<p> Advances in robotics and information technology are leading to the development of virtual reality-based surgical simulators as an alternative to the conventional means of medical training. Modeling and simulation of medical procedures also have numerous applications in pre-operative and intra-operative surgical planning as well as robotic (semi)-autonomous execution of surgical tasks. </p> <p> Surgical simulation requires modeling of human soft-tissue organs. Soft-tissues exhibit geometrical and material nonlinearities that should be taken into account for realistic modeling of the deformations and interaction forces between the surgical tool and tissues during medical procedures. However, most existing work in the literature, particularly for modeling of cutting, use linear deformation models. In this thesis, modeling of two common surgical tasks, i.e. palpation and cutting, using nonlinear modeling techniques has been studied. The complicated mechanical behavior of soft-tissue deformation is modeled by considering both geometrical and material nonlinearities. Large deformations are modeled by employing a nonlinear strain measure, the Green-Lagrange strain tensor, and a nonlinear stress-strain curve is employed by using an Ogden-based hyperelastic constitutive equation. The incompressible property of soft-tissue material during the deformation is enforced by modifying the strain energy function to include a term that penalizes changes in the object's area/volume. The problem of simulating the tool-tissue interactions using nonlinear dynamic analysis is formulated within a total Lagrangian framework. The finite element method is utilized to discretize the deformable object model in space and an explicit time integration is employed to solve for the resulting deformations. </p> <p> In this thesis, the nonlinear finite element analysis with the Ogden-based constitutive equation has also been applied to the modeling of soft-tissue cutting. Element separation and node snapping are used to create a cut in the mesh that is close to the tool trajectory. The external force applied on the object along the tool direction is used as a physical cutting criterion. The possibility of producing degenerated elements by node snapping that can cause numerical instability in the simulation is eliminated by remeshing the local elements when badly shaped elements are generated. The remeshing process involves retriangulation of the local elements using the Delaunay function and/ or moving a node depending on what is needed in order to generate elements with the required quality. </p> <p> Extensive simulations have been carried out in order to evaluate and demonstrate the effectiveness of the proposed modeling techniques and the results are reported in the thesis. A two-dimensional object with a concentrated external force has been considered in the simulations. </p> / Thesis / Master of Applied Science (MASc)

Esta dissertação de mestrado propõe o estudo e a implementação de um método de deformação usando modelos tridimensionais sem o uso de malhas baseado na técnica Smoothed Particles Hydrodynamics (SPH), que consiste num sistema de resolução de equações diferenciais para aplicação de conceitos físicos para simular deformação de tecidos moles. A opção pelo método sem malha para processo de deformação é apresentado nesta dissertação como alternativa a um dos métodos mais comuns em simulação de deformação de tecidos, o método massa-mola, explorando questões referentes ao uso de recursos computacionais. Para chegada a definição do método foram analisados os temas envolvendo métodos de deformação, modelos baseados em pontos e o SPH como plataformas para alcançar o desenvolvimento do método proposto pela dissertação. Como forma de comprovar as propriedades do método desenvolvido foi realizada a implementação e testes levando em consideração os modelos de deformação e a interação em tempo real num ambiente de simulação que contempla a deformação de uma mama, levando em conta a comparação com o método massa-mola, o uso de recursos do próprio método em função do aumento de detalhe e do uso de objeto com múltiplas propriedades / This master thesis proposes a study and implementation of deformation method using tridimensional models without edge composed meshes based on Smoothed Particles Hydrodynamics (SPH) technique, that consists on diferential equation solving system to reproduce physical concepts to simulate soft tissue deformation. The option for a meshless method to deformation process is shown in this thesis as an alternative to a very common method in tissue deform simulation, the mass-spring method, reviewing a comparison based on computational resources. To achieve a method definition were analyzed fields of study involving deformation methods, point-based models and SPH as platforms to build and deploy the proposed method for this thesis. To show the characteristics for this developed deformation method was realized the implementation and tests based on deformation models and real time interaction on a simulation environment that includes a breast deformation, taking in account the comparison to mass-spring, number of points of the cloud model and multiple properties

Esta dissertação de mestrado propõe o estudo e a implementação de um método de deformação usando modelos tridimensionais sem o uso de malhas baseado na técnica Smoothed Particles Hydrodynamics (SPH), que consiste num sistema de resolução de equações diferenciais para aplicação de conceitos físicos para simular deformação de tecidos moles. A opção pelo método sem malha para processo de deformação é apresentado nesta dissertação como alternativa a um dos métodos mais comuns em simulação de deformação de tecidos, o método massa-mola, explorando questões referentes ao uso de recursos computacionais. Para chegada a definição do método foram analisados os temas envolvendo métodos de deformação, modelos baseados em pontos e o SPH como plataformas para alcançar o desenvolvimento do método proposto pela dissertação. Como forma de comprovar as propriedades do método desenvolvido foi realizada a implementação e testes levando em consideração os modelos de deformação e a interação em tempo real num ambiente de simulação que contempla a deformação de uma mama, levando em conta a comparação com o método massa-mola, o uso de recursos do próprio método em função do aumento de detalhe e do uso de objeto com múltiplas propriedades / This master thesis proposes a study and implementation of deformation method using tridimensional models without edge composed meshes based on Smoothed Particles Hydrodynamics (SPH) technique, that consists on diferential equation solving system to reproduce physical concepts to simulate soft tissue deformation. The option for a meshless method to deformation process is shown in this thesis as an alternative to a very common method in tissue deform simulation, the mass-spring method, reviewing a comparison based on computational resources. To achieve a method definition were analyzed fields of study involving deformation methods, point-based models and SPH as platforms to build and deploy the proposed method for this thesis. To show the characteristics for this developed deformation method was realized the implementation and tests based on deformation models and real time interaction on a simulation environment that includes a breast deformation, taking in account the comparison to mass-spring, number of points of the cloud model and multiple properties

Biomechanical imaging (BMI) is the process of non-invasively measuring the spatial distribution of mechanical properties of biological tissues. The most common approach uses ultrasound to non-invasively measure soft tissue deformations. The measured deformations are then used in an inverse problem to infer local tissue mechanical properties. Thus quantifying local tissue mechanical properties can enable better medical diagnosis, treatment, and understanding of various diseases. A major difficulty with ultrasound biomechanical imaging is getting accurate measurements of all components of the tissue displacement vector field. One component of the displacement field, that parallel to the direction of sound propagation, is typically measured accurately and precisely; the others are available at such low precision that they may be disregarded in the first instance. If all components were available at high precision, the inverse problem for mechanical properties could be solved directly, and very efficiently. When only one component is available, the inverse problem solution is necessarily iterative, and relatively speaking, computationally inefficient. The goal of this thesis, therefore, is to develop a processing method that can be used to recover the missing displacement data with sufficient precision to allow the direct reconstruction of the linear elastic modulus distribution in tissue. This goal was achieved by using a novel spatial regularization to adaptively enforce and locally relax a special form of momentum conservation on the measured deformation field. The new processing method was implemented with the Finite Element Method (FEM). The processing method was tested with simulated data, measured data from a tissue mimicking phantom, and in-vivo clinical data of breast masses, and in all cases it was able to recover precise estimates the full 2D displacement and strain fields. The recovered strains were then used to calculate the material property distribution directly.