A comparison of projection-based model reduction concepts in the context of nonlinear biomechanics

Computational assistance gains increasing importance in the field of medical surgery. As an example, in the present work, we look at functional endoscopic sinus surgery. Simulations for surgery training programs or online support during surgeries require simulation tools which are characterized by a preferably short simulation time (real time) and a high degree of accuracy. The nonlinear finite element method is most suitable to yield qualitatively and quantitatively reliable results. The problem is, however, to achieve such results in real time. One possibility to reach both, short computational time and high accuracy, is to combine model reduction and finite element techniques. Therefore, in this paper, various projection-based model reduction methods are discussed and compared with respect to their possible application in biomechanics. The modal basis, the load-dependent Ritz and the proper orthogonal decomposition (POD) method were used to reduce the model of a cube under compression considering different material nonlinearities and large deformations. The POD method led to the lowest errors in displacement and stress while providing the largest reduction in CPU time. Further, the influence of different POD parameters was investigated. According to this study, the snapshots upon which the POD is based had to agree as closely as possible with the original deformation of the reduced system. The POD method applied to the finite element model of an inferior turbinate led to an adequate accuracy for surgery simulations within less than one-third of the computational time of the unreduced finite element simulation.