Empirical formula for the prediction of off axis ratios and isodose curves for a treatment planning system

Abstract

A mathematical model has been developed for prediction of off axis ratio (OAR), using Wood - Saxon term used to represent nuclear potential. This method has been satisfactorily applied for predicting OAR in case of 60Co γ-rays and high energy X-rays. Investigations are considered upto a depth of 25 cm in the case of 4MV LINAC for which measurements were carried out in our laboratory using indigenously developed Radiation Field Analyzer. For 60Co γ-rays as well as 6 and 18MV LINAC beams we could get off-axis profiles only upto 20 cm. The shift δ between measured and predicted OAR is within ±2 mm except for 20 cm depth near the falling edge of the penumbra, where it is 2.80 mm. Software has been developed in Visual Basic 6 on Windows platform to plot Isodose curves, which is based on the mathematical modeling of OAR and central axis percentage depth dose.

Analytical approach for determining beam profiles in water phantom of symmetric and asymmetric fields of wedged, blocked, and open photon beams

“…Since the photon source has a Gaussian distribution (normal distribution), the dose falloff around the geometric beam edge is sigmoid in shape, for which an error function has been employed. However, considering the fact that the Gaussian distribution alone, like the models proposed by Pal et al (7) The Kornelsen and Batho (23) model suffer from lack of electronic disequilibrium; therefore, a correction factor, , has been considered here.…”

“…The correction‐based algorithm ( 1 , 2 ) and the previous methods mentioned ( 7 , 23 ) need beam profile data for a large number of depths to predict the off‐axis ratio. In addition, a general problem with empirical scatter scaling techniques is that they are developed for open, not modulated beams, and there is a great need to improve these models to include effects from modulations (3) .…”

“…Various methods have been used for the prediction of off‐axis ratio for a symmetric open field. Fermi‐Dirac distribution function suggested by Kornelson and Young (6) and Wood‐Saxon term applied by Pal et al (7) represent the off‐axis ratio (OAR) in the SAD and SSD techniques, respectively. Usually these methods need data fitting at several depths.…”