Hawkins, R. B. 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 (α_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 (β_i) of the various components of the mixture minus one-half the variance of the distribution of the values of α_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 α and β 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 β 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.