A new formula for normal tissue complication probability (NTCP) as a function of equivalent uniform dose (EUD)

To facilitate the use of biological outcome modeling for treatment planning, an exponential function is introduced as a simpler equivalent to the Lyman formula for calculating normal tissue complication probability (NTCP). The single parameter of the exponential function is chosen to reproduce the Lyman calculation to within similar to 0.3%, and thus enable easy conversion of data contained in empirical fits of Lyman parameters for organs at risk (OARs). Organ parameters for the new formula are given in terms of Lyman model m and TD50, and conversely m and TD50 are expressed in terms of the parameters of the new equation. The role of the Lyman volume-effect parameter n is unchanged from its role in the Lyman model. For a non-homogeneously irradiated OAR, an equation relates d(ref), n, v(eff) and the Niemierko equivalent uniform dose (EUD), where d(ref) and v(eff) are the reference dose and effective fractional volume of the Kutcher-Burman reduction algorithm (i.e. the LKB model). It follows in the LKB model that uniform EUD irradiation of an OAR results in the same NTCP as the original non-homogeneous distribution. The NTCP equation is therefore represented as a function of EUD. The inverse equation expresses EUD as a function of NTCP and is used to generate a table of EUD versus normal tissue complication probability for the Emami-Burman parameter fits as well as for OAR parameter sets from more recent data.