Cette thèse s’inscrit dans un projet à long terme de conception de nouvelle prothèse de l’Articulation Temporo-Mandibulaire (ATM). Afin de faciliter une caractérisation non invasive de l’ATM, elle a conduit à l’élaboration d’un modèle élément finis plan de l’ATM. Le modèle, construit à partir de relevés IRM, intègre le ménisque ainsi que les insertions musculaires et ligamentaires. Il est commandé en déplacements imposés tout d’abord et en efforts imposés ensuite. Les déplacements ont été mesurés par analyse vidéo 3D et les efforts musculaires ont été évalués par EMG au cours de travaux antérieurs réalisés au sein du laboratoire. Le modèle est ici exploité pour simuler un mouvement d’ouverture et un serrage inter-incisives dans trois configurations qui correspondent à des ouvertures de 5 mm, 25 mm et 30 mm. Les résultats de ces simulations, validés par IRM, ont permis de caractériser le rôle du disque articulaire de l’ATM dans la réalisation des déplacements et la transmission des efforts. L’étude souligne la nécessité de rechercher des solutions technologiques de remplacement du disque articulaire lors de la conception d’une nouvelle prothèse. / This study presents a part of a long-term project that aims to design a new prosthesis for the Temporomandibular Joint (TMJ). In order to facilitate a non-invasive characterization of the TMJ, a plane finite element model of the joint has been elaborated starting from MRI images. The model integrates the meniscus as well as the principal ligaments and the main muscular insertions. It has been driven firstly with displacements and then with forces. The displacements have been measured using a 3D motion analysis system and the muscles forces have been taken from anterior former EMG studies led in the laboratory. An opening movement and inter-incisors clenching in three configurations which correspond to openings of 5, 25 and 30 mm have been simulated. The results of these simulations, validated by MRI, made it possible to characterize the function of the articular disk during the movement and the transmission of actions. This study underlines the necessity of seeking technological solutions to replace the meniscus when designing a new prosthesis.

Brain tumors pose a big challenge in the field of neuro-oncology. Gliomas are the largest subgroup. Magnetic resonance imaging is a non-invasive tool for detecting and characterizing these tumors. Mathematical models, such as the reaction-diffusion equation, can be used for understanding the intricate behavior of gliomas. This thesis aims to improve the understanding and prediction of tumor growth by modifying and evaluating a reaction-diffusion mathematical model and incorporating magnetic resonance (MR) images, namely intensity from T1-weighted and T2-weighted images, and apparent diffusion coefficient values. Image data from five patients was used. The finite difference method was used to approximate the solution, and brain segmentation is performed using the software package FSL. The Jaccard index is used to compare the simulation results with the ground truth, being the segmented tumor area. A spatially varying proliferation rate is introduced and histology images are used to construct an initial condition for the reaction-diffusion mathematical model. The results show improvement in performance based on the Jaccard index, with the highest values achieved when using a diffusion matrix given as an affine function of intensity in T1-weighted images. Incorporating a spatially varying proliferation rate reduces the number of iterations required to reach the maximum Jaccard index compared to a constant proliferation rate, but this does not influence the simulation time. The introduction of the p-Laplace operator, particularly with a value of p = 1.8 instead of the usual Laplace operator (where p = 2), leads to a higher Jaccard index, indicating an improvement in the model’s performance. The best Jaccard index achieved was 0.4909 with p = 1.8 compared to the basic model (JI = 0.4382 with p = 2). An initial tumor cell density is constructed using histology images. In conclusion, insights are provided into improving tumor growth modeling by incorporating MR images, the p-Laplace operator, a spatially varying proliferation rate and possibility of constructing the initial conditions for tumor cell density based on histology images.

O disco intervertebral é uma estrutura cuja função é receber, amortecer e distribuir o impacto das cargas impostas sobre a coluna vertebral. O aumento da idade e a postura adotada pelo indivíduo podem levar à degeneração do disco intervertebral. Atualmente, a Ressonância Magnética (RM) é considerada o melhor e mais sensível método não invasivo de avaliação por imagem do disco intervertebral. Neste trabalho foram desenvolvidos métodos quantitativos computadorizados para auxílio ao diagnóstico da degeneração do disco intervertebral em imagens de ressonância magnética ponderadas em T2 da coluna lombar, de acordo com a escala de Pfirrmann, uma escala semi-quantitativa, com cinco graus de degeneração. Os algoritmos computacionais foram testados em um conjunto de dados que consiste de imagens de 300 discos, obtidos de 102 indivíduos, com diferentes graus de degeneração. Máscaras binárias de discos segmentados manualmente foram utilizadas para calcular seus centroides, visando criar um ponto de referência para possibilitar a extração de atributos. Uma análise de textura foi realizada utilizando a abordagem proposta por Haralick. Para caracterização de forma, também foram calculados os momentos invariantes definidos por Hu e os momentos centrais para cada disco. A classificação do grau de degeneração foi realizada utilizando uma rede neural artificial e o conjunto de atributos extraídos de cada disco. Uma taxa média de acerto na classificação de 87%, com erro padrão de 6,59% e uma área média sob a curva ROC (Receiver Operating Characteristic) de 0,92 indicam o potencial de aplicação dos algoritmos desenvolvidos como ferramenta de apoio ao diagnóstico da degeneração do disco intervertebral. / The intervertebral disc is a structure whose function is to receive, absorb and transmit the impact loads imposed on the spine. Increasing age and the posture adopted by the individual can lead to degeneration of the intervertebral disc. Currently, Magnetic Resonance Imaging (MRI) is considered the best and most sensitive noninvasive method to imaging evaluation of the intervertebral disc. In this work were developed methods for quantitative computer-aided diagnosis of the intervertebral disc degeneration in MRI T2 weighted images of the lumbar column according to Pfirrmann scale, a semi-quantitative scale with five degrees of degeneration. The algorithms were tested on a dataset of 300 images obtained from 102 subjects with varying degrees of degeneration. Binary masks manually segmented of the discs were used to calculate their centroids, to create a reference point to enable extraction of attributes. A texture analysis was performed using the approach proposed by Haralick. For the shape characterization, invariant moments defined by Hu and central moments were also calculated for each disc. The rating of the degree of degeneration was performed using an artificial neural network and the set of extracted attributes of each disk. An average rate of correct classification of 87%, with standard error 6.59% and an average area under the ROC curve (Receiver Operating Characteristic) of 0.92 indicates the potential application of the algorithms developed as a diagnostic support tool to the degeneration of the intervertebral disc.

O disco intervertebral é uma estrutura cuja função é receber, amortecer e distribuir o impacto das cargas impostas sobre a coluna vertebral. O aumento da idade e a postura adotada pelo indivíduo podem levar à degeneração do disco intervertebral. Atualmente, a Ressonância Magnética (RM) é considerada o melhor e mais sensível método não invasivo de avaliação por imagem do disco intervertebral. Neste trabalho foram desenvolvidos métodos quantitativos computadorizados para auxílio ao diagnóstico da degeneração do disco intervertebral em imagens de ressonância magnética ponderadas em T2 da coluna lombar, de acordo com a escala de Pfirrmann, uma escala semi-quantitativa, com cinco graus de degeneração. Os algoritmos computacionais foram testados em um conjunto de dados que consiste de imagens de 300 discos, obtidos de 102 indivíduos, com diferentes graus de degeneração. Máscaras binárias de discos segmentados manualmente foram utilizadas para calcular seus centroides, visando criar um ponto de referência para possibilitar a extração de atributos. Uma análise de textura foi realizada utilizando a abordagem proposta por Haralick. Para caracterização de forma, também foram calculados os momentos invariantes definidos por Hu e os momentos centrais para cada disco. A classificação do grau de degeneração foi realizada utilizando uma rede neural artificial e o conjunto de atributos extraídos de cada disco. Uma taxa média de acerto na classificação de 87%, com erro padrão de 6,59% e uma área média sob a curva ROC (Receiver Operating Characteristic) de 0,92 indicam o potencial de aplicação dos algoritmos desenvolvidos como ferramenta de apoio ao diagnóstico da degeneração do disco intervertebral. / The intervertebral disc is a structure whose function is to receive, absorb and transmit the impact loads imposed on the spine. Increasing age and the posture adopted by the individual can lead to degeneration of the intervertebral disc. Currently, Magnetic Resonance Imaging (MRI) is considered the best and most sensitive noninvasive method to imaging evaluation of the intervertebral disc. In this work were developed methods for quantitative computer-aided diagnosis of the intervertebral disc degeneration in MRI T2 weighted images of the lumbar column according to Pfirrmann scale, a semi-quantitative scale with five degrees of degeneration. The algorithms were tested on a dataset of 300 images obtained from 102 subjects with varying degrees of degeneration. Binary masks manually segmented of the discs were used to calculate their centroids, to create a reference point to enable extraction of attributes. A texture analysis was performed using the approach proposed by Haralick. For the shape characterization, invariant moments defined by Hu and central moments were also calculated for each disc. The rating of the degree of degeneration was performed using an artificial neural network and the set of extracted attributes of each disk. An average rate of correct classification of 87%, with standard error 6.59% and an average area under the ROC curve (Receiver Operating Characteristic) of 0.92 indicates the potential application of the algorithms developed as a diagnostic support tool to the degeneration of the intervertebral disc.