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Year : 2019  |  Volume : 15  |  Issue : 8  |  Page : 140-143

An analytical study of effect of the cell proliferation, half-life, and energy of radionuclides in targeted radiotherapy

Material and Nuclear Fuel Cycle Research School, Nuclear Science and Technology Research Institute, Tehran, Iran

Date of Web Publication22-Mar-2019

Correspondence Address:
Dr. Hassan Ranjbar
Material and Nuclear Fuel Cycle Research School, Nuclear Science and Technology Research Institute, P. O. Box: 11365-8486, Tehran
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Source of Support: None, Conflict of Interest: None

DOI: 10.4103/jcrt.JCRT_78_18

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 > Abstract 

Aim: The treatment of the cancers is one of the most important challenges of nuclear medicine. Using targeted radiotherapy has increased the hope for the cure of the cancers. In the targeted radiotherapy, proliferations of tumor cells during radiotherapy are believed to be main reasons of treatment defeat. The aim of this work is the investigation of the cell proliferation on tumor treatment.
Materials and Methods: For this purpose, two scenarios were considered. The first scenario, in case of the tumor cells nonproliferation, surviving curve of irradiated cells is an exponential function of accumulated dose. The second scenario, Tumor cells proliferate exponentially with a growth constant and all tumor cells are assumed to be proliferating throughout irradiation.
Results: In the nonproliferation condition, the surviving fraction of tumor cells decreases with time. In the proliferation cases, at the beginning of the irradiation, the surviving fraction of cells decreases. If the remained fraction of cells is reduced sufficiently by this time, the tumor may be treated. Unless, as the dose rate continues to decrease, the proliferation exceeds from the sterilization and the tumor cell population increases.
Conclusion: Due to high dose-rate, the shorter decay half-life is more effective in comparison to longer ones.

Keywords: Cell proliferation, dose-rate, radionuclide, targeted radiotherapy, tumor treatment

How to cite this article:
Ranjbar H. An analytical study of effect of the cell proliferation, half-life, and energy of radionuclides in targeted radiotherapy. J Can Res Ther 2019;15, Suppl S1:140-3

How to cite this URL:
Ranjbar H. An analytical study of effect of the cell proliferation, half-life, and energy of radionuclides in targeted radiotherapy. J Can Res Ther [serial online] 2019 [cited 2021 Sep 22];15:140-3. Available from: https://www.cancerjournal.net/text.asp?2019/15/8/140/244474

 > Introduction Top

Patient health or longevity with the assurance of his good life quality is the purpose from cancer treatment. The essential treatment methods used alone or with another ones are surgery, chemotherapy, and radiotherapy.[1] Radiotherapy has known as a main part of the cancer treatment. In the reality, more than half of the patients sufferings from cancer are treated using radiotherapy.[2]

Radiotherapy is based on the irradiation of malignant tumor cells with considerable doses to annihilate them. As soon as only the cancer and adjacent cells are affected by radiation in this method, this method is considered as a local treatment.[3],[4] Maximize the tumor dose and minimize healthy tissues dose are the purpose of radiotherapy.[5],[6] The radiation energy, half-life, stopping power, linear energy transfer, and biological effects are of the main important parameters in the treatment planning which should be studied and investigated carefully.[7]

In targeted radiotherapy, from the biological difference between the tumor and the healthy cells are used for radionuclides aggregation in the tumor. Therefore, the radiation dose or energy is given to the tumor cells by their biological characteristics, while the physical situation of tumor in other methods is determinant. The main radiobiological mechanisms governing the response of tumors to radiation exposure have been called the “five-R's” which include Radiosensitivity, Repair, Repopulation, Reoxygenation, and Redistribution. In this report, one of these mechanisms, tumor cell repopulation or proliferation, and its likely relevance to targeted radiotherapy, are discussed.

In the targeted radiotherapy, proliferation of tumor cells during radiotherapy is of the main reasons for treatment defeat.[8],[9] The main goal of this research in complementary and continuing the former research of authors,[10] is the investigation on the tumor cell proliferation effects on the tumor treatment in radiotherapy method.

 > Materials and Methods Top

By considering to an important mechanism such as tumor cells proliferation during radiotherapy in the targeted radiotherapy, the treatment planning and effectiveness are different from the situation in which forgoing from this mechanism.

Radionuclides accumulate and after that, the biological clearance and radionuclide physical decay is used in the targeted radiotherapy complicate the absorbed dose index. [Figure 1] indicates the absorbed dose rate. Initially, the absorbed dose rate increases while reaching a maximum, then decreases because of physical decay and biological clearance. As a result, the index dose rate is where that the cell proliferation is equal to the tumor cells sterilization.
Figure 1: Tumor absorbed dose rate in the targeted radiotherapy

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Cell nonproliferation

In case of the tumor cells nonproliferation, surviving curve of irradiated cells is an exponential function of accumulated dose which could be described with a definite parameter (α), such as:[11]

In which S(D) is the fraction of survived cells, Ns is the number of remaining clonogenic tumor cells after cumulated dose D and N0 is the initial number of the tumor clonogenic cells.

The coefficient of alpha must be inferred by regression from human exposure data, such as the Hiroshima Leukemia data. Laboratory experiments on animals and tissue samples are of limited value. Most of the high-quality human data available are from high-dose individuals, above 0.1 Sv.

The amount of absorbed dose in a short time interval “t” after absorption of initial dose with rate r0 is:

Therefore, the cumulated dose in time interval T after the accumulation of radionuclide is:

Considering that the variation of the irradiated cells is:

Then, regarding to 1 and 3 and solving this equation, the fraction of the remained cells become as a function of time:

Existence of the cell proliferation

With supposing a situation in which the tumor cells increase with constant K, the differential equation for the tumor cells would be:

The first and the second sentences in 6 are for cells annihilation and generation from cell proliferation, respectively. Therefore, the fraction of the remained tumor cells with considering the cell proliferation is:

 > Results and Discussions Top

[Figure 2] shows the remained cells after irradiation for two conditions of with and without proliferation. The nonproliferation curve indicates how the remained tumor cells decrease with time. This decrease is exponential same as the cumulated dose curve. The curve slope decreases gradually and finally becomes zero. The curve decreases asymptotically with time and finally reaches to a value which has determined with cumulated irradiative dose.
Figure 2: The remained cells fraction curve per time without and with proliferation

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In the curve of cell proliferation state, the fraction of remained cells decreases at first and again increases after a determined time. This curve indicates that the dose rate in the first of irradiation is high enough for prevailing on proliferation effects and therefore the remained cells accumulation decreases. After that, the dose rate decreases to the critical amount and the cells sterilization reach equilibrium with cells proliferation. This is a time at which the fraction of remained cells is minimum and the biological effects on the tumor are maximum. If the remained fraction of cell decreases enough, it would be possible to the tumor treatment, unless, the dose rate continues to decrease and the proliferation exceeds from the sterilization and the tumor cells increase as a consequence.

[Figure 3] shows the curves of remained the tumor cell fractions that irradiated with two radionuclides having different energies. As could be seen from this figure, as well as using from the higher radionuclide energy, there is less remained cells fraction. In the other word, with increasing radionuclide beta particles, the damage to the tumor cells increases which leads to a better treatment.
Figure 3: The remained cell fraction curve versus time for radionuclide with low and high energy

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For targeted radiotherapy, the radiation dose-rate profile in the tumor is a critical feature, to a significant extent set by the effective radionuclide half-life. It determines the importance of the radiobiological mechanisms of repair of radiation damage, cell cycle redistribution, and tumor cell proliferation.

[Figure 4] shows the irradiated tumor cell remained fraction by two radionuclides of short and long half-life time. The implied point of this figure is that as well as a longer half-life, the fraction of remained cells is lower. The reason is that the cells are irradiated throughout the decay of radionuclides. In other words, cell damage is more likely if radionuclide decay is greater. The important and principal point of this curve is that the needed time to minimize tumor cells for the short life radionuclides are sooner than the long life radionuclides.
Figure 4: The remained cells fraction curve per time for short half-life and long half-life radionuclide

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 > Conclusion Top

In the treatments based on the irradiation, the tumor cells respond to the radiation, tumor cells numbers, absorbed radiation dose in tumor, and condition of the radiation transport to it are of the main factors in the tumor treatment. In the targeted radiotherapy based on the beta emitter radionuclide, the physical characteristics of the radionuclide are important and determine the usefulness of the treatment.

In this research, damage to the tumor (annihilate the tumor cells) when using the targeted radiotherapy investigated for the two different conditions. The first condition was for the nonproliferative tumor cells during radiotherapy and the second was for the proliferative tumor cells during radiotherapy. Furthermore, with assuming cell proliferation, the nuclide half-life and the energy effects were studied in the cells annihilation.

The results showed that in the nonproliferation condition, the remained fraction of the tumor cells reduces with time and this decrease becomes zero finally. However, in the proliferation condition, the fraction of the remained cells decreases first, and the tumor may be treated if the remained fraction of cell decreases enough at this time. Unless the dose rate decreases and the proliferation exceeds from the annihilation which leads to increase the tumor cells accumulation. Furthermore, the results showed that as well as the radionuclide being more, the remained cells fraction will be less. The time for reaching the minimum of the tumor cells for faster treatment is happened faster for the short life radionuclides in comparison to the long-life radionuclides.

Therefore, with considering to the difference of the half-life and the energy of the emitted particles from the radionuclide, the cells response is different for the various radionuclides. In other words, a radionuclide with the long half-life has a slow response (treatment start) when the radionuclide with the lower half-life has fast response although having the shorter treatment duration. Namely, the short-life radionuclides are more effective in comparison to the long-life radionuclides regarding the fast response time and prescription of higher activity for treatment.

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Conflicts of interest

There are no conflicts of interest.

 > References Top

World Health Organization. Cancer Control: Knowledge into Action: WHO Guide for Effective Programmes. World Health Organization; 2007.  Back to cited text no. 1
Rath M. Cellular Health Series: Cancer. M/R Pub.; 2002.  Back to cited text no. 2
Ranjbar H, Bahrami-Samani A, Yazdani MR, Ghannadi-Maragheh M. Determination of human absorbed dose of cocktail of 153Sm/177Lu-EDTMP, based on biodistribution data in rats. J Radioanal Nucl Chem 2016;307:1439-44.  Back to cited text no. 3
Ranjbar H, Bahrami-Samani A, Beiki D, Shirvani-Arani S, Ghannadi-Maragheh M. Evaluation of 153Sm/177Lu-EDTMP mixture in wild-type rodents as a novel combined palliative treatment of bone pain agent. J Radioanal Nucl Chem 2015;303:71-9.  Back to cited text no. 4
Ranjbar H, Shamsaei M, Ghasemi MR. Investigation of the dose enhancement factor of high intensity low mono-energetic X-ray radiation with labeled tissues by gold nanoparticles. Nukleonika 2010;55:307-12.  Back to cited text no. 5
Ranjbar H, Bahrami-Samani A, Beiki D, Ghannadi-Maragheh M. Development of 153Sm/177Lu-EDTMP as a possible therapeutic complex. Iran J Nucl Med 2017;25:11-6.  Back to cited text no. 6
Ranjbar H, Ghannadi-Maragheh M, Bahrami-Samani A, Beiki D. Dosimetric evaluation of 153 Sm-EDTMP, 177 Lu-EDTMP and 166 Ho-EDTMP for systemic radiation therapy: Influence of type and energy of radiation and half-life of radionuclides. Radiat Phys Chem 2015;108:60-4.  Back to cited text no. 7
Trott KR. Cell repopulation and overall treatment time. Int J Radiat Oncol Biol Phys 1990;19:1071-5.  Back to cited text no. 8
Fowler JF. The linear-quadratic formula and progress in fractionated radiotherapy. Br J Radiol 1989;62:679-94.  Back to cited text no. 9
Ranjbar H, Bahrami Samani A, Ghannadi Maragheh M, Beiki D. Investigation of the effects of tumor size and type of radionuclide on tumor curability in targeted radiotherapy. ISMJ 2015;18:567-74.  Back to cited text no. 10
National Research Council. Health Risks from Exposure to Low Levels of Ionizing Radiation: BEIR VII Phase 2. Vol. 7. National Academies Press; 2006.  Back to cited text no. 11


  [Figure 1], [Figure 2], [Figure 3], [Figure 4]


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