WAM to SeeSaw model for cancer therapy - overcoming LQM difficulties

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.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 α and β in the LQ based models provide us with valuable pieces of information on the corresponding parameterThe 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.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