An Accurate Pencil Beam Model And Its Application In Treatment Planning For Heavy Ion Therapy

Heavy ion beam is the state of the art for radiation therapy,which is praised as the optimal radioactive ray in 21 century.It is a powerful tool for treating malignant tumors attributed to its evident advantages in physics and biology.Spot scanning system for delivery of charged particles is the development trend due to its flexibility and accuracy for highly conformal radiotherapy,and its facility for intensity modulated particle therapy(IMPT).In this technique,beam is laterally guided by scanning magnets in the same energy slice and is longitudinally guided with accelerator or range shifter for energy conversion.As a basis of this technique,the dose calculation accuracy of elementary beam is of vital importance for precise treatment.It can directly influence the calculation of the total dose in space,and can even affect the efficacy of the whole radiotherapy.Laterally Gaussian-shaped beam spot in intensity is generally used in particle radiotherapy,which is called pencil beam.Two-dimension single Gaussian model is usually used to calculate the lateral dose distribution of pencil beam in many primary version of treatment planning system(TPS)for particle therapy.However,it was discovered that the single Gaussian model dose not depict adequately the dose contributed from secondary particles especially for low dose envelope,which is located far away from the beam's central axis and mainly consists of particles undergoing multiple Coulomb scattering,as well as secondary particles produced by nuclear interactions.Although the dose level of the low dose envelope is extremely low and is under about 3 order of magnitude to the dose in the beam's central axis,it has been reported that even small deviations in characterizing the low dose envelope of individual pencil beams may accumulate to a clinically significant dose error when the dose contributions from all beam spots are superimposed in spot scanning technology,which cannot be neglected.However,the single Gaussian model is still used in our initial version of TPS,which does not take the low dose envelope into consideration.Therefore,it is urgent to improve the existing pencil beam model.Based on the GATE 7.1/GEANT4 10.01 MC simulation platform,the optimized therapy beam line of the Heavy Ion Research Facility in Lanzhou(HIRFL)at the Institute of Modern Physics(IMP),Chinese Academy of Sciences was adopted to obtain the three-dimensional dose distributions of carbon-ion pencil beams with various energies in water.Through a comprehensive analysis of the dose composition of the heavy ion pencil beam,the existence of the low dose envelope was confirmed,and the low dose envelope was mainly composed of proton for heavy ion pencil beam.Then,the influence of the secondary particles on the total dose of heavy ion pencil beam under different conditions was focused,and the results showed that this effect was the most obvious for the small fields at the medium depth with high energy beam.On the basis of the existing researches from others,a novel double Gaussian-logistic model based on the MC simulated data was proposed to depict the lateral dose distribution of heavy ion pencil beam in water.Then,Matlab was used for fitting the simulated data of single pencil beam based on the single,double,triple Gaussian models and our novel beam model,and the calculated parameters of different models were obtained.The accuracy of dose calculation with different pencil beam models was compared in the single pencil beams,monoenergetic fields and the Field Size Factor(FSF)curves.It was found that the triple Gaussian and the double Gaussian-logistic models were more precise to calculate the lateral dose distributions of pencil beam,not only in the region far away from the beam axis,but also in the central region of fields,especially at the medium penetration depths for small fields of high energy beams,where the secondary particles affected the total dose considerably.Compared with the triple Gaussian model,our newly-proposed beam model was on a par with it,even better than it in the most cases.Furthermore,based on the MC simulations and the iterative least square method used for dose optimization in spot-scanning beam delivery for charged particle therapy,the dosimetric effect of the low dose envelope and the accuracy of the dose calculation for carbon-ion pencil beams with the single,double,triple Gaussian models and the double Gaussian-logistic one were investigated in virtual homocentric spherical target volumes with different sizes,as well as the same-sized small spherical target volumes located at various depths in water.The results showed that the dosimetric effect of the low dose envelope increased in depth along the beam incidence direction for the same-sized spherical target volumes in the water tank,while it was irregular for the concentric spherical target volumes with the various diameters.The superiority of the double Gaussian-logistic model over the others was demonstrated further and manifested most obviously in small target volumes,especially at deeper depths.With our newly-proposed beam model,the calculation accuracy could be improved by 99.5%,98.0% and 40%,compared with the single,double and triple Gaussian models respectively,counted at the perpendicular central plane of the same-sized spherical targets in diameter of 3 cm,located at the depths of 186.5 mm.Furthermore,dose volume histograms(DVHs)of the spherical target volume in diameter of 5 cm and a hypothetical organ at risk(OAR)were also evaluated.It was found that imprecise description about the low dose envelope will lead to dose deficiency in the target volumes and wrong dose prediction in the OARs and our newly-proposed model can address this issue efficiently.Based on the double Gaussian-logistic model,various treatment planning methods were researched using the iterative least square method.TG119 test model were adopted to evaluate the results optimized by single field uniform dose(SFUD)and multifield optimization-intensity modulated particle treatment(MFO-IMPT).For SFUD,the weight of the single field should be adjusted constantly to meet both target conformity and the dose limit in OAR when designing the treatment planning.For MFO-IMPT,although the realization of the algorithm is slightly more complex than SFUD due to more factors need to be considered,its flexibility is more suitable for intensity modulated particle treatment and is a development tendency.Compared with SFUD,MFO-IMPT increased the dose conformity for target,and significantly improved sparing for OAR.The dose limit in OAR and the physician's priority for target and OAR were key in MFO-IMPT treatment planning,which could influence the total dose directly and should be adjusted constantly to meet a better result.This work lays a foundation for further developing practical and accurate pencil beam model,provides a reference for dose calculation method of existing planning system for heavy ion radiotherapy,and provides a theoretical basis for further optimizing and upgrading the treatment planning system.