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UBC Theses and Dissertations

Simulation of linear elastic media with fluid inclusions Gosline, Andrew Havens

Abstract

This work presents a methodology for haptic rendering of fluid filled structures that are enclosed in linear elastic media using the Finite Element Method. Haptic medical simulation is a growing field of research motivated by creating risk-free virtual environments for medical students to learn and practise surgical procedures. One of the challenges in creating medical simulators is modeling the deformation of living tissues. Due to minimum haptic update rate requirements, the deformable methods are simplified and precomputed. Most medical simulators model anatomy as elastic material with constant or varying stiffness. However, human anatomy includes a variety of fluid filled structures. To improve the realism of these simulators, fluid filled bodies should be modeled in addition to elastic media. This thesis presents a method for simulating fluid effects by adding hydrostatic fluid pressure to a body of elastic material modeled with the Finite Element Method. By distributing fluid pressure across an interior cavity surface, the fluid can be modeled using a force boundary condition. Proportional feedback is used to solve for an incompressible fluid relationship between the cavity pressure and volume. Linear finite elements are used so the stiffness matrix can be condensed to achieve real-time haptic rates. To validate that this method predicts deformation of a fluid filled cavity in a realistic manner, the deformation a fluid filled phantom is tracked and compared to a Finite Element simulation of the same phantom. The data is found to agree well with the simulation. A real-time haptic simulation of elastic media enclosing incompressible fluid, based on an existing 2D needle insertion simulation, is presented. Numerical tests show that simulation of a relatively large 3D fluid body will be possible at haptic rates.

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