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Optimisation quadratique et géométrique de problèmes de dosimétrie inverse

Yann Menguy 1
1 TIMC-GMCAO - Gestes Medico-chirurgicaux Assistés par Ordinateur
TIMC - Techniques de l'Ingénierie Médicale et de la Complexité - Informatique, Mathématiques et Applications, Grenoble - UMR 5525
Abstract : Radiation therapy uses the energy imparted by X-rays, usually called dose, in order to kill tumours: this method offers the advantage to be non-invasive. Because all parts of the body get some dose, it requires, however, a great prudence. The dosimetric planning is necessary for concentrating the dose in the tumour and saving healthy tissues as far as possible. This task is performed by radiophysicists, who determine a treatment plan after several tests. The aim of our work, which has been applied to the treatment of the prostate, is to automate this stage. We deal first with the dose calculation problem. We recall the main methods, and detail particularly one of them, the Clarkson method. Then we build, for a circular field, a dose model based on spline functions and using tridimensional experimental data. We compare this model to multilinear interpolations of the data. In order to choose a central target within the prostate, we deal with the problem of finding the smallest ball enclosing a finite number of points. We develop an algorithm based on geometric properties, which represents an extension of the well-known Chrystal-Peirce algorithm to all dimensions. We prove that this algorithm stops after a finite number of iterations and present many experimental tests in order to show its efficiency. Finally, we display its analytical side and prove that it is in fact a subgradient algorithm. The last part of this thesis is devoted to the treatment plan optimization. We decide to keep a multi-beams treatment, and define the problem as the minimization of a function with several constraints. We compare the results for different shapes of beams and note a real improvement in comparison with present treatments.
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Submitted on : Monday, February 23, 2004 - 4:19:51 PM
Last modification on : Tuesday, November 24, 2020 - 4:18:04 PM
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  • HAL Id : tel-00005003, version 1



Yann Menguy. Optimisation quadratique et géométrique de problèmes de dosimétrie inverse. Autre [cs.OH]. Université Joseph-Fourier - Grenoble I, 1996. Français. ⟨tel-00005003⟩



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