G. Yunwen: Radioprotection 2025, 60( 1), 91 – 98 93
institutions per single discharge is determined to be no more than 1 ALI min. According to Sections B1.3.4 and B1.3.5 of GB 18871, the ALI min for Lu-177 is:
20 10 �3 Sv 1:0 10 �9 Sv = Bq ¼ 2: 0 107 Bq: ð4Þ
where 1.0 10 �9 Sv / Bq is the corresponding value of the committed effective dose per unit intake of 177 Lu via inhalation and is cited from Table B3 of GB 18871. The monthly discharged activity of 177 Lu must not exceed 10 ALI min, which is 2.0 10 8 Bq.
Specific activity: according to the Discharge standard of water pollutants for medical organization( GB 18466)( SBEP et al., 2005), the specific activity of total beta-emitting radionuclides at the outlet of the decay tank must not exceed 10 Bq / L, which means the specific activity of 177 Lu must not exceed 10 Bq / L. If the specific activity of the liquid radioactive effluent is 10 Bq / L, it would require discharging 2.0 10 4 m 3 of liquid effluent to reach the monthly maximum allowable discharged activity specified in Section 8.6.2 of GB 18871, whereas the nuclear medicine department generates far less than 2.0 10 4 m 3 of liquid effluent per month.
Upon the evaluation of this section, it is evident that compliance with the specific activity requirement inherently ensures adherence to the total activity requirement. Therefore, for 177 Lu, the limit on specific activity serves as the practical requirement.
4 Radioactivity in the decay tank
To figure out the minimum storage time and to determine the requisite volume of decay tanks, it is essential to quantify the total radioactivity within the decay tanks. This chapter delineates a methodology for estimating the radioactivity in decay tanks.
4.1 Iodine-131
Assuming full-load continuous operation without any interruptions, the hospitalization cycle is 3 days, and the proportions of the excreted activity relative to the administered activity are denoted as P 1, P 2, and P 3, respectively. The decay constant for 131 I is denoted as l. The average dose administered to a single patient is denoted as A, and the number of patients per hospitalization cycle is denoted as N.
For a decay tank filled after T days of operation, the activity contained in the first day’ s excreta of patients is P 1 NA. Assume that the tank is full after T days of operation, the residual activity of the first day’ s excreta of the first batch of patients is P 1 NAexp(– l( T – 1)) when the tank is full. Similarly, it can be derived that the residual activity of the first day’ s excreta of the first batch of patients is P 1 NAexp(-l( T � 4)) when then tank is full. Summing all the terms and using the geometric series sum formula, the activity due to the first day’ s excreta of the patients( denoted as D 1) when the tank is full can be calculated as:
D 1 ¼ Xn
¼ j¼1
P 1 NAexpf�l ½ T �ð3j�2ÞŠg
P 1e l e 3l � 1 NAð1 � e�lT Þ ð5Þ
In the above equation, n = T / 3 represents the number of hospitalization cycles from the empty to full state of the decay tank. For instance, if the decay tank takes 60 days to fill up, the value of n would be 20. For ease of calculation, T = 3n is assumed, where n is an integer.
Using the same method, the activity due to the second, the third day’ s excreta of the patients when the tank is full( denoted as D 2, D 3), can be calculated respectively as follows:
D 2 ¼ Xn j¼1
P 2 NAexpf�l ½ T �ð3j�1ÞŠg
¼ P 2e 2l e 3l � 1 NAð1 � e�lT Þ
D 3 ¼ Xn j¼1
P 3 NAexpf�l ½ T � 3jŠg
¼ P 3e 3l e 3l � 1 NAð1 � e�lT Þ ð6Þ ð7Þ
The retention ratio of 131 I within cells is related to cellular metabolic activity( Wyszomirska, 2012). Typically, it is assumed that 30 % of 131 I is retained in the body while 70 % is excreted through urine( Clarke, 1994; Ward, 2006). However, for radiation protection, a conservative approach should be taken. Referring to ICRP Publication 94, the values of P 1, P 2, P 3 are taken as 55 %, 22 %, and 6 %, respectively( Driver et al., 2001; ICRP, 2004;. The decay constant of 131 Iis 0.0864 / day. Based on these parameters, the following results are obtained:
D 1 ¼ 2:02NAð1 � e �lT Þ D 2 ¼ 0:88NAð1 � e �lT Þ D 3 ¼ 0:26NAð1 � e �lT Þ ð8Þ
The total theoretical activity D of 131 I in the decay tank, when it is full, can be calculated using the following formula:
D ¼ D 1 þ D 2 þ D 3 ¼ kNAð1 � e �lT Þ ¼ 3:16NAð1 � e �lT Þ ð9Þ
In China, liquid effluent containing 131 I generally needs to be stored for more than 10 half-lives, i. e., T ≥ 81 days. Under this condition, 1 – exp(– lT) can be approximated as 1. Therefore, the theoretical activity of 131 I can be approximated as kNA. In this formula, the value of k is related to the hospitalization cycle and the number of days it takes for the decay tank to fill. When the hospitalization cycle is 3 days and the number of days required to fill the decay tank is exactly a multiple of 3, the value of k is 3.16.