Radiotherapy Conformal Wedge Computational Simulations,Optimization Algorithms, and Exact Limit Angle Approach
Keywords:
Dose,Attenuation Exponential Factor (AEF) Simulations, Nonlinear Optimization.Abstract
Radiotherapy wedges constitute an important group within the generic classification of so-called Beam Modification Devices (BMD). Wedges are subdivided into Static, Dynamic, and Omni Wedges sug-groups. The standard static wedge attenuates the beam progressively, in such a way that the dose delivery is higher at the thin side, and lower at the broader side. The slope of the inferior surface has the geometry of the hypotenuse of a triangle, formed by the lateral wall of the wedge. Conformal/Standard radiotherapy wedges [refs 3-7,Casesnoves 2005] present several bioengineering-industrial design difficulties to obtain an optimal beam/beamlets-IMRT upper-surface radiation distribution,avoiding that them could emerge undesirably from lateral walls instead the lower wedge plane.We calculated the improved exact beamlet limit-angle mathematical method for a standard/conformal wedge filter design.It was developed with basic mathematical algorithms,geometrical design,and Numerical Simulations linked to this mathematical formulation.All that was done using the AAA algorithm integral attenuation exponential factor [AEF],which modulates the convolution kernel of the integral dose delivery.Results comprise the geometrical design of the conformal wedge,showed in several sketches,and simulations with appropriate software. In addition,a series of geometrical formulas/tables for the beamlets limits,trigonometric AEF background,and mathematical formulation with the simulations of the AEF for a 2-steps conformal wedge are obtained.
References
[1] Ahnesjö A.,Saxner M., A. Trepp. 'A pencil beam model for photon dose calculations'. Med. Phys. 19, pp 263-273, 1992.
[2] Brahme, A. 'Development of Radiation Therapy Optimization'. Acta Oncologica Vol 39, No 5, 2000.
[3] Bortfeld, T,Hong T, Craft, D, Carlsson F. 'Multicriteria Optimization in Intensity-Modulated Radiation Therapy Treatment Planning for Locally Advanced Cancer of the Pancreatic Head'.International Journal of Radiation Oncology and Biology Physics. Vol 72, Issue 4.
[4] Censor Y, and S A Zenios. 'Parallel Optimization: Theory, Algorithms and Applications'. UOP, 1997.
[5] Casesnoves, F. ‘Determination of absorbed doses in common radiodiagnostic explorations’.5th National Meeting of Medical Physics.Madrid, Spain. September 1985.
reatment Planning’. Kuopio University. Radiotherapy Department of Kuopio University Hospital and Radiotherapy Physics Group. Finland. 2001.
[6] Casesnoves, F. ‘Large-Scale Matlab Optimization Toolbox (MOT) Computing Methods in Radiotherapy Inverse Treatment Planning’. High Performance Computing Meeting. Nottingham University. January 2007.
[7] Casesnoves, F. ‘A Computational Radiotherapy Optimization Method for Inverse Planning with Static Wedges’. High Performance Computing Conference. Nottingham University. January 2008.
[8].-Casesnoves, F 'Exact/Approximated Geometrical Determinations of IMRT Photon Pencil-Beam Path Through Alloy Static Wedges in Radiotherapy Using Anisothropic Analytic Algorithm (AAA)' peer-reviewed ASME Conference paper-poster. Proceedings of ASME 2011 IMECE (International Mechanical Engineering Conference) Conference. Denver, Nov 2011. CO, USA.2011.
[9] Casesnoves, F 'Geometrical Determinations of Limit Angle (LA) related to Maximum Pencil-Beam Divergence Angle in Radiotherapy Wedges' Casesnoves, F.Peer-reviewed ASME Conference Paper. ASME 2012 International Mechanical Engineering Congress.Houston.Nov 2012.USA.IMECE2012-86638.
[10.1] 'A Conformal Radiotherapy Wedge Filter Design. Computational and Mathematical Model/Simulation’ Casesnoves, F. Peer-Reviewed Poster IEEE (Institute for Electrical and Electronics Engineers), Northeast Bioengineering Conference. Syracuse New York, USA. Presented in the Peer-Reviewed Poster Session on 6th April 2013. Sessions 1 and 3 with Poster Number 35. Page 15 of Conference Booklet. April 6th 2013.
[10.2] 'Geometrical determinations of IMRT photon pencil-beam path in radiotherapy wedges and limit divergence angle with the Anisotropic Analytic Algorithm (AAA)' Casesnoves, F. Peer-Reviewed scientific paper, both Print and online. International Journal of Cancer Therapy and Oncology 2014; 2(3):02031. DOI: 10.14319/ijcto.0203.1
[10.3]-‘Radiotherapy Conformal Wedge Computational Simulations and Nonlinear Optimization Algorithms’. Casesnoves, F. Peer-reviewed Article, Special Double-Blind Peer-reviewed paper by International Scientific Board with contributed talk. Official Proceedings of Bio- and Medical Informatics and Cybernetics: BMIC 2014 in the context of The 18th Multi-conference on Systemics, Cybernetics and Informatics: WMSCI 2014 July 15 - 18, 2014 – Orlando, Florida, USA.
[11] Censor, Y. 'Mathematical Optimization for the Inverse problem of Intensity-Modulated Radiation Therapy'. Laboratory Report, Department of Mathematics, University of Haifa, Israel, 2005.
[12] Capizzello A, Tsekeris PG, Pakos EE, Papathanasopoulou V, Pitouli EJ. 'Adjuvant Chemo-Radiotherapy in Patients with Gastric Cancer'. Indian Journal of Cancer, Vol 43, Number 4. 2006.
[13] Do, SY, David A, Bush Jerry D Slater. 'Comorbidity-Adjusted Survival in Early Stage Lung Cancer Patients Treated with Hypofractioned Proton Therapy'. Journal of Oncology, Vol 2010.
[14] Ehrgott, M, Burjony, M. 'Radiation Therapy Planning by Multicriteria Optimization'. Department of Engineering Science. University of Auckland. New Zealand.
[15] Ezzel, G A. 'Genetic and geometric optimization of three dimensional radiation therapy treatment planning'. Med. Phys.23, 293-305.1996.
[16] Effective Health Care, Number 13. 'Comparative Efectiveness of Therapies for Clinically Localized Prostate cancer'. 2008.
[17] Haas, O.C.L.'Radiotherapy treatment planning, new systems approaches'. Springer Engineering.1998.
[18] Hansen, P. 'Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion'. SIAM monographs on mathematical modelling and computation, 1998.
[19] Hashemiparast, SM, Fallahgoul, H. Modified Gauss quadrature for ill-posed integral transform. International Journal of Mathematics and Computation. Vol 13, No. D11. 2011.
[20] Johansson, K-A , Mattsson S, Brahme A, Turesson I. 'Radiation Therapy Dose Delivery'. Acta Oncologica Vol 42, No 2, 2003.
[21] Kufer,K.H. Hamacher HW, Bortfeld T.. 'A multicriteria optimisation approach for inverse radiotherapy planning'. University of Kaiserslautern, Germany.
[22] Kirsch, A. 'An introduction to the Mathematical Theory of Inverse Problems'. Spinger Applied Mathematical Sciences, 1996.
[23] Luenberger D G. 'Linear and Nonlinear Programming 2nd edition'. Addison-Wesley, 1989.
[24] Moczko, JA, Roszak, A. 'Application of Mathematical Modeling in Survival Time Prediction for Females with Advanced Cervical cancer treated Radio-chemotherapy'. Computational Methods in science and Technology, 12 (2). 2006.
[25] Numrich, RW. 'The computational energy spectrum of a program as it executes'. Journal of Supercomputing, 52. 2010.
[26] Ragaz, J, and collaborators. 'Loco-regional Radiation Therapy in Patients with High-risk Breast Cancer Receiving Adjuvant Chemotherapy: 20-Year Results of the Columbia Randomized Trial'. Journal of National Cancer Institute, Vol 97, Number 2. 2005.
[27] Steuer, R. 'Multiple Criteria Optimization:Theory, Computation and Application'. Wiley, 1986.
[28] Spirou, S.V. and Chui, C.S. 'A gradient inverse planning algorithm with dose-volume constraints'. Med. Phys. 25, 321-323.1998.
[29] Sharma, SC. 'Beam Modification Devices in Radiotherapy'. Lecture at Radiotherapy Department, PGIMER. 2008.
[29.1].-Sievinen J, Waldemar U, Kaissl W. AAA Photon Dose Calculation Model in Eclipse™.Varian Medical Systems Report.Rad #7170A.
[30] Ulmer, W, and Harder, D. 'A triple Gaussian pencil beam model for photon beam treatment planning'. Med. Phys. 5, 25-30, 1995.
[31] Ulmer, W, and Harder, D. 'Applications of a triple Gaussian pencil beam model for photon beam treatment planning'. Med. Phys. 6, 68-74, 1996.
[32] Ulmer, W, Pyyry J, Kaissl W. 'A 3D photon superposition/convolution algorithm and its foundation on results of Monte Carlo calculations'. Phys. Med. Biol. 50, 2005.
[33] Ulmer, W . Laboratory Report. Phys. Med. Biol. 50, 2005.
[34] Ulmer, W, and Harder, D. 'Applications of the triple Gaussian Photon Pencil Beam Model to irregular Fields, dynamical Collimators and circular Fields'. Phys. Med. Biol.1997.
[35] Ulmer, W, Schaffner, B. 'Foundation of an analytical proton beamlet model for inclusion in a general proton dose calculation system'. Radiation Physics and
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