  Starting from a general equation for organism (or cell system) growth and
attributing additional cell death rate (besides the natural rate) to therapy,
we derive an equation for cell response to {\alpha} radiation. Different from
previous models that are based on statistical theory, the present model
connects the consequence of radiation with the growth process of a biosystem
and each variable or parameter has meaning regarding the cell evolving process.
We apply this equation to model the dose response for {\alpha}-particle
radiation. It interprets the results of both high and low linear energy
transfer (LET) radiations. When LET is high, the additional death rate is a
constant, which implies that the localized cells are damaged immediately and
the additional death rate is proportional to the number of cells present. While
at low LET, the additional death rate includes a constant term and a linear
term of radiation dose, implying that the damage to some cell nuclei has a time
accumulating effect. This model indicates that the oxygen-enhancement ratio
(OER) decreases while LET increases consistently.
