Univerzita Karlova v Praze 1. lékařská fakulta Postgraduální doktorský program v biomedicíně Studijní obor: Experimentální chirurgie Disertační práce MUDr. Jan Klouda: Preoperative planning of the reconstructive surgery of the forefoot Abstract The presented thesis describes a study aimed at the change of articular surface position in the region of first metatarsophalangeal joint after operative reconstruction due to hallux valgus deformity, done by performing Lapidus arthrodesis. The study evaluates a cohort of patients, who underwent surgery in Department of Orthopaedics, First Faculty of Medicine, Charles University in Prague at Motol University Hospital from 2010 to 2015. The results and clinical implications of the aforementioned retrospective study were published in 2018. The observers evaluated several defined angles on preoperative and postoperative radiographs of the forefoot. The angles were thoroughly selected with regard to the exact representation of first metatarsophalangeal joint articular surface position in relation to the axes of first metatarsal and the whole forefoot. The executed measurements allowed us to assess the overall effectivity of the performed surgery in deformity correction, as well as to describe possible pitfalls and disadvantages resulting from the change of structural...

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Cameras generally have a field of view only large enough to capture a portion of their surroundings. The goal of immersion is to replace many of your senses with virtual ones, so that the virtual environment will feel as real as possible. Panoramic cameras are used to capture the entire 360°view, also known as panoramic images.Virtual reality makes use of these panoramic images to provide a more immersive experience compared to seeing images on a 2D screen. This thesis, which is in the field of Computer vision, focuses on establishing a multi-camera geometry to generate a cylindrical panorama image and successfully implementing it with the cheapest cameras possible. The specific goal of this project is to propose the cameras geometry which will decrease artifact problems related to parallax in the panorama image. We present a new approach of cylindrical panoramic images from multiple cameras which its setup has cameras placed evenly around a circle. Instead of looking outward, which is the traditional ”radial” configuration, we propose to make the optical axes tangent to the camera circle, a ”tangential” configuration. Beside an analysis and comparison of radial and tangential geometries, we provide an experimental setup with real panoramas obtained in realistic conditions / Les caméras ont généralement un champ de vision à peine assez grand pour capturer partie de leur environnement. L’objectif de l’immersion est de remplacer virtuellement un grand nombre de sens, de sorte que l’environnement virtuel soit perçu comme le plus réel possible. Une caméra panoramique est utilisée pour capturer l’ensemble d’une vue 360°, également connue sous le nom d’image panoramique. La réalité virtuelle fait usage de ces images panoramiques pour fournir une expérience plus immersive par rapport aux images sur un écran 2D. Cette thèse, qui est dans le domaine de la vision par ordinateur, s’intéresse à la création d’une géométrie multi-caméras pour générer une image cylindrique panoramique et vise une mise en œuvre avec les caméras moins chères possibles. L’objectif spécifique de ce projet est de proposer une géométrie de caméra qui va diminuer au maximum les problèmes d’artefacts liés au parallaxe présent dans l’image panoramique. Nous présentons une nouvelle approche de capture des images panoramiques cylindriques à partir de plusieurs caméras disposées uniformément autour d’un cercle. Au lieu de regarder vers l’extérieur, ce qui est la configuration traditionnelle ”radiale”, nous proposons de rendre les axes optiques tangents au cercle des caméras, une configuration ”tangentielle”. Outre une analyse et la comparaison des géométries radiales et tangentielles, nous fournissons un montage expérimental avec de vrais panoramas obtenus dans des conditions réalistes

A mecânica celular jaz nas propriedades materiais da membrana plasmática, fundamentalmente uma bicamada fosfolipídica com espessura de dimensões moleculares. Além de forças elásticas, tal material bidimensional também experimenta tensões viscosas devido ao seu comportamento fluido (presumivelmente newtoniano) na direção tangencial. A despeito da notável concordância entre teoria e experimentos biofísicos sobre a geometria de membranas celulares, ainda não se faz presente um método computacional para simulação de sua (real) dinâmica viscosa governada pela lei de Boussinesq-Scriven. Assim sendo, introduzimos uma formulação variacional mista de três campos para escoamentos viscosos de superfícies fechadas curvas. Nela, o fluido circundante é levado em conta considerando-se uma restrição de volume interior, ao passo que uma restrição de área corresponde à inextensibilidade. As incógnitas são a velocidade, o vetor curvatura e a pressão superficial, todas estas interpoladas com elementos finitos lineares contínuos via estabilização baseada na projeção do gradiente de pressão. O método é semi-implícito e requer a solução de apenas um único sistema linear por passo de tempo. Outro ingrediente numérico proposto é uma força que mimetiza a ação de uma pinça óptica, permitindo interação virtual com a membrana, onde a qualidade e o refinamento de malha são mantidos por remalhagem adaptativa automática. Extensivos experimentos numéricos de dinâmica de relaxação são apresentados e comparados com soluções quasi-analíticas. É observada estabilidade temporal condicional com uma restrição de passo de tempo que escala como o quadrado do tamanho de malha. Reportamos a convergência e os limites de estabilidade de nosso método e sua habilidade em predizer corretamente o equilíbrio dinâmico de compridas e finas elongações cilíndricas (tethers) que surgem a partir de pinçamentos membranais. A dependência de forma membranal com respeito a uma velocidade imposta de pinçamento também é discutida, sendo que há um valor limiar de velocidade abaixo do qual um tether não se forma de início. Testes adicionais ilustram a robustez do método e a relevância dos efeitos viscosos membranais quando sob a ação de forças externas. Sem dúvida, ainda há um longo caminho a ser trilhado para o entendimento completo da mecânica celular (há de serem consideradas outras estruturas tais como citoesqueleto, canais iônicos, proteínas transmembranares, etc). O primeiro passo, porém, foi dado: a construção de um esquema numérico variacional capaz de simular a intrigante dinâmica das membranas celulares. / Cell mechanics lies on the material properties of the plasmatic membrane, fundamentally a two-molecule-thick phospholipid bilayer. Other than bending elastic forces, such a two-dimensional interfacial material also experiences viscous stresses due to its (presumably Newtonian) surface fluid tangential behaviour. Despite the remarkable agreement on membrane shapes between theory and biophysical experiments, there is no computational method for simulating its (actual) viscous dynamics governed by the Boussinesq- Scriven law. Accordingly, we introduce a mixed three-field variational formulation for viscous flows of closed curved surfaces. In it, the bulk fluid is taken into account by means of an enclosed-volume constraint, whereas an area constraint stands for the membranes inextensible character. The unknowns are the velocity, vector curvature and surface pressure fields, all of which are interpolated with linear continuous finite elements by means of a pressure-gradient-projection scheme. The method is semi-implicit and it requires the solution of a single linear system per time step. Another proposed ingredient is a numerical force that emulates the action of an optical tweezer, allowing for virtual interaction with the membrane, where mesh quality and refinement are maintained by adaptively remeshing. Extensive relaxation experiments are reported and compared with quasi-analytical solutions. Conditional time stability is observed, with a time step restriction that scales as the square of the mesh size. We discuss both convergence and the stability limits of our method, its ability to correctly predict the dynamical equilibrium of the tether due to tweezing. The dependence of the membrane shape on imposed tweezing velocities is also addressed. Basically, there is a threshold velocity value below which the tethers shape does not arise at first. Further tests illustrate the robustness of the method and show the significance of viscous effects on membranes deformation under external forces. Undoubtedly, there is still a long way to track toward the understanding of celullar mechanics (one still has to account other structures such as cytoskeleton, ion channels, transmembrane proteins, etc). The first step has given, though: the design of a numerically robust variational scheme capable of simulating the engrossing dynamics of fluid cell membranes.

The suspension of the motor vehicle is one of the most important elements of the flexible mounted and inflexible mounted masses of the vehicle bodywork, and most attention is paid to its exploration and improvement. Analysis of models of equivalent oscillation systems of motor vehicles testifies that the evaluation of motor vehicle oscillations and modelling of its motion modes is still very topical and requires further research. Suspension models of motor vehicles offered in publications regard only the influence of road irregularities, and the modernisation of these models is directed towards the improvement of passengers’ comfort. However not much research has been done on the influence of oscillations of flexible mounted and inflexible mounted masses of the bodyworks of vehicles in the process of braking; also there is not much investigation of the post-accident identification of the vehicle’s movement mode corresponding to the deformations of the suspension and the longitudinal pitch of the bodywork. Research of oscillations in the conditions of emergency braking is primarily important for the work in two practical directions: 1) improvement of calculation methods of motor vehicle’s response to external impact in the conditions of real operation; 2) further improvement of research methods on the road, and analysis of fait accompli road accidents related to oscillations in the emergency braking. Methodology defining the oscillations occurring in the braking may be applied... [to full text]

The suspension of the motor vehicle is one of the most important elements of the flexible mounted and inflexible mounted masses of the vehicle bodywork, and most attention is paid to its exploration and improvement. Analysis of models of equivalent oscillation systems of motor vehicles testifies that the evaluation of motor vehicle oscillations and modelling of its motion modes is still very topical and requires further research. Suspension models of motor vehicles offered in publications regard only the influence of road irregularities, and the modernisation of these models is directed towards the improvement of passengers’ comfort. However not much research has been done on the influence of oscillations of flexible mounted and inflexible mounted masses of the bodyworks of vehicles in the process of braking; also there is not much investigation of the post-accident identification of the vehicle’s movement mode corresponding to the deformations of the suspension and the longitudinal pitch of the bodywork. Research of oscillations in the conditions of emergency braking is primarily important for the work in two practical directions: 1) improvement of calculation methods of motor vehicle’s response to external impact in the conditions of real operation; 2) further improvement of research methods on the road, and analysis of fait accompli road accidents related to oscillations in the emergency braking. Methodology defining the oscillations occurring in the braking may be applied... [to full text]

Réduire l’énergie générée par le frottement et dissipée dans les systèmes mécaniques réels est un des challenges actuels en tribologie. Ce point représente une importance toute particulière dans le domaine des transports terrestres. En réponse à cette nécessité, les constructeurs automobiles se concentrent sur la réduction de la consommation d'énergie en sélectionnant des lubrifiants et des matériaux appropriés d'une part et les systèmes mécaniques performants d'autre part. Grâce à leurs propriétés physiques et tribologiques en termes de réduction de la friction et de l'usure, les couches minces de DLC (Diamond-like Carbon) sont considérées comme l'une des solutions. Le comportement tribologique de couches minces de ta-C (carbone amorphe très dur dépourvu d’hydrogène) et de a-C:H (carbone amorphe hydrogéné) est ici exploré. D’autre part, des “lubrifiants verts“ et des additifs participant aussi à la réduction du frottement et de l'usure sont testés. Ces essais sont effectués dans différentes conditions en utilisant une nouvelle méthodologie expérimentale. Le tribomètre dynamique oscillant développé au LTDS possède la capacité de quantifier avec une très grande précision et sans recourir à une quelconque mesure de force, des niveaux de frottement faibles (dans la gamme 10 – 5 à 10 – 2), et permet en plus d’identifier différentes contributions du frottement. Dans un premier temps, une loi de frottement linéaire a été utilisée afin d’évaluer deux contributions de frottement. La première, μ0 est le coefficient transitoire de frottement quand la vitesse s’annule au changement de direction (du type frottement de Coulomb). La seconde, μ1, est une contribution dépendante de la vitesse de glissement. Ensuite, une étude numérique a été réalisée en appliquant une loi de frottement quadratique afin de mieux comprendre l'aspect dynamique des réponses libres. Cela nous a permis d'étudier numériquement la décroissance d’amplitude des oscillations déterminée grâce à la méthode de moindres carrés. Nous nous intéressons aussi à l‘étude des formes de l'enveloppe de ces oscillations en relation avec le modèle de frottement. Les résultats numériques et expérimentaux pour les lois de frottement linéaire et quadratique sont ensuite comparés. En complément, nous avons mesuré la force tangentielle correspondant aux tribosystèmes testés. Finalement, nous avons étudié numériquement un système dynamique masse-ressort à un degré de liberté, modélisé par la loi de frottement LuGre. Cette loi est décrite par le phénomène d’hystérésis et l’effet de décalage de temps qui ont été détectés expérimentalement. Les résultats expérimentaux obtenus avec le tribomètre oscillant montrent qu'ils sont qualitativement comparables à ceux obtenus en configuration classique cylindre-plan, travaillant à vitesse de glissement constante. Dans tous les cas, les résultats montrent la supériorité du tribosystème ta-C/ta-C dans la réduction du frottement μ0. De plus, les résultats numériques et expérimentaux sont cohérents. Cette étude montre qu’une loi de frottement quadratique est capable de décrire correctement toutes les formes d’enveloppes obtenues expérimentalement : droite, convexe, concave et une combinaison des formes convexe et concave. / Controlling friction is a one of the most significant challenges in the field of tribology. Its major purpose is directed towards the reduction of energy in real mechanical systems, especially in the area of transportation. In response to this necessity, the automobile industries are emphasizing on minimizing the consumption of energy by selecting the appropriate lubricants and materials on one hand and mechanical system with high performance on the other hand. DLC (Diamond-like carbon) coated surfaces are considered one of the solutions thanks to their physical and tribological properties in reducing friction and wear. In this study, we have been interested in investigating the friction behavior of both amorphous hydrogenated (a-C:H) and hydrogen-free tetrahedral amorphous carbon (ta-C) DLC coatings. Furthermore, some “green lubricants” and additives are tested which play a role in reducing friction and wear. These latter tests are performed at different operating conditions using a new experimental methodology, known as the dynamic oscillating tribometer. This original tribometer, developed at the Laboratory of Tribology and System Dynamics (LTDS), is able to measure the oscillatory motion corresponding to various tribosystems having low friction. This technique has the ability to quantify with remarkable precision and without any force transducer, low friction values (in the range of 10 – 5 to 10 – 2 ) and also to evaluate different friction contributions from the displacement and velocity-time responses of a mass-springdamper oscillating system. First, a linear friction law has been used for the systems tested in order to calculate two contributions of friction. The first one, μ0 is the transient friction coefficient at zero speed and the second one (Coulomb-type fiction), μ is a velocitydependent friction coefficient. Then, a numerical study is carried out in order to better understand the dynamic aspect of the oscillatory vibratory free responses. A quadratic friction law is used to model on the mechanical system of the apparatus. This allows us to study numerically the behavior of the decreasing amplitudes of the damping responses which are determined using the Averaging method. Furthermore, we are interested in studying the various forms of these oscillations’ envelop in relation with the polynomial expansion of the friction model. Also, numerical and experimental results are compared using both the linear and quadratic friction models. In addition, a particular attention is given to the measured tangential forces corresponding to our tribosystems. Finally, we study numerically a damped mass-spring single degree-of-freedom mechanical system, induced by LuGre friction law described by both hysteresis and lag effect which have been detected experimentally. Results show that friction tests performed with the oscillating tribometer can be qualitatively compared to those obtained with a conventional tribometer. Moreover, ta-C/ta-C surfaces reveal the lowest friction μ0 when tested by both oscillating and reciprocating tribometers. Also, both numerical and experimental results are found to be of good agreement. This study shows that a quadratic friction law is able to describe correctly the envelopes observed in our experimental tests: straight, convex, concave and a combination of both convex and concave.

Ce mémoire de thèse est consacrée à l'étude des problèmes d'évolution où la dynamique est régi par l'opérateur de diffusion de sous-gradient. Nous nous intéressons à deux types de problèmes d'évolution. Le premier problème est régi par un opérateur local de type Leray-Lions avec un domaine borné. Dans ce problème, l'opérateur est maximal monotone et ne satisfait pas la condition standard de contrôle de la croissance polynomiale. Des exemples typiques apparaît dans l'étude de fluide non-Neutonian et aussi dans la description de la dynamique du flux de sous-gradient. Pour étudier le problème nous traitons l'équation dans le contexte de l'EDP non linéaire avec le flux singulier. Nous utilisons la théorie de gradient tangentiel pour caractériser l'équation d'état qui donne la relation entre le flux et le gradient de la solution. Dans le problème stationnaire, nous avons l'existence de la solution, nous avons également l'équivalence entre le problème minimisation initial, le problème dual et l'EDP. Dans l'équation de l'évolution, nous proposons l'existence, l'unicité de la solution. Le deuxième problème est régi par un opérateur discret. Nous étudions l'équation d'évolution discrète qui décrivent le processus d'effondrement du tas de sable. Ceci est un exemple typique de phénomènes auto-organisés critiques exposées par une slope critique. Nous considérons l'équation d'évolution discrète où la dynamique est régie par sous-gradient de la fonction d'indicateur de la boule unité. Nous commençons par établir le modèle, nous prouvons existence et l'unicité de la solution. Ensuite, en utilisant arguments de dualité nous étudions le calcul numérique de la solution et nous présentons quelques simulations numériques. / This thesis is devoted to the study of evolution problems where the dynamic is governed by sub-gradient diffusion operator. We are interest in two kind of evolution problems. The first problem is governed by local operator of Leray-Lions type with a bounded domain. In this problem, the operator is maximal monotone and does not satisfied the standard polynomial growth control condition. Typical examples appears in the study of non-Neutonian fluid and also in the description of sub-gradient flows dynamics. To study the problem we handle the equation in the context of nonlinear PDE with singular flux. We use the theory of tangential gradient to characterize the state equation that gives the connection between the flux and the gradient of the solution. In the stationary problem, we have the existence of solution, we also get the equivalence between the initial minimization problem, the dual problem and the PDE. In the evolution one, we provide the existence, uniqueness of solution and the contractions. The second problem is governed by a discrete operator. We study the discrete evolution equation which describe the process of collapsing sandpile. This is a typical example of Self-organized critical phenomena exhibited by a critical slop. We consider the discrete evolution equation where the dynamic is governed by sub-gradient of indicator function of the unit ball. We begin by establish the model, we prove existence and uniqueness of the solution. Then by using dual arguments we study the numerical computation of the solution and we present some numerical simulations.

A mecânica celular jaz nas propriedades materiais da membrana plasmática, fundamentalmente uma bicamada fosfolipídica com espessura de dimensões moleculares. Além de forças elásticas, tal material bidimensional também experimenta tensões viscosas devido ao seu comportamento fluido (presumivelmente newtoniano) na direção tangencial. A despeito da notável concordância entre teoria e experimentos biofísicos sobre a geometria de membranas celulares, ainda não se faz presente um método computacional para simulação de sua (real) dinâmica viscosa governada pela lei de Boussinesq-Scriven. Assim sendo, introduzimos uma formulação variacional mista de três campos para escoamentos viscosos de superfícies fechadas curvas. Nela, o fluido circundante é levado em conta considerando-se uma restrição de volume interior, ao passo que uma restrição de área corresponde à inextensibilidade. As incógnitas são a velocidade, o vetor curvatura e a pressão superficial, todas estas interpoladas com elementos finitos lineares contínuos via estabilização baseada na projeção do gradiente de pressão. O método é semi-implícito e requer a solução de apenas um único sistema linear por passo de tempo. Outro ingrediente numérico proposto é uma força que mimetiza a ação de uma pinça óptica, permitindo interação virtual com a membrana, onde a qualidade e o refinamento de malha são mantidos por remalhagem adaptativa automática. Extensivos experimentos numéricos de dinâmica de relaxação são apresentados e comparados com soluções quasi-analíticas. É observada estabilidade temporal condicional com uma restrição de passo de tempo que escala como o quadrado do tamanho de malha. Reportamos a convergência e os limites de estabilidade de nosso método e sua habilidade em predizer corretamente o equilíbrio dinâmico de compridas e finas elongações cilíndricas (tethers) que surgem a partir de pinçamentos membranais. A dependência de forma membranal com respeito a uma velocidade imposta de pinçamento também é discutida, sendo que há um valor limiar de velocidade abaixo do qual um tether não se forma de início. Testes adicionais ilustram a robustez do método e a relevância dos efeitos viscosos membranais quando sob a ação de forças externas. Sem dúvida, ainda há um longo caminho a ser trilhado para o entendimento completo da mecânica celular (há de serem consideradas outras estruturas tais como citoesqueleto, canais iônicos, proteínas transmembranares, etc). O primeiro passo, porém, foi dado: a construção de um esquema numérico variacional capaz de simular a intrigante dinâmica das membranas celulares. / Cell mechanics lies on the material properties of the plasmatic membrane, fundamentally a two-molecule-thick phospholipid bilayer. Other than bending elastic forces, such a two-dimensional interfacial material also experiences viscous stresses due to its (presumably Newtonian) surface fluid tangential behaviour. Despite the remarkable agreement on membrane shapes between theory and biophysical experiments, there is no computational method for simulating its (actual) viscous dynamics governed by the Boussinesq- Scriven law. Accordingly, we introduce a mixed three-field variational formulation for viscous flows of closed curved surfaces. In it, the bulk fluid is taken into account by means of an enclosed-volume constraint, whereas an area constraint stands for the membranes inextensible character. The unknowns are the velocity, vector curvature and surface pressure fields, all of which are interpolated with linear continuous finite elements by means of a pressure-gradient-projection scheme. The method is semi-implicit and it requires the solution of a single linear system per time step. Another proposed ingredient is a numerical force that emulates the action of an optical tweezer, allowing for virtual interaction with the membrane, where mesh quality and refinement are maintained by adaptively remeshing. Extensive relaxation experiments are reported and compared with quasi-analytical solutions. Conditional time stability is observed, with a time step restriction that scales as the square of the mesh size. We discuss both convergence and the stability limits of our method, its ability to correctly predict the dynamical equilibrium of the tether due to tweezing. The dependence of the membrane shape on imposed tweezing velocities is also addressed. Basically, there is a threshold velocity value below which the tethers shape does not arise at first. Further tests illustrate the robustness of the method and show the significance of viscous effects on membranes deformation under external forces. Undoubtedly, there is still a long way to track toward the understanding of celullar mechanics (one still has to account other structures such as cytoskeleton, ion channels, transmembrane proteins, etc). The first step has given, though: the design of a numerically robust variational scheme capable of simulating the engrossing dynamics of fluid cell membranes.