Real-time simulation of biological soft tissues: a PGD approach.

We introduce here a novel approach for the numerical simulation of nonlinear, hyperelastic soft tissues at kilohertz feedback rates necessary for haptic rendering. This approach is based upon the use of proper generalized decomposition techniques, a generalization of PODs. Proper generalized decomposition techniques can be considered as a means of a priori model order reduction and provides a physics-based meta-model without the need for prior computer experiments. The suggested strategy is thus composed of an offline phase, in which a general meta-model is computed, and an online evaluation phase in which the results are obtained at real time. Results are provided that show the potential of the proposed technique, together with some benchmark test that shows the accuracy of the method.

Accounting for large deformations in real-time simulations of soft tissues based on reduced-order models.

Model reduction techniques have shown to constitute a valuable tool for real-time simulation in surgical environments and other fields. However, some limitations, imposed by real-time constraints, have not yet been overcome. One of such limitations is the severe limitation in time (established in 500Hz of frequency for the resolution) that precludes the employ of Newton-like schemes for solving non-linear models as the ones usually employed for modeling biological tissues. In this work we present a technique able to deal with geometrically non-linear models, based on the employ of model reduction techniques, together with an efficient non-linear solver. Examples of the performance of the technique over some examples will be given.

Real-time simulation of surgery by reduced-order modeling and X-FEM techniques.

This paper describes a novel approach for the simulation of surgery by a combined technique of model order reduction and extended finite element method (X-FEM) methods. Whereas model order reduction techniques employ globally supported (Ritz) shape functions, a combination with X-FEM methods on a locally superimposed patch is developed for cutting simulation without remeshing. This enables to obtain models with very few degrees of freedom that run under real-time constrains even for highly non-linear tissue constitutive equations. To show the performance of the technique, we studied an application to refractive surgery in the cornea.

Real-time deformable models of non-linear tissues by model reduction techniques.

In this paper we introduce a new technique for the real-time simulation of non-linear tissue behavior based on a model reduction technique known as proper orthogonal (POD) or Karhunen-Loève decompositions. The technique is based upon the construction of a complete model (using finite element modelling or other numerical technique, for instance, but possibly from experimental data) and the extraction and storage of the relevant information in order to construct a model with very few degrees of freedom, but that takes into account the highly non-linear response of most living tissues. We present its application to the simulation of palpation a human cornea and study the limitations and future needs of the proposed technique.