The probability of correct target dosage: dose-population histograms for deriving treatment margins in radiotherapy

Van Herk and colleagues described mathematically what set-up and movement errors do to the dose a target receives across a population of patients. They separated errors made once, in preparing the treatment (systematic), from errors that vary at each session (random). Random errors blur the dose a little for many patients; the same size of systematic error shifts the whole dose distribution and leaves some patients badly underdosed.

From this they derived a recipe. To give at least 95 per cent of the prescribed dose to the whole clinical target volume in 90 per cent of patients, the margin should be 2.5 times the standard deviation of systematic errors plus 1.64 times that of random errors combined with the beam penumbra, which for a typical penumbra simplifies to 2.5 Sigma plus 0.7 sigma. The authors call it a lower limit, because it leaves out rotations and changes of shape.