Title: Proper orthogonal decomposition-based model reduction for non-linear biomechanical analysis

Authors: Annika Radermacher; Stefanie Reese

Addresses: Institute of Applied Mechanics, RWTH Aachen University, Mies-van-der-Rohe-Straße 1, 52074 Aachen, Germany ' Institute of Applied Mechanics, RWTH Aachen University, Mies-van-der-Rohe-Straße 1, 52074 Aachen, Germany

Abstract: Simulations for surgery training programmes or online support during surgeries should be carried out in a minimal simulation time, even real time. Another requirement is a high degree of accuracy. A possible way to develop such a simulation tool is to use model reduction. This paper discusses the method of proper orthogonal decomposition (POD) in the context of biomechanics. The POD method belongs to the class of singular value decomposition-based model reduction methods. In the authors' experience this method is the most promising method among the investigated approaches. In this paper the influence of two different implementations of the POD method and two different ways to solve the reduced equation system is investigated. It turns out that the POD combined with a BFGS solver leads to the largest CPU time reduction in case of the investigated models.

Keywords: biomechanics; model reduction; singular value decomposition; SVD; proper orthogonal decomposition; POD; hyperelasticity; inferior turbinate; nonlinear biomechanical analysis; healthcare technology; simulation; surgery training; online surgical support.

DOI: 10.1504/IJMATEI.2013.054393

International Journal of Materials Engineering Innovation, 2013 Vol.4 No.2, pp.149 - 165

Published online: 06 Jun 2013 *

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