3D dose reconstruction for narrow beams using ion chamber array measurements.

3D dose reconstruction is a verification of the delivered absorbed dose. Our aim was to describe and evaluate a 3D dose reconstruction method applied to phantoms in the context of narrow beams. A solid water phantom and a phantom containing a bone-equivalent material were irradiated on a 6 MV linac. The transmitted dose was measured by using one array of a 2D ion chamber detector. The dose reconstruction was obtained by an iterative algorithm. A phantom set-up error and organ interfraction motion were simulated to test the algorithm sensitivity. In all configurations convergence was obtained within three iterations. A local reconstructed dose agreement of at least 3% / 3mm with respect to the planned dose was obtained, except in a few points of the penumbra. The reconstructed primary fluences were consistent with the planned ones, which validates the whole reconstruction process. The results validate our method in a simple geometry and for narrow beams. The method is sensitive to a set-up error of a heterogeneous phantom and interfraction heterogeneous organ motion.

Influence of scatter reduction method and monochromatic beams on image quality and dose in mammography.

In mammography, the image contrast and dose delivered to the patient are determined by the x-ray spectrum and the scatter to primary ratio S/P. Thus the quality of the mammographic procedure is highly dependent on the choice of anode and filter material and on the method used to reduce the amount of scattered radiation reaching the detector. Synchrotron radiation is a useful tool to study the effect of beam energy on the optimization of the mammographic process because it delivers a high flux of monochromatic photons. Moreover, because the beam is naturally flat collimated in one direction, a slot can be used instead of a grid for scatter reduction. We have measured the ratio S/P and the transmission factors for grids and slots for monoenergetic synchrotron radiation. In this way the effect of beam energy and scatter rejection method were separated, and their respective importance for image quality and dose analyzed. Our results show that conventional mammographic spectra are not far from optimum and that the use of a slot instead of a grid has an important effect on the optimization of the mammographic process. We propose a simple numerical model to quantify this effect.

Low doses of ionizing radiation promote tumor growth and metastasis by enhancing angiogenesis.

Radiotherapy is a widely used treatment option in cancer. However, recent evidence suggests that doses of ionizing radiation (IR) delivered inside the tumor target volume, during fractionated radiotherapy, can promote tumor invasion and metastasis. Furthermore, the tissues that surround the tumor area are also exposed to low doses of IR that are lower than those delivered inside the tumor mass, because external radiotherapy is delivered to the tumor through multiple radiation beams, in order to prevent damage of organs at risk. The biological effects of these low doses of IR on the healthy tissue surrounding the tumor area, and in particular on the vasculature remain largely to be determined. We found that doses of IR lower or equal to 0.8 Gy enhance endothelial cell migration without impinging on cell proliferation or survival. Moreover, we show that low-dose IR induces a rapid phosphorylation of several endothelial cell proteins, including the Vascular Endothelial Growth Factor (VEGF) Receptor-2 and induces VEGF production in hypoxia mimicking conditions. By activating the VEGF Receptor-2, low-dose IR enhances endothelial cell migration and prevents endothelial cell death promoted by an anti-angiogenic drug, bevacizumab. In addition, we observed that low-dose IR accelerates embryonic angiogenic sprouting during zebrafish development and promotes adult angiogenesis during zebrafish fin regeneration and in the murine Matrigel assay. Using murine experimental models of leukemia and orthotopic breast cancer, we show that low-dose IR promotes tumor growth and metastasis and that these effects were prevented by the administration of a VEGF receptor-tyrosine kinase inhibitor immediately before IR exposure. These findings demonstrate a new mechanism to the understanding of the potential pro-metastatic effect of IR and may provide a new rationale basis to the improvement of current radiotherapy protocols.

Evaluation of organ-specific peripheral doses after 2-dimensional, 3-dimensional and hybrid intensity modulated radiation therapy for breast cancer based on Monte Carlo and convolution/superposition algorithms: implications for secondary cancer risk assessment.

To make a comprehensive evaluation of organ-specific out-of-field doses using Monte Carlo (MC) simulations for different breast cancer irradiation techniques and to compare results with a commercial treatment planning system (TPS). Three breast radiotherapy techniques using 6MV tangential photon beams were compared: (a) 2DRT (open rectangular fields), (b) 3DCRT (conformal wedged fields), and (c) hybrid IMRT (open conformal+modulated fields). Over 35 organs were contoured in a whole-body CT scan and organ-specific dose distributions were determined with MC and the TPS. Large differences in out-of-field doses were observed between MC and TPS calculations, even for organs close to the target volume such as the heart, the lungs and the contralateral breast (up to 70% difference). MC simulations showed that a large fraction of the out-of-field dose comes from the out-of-field head scatter fluence (>40%) which is not adequately modeled by the TPS. Based on MC simulations, the 3DCRT technique using external wedges yielded significantly higher doses (up to a factor 4-5 in the pelvis) than the 2DRT and the hybrid IMRT techniques which yielded similar out-of-field doses. In sharp contrast to popular belief, the IMRT technique investigated here does not increase the out-of-field dose compared to conventional techniques and may offer the most optimal plan. The 3DCRT technique with external wedges yields the largest out-of-field doses. For accurate out-of-field dose assessment, a commercial TPS should not be used, even for organs near the target volume (contralateral breast, lungs, heart).

Dummy run and conformity indices in the ongoing EORTC low-grade glioma trial 22033-26033: First evaluation of quality of radiotherapy planning.

PURPOSE: Early assessment of radiotherapy (RT) quality in the ongoing EORTC trial comparing primary temozolomide versus RT in low-grade gliomas. MATERIALS AND METHODS: RT plans provided for dummy cases were evaluated and compared against expert plans. We analysed: (1) tumour and organs-at-risk delineation, (2) geometric and dosimetric characteristics, (3) planning parameters, compliance with dose prescription and Dmax for OAR (4) indices: RTOG conformity index (CI), coverage factor (CF), tissue protection factor (PF); conformity number (CN = PF x CF); dose homogeneity in PTV (U). RESULTS: Forty-one RT plans were evaluated. Only two (5%) centres were requested to repeat CTV-PTV delineations. Three (7%) plans had a significant under-dosage and dose homogeneity in one deviated > 10%. Dose distribution was good with mean values of 1.5, 1, 0.68, and 0.68 (ideal values = 1) for CI, CF, PF, and CN, respectively. CI and CN strongly correlated with PF and they correlated with PTV. Planning with more beams seems to increase PTV(Dmin), improving CF. U correlated with PTV(Dmax). CONCLUSION: Preliminary results of the dummy run procedure indicate that most centres conformed to protocol requirements. To quantify plan quality we recommend systematic calculation of U and either CI or CN, both of which measure the amount of irradiated normal brain tissue.

Dose reconstruction in the context of tomotherapy

In vivo dosimetry is a way to verify the radiation dose delivered to the patient in measuring the dose generally during the first fraction of the treatment. It is the only dose delivery control based on a measurement performed during the treatment. In today's radiotherapy practice, the dose delivered to the patient is planned using 3D dose calculation algorithms and volumetric images representing the patient. Due to the high accuracy and precision necessary in radiation treatments, national and international organisations like ICRU and AAPM recommend the use of in vivo dosimetry. It is also mandatory in some countries like France. Various in vivo dosimetry methods have been developed during the past years. These methods are point-, line-, plane- or 3D dose controls. A 3D in vivo dosimetry provides the most information about the dose delivered to the patient, with respect to ID and 2D methods. However, to our knowledge, it is generally not routinely applied to patient treatments yet. The aim of this PhD thesis was to determine whether it is possible to reconstruct the 3D delivered dose using transmitted beam measurements in the context of narrow beams. An iterative dose reconstruction method has been described and implemented. The iterative algorithm includes a simple 3D dose calculation algorithm based on the convolution/superposition principle. The methodology was applied to narrow beams produced by a conventional 6 MV linac. The transmitted dose was measured using an array of ion chambers, as to simulate the linear nature of a tomotherapy detector. We showed that the iterative algorithm converges quickly and reconstructs the dose within a good agreement (at least 3% / 3 mm locally), which is inside the 5% recommended by the ICRU. Moreover it was demonstrated on phantom measurements that the proposed method allows us detecting some set-up errors and interfraction geometry modifications. We also have discussed the limitations of the 3D dose reconstruction for dose delivery error detection. Afterwards, stability tests of the tomotherapy MVCT built-in onboard detector was performed in order to evaluate if such a detector is suitable for 3D in-vivo dosimetry. The detector showed stability on short and long terms comparable to other imaging devices as the EPIDs, also used for in vivo dosimetry. Subsequently, a methodology for the dose reconstruction using the tomotherapy MVCT detector is proposed in the context of static irradiations. This manuscript is composed of two articles and a script providing further information related to this work. In the latter, the first chapter introduces the state-of-the-art of in vivo dosimetry and adaptive radiotherapy, and explains why we are interested in performing 3D dose reconstructions. In chapter 2 a dose calculation algorithm implemented for this work is reviewed with a detailed description of the physical parameters needed for calculating 3D absorbed dose distributions. The tomotherapy MVCT detector used for transit measurements and its characteristics are described in chapter 3. Chapter 4 contains a first article entitled '3D dose reconstruction for narrow beams using ion chamber array measurements', which describes the dose reconstruction method and presents tests of the methodology on phantoms irradiated with 6 MV narrow photon beams. Chapter 5 contains a second article 'Stability of the Helical TomoTherapy HiArt II detector for treatment beam irradiations. A dose reconstruction process specific to the use of the tomotherapy MVCT detector is presented in chapter 6. A discussion and perspectives of the PhD thesis are presented in chapter 7, followed by a conclusion in chapter 8. The tomotherapy treatment device is described in appendix 1 and an overview of 3D conformai- and intensity modulated radiotherapy is presented in appendix 2. - La dosimétrie in vivo est une technique utilisée pour vérifier la dose délivrée au patient en faisant une mesure, généralement pendant la première séance du traitement. Il s'agit de la seule technique de contrôle de la dose délivrée basée sur une mesure réalisée durant l'irradiation du patient. La dose au patient est calculée au moyen d'algorithmes 3D utilisant des images volumétriques du patient. En raison de la haute précision nécessaire lors des traitements de radiothérapie, des organismes nationaux et internationaux tels que l'ICRU et l'AAPM recommandent l'utilisation de la dosimétrie in vivo, qui est devenue obligatoire dans certains pays dont la France. Diverses méthodes de dosimétrie in vivo existent. Elles peuvent être classées en dosimétrie ponctuelle, planaire ou tridimensionnelle. La dosimétrie 3D est celle qui fournit le plus d'information sur la dose délivrée. Cependant, à notre connaissance, elle n'est généralement pas appliquée dans la routine clinique. Le but de cette recherche était de déterminer s'il est possible de reconstruire la dose 3D délivrée en se basant sur des mesures de la dose transmise, dans le contexte des faisceaux étroits. Une méthode itérative de reconstruction de la dose a été décrite et implémentée. L'algorithme itératif contient un algorithme simple basé sur le principe de convolution/superposition pour le calcul de la dose. La dose transmise a été mesurée à l'aide d'une série de chambres à ionisations alignées afin de simuler la nature linéaire du détecteur de la tomothérapie. Nous avons montré que l'algorithme itératif converge rapidement et qu'il permet de reconstruire la dose délivrée avec une bonne précision (au moins 3 % localement / 3 mm). De plus, nous avons démontré que cette méthode permet de détecter certaines erreurs de positionnement du patient, ainsi que des modifications géométriques qui peuvent subvenir entre les séances de traitement. Nous avons discuté les limites de cette méthode pour la détection de certaines erreurs d'irradiation. Par la suite, des tests de stabilité du détecteur MVCT intégré à la tomothérapie ont été effectués, dans le but de déterminer si ce dernier peut être utilisé pour la dosimétrie in vivo. Ce détecteur a démontré une stabilité à court et à long terme comparable à d'autres détecteurs tels que les EPIDs également utilisés pour l'imagerie et la dosimétrie in vivo. Pour finir, une adaptation de la méthode de reconstruction de la dose a été proposée afin de pouvoir l'implémenter sur une installation de tomothérapie. Ce manuscrit est composé de deux articles et d'un script contenant des informations supplémentaires sur ce travail. Dans ce dernier, le premier chapitre introduit l'état de l'art de la dosimétrie in vivo et de la radiothérapie adaptative, et explique pourquoi nous nous intéressons à la reconstruction 3D de la dose délivrée. Dans le chapitre 2, l'algorithme 3D de calcul de dose implémenté pour ce travail est décrit, ainsi que les paramètres physiques principaux nécessaires pour le calcul de dose. Les caractéristiques du détecteur MVCT de la tomothérapie utilisé pour les mesures de transit sont décrites dans le chapitre 3. Le chapitre 4 contient un premier article intitulé '3D dose reconstruction for narrow beams using ion chamber array measurements', qui décrit la méthode de reconstruction et présente des tests de la méthodologie sur des fantômes irradiés avec des faisceaux étroits. Le chapitre 5 contient un second article intitulé 'Stability of the Helical TomoTherapy HiArt II detector for treatment beam irradiations'. Un procédé de reconstruction de la dose spécifique pour l'utilisation du détecteur MVCT de la tomothérapie est présenté au chapitre 6. Une discussion et les perspectives de la thèse de doctorat sont présentées au chapitre 7, suivies par une conclusion au chapitre 8. Le concept de la tomothérapie est exposé dans l'annexe 1. Pour finir, la radiothérapie «informationnelle 3D et la radiothérapie par modulation d'intensité sont présentées dans l'annexe 2.

Focused ion beam scanning electron microscopy in biology.

Since the end of the last millennium, the focused ion beam scanning electron microscopy (FIB-SEM) has progressively found use in biological research. This instrument is a scanning electron microscope (SEM) with an attached gallium ion column and the 2 beams, electrons and ions (FIB) are focused on one coincident point. The main application is the acquisition of three-dimensional data, FIB-SEM tomography. With the ion beam, some nanometres of the surface are removed and the remaining block-face is imaged with the electron beam in a repetitive manner. The instrument can also be used to cut open biological structures to get access to internal structures or to prepare thin lamella for imaging by (cryo-) transmission electron microscopy. Here, we will present an overview of the development of FIB-SEM and discuss a few points about sample preparation and imaging.

Dosimetric comparison of different treatment modalities for stereotactic radiosurgery of arteriovenous malformations and acoustic neuromas.

PURPOSE: We investigated the influence of beam modulation on treatment planning by comparing four available stereotactic radiosurgery (SRS) modalities: Gamma-Knife-Perfexion, Novalis-Tx Dynamic-Conformal-Arc (DCA) and Dynamic-Multileaf-Collimation-Intensity-Modulated-radiotherapy (DMLC-IMRT), and Cyberknife. MATERIAL AND METHODS: Patients with arteriovenous malformation (n = 10) or acoustic neuromas (n = 5) were planned with different treatment modalities. Paddick conformity index (CI), dose heterogeneity (DH), gradient index (GI) and beam-on time were used as dosimetric indices. RESULTS: Gamma-Knife-Perfexion can achieve high degree of conformity (CI = 0.77 ± 0.04) with limited low-doses (GI = 2.59 ± 0.10) surrounding the inhomogeneous dose distribution (D(H) = 0.84 ± 0.05) at the cost of treatment time (68.1 min ± 27.5). Novalis-Tx-DCA improved this inhomogeneity (D(H) = 0.30 ± 0.03) and treatment time (16.8 min ± 2.2) at the cost of conformity (CI = 0.66 ± 0.04) and Novalis-TX-DMLC-IMRT improved the DCA CI (CI = 0.68 ± 0.04) and inhomogeneity (D(H) = 0.18 ± 0.05) at the cost of low-doses (GI = 3.94 ± 0.92) and treatment time (21.7 min ± 3.4) (p<0.01). Cyberknife achieved comparable conformity (CI = 0.77 ± 0.06) at the cost of low-doses (GI = 3.48 ± 0.47) surrounding the homogeneous (D(H) = 0.22 ± 0.02) dose distribution and treatment time (28.4min±8.1) (p<0.01). CONCLUSIONS: Gamma-Knife-Perfexion will comply with all SRS constraints (high conformity while minimizing low-dose spread). Multiple focal entries (Gamma-Knife-Perfexion and Cyberknife) will achieve better conformity than High-Definition-MLC of Novalis-Tx at the cost of treatment time. Non-isocentric beams (Cyberknife) or IMRT-beams (Novalis-Tx-DMLC-IMRT) will spread more low-dose than multiple isocenters (Gamma-Knife-Perfexion) or dynamic arcs (Novalis-Tx-DCA). Inverse planning and modulated fluences (Novalis-Tx-DMLC-IMRT and CyberKnife) will deliver the most homogeneous treatment. Furthermore, Linac-based systems (Novalis and Cyberknife) can perform image verification at the time of treatment delivery.

Patterns of gravity induced aggregate migration during casting of fluid concretes

In this paper, aggregate migration patterns during fluid concrete castings are studied through experiments, dimensionless approach and numerical modeling. The experimental results obtained on two beams show that gravity induced migration is primarily affecting the coarsest aggregates resulting in a decrease of coarse aggregates volume fraction with the horizontal distance from the pouring point and in a puzzling vertical multi-layer structure. The origin of this multi layer structure is discussed and analyzed with the help of numerical simulations of free surface flow. Our results suggest that it finds its origin in the non Newtonian nature of fresh concrete and that increasing casting rate shall decrease the magnitude of gravity induced particle migration. (C) 2012 Elsevier Ltd. All rights reserved.

Hypofractionated radiotherapy in the treatment of diffuse intrinsic pontine glioma in children: a single institution's experience

Objective: To demonstrate our institutional experience in the treatment ofdiffuse intrinsic pontine glioma (DIPG) with an hypofractionated external beam radiotherapy schedule.Materials and Methods: Between April 1996 and January 2004, 22 patients, ages 2.9-12.5 years, with newly diagnosed DIPG were treated by hypofractionated radiation therapy delivering a total dose of 45 Gy in daily fraction of 3 Gy, given over 3 weeks. No other treatment was applied concomittently.Results: Fourteen of the 22 patients received the prescribed dose of 45 Gy in 15 fractions of 3 Gy, two patients received a total dose of 60 and 45 Gy with a combination of two different beams (photons and neutrons), in 5 cases the daily fraction was modified to 2 Gy because of bad tolerance and one patient died due to serious intracranial hypertension after 2 fractions of 3 Gy and one of 2 Gy. Fourteen patients of 22 patients/of the total showed a clinical improvement, usually starting in the second week of treatment. No grade 3 or 4 acute toxicity from radiotherapy was observed. No treatment interruption was needed. In six patients, steroids could be discontinued within one month after the end of radiotherapy. The median time to progression and the median overall survival were 5.7 months and 7.6 months, respectively.Conclusion: External radiotherapy with a radical hypofractionated regimen is feasible and well tolerated in children with newly diagnosed DIPG. This regimen does not seem however to change the overall survival in this setting. It could represent an alternative option of short duration to more protracted regimens.

Accuracy of out-of-field dose calculation of tomotherapy and cyberknife treatment planning systems: A dosimetric study.

PURPOSE: Late toxicities such as second cancer induction become more important as treatment outcome improves. Often the dose distribution calculated with a commercial treatment planning system (TPS) is used to estimate radiation carcinogenesis for the radiotherapy patient. However, for locations beyond the treatment field borders, the accuracy is not well known. The aim of this study was to perform detailed out-of-field-measurements for a typical radiotherapy treatment plan administered with a Cyberknife and a Tomotherapy machine and to compare the measurements to the predictions of the TPS. MATERIALS AND METHODS: Individually calibrated thermoluminescent dosimeters were used to measure absorbed dose in an anthropomorphic phantom at 184 locations. The measured dose distributions from 6 MV intensity-modulated treatment beams for CyberKnife and TomoTherapy machines were compared to the dose calculations from the TPS. RESULTS: The TPS are underestimating the dose far away from the target volume. Quantitatively the Cyberknife underestimates the dose at 40cm from the PTV border by a factor of 60, the Tomotherapy TPS by a factor of two. If a 50% dose uncertainty is accepted, the Cyberknife TPS can predict doses down to approximately 10 mGy/treatment Gy, the Tomotherapy-TPS down to 0.75 mGy/treatment Gy. The Cyberknife TPS can then be used up to 10cm from the PTV border the Tomotherapy up to 35cm. CONCLUSIONS: We determined that the Cyberknife and Tomotherapy TPS underestimate substantially the doses far away from the treated volume. It is recommended not to use out-of-field doses from the Cyberknife TPS for applications like modeling of second cancer induction. The Tomotherapy TPS can be used up to 35cm from the PTV border (for a 390 cm(3) large PTV).

Développement et validation d'une méthode de calcul indépendant des unités moniteur basée sur les simulations Monte Carlo pour la vérification des traitements IMRT

Résumé : La radiothérapie par modulation d'intensité (IMRT) est une technique de traitement qui utilise des faisceaux dont la fluence de rayonnement est modulée. L'IMRT, largement utilisée dans les pays industrialisés, permet d'atteindre une meilleure homogénéité de la dose à l'intérieur du volume cible et de réduire la dose aux organes à risque. Une méthode usuelle pour réaliser pratiquement la modulation des faisceaux est de sommer de petits faisceaux (segments) qui ont la même incidence. Cette technique est appelée IMRT step-and-shoot. Dans le contexte clinique, il est nécessaire de vérifier les plans de traitement des patients avant la première irradiation. Cette question n'est toujours pas résolue de manière satisfaisante. En effet, un calcul indépendant des unités moniteur (représentatif de la pondération des chaque segment) ne peut pas être réalisé pour les traitements IMRT step-and-shoot, car les poids des segments ne sont pas connus à priori, mais calculés au moment de la planification inverse. Par ailleurs, la vérification des plans de traitement par comparaison avec des mesures prend du temps et ne restitue pas la géométrie exacte du traitement. Dans ce travail, une méthode indépendante de calcul des plans de traitement IMRT step-and-shoot est décrite. Cette méthode est basée sur le code Monte Carlo EGSnrc/BEAMnrc, dont la modélisation de la tête de l'accélérateur linéaire a été validée dans une large gamme de situations. Les segments d'un plan de traitement IMRT sont simulés individuellement dans la géométrie exacte du traitement. Ensuite, les distributions de dose sont converties en dose absorbée dans l'eau par unité moniteur. La dose totale du traitement dans chaque élément de volume du patient (voxel) peut être exprimée comme une équation matricielle linéaire des unités moniteur et de la dose par unité moniteur de chacun des faisceaux. La résolution de cette équation est effectuée par l'inversion d'une matrice à l'aide de l'algorithme dit Non-Negative Least Square fit (NNLS). L'ensemble des voxels contenus dans le volume patient ne pouvant être utilisés dans le calcul pour des raisons de limitations informatiques, plusieurs possibilités de sélection ont été testées. Le meilleur choix consiste à utiliser les voxels contenus dans le Volume Cible de Planification (PTV). La méthode proposée dans ce travail a été testée avec huit cas cliniques représentatifs des traitements habituels de radiothérapie. Les unités moniteur obtenues conduisent à des distributions de dose globale cliniquement équivalentes à celles issues du logiciel de planification des traitements. Ainsi, cette méthode indépendante de calcul des unités moniteur pour l'IMRT step-andshootest validée pour une utilisation clinique. Par analogie, il serait possible d'envisager d'appliquer une méthode similaire pour d'autres modalités de traitement comme par exemple la tomothérapie. Abstract : Intensity Modulated RadioTherapy (IMRT) is a treatment technique that uses modulated beam fluence. IMRT is now widespread in more advanced countries, due to its improvement of dose conformation around target volume, and its ability to lower doses to organs at risk in complex clinical cases. One way to carry out beam modulation is to sum smaller beams (beamlets) with the same incidence. This technique is called step-and-shoot IMRT. In a clinical context, it is necessary to verify treatment plans before the first irradiation. IMRT Plan verification is still an issue for this technique. Independent monitor unit calculation (representative of the weight of each beamlet) can indeed not be performed for IMRT step-and-shoot, because beamlet weights are not known a priori, but calculated by inverse planning. Besides, treatment plan verification by comparison with measured data is time consuming and performed in a simple geometry, usually in a cubic water phantom with all machine angles set to zero. In this work, an independent method for monitor unit calculation for step-and-shoot IMRT is described. This method is based on the Monte Carlo code EGSnrc/BEAMnrc. The Monte Carlo model of the head of the linear accelerator is validated by comparison of simulated and measured dose distributions in a large range of situations. The beamlets of an IMRT treatment plan are calculated individually by Monte Carlo, in the exact geometry of the treatment. Then, the dose distributions of the beamlets are converted in absorbed dose to water per monitor unit. The dose of the whole treatment in each volume element (voxel) can be expressed through a linear matrix equation of the monitor units and dose per monitor unit of every beamlets. This equation is solved by a Non-Negative Least Sqvare fif algorithm (NNLS). However, not every voxels inside the patient volume can be used in order to solve this equation, because of computer limitations. Several ways of voxel selection have been tested and the best choice consists in using voxels inside the Planning Target Volume (PTV). The method presented in this work was tested with eight clinical cases, which were representative of usual radiotherapy treatments. The monitor units obtained lead to clinically equivalent global dose distributions. Thus, this independent monitor unit calculation method for step-and-shoot IMRT is validated and can therefore be used in a clinical routine. It would be possible to consider applying a similar method for other treatment modalities, such as for instance tomotherapy or volumetric modulated arc therapy.