WAM to SeeSaw model for cancer therapy - overcoming LQM difficulties

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 α and β 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 β, 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.

Review of microbial resistance to chronic ionizing radiation exposure under environmental conditions

Ionizing radiation (IR) produces multiple types of damage to nucleic acids, proteins and other crucial cellular components. Nevertheless, various microorganisms from phylogenetically distant taxa (bacteria, archaea, fungi) can resist IR levels many orders of magnitude above natural background. This intriguing phenomenon of radioresistance probably arose independently many times throughout evolution as a byproduct of selective pressures from other stresses (e.g. desiccation, UV radiation, chemical oxidants). Most of the literature on microbial radioresistance is based on acute γ-irradiation experiments performed in the laboratory, typically involving pure cultures grown under near-optimal conditions. There is much less information about the upper limits of radioresistance in the field, such as in radioactively-contaminated areas, where several radiation types (e.g. α and β, as well as γ) and other stressors (e.g. non-optimal temperature and nutrient levels, toxic chemicals, interspecific competition) act over multiple generations. Here we discuss several examples of radioresistant microbes isolated from extremely radioactive locations (e.g. Chernobyl and Mayak nuclear plant sites) and estimate the radiation dose rates they were able to tolerate. Some of these organisms (e.g. the fungus Cladosporium cladosporioides, the cyanobacterium Geitlerinema amphibium) are widely-distributed and colonize a variety of habitats. These examples suggest that resistance to chronic IR and chemical contamination is not limited to rare specialized strains from extreme environments, but can occur among common microbial taxa, perhaps due to overlap between mechanisms of resistance to IR and other stressors.