Estimation of Inflection Point of Interpolated FFF Beam Data Profile from a Medical Linear Accelerator using Five Point Central Difference Method

Abstract

Background: Treating Malignant and Benign tumours with High energy Photon beam radiotherapy from Linear accelerator (Linac) is a common practice in Medicine. To deliver uniform doses throughout the field of irradiation, Flattening filters are used in the Linacs conventionally. But Modern radiotherapy techniques uses the same high energy photon beams in Flattening Filter Free (FFF) mode with very high dose rate delivery to make high dose gradient and faster dose delivery. Hence the analysis of these FFF beam profiles are extremely important from quality assurance perspective before delivering on the patients.
Aim: To determine the inflection points and Penumbra for 6MV FFF and 10MV FFF beam profiles through software coding and compare with the existing conventional graphical method.
Method & Materials: In plane and cross plane beam profiles of a 20x20sqcm field is taken as standard for analysing and comparing the symmetry and penumbra of 6MV FFF and 10MV FFF beams. Conventionally the tangents are drawn at the beam edges of the profiles and midpoint of tangents are fixed as Inflection points. In this study, by taking the second derivative and five point central deviation formula the inflection points are found and the coding to determine the infection points, thereby penumbra are written in python3. To see the consistency of data comparable with conventional method, 12 different profiles taken during different part of a year is studied and presented.
Results: Infection points and penumbra of 6MV FFF and 10 MV FFF beams determined by python programming is having less deviation compared with Conventional method. The values obtained are well within the tolerance limits set by national standards. The maximum variation of penumbra values for 6mv FFF beam in plane is 2.3 mm and cross plane is 2.6mm from conventional method. The same variation for 10FFF beam is 2mm for in plane and 2.5mm for cross plane. Inflection points variation also within 3% of manual methods for both the energies.