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The determination of virtual source position using convergent anti-trigonometric functions (arcCOS and arcSIN) method for scanning-passive scatter beam in carbon ion therapy

Ye Yan-Cheng, Zhang Wen-Hua, Wang Jian, Zhang Yan-Shan, Wu Jia-Ming

Polish Journal of Medical Physics and Engineering

2023

Vol. 29, Iss. 1

10--25

Introduction: We developed a convergent trigonometric functions technique (arcCOS, arcSIN) capable of dealing with the virtual source position delivered by different carbon ion energies from the pattern of scanning-passive scatter beam in this study. Materials and Methods: A home-made large-format CMOS sensor and Gaf Chromic EBT3 films were used for the virtual source position measurement. The Gaf films were embedded in a self-designed rectangular plastic frame to tighten the films and set up on a treatment couch for irradiation in the air with the film perpendicular to the carbon ion beam at the nominal source-axis-distance (SAD) as well as upstream and downstream from the SAD. The horizontal carbon ion beam with 5 energies at a machine opening field size was carried out in this study. The virtual source position was determined with a convergent arcCOS and arcSIN methods and compared with the linear regression by back-projecting the FWHM to zero at a distance upstream from the various source-film-distance. Results: The film FWHM measurement error of 0.5 mm (the large-format CMOS detectors was in pixel, a pixel equals 0.5 mm) leads to 1×10-3% deviation of α(cACOS and cASIN) at every assumed virtual source position. The overall uncertainty for the reproducibility of the calculated virtual source position by the assumed t in the vertical and horizontal directions amounts to 0.1%. The errors of calculated virtual source position by assumed t with back projecting FWHM to zero methods were within 1.1 ± 0.001, p = 0.033. The distance of virtual source positions is decreased from SAD with high to low energy. Conclusion: We have developed a technique capable of dealing with the virtual source position with a convergent arcCOS and arcSIN methods to avoid any manual measurement mistakes in scanning-passive scatter carbon ion beam. The method for investigating the virtual source position in the carbon ion beam in this study can also be used for external electrons and the proton.

Empirical method for modeling the percent depth dose curves of electron beam in radiation therapy

Chen Dong-Ji, Zhang Yan-Shan, Ye Yan-Cheng, Wu Jia-Ming

Polish Journal of Medical Physics and Engineering

2021

Vol. 27, Iss. 4

315--321

Introduction: This study presents an empirical method to model the electron beam percent depth dose curve (PDD) using the primary and tail functions in radiation therapy. The modeling parameters N and n can be used to derive the depth relative stopping power of the electron energy in radiation therapy. Methods and Materials: The electrons PDD curves were modeled with the primary-tail function in this study. The primary function included exponential function and main parameters of N, µ while the tail function was composed by a sigmoid function with the main parameter of n. The PDD for five electron energies were modeled by the primary and tail function by adjusting the parameters of N, µ and n. The R50 and Rp can be derived from the modeled straight line of 80% to 20% region of PDD. The same electron energy with different cone sizes was also modeled with the primary-tail function. The stopping power for different electron energies at different depths can also be derived from the parameters of N, µ and n. Percent ionization depth curve can then be derived from the percent depth dose by dividing its depth relevant stopping power for comparing with the original water phantom measurement. Results: The main parameters N, n increase, but µ decreases in primary-tail function when electron energy increased. The relationship of parameters n, N and LN(-µ) with electron energy are n = 31.667 E0 - 88, N = 0.9975 E0 - 2.8535, LN(-µ) = -0.1355 E0 - 6.0986, respectively. Stopping power of different electron energy can be derived from n and N with the equation: stopping power = (−0.042 ln NE0 + 1.072)e(−n−E0·5·10−5+0.0381·d), where d is the depth in water. Percent depth dose was derived from the percent reading curve by multiplying the stopping power relevant to the depth in water at certain electron energy. Conclusion: The PDD of electrons at different energies and field sizes can be modeled with an empirical model to deal with the stopping power calculation. The primary-tail equation provides a uncomplicated solution than a pencil beam or other numerical algorism for investigators to research the behavior of electron beam in radiation therapy.