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Depending on the amount of energy imparted to biological tissue, it is common to divide received doses of ionizing radiation into low, intermediate, and high dose range. Low doses are usually defined as the region below 0.2 Sv [Brill 82, UNSCEAR 94, Schi 95], intermediate as between 0.2 Sv and 2.5 Sv, and high dose range is above 2.5 Sv.

Most of our knowledge of radiation effects on human health are derived from data from explosions of atomic bombs over Hiroshima and Nagasaki, accidents in nuclear industry, follow up of uranium miners and follow up of children and adults who have received high doses for therapeutic purposes [Shap 90].

Additional knowledge about the low dose influence on human health has been obtained through studies of influence of radon concentration in air on death excess due to lung cancers, investigation of mortality in regions with high levels of natural exposure and studies of professionally exposed persons in the nuclear industry.

Two main biological effects of ionizing radiation are genetic mutations and induction of cancers. A linear no-threshold hypothesis is generally assumed for induction of all solid cancers in the low dose region. This means, that even the smallest exposures received by someone causes risk of cancer developing.

Validity of the linear no-threshold model in the low dose region has been contradicted by some relatively recent environmental and biological studies. Some experimental evidence showed that relatively low doses of ionizing radiation can produce adaptive response that stimulates repair mechanisms of cells [Okam 92, UNSCEAR 94]. Studies of populations that live in regions with high levels of natural radiation did not find an increase in carcinoma mortality, when compared with regions with low levels [UNSCEAR 94]. Also, studies of incidence and mortality due to radon-induced lung cancers did not find any significant difference between areas with high and low concentration of radon [UNSCEAR 94, Losal 95]. Some authors have found a negative correlation between lung cancer mortality and concentration of radon in dwellings [Cohe 97]. These findings indicate that low levels of ionizing radiation may, in fact, be beneficial. This beneficial effect is called hormesis [Lucke 91, Lucke 92, Kondo 93]. Clearly, the hormesis model is incompatible with the linear no-threshold model in the low level region of ionizing radiation.


Possible existence of a threshold in the linear model for cancer and leukemia induction, and possible existence of hormesis effect for leukemia are studied.

It is done by applying a standard least-squares fit (Chi-square analysis) and performing a Monte Carlo simulation on the data of the atomic bomb survivors.

Statistically significant results of ionizing radiation effects in the low dose region are very difficult to obtain because that effect is very small and conclusive research would require large number of subjects to observe.

Because of high relative uncertainties, standard formulae for calculation of estimator uncertainties should be used with caution.

It is why Monte Carlo simulations were used. The simulations started from the empirical data sets and have generated, using appropriate computer programs, and many artificial data sets. Each generated data set represents one artificial experiment. Statistical analysis of many (in our case one thousand) artificial experiments gives opportunity to obtain values for estimators and their uncertainties in a more reliable manner than using standard formulae.


Variable definition:

The cancer mortality rate MR in the exposed group,

O the observed number of deaths in the exposed group

N the number of persons in the exposed group with

The cancer mortality rate MR in the control group,

The excess mortality rate:

Model forms:

A proposed relationship between the effect of ionizing radiation on human health (Y(d)) and received dose (d) is defined as expected value of Y(d);

in low and medium dose ranges [Brill 82].


The linear no-threshold model has the form:

The threshold model has the form:

The hormesis effect in its simplest form can be described by a linear-quadratic

ß negative,  positive.

The excess mortality rates introduce correlations amongexcess mortality rates:

Models for cancer and leukemia mortality rates:



threshold parameter



data set 1

Monte Carlo





Monte Carlo simulation


data set 2



Empirical set of



Estimators of

empirical set of data

Threshold value


data set N



DiagramofaMonte Carlo Simulation

The example presents experiment with linear fit.The figure is

plotted according Figure 15.6.2 from [Pres 92, p. 686].