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Delta Function Based Analysis of Why FFF Does Not Exhibit Any Dosimetric Advantage Over Flatten Beam

B Sarkar1*, A Manikandan2 , (1) AMRI Cancer Centre, Kolkata, ,(2) Apollo Proton Centre, Chennai,


(Sunday, 7/14/2019)  

Room: ePoster Forums

Purpose: To mathematically evaluate why FFF beam does not exhibit any dosimetric advantage over the flatten beam for small lesions or in out of field dose, except reduced MU.

Methods: Flatten beam can be approximated by a square function. FFF poses an additional (+20%) Gaussian crown. Due to MLC segmentation FFF/flatten beams were reduce to a squire function . The squire functions were converted to the Dirac delta function by Furrier transformation. A 10×10 cm2 FFF and flatten beam was mathematically segmented to obtain 8 mm width delta (δFFF/δFalten) functions. Equally spaced 36 δFFF and δFalten beams were placed on a 2.5 cm , 3 cm and 4 cm PTV with PTV_hot 1 cm, 1.5 and 2 cm respectively (+20% dose). Intensity integration was carried out using Matlab software in a cylindrical co-ordinate system.

Results: Dose conformity for PTV_hot was 0.86±0.11 and 0.84±0.11 for the FFF and flattened beams respectively. As for PTV the values were 0.73±0.09 and 0.76±0.13. The dose coverage index I98% (intensity) for both PTV_hot and PTV did not show any significant differences between FFF and flattened beams with the values being 98.3±1.3% and 97.7±1.0% for PTV_hot and 96.5±1.8% and 97.1±1.6% for PTV respectively. Average out-of-the-PTV dose falloff for FFF beam in the 100%-50% and 100%-20% regions were 6.5±1.7%/mm and 6.2±2.3%/mm respectively. FFF shows a slightly reduced (3.7%) and increased (1.7%) 50% and 20% isodose volume. Average un-normalised intensity (MU) for FFF was 18.3% higher than flatten beam.

Conclusion: MLC segmented un-intensity modulated beam failed to prove its dosimetric superiority over the flatten beam. Reduction in Intensity proportional to height of Gaussian. Segmentation nullify the beam specific characteristic reducing FFF/Flatten beam to δ function. Intensity modulated/unmodulated dose distribution is an angular summation of the δ functions hence does not yields no difference between FFF or flatten beam.


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