4.1.1. Daughter Nuclide Build-up Optimisation and New Characteristic Parameter of Formation-Decay Kinetics of Parent/Daughter Nuclide System (Referred to Section 2.1.1 and Section 2.1.2)
The results of optimisation assessment for 50 parent/daughter nuclide pairs of different half-lives are reported in
Table 1 and in
Figure 9,
Figure 10 and
Figure 11. The diagrams of the build-up time ratio (
topt(t)/
tmax) and daughter nuclide activity ratio (
A2,opt(t)/
A2,max) plotted against decay constant ratio (
λ2/
λ1), which are based on the results of the optimisation of the daughter nuclide activity build-up
versus build-up time reported in
Table 1, are shown in
Figure 9. The plots show defined characteristics of daughter nuclide build-up kinetics in relation with the decay constant ratio (
λ2/
λ1) of parent/daughter nuclide systems. The diagram in
Figure 9 reveals a maximum value (
topt(t)/
tmax) = 0.5 at the ratio value (
λ2/
λ1) = 1 and a variation in the (
topt(t)/
tmax) values from 0.05 to 0.5 for the whole range of different parent/daughter nuclide pairs. Accordingly, a maximum value (
A2,opt(t)/
A2,max) = 0.823 at the ratio value (
λ2/
λ1) = 1 and a variation in the (
A2,opt(t)/
A2,max) values from 0.714 to 0.823 for the whole range of different parent/daughter nuclide pairs are presented. Both diagrams in
Figure 9 show a beautiful symmetric shape irrespective of the daughter nuclide living longer or shorter than its parent.
This characteristics means that the value (topt(t)/tmax) and accordingly the value (A2,opt(t)/A2,max) only depend on the decay constant ratio (λ2/λ1) of parent/daughter nuclide systems, but not on any other specified parameter of the parent or its daughter nuclide. This statement is clearly justified by Equation (11) and thus the value topt(t) is proved as a characteristic physical parameter of the formation-decay process kinetics of given parent/daughter nuclide pair system.
Table 1.
Optimal build-up time and radioactivity of daughter nuclide in different radionuclide generator systems:
tmax,
topt(t), and
topt(SA) values are calculated using Equations (2), (11) and (14), respectively.
A2,max,
A2,opt(t), and
A2,opt(SA) are the daughter nuclide activities at the build-up time
tmax,
topt(t), and
topt(SA), respectively, which are calculated using Equation (1) and relevant build-up time values. The half-life time data are from References [
19,
20].
Table 1.
Optimal build-up time and radioactivity of daughter nuclide in different radionuclide generator systems: tmax, topt(t), and topt(SA) values are calculated using Equations (2), (11) and (14), respectively. A2,max, A2,opt(t), and A2,opt(SA) are the daughter nuclide activities at the build-up time tmax, topt(t), and topt(SA), respectively, which are calculated using Equation (1) and relevant build-up time values. The half-life time data are from References [19,20].
Radioisotope
Parent R1-Daughter R2 | Half life | λ2/λ1 | tmax | topt(t) | (topt(t)/tmax) | (A2,opt(t)/A2,max) | topt(SA) | (topt(SA)/tmax) | (A2,opt(SA)/A2,max) |
---|
Parent Nuclide
T1 | Daughter Nuclide
T2 |
---|
99mTc–99Tc | 6.02 h | 214000 y | 3.21 × 10−9 | 170.09 | 10.91 | 0.064 | 0.714 | - | - | - |
93mMo–93Mo | 6.9 h | 3500 y | 2.25 × 10−7 | 152.14 | 12.51 | 0.082 | 0.715 | - | - | - |
83mSr–83Sr | 5.0 s | 1.35 d | 4.27 × 10−5 | 0.0201 | 0.0025 | 0.125 | 0.715 | - | - | - |
131Te–131I | 25 min | 192.96 h | 2.16 × 10−3 | 3.6984 | 0.75 | 0.203 | 0.721 | 3.29 | 0.889 | 0.999 |
82mBr–82Br | 6.13 min | 35.3 h | 2.90 × 10−3 | 0.8641 | 0.184 | 0.219 | 0.723 | - | - | - |
67Ge–67Ga | 18.7 min | 78.26 h | 3.98 × 10−3 | 2.4955 | 0.56 | 0.224 | 0.725 | 2.19 | 0.877 | 0.998 |
57Ni–57Co | 36.16 h | 270.9 d | 5.56 × 10−3 | 272.10 | 64.73 | 0.238 | 0.729 | 237.5 | 0.872 | 0.998 |
125Xe–125I | 17 h | 59.89 d | 1.18 × 10−2 | 110.13 | 30 | 0.272 | 0.737 | 94 | 0.853 | 0.996 |
149Nd–149Pm | 1.73 h | 53.08 h | 3.26 × 10−2 | 8.8358 | 2.92 | 0.330 | 0.756 | 7.28 | 0.823 | 0.992 |
95Ru–95Tc | 1.63 h | 20 h | 8.15 × 10−2 | 6.4218 | 2.52 | 0.392 | 0.780 | 5.05 | 0.786 | 0.982 |
131mTe–131I | 30 h | 8.04 d | 1.55 × 10−1 | 95.425 | 41.52 | 0.435 | 0.797 | 72.65 | 0.761 | 0.973 |
123Xe–123I | 2.08 h | 13.3 h | 1.56 × 10−1 | 6.6033 | 2.87 | 0.435 | 0.797 | 5.02 | 0.760 | 0.973 |
52Ti–52V | 1.7 min | 3.76 min | 4.52 × 10−1 | 0.0592 | 0.029 | 0.489 | 0.821 | 0.042 | 0.709 | 0.950 |
131Ba–131Cs | 11.8 d | 9.69 d | 1.22 | 369.75 | 184.5 | 0.499 | 0.823 | 232.1 | 0.627 | 0.911 |
47Ca–47Sc | 4.536 d | 3.351 d | 1.35 | 134.63 | 67 | 0.498 | 0.823 | 83.25 | 0.618 | 0.906 |
95Zr–95Nb | 64.05 d | 34.98 d | 1.83 | 1613.3 | 795.1 | 0.493 | 0.821 | 957.2 | 0.593 | 0.893 |
38S–38Cl | 169.7 min | 37.24 min | 4.56 | 1.7401 | 0.79 | 0.454 | 0.804 | 0.88 | 0.505 | 0.847 |
14°Ba–14°La | 12.74 d | 40.272 h | 7.59 | 135.65 | 57.61 | 0.425 | 0.793 | 62.16 | 0.458 | 0.823 |
72Se–72As | 8.4 d | 26 h | 7.76 | 88.231 | 37.3 | 0.423 | 0.792 | 40.2 | 0.455 | 0.821 |
99Mo–99mTc | 66.02 h | 6.007 h | 11.00 | 22.849 | 9.145 | 0.400 | 0.783 | 9.685 | 0.423 | 0.805 |
115Cd–115mIn | 53.46 h | 4.486 h | 11.90 | 17.460 | 6.9 | 0.395 | 0.781 | 7.3 | 0.418 | 0.803 |
97Zr–97Nb | 16.9 h | 72.1 min | 14.10 | 4.9339 | 1.89 | 0.383 | 0.776 | 1.98 | 0.401 | 0.794 |
8°mBr–8°Br | 4.42 h | 17.4 min | 15.20 | 1.2196 | 0.461 | 0.378 | 0.774 | - | - | - |
125Sb–125mTe | 2.77 y | 58 d | 17.40 | 6090.6 | 2245 | 0.368 | 0.771 | 2335 | 0.383 | 0.786 |
52Fe–52mMn | 8.3 h | 21.1 min | 23.60 | 1.6755 | 0.58 | 0.346 | 0.761 | 0.6 | 0.358 | 0.774 |
87Y–87mSr | 80.3 h | 2.8 h | 28.60 | 14.069 | 4.7 | 0.334 | 0.757 | 4.8 | 0.341 | 0.765 |
132Te–132I | 78.2 h | 2.3 h | 34.10 | 12.063 | 3.91 | 0.324 | 0.754 | 4 | 0.331 | 0.762 |
62Zn–62Cu | 9.2 h | 9.7 min | 56.90 | 0.9595 | 0.28 | 0.292 | 0.741 | 0.289 | 0.301 | 0.753 |
188W–188Re | 69.4 d | 16.98 h | 98.20 | 113.49 | 30.1 | 0.265 | 0.736 | 30.35 | 0.267 | 0.739 |
122Xe–122I | 20.1 h | 3.6 min | 3.35 × 102 | 0.5049 | 0.108 | 0.214 | 0.723 | 0.108 | 0.213 | 0.723 |
1°3Pd–1°3mRh | 16.96 d | 56.12 min | 4.37 × 102 | 8.2235 | 1.69 | 0.205 | 0.722 | 1.69 | 0.205 | 0.722 |
28Mg–28Al | 20.91 h | 2.24 min | 5.60 × 102 | 0.3415 | 0.067 | 0.196 | 0.718 | 0.067 | 0.196 | 0.718 |
128Ba–128Cs | 2.4 d | 3.6 min | 9.58 × 102 | 0.5950 | 0.109 | 0.183 | 0.720 | 0.109 | 0.183 | 0.720 |
1°3Ru–1°3mRh | 39.35 d | 56.12 min | 1.01 × 103 | 9.3456 | 1.692 | 0.181 | 0.718 | 1.692 | 0.181 | 0.718 |
1°9Pd–1°9mAg | 13.43 h | 39.8 s | 1.21 × 103 | 0.1133 | 0.02 | 0.176 | 0.718 | 0.02 | 0.176 | 0.718 |
81Rb–81mKr | 4.6 h | 13.1 s | 1.27 × 103 | 0.0375 | 0.0065 | 0.173 | 0.713 | 0.0065 | 0.173 | 0.713 |
113Sn–113mIn | 115.1 d | 1.7 h | 1.62 × 103 | 18.146 | 3.1 | 0.171 | 0.720 | 3.1 | 0.170 | 0.720 |
118Te–118Sb | 6 d | 3.5 min | 2.47 × 103 | 0.6577 | 0.106 | 0.161 | 0.718 | 0.106 | 0.161 | 0.718 |
178W–178Ta | 21.5 d | 9.3 min | 3.33 × 103 | 1.8148 | 0.28 | 0.155 | 0.715 | 0.28 | 0.154 | 0.715 |
9°Sr–9°Y | 28.82 y | 64 h | 3.95 × 103 | 763.72 | 116 | 0.152 | 0.717 | 116 | 0.151 | 0.717 |
195mHg–195mAu | 40 h | 30.6 s | 4.71 × 103 | 0.1037 | 0.0155 | 0.149 | 0.718 | 0.0155 | 0.149 | 0.718 |
68Ge–68Ga | 271 d | 68.3 min | 5.71 × 103 | 14.211 | 2.063 | 0.145 | 0.716 | 2.063 | 0.145 | 0.716 |
42Ar–42K | 32.9 y | 12.36 h | 2.34 × 104 | 179.43 | 22.4 | 0.125 | 0.715 | 22.4 | 0.124 | 0.715 |
144Ce–144Pr | 284.9 d | 17.28 min | 2.37 × 104 | 4.1869 | 0.522 | 0.125 | 0.715 | 0.522 | 0.124 | 0.715 |
82Sr–82Rb | 25 d | 1.3 min | 2.77 × 104 | 0.3198 | 0.039 | 0.122 | 0.712 | 0.039 | 0.121 | 0.712 |
44Ti–44Sc | 48.2 y | 3.9 h | 1.09 × 105 | 65.068 | 7.07 | 0.109 | 0.716 | 7.07 | 0.108 | 0.716 |
191Os–191mIr | 15.4 d | 4.96 s | 2.68 × 105 | 0.0248 | 0.0025 | 0.101 | 0.715 | 0.0025 | 0.100 | 0.715 |
1°9Cd–1°9mAg | 453 d | 39.8 s | 9.82 × 105 | 0.2201 | 0.02 | 0.091 | 0.714 | 0.02 | 0.090 | 0.714 |
137Cs–137mBa | 30.14 y | 2.552 min | 6.20 × 106 | 0.9599 | 0.077 | 0.080 | 0.714 | 0.077 | 0.080 | 0.714 |
The rule controlled in the relationship between the (topt(t)/tmax) and (λ2/λ1) values described in Equation (11) is independent on the fact that the daughter nuclide lives longer or shorter than its parent and that how long they live. In other words, this rule is the following:
The shorter or longer the daughter nuclide lives compared with the lifetime of its parent, the shorter is the optimal build-up time topt(t) of daughter nuclide compared with its maximal build-up time tmax. The value of ratio (topt(t)/tmax) is 0.5 for any parent/daughter nuclide pair of equal lifetime. The value of ratio (topt(t)/tmax) is 0.05 for any parent/daughter nuclide pair of a lifetime difference of >3 × 108 times.
Accordingly, the shorter or longer the daughter nuclide lives compared with the lifetime of its parent, the smaller is the build-up activity achieved at the time topt(t) of daughter nuclide compared with its maximal build-up activity at the time tmax .The value of ratio (A2,opt(t)/A2,max) is 0.823 for any parent/daughter nuclide pair of equal lifetime. The value of ratio (A2,opt(t)/A2,max) is 0.70 for any parent/daughter nuclide pair of a lifetime difference of >3 × 108 times.
Figure 9.
Optimal build-up time value topt(t) and radioactivity value A2,opt(t) of daughter nuclides compared with values tmax and A2,max, respectively, in function of decay constant ratio (λ2/λ1): (a) Ratio (topt(t)/tmax); (b) Ratio (A2,opt(t)/A2,max); T1 and T2 are the half-life times of the parent and daughter nuclides, respectively.
Figure 9.
Optimal build-up time value topt(t) and radioactivity value A2,opt(t) of daughter nuclides compared with values tmax and A2,max, respectively, in function of decay constant ratio (λ2/λ1): (a) Ratio (topt(t)/tmax); (b) Ratio (A2,opt(t)/A2,max); T1 and T2 are the half-life times of the parent and daughter nuclides, respectively.
Figure 10.
Optimal build-up time topt(SA) and radioactivity A2,opt(SA) of daughter nuclides compared with tmax and A2,max values, respectively, in function of decay constant ratio (λ2/λ1): (a) Ratio (topt(SA)/tmax); (b) Ratio (A2,opt(SA)/A2,max); T1 and T2 are the half-life times of the parent and daughter nuclides, respectively.
Figure 10.
Optimal build-up time topt(SA) and radioactivity A2,opt(SA) of daughter nuclides compared with tmax and A2,max values, respectively, in function of decay constant ratio (λ2/λ1): (a) Ratio (topt(SA)/tmax); (b) Ratio (A2,opt(SA)/A2,max); T1 and T2 are the half-life times of the parent and daughter nuclides, respectively.
Figure 11.
Ratio of optimal build-up times (topt(t)/topt(SA)) and Ratio of optimal build-up radioactivity (A2,opt(t)/A2,opt(SA)) of daughter nuclides in function of decay constant ratio (λ2/λ1): (a) Ratio (topt(t)/topt(SA)); (b) Ratio (A2,opt(t)/A2,opt(SA)); T1 and T2 are the half-life times of the parent and daughter nuclides, respectively.
Figure 11.
Ratio of optimal build-up times (topt(t)/topt(SA)) and Ratio of optimal build-up radioactivity (A2,opt(t)/A2,opt(SA)) of daughter nuclides in function of decay constant ratio (λ2/λ1): (a) Ratio (topt(t)/topt(SA)); (b) Ratio (A2,opt(t)/A2,opt(SA)); T1 and T2 are the half-life times of the parent and daughter nuclides, respectively.
It is found that at the optimal build-up time topt(t) the daughter nuclide activity varies in the range from 71.4% to 82.23% of the maximal build-up activity at the maximal time tmax, whereas the optimal build-up time topt(t) changes only from 5% to 50%. This fact leads to a useful application in the cost-effective operation of radionuclide generators that all generator elutions could be performed at the optimal build-up time topt(t) instead of being performed at the maximal time tmax. The elutions performed at optimal build-up time topt(t) result in a significant saving in the standby time of the generator, thus economic use of the generator. The following examples will clarify the effectiveness of the elution plan performed at the optimal build-up time topt(t).
First example for the case of the parent and daughter nuclides of moderate difference in their half lives: The maximal build-up time of
99mTc nuclide in
99Mo
/99mTc generator system is
tmax = 22.86 h. The
99mTc radioactivity build-up for the elution performed at optimal build-up time
topt(t) = 9.145 h is 78.3% of the maximal build-up at the time
tmax = 22.86 h. This fact dictates that the elution performed at optimal build-up time
topt(t) saves 13.715 h or 60% of standby time of the generator whereas the optimal
99mTc-activity build-up loses only 21.7% compared with the elution performed at the time
tmax. Despite the 21.7% loss in each elution performed at the optimal time
topt(t), the total yields of consecutive elutions performed at optimal 9.145-h build-up time will be 1.75 times higher than the yield of one elution performed at the time
tmax as evaluated by the method of early elution schedule described in
Section 2.1.3 (Results shown in
Figure 12).
Second example for the case of the parent and daughter nuclides of big difference in their half life: The maximal build-up time of
68Ga nuclide in
68Ge/
68Ga generator system is
tmax = 14.1 h. The
68Ga radioactivity build-up for the elution performed at optimal build-up time
topt(t) = 2.063 h is 71.6% of maximal build-up at the time
tmax = 14.1 h. This fact dictates that the elution performed at optimal build-up time
topt(t) saves 12.037 h or 85.5% of standby time of the generator, whereas the optimal
68Ga–build-up activity loses only 28.4% compared with the elution performed at the time
tmax. Despite the 28.4% loss in each elution performed at the optimal time
topt(t), the total yields of consecutive elutions performed at 2.063-h optimal build-up time will be 5.0 times higher than the yield of one elution performed at the time
tmax as evaluated by the method of early elution schedule described in
Section 2.1.3 (Results shown in
Figure 12). In conclusion, it is stated that the optimal build-up time
topt(t) defined by the mathematical equation:
is the second characteristic parameter of the kinetics of formation-decay process of the parent/daughter nuclide system, which has a defined physical meaning and can be effectively used in the optimal management of practical radionuclide generator operation . This parameter and the first one (the maximal build-up time
tmax = [ln(
λ2 /
λ1)] / (
λ2 −
λ1)) are equally significant to better understand the kinetics of the formation-decay process of parent/daughter nuclide systems and to be used in the practice of radionuclide generator production and application as well.
Figure 12.
Effectiveness of daughter nuclide activity utilisation of generators eluted with an early elution schedule compared with that normally eluted at the maximal time of daughter nuclide build-up (Data mark-points are experimental and dashed lines are theoretical calculation results): (a) 99mTc from 99Mo/99mTc generator; (b) 68Ga from 68Ge/68Ga generator.
Figure 12.
Effectiveness of daughter nuclide activity utilisation of generators eluted with an early elution schedule compared with that normally eluted at the maximal time of daughter nuclide build-up (Data mark-points are experimental and dashed lines are theoretical calculation results): (a) 99mTc from 99Mo/99mTc generator; (b) 68Ga from 68Ge/68Ga generator.
The diagrams of the build-up time ratio (
topt(SA)/
tmax) and build-up radioactivity ratio (
A2,opt(SA)/
A2,max) plotted against decay constant ratio (
λ2/
λ1), which are based on the results of the optimisation of daughter nuclide activity build-up
versus specific activity (or
versus total build-up daughter nuclide atom numbers per unit of daughter nuclide build-up activity) reported in
Table 1, are shown in
Figure 10. The plots show defined characteristics of daughter nuclide build-up kinetics in relation with the decay constant ratio (
λ2/
λ1) of parent/daughter nuclide systems. The diagrams reveals the upper limits of ratio (
topt(SA)/
tmax) ≈ 0.96 and ratio (
A2,opt(SA)/
A2,max) ≈ 1 at the ratio value (
λ2/
λ1) < 10
−9 and the lower limits of ratio (
topt(SA)/
tmax) ≈ 0.05 and ratio (
A2,opt(SA)/
A2,max) ≈ 0.714 at the ratio value (
λ2/
λ1) > 10
7. A variation in the (
topt(SA)/
tmax) values from 0.05 to 0.96 for the whole range of different parent/daughter nuclide pairs and the (
A2,opt(SA)/
A2,max) values from 0.714 to 1.0 have been noted accordingly. Both diagrams show no maximum and they are inflected at the (
λ2/
λ1) ratio value between (
λ2/
λ1) = 1 and (
λ2/
λ1) = 10. The values (
topt(SA)/
tmax) = 0.627 and (
A2,opt(SA)/
A2,max) = 0.911 are found at the ratio value (
λ2/
λ1) = 1. The rule controlled in the relationship between the (
topt(SA)/
tmax) values (and accordingly (
A2,opt(SA)/
A2,max) values) and (
λ2/
λ1) values described in Equation (14) is the following:
The shorter the daughter nuclide lives compared with the life time of its parent, the smaller is the optimal build-up time topt(SA) of daughter nuclide compared with its maximal build-up time tmax. Accordingly, the shorter the daughter nuclide lives compared with the life time of its parent, the smaller is the build-up activity achieved at the optimal time topt(SA) of daughter nuclide compared with its maximal build-up activity at the time tmax. The value of ratio (A2,opt(SA)/A2,max) is achievable in the range 0.714–1.0 for all parent/daughter nuclide pairs.
These results mean that the value (
topt(SA)/
tmax) and accordingly (
A2,opt(SA)/
A2,max) only depend on the decay constant ratio (
λ2/
λ1) of parent/daughter nuclide systems, but not on any other specified parameter of parent or its daughter nuclides, with an assumption of using the specific activity formulation which is based on the equality between the total atom numbers of all involved daughter nuclides and the atom numbers of decayed parent nuclides
N =
N1,0 × (1 −
e−λ1·t) as described in
Section 2.1 (the isomer transformations of parent nuclides to form daughter nuclides are excluded). Obviously, this assumption makes the optimal build-up time
topt(SA) become a non-characteristic parameter in a general meaning. However, it still plays an important role in the practical application in the production and use of radionuclide generators, because it is specifically characterised for a specified nuclear transformation process which generates a daughter nuclide of total atom numbers equal to the numbers of decayed parent nuclides as mentioned above. This justification is clarified by a coordinative discussion on the combination of
topt(SA) with the characteristic parameter
topt(t) mentioned previously in this section.
As shown in
Figure 11, the difference between
topt(t) and
topt(SA) values is small for the range of half-lives
T1 >
T2 (or
λ2 >
λ1). So the use of
topt(t) and
topt(SA) values in the optimal daughter nuclide build-up management of practical generator production and utilisation is harmonised in term of effective and optimal generator use for an improved quality (
i.e., specific activity) of daughter nuclide solution.
4.1.2. Early Elution Schedule for Improvement of Daughter Nuclide Production Yield and Specific Radioactivity, Elution of 99Mo/99mTc and 68Ge/68Ga Generator-Concentrator Systems as the Cases
The early elution schedule method described in
Section 2.1.3 is used to evaluate the total yield of daughter nuclides produced from the generator by performing multiple elutions/separations. The partial build-up radioactivities of daughter nuclides at given standby times are eluted and the sum of all radioactivities obtained is compared with the radioactivity obtained in the elution performed at maximal build-up time (
tmax). The calculation (using Equations (15)–(17),
Section 2.1.3) and experimental results of
Ry yield ratio assessment are reported in two typical examples below.
Example 1. 99Mo/99mTc generator-concentrator system: The maximal build-up time of
99mTc daughter nuclide in
99Mo
/99mTc generator system is
tmax = 22.86 h.
99mTc build-up radioactivities achieved in the consecutive elutions performed at optimal
99mTc-radioactivity build-ups 78.3% (at
topt(t) = 9.145 h) and 80.5% (at
topt(SA) = 9.685 h) are shown in
Table 1 and
Figure 1. Despite the optimal build-up times of
99mTc daughter nuclide in
99Mo
/99mTc generator system between 40.0% and 42.3% compared with maximal build-up time as evaluated in the above mentioned optimisation assessment, more effective utilisation of hot
99mTc atoms may be found if only a partial build-up of
99mTc in the generator is allowed to occur at a build-up time shorter than optimal build-up time (<9.145 h) before milking the
99mTc from the generator column and repeating this partial elution (early elution) several times. As an example, the
99mTc radioactivity build-up 61.5% at build-up time
tb = 6 h (compared with a relevant maximal
99mTc activity in the generator) for a consecutive early elution schedule performed at 6-h build-up time are described in
Figure 5. The results of
Ry parameter evaluation based on Equations (15)–(17) in
Section 2.1.3 are shown in
Figure 12. As shown, the
99mTc yield of the generator eluted with a early elution schedule of build-up/standby time <6 h increases by a factor >2. Another advantage of consecutive early elutions performed at
99mTc activity build-up 61.5% (compared with maximal
99mTc build-up value) is the improvement in quality of
99mTc solution in terms of higher
99mTc specific activity, 200 Ci/μmol compared with 150 Ci/μmol obtained in an elution at
tmax = 22.86 h.
Example 2. 68Ge/68Ga generator-concentrator system: The maximal build-up time of
68Ga daughter nuclide in
68Ge/
68Ga generator system is
tmax = 14.1 h.
68Ga build-up radioactivity achieved in the consecutive elutions performed at optimal
68Ga-radioactivity build-up 71.6% (at
topt(t) =
topt(SA) = 2.063 h) are shown in
Table 1 and
Figure 2. Despite the optimal build-up times of
68Ga daughter nuclide in
68Ge/
68Ga generator system at 14.5% of maximal build-up time as evaluated in the above mentioned optimisation assessment, more effective utilisation of hot
68Ga atoms may be found if only partial build-up of
68Ga in the generator is allowed to occur at a build-up time shorter than optimal build-up time (<2.063 h) before milking the
68Ga from the generator column and repeating this partial elution (early elution) several times. As an example, the
68Ga radioactivity build-up 50.0% at build-up time
tb = 1.128 h (compared with a relevant maximal
68Ga activity in the generator) for a consecutive early elution schedule performed at 1.128-h build-up time are evaluated. The results of
Ry parameter evaluation based on Equations (15)–(17) in
Section 2.1.3 are shown in
Figure 12. This elution schedule can result in a much higher overall
68Ga radioactivity yield and satisfactory
68Ga/
68Zn ratio. The total useful
68Ga radioactivity gathered in 12 consecutive elutions (overall time period around 14 h) is six times higher than that eluted once at time
tmax (
Figure 12). Thus this elution plan offers cost-effective utilisation of the generator system. Another advantage of consecutive elution performed at 50%
68Ga build-up is the improvement in the quality of
68Ga solution in terms of reduction of Zn content in the eluate. An amount of 6.97 × 10
−3 nmol Zn-68 was evaluated at the 50%
68Ga build-up compared with the value of 0.2 nanomoles at the maximum
68Ga build-up time
tmax = 14.1 h for the 100 mCi
68Ge/
68Ga generator system. With this elution plan, a
68Ga/
68Zn molar ratio of approximately 3.0 in the eluate is achievable compared with the value of 0.1 at the time t
100% build-up. Moreover, this 1.128 h-elution plan ( with 50%
68Ga build-up) conforms with the time required for labelling peptide radiopharmaceutical plus consequently performing PET imaging (around 1.0 h in total) before starting a subsequent
68Ga generator elution. This statement is based on a unique dose of
68Ga-peptide injection prepared from the elution of 18 mCi activity
68Ga generator as a whole.