Rozprawy doktorskie na temat „Multileaf collimator”

Bibliography: leaves 241-250. A multileaf collimator for radiation therapy has been designed that splits each leaf bank into two vertically displaced assemblies or levels with each level consisting of alternate leaves and leaf spaces. The radiation profiles transmitted for image formation through the collimator design were investigated to examine their dependence on the collimator design features.

Intensity Modulated Radiation Therapy (IMRT) is a modern radiotherapy treatment technique used to obtain highly conformal dose distributions. The delivery of IMRT is commonly achieved through the use of a multileaf collimator (MLC). One of the hindrances at present to the widespread use of IMRT is the increased time required for its planning, delivery and verification. In this thesis one particular method of MLC based IMRT, known as Static Multileaf Collimator based IMRT (SMLC-IMRT), has been studied along with methods for improving it???s delivery efficiency. The properties of an MLC commonly used in SMLC-IMRT have been characterised. The potential ramifications of these properties on the dosimetric accuracy of the delivered IMRT field were also investigated. An Interactive Leaf Sequencing (ILS) program was developed that allowed for the manipulation and processing of intensity maps using a variety of methods. The objective of each method was to improve the delivery efficiency whilst maintaining the dosimetric quality of the IMRT treatment. The different methods investigated were collimator angle optimisation, filtration, and intensity level optimisation. The collimator was optimised by identifying the angle at which the minimum monitor unit???s (MU???s) were required when using a sliding-window delivery method. A Savitzky-Golay filter was applied to random intensity maps and suitable filtration parameters identified for filtering clinical IMRT fields, and the intensity levels were optimised based on a deviation threshold. The deviation threshold identified the acceptable level of difference tolerable between the original and modified intensity map. Several IMRT cases were investigated and the impact of each the methods on MU???s, segments and dose distribution observed. As the complexity of IMRT fields increases the dosimetric impact of the MLC properties increases. Complex SMLC-IMRT fields require longer delivery times due to the increased number of MU???s and segments. Collimator optimisation was shown to be a fast and effective means of improving delivery efficiency with negligible dosimetric change to the optimised plan. Modifying intensity maps by applying a filter and optimising the intensity levels did reduce the complexity and improve the delivery efficiency, but also required a dosimetric compromise of the optimised plan.

Dissertação para obtenção do Grau de Doutor em Engenharia Biomédica
One of the primary requirements for successful radiotherapy treatments is the accurate calculation of dose distributions in the treatment planning process. Monte Carlo (MC) dose calculation algorithms are currently recognized as the most accurate method to meet this requirement and to increase even further dose accuracy. The improvements in computer processor technology and the development of variance reduction techniques for calculations have led to the recent implementation and use of MC algorithms for radiotherapy treatment planning at many clinical departments. The work conducting to the present thesis consists of several dosimetric studies which demonstrate the potential use of MC dose calculations as a robust tool of dose verification in two different fields of external radiotherapy: electron and photon beam radiotherapy. The first purpose of these studies is to evaluate dose distributions in challenging situations where conventional dose calculation algorithms have shown some limitations and it is very difficult to measure using typical clinical dosimetric procedures, namely in regions containing tissue inhomogeneities, such as air cavities and bones, and in superficial regions. A second goal of the present work is to use MC simulations to provide a detailed characterization of photon beams collimated by a multileaf collimator (MLC) in order to assess the dosimetric influences of these devices for the MC modeling of Intensity Modulated Radiotherapy (IMRT) plans. Detailed MC model of a Varian 2100 C/D linear accelerator and the Millenium MLC incorporated in the treatment head is accurately verified against measurements performed with ionization chambers and radiographic films. Finally, it is also an aim of this thesis to make a contribution for solving one of the current problems associated with the implementation and use of the MC method for radiotherapy treatment planning, namely the clinical impact of converting dose-to-medium to dose-to-water in treatment planning and dosimetric evaluation. For this purpose, prostate IMRT plans previously generated by a conventional dose algorithm are validated with the MC method using an alternative method, which involves the use of non-standard CT conversion ramps to create CT-based simulation phantoms.
Fundação para a Ciência e Tecnologia; Centro de Física Nuclear da Universidade de Lisboa

The dosimetric characteristics of a standard Varian 52-leaf multileaf collimator (MLC) and BrainLAB m3 micro-multileaf collimator (micro-MLC) have been investigated for square, rectangular, and irregular fields for 6 MV and 18 MV photon beams provided by a Varian Clinac 2300 C/D linear accelerator (linac). The percentage depth dose data and the conventional collimator factor are unaffected by the addition of MLC or micro-MLC shaped field unless, in the latter case, the tertiary field is much less than the jaw setting. However, relative dose factors for a given MLC or micro-MLC field size depend on the jaw setting. The penumbra is generally sharpest for fields defined by the micro-MLC and the least sharp for fields defined by the MLC. Average transmission values were found to be between 1.5% and 2.5%. Comparison and evaluation of two treatments, one delivered using the MLC and the other using the micro-MLC, for the same radiosurgical target volume are described.

En proton thérapie, la technique de balayage, permet de traiter efficacement le patient vis à vis de l'irradiation de la tumeur et la protection des tissus sains. Ces bénéfices dosimétriques peuvent cependant être grandement dégradés par les mouvements intra-fraction. Par conséquent, l'étude de méthodes d'atténuation ou d'adaptation est nécessaire. C'est pour cela, que nous avons développé un logiciel ”open-source” de calcul et d'évaluation de dose en 4D, MSPT (Motion Simulator for Proton Therapy), pour la technique de balayage. Son but est de mettre en avant l'impact des mouvements intra-fraction en calculant la répartition de dose dans le patient. En outre, l'utilisation de MSPT nous a permis de mettre au point et de proposer une nouvelle méthode d'atténuation du mouvement basée sur l'ajustement du poids du faisceau quand celui-ci balaye la tumeur. En photon thérapie, un enjeu principal pour les traitements délivrés à l'aide de collimateurs multi-lames (MLC) consiste à trouver un ensemble de configurations du MLC permettant d'irradier correctement la tumeur. L'efficacité d'un tel ensemble se mesure par le total beam-on time et le total setup time. Dans notre étude, nous nous intéressons à la minimisation de ces critères, d'un point de vue algorithmique, pour de nouvelles technologies de MLC: le MLC rotatif et le MLC à double couche. De plus, nous proposons un algorithme d'approximation pour trouver un ensemble de configurations minimisant le total beam-on time pour le MLC rotatif
In proton therapy, the delivery method named spot scanning, can provide a particularly efficient treatment in terms of tumor coverage and healthy tissues protection. The dosimetric benefits of proton therapy may be greatly degraded due to intra-fraction motions. Hence, the study of mitigation or adaptive methods is necessary. For this purpose, we developed an open-source 4D dose computation and evaluation software, MSPT (Motion Simulator for Proton Therapy), for the spot-scanning delivery technique. It aims at highlighting the impact of intra-fraction motions during a treatment delivery by computing the dose distribution in the moving patient. In addition, the use of MSPT allowed us to develop and propose a new motion mitigation strategy based on the adjustment of the beam's weight when the proton beam is scanning across the tumor. In photon therapy, a main concern for deliveries using a multileaf collimator (MLC) relies on finding a series of MLC configurations to deliver properly the treatment. The efficiency of such series is measured by the total beam-on time and the total setup time. In our work, we study the minimization of these efficiency criteria from an algorithmic point of view, for new variants of MLCs: the rotating MLC and the dual-layer MLC. In addition, we propose an approximation algorithm to find a series of configurations that minimizes the total beam-on time for the rotating MLC

A model based on Monte Carlo techniques is developed to transport ionising radiation through the radiation head of a 6MV linear accelerator fitted with multileaf collimators Major emphasis is given to the detailed geometrical descriptiqn of the multileaf collimator. The model produces dose distributions in water from photon beams defined by the jaws and the multileaf collimator. The model accounts for contaminant electrons in the photon beam, off-axis x-ray radiation originating at the collimator and the transmission and penumbra effects of the side planes and front face of the leaves in the multileaf collimator Dose distributions in water calculated by the model are compared with experiment using lonisation chambers, diodes and film and found to be within 1 5% The transmission and the penumbra of the multileaf collimator leaves calculated by the Monte Carlo model are compared with experiment and found to be in good agreement

A Dissertation submitted to the faculty of science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science. May 2016
The multileaf collimator (MLC) system introduction into clinical linear accelerators (Linacs), facilitated computer-control and verification of complex treatment, and results in an increase in patient set up speed. An MLC system thus requires a re-evaluation of the quality assurance (QA) requirements for beam collimation. This study investigated, developed, performed and evaluated QA effors for conventional MLCs with the aim to evaluate the efficacy and reproducibility of the quality control (QC) procedures with different detectors. The performance of MLCs for an Elekta (Livingstone hospital) and siemens (Charlotte Maxeke Johannesburg academic hospital) linac were examined. The major QC procedures studied were leaf matching, leaf position accuracy, intraleaf leakage and transmission through abutting leaves. Three portal imaging devices (radiographic film, radiochromic film and an electronic portal imaging device) and a PTW LA48 linear array were used as detectors. Record and verify data management systems were used to set up and execute the procedures. The calibration of all the potal imaging devices was also performed. The calibration procedure of the portal imaging devices is linac specific in execution. The profiles obtained indicated consistency across device and time. A combined single execution procedure is viable and reproducible on all platforms. The results show tha the calibration of imaging devices is of great importance. The MLC design influences the range and extent of QC that can be performed. This may impact on the accuracy with advanced technologies requiring high conformity and reproducible leaf movement, can be deliverd. Imaging devices each have specific resource requirement issues affecting the efficacy of their use.

碩士
國立清華大學
工業工程與工程管理學系
96
Radiation therapy is a common treatment for some specific tumors in the treatment of cancer now. In recent years, there has been a new development in radiation therapy, which is called intensity modulated radiation therapy (IMRT). The outstanding advantage of IMRT is it can modulate the intensity of the radiation beam effectively, and focus a higher radiation dose on the tumor while minimizing radiation exposure to surrounding normal tissues. Multileaf Collimator (MLC) is one of the essential equipments when IMRT is executed. MLC is composed by several pairs of leaves, and it can achieve the objective of intensity modulated by series moving of leaves. Although the medical radiation therapy has been studied for a long time, the efficiency of MLC operations can be further improved. For a radiation therapy plan, a long total delivery time may not only diminish the quality of therapy but also cause uncomfortable perception to a patient. Three criteria which effect total delivery time are number of monitor units (MUs), number of segments, and distance of leaf traveled. This study aims to develop a three-stage-optimization algorithm to achieve a shortest total delivery time. We minimize the number of monitor units at first. Then we minimize the number of segments with minimum number of monitor units. Finally, we try to shorten the distance of leaf traveled when minimum number of monitor units and segments are used. According to the outcomes of series of experiments, we show that the performance of our algorithm is better than previous works significantly to solve a radiation therapy plan.

This thesis describes the development and implementation of a novel method of delivering intensity modulated radiation therapy (IMRT) that provides greater accuracy and spatial resolution than currently available methods. Through improvements in multileaf collimator (MLC) based fluence generation, a dose distribution may be generated that conforms more closely to the tumour target volume. Healthy tissue surrounding the target volume will therefore receive less dose, reducing the probability of side effects and allowing the physician to increase the prescribed tumour dose (dose escalation). MLC based IMRT techniques are well established but suffer several physical limitations. Dosimetric spatial resolution is limited by the MLC leaf width, interleaf leakage and tongue-and-groove effects degrade dosimetric accuracy and the range of leaf motion limits the maximum deliverable field size. Based on observations from a linear systems model of dosimetric spatial resolution degradation it is hypothesized that, by rotating the entire MLC between each sub-field, improvements will be obtained in spatial resolution, dosimetric accuracy and maximum deliverable field size. To generate arbitrary fluence maps in this way, a series of unique algorithms were developed that are capable of determining the necessary rotated MLC segments. These IMRT fields may be delivered statically (with the collimator rotating to a new position in between sub-fields) or dynamically (with the collimator rotating and leaves moving simultaneously during irradiation). A full description of the rotational leaf motion algorithms is provided. An analysis of the rotating leaf motion calculation algorithms with focus on radiation efficiency, the range of collimator rotation and number of segments is provided. The mechanical and radiation producing characteristics of standard linear accelerators under collimator rotation conditions are also investigated. The technique is evaluated by characterizing the ability of the algorithms to generate rotating leaf sequences for desired fluence maps. Comparisons are also made between our method and conventional sliding window and step-and-shoot techniques. Results show improvements in spatial resolution, reduced interleaf effects and maximum deliverable field size over conventional techniques. Clinical application of these enhancements can be realized immediately with static rotational delivery although improved control of the MLC will be required for dynamic delivery.

碩士
國立陽明大學
放射醫學科學研究所
90
Dose uniformity is directly related to tumor control probability (TCP) and normal tissue complication probability (NTCP). An ideal situation is one in which a uniform high dose is focused on the tumor target region and normal tissue surrounding the target volume receives minimal radiation. Dose distribution and uniformity must take into account the irregular contours and density changes within the body, especially the head, neck, and breast. A physical wedge has been used to compensate for irregular contours during traditional treatment, but a physical wedge is limited by its fixed angle and size. In addition, it cannot compensate for two dimensions simultaneously. We have developed a two-dimensional dynamic wedge to overcome these limitations A wedge-shaped dose map was calculated for this study. The dose map was transferred to a fluence map in a CadPlan treatment planning program to generate a multileaf motion file. We created 6 dynamic wedges and verified them by phantom measurements. The maximum differences in the beam profiles between the calculated values and the measured values were 1.8%, 1.7%, and -1.8% when measured for wedges at 45 degrees, 15 degrees, and 38 degrees in the X direction, and -2.6% and -2.3% when measured for wedges at 20 and 30 degrees in the Y direction. The differences between the isodose curves for the two-dimensional dynamic wedges were less than 2% and 2mm. Absolute doses also showed good agreement between calculated and measured values in this study such that all differences were less than 3%. The two-dimensional dynamic wedge developed in this study may be valuable for simulating isodose curves and can be used for CadPlan treatment planning which is currently used in many hospitals.

碩士
國立高雄應用科技大學
電機工程系博碩士班
104
Purpose: To evaluate and quantify the dosimetric and physical benefits on CyberKnife M6 for stereotactic radiosurgery (SRS). Materials and methods: Three different collimators treatment technologies were analyzed, including the treatment with a dynamic multileaf collimator (MLC), a fixed cone collimator, and a variable aperture collimator (IRIS). We aimed to analyze the physical characteristics of output factors and physical profiles of different field sizes. In order to apply these physical characteristics to clinical treatment, this study used a Rando head phantom to simulate various changes of brain tumors. Then, we analyzed and compared the difference of treatment quality among these three collimators treatment technologies by applying the sequential optimization by Ray tracing and finite size pencil beam (FSPB) algorithm on the Multiplan treatment planning system. Results: At 800 mm SAD, the differences for the output factors are as follows: 25.88% for 5mm-cone, 3.4% for 7.5mm-cone, and less than 1% for others. For radius check, the value of maximum difference is 1.0 mm, which stands on the cone size of 40 and 50 mm. For the penumbra test, the biggest difference is -0.5mm which stands on 60 mm cone size. Regarding treatment planning, evaluation under the PTV coverage was reached that the 95% isodose line encompassed 95% of the PTV. For the shape condition of regular tumor analysis, the absorbed dose of normal tissue R30~R100 with MLC treatment was less than the treatment with the fixed cone collimator and IRIS. The treatment numbers of MU and treatment time were reduced by 78% and 65%, respectively. On irregular shape of tumor analysis, the absorbed dose of normal tissue was the lowest one with the MLC treatment than the other two. The treatment numbers of MU and treatment time were reduced by 54% and 65%, respectively. Conclusion: Despite of in the treatment of regular shape tumor or irregular shape tumor analyses, the treatment time of MLC treatment is less than that of fixed cone collimator and IRIS. For the absorbed dose of normal tissue in irregular shape tumor analysis, MLC treatment is lower than the other two. Keywords: Stereotactic radiosurgery, CyberKnife, Multileaf collimator, Fixed cone collimator, IRIS

In treatment of cancer using high energetic radiation the problem arises how to irradiate the tumor without damaging the healthy tissue in the immediate vicinity. In order to do this, intensity modulated radiation therapy (IMRT) is used. In this thesis, the general goal is to modulate the homogeneous radiation field delivered by an external accelerator using a multileaf collimator in comparison with beam modifying devices. In order to generate intensity modulated fields in a static mode with multileaf collimators, the heuristic algorithm of Galvin, Chen and Smith is used. This method aims at finding a segmentation with a small number of segments, taking account of mechanical constraints such as leaves can move only in one direction, on one row, the right and left leaves cannot overlap (Interleaf Collision) and also every element between the leaf and the side of the collimator to which the leaf is connected is also covered (no holes in leaves). During the implementation of the algorithm, the initial intensity matrix with the desired radiation rates is inserted and using essential transformations, a positive combination of special matrices, segments, corresponding to fixed positions of multileaf collimator are obtained. All calculations end with the superposition of segments which leads to the creation of the 3-D matrix that will be used to irradiate the tumor. The algorithm is implemented in C++. The calculations are fast and the procedure is user friendly. The model is implemented for the case of protection the spinal cord while treating a tumor in the neck area. Furthermore, dose distributions obtained with this model and beam modifying devices in the neck area were compared.
Κατά τη θεραπεία του καρκίνου με χρήση υψηλής ενέργειας ακτινοβολίας, πρόβλημα αποτελεί ο περιορισμός της ακτινοβολίας στον όγκο στόχο και ο περιορισμός της συμμετοχής του υγιούς ιστού, της γειτονικής περιοχής, στο ελάχιστο. Προκειμένου να επιλυθεί το πρόβλημα αυτό χρησιμοποιείται ακτινοθεραπεία με πεδία ακτινοβολίας διαμορφωμένης έντασης (Ιntensity Μodulated Radiαtion Therapy – IMRT), με τη βοήθεια των κατευθυντήρων πολλαπλών φύλλων (Multileaf Collimators- MLC). Στόχος της συγκεκριμένης διπλωματικής εργασίας είναι η διαμόρφωση του ομοιογενούς πεδίου ακτινοβολίας, που διανέμεται μέσω του γραμμικού επιταχυντή χρησιμοποιώντας κατευθυντήρα πολλαπλών φύλλων και η σύγκριση των αποτελεσμάτων της προσομοίωσης με τις συσκευές διαμόρφωσης δέσμης (Beam Modifying Devices). Προκειμένου να παραχθούν τα διαμορφωμένης έντασης πεδία ακτινοβολίας, σε στατική μορφή, χρησιμοποιήθηκε ο αλγόριθμος των Galvin, Chen και Smith. H μέθοδος αποσκοπεί στην τμηματοποίηση του πίνακα με τα επιθυμητά ποσοστά ακτινοβολίας σε έναν μικρό αριθμό τμημάτων “segments”, λαμβάνοντας υπόψιν μηχανικούς περιορισμούς. (i) Τα φύλλα δύναται να κινηθούν μόνο κατά μήκος μιας διεύθυνσης, (ii) σε μια γραμμή, το αριστερό και το δεξί φύλλο δεν μπορούν να επικαλυφτούν (Interleaf Collision) και (iii) κάθε στοιχείο μεταξύ του φύλλου και της πλευράς του διαμορφωτή, με την οποία είναι συνδεδεμένο, είναι πάντα καλυμμένο (Νo holes in leaves). Κατά την υλοποίηση του αλγορίθμου, εισάγεται ο αρχικός πίνακας με τα επιθυμητά ποσοστά ακτινοβολίας και με τη χρήσης κατάλληλων μετασχηματισμών, προκύπτει ένας συνδυασμός από ειδικούς πίνακες (segments), οι οποίοι αντιστοιχούν σε θέσεις των κατευθυντήρων πολλαπλών φύλλων και θα χρησιμοποιηθούν για την ακτινοβόληση του όγκου. Ο αλγόριθμος υλοποιήθηκε σε C++. Οι υπολογισμοί είναι γρήγοροι και η διεργασία είναι φιλική προς το χρήστη. Το μοντέλο υλοποιήθηκε για την περίπτωση προστασίας της σπονδυλικής στήλης κατά τη θεραπεία όγκου στην περιοχή του λαιμού. Τέλος, οι κατανομές δόσεις που προέκυψαν με την προαναφερθέν μοντέλο συγκρίθηκαν με αυτές των συσκευών διαμόρφωσης δέσμης.

博士
國立清華大學
生醫工程與環境科學系
101
we applied an aperture adaptive technique with a visual guiding system to tackle the problem of respiratory motion. A homemade computer program showing a cyclic respiratory pattern was projected onto the ceiling to visually help the patient adjust their respiration. Once the respiratory motion became regular, the leaf sequence could be synchronized with the target motion. An oscillator was employed to simulate the patient’s breathing pattern. Two simple fields and one IMRT field were measured to verify the accuracy. Preliminary results showed that after appropriate training, the amplitude and duration of a volunteer’s breathing could be well controlled by the visual guiding system. The high dose gradient at the edges of the radiation fields were successfully retained. The aperture adaptive technique with the visual guiding system can be an inexpensive and feasible alternative without compromising delivery efficiency in clinical practice. this study was to develop a total body irradiation technique that does not require additional devices or sophisticated procedures to overcome the space limitation of a small treatment room by modifying the leaf sequences of intensity modulated fields.The technique treated the patient lying on the floor anteriorly and posteriorly. For each AP/PA treatment, two complementary fields with dynamic field edges were matched over an overlapped region defined by the marks on the body surface.The results confirmed that the technique is capable of delivering a uniform dose distribution to the midline of the body in a small treatment room while keeping the lung dose within the tolerance level.

Ngar, Yuen Kan.
Thesis (Ph.D.)--Chinese University of Hong Kong, 2013.
Includes bibliographical references (leaves 157-159).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Abstract also in Chinese.

碩士
慈濟科技大學
放射醫學科學研究所
107
The tongue and groove design of the multi-leaf collimator (MLC) of the linear accelerator (LINAC) may result in the radiation leakage. In this study, the Varian TrueBeamTM phase space particle files were used to construct the Millennium 120 multi-leaf collimator module for Monte Carlo simulations of such tongue and groove effect. The simulations have been carried out in conditions of different energies, field sizes, depths, and two different LINAC modes, i.e., the flattening filter (FF) and the flattening filter free (FFF) modes. The leakages were also measured by the films for the specific conditions as used in the Monte Carlo simulations. The total average radiation leakage rates found by the Monte Carlo simulations and the measurements were 0.69% ± 0.04% and 1.60% ± 0.23% respectively. The leakage does not increase with energies. The average leakage increases with the filed sizes and depths. No significant differences in leakage rate of the tongue and groove effect were found between the FF and the FFF modes.

Dissertação de Mestrado em Matemática apresentada à Faculdade de Ciências e Tecnologia
Este trabalho aborda um problema de otimização relacionado com o tratamento de estruturas tumorais, conhecido por Radioterapia de Intensidade Modulada. Este método de tratamento baseia-se na incidência de radiação raio-X, que visa destruir as células malignas, preservando, na medida do possível, os órgãos vitais circundantes. Este texto analisa este tipo de tratamento e seu planeamento com o objetivo de tornar eficaz sua aplicação.Radioterapia é um tratamento médico que consiste em utilizar radiação ionizante contra o tumor, que é absorvida, danificando o ácido desoxirribonucleico (ADN) das células cancerígenas, destruindo-as. A intensidade necessária para cessar a reprodução das células tumorais é menor do que para células não cancerosas. Além disso, essas células não-cancerosas têm a capacidade de se reproduzirem mesmo com ADN danificado, ao contrário das células cancerígenas. Isto torna-se uma vantagem para o tratamento, mas não suficiente. Embora as células tumorais sejam mais sensíveis à radiação, na maioria das vezes, a sua erradicação envolve a destruição de células não cancerosas. Na radioterapia é quase impraticável administrar uma quantidade nula de dose ao tecido normal adjacentes às estruturas alvo (isto é, o tumor).Como tal, o objetivo passa por entregar uma dose cumulativa razoável ao tumor, minimizando a dose administrada ao tecido normal.Esta é uma das maiores dificuldades deste processo, uma vez que existem células críticas que não podem ser destruídas para certificar a manutenção dos correspondentes órgãos em risco.Nas últimas décadas, várias abordagens computacionais foram desenvolvidas para melhorar a precisão e eficácia da radioterapia. Diferentes técnicas de digitalização surgiram, como tomografia computadorizada (TC), ressonância magnética (RM), sistemas de planeamento de tratamento 3D, entre outros, o que significou um grande passo nesta área. Essas técnicas foram cruciais não apenas para diagnosticar os tumores, mas também para caracterizar a sua composição e melhorar a sua representação.Esses avanços foram seguidos por outras melhorias que poderiam superar os primeiros equipamentos de radiografia. A radioterapia era administrada de forma manual e intuitiva por um médico, o que implicava uma grande margem de possíveis erros.O desenvolvimento do software e hardware na tecnologia médica permitiu que este processo fosse mais preciso na determinação da posição mais apropriada para o paciente paciente, o número e a distribuição dos ângulos de feixe, o tipo de energia e intensidade de radiação.Esse desenvolvimento tecnológico eliminou a metodologia de planeamento manual, mas não a abordagem de tentativa e erro, na qual os parâmetros são fixados e a distribuição da dose é feita através de várias tentativas no paciente, até que um resultado razoável seja encontrado.Nesta tese, considera-se uma formulação proposta por Bertsimas et al, que visa encontrar um conjunto de ângulos e intensidades de feixe, minimizando o efeito da radiação incidente sobre os corpos vitais e maximizando a radiação absorvida pelas células malignas representando as consequências biológicas da radiação.   Para contornar a não-linearidade da formulação, métodos heurísticos são descritos e aplicados a um caso fantasma, composto por células tumorais e um órgão circundante. Resultados experimentais comparam diferentes variantes dos métodos, a fim de avaliá-los em termos dos valores da função objetivo e dos tempos de execução.
The present work deals with an optimization problem related to the treatment of tumor forms, known as intensity modulated radiotherapy. This treatment method is based on the incidence of X-ray radiation, which aims to destroy malignant cells, whilst preserving, as far as possible, the surrounding vital organs. This text reviews this type of treatment and its planning with the goal of making its application effective.Radiotherapy or radiation therapy is a medical treatment of cancerous cells on the human tissue. This treatment consists on using ionizing radiation against the tumor, which is absorbed and damages the deoxyribonucleic acid (DNA) of the cancerous cells, destroying them. The intensity required to disable the reproduction of the tumor cells is smaller than for non-cancerous cells. Moreover, these non-cancerous cells have the merit of reproducing themselves even with damaged DNA, unlike the cancerous-cells. This turns into an advantage for the radiotherapy treatment, but it is not enough. Although tumor cells are more sensitive to radiation, most of the times, their eradication involves the destruction of non-cancerous cells. In radiation therapy it is almost impractical to deliver zero dose to the normal tissue (all the body cells which do not belong to any particular tumor structure) adjoining the target volumes (i.e., the tumor).As such, the goal is to deliver a reasonable cumulative dose to the tumor body while minimizing the dose delivered to normal tissue \cite{ehrgott2010mathematical,webb1989optimisation}. This is one of the biggest difficulties of this process, since there are critical cells that cannot be destroyed in order to certify the sustention of the corresponding organs at risk (OARs). In the last decades, several computational approaches have been developed in order to improve the accuracy and effectiveness of radiation therapy. Distinct scanning techniques have emerged, such as computed tomography (CT), magnetic resonance imaging (MRI), 3D treatment planning systems, among others, which meant a huge step in this area. These techniques were crucial not only to diagnose the tumors, but also to characterize their composition and to image them in a better way.These advances were followed by other improvements that could overcome early radiography equipments. The radiotherapy used to be managed manually and intuitively by a physician, which incurs, evidently, in a large margin of possible errors. The development of the software and hardware in medical technology (3D planning, velocity of calculations, delivery of radiation) allowed this process to be more accurate in the determination of the most appropriate patient position, the number and distribution of beam angles, the type of energy and intensity of radiation and dose disposal through the tumor. Additionally, it also improved the outline of tumors' shape (Clinical Target Volume) and the OARs.This technological development eliminated the hand planning methodology, but not the trial and error approach, in which the parameters are fixed and the dose distribution is made through several attempts on the patient, until a reasonable outcome is found.In this thesis, a formulation proposed by Bertsimas et al is considered, which aims at finding a set of angles and the beamlet intensities while minimizing the effect of incident radiation on vital bodies and maximizing the radiation absorbed by the malignant cells representing the biological consequences of radiation. In order to circumvent the nonlinearity of the formulation, heuristic methods are described and applied to one phantom case, composed by tumor cells and one surrounding organ, both discretized in voxels. The set of beamlets per beam are defined by bixels and the combination of one, three, five and seven angles are applied. Experimental results compare different variants of the methods, in order to assess them in terms of the objective function values and the run times.