A peripheral dose calculation model for estimating second cancer risk after breast radiotherapy

AbstractBreast cancer is one of the most common cancers affecting one in eight women during their lives. Survival rates have increased steadily thanks to early diagnosis with mammography screening and more efficient treatment strategies. Post-operative radiation therapy is a standard of care in the management of breast cancer and has been shown to reduce efficiently both local recurrence rate and breast cancer mortality. Radiation therapy is however associated with some late effects for long-term survivors. Radiation-induced secondary cancer is a relatively rare but severe late effect of radiation therapy. Currently, radiotherapy plans are essentially optimized to maximize tumor control and minimize late deterministic effects (tissue reactions) that are mainly associated with high doses (» 1 Gy). With improved cure rates and new radiation therapy technologies, it is also important to evaluate and minimize secondary cancer risks for different treatment techniques. This is a particularly challenging task due to the large uncertainties in the dose-response relationship.In contrast with late deterministic effects, secondary cancers may be associated with much lower doses and therefore out-of-field doses (also called peripheral doses) that are typically inferior to 1 Gy need to be determined accurately. Out-of-field doses result from patient scatter and head scatter from the treatment unit. These doses are particularly challenging to compute and we characterized it by Monte Carlo (MC) calculation. A detailed MC model of the Siemens Primus linear accelerator has been thoroughly validated with measurements. We investigated the accuracy of such a model for retrospective dosimetry in epidemiological studies on secondary cancers. Considering that patients in such large studies could be treated on a variety of machines, we assessed the uncertainty in reconstructed peripheral dose due to the variability of peripheral dose among various linac geometries. For large open fields (> 10x10 cm2), the uncertainty would be less than 50%, but for small fields and wedged fields the uncertainty in reconstructed dose could rise up to a factor of 10. It was concluded that such a model could be used for conventional treatments using large open fields only.The MC model of the Siemens Primus linac was then used to compare out-of-field doses for different treatment techniques in a female whole-body CT-based phantom. Current techniques such as conformai wedged-based radiotherapy and hybrid IMRT were investigated and compared to older two-dimensional radiotherapy techniques. MC doses were also compared to those of a commercial Treatment Planning System (TPS). While the TPS is routinely used to determine the dose to the contralateral breast and the ipsilateral lung which are mostly out of the treatment fields, we have shown that these doses may be highly inaccurate depending on the treatment technique investigated. MC shows that hybrid IMRT is dosimetrically similar to three-dimensional wedge-based radiotherapy within the field, but offers substantially reduced doses to out-of-field healthy organs.Finally, many different approaches to risk estimations extracted from the literature were applied to the calculated MC dose distribution. Absolute risks varied substantially as did the ratio of risk between two treatment techniques, reflecting the large uncertainties involved with current risk models. Despite all these uncertainties, the hybrid IMRT investigated resulted in systematically lower cancer risks than any of the other treatment techniques. More epidemiological studies with accurate dosimetry are required in the future to construct robust risk models. In the meantime, any treatment strategy that reduces out-of-field doses to healthy organs should be investigated. Electron radiotherapy might offer interesting possibilities with this regard.RésuméLe cancer du sein affecte une femme sur huit au cours de sa vie. Grâce au dépistage précoce et à des thérapies de plus en plus efficaces, le taux de guérison a augmenté au cours du temps. La radiothérapie postopératoire joue un rôle important dans le traitement du cancer du sein en réduisant le taux de récidive et la mortalité. Malheureusement, la radiothérapie peut aussi induire des toxicités tardives chez les patients guéris. En particulier, les cancers secondaires radio-induits sont une complication rare mais sévère de la radiothérapie. En routine clinique, les plans de radiothérapie sont essentiellement optimisées pour un contrôle local le plus élevé possible tout en minimisant les réactions tissulaires tardives qui sont essentiellement associées avec des hautes doses (» 1 Gy). Toutefois, avec l'introduction de différentes nouvelles techniques et avec l'augmentation des taux de survie, il devient impératif d'évaluer et de minimiser les risques de cancer secondaire pour différentes techniques de traitement. Une telle évaluation du risque est une tâche ardue étant donné les nombreuses incertitudes liées à la relation dose-risque.Contrairement aux effets tissulaires, les cancers secondaires peuvent aussi être induits par des basses doses dans des organes qui se trouvent hors des champs d'irradiation. Ces organes reçoivent des doses périphériques typiquement inférieures à 1 Gy qui résultent du diffusé du patient et du diffusé de l'accélérateur. Ces doses sont difficiles à calculer précisément, mais les algorithmes Monte Carlo (MC) permettent de les estimer avec une bonne précision. Un modèle MC détaillé de l'accélérateur Primus de Siemens a été élaboré et validé avec des mesures. La précision de ce modèle a également été déterminée pour la reconstruction de dose en épidémiologie. Si on considère que les patients inclus dans de larges cohortes sont traités sur une variété de machines, l'incertitude dans la reconstruction de dose périphérique a été étudiée en fonction de la variabilité de la dose périphérique pour différents types d'accélérateurs. Pour de grands champs (> 10x10 cm ), l'incertitude est inférieure à 50%, mais pour de petits champs et des champs filtrés, l'incertitude de la dose peut monter jusqu'à un facteur 10. En conclusion, un tel modèle ne peut être utilisé que pour les traitements conventionnels utilisant des grands champs.Le modèle MC de l'accélérateur Primus a été utilisé ensuite pour déterminer la dose périphérique pour différentes techniques dans un fantôme corps entier basé sur des coupes CT d'une patiente. Les techniques actuelles utilisant des champs filtrés ou encore l'IMRT hybride ont été étudiées et comparées par rapport aux techniques plus anciennes. Les doses calculées par MC ont été comparées à celles obtenues d'un logiciel de planification commercial (TPS). Alors que le TPS est utilisé en routine pour déterminer la dose au sein contralatéral et au poumon ipsilatéral qui sont principalement hors des faisceaux, nous avons montré que ces doses peuvent être plus ou moins précises selon la technTque étudiée. Les calculs MC montrent que la technique IMRT est dosimétriquement équivalente à celle basée sur des champs filtrés à l'intérieur des champs de traitement, mais offre une réduction importante de la dose aux organes périphériques.Finalement différents modèles de risque ont été étudiés sur la base des distributions de dose calculées par MC. Les risques absolus et le rapport des risques entre deux techniques de traitement varient grandement, ce qui reflète les grandes incertitudes liées aux différents modèles de risque. Malgré ces incertitudes, on a pu montrer que la technique IMRT offrait une réduction du risque systématique par rapport aux autres techniques. En attendant des données épidémiologiques supplémentaires sur la relation dose-risque, toute technique offrant une réduction des doses périphériques aux organes sains mérite d'être étudiée. La radiothérapie avec des électrons offre à ce titre des possibilités intéressantes.

Dinàmica de sistemes mesoscòpics amb correlacions quàntiques mitjançant la formulació de de Broglie-Bohm

Per a determinar la dinàmica espai-temporal completa d’un sistema quàntic tridimensional de N partícules cal integrar l’equació d’Schrödinger en 3N dimensions. La capacitat dels ordinadors actuals permet fer-ho com a molt en 3 dimensions. Amb l’objectiu de disminuir el temps de càlcul necessari per a integrar l’equació d’Schrödinger multidimensional, es realitzen usualment una sèrie d’aproximacions, com l’aproximació de Born–Oppenheimer o la de camp mig. En general, el preu que es paga en realitzar aquestes aproximacions és la pèrdua de les correlacions quàntiques (o entrellaçament). Per tant, és necessari desenvolupar mètodes numèrics que permetin integrar i estudiar la dinàmica de sistemes mesoscòpics (sistemes d’entre tres i unes deu partícules) i en els que es tinguin en compte, encara que sigui de forma aproximada, les correlacions quàntiques entre partícules. Recentment, en el context de la propagació d’electrons per efecte túnel en materials semiconductors, X. Oriols ha desenvolupat un nou mètode [Phys. Rev. Lett. 98, 066803 (2007)] per al tractament de les correlacions quàntiques en sistemes mesoscòpics. Aquesta nova proposta es fonamenta en la formulació de la mecànica quàntica de de Broglie– Bohm. Així, volem fer notar que l’enfoc del problema que realitza X. Oriols i que pretenem aquí seguir no es realitza a fi de comptar amb una eina interpretativa, sinó per a obtenir una eina de càlcul numèric amb la que integrar de manera més eficient l’equació d’Schrödinger corresponent a sistemes quàntics de poques partícules. En el marc del present projecte de tesi doctoral es pretén estendre els algorismes desenvolupats per X. Oriols a sistemes quàntics constituïts tant per fermions com per bosons, i aplicar aquests algorismes a diferents sistemes quàntics mesoscòpics on les correlacions quàntiques juguen un paper important. De forma específica, els problemes a estudiar són els següents: (i) Fotoionització de l’àtom d’heli i de l’àtom de liti mitjançant un làser intens. (ii) Estudi de la relació entre la formulació de X. Oriols amb la aproximació de Born–Oppenheimer. (iii) Estudi de les correlacions quàntiques en sistemes bi- i tripartits en l’espai de configuració de les partícules mitjançant la formulació de de Broglie–Bohm.

The new direct oral anticoagulants in special indications: rationale and preliminary data in cancer, mechanical heart valves, anti-phospholipid syndrome, and heparin-induced thrombocytopenia and beyond.

The present review will briefly summarize the interplay between coagulation and inflammation, highlighting possible effects of direct inhibition of factor Xa and thrombin beyond anticoagulation. Additionally, the rationale for the use of the new direct oral anticoagulants (DOACs) for indications such as cancer-associated venous thromboembolism (CAT), mechanical heart valves, thrombotic anti-phospholipid syndrome (APS), and heparin-induced thrombocytopenia (HIT) will be explored. Published data on patients with cancer or mechanical heart valves treated with DOAC will be discussed, as well as planned studies in APS and HIT. Although at the present time published evidence is insufficient for recommending DOAC in the above-mentioned indications, there are good arguments in favor of clinical trials investigating their efficacy in these contexts. Direct inhibition of factor Xa or thrombin may reveal interesting effects beyond anticoagulation as well.

Direct Determination of mechanical properties in shallow formations by (ultra) sonic methods

For several decades mechanical properties of shallow formations (soil) obtained by sonic to ultrasonic wave testing were reported to be greater than those based on mechanical tests. The present article relying on a statistical analysis of more than 300 tests shows that elastic moduli of the soil can indeed be obtained from (ultra)sonic tests and that they are identical to those resulting from mechanical tests.

The metaphysics of quantum gravity : a causal approach

The dissertation investigates some relevant metaphysical issues arising in the context of spacetime theories. In particular, the inquiry focuses on general relativity and canonical quantum gravity. A formal definition of spacetime theory is proposed and, against this framework, an analysis of the notions of general covariance, symmetry and background independence is performed. It is argued that many conceptual issues in general relativity and canonical quantum gravity derive from putting excessive emphasis on general covariance as an ontological prin-ciple. An original metaphysical position grounded in scientific essential- ism and causal realism (weak essentialism) is developed and defended. It is argued that, in the context of general relativity, weak essentialism supports spacetime substantivalism. It is also shown that weak essentialism escapes arguments from metaphysical underdetermination by positing a particular kind of causation, dubbed geometric. The proposed interpretive framework is then applied to Bohmian mechanics, pointing out that weak essentialism nicely fits into this theory. In the end, a possible Bohmian implementation of loop quantum gravity is considered, and such a Bohmian approach is interpreted in a geometric causal fashion. Under this interpretation, Bohmian loop quantum gravity straightforwardly commits us to an ontology of elementary extensions of space whose evolution is described by a non-local law. The causal mechanism underlying this evolution clarifies many conceptual issues related to the emergence of classical spacetime from the quantum regime. Although there is as yet no fully worked out physical theory of quantum gravity, it is argued that the proposed approach sets up a standard that proposals for a serious ontology in this field should meet.

Assessment and analysis of mechanical allodynia-like behavior induced by spared nerve injury (SNI) in the mouse

Rrésumé: La première description dans une publication médicale des douleurs neuropathiques remonte à 1872, le Dr S.W. Mitchell les résumant ainsi [...]" la causalgie est la plus terrible des tortures qu'une lésion nerveuse puisse entraîner "[...]. Par définition, la douleur neuropathique est une douleur chronique faisant suite à une lésion ou dysfonction du système nerveux. Malgré les progrès faits dans la compréhension de ce syndrome, le détail des mécanismes impliqués nous échappe encore et son traitement reste insuffisant car moins de 50% des patients sont soulagés par les thérapies actuelles. Différents modèles expérimentaux ont été élaborés chez l'animal de laboratoire, en particulier des modèles de lésion de nerfs périphériques chez le rat, permettant des investigations tant moléculaires que fonctionnelles des mécanismes impliqués dans le développement de ces douleurs. En revanche, peu de modèles existent chez la souris, alors que cet animal, grâce à la transgénèse, est très fréquemment utilisé pour l'approche fonctionnelle ciblée sur un gène. Dans l'étude présentée ici, nous avons évalué chez la souris C57BL/6 l'adaptation d'un modèle neuropathique, proposé une nouvelle modalité de mesure de la sensibilité douloureuse adaptée à la souris et défini une méthode d'analyse performante des résultats. Ce modèle, dit de lésion avec épargne nerveuse (spared Werve injury, SNI), consiste en la lésion de deux des trois branches du nerf sciatique, soit les nerfs peronier commun et tibial. La troisième branche, le nerf sural est laissé intact et c'est dans le territoire cutané de ce dernier que la sensibilité douloureuse à des stimulations mécaniques est enregistrée. Des filaments calibrés de force croissante sont appliqués sur la surface de la patte impliquée et la fréquence relative de retrait de la patte a été modélisée mathématiquement et analysée par un modèle statistique intégrant tous les paramètres de l'expérience (mixed-effects model). Des variantes chirurgicales lésant séquentiellement les trois branches du nerf sciatique ainsi que la réponse en fonction du sexe de l'animal ont également été évaluées. La lésion SNI entraîne une hypersensibilité mécanique marquée comparativement aux souris avec chirurgie contrôle; cet effet est constant entre les animaux et persiste durant les quatre semaines de l'étude. De subtiles différences entre les variables, y compris une divergence de sensibilité mécanique entre les sexes, ont été démontrées. La nécessité de léser le nerf tibial pour le développement des symptômes a également été documentée par notre méthode d'évaluation et d'analyse. En conclusion, nous avons validé le modèle SNI chez la souris par l'apparition d'un symptôme reproductible et apparenté à l'allodynie mécanique décrite par les patients souffrant de douleurs neuropathiques. Nous avons développé des méthodes d'enregistrement et d'analyse de la sensibilité douloureuse sensibles qui permettent la mise en évidence de facteurs intrinsèques et extrinsèques de variation de la réponse. Le modèle SNI utilisé chez des souris génétiquement modifiées, de par sa précision et reproductibilité, pourra permettre la discrimination de facteurs génétiques et épigénétiques contribuant au développement et à la persistance de douleurs neuropathiques.

Is PaCO2 management optimal under controlled mechanical ventilation (CMV) during neuro-resuscitation?

INTRODUCTION. Both hypocapnia and hypercapnia can be deleterious to brain injured patients. Strict PaCO2 control is difficult to achieve because of patient's instability and unpredictable effects of ventilator settings changes. OBJECTIVE. The aim of this study was to evaluate our ability to comply with a protocol of controlled mechanical ventilation (CMV) aiming at a PaCO2 between 35 and 40 mmHg in patients requiring neuro-resuscitation. METHODS. Retrospective analysis of consecutive patients (2005-2011) requiring intracranial pressure (ICP) monitoring for traumatic brain injury (TBI), subarachnoid haemorrhage (SAH), intracranial haemorrhage (ICH) or ischemic stroke (IS). Demographic data, GCS, SAPS II, hospital mortality, PaCO2 and ICP values were recorded. During CMV in the first 48 h after admission, we analyzed the time spent within the PaCO2 target in relation to the presence or absence of intracranial hypertension (ICP[20 mmHg, by periods of 30 min) (Table 1). We also compared the fraction of time (determined by linear interpolation) spent with normal, low or high PaCO2 in hospital survivors and non-survivors (Wilcoxon, Bonferroni correction, p\0.05) (Table 2). PaCO2 samples collected during and after apnoea tests were excluded. Results given as median [IQR]. RESULTS. 436 patients were included (TBI: 51.2 %, SAH: 20.6 %, ICH: 23.2 %, IS: 5.0 %), age: 54 [39-64], SAPS II score: 52 [41-62], GCS: 5 [3-8]. 8744 PaCO2 samples were collected during 150611 h of CMV. CONCLUSIONS. Despite a high number of PaCO2 samples collected (in average one sample every 107 min), our results show that patients undergoing CMV for neuro- resuscitation spent less than half of the time within the pre-defined PaCO2 range. During documented intracranial hypertension, hypercapnia was observed in 17.4 % of the time. Since non-survivors spent more time with hypocapnia, further analysis is required to determine whether hypocapnia was detrimental per se, or merely reflects increased severity of brain insult.

Early functional differentiation in the chick embryonic disc: interaction between mechanical activity and extracellular matrix

The mechanical behaviour of ectodermal cells in the area opaca and the supracellular organization of fibronectin in the adjacent extracellular matrix were studied in whole chick blastoderms developing in vitro. The pattern of spontaneous mechanical activity and its modification by immunoglobulins against fibronectin were determined using a real-time image-analysis system. The pattern of fibronectin was studied using immunocytochemical techniques. It was found that the ectodermal cells in the area opaca actively develop a radially oriented contraction, which leads to a distension of the area pellucida from which the embryo develops. Abnormally increased tension resulted in perturbations of gastrulation and neurulation. An optimized mechanical equilibrium within the blastoderm seems to be necessary for normal development. Anti-fibronectin antibodies applied to the basal side of the blastoderm led rapidly and reversibly to an increase of tension in the contracted cells. This observation indicates that modifications of the extracellular matrix can be transmitted to cytoskeletal elements within adjacent cells. The extracellular matrix of the area opaca contains fibronectin arranged in radially oriented fibrils. This orientation corresponds to the direction of migration of the mesodermal cells. Interestingly, the radial pattern of fibronectin is found in the regions where the ectodermal cells are contracted and develop radially oriented forces. This observation suggests that the supracellular assembly of the extracellular materials could be influenced by the mechanical activity of adjacent cells. Possible modulations of the supracellular organization of extracellular matrix by other factors, e.g. diffusible metabolites, is also discussed. The presence of characteristically organized extracellular matrix components, of spatially differentiated cell activities and of reciprocal interactions between them makes the young chick blastoderm an excellent system for physiological studies of the coordinated cellular activities that lead to changes in form, complexity and function.

Wellposedness of a nonlinear, logarithmic Schrödinger equation of Doebner-Goldin type modeling quantum dissipation

This paper is concerned with the modeling and analysis of quantum dissipation phenomena in the Schrödinger picture. More precisely, we do investigate in detail a dissipative, nonlinear Schrödinger equation somehow accounting for quantum Fokker–Planck effects, and how it is drastically reduced to a simpler logarithmic equation via a nonlinear gauge transformation in such a way that the physics underlying both problems keeps unaltered. From a mathematical viewpoint, this allows for a more achievable analysis regarding the local wellposedness of the initial–boundary value problem. This simplification requires the performance of the polar (modulus–argument) decomposition of the wavefunction, which is rigorously attained (for the first time to the best of our knowledge) under quite reasonable assumptions.

Modelling the mechanical aspects of the curing process of magneto-sensitive elastomeric materials

In this paper, a phenomenologically motivated magneto-mechanically coupled finite strain elastic framework for simulating the curing process of polymers in the presence of a magnetic load is proposed. This approach is in line with previous works by Hossain and co-workers on finite strain curing modelling framework for the purely mechanical polymer curing (Hossain et al., 2009b). The proposed thermodynamically consistent approach is independent of any particular free energy function that may be used for the fully-cured magneto-sensitive polymer modelling, i.e. any phenomenological or micromechanical-inspired free energy can be inserted into the main modelling framework. For the fabrication of magneto-sensitive polymers, micron-size ferromagnetic particles are mixed with the liquid matrix material in the uncured stage. The particles align in a preferred direction with the application of a magnetic field during the curing process. The polymer curing process is a complex (visco) elastic process that transforms a fluid to a solid with time. Such transformation process is modelled by an appropriate constitutive relation which takes into account the temporal evolution of the material parameters appearing in a particular energy function. For demonstration in this work, a frequently used energy function is chosen, i.e. the classical Mooney-Rivlin free energy enhanced by coupling terms. Several representative numerical examples are demonstrated that prove the capability of our approach to correctly capture common features in polymers undergoing curing processes in the presence of a magneto-mechanical coupled load.

Differential gene expression in response to mechanical wounding and insect feeding in Arabidopsis.

Wounding in multicellular eukaryotes results in marked changes in gene expression that contribute to tissue defense and repair. Using a cDNA microarray technique, we analyzed the timing, dynamics, and regulation of the expression of 150 genes in mechanically wounded leaves of Arabidopsis. Temporal accumulation of a group of transcripts was correlated with the appearance of oxylipin signals of the jasmonate family. Analysis of the coronatine-insensitive coi1-1 Arabidopsis mutant that is also insensitive to jasmonate allowed us to identify a large number of COI1-dependent and COI1-independent wound-inducible genes. Water stress was found to contribute to the regulation of an unexpectedly large fraction of these genes. Comparing the results of mechanical wounding with damage by feeding larvae of the cabbage butterfly (Pieris rapae) resulted in very different transcript profiles. One gene was specifically induced by insect feeding but not by wounding; moreover, there was a relative lack of water stress-induced gene expression during insect feeding. These results help reveal a feeding strategy of P. rapae that may minimize the activation of a subset of water stress-inducible, defense-related genes.

Use of quantum dots in aqueous solution to detect blood fingermarks on non-porous surfaces.

A new and original reagent based on the use of highly fluorescent cadmium telluride (CdTe) quantum dots (QDs) in aqueous solution is proposed to detect weak fingermarks in blood on non-porous surfaces. To assess the efficiency of this approach, comparisons were performed with one of the most efficient blood reagents on non-porous surfaces, Acid Yellow 7 (AY7). To this end, four non-porous surfaces were studied, i.e. glass, transparent polypropylene, black polyethylene, and aluminium foil. To evaluate the sensitivity of both reagents, sets of depleted fingermarks were prepared, using the same finger, initially soaked with blood, which was then successively applied on the same surface without recharging it with blood or latent secretions. The successive marks were then cut in halves and the halves treated separately with each reagent. The results showed that QDs were equally efficient to AY7 on glass, polyethylene and polypropylene surfaces, and were superior to AY7 on aluminium. The use of QDs in new, sensitive and highly efficient latent and blood mark detection techniques appears highly promising. Health and safety issues related to the use of cadmium are also discussed. It is suggested that applying QDs in aqueous solution (and not as a dry dusting powder) considerably lowers the toxicity risks.

Mechanical properties of rat cardiac skinned fibers are altered by chronic growth hormone hypersecretion.

Chronic growth hormone (GH) hypersecretion in rats leads to increased isometric force without affecting the unloaded shortening velocity of isolated cardiac papillary muscles, despite a marked isomyosin shift toward V3. To determine if alterations occurred at the level of the contractile proteins in rats bearing a GH-secreting tumor (GH rats), we examined the mechanical properties of skinned fibers to eliminate the early steps of the excitation-contraction coupling mechanism. We found that maximal active tension and stiffness at saturating calcium concentrations (pCa 4.5) were markedly higher in GH rats than in control rats (tension, 52.9 +/- 5.2 versus 38.1 +/- 4.6 mN.mm-2, p < 0.05; stiffness, 1,105 +/- 120 versus 685 +/- 88 mN.mm-2.microns-1, p < 0.01), whereas values at low calcium concentrations (pCa 9) were unchanged. In addition, the calcium sensitivity of the contractile proteins was slightly but significantly higher in GH rats than in control rats (delta pCa 0.04, p < 0.001). The crossbridge cycling rate, reflected by the response to quick length changes, was lower in GH rats than in control rats (62.0 +/- 2.6 versus 77.4 +/- 6.6 sec-1, p < 0.05), in good agreement with a decrease in the proportion of alpha-myosin heavy chains in the corresponding papillary muscles (45.5 +/- 2.0% versus 94.6 +/- 2.4%, p < 0.001). The changes in myosin heavy chain protein phenotype were paralleled by similar changes of the corresponding mRNAs, indicating that the latter occurred mainly at a pretranslational level. These results demonstrate that during chronic GH hypersecretion in rats, alterations at the myofibrillar level contribute to the increase in myocardial contractility observed in intact muscle.

Calculation of correction factors for ionization chamber measurements with small fields in low-density media.

The quantity of interest for high-energy photon beam therapy recommended by most dosimetric protocols is the absorbed dose to water. Thus, ionization chambers are calibrated in absorbed dose to water, which is the same quantity as what is calculated by most treatment planning systems (TPS). However, when measurements are performed in a low-density medium, the presence of the ionization chamber generates a perturbation at the level of the secondary particle range. Therefore, the measured quantity is close to the absorbed dose to a volume of water equivalent to the chamber volume. This quantity is not equivalent to the dose calculated by a TPS, which is the absorbed dose to an infinitesimally small volume of water. This phenomenon can lead to an overestimation of the absorbed dose measured with an ionization chamber of up to 40% in extreme cases. In this paper, we propose a method to calculate correction factors based on the Monte Carlo simulations. These correction factors are obtained by the ratio of the absorbed dose to water in a low-density medium □D(w,Q,V1)(low) averaged over a scoring volume V₁ for a geometry where V₁ is filled with the low-density medium and the absorbed dose to water □D(w,QV2)(low) averaged over a volume V₂ for a geometry where V₂ is filled with water. In the Monte Carlo simulations, □D(w,QV2)(low) is obtained by replacing the volume of the ionization chamber by an equivalent volume of water, according to the definition of the absorbed dose to water. The method is validated in two different configurations which allowed us to study the behavior of this correction factor as a function of depth in phantom, photon beam energy, phantom density and field size.