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.

Haptic simulation of tissue tearing during surgery.

We present a method for the real-time, interactive simulation of tissue tearing during laparoscopic surgery. The method is designed to work at haptic feedback rates (ie, around 1 kHz). Tissue tearing is simulated under the general framework of continuum damage mechanics. The problem is stated as a general, multidimensional parametric problem, which is solved by means of proper generalized decomposition methods. One of the main novelties is the reduction of history-dependent problems, such as damage mechanics, by resorting to an approach in which a reduced-order field of initial damage values is considered as a parameter of the formulation. We focus on the laparoscopic cholecystectomy procedure as a general example of the performance of the method.

An advanced system for the simulation and planning of orthodontic treatment.

This paper presents a new system for three-dimensional (3-D) orthodontic treatment planning and movement of teeth. We describe a computer vision technique for the acquisition and processing of 3-D images of the profile of hydrocolloid dental imprints. Profile measurement is based on the triangulation method which detects deformation of the projection of a laser line on the dental imprints. The system is computer-controlled and designed to achieve depth and lateral resolutions of 0.1 and 0.2 mm, respectively, within a depth range of 40 mm. The 3-D image of the imprint is segmented in order to identify different teeth. Two operators are presented: one for the detection of molars and premolars based on a directional gradient, and one for incisors and canines based on 3-D registration with dental models contained in a database. We apply these 3-D dental models to simulate the 3-D movement of teeth, including rotations, during orthodontic treatment. With this objective, we have developed an original simplified model of arch-wire behaviour and a viscoplastic behaviour law for the alveolar bone in order to simulate teeth displacements during orthodontic treatment. The contribution of the paper is part of a diagnosis system (called MAGALLANES) that is designed to replace manual measurement methods, which use costly plaster models, with computer measurement methods and teeth movement simulation using cheap hydrocolloid dental wafers. This procedure will reduce the cost and acquisition time of orthodontic data and facilitate the conduct of epidemiological studies.

A new approach for the real-time simulation of tissue deformations in surgery simulation.

Simulation of the behaviour of elastic objects in real time is one of the present objectives of computer graphics. One of its fields of application lies in virtual reality, mainly in surgery simulation systems. Models used for the construction of objects with deformable behaviour in computer graphics are known as deformable models. These have two conflicting characteristics: interactivity and movement realism. The deformable models developed up till now have promoted one characteristic to the detriment of the other. In this paper, a new approach is proposed based on boundary element methods (BEM). This is characterised by a positive equilibrium between speed and realism and great robustness. These properties along with the experimental results described in this paper permit one to assert that establishing deformable models with BEM is a reliable method to model objects in virtual reality environments for surgery simulation. In addition to that, the required elasticity parameters could be obtained experimentally through the use of a pig's liver.

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.

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.

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.

Development and Validation of a Mathematical Model for HTST Processing of Foods Containing Large Particles.

A mathematical treatment for a heat penetration phenomenon with variable boundary conditions is presented. The system of differential equations for determining the unsteady-state temperature distribution inside a particle was solved by use of spectral methods as a new tool in food process development. A preliminary study was conducted on the use of a mathematical model to predict lethality in a sterilizing process. The model was validated using a calibrated time-temperature integrator (TTI) with immobilized Bacillus stearothermophilus spores, commonly used in TTIs for process validation. A comparison between the experimental data using Bacillus stearothermophilus and the predicted data obtained with the proposed model showed good agreement.