Developmental dysplasia of the hip (DDH) is a common newborn condition where the femoral head is not located in its natural position in the acetabulum (hip socket). Several treatment methods are being implemented worldwide to treat this abnormal condition. One of the most effective methods of treatment is the use of Pavlik Harness, which directs the femoral head toward the natural position inside the acetabulum. This dissertation presents a developed method for identifying the least energy path that the femoral head would follow during reduction. This is achieved by utilizing a validated computational biomechanical model that allows the determination of the potential energy, and then implementing the principle of stationary potential energy. The potential energy stems from strain energy stored in the muscles and gravitational potential energy of four rigid-body components of lower limb bones. Five muscles are identified and modeled because of their effect on DDH reduction. Clinical observations indicate that reduction with the Pavlik Harness occurs passively in deep sleep under the combined effects of gravity and the constraints of the Pavlik Harness. A non-linear constitutive equation, describing the passive muscle response, is used in the potential energy computation. Different DDH abnormalities with various flexion, abduction, and hip rotation angles are considered, and least energy paths are identified. Several constraints, such as geometry and harness configuration, are considered to closely simulate real cases of DDH. Results confirm the clinical observations of two different pathways for closed reduction. The path of least energy closely approximated the modified Hoffman-Daimler method. Release of the pectineus muscle favored a more direct pathway over the posterior rim of the acetabulum. The direct path over the posterior rim of the acetabulum requires more energy. This model supports the observation that Grade IV dislocations may require manual reduction by the direct path. However, the indirect path requires less energy and may be an alternative to direct manual reduction of Grade IV infantile hip dislocations. Of great importance, as a result of this work, identifying the minimum energy path that the femoral head would travel would provide a non-surgical tool that effectively aids the surgeon in treating DDH.

In 1952 Alan Turing published his paper "The Chemical Basis of Morphogenesis", which described a model for how naturally occurring patterns, such as the stripes of a zebra and the spots of a leopard, can arise from a spatially homogeneous steady state through diffusion. Turing suggested that the concentration of the substances producing the patterns is determined by the reaction kinetics, how the substances interact, and diffusion.  In this project Turing's model with linear reactions kinetics was studied. The model was first solved using two different numerical methods; the finite difference method (FDM) and the finite element method (FEM) with different boundary conditions. A parameter study was then conducted, investigating the effect on the patterns of changing the parameters of the model. Lastly the controllability of the model and the least energy control was considered. The simulations were found to produce patterns provided the right parameters, as expected. From the investigation of the parameters it could be concluded that the size/tightness of the pattern and similarity of the substance concentration distributions depended on the choice of parameters. As for the controllability, a desired final state could be produced thorough simulations using control of the boundary and the energy cost of producing the pattern increased when decreasing the number of controls.

Submitted by isabela.moljf@hotmail.com (isabela.moljf@hotmail.com) on 2016-12-19T12:23:36Z No. of bitstreams: 1 pedrobelchior.pdf: 465178 bytes, checksum: 997aa94857f2f7478cb38dc9980463d3 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-02-02T11:10:14Z (GMT) No. of bitstreams: 1 pedrobelchior.pdf: 465178 bytes, checksum: 997aa94857f2f7478cb38dc9980463d3 (MD5) / Made available in DSpace on 2017-02-02T11:10:14Z (GMT). No. of bitstreams: 1 pedrobelchior.pdf: 465178 bytes, checksum: 997aa94857f2f7478cb38dc9980463d3 (MD5) Previous issue date: 2013-03-01 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / As soluções de energia mínima são de nidas como as soluções que indicam valor ín fimo para imagem do funcional energia associado a uma classe de problemas variacionais não lineares −∆u = g(u) u ∈ H1(RN) Oobjetivodestetrabalhoémostrarqueatravésdassoluçõesdeenergiamínimadaequação não linear acima, o valor do passo da Montanha sem a condição de Palais Smaile é um ponto crítico. Para isto provaremos que sob certas hipóteses para a função g e sob um vínculo é possível obter uma solução positiva para o problema acima, esfericamente simétrica e decrescente com o raio. Em seguida mostra-se que a solução sujeita a esse vínculo é a que possui o menor valor no funcional energia dentre todas as soluções do problema acima aplicadas no mesmo funcional. Neste contexto, garante-se a existência de pelo menos uma solução de energia mínima. Os resultados citados foram estudados em [2] e [1]. / The least energy solutions are de ned as solutions that indicate infi mum value to the energy functional image associated with a class of nonlinear variational problems −∆u = g(u) u ∈ H1(RN) The objective of this work is to show that through least energy solutions of nonlinear equation above, the Mountain pass value without the Palais Smale condition is critical point. For this, we will prove that under certain hypotheses on the function g and under a constraint assumption is possible to obtain a positive solution for the above problem, spherically symmetric and decreasing with the radius. Then the solution of the problem subject to this constraint has the lowest value in the energy functional among all solutions of the above problem applied in the same functional. In this context, it guarantee the existence of at least one solution of the least energy. The above results were obtained in [2] and [1]. Key Words: Least Energy, Mountain Pass, Minimization, Minimum of the Action.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-05-29T15:09:36Z No. of bitstreams: 1 pedrobelchior.pdf: 465178 bytes, checksum: 997aa94857f2f7478cb38dc9980463d3 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-05-29T19:48:54Z (GMT) No. of bitstreams: 1 pedrobelchior.pdf: 465178 bytes, checksum: 997aa94857f2f7478cb38dc9980463d3 (MD5) / Made available in DSpace on 2017-05-29T19:48:54Z (GMT). No. of bitstreams: 1 pedrobelchior.pdf: 465178 bytes, checksum: 997aa94857f2f7478cb38dc9980463d3 (MD5) Previous issue date: 2013-03-01 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / As soluções de energia mínima são definidas como as soluções que indicam valor ínfimo para imagem do funcional energia associado a uma classe de problemas variacionais não lineares -Δu = g(u) u ∈ H1(RN). O objetivo deste trabalho é mostrar que através das soluções de energia mínima da equação não linear acima, o valor do passo da Montanha sem a condição de Palais Smaile é um ponto crítico. Para isto provaremos que sob certas hipóteses para a função g e sob um vínculo é possível obter uma solução positiva para o problema acima, esfericamente simétrica e decrescente com o raio. Em seguida mostra-se que a solução sujeita a esse vínculo é a que possui o menor valor no funcional energia dentre todas as soluções do problema acima aplicadas no mesmo funcional. Neste contexto, garante-se a existência de pelo menos uma solução de energia mínima. Os resultados citados foram estudados em [2] e [1]. / The least energy solutions are defined as solutions that indicate infimum value to the energy functional image associated with a class of nonlinear variational problems -Δu = g(u) u ∈ H1(RN). The objective of this work is to show that through least energy solutions of nonlinear equation above, the Mountain pass value without the Palais Smale condition is critical point. For this, we will prove that under certain hypotheses on the function g and under a constraint assumption is possible to obtain a positive solution for the above problem, spherically symmetric and decreasing with the radius. Then the solution of the problem subject to this constraint has the lowest value in the energy functional among all solutions of the above problem applied in the same functional. In this context, it guarantee the existence of at least one solution of the least energy. The above results were obtained in [2] and [1].