WAM to SeeSaw model for cancer therapy – overcoming LQM difficulties –

Abstract

Purpose: The assessment of biological effects caused by radiation exposure has been currently carried out with the linear-quadratic (LQ) model as an extension of the linear non-threshold (LNT) model. In this study, we suggest a new mathematical model named as SeaSaw (SS) model, which describes proliferation and cell death effects by taking account of Bergonie-Tribondeau's law in terms of a differential equation in time. We show how this model overcomes the long-standing difficulties of the LQ model. Materials and methods: We construct the SS model as an extended Wack-A-Mole (WAM) model by using a differential equation with respect to time in order to express the dynamics of the proliferation effect. A large number of accumulated data of such parameters as a and b in the LQ based models provide us with valuable pieces of information on the corresponding parameter b 1 and the maximum volume V m of the SS model. The dose rate b 1 and the notion of active cell can explain the present data without introduction of b, which is obtained by comparing the SS model with not only the cancer therapy data but also with in vitro experimental data. Numerical calculations are presented to grasp the global features of the SS model. Results: The SS model predicts the time dependence of the number of active-and inactive-cells. The SS model clarifies how the effect of radiation depends on the cancer stage at the starting time in the treatment. Further, the time dependence of the tumor volume is calculated by changing individual dose strength, which results in the change of the irradiation duration for the same effect. We can consider continuous irradiation in the SS model with interesting outcome on the time dependence of the tumor volume for various dose rates. Especially by choosing the value of the dose rate to be balanced with the total growth rate, the tumor volume is kept constant. Conclusions: The SS model gives a simple equation to study the situation of clinical radiation therapy and risk estimation of radiation. The radiation parameter extracted from the cancer therapy is close to the value obtained from animal experiment in vitro and in vivo. We expect the SS model leads us to a unified description of radiation therapy and protection and provides a great development in cancer-therapy clinical-planning.

Summary of the 2021 ICRP workshop on the future of radiological protection

“…In addition, several presentations focused on better understanding of the dose-response relationship, for example, by considering potential thresholds (Jeffries 2021), the linear no-threshold (LNT) model (Hamaoka 2021), the role of stem cell competition (Sasaki et al 2021) and the models used to describe radiation-related chronic risks (Bando et al 2021). Informed by these discussions and two pre-existing ICRP working parties, shortly after the Workshop, ICRP prioritized the establishment of task groups on several topics, including cancer risk models and non-radiation factors in the calculation of detriment (ICRP 2021b).…”

“…By considering cell exclusion effects, the WAM model can describe the effects of dose fractionation as a case of low-dose rate, without any need to apply the DDREF concept. In this way, the WAM model can be applied to predict the progress of tumour eradication during radiation therapy (Bando et al 2021).…”