Exact Integral Equation Determination with 3D Wedge Filter Convolution Factor Solution in Radiotherapy. Series of Computational, Programming 3D-2D-Dosimetry Simulations

Authors

  • F Casesnoves  MSc (Physics/Applied Mathematics) MD Computational Engineering Researcher

Keywords:

Radiation Dose, Attenuation Exponential Factor (AEF), Simulations, Nonlinear Optimization, Matrix Algebra, Spherical-Spatial Analytical Geometry, Series Approximations.

Abstract

Analytical and numerical Gaussian models have been used in recent decades for radiotherapy treatment planning software/calculations, to perform accurately radiation dose delivery –numerical, analytical, or numerical-analytical. The objective of this contribution was to obtain an exact dose delivery, 3D analytical-integral-equation solution, for the triple Gaussian model of wedge filters, since previous/initial 2D approximations of other authors, although correct, were not completely exact. The generic triple Gaussian model of Ulmer and Harder sets an Attenuation Exponential Factor, AEF, well approximated in 2 variables, namely, u and z. In this paper we set a detailed spatial-spherical geometry discussion/proof towards the determination of a 3D integral form of the delivery dose in water. In other words, with an AEF for magnitude-values of variables u,v, and z. Simulations, based on these new determinations were shown with sharp presentation of the numerical-computational software and functional programming series development. Computing encode techniques are explained with some practical examples for numerical radiotherapy calculus.

References

Principal References

 

  1. 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.ASME 2011 International Mechanical Eng Congress.Denver.USA.IMECE2011-65435.2011.
  2. Casesnoves,F.'Geometrical Determinations of Limit angle (LA) related to maximum Pencil-Beam Divergence Angle in Radiotherapy Wedges’.Peer-reviewed ASME Conference Paper.ASME 2012 International Mechanical Eng Congress.Houston.USA.IMECE2011-65435.2011.
  3. Casesnoves, F '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. April 6th 2013. Peer-Reviewed Poster Session on 6th April 2013. Sessions 1 and 3 with Poster Number 35. Page 15 of Conference Booklet.
  4. Casesnoves, F. Mathematical and Geometrical Formulation/Analysis for Beam Limit Divergence Angle in Radiotherapy Wedges. Peer-Reviewed International Engineering Article. International Journal of Engineering and Innovative Technology (IJEIT) Volume 3, Issue 7, January 2014. ISSN: 2277-3754 ISO 9001:2008 Certified. http://www.ijeit.com/archivedescription.php?id=27.
  5. Sharma, SC. Beam Modification Devices in Radiotherapy.Lecture at Radiotherapy Department,PGIMER.India.2008.
  6. Casesnoves, F.'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
  7. Casesnoves, F.‘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.
  8. Casesnoves, F. ‘Large-Scale Matlab Optimization Toolbox (MOT) Computing Methods in Radiotherapy Inverse Treatment Planning’. High Performance Computing Meeting. Nottingham University. January 2007.
  9. Casesnoves,F.‘A Computational Radiotherapy Optimization Method for Inverse Planning with Static Wedges’. High Performance Computing Conference.Nottingham University,.January 2008.
  10. Casesnoves, F.‘Radiotherapy Conformal Wedge Computational Simulations,Optimization Algorithms, and Exact Limit Angle Approach ‘. International Journal of Scientific Research in Science, Engineering and Technology. Publication Details, Published in : Volume 1 | Issue 2 | March-April – 2015 Date of Publication Print ISSN Online ISSN Date 2015-04-25 2395-1990 2394-4099. Journal Print ISSN : 2395-1990 | Online ISSN : 2394-4099. Page(s) Manuscript Number Publisher 353-362. IJSRSET152259 Technoscience Academy - See more at: http://ijsrset.com/IJSRSET152259.php#sthash.GXW6At87.dpuf. http://ijsrset.com/IJSRSET152259.php.Print ISSN : 2395-1990 Online ISSN : 2394-4099.
  11. Casesnoves, F.‘Radiotherapy Standard/Conformal Wedge IMRT-Beamlet Divergence Angle Limit Exact Method, Mathematical Formulation, and Bioengineering Applications’.International Article-Poster.Published in Proceedings of Conference. 41st Annual Northeast Bioengineering Conference. Rensselaer Polytechnic Institute. Troy, New York USA, April 17-19, 2015.
  12. Casesnoves, F.‘Radiotherapy Standard/Conformal Wedge IMRT-Beamlet Divergence Angle Limit Exact Method, Mathematical Formulation, and Bioengineering Applications’.IEEE (Institute for Electrical and Electronics Engineers), International Article-Poster.Published in http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=7117152. Date of Conference:17-19 April 2015 Page(s): 1 - 2 Print ISBN: 978-1-4799-8358-2 INSPEC Accession Number:15203213.
  13. Casesnoves, F.ABSTRACT-JOURNAL. ‘Radiotherapy Standard/Conformal Wedge IMRT-Beamlet Divergence Angle Limit Exact Method, Mathematical Formulation’. International Conference on Significant Advances in Biomedical Engineering. 252nd OMICS International Conference. April 2015. Volume 5, Issue 1. ISSN 2155-9538. Page 77. Philadelphia USA.

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International Journal of Scientific Research in Science, Engineering and Technology

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Published

2016-08-30

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Volume 2, Issue 4, July-August-2016

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Research Articles

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[1]
F Casesnoves, " Exact Integral Equation Determination with 3D Wedge Filter Convolution Factor Solution in Radiotherapy. Series of Computational, Programming 3D-2D-Dosimetry Simulations, International Journal of Scientific Research in Science, Engineering and Technology(IJSRSET), Print ISSN : 2395-1990, Online ISSN : 2394-4099, Volume 2, Issue 4, pp.699-716, July-August-2016.