It was reported that one derivative of this multifunctional resin can be used to purify and concentrate ^99mTc in a small column. It was further noted that the recovery yield of the daughter nuclide ^99mTc was greater than 95%. An integrated generator system using this multifunctional resin and its derivative can be used to concentrate ^99mTc, therefore, ^99mTc with high specific activity (1 Ci/mL) is possible from a ⁹⁹Mo/^99mTc (n, γ) generator. Table 4 shows typical example of adsorption capacity of different sorbents for molybdenum from aqueous solution.

Table 4 Adsorption capacity of various adsorbents for molybdenum

3.2 Molybdate gel-generator

Several researchers proposed a zirconium molybdate based gel generator which is applicable to ⁹⁹Mo obtained easily by the (n, γ) reaction of natural molybdenum [90,91,92]. El-Amir et al. [93] prepared cerium (IV) tellurium molybdate based gel bed for chromatographic ⁹⁹Mo/^99mTc generator. The ^99mTc elution yield from this generator was 77.8 ± 3.0% with a radionuclidic purity of ≥ 99.99%, radiochemical purity of 96.5 ± 1.3% (as ^99mTcO₄ ⁻) and pH-value in the range of 5–7. Sarkar et al. [94] reported zirconium [⁹⁹Mo]molybdate (Zr⁹⁹Mo) gel column generator. Generator was prepared using 6–7 g Zr⁹⁹Mo gel column containing up to 22.2 GBq (600 mCi) ⁹⁹Mo. The radioactive concentration of ^99mTc up to 4 GBq/mL (110 mCi/mL) was obtained on the first day of use. An acidic alumina guard column was used to remove the co-eluted traces of ⁹⁹Mo and to retain the pertechnetate. The overall recovery of ^99mTc was > 90%, ⁹⁹Mo breakthrough was 10^–3 to 10^–4% and the duration of concentration was 3–5 min. Monoroy-Guzman et al. [91] suggested to prepare gels from molybdate solutions at pH 4.5, where a mixture of ${Mo}_{7}{O}_{24}^{6-}$ and ${Mo}_{x}{O}_{y}^{x-y-}$ ions is present, and 0.1 mol/ L ${\mathrm{ZrOCl}}_{2}.8{\mathrm{H}}_{2}\mathrm{O}$ solutions aged for 1 day, where the formation of $ZrOO{H}^{+}$ ions is favored. The overall reaction is given in Eq. 13 [91]:

$$ZrOOH^{ + } + wMo_{x} O_{z} \left( {OH} \right)_{8x - y - 2z}^{{\left( {2x - y} \right) - }} \to \left[ {ZrO_{2} .\left( {x - w} \right)H_{2} O.Mo_{x} O_{z} \left( {OH} \right)_{{\left( {8x - y - 2z} \right)}}^{{\left( {2x - y} \right)}} } \right]^{ - } + wH_{2} O$$

(13)

A typical zirconium molybdenum gel preparation flow sheet is given in Fig. 13. Marageh et al. [92] reported that the produced sodium pertechnetate solution from the zirconium molybdate gel-type ⁹⁹Mo/ ^99mTc generators fulfills all requirements of U.S. pharmacopoeia as all of these generators provide high-yield and pure elution as well as sterile and pyrogen-free pertechnetate solutions. In addition, it shows favorable-quality features to prepare various ^99mTc complexes.

Fig. 13

Typical flow-chart of gel processing plant [92]

Several difficulties of the gel preparations have been reported due to its dependence on many complex factors such as molybdenum and zirconium concentrations (ratio of Mo and Zr in the gel) and gel reaction temperatures which can greatly influence the ^99mTc elution.

Chakravarty et al. [95] uses electrochemical method to concentrate ^99mTc obtained from a zirconium molybdate (Zr⁹⁹Mo) gel generator. The overall recovery of ^99mTc was 90% with 99.99% radionuclidic purity and 99% radiochemical purity. Saraswathy et al. [96] reported the effect of subtle variations on zirconium molybdate-⁹⁹Mo gel preparatory conditions to achieve high ^99mTc release and minimal ⁹⁹Mo breakthrough upon elution with normal saline. They prepared Zirconium molybdate-⁹⁹Mo gels at a pH of 4–5 by reacting [Zr]: [Mo] in the mole ratio of 1.25: 1. Monoroy-Guzman et al. [91] reported that a rigid and regular lattice (structure) of the zirconium molybdate gels acts as a “molecular sieve” preventing the mobility of the ^99mTc in the gel and causing the decrease of the generator efficiency. The best performances of the ⁹⁹Mo/^99mTc zirconium molybdate gel generators are attained using gels with random network which allow a more diffusion of the ^99mTcO₄⁻ increasing the generator efficiency.

3.3 Solvent extraction

The ⁹⁹Mo/^99mTc separation processes in solvent extraction systems are carried out in well shielded hot cells usually installed within the premises of a nuclear research establishment under the supervision of well trained and qualified staff. It essentially consists of a glass-quartz or stainless steel apparatus in which activated ⁹⁹MoO₃ is dissolved in an acid or base (HC1, NaOH) and mixed with an organic solvent such as methyl-ethyl-ketone (MEK) to preferentially concentrate ^99mTc over ⁹⁹Mo. Once equilibrium is reached, the organic solvent containing decay-produced ^99mTc is separated from the aqueous layer into a different vessel and evaporated out leaving behind a white powder of technetium salt. This water soluble salt is then dissolved in a sterilized physiological saline solution (0.9% NaCl) for distribution to the users in hospitals after proper quality control procedures have been satisfactorily performed. The parent ⁹⁹Mo contained in the aqueous layer continues to produce further ^99mTc which, after a proper equilibration period of approximately one day, is ready for subsequent extractions with an organic solvent.

3.4 Sublimation generator

The separation of ^99mTc from ⁹⁹Mo in the sublimination generator is achieved by subjecting the activated MoC₃ to high temperatures of over 900 °C to sublimate an oxide of ^99mTc for collection and dissolution in a physiological saline solution. While sublimation systems produce ^99mTc of the highest purity and high radioactivity concentration, they must be installed in a shielded hot cell.

3.5 Comparison of separation techniques

Alternative technologies for ^99mTc generator using relatively low specific activity ⁹⁹Mo produced by the neutron activation of natural molybdenum would provide a less complex, less expensive, and more practical route for indigenous production and use of ^99mTc. Many attempts have been made to develop different alternative technologies based on (n,γ) ⁹⁹Mo by exploiting the differences in the volatility of technetium and molybdenum oxides (sublimation generators) [4]. The separation can be achieved by extraction, usually by using methyl ethyl ketone (extraction generator). The chromatographic-type generators are very simple to use and safe for handling. It has several advantages over other separation methods that include compact size, easy transportability, single step rapid operation, radiological and pharmaceutical safety, and ^99mTc separation with high yield and purity [97]. Note that solvent extraction and sublimation separation techniques are also widely utilized in India, Peru, and Thailand with low specific activity ⁹⁹Mo while Kazakhstan and Romania employ gel-generators. Typical example of different separation methods used in ^99mTc/⁹⁹Mo generator systems to separate ^99mTc is given in Table 5.

Table 5 Various methods used to separate ^99mTc from ⁹⁹Mo [4, 41, 97]

4 Generator performance

The performance of a chromatographic generator involves several factors including elution profile, elution efficiency, radionuclidic purity, chemical purity, and the radiochemical purity of the eluted ^99mTc [97].

4.1 Elution efficiency

The elution efficiency of a generator can be defined as the fraction of the theoretically available ^99mTc activity in the system which is separated during the elution process. In practice, the ^99mTc elution efficiency is determined by the following relation:

$$Elution\,\,Yield\left( \% \right) = \frac{{A_{Tc(measured)} }}{{A_{Tc(theoretical)} }} \times 100$$

(14)

where $A_{Tc(measured)}$ is the activity of ^99mTc measured in the eluate, and $A_{Tc(theoretical)}$ is the activity of ^99mTc calculated according to the activity of ⁹⁹Mo adsorbed on the column and time elapsed after adsorption or previous elution. The elution efficiency of a generator mainly depends on physical size and shape of a generator. It may vary randomly time to time, possibly due to complex chemical, physicochemical and radiochemical processes in the generator [4].

The valence state of technetium may also play a role on elution yield [98]. Boyd [97] concluded that extensively washed and frequently eluted generators have the sharpest elution profiles and highest elution efficiencies. Improper eluent, reduction of pertechnetate by radiolysis, organic impurities, mechanical problems etc., are few noted factors that may cause low elution yield [48, 58]. The dissolved oxygen aids in keeping the technetium in the pertechnetate form i.e., oxygen is essential in maintaining a high elution yield.

4.2 Breakthrough

One major concern with ^99mTc generators is ⁹⁹Mo ‘breakthrough” i.e., partial elution of the ⁹⁹Mo parent along with ^99mTc from the generator. From the stand point of patient radiation safety, the amount of ⁹⁹Mo in the elution should be as low as possible because the presence of ⁹⁹Mo in the elution may interfere with labeling process and lead to clumping of red blood cells and possible microemboli. In case of alumina as adsorbent in the column, some possible causes of ⁹⁹Mo breakthrough are [58]:

• Exceeding the ion exchange capacity of the alumina

• pH of the alumina is greater than 7

• channeling or disrupted alumina bed

• excessive elution

According to NRC regulation, the acceptable limit of ⁹⁹Mo breakthrough is 1.0 μCi ⁹⁹Mo/mCi ^99mTc (10⁻³Bq⁹⁹Mo/Bq^99mTc), not to exceed 5 μCi (185 kBq) per human dose at the time of injection. The breakthrough of a generator can be calculated as follows:

$$Breakthrough = \frac{{A_{{{}^{99}Mo}} }}{{A_{{{}^{99m}Tc}} }}$$

(15)

where $A_{{{}^{99}Mo}}$ is the measured activity of the ⁹⁹Mo and $A_{{{}^{99m}Tc}}$ that of ^99mTc. A NaI (Tl) counting systems is capable of detecting the activity of ⁹⁹Mo in the presence of much larger amounts of ^99mTc and some dose calibrators with a lead-lined container are available specifically for this purpose.

4.3 Radionuclide purity

Radionuclidic purity for ^99mTc refers to the percentage of radioactivity of ^99mTc present in the total radioactivity of product. For effective utilization of the radioisotope ^99mTc, it must be free of isotopic contamination when it is used for labeling or intravenous administration to humans. Current U.S. Pharmacopeia requires ^99mTc from a generator (fission) to be at least 99.96% pure as a radionuclide, whereas European Pharmacopeia expects 99.88% radioactivity due to ^99mTc. Boyd [97] reported that an ideal generator would produce ^99mTc with a purity that satisfies Pharmacopoeia specification for a period of three ^99mTc half-lives (~ 18 h). Table 6 shows that the sodium pertechnetate (^99mTc) injection should contain not less than 90% and not more than 110% of the declared ^99mTc radioactivity stated on the label at the reference date and time.

Table 6 Sodium pertechnetate (^99mTc) injection (fission) US and European Pharmacopeia [99, 100]

The European and the US Pharmacopeia specifies the limits of radionuclidic impurities that should not exceed at the time of administration (Table 6). The most probable radionuclide contaminant in the final product of ^99mTc is the parent ⁹⁹Mo (most likely due to excessive breakthrough). The choice of target material and its purity are also important factors as some radionuclidic impurities may occur from the activation of impurities present in the target. The radioactivity due to ⁹⁹Mo does not exceed 0.1% of the total radioactivity of the test solution. Other γ-ray emitting radionuclidic impurities including ⁹⁹Mo, ¹³¹I, ¹³²I, ¹⁰³Ru, and ⁸⁹Sr shall not exceed 0.5 μCi per mCi of ^99mTc at the time of administration. Some of the possible causes of fission-product contamination are [58, 101]:

• production route of the parent ⁹⁹Mo

• Improper separation procedures used in the manufacture of the ⁹⁹Mo

• Insufficient washing of the generator during preparation

4.4 Chemical purity

The presence of chemical impurity in the final ^99mTc product may cause detrimental effect on the clinical application and is to be controlled strictly. The chemical impurity of ^99mTc, that reflects the composition of non-radioactive components, may originate from the generator bed or from the eluent. The most probable chemical impurity that may be detected in the eluent is aluminum. In general, the generator column is prepared using aluminum oxide (alumina) as a support for the parent ⁹⁹Mo. Aluminum cations can be formed during adsorption of ⁹⁹Mo as the bed is expose to acidic pH condition. Cationic aluminum can be washed away from the generator column during the subsequent elution of the daughter radionuclide ^99mTc (pertechnetate). The aluminum ion concentration in the eluent should not be more than 10 µg/mL of the generator eluate.

4.5 Radiochemical purity

Radiochemical purity of radiopharmaceuticals is defined as the proportion of the total radioactivity in the sample associated with desired radiolabeled species [102]. For instance, the presence of ^99mTc in pertechnetate form (+ 7 state) is most desirable as this species can easily be converted to other oxidation states prior to complexation with suitable ligands [70]. Radiochemical purity is also used as the index of biological performance of radiopharmaceuticals that are administered to human. The possible radiochemical contamination in the ^99mTc labeled product may occur from decomposition due to action of solvent, change in temperature or pH, light and radiolysis in the generator systems [103]. The presence of any undesirable radiochemical impurity will reduce efficacy of the final radiopharmaceutical product.

5 Conclusion

The growing demand of ^99mTc and the inherent problem associated with ⁹⁹Mo production from fission products has increased the interest for economically feasible alternative sources of ⁹⁹Mo. Production of ⁹⁹Mo via the neutron capture method can be a feasible alternative to fission derived ⁹⁹Mo but the significant lower Curie yield and lower specific activity is of great concern. Therefore, use of lower specific activity molybdate is only feasible with a more efficient absorbent to reduce the generator size. Several highly efficient adsorbents for molybdenum have been reported in the literature with some success. In addition, several technetium selective resins are also reported for their use in purification and concentration of ^99mTc. Therefore, it was envisaged that ^99mTc with high specific activity can be obtained by adding a concentrator column unit in a chromatographic ⁹⁹Mo/^99mTc (n,γ) generator system.

Appendices

Appendix A: Fission Production Derivation

Molybdenum-99 (⁹⁹Mo) is generally produced through the thermal fission of highly enriched uranium (HEU). The amount of ⁹⁹Mo produced from this reaction is dependent on the thermal neutron flux, the amount of ²³⁵U present in the system, and the time exposed. Since the amount of ⁹⁸Mo present in the system is continuously changing, it is first necessary to establish the ²³⁵U population with respect to time. Since ²³⁵U is long lived (half-life of seven billion years) and is not being produced by other reactions, loss due to decay is neglected so the change in its population is due entirely to thermal neutron interactions. Therefore, the amount of ²³⁵U present in the system at time, t, is determined through integration of

$$\frac{{dN_{U - 235} }}{dt} = - \varphi \left( {\sigma_{U - 235,a} + \sigma_{U - 235,f} } \right)N_{U - 235}$$

(16)

where $\varphi$ is the neutron flux, $\sigma_{U - 235,a}$ and $\sigma_{U - 235,f}$ are the thermal neutron absorption and fission cross sections, respectively, and $N_{U - 235}$ is the number of ²³⁵U nuclei present in the system at time t. Note that it is assumed that the neutron cross sections and flux are constant with respect to time. Both sides of Eq. (1) are divided by $N_{U - 235}$ to separate the variables and yield

$$\int {\frac{{dN_{U - 235} }}{{N_{U - 235} }}} = - \int {\varphi \left( {\sigma_{U - 235,a} + \sigma_{U - 235,f} } \right)dt}$$

(17)

Both sides of Eq. (2) may now be integrated so that

$$\ln \left( {N_{U - 235} } \right) = - \varphi \left( {\sigma_{U - 235,a} + \sigma_{U - 235,f} } \right)t + C$$

(18)

where C is a constant of integration. The imposed initial condition is

$$N_{U - 235} \left( {t = 0} \right) = N_{U - 235,0}$$

(19)

where $N_{U - 235,0}$ is the number of ²³⁵U atoms present prior to exposure to the neutron field. The initial condition is used to determine the constant of integration

$$C = \ln \left( {N_{U - 235,0} } \right)$$

(20)

which is then substituted back into Eq. (3) to yield

$$\ln \left( {N_{U - 235} } \right) - \ln \left( {N_{U - 235,0} } \right) = - \varphi \left( {\sigma_{U - 235,a} + \sigma_{U - 235,f} } \right)t$$

(21)

Finally, Eq. (21) is rearranged and the natural log terms removed with exponentials to express the number of ²³⁵U atoms present at time, t

$$N_{U - 235} = N_{U - 235,0} e^{{ - \varphi \left( {\sigma_{U - 235,a} + \sigma_{U - 235,f} } \right)t}}$$

(22)

Now that the amount of target material is known, it is necessary to develop an expression for the amount of ⁹⁹Mo present in the system at time, t. Molybdenum-99 is produced by approximately six percent of all thermal fissions of Uranium and can be lost through radioactive decay or further neutron capture. The amount of ⁹⁹Mo present in the system at time, t, is determined through integration of

$$\frac{{dN_{Mo - 99} }}{dt} = \varphi \sigma_{U - 235,f} \gamma_{Mo - 99} N_{U - 235} - \lambda_{Mo - 99} N_{Mo - 99} - \varphi \sigma_{Mo - 99} N_{Mo - 99}$$

(23)

where $N_{Mo - 99}$ is the number of ⁹⁹Mo atoms present with respect to time, $\sigma_{Mo - 99}$ is the thermal neutron absorption cross section, $\gamma_{Mo - 99}$ is the probability of ⁹⁹Mo production through fission, and $\lambda_{Mo - 99}$ is the decay constant which is calculated using ⁹⁹Mo’s half-life as

$$\lambda_{Mo - 99} = \frac{\ln \left( 2 \right)}{{t_{\frac{1}{2}} }} = \frac{0.693}{{66\,hours}} = 0.0105\,hours^{ - 1}$$

(24)

The terms corresponding to the ⁹⁹Mo population are moved to the left side of Eq. (23) while Eq. (22) is substituted into the right side so that

$$\frac{{dN_{Mo - 99} }}{dt} + \left( {\lambda_{Mo - 99} + \varphi \sigma_{Mo - 99} } \right)N_{Mo - 99} = \varphi \sigma_{U - 235,f} \gamma_{Mo - 99} N_{U - 235,0} e^{{ - \varphi \left( {\sigma_{U - 235,a} + \sigma_{U - 235,f} } \right)t}}$$

(25)

The integral can be further simplified by defining a dummy variable

$$k = \lambda_{Mo - 99} + \varphi \sigma_{Mo - 99}$$

(26)

and multiplying both sides of Eq. (25) by the integrating factor

$$IF = e^{kt}$$

(27)

so that Eq. (25) reduces to

$$\frac{{dN_{Mo - 99} }}{dt}e^{kt} + kN_{Mo - 99} e^{kt} = \varphi \sigma_{U - 235,f} \gamma_{Mo - 99} N_{U - 235,0} e^{{\left( {k - \varphi \left( {\sigma_{U - 235,a} + \sigma_{U - 235,f} } \right)} \right)t}}$$

(28)

and then further reduces to

$$\int {d\left( {N_{Mo - 99} e^{kt} } \right)} = \int {\varphi \sigma_{U - 235,f} \gamma_{Mo - 99} N_{U - 235,0} e^{{\left( {k - \varphi \left( {\sigma_{U - 235,a} + \sigma_{U - 235,f} } \right)} \right)t}} } dt$$

(29)

Both sides of Eq. (29) may now be integrated so that

$$N_{Mo - 99} e^{kt} = \frac{{\varphi \sigma_{U - 235,f} \gamma_{Mo - 99} N_{U - 235,0} }}{{k - \varphi \left( {\sigma_{U - 235,a} + \sigma_{U - 235,f} } \right)}}e^{{\left( {k - \varphi \left( {\sigma_{U - 235,a} + \sigma_{U - 235,f} } \right)} \right)t}} + C$$

(30)

Since the ⁹⁹Mo is created entirely from the six percent of ²³⁵U fissions, it can be assumed that there is none present at the beginning of irradiation so that

$$N_{Mo - 99} \left( {t = 0} \right) = 0$$

(31)

which can be used in conjunction with Eq. (30) to determine the constant of integration

$$C = - \frac{{\varphi \sigma_{U - 235,f} \gamma_{Mo - 99} N_{U - 235,0} }}{{k - \varphi \left( {\sigma_{U - 235,a} + \sigma_{U - 235,f} } \right)}}$$

(32)

and can be substituted back into Eq. (30) to yield

$$N_{Mo - 99} e^{kt} = \frac{{\varphi \sigma_{U - 235,f} \gamma_{Mo - 99} N_{U - 235,0} }}{{k - \varphi \left( {\sigma_{U - 235,a} + \sigma_{U - 235,f} } \right)}}\left[ {e^{{\left( {k - \varphi \left( {\sigma_{U - 235,a} + \sigma_{U - 235,f} } \right)} \right)t}} - 1} \right]$$

(33)

Equation (33) can now be expanded by dividing both sides by the integrating factor

$$N_{Mo - 99} = \frac{{\varphi \sigma_{U - 235,f} \gamma_{Mo - 99} N_{U - 235,0} }}{{k - \varphi \left( {\sigma_{U - 235,a} + \sigma_{U - 235,f} } \right)}}\left[ {e^{{ - \varphi \left( {\sigma_{U - 235,a} + \sigma_{U - 235,f} } \right)t}} - e^{ - kt} } \right]$$

(34)

and the final answer can be obtained by combining Eqs. (34) and (26)

$$N_{Mo - 99} = \frac{{\varphi \sigma_{U - 235,f} \gamma_{Mo - 99} N_{U - 235,0} }}{{\lambda_{Mo - 99} + \varphi \left( {\sigma_{Mo - 99} - \sigma_{U - 235,a} - \sigma_{U - 235,f} } \right)}}\left[ {e^{{ - \varphi \left( {\sigma_{U - 235,a} + \sigma_{U - 235,f} } \right)t}} - e^{{ - \left( {\lambda_{Mo - 99} + \varphi \sigma_{Mo - 99} } \right)t}} } \right]$$

(35)

Note that Eq. (35) can be simplified to

$$N_{Mo - 99} = \frac{{\varphi \sigma_{U - 235,f} \gamma_{Mo - 99} N_{U - 235,0} }}{{\lambda_{Mo - 99} }}\left[ {1 - e^{{ - \lambda_{Mo - 99} t}} } \right]$$

(36)

by neglecting secondary absorptions.

Appendix B: Neutron Capture Production Derivation

Molybdenum-99 (⁹⁹Mo) can also be produced via neutron capture in which a ⁹⁸Mo target is bombarded with a neutron flux for a given time. As with the thermal fission case, the amount of ⁹⁹Mo produced from this reaction is dependent on the thermal neutron flux, the amount of ⁹⁸Mo present in the system, and the irradiation time. Since some amount of ⁹⁸Mo will be consumed by the reaction, it is first necessary to establish the variable ⁹⁸Mo population. Since ⁹⁸Mo is stable and is not being produced by other reactions, the change in its population is due entirely to thermal neutron capture. Therefore, the amount of ⁹⁸Mo present in the system at time, t, is determined through integration of

$$\frac{{dN_{Mo - 98} }}{dt} = - \varphi \sigma_{Mo - 98} N_{Mo - 98}$$

(37)

where $\varphi$ is the neutron flux, $\sigma_{Mo - 98}$ is the thermal neutron absorption cross section for ⁹⁸Mo, and $N_{Mo - 98}$ is the number of ⁹⁸Mo nuclei present in the system at time t. Both sides of Eq. (37) are divided by $N_{Mo - 98}$ to separate the variables and yield

$$\int {\frac{{dN_{Mo - 98} }}{{N_{Mo - 98} }}} = - \int {\varphi \sigma_{Mo - 98} dt}$$

(38)

Both sides of Eq. (38) may now be integrated so that

$$\ln \left( {N_{Mo - 98} } \right) = - \varphi \sigma_{Mo - 98} t + C$$

(39)

where C is a constant of integration. The imposed initial condition is

$$N_{Mo - 98} \left( {t = 0} \right) = N_{Mo - 98,0}$$

(40)

where $N_{Mo - 98,0}$ is the number of ⁹⁸Mo atoms present prior to exposure to the neutron field. The initial condition is used to determine the constant of integration

$$C = \ln \left( {N_{Mo - 98,0} } \right)$$

(41)

which is then substituted back into Eq. (39) to yield

$$\ln \left( {N_{Mo - 98} } \right) - \ln \left( {N_{Mo - 98,0} } \right) = - \varphi \sigma_{Mo - 98} t$$

(42)

Finally, Eq. (42) is rearranged and the natural log terms removed with exponentials to express the number of ⁹⁸Mo atoms present at time, t

$$N_{Mo - 98} = N_{Mo - 98,0} e^{{ - \varphi \sigma_{Mo - 98} t}}$$

(43)

Now that the amount of target material is known, it is necessary to develop an expression for the amount of ⁹⁹Mo present in the system at time, t. Molybdenum-99 is produced only through the neutron capture of ⁹⁸Mo and can be lost through radioactive decay or further neutron capture. The amount of ⁹⁹Mo present in the system at time, t, is determined through integration of

$$\frac{{dN_{Mo - 99} }}{dt} = \varphi \sigma_{Mo - 98} N_{Mo - 98} - \lambda_{Mo - 99} N_{Mo - 99} - \varphi \sigma_{Mo - 99} N_{Mo - 99}$$

(44)

where $N_{Mo - 99}$ is the number of ⁹⁹Mo atoms present with respect to time and $\sigma_{Mo - 99}$ is the thermal neutron absorption cross section. The terms corresponding to the ⁹⁹Mo population are moved to the left side of Eq. (44) while Eq. (43) is substituted into the right side so that

$$\frac{{dN_{Mo - 99} }}{dt} + \left( {\lambda_{Mo - 99} + \varphi \sigma_{Mo - 99} } \right)N_{Mo - 99} = \varphi \sigma_{Mo - 98} N_{Mo - 98,0} e^{{ - \varphi \sigma_{Mo - 98} t}}$$

(45)

The integral can be further simplified by using the dummy variable defined in Eq. (26) and integrating factor in Eq. (27) so that Eq. (45) reduces to

$$\frac{{dN_{Mo - 99} }}{dt}e^{kt} + kN_{Mo - 99} e^{kt} = \varphi \sigma_{Mo - 98} N_{Mo - 98,0} e^{{\left( {k - \varphi \sigma_{Mo - 98} } \right)t}}$$

(46)

and then further reduces to

$$\int {d\left( {N_{Mo - 99} e^{kt} } \right)} = \int {\varphi \sigma_{Mo - 98} N_{Mo - 98,0} e^{{\left( {k - \varphi \sigma_{Mo - 98} } \right)t}} } dt$$

(47)

Both sides of Eq. (47) may now be integrated so that

$$N_{Mo - 99} e^{kt} = \frac{{\varphi \sigma_{Mo - 98} N_{Mo - 98,0} }}{{k - \varphi \sigma_{Mo - 98} }}e^{{\left( {k - \varphi \sigma_{Mo - 98} } \right)t}} + C$$

(48)

Since the ⁹⁹Mo is created entirely from the ⁹⁸Mo being consumed in the neutron field, it can be assumed that there is none present at the beginning of irradiation so that

$$N_{Mo - 99} \left( {t = 0} \right) = 0$$

(49)

which can be used in conjunction with Eq. (48) to determine the constant of integration

$$C = - \frac{{\varphi \sigma_{Mo - 98} N_{Mo - 98,0} }}{{k - \varphi \sigma_{Mo - 98} }}$$

(50)

and can be substituted back into Eq. (48) to yield

$$N_{Mo - 99} e^{kt} = \frac{{\varphi \sigma_{Mo - 98} N_{Mo - 98,0} }}{{k - \varphi \sigma_{Mo - 98} }}\left[ {e^{{\left( {k - \varphi \sigma_{Mo - 98} } \right)t}} - 1} \right]$$

(51)

Equation (51) can now be expanded by dividing both sides by the integrating factor

$$N_{Mo - 99} = \frac{{\varphi \sigma_{Mo - 98} N_{Mo - 98,0} }}{{k - \varphi \sigma_{Mo - 98} }}\left[ {e^{{ - \varphi \sigma_{Mo - 98} t}} - e^{ - kt} } \right]$$

(52)

and the final answer can be obtained by combining Eqs. (52) and (26)

$$N_{Mo - 99} = \frac{{\varphi \sigma_{Mo - 98} N_{Mo - 98,0} }}{{\lambda_{Mo - 99} + \varphi \left( {\sigma_{Mo - 99} - \sigma_{Mo - 98} } \right)}}\left[ {e^{{ - \varphi \sigma_{Mo - 98} t}} - e^{{ - \left( {\lambda_{Mo - 99} + \varphi \sigma_{Mo - 99} } \right)t}} } \right]$$

(53)

As with Eq. (35), Eq. (53) can be simplified to

$$N_{Mo - 99} = \frac{{\varphi \sigma_{Mo - 98} N_{Mo - 98,0} }}{{\lambda_{Mo - 99} }}\left[ {1 - e^{{ - \lambda_{Mo - 99} t}} } \right]$$

(54)

if secondary absorptions are neglected.

Appendix C: Radioactive decay derivation

Once the ⁹⁹Mo has been removed from the reactor, it can only be lost through radioactive decay so that

$$\frac{{dN_{Mo - 99} }}{dt} = - \lambda_{Mo - 99} N_{Mo - 99}$$

(55)

where $N_{Mo - 99}$ is the number of ⁹⁹Mo atoms present with respect to time and $\lambda_{Mo - 99}$ is the decay constant which is calculated using ⁹⁹Mo’s half-life as

$$\lambda_{Mo - 99} = \frac{\ln \left( 2 \right)}{{t_{\frac{1}{2}} }} = \frac{0.693}{{66\,hours}} = 0.0105\,hours^{ - 1}$$

(56)

Both sides of Eq. (55) are divided by $N_{Mo - 99}$ to separate the variables and yield

$$\int {\frac{{dN_{Mo - 99} }}{{N_{Mo - 99} }}} = - \int {\lambda_{Mo - 99} dt}$$

(57)

Both sides of Eq. (57) may now be integrated so that

$$\ln \left( {N_{Mo - 99} } \right) = - \lambda_{Mo - 99} t + C$$

(58)

where C is a constant of integration. The imposed initial condition is

$$N_{Mo - 99} \left( {t = 0} \right) = N_{Mo - 99,0}$$

(59)

where $N_{Mo - 99,0}$ is the number of ⁹⁹Mo atoms present after the sample is removed from the neutron source. The initial condition is used to determine the constant of integration

$$C = \ln \left( {N_{Mo - 99,0} } \right)$$

(60)

which is then substituted back into Eq. (58) to yield

$$\ln \left( {N_{Mo - 99} } \right) - \ln \left( {N_{Mo - 99,0} } \right) = - \lambda_{Mo - 99} t$$

(61)

Finally, Eq. (61) is rearranged and the natural log terms removed with exponentials to express the number of ⁹⁹Mo atoms present at time, t

$$N_{Mo - 99} = N_{Mo - 99,0} e^{{ - \lambda_{Mo - 99} t}}$$

(62)

Since the purpose of creating the ⁹⁹Mo is to obtain a continually replenished supply of ^99mTc, it is necessary to determine the amount of ^99mTc present in the system with respect to time. Technetium-99 m is produced solely from the decay of ⁹⁹Mo and is lost through gamma decay to ⁹⁹Tc with a six hour half-life. Therefore, the amount of ^99mTc present in the system at time, t, is determined through integration of

$$\frac{{dN_{Tc - 99m} }}{dt} = \lambda_{Mo - 99} N_{Mo - 99} - \lambda_{Tc - 99m} N_{Tc - 99m}$$

(63)

where $N_{Tc - 99m}$ is the number of ^99mTc atoms present with respect to time and $\lambda_{Tc - 99m}$ is the decay constant which is calculated using ^99mTc’s half-life as

$$\lambda_{Mo - 99} = \frac{\ln \left( 2 \right)}{{t_{\frac{1}{2}} }} = \frac{0.693}{{6\,hours}} = 0.1155\,hours^{ - 1}$$

(64)

The terms corresponding to the ^99mTc population are moved to the left side of Eq. (62) while Eq. (61) is substituted into the right side so that

$$\frac{{dN_{Tc - 99m} }}{dt} + \lambda_{Tc - 99m} N_{Tc - 99m} = \lambda_{Mo - 99} N_{Mo - 99} = \lambda_{Mo - 99} N_{Mo - 99,0} e^{{ - \lambda_{Mo - 99} t}}$$

(65)

an integrating factor may be used to simplify the differential equation

$$IF = e^{{\lambda_{Tc - 99m} t}}$$

(66)

so that Eq. (64) reduces to

$$\frac{{dN_{Tc - 99m} }}{dt}e^{{\lambda_{Tc - 99m} t}} + \lambda_{Tc - 99m} N_{Tc - 99m} e^{{\lambda_{Tc - 99m} t}} = \lambda_{Mo - 99} N_{Mo - 99,0} e^{{\left( {\lambda_{Tc - 99m} - \lambda_{Mo - 99} } \right)t}}$$

(67)

and then further reduces to

$$\int {} d\left( {N_{Tc - 99m} e^{{\lambda_{Tc - 99m} t}} } \right) = \int {\lambda_{Mo - 99} N_{Mo - 99,0} e^{{\left( {\lambda_{Tc - 99m} - \lambda_{Mo - 99} } \right)t}} } dt$$

(68)

Both sides of Eq. (68) may now be integrated so that

$$N_{Tc - 99m} e^{{\lambda_{Tc - 99m} t}} = \frac{{\lambda_{Mo - 99} }}{{\lambda_{Tc - 99m} - \lambda_{Mo - 99} }}N_{Mo - 99,0} e^{{\left( {\lambda_{Tc - 99m} - \lambda_{Mo - 99} } \right)t}} + C$$

(69)

Although ^99mTc accumulates during the irradiation period, it is assumed that all traces are removed from the ⁹⁹Mo source prior to creation of the generator. Therefore, it is assumed that there is no ^99mTc present initially so that

$$N_{Tc - 99m} \left( {t = 0} \right) = 0$$

(70)

which can be used in conjunction with Eq. (69) to determine the constant of integration

$$C = - \frac{{\lambda_{Mo - 99} }}{{\lambda_{Tc - 99m} - \lambda_{Mo - 99} }}N_{Mo - 99,0} e^{{\left( {\lambda_{Tc - 99m} - \lambda_{Mo - 99} } \right)t}}$$

(71)

and can be substituted back into Eq. (69) to yield

$$N_{Tc - 99m} e^{{\lambda_{Tc - 99m} t}} = \frac{{\lambda_{Mo - 99} }}{{\lambda_{Tc - 99m} - \lambda_{Mo - 99} }}N_{Mo - 99,0} \left[ {e^{{\left( {\lambda_{Tc - 99m} - \lambda_{Mo - 99} } \right)t}} - 1} \right]$$

(72)

The final answer can be obtained by removing the integrating factor from the both sides

$$N_{Tc - 99m} = \frac{{\lambda_{Mo - 99} }}{{\lambda_{Tc - 99m} - \lambda_{Mo - 99} }}N_{Mo - 99,0} \left[ {e^{{\lambda_{Mo - 99} t}} - e^{{\lambda_{Tc - 99m} t}} } \right]$$

(73)

The ⁹⁹Mo /^99mTc generator is eluted with saline to remove the ^99mTc for use in diagnostic and treatment facilities. Due to the nature of this type of decay, there is a optimum time required between elution so that the maximum amount of ^99mTc is acquired. To determine the time at which the maximum amount of ^99mTc is present in the system, it is necessary to take the derivative of Eq. (73) with respect to time so that

$$\frac{{dN_{Tc - 99m} }}{dt} = \left( {\frac{{\lambda_{Mo - 99} }}{{\lambda_{Tc - 99m} - \lambda_{Mo - 99} }}} \right)N_{Mo - 99,0} \left[ {\lambda_{Tc - 99m} e^{{ - \lambda_{Tc - 99m} t}} - \lambda_{Mo - 99} e^{{ - \lambda_{Mo - 99} t}} } \right]$$

(74)

Setting the right side of Eq. (74) equal to zero and solving for time

$$0 = \left( {\frac{{\lambda_{Mo - 99} }}{{\lambda_{Tc - 99m} - \lambda_{Mo - 99} }}} \right)N_{Mo - 99,0} \left[ {\lambda_{Tc - 99m} e^{{ - \lambda_{Tc - 99m} t_{\max } }} - \lambda_{Mo - 99} e^{{ - \lambda_{Mo - 99} t_{\max } }} } \right]$$

(75)

$$\lambda_{Mo - 99} e^{{ - \lambda_{Mo - 99} t_{\max } }} = \lambda_{Tc - 99m} e^{{ - \lambda_{Tc - 99m} t_{\max } }}$$

(76)

$$\ln \left( {\frac{{\lambda_{Mo - 99} }}{{\lambda_{Tc - 99m} }}} \right) = \ln \left( {\frac{{e^{{ - \lambda_{Tc - 99m} t_{\max } }} }}{{e^{{ - \lambda_{Mo - 99} t_{\max } }} }}} \right) = \left( {\lambda_{Mo - 99} - \lambda_{Tc - 99m} } \right)t_{\max }$$

(77)

$$t_{\max } = \left| {\frac{{\ln \left( {\frac{{\lambda_{Mo - 99} }}{{\lambda_{Tc - 99m} }}} \right)}}{{\left( {\lambda_{Mo - 99} - \lambda_{Tc - 99m} } \right)}}} \right|$$

(78)

So, the maximum amount of ^99mTc will accumulate every

$$t_{\max } = \frac{{\ln \left( {\frac{{0.0105\,hour^{ - 1} }}{{0.1155\,hour^{ - 1} }}} \right)}}{{\left( {0.0105\,hour^{ - 1} - 0.1155\,hour^{ - 1} } \right)}} = 22.8371\,hours$$

(79)

So that elution should occur every 22.8371 h to obtain the maximum amount of ^99mTc from the generator.