النماذج الرياضية المستخدمة لتخطيط العلاج الموضعي خوارزميات حساب الجرعة

Morén B, Larsson T, Tedgren AC, Mathematical optimization of high dose-rate brachytherapy-derivation of a linear penalty model from a dose-volume model. Phys Med Biol. 2018; 63(6): 065011.

Hong W, Zhang G. Simulation analysis for tumor radiotherapy based on three-component mathematical models. J Appl Clin Med Phys. 2019; 20(3): 22–26.

Ahmed I, Nowrin H, Dhar H, Stopping power and range calculations of protons in human tissues. Baghdad Sci J. 2020; 17(4): 1223 – 1233. https://doi.org/10.21123/bsj.2020.17.4.1223

Ali RMKM, Mraity HAAB. Estimation of radiation dose from most common pediatrics radiographic examinations within main central hospitals in Najaf City, Iraq. Baghdad Sci J. 2022; 19(3): 654 – 659. https://doi.org/10.21123/bsj.2022.19.3.0654

Galea F, Roucairol C. Mathematical modelling of HDR/PDR brachytherapy treatment planning problems. 2004.

Kanwar S, Kumar SA, Shukla P. Bio-Medical Applications of different radionuclides. Ann Romanian Soc Cell Biol. 2021; 25(4): 11676-11681.

https://www.researchgate.net/publication/255533497_Mathematical_modelling_of_HDRPDR_brachytherapy_treatment_planning_problems

Rihan F A, Alsakaji H J. Dynamics of a stochastic delay differential model for COVID-19 infection with asymptomatic infected and interacting people: Case study in the UAE, Results Phys, 2021 104658.

Rihan F A, Alsakaji H J, Rajivganthi C. Rajivganthi Stochastic SIRC epidemic model with time-delay for COVID-19, Adv Differ Equ. 2020: 502 https://dx.doi.org/10.1186/s13662-020-02964-8 . Epub 2020 Sep 18.

Elcim Y, Dirican B, Yavas O. Dosimetric comparison of pencil beam and Monte Carlo algorithms in conformal lung radiotherapy. J Appl Clin Med Phys. 2018; 19(5): 616–624.

Pourkaveh M, Haghparast A, Eivazi MT, Ghazikhanlu Sani K. Optimization of Clarkson’s Method for Calculating Absorbed Dose under Compensator Filters used in Intensity-modulated Radiation Therapy. J Biomed Phys Eng. 2020; 10(5): 575-582.

Shahban M, Waqar M, Soomro Q, Qasim M, Ijaz U. Absorbed Dose Calculation In Irregular Blocked Radiation Fields: Evaluation of Clarkson’s Sector Integration Method for Radiation Fields Commonly Used in Conventional Radiotherapy. Iran J Med Phys. Jan 2019; 16(1): 103-111.

Andreo P. Monte Carlo simulations in radiotherapy dosimetry. Radiat Oncol. 2018; 13(1): 121.

Korhonen L. Methods for dose calculation and beam characterization in external photon beam radiotherapy. Dissertation for the degree of Doctor of Science in Technology. Helsinki University of Technology; 2009.

Zhu J, Yin FF, Kim JH. Point dose verification for intensity modulated radiosurgery using Clarkson’s method. Med Phys. 2003; 30: 2218-21.

Muralidhar KR, Murthy NP, Raju AK, Sresty NVNM. Comparative study of convolution, superposition, and fast superposition algorithms in conventional radiotherapy, three-dimensional conformal radiotherapy, and intensity modulated radiotherapy techniques for various sites, done on CMS XIO planning system. J Med Phys. 2009; 34(1): 12–22.

Tajiri M, Maeda T, Koba Y, Isobe Y, Kuroiwa T, Fukuda S, et al. Calculation method using Clarkson integration for the physical dose at the center of the spread-out Bragg peak in carbon-ion radiotherapy. Med Phys 2013; 40(7): 071733.

Vanderstraeten B, Reynaert N, Paelinck L, Madani I, De Wagter C, De Gersem W, et al. Accuracy of patient dose calculation for lung IMRT: A comparison of Monte Carlo, convolution/superposition, and pencil beam computations. Med Phys. 2006; 33(9): 3149-3158.

Kyeremeh PO, Nani EK, Addison EKT, Doughan F, Acquah GF, Tagoe SA, et al. Implementation of 3-D Anisotropy Corrected Fast Fourier Transform Dose Calculation around Brachytherapy Seeds. Int J Sci Environ Technol. 2012; 2(3): 116-124.

Nani EK, Francescon P, Cora S, Amuasi JH, Akaho EHK. (2009). Fast Fourier Transform in the dosimetry of brachytherapy. Int At Energy Agency. ICRP Report R148030. Vienna. 2009.

Kemmerer T, Lahanas M, Baltas D, Zamboglou N. Dose-volume histograms computation comparisons using conventional methods and optimized fast Fourier transforms algorithms for brachytherapy. Med Phys. 2000; 27(10): 2343-2356. https://dx.doi.org/10.1118/1.1312810.

Mathews S, Azariah MB, Mohandas S, Menon SV, George P, Jayaprakash PG. Comparison of volume doses from conventional two-dimensional brachytherapy with corresponding doses from three-dimensional magnetic resonance imaging-based brachytherapy in carcinoma cervix. J Cancer Res Ther. 2019; 15(6): 1332-1337.

Derek Liu,Ron S. Sloboda, Fast dose kernel interpolation using Fourier transform with application to permanent prostate brachytherapy dosimetry. Med Phys. 8 April 2014; 41(5):051701. https://dx.doi.org/10.1118/1.4870440 .

Fu Q, Xu Y, Zuo J, An J, Huang M, Yang X, et al. Comparison of two inverse planning algorithms for cervical cancer brachytherapy. J Appl Clin Med Phys. 2021 Mar; 22(3): 157–165.

Lessard E, Pouliot J. Inverse planning anatomy-based dose optimization for HDR-brachytherapy of the prostate using fast simulated annealing algorithm and dedicated objective function. Med Phys. 2001; 28(5): 773-779. https://dx.doi.org/10.1118/1.1368127 .

Wang X, Wang P, Tang B, Kang S, Hou Q, Wu Z, et al. An Inverse Dose Optimization Algorithm for Three-Dimensional Brachytherapy. Front Oncol. 2020;10: https://dx.doi.org/10.3389/fonc.2020.564580.

Sharpe MB, Battista JJ. Dose calculations using convolution and superposition principles: the orientation of dose spread kernels in divergent x-ray beams. Med Phys. 1993; 20(6): 1685-94.

Barik BK, Dhar SS, Singh R, Mandal A, Aggarwal LM, Shahi UP, et al. Dose optimization comparison study of inverse planning simulated annealing [IPSA] and hybrid inverse planning optimization [HIPO] in interstitial brachytherapy of head and neck cancer. J Med Imaging Radiat Sci. 2021; 52(3): 417-421.

Fröhlich G, Geszti G, Vízkeleti J, Ágoston P, Polgár C, Major T. Dosimetric comparison of inverse optimisation methods versus forward optimisation in HDR brachytherapy of breast, cervical and prostate cancer. Strahlenther Onkol 2019; 195(11): 991-1000.