There are numerous models which attempt to describe or explain the shape of cell survival curves using a mathematical formula.
Single Target Single Hit Inactivation Model
This theory proposes that a single hit on a single sensitive target within the cell leads to cell death. This generates an exponential cell survival curve which appears as a straight line on a semi-logarithmic scale. This model is useful for highly sensitive human tissues, if high LET radiation is used, or if a low dose rate is used. Mammalian cells usually have a shoulder on their cell survival curves, which is not seen in this model.
Multi-Target Single Hit Inactivation Model
In an attempt to model the shoulder of the cell survival curve, this model was generated. It proposes that a single hit to each of n sensitive targets within the cell is sufficient to cause cell death. The generated curve has a shoulder and decreases linearly with increasing dose. Unfortunately, it does not model the low dose region well as for low doses it predicts no cell death.
Two Component Model
To account for the cell killing that occurs at low radiation doses, the two-component model adds another factor (D1) which adjusts for this. The two component model is based on both the single and multi target models and requires an extensive formula to calculate, based on D0, D1, and n the number of targets within the cell.
Although the two component model predicts cell killing in the lower dose regions better than either single or multi-target models, the regions is still linear which is incorrect.
Linear Quadratic Model
The linear quadratic model uses a polynomial equation $(\alpha D + \beta D^2)$. The probability of survival is equal to the exponential of this – ie: $e^{-(\alpha D + \beta D)^2}$. The generated curve is perhaps the best approximation of the actual cell kill seen after radiation exposure. It has the added benefit of two constants (α and β) which can be determined for specific tissues and cancers to predict dose response.
