Survival of a mixture of cells of variable linear-quadratic sensitivity to radiation

The experimentally observed survival of a heterogeneous mixture of cells, each component of which obeys a different linear-quadratic survival response to ionizing radiation, is examined. It is shown that the survival relationship for the mixed population approaches a linear-quadratic form for low doses. The linear parameter of the low-dose relationship approached is equal to the average of the distribution of values of the linear parameter (alpha(i)) of the various components of the mixture. The quadratic parameter of the low-dose relationship approached is equal to the average of the distribution of values of the quadratic parameter (beta(i)) of the various components of the mixture minus one-half the variance of the distribution of the values of alpha(i). A numerical example of the survival expected for an exponentially growing population of Chinese hamster V79 cells is presented. From this it can be appreciated that the apparent value of the alpha and beta parameters obtained by fitting an experimentally obtained survival curve will depend on the range of doses over which survival is determined. The apparent value of beta is decreased at higher doses, producing a straightening of the survival curve to approach the exponential decrease in survival commonly observed for the terminal high-dose portion of survival curves. Apparent exponential survival at high doses is not inconsistent with linear-quadratic survival and may not indicate a multitarget or other mechanism of cell killing.