@misc{oai:repo.qst.go.jp:00061801,
 author = {Kawaguchi, Isao and 川口 勇生},
 month = {Sep},
 note = {Cancer is one of the major causes of death in the developed countries. Under the circumstances of modern lifestyle, cancer cause could be ascribed to exposure to not single carcinogen but combinations of multiple ones. They interact with each other, and dose-effect relationship of combined exposures is not necessarily additive, but sometimes more than additive (synergistic) or less than additive (antagonistic).
 We have found a synergistic effect of repeated X-ray irradiation to mice, and followed by chronic exposure to ethylnitrosourea (ENU) in drinking water. Each treatment alone induced thymic lymphomas in 10% mice exposed, whereas combined treatment induced lymphomas in more than 90% mice. However, when the order was reversed, ENU followed by X-rays, the combination of these two treatments induced thymic lymphomas in an additive or slightly supra-additive manner
 To explain the combined exposures, we developed the simple mathematical two-stage model, which takes account of the exposure order (sequence) of two carcinogens (e.g. X-ray and ENU). We consider three states (normal, intermediate, and malignant) in the population. The transition rates from normal to intermediate,  , and from intermediate to malignant,  , are enhanced by the carcinogens. We assumed each transition rate as monotonically increasing function of each carcinogen. We examined the model for the several cases of which change the effect of the carcinogens to transition rates. From the analysis, we found that the X-ray mainly acts at the first step and ENU acts at the second step., Japanese-Korean Joint Meeting for Mathematical Biology},
 title = {Synergy and additivity on the combined exposure of X-ray and ENU on lymphomagenesis},
 year = {2006}
}