Real-Time simulation of surgery by model reduction and X-Fem techniques

Niroomandi, Siamak
Alfaro Ruiz, Icíar (dir.) ; Cueto Prendes, Elias (dir.)

Universidad de Zaragoza, 2011


ISBN: 978-84-694-9903-0

Abstract: Interactive (that with haptic feedback) simulation of surgery needs for increasingly fast simulation techniques. Feedback rates are nowadays fixed around 1 kHz for haptic peripherals and around 30Hz for visual display. Such tremendous rates impose very drastic limitations to the simulation procedure. In order to achieve haptic realism, several techniques have been tested in the literature. These include mass-spring systems, the use of linear elastic explicit finite element codes or, more recently, the use of Graphic Processing Units (GPU) to speedup the simulation. In any case, in order to achieve realistic results compatible with the sense of touch, large strains must be taken into account, together with sophisticated, state of the art constitutive models for the soft tissues. This has not been achieved to date, up to the author's knowledge. Techniques based on model order reduction (MOR) have received an increasing attention in the last years, and have been employed for interactive simulation of linear elastic solids undergoing large strains (Barbic and James, 2005). In this thesis, however, a study has been made in order to discern if MOR techniques are suitable for the simulation of soft living tissues. In chapter 2 a technique based upon Proper Orthogonal Decomposition (POD) has been employed to simulate at haptic rates the governing equations for a human cornea under a hyperelastic, fiber-reinforced constitutive model. While the technique is able to efficiently simulate these models, errors up to 20% have been noticed, still cceptable. In chapter 3 a novel technique has been developed that allows for an accurate solution of material and geometrical non-linear hyperelastic models without the need of stiffness matrix inversions. It is based upon the combination of POD techniques and Asymptotic Numerical Methods, which provide an accurate description of the nonlinear stress-strain curve of these organs in a convergence interval of sufficient width. Finally, the use of globally supported basis functions, an essential characteristic of POD techniques, very much complicates the task of simulating surgical cutting. To that end, a multiscale method has been developed that enriches the displacement field with an X-FEM-like, discontinuous, field that avoids the need of remeshing, impossible under such severe time restrictions.

Pal. clave: mecánica de medios continuos ; simulación

Knowledge area: Mecánica de medios continuos y teoría de estructuras

Department: Ingeniería Mecánica

Nota: Presentado: 04 07 2011

Nota: Tesis-Univ. Zaragoza