© G. Yunwen, Published by EDP Sciences, 2025

1 Introduction

Currently, in China, ¹³¹I radionuclide is primarily used for thyroid cancer treatment in nuclear medicine departments, while the usage of ¹⁷⁷Lu and the number of patients treated with it are also increasing. According to the Medium and Long-term Development Plan for Medical Isotopes (2021–2035) (CAEA et al., 2021), the usage of ¹³¹I in China was 3.7 × 10¹⁴ Bq in 2019, with an expected annual growth rate of 15%. ¹⁷⁷Lu is highly effective in treating neuroendocrine tumors and prostate cancer. The usage of ¹⁷⁷Lu was 1.85 × 10¹²Bq, with domestic demand projected to grow at an annual rate of 30%. According to the data from the National Radiation Safety Management System for Nuclear Utilization, as of the end of December 2023, about 100 hospitals had obtained radiation safety licenses for using ¹⁷⁷Lu, and many more hospitals were planning to apply for such licenses.

The Medium and Long-term Development Plan for Medical Isotopes (2021–2035) aims to establish at least one nuclear medicine department in each county across China by 2035. Following the release of this plan, the construction of nuclear medicine departments in China has significantly accelerated, with many new departments planning to set up treatment wards for radionuclide therapy using ¹³¹I or ¹⁷⁷Lu. The management of patients undergoing radionuclide therapy varies across countries (Barquero et al.,2008). For instance, since the late 20th century, the United States has not required patients treated with ¹³¹I to be hospitalized, allowing their excreta to enter municipal sewage systems directly (US NRC, 1997). In contrast, China and most European countries, following recommendations from the International Atomic Energy Agency and other organizations, require patients to be hospitalized until the ¹³¹I level in the patient’ s body meets certain standards (ICRP, 1991; IAEA, 2002). During hospitalization, the excreta of patients containing ¹³¹I is stored in decay tanks until it meets discharge requirements. Regarding ¹⁷⁷Lu therapy, currently, it is not explicitly required in China for patients receiving ¹⁷⁷Lu treatment to be hospitalized. Medical institutions generally adopt an outpatient treatment model where patients receive injections in the morning and are released in the afternoon, with their excreta entering the decay tanks during this period.

2 Materials and methods

This paper is the original work of the author, composed without AI assistance. Post-initial drafting, Kimi (a generative AI tool, developers have not specified version information) was utilized solely for linguistic refinement, including grammar correction and word suggestion, to enhance the manuscript’s clarity. Kimi was mainly used in Section 4.1.

3 Requirements for the discharge of liquid radioactive effluent containing ¹³¹I and ¹⁷⁷Lu

Should the liquid radioactive waste be directly discharged into the sewer system, the annual dose for workers within the sewer system may potentially exceed the regulatory limit of 0.1mSv. To minimize the radiological risks to both workers and the general public, China has established stringent regulatory standards. In this chapter, the standards for ¹³¹I and ¹⁷⁷Lu are introduced.

3.1 Iodine-131

In September 2023, the Department of Radiation Source Safety Regulation, Ministry of Ecology and Environment issued the Reply to Consultation on Several Clauses of the Nuclear Medicine Standard (Department of Radiation Source Safety Regulation of Ministry of Ecology and Environment, 2023) publicly, which clarifies that the liquid radioactive effluent containing ¹³¹I in decay tanks can be discharged according to any one of the following methods:

1. According to Article 8.6.2 of the Basic standards for protection against ionizing radiation and for the safety of radiation sources(GB 18871) (AQSIQ, 2002), upon confirmation by the regulatory authorities, the activity of ¹³¹I in the liquid effluent discharged into the regular sewer system should not exceed 1 ALI_min (9 × 10⁵ Bq) per single discharge, and the total activity of ¹³¹I in the liquid effluent discharged per month should not exceed 10 ALI_min (9 × 10⁶ Bq).

2. If liquid effluent has been stored up to 180 days, it can be discharged directly.

3. Liquid effluent stored for less than 180 days can also be discharged if monitoring results show that the specific activity of ¹³¹I has decreased to 10 Bq/L or below.

According to Sections B1.3.4 and B1.3.5 of GB 18871, the calculation formula for ALI_min is as follows: $$AL{I}_{\text{min}}=DL/e_j.$$(1)

Among them, DL is the annual effective dose limit, which should be taken as 20mSv. e_j is the larger value between the corresponding values of the committed effective dose per unit intake of a certain radionuclide j via inhalation or ingestion. According to Table B3 of GB 18871, for ¹³¹I, e_j should be taken as 2.2 × 10⁻⁸ Sv/Bq. Substituting these values into the calculation, the ALI_min for iodine-131 is 9 × 10⁵Bq.

It can be demonstrated that, among the three methods mentioned above, discharging according to the method specified in GB 18871 is most beneficial for hospital operations:

Firstly, assuming that the specific activity of ¹³¹I is 10 Bq/L, if the monthly discharge of ¹³¹I reaches the limit specified in GB 18871, which is 9 × 10⁶ Bq, the corresponding volume of liquid radioactive effluent would be: $$\frac{9\times {10}^6\text{Bq}}{10\text{Bq/L}}=9\times {10}^5\text{L}=9\times {10}^2{\text{m}}^3.$$(2)

In practice, the monthly volume of liquid radioactive effluent produced from hospital wards treating with ¹³¹I is far below 900 m³. Therefore, discharging according to GB 18871, is easier for operation than storing liquid effluent until the specific activity reaches 10 Bq/L.

Secondly, if a hospital chooses to discharge after a storage period of 180 days and assuming the monthly total activity of ¹³¹I in the discharged liquid effluent is 9 × 10⁶ Bq, the activity of ¹³¹I in the decay tank can be calculated as: $$9\times {10}^6\times \exp (0.0864/\text{d}\times 180\text{d})\approx 5.10\times {10}^{13}\text{Bq}.$$(3)

Among the above formula, 0.0864/d is the decay constant for ¹³¹I.

In 2019, the total usage of ¹³¹I across all of China was only 3.7 × 10¹⁴ Bq. The monthly usage of ¹³¹I in a single hospital’s nuclear medicine department is definitely far lower than 5.10 × 10¹³ Bq. Considering decay, the accumulated total activity of ¹³¹I in the decay tank when full is even lower than 5.10 × 10¹³ Bq. Therefore, discharging according to GB 18871 is easier for operation than discharging after storing liquid effluent for 180 days.

According to the analysis presented in the above, if either a storage period of up to 180 days is met or the activity concentration of 10 Bq/L is achieved, the discharged radioactivity will not surpass the permissible threshold. Conversely, if these conditions are not met, the limit is still likely to be not exceeded. Since medical institutions have the option to select any one of the three methods outlined in Section 3.1 for the disposal of decay tank water, a rational operator would opt for the approach that confers the greatest benefit. Consequently, it is anticipated that all hospitals will prefer the method delineated in the national standard GB 18871. Therefore, the discharge limit established by GB 18871 serves as the regulatory criterion for the effluent liquid containing ¹³¹I.

3.2 Lutecium-177

Discharging ¹⁷⁷Lu is subject to dual restrictions on both the specific activity and the total activity.

Total activity limit: similar to ¹³¹I, the maximum allowable total activity of ¹⁷⁷Lu that can be discharged by medical 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: $$\frac{20\times {10}^{-3}\text{Sv}}{1.0\times {10}^{-9}\text{Sv/Bq}}=2.0\times {10}^7\text{Bq}.$$(4)

where 1.0 × 10⁻⁹ Sv/Bq is the corresponding value of the committed effective dose per unit intake of ¹⁷⁷Lu via inhalation and is cited from Table B3 of GB 18871. The monthly discharged activity of ¹⁷⁷Lu must not exceed 10 ALI_min, which is 2.0 × 10⁸ 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 ¹⁷⁷Lu 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 × 10⁴ m³of 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 × 10⁴ m³of 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 ¹⁷⁷Lu, 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 P₁, P₂, and P₃, respectively. The decay constant for ¹³¹I is denoted as λ. 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 P₁NA. 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 P₁NAexp(–λ(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 P₁NAexp(-λ(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 D₁) when the tank is full can be calculated as: $$D_1={\displaystyle \sum _{j=1}^n}{P}_{1}NA\exp \left\{-\lambda \left[T-(3j-2)\right]\right\}=\frac{P_1{e}^{\lambda }}{e^{3\lambda }-1}NA(1-e^{-\lambda T})$$(5)

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 D₂, D₃), can be calculated respectively as follows: $$D_2={\displaystyle \sum _{j=1}^n}{P}_{2}NA\exp \left\{-\lambda \left[T-(3j-1)\right]\right\}=\frac{P_2{e}^{2\lambda }}{e^{3\lambda }-1}NA(1-e^{-\lambda T})$$(6) $$D_3={\displaystyle \sum _{j=1}^n}{P}_{3}NA\exp \left\{-\lambda \left[T-3j\right]\right\}=\frac{P_3{e}^{3\lambda }}{e^{3\lambda }-1}NA(1-e^{-\lambda T})$$(7)

The retention ratio of ¹³¹I within cells is related to cellular metabolic activity (Wyszomirska, 2012). Typically, it is assumed that 30% of ¹³¹I 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 P₁, P₂, P₃ are taken as 55%, 22%, and 6%, respectively (Driver et al., 2001; ICRP, 2004;. The decay constant of ¹³¹I is 0.0864/day. Based on these parameters, the following results are obtained: $$\begin{array}{ccc}\hfill D_1=2.02NA(1-e^{-\lambda T})\hfill & \hfill D_2=0.88NA(1-e^{-\lambda T})\hfill & \hfill D_3=0.26NA(1-e^{-\lambda T})\hfill \end{array}$$(8)

The total theoretical activity D of ¹³¹I in the decay tank, when it is full, can be calculated using the following formula: $$D=D_1+D_2+D_3=kNA(1-e^{-\lambda T})=3.16NA(1-e^{-\lambda T})$$(9)

In China, liquid effluent containing ¹³¹I generally needs to be stored for more than 10 half-lives, i.e., T ≥ 81 days. Under this condition, 1–exp(–λT) can be approximated as 1. Therefore, the theoretical activity of ¹³¹I 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.

4.2 Lutecium-177

Similar to ¹³¹I, most of the ¹⁷⁷Lu injected into the human body is excreted through the patient’s urine and other excreta (ICRP, 2004; Zaknun et al., 2013). According to available environmental impact assessment documents, hospitals planning to carry out ¹⁷⁷Lu treatments generally administer the medication to patients on a specific day of the week, with patients receiving the injection in the morning and leaving in the evening, roughly resulting in a hospital stay of 6∼9 hours. During their stay, the excreta must enter the decay tank.

The average dose administered to a single patient is denoted as A, and the number of patients is denoted as N. The proportion of ¹⁷⁷Lu excreted by the patient during their stay in the hospital is denoted as P. The value of P varies across studies. Levart et al. found that the retention rate of ¹⁷⁷Lu in the body 18.1 hours post-administration of ¹⁷⁷Lu-DOTATATE was approximately 36% (Levart et al., 2019). Esser JP’s team measured that approximately 71% and 81% of the administered dose of ¹⁷⁷Lu-DOTATATE or ¹⁷⁷Lu-DOTATOC, respectively, was excreted in urine within 24 hours (Esseret al., 2006). Kwekkeboom et al. indicated that about 64% of ¹⁷⁷Lu was excreted in urine within the first 24 hours following the administration of ¹⁷⁷Lu-DOTATATE (Kwekkeboom et al., 2001). Referring to the above results and the conservative principle, it is assumed that 50% of ¹⁷⁷Lu is excreted during the patient’s stay, i.e., P = 0.5.

Assuming the decay tank fills in T = 7n + 1 days (the excreta of a new batch of patients enters the decay tank, resulting in higher activity levels than any other day in the 7-day cycle). Under this assumption, the total activity of ¹⁷⁷Lu in the decay tank when it is full, denoted as D, is: $$D={\displaystyle \sum _{j=1}^n}PNA\exp \left[-\lambda (7j-6)\right]+PNA=\frac{P{e}^{\lambda }}{e^{7\lambda }-1}NA(1-e^{-\lambda T})+PNA=kNA=1.02NA(1-e^{-\lambda T})$$(10)

where λ is the decay constant of ¹⁷⁷Lu.

In most cases, T ≥ 81 days, and 1–exp(–λT) can be approximated as 1. Therefore, the total activity of ¹⁷⁷Lu in the tank can also be simplified to kNA. When T = 7n + 1, the value of k is 1.02. If T = 7n + 1 + g, the total activity of ¹⁷⁷Lu in the tank can be considered as the activity at 7n + 1 days, further decayed by g days, that is kNA × exp(–λg).

5 Theoretical minimum storage days and required volume of decay tank

According to China’s regulatory requirements, the hospital needs to conduct an EIA and obtain approval from regulatory authorities before constructing a nuclear medicine department. The EIA document must determine the volume of the decay tank. The volume varies significantly, influenced by factors such as patient load, location, and notably, the year of the hospital’s establishment. Generally, hospitals founded prior to 2021 are equipped with 2 to 4 decay tanks, with individual tank volumes varying between 20 to 80 cubic meters. After the Radiation protection and safety requirements for nuclear medicine (HJ 1188) (Ministry of Ecology and Environment, 2021) was issued in 2021, the newly-built hospitals usually determine the volume of tanks based on a storage period of 180 days. As a result, the volume of decay tanks increases significantly. The hospitals typically possess 3 to 5 decay tanks, with tank volumes ranging from 60 to 120 cubic meters.

Utilizing the radioactivity levels within the decay tank as a foundation, this chapter presents a theoretical framework for calculating the minimum storage period and the requisite tank volume. Using the new framework, the required volume of the decay tanks can be significantly reduced while ensuring compliance with regulatory requirements.

5.1 Theoretical minimum decay days for ¹³¹I

Since the total activity specified in Section 8.6.2 of GB 18871 is the practical restriction for the discharge of ¹³¹I, Let E_m represent the monthly allowable discharged activity (9 × 10⁶ Bq) and T_min represents the theoretical minimum decay days for ¹³¹I. T_min should satisfy: $$D{e}^{-\lambda T_{\min }}=E_m$$(11)

Thus $$T_{\min }=\frac{\ln (D/E_m)}{\lambda }$$(12)

The volume of the decay tank, V, should satisfy: $$V\ge \frac{W_1{T}_{\min }}{M-1}$$(13)

where M represents the number of decay tanks, W₁ represents the daily liquid effluent volume discharged into a decay tank. When equation (13) is taken as equality, the volume V obtained is the minimum required volume of the decay tanks. Table 1 shows the minimum required volume of the decay tank for different numbers of patients, assuming an average dose of 7.4 GBq per patient, a hospitalization cycle of 3 days, and 3 decay tanks.

5.2 Theoretical minimum decay days for Lutecium-177

Since the specific activity of ¹⁷⁷Lu at the outlet of the decay tank must not exceed 10 Bq/L, Similarly, let T_min represent the theoretical minimum decay days for ¹⁷⁷Lu. T_min should satisfy: $$\frac{kNA}{V}\times e^{-\lambda T_{\min }}=10\text{Bq/L}={10}^3\text{Bq}/{\text{m}}^3$$(14)

where kNA represents the activity when the decay tank is just filled, V is the volume of the decay tank. kNA/V is the specific activity of ¹⁷⁷Lu. Equation (14) means that if the liquid effluent has been stored for T_min, the specific activity of ¹⁷⁷Lu complies with discharge criteria.

Assuming the number of decay tanks is M and the daily liquid effluent volume discharged into a decay tank is W₁, the volume V of a single decay tank should satisfy: $$V\ge \frac{W_1{T}_{\min }}{M-1}$$(15)

When equation (15) is taken as equality, V obtained is the minimum required volume of the decay tank. W₁ is roughly proportional to the number of patients, so W₁ can be expressed as W₀ × N, where W₀ represents the daily water consumption per patient, and N is the number of patients per batch. Equation (15) can be rewritten as: $$V=\frac{W_1{T}_{\min }}{M-1}=\frac{W_{0}N{T}_{\min }}{M-1}$$(16)

This leads to: $$T_{\min }=\frac{\left(M-1\right)V}{W_{0}N}$$(17)

Substituting equation (17) into equation (14): $$\frac{kNA}{V}\exp \left(-\lambda \frac{(M-1)V}{W_{0}N}\right)=10000$$(18)

Let X = V/N, and substitute it into equation (18): $$\frac{kA}{X}\exp \left[-\frac{\lambda X\left(M-1\right)}{W_0}\right]=10000$$(19)

Assuming W₀ is 0.11 m³ and the number of decay tanks M = 3, solving equation (19) gives X = V/N = 6.25 m³/person, meaning the volume of the decay tank required per patient is 6.25 m³; the corresponding minimum storage time is 113.6 days. Table 2 shows the required volume of the decay tank for different numbers of patients.

5.3 Minimum storage time considering both ¹⁷⁷Lu and ¹³¹I exists in the decay tank

If a hospital uses both ¹³¹I and ¹⁷⁷Lu for treatment, the storage time for liquid effluent should be the larger value between the minimum storage time for ¹³¹I and ¹⁷⁷Lu. From Tables 1 and 2, it can be seen that under the assumed circumstance, the minimum storage time required for ¹⁷⁷Lu is slightly larger when the number of patients is ≤9. When the number of patients is ≥10, the volume required for ¹³¹I exceeds that for ¹⁷⁷Lu.

5.4 Actual measurement results

Currently, nuclear medicine departments in China’s hospitals mainly conduct ¹³¹I treatment, while ¹⁷⁷Lu is still in clinical trial stages. Therefore, it is difficult to obtain monitoring data for ¹⁷⁷Lu, so the actual measurement results mainly focus on ¹³¹I.

Four hospitals were selected, and the activity concentration of ¹³¹I in decay tanks when full was monitored. The results are shown in Table 3. From Table 3, it can be seen that:

1. The actual activity of ¹³¹I in the decay tanks when full is lower than the theoretically calculated value;

2. In the case of operation at full capacity (hospital No. 3), the actual measured value is close to the theoretically calculated value;

3. Based on the methods presented in this article, the monthly discharged activity of ¹³¹I from the four hospitals is below the discharge limit, complying with regulatory requirements.

6 Discussion and analysis

According to the theoretical activity formula for ¹³¹I and ¹⁷⁷Lu in a full decay tank, the total activity is proportional to the number of patients and the dosage per patient. The theoretical activity is derived under the assumption of the hospital operating at full capacity, with consecutive batches of patients and no intervals, and with conservative assumptions in terms of discharge ratio. Therefore, the result obtained from the calculation formula is actually the upper limit of the total activity of ¹³¹I or ¹⁷⁷Lu in the tank.

For the ¹³¹I isotope, the minimum storage time T_min is proportional to ln(N), where N is the number of patients. The volume of liquid effluent discharged into the decay tank from the ¹³¹I treatment ward per day is also proportional to N. According to equations (12) and (13), the volume of the decay tank required for ¹³¹I is proportional to N ln(N).

For the ¹⁷⁷Lu isotope, the required minimum volume of the decay tank is directly proportional to the number of patients.

The daily water consumption per patient W₀ has a significant influence on the required volume of decay tanks. For medical institutions with limited expandable land space, limiting the daily water consumption per patient can reduce the required volume of the decay tanks, thereby lowering land requirements and construction costs.

7 Conclusions

This paper presents the theoretical activity formulas for ¹³¹I and ¹⁷⁷Lu in a full decay tank, demonstrating the limit on maximum allowable discharged activity specified in Section 8.6.2 of GB 18871and the specific activity of total beta-emitting radionuclides at the outlet of decay tanks specified in GB 18846 are the practical restrictions for the isotopes ¹³¹I and ¹⁷⁷Lu, respectively. It also proposes a method for determining the decay tank volume and the minimum storage time for liquid effluent.

For hospitals and regulatory authorities, if the intended number of patients, hospitalization cycle, average dosage, daily liquid effluent volume discharged into the decay tank are determined, the method provided in this paper can be used to determine the required volume of decay tanks. The minimum storage time can also be calculated. For regulatory authorities, this serves as a basis for assessing whether the planned decay tank volume meets the requirements when approving environmental impact assessment documents.

Given that the theoretical activity derived in this paper represents the upper limit of the actual total activity of ¹³¹I or ¹⁷⁷Lu in the decay tank, the actual total activity is often significantly lower than the theoretical calculation provided by this method. Therefore, if the storage time of the liquid radioactive effluent exceeds the calculated minimum storage time, it can be theoretically proven that the discharge meets regulatory requirements without the need for monitoring data. Actual monitoring results from four hospitals also proved the conclusion.

Acknowledgments

The author would like to thank the Provincial Radiation Station for providing the monitoring data support.

Funding

This research did not receive any specific funding.

Conflicts of interest

The author declares that they have no conflict of interest.

Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Author contribution statement

This paper was solely authored by Ge Yunwen. She was responsible for the conception, design, data collection, analysis, and manuscript writing.

Ethics approval

Ethical approval was not required.

Informed consent

The article does not contain any studies involving human subjects.

Supplementary Material

Table B3 in GB 18871: provides committed effective dose per unit intake e(g) via inhalation and ingestion for radioactive isotopes. For iodine-131, the value is 7.6×10^-9, 1.1×10^-8, and 2.2×10^-8 Sv/Bq. So, ej should be taken as 2.2×10-8 Sv/Bq. Access here

References

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