Various mathematical models of varying degrees of complexity have been developed to define the shape of the curves for cell survival. All of the models are based on the concept of random nature deposition of energy by radiation.

The linear-quadratic model is used to describe the curve of cell survival, assuming that there are two components of cell death by radiation:

where S(D) is the fraction of surviving cells at dose D, α is a constant describing the initial slope of the cell survival curve, and β is a smaller constant describing the quadratic component of cell killing. The ratio of alpha to beta gives the dose at which the linear and quadratic components of cell killing are equal.

Although it has several limitations, this ratio is used in predicting clinical effects in response to radiation as one of parameters to model cell death by radiation. In radiotherapy (RT), the sensitivity to changes in fractionation can be quantified in terms of the alpha/beta ratio. For many human tumors, the ratio is high (typically 10 Gy). This ratio is obtained from isoeffect curves plotted using the survival fractions of a single cell line at different doses per fraction [4]. It is the byproduct of the linear quadratic model, which describes cell killing as a single-hit versus double-hit hypothesis: linear cell kill is expressed by the alpha component, whereas quadratic cell kill is expressed by the beta component. A high alpha/beta ratio (6–14 Gy), seen in many human tumors, suggests a predominance of alpha component, implying a decreased response to fractionation and, thus, a decreased clinical benefit of hyperfractioning. A low alpha/beta ratio (1.5–5 Gy) is usually associated with a delayed response of normal tissue and is the basis for the therapeutic gain achieved by using hypofractionation (Table 4.1).