Derivation of equations to define inflection point and its analysis in flattening filter free photon beams based on the principle of polynomial function

Abstract

Purpose: The objective of this work is to (1) present a mechanism for calculating inflection points on profiles at various depths and field sizes, and (2) study the doses at the inflection points for various field sizes at depth of maximum dose (D_max) for flattening filter free (FFF) photon beam profiles.

Methods: Graphical representation was done on percentage of dose versus inflection points. Also, using the polynomial function, the author formulated equations for calculating spot-on inflection point on the profiles for both the 6MV and 10 MV energies for different field sizes at various depths.

Results: In a 10 MV FFF radiation beam, the dose at inflection point of the profile decreases as the field size increases. However, in 6MV FFF radiation beam, the dose at the inflection point initially increases with an increase in the field size up to 10 ×10 cm² and decreases after 10 ×10 cm². The polynomial function was fitted for both the 6 MV and 10 MV FFF beams for all field sizes and depths.

Conclusion: Polynomial function is one of the easiest ways of identifying the inflection point in FFF beam for various field sizes and depths. Graphical representation of dose versus inflection point for both FFF energies was derived.