One of the main problems in curing cancer resides in the different microenvironment existing in tumours compared to the normal tissues. The mechanisms of failure are different for radiotherapy and chemotherapy, but they all relate to the poor blood supply known to exist in tumours. It is therefore very important to know the tumour microenvironmental conditions in order to devise techniques that will overcome the problems and will therefore improve the result of the treatment. The aims of the thesis were the modelling of tumour oxygenation and the simulation of polarographic oxygen measurements in order to assess and possibly to improve the accuracy of the electrode in measuring tumour oxygenation. It also aimed to evaluate the implications of tumour microenvironment for the radiotherapy outcome. The project used theoretical modelling as the main tool. The processes of oxygen diffusion and consumption were described mathematically for different conditions, the result being very accurate distributions of oxygen in tissues. A first simple model of tissue oxygenation was based on the oxygen diffusion around a single blood vessel. A more complex model built from the basic physical processes and measurable parameters allowed the simulation of realistical tissues with heterogeneous vasculature. This model also allowed the modelling of the two types of hypoxia known to appear in tumours and their influence on the tumour microenvironment. The computer simulation of tissues was also used for assessing the accuracy of the polarographic technique for measuring tumour oxygenation. The results of this study have shown that it is possible to model theoretically the tissue oxygenation starting from the basic physical processes. The particular application of our theoretical simulation to the polarographic oxygen electrode has shown that this experimental method does not give the oxygen values in individual cells. Because the electrode measures the average oxygenation in a relatively large tissue volume, the resulting oxygen distributions are different from the real ones and the extreme high and low values are not detected. It has further been found that the polarographic electrode cannot make distinction between various types of hypoxia existing in tumours, the geometrical distribution of the hypoxic cells influencing mostly the accuracy of the measurement. It was also shown that because of the averaging implied by the measurement process, electrode results should not be used directly to predict the response to radiation. Thus, the differences between the predictions in clinical tumour control obtained from the real or the measured oxygenations are of the order of tens of percents in absolute value. A method to improve the accuracy of the electrode, i.e. to improve the correlation between the results of the measurements and the actual tissue oxygenation, was proposed. In conclusion, theoretical modelling has been shown to be a very powerful tool for predicting the outcome of radiotherapy and it has the advantage of describing the tumour oxygenation in the least invasive manner. Furthermore it allows the investigation of the invasiveness and the accuracy of various experimental methods.

Ce travail porte sur l’étude expérimentale et numérique de l’écoulement des mousses humides dans un canal horizontal droit de section carrée avec ou sans singularités. Il est consacré tout particulièrement à déterminer les paramètres pertinents de l’écoulement dont la chute de pression longitudinale, les champs de vitesse de l’écoulement de mousse en proche parois, les épaisseurs de films liquides minces et épais en paroi et l’évolution de la contrainte pariétale pour une mousse humide dont la fraction gazeuse varie de 55 à 85% et la vitesse débitante de la mousse est 2, 4 puis 6 cm/s. Une fois ces paramètres déterminés en conduite horizontale droite, nous avons ensuite effectué des mesures sur différentes géométries représentant un élargissement brusque, une chicane verticale et écoulement de mousse autour d’un cylindre, dont le but est d’étudier la réorganisation de l’écoulement en vue de déterminer le comportement rhéologique des mousses en écoulement à l’aval et à l’amont des singularités. Finalement, une étude de simulation numérique (CFD) en utilisant les lois de comportement de type Bingham, pour fluides non newtoniens, a été effectuée afin de tester sa capacité de représenter des écoulements type mousse humide dans une conduite horizontale avec ou sans singularités. Nous avons vérifié tout d’abord l’évolution longitudinale de la pression statique qui est linéaire à l’amont comme à l’aval loin des zones influencées par les singularités. La chute de pression singulière reste à peu près constante pour une vitesse débitante donnée de la mousse. À partir de la technique de Vélocimétrie par Image de Particule (PIV), nous avons déterminé les composantes de vitesse au voisinage immédiat des singularités. Ces mesures nous ont permis de mettre en évidence l’existence de différents régimes d’écoulement, et de déterminer la réorganisation et le comportement rhéologique de l’écoulement de mousse autour des géométries étudiées. L’analyse des mesures d’épaisseur de films liquides, obtenues par la méthode conductimétrique, indique que la paroi reste mouillée par un film liquide suffisamment épais pour qu’on puisse appliquer la méthode électrochimique. Les signaux polarographiques obtenus avec la mousse présentent alors de fortes fluctuations. La comparaison de celles-ci avec les contraintes pariétales déduites à partir des mesures de la chute de pression montre bien une bonne concordance. L’étude numérique (CFD), effectuée pour une fraction volumique de gaz égale à 70% et qui s’écoule avec une vitesse débitante de 2 cm/s, montre que le modèle rhéologique de Bingham pourrait être bien adapté à ce genre de mousse humide évoluant en écoulement en bloc. / This work is an experimental and numerical study of aqueous foam flow inside a horizontal square duct, with and without flow disruption devices (fdd). It is especially devoted to determine the pertinent parameters of the flow: longitudinal pressure losses, velocity fields of foam flow near the walls, liquid film thickness (thick and thin), and the wall shear stress evolution, for an aqueous foam with a void fraction range between 55 and 85%, for a mean foam flow velocity of 2, 4 and 6 cm/s. Once they were determined, inside the horizontal channel, we carried out measurements over different geometries: half-sudden expansion, vertical fence and foam flow around a cylinder. The goal was to study the foam flow reorganization to well understand the rheological behavior of aqueous foam flow in the vicinities of different fdd. Finally, a numerical simulation (CFD), using the Bingham behavior model of non-Newtonian fluid, was undertaken to test its capacity to represent the aqueous foam flow inside the horizontal duct with flow disruption devices. First of all, we verified the static longitudinal pressure evolution, which varies linearly upstream and downstream far from the fdd. The singular pressure loss remains constant for a given mean foam velocity and a foam quality (void fraction). From the Particle Imaging Velocimetry (PIV) technique (2D), we determined the two velocity components in the immediate vicinities of the disruption devices. They allowed us to put into evidence the different foam flow regimes and to observe the foam flow reorganization and rheological behavior through the studied fdd. The slip-layer thickness analysis, obtained using the conductimetry method, shows that the wall presents a liquid film thick enough to apply an electrochemical technique (polarography). Thus, the polarographic signals, obtained for the foam flow, present important fluctuations. They were compared to the wall shear stress deducted from the measurement of pressure losses, showing a good similarity between them. The numerical study (CFD), carried out for aqueous foam flow with a void fraction of 70% and a mean foam flow velocity of 2 cm/s, shows that the Bingham rheological model can be adapted to this kind of aqueous foam flow which is flowing like a block.